Finite Group Databasebeta

← #28270350

Subgroups — #28270350

Order 13568.

2110 conjugacy classes of subgroups.

The subgroup lattice has 1902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288376C211yesmaximal, characteristic, complemented
2#20286850C211yesmaximal, characteristic, complemented
3#20286835C211yesmaximal, characteristic, complemented
4#20286820C211yesmaximal, characteristic, complemented
5#20286745C211yesmaximal, characteristic, complemented
6#20286648C211yesmaximal, characteristic, complemented
7#20286611C211yesmaximal, characteristic, complemented
8#20286544C211yesmaximal, characteristic, complemented
9#20286533C211yesmaximal, characteristic, complemented
10#20286452C211yesmaximal, characteristic, complemented
11#20286441C211yesmaximal, characteristic, complemented
12#20286423C211yesmaximal, characteristic, complemented
13D4×#11719924C211yesmaximal, characteristic, complemented
14#20286301C211yesmaximal, characteristic, complemented
15#20286286C211yesmaximal, characteristic, complemented
16#20286241C211yesmaximal, characteristic, complemented
17#20286211C211yesmaximal, characteristic, complemented
18#20285803C211yesmaximal, characteristic, complemented
19#20285781C211yesmaximal, characteristic, complemented
20#20285621C211yesmaximal, characteristic, complemented
21#20285597C211yesmaximal, characteristic, complemented
22#20285476C211yesmaximal, characteristic, complemented
23#20285468C211yesmaximal, characteristic, complemented
24#20284986C211yesmaximal, characteristic, complemented
25#20284923C211yesmaximal, characteristic, complemented
26#20284016C211yesmaximal, characteristic, complemented
27#20283990C211yesmaximal, characteristic, complemented
28#20283931C211yesmaximal, characteristic, complemented
29C2×#16810783C211yesmaximal, characteristic, complemented
30#20283771C211yesmaximal, characteristic, complemented
31C53×#3541C211yesmaximal, characteristic, complemented
32C2×#13133263C2211yescharacteristic
33C22×#11719945C2211yescharacteristic
34C2×#13133248C2211yescharacteristic, complemented
35C2×#13133242C2211yescharacteristic, complemented
36C2×#13133237C2211yescharacteristic, complemented
37C2×#13133237C2211yescharacteristic, complemented
38C2×#13133237C2211yescharacteristic, complemented
39C22×#11719925C2211yescharacteristic, complemented
40C22×#11719924C2211yescharacteristic, complemented
41C22×#11719924C2211yescharacteristic, complemented
42#16811294C2211yescharacteristic
43#16811294C2211yescharacteristic
44#16811282C2211yescharacteristic
45#16811282C2211yescharacteristic
46#16811269C2211yescharacteristic
47#16811269C2211yescharacteristic
48#16811265—21no—
49#16811265—21no—
50D4×D212C2211yescharacteristic
51D4×D212C2211yescharacteristic
52#16811255—21no—
53#16811255—21no—
54#16811203—21no—
55#16811201C2211yescharacteristic
56#16811192C2211yescharacteristic
57#16811189—21no—
58#16811136—21no—
59C2×#13133191C2211yescharacteristic
60#121×D53—21no—
61#16811103C2211yescharacteristic
62#16811015C2211yescharacteristic, complemented
63#16811013C2211yescharacteristic, complemented
64#16811005C2211yescharacteristic, complemented
65#16810997C2211yescharacteristic, complemented
66#16810989C2211yescharacteristic, complemented
67#16810985C2211yescharacteristic, complemented
68#16810980C2211yescharacteristic, complemented
69#16810971C2211yescharacteristic, complemented
70#16810964C2211yescharacteristic, complemented
71#16810956C2211yescharacteristic, complemented
72#16810953C2211yescharacteristic, complemented
73#16810951C2211yescharacteristic, complemented
74#16810951C2211yescharacteristic, complemented
75#16810947C2211yescharacteristic, complemented
76#16810947C2211yescharacteristic, complemented
77#16810947C2211yescharacteristic, complemented
78#16810941C2211yescharacteristic, complemented
79#16810941C2211yescharacteristic, complemented
80#16810941C2211yescharacteristic, complemented
81#16810939C2211yescharacteristic, complemented
82#16810927C2211yescharacteristic, complemented
83#16810920C2211yescharacteristic, complemented
84#16810910C2211yescharacteristic, complemented
85#16810905C2211yescharacteristic, complemented
86#16810879C2211yescharacteristic, complemented
87#16810879C2211yescharacteristic, complemented
88#16810874C2211yescharacteristic, complemented
89#16810871C2211yescharacteristic, complemented
90#16810862C2211yescharacteristic, complemented
91#16810857C2211yescharacteristic, complemented
92#16810857C2211yescharacteristic, complemented
93#16810854C2211yescharacteristic, complemented
94#16810854C2211yescharacteristic, complemented
95#16810854C2211yescharacteristic, complemented
96#16810854C2211yescharacteristic, complemented
97#16810854C2211yescharacteristic, complemented
98#16810854C2211yescharacteristic, complemented
99#16810854C2211yescharacteristic, complemented
100#16810854C2211yescharacteristic, complemented
101#16810850C2211yescharacteristic, complemented
102#16810845C2211yescharacteristic, complemented
103#16810845C2211yescharacteristic, complemented
104#16810845C2211yescharacteristic, complemented
105#16810842C2211yescharacteristic, complemented
106#16810838C2211yescharacteristic, complemented
107#16810835C2211yescharacteristic, complemented
108#16810830C2211yescharacteristic, complemented
109#16810825C2211yescharacteristic, complemented
110#16810823C2211yescharacteristic, complemented
111#16810823C2211yescharacteristic, complemented
112#16810823C2211yescharacteristic, complemented
113#16810818C2211yescharacteristic, complemented
114#16810785C2211yescharacteristic, complemented
115#16810783C2211yescharacteristic
116#16810783C2211yescharacteristic
117#16810783C2211yescharacteristic
118#16810783C2211yescharacteristic, complemented
119#16810783C2211yescharacteristic, complemented
120#16810783C2211yescharacteristic, complemented
121#16810783C2211yescharacteristic, complemented
122#16810783C2211yescharacteristic, complemented
123#16810783C2211yescharacteristic, complemented
124#16810783C2211yescharacteristic, complemented
125#16810783C2211yescharacteristic, complemented
126#16810783C2211yescharacteristic, complemented
127#16810783C2211yescharacteristic, complemented
128#16810779C2211yescharacteristic, complemented
129#16810778C2211yescharacteristic, complemented
130#16810773C2211yescharacteristic, complemented
131#16810773C2211yescharacteristic, complemented
132#16810773C2211yescharacteristic, complemented
133#16810773C2211yescharacteristic, complemented
134#16810773C2211yescharacteristic, complemented
135#16810773C2211yescharacteristic, complemented
136#16810773C2211yescharacteristic, complemented
137#16810768C2211yescharacteristic, complemented
138#16810768C2211yescharacteristic, complemented
139#16810768C2211yescharacteristic, complemented
140#16810766C2211yescharacteristic
141#16810766C2211yescharacteristic, complemented
142#16810766C2211yescharacteristic, complemented
143#16810762C2211yescharacteristic, complemented
144#16810762C2211yescharacteristic, complemented
145#16810762C2211yescharacteristic, complemented
146#16810761C2211yescharacteristic, complemented
147#16810756C2211yescharacteristic, complemented
148#16810756C2211yescharacteristic, complemented
149#16810756C2211yescharacteristic, complemented
150#16810733C2211yescharacteristic, complemented
151#16810728C2211yescharacteristic, complemented
152#16810728C2211yescharacteristic, complemented
153#16810721C2211yescharacteristic, complemented
154C4×#11719925C2211yescharacteristic, complemented
155C4×#11719924C2211yescharacteristic, complemented
156C4×#11719924C2211yescharacteristic, complemented
157C4×#11719923C2211yescharacteristic, complemented
158#16810695C2211yescharacteristic, complemented
159#16810695C2211yescharacteristic, complemented
160#16810695C2211yescharacteristic, complemented
161#16810695C2211yescharacteristic, complemented
162D4×#88322C2211yescharacteristic, complemented
163D4×#88322C2211yescharacteristic, complemented
164D4×#88322C2211yescharacteristic, complemented
165D4×#88322C2211yescharacteristic, complemented
166#16810684C2211yescharacteristic, complemented
167#16810684C2211yescharacteristic, complemented
168#16810627C2211yescharacteristic, complemented
169#16810622C2211yescharacteristic, complemented
170#16810617C2211yescharacteristic, complemented
171#16810617C2211yescharacteristic, complemented
172#16810617C2211yescharacteristic, complemented
173C2×#13133140C2211yescharacteristic, complemented
174C2×#13133137C2211yescharacteristic, complemented
175C2×#13133137C2211yescharacteristic, complemented
176#16810590C2211yescharacteristic, complemented
177#16810590C2211yescharacteristic, complemented
178C2×C22⋊#88322C2211yescharacteristic, complemented
179C2×C22⋊#88322C2211yescharacteristic, complemented
180C53×#563—21no—
181C53×#562—21no—
182C53×#556C2211yescharacteristic, complemented
183C53×#554—21no—
184C53×#554C2211yescharacteristic, complemented
185C53×#553—21no—
186C53×#553C2211yescharacteristic, complemented
187C53×#552C2211yescharacteristic, complemented
188D4×Q8×C53C2211yescharacteristic, complemented
189C53×#548C2211yescharacteristic, complemented
190C53×#548C2211yescharacteristic, complemented
191C53×#547C2211yescharacteristic, complemented
192C53×#542—21no—
193C53×#542C2211yescharacteristic, complemented
194C53×#541C2211yescharacteristic, complemented
195C53×#539—21no—
196C53×#538—21no—
197C53×#538—21no—
198C53×#537C2211yescharacteristic, complemented
199C53×#536C2211yescharacteristic, complemented
200C53×#525C2211yescharacteristic
201C53×#525C2211yescharacteristic, complemented
202C2×C22⋊Q8×C53C2211yescharacteristic, complemented
203#13133263—42no—
204#13133263—42no—
205C2×#11719949—21no—
206C2×#11719945—21no—
207C2×#11719945—21no—
208C2×#11719945—42no—
209C2×#11719945—42no—
210C2×#11719945C2311yescharacteristic
211C2×#11719945C2311yescharacteristic
212C2×#11719945C2311yescharacteristic
213C2×#11719945C2311yescharacteristic
214C2×#11719945C2311yescharacteristic
215C2×#11719945C2311yescharacteristic
216C22×Dic106C2311yescharacteristic
217C22×D212C2311yescharacteristic
218C22×D212C2311yescharacteristic
219C22×D212C2311yescharacteristic
220C22×D212C2311yescharacteristic
221C22×C22⋊D53—21no—
222C22×C22⋊D53—21no—
223C2×D4×D53—21no—
224C2×D4×D53—21no—
225C2×D4×D53—21no—
226C2×D4×D53—21no—
227C2×D4×D53—21no—
228C22×C4×D53—21no—
229#13133248—42no—
230#13133242—42no—
231#13133237—42no—
232#13133237—42no—
233#13133237—42no—
234C2×#11719925—42no—
235C2×#11719925C2311yescharacteristic
236C2×#11719925C2311yescharacteristic
237C2×#11719925C2311yescharacteristic
238C2×#11719925C2311yescharacteristic
239C2×#11719925C2311yescharacteristic
240C2×#11719925C2311yescharacteristic
241C2×#11719923C2311yescharacteristic
242C2×#11719923C2311yescharacteristic
243C2×#11719924—42no—
244C2×#11719924—42no—
245C2×#11719924C2311yescharacteristic
246C2×#11719924C2311yescharacteristic
247C2×#11719924C2311yescharacteristic
248C2×#11719924C2311yescharacteristic
249C2×#11719924C2311yescharacteristic
250C2×#11719924C2311yescharacteristic
251C2×#11719924C2311yescharacteristic
252C2×#11719924C2311yescharacteristic
253C2×#11719924C2311yescharacteristic
254C2×#11719924C2311yescharacteristic
255C2×#11719924C2311yescharacteristic
256C2×#11719924C2311yescharacteristic
257C2×#11719922C2311yescharacteristic
258C2×#11719922C2311yescharacteristic
259C2×#11719922C2311yescharacteristic
260C2×#11719922C2311yescharacteristic
261C2×#11719917C2311yescharacteristic
262C2×#11719917C2311yescharacteristic
263C22×#88322C2311yescharacteristic
264C22×#88322C2311yescharacteristic
265C22×#88322C2311yescharacteristic
266C22×#88322C2311yescharacteristic
267C22×#88322C2311yescharacteristic
268C22×#88322C2311yescharacteristic
269#13133214C2311yescharacteristic
270#13133214C2311yescharacteristic
271#13133213—21no—
272#13133213—21no—
273#13133205C2311yescharacteristic
274#13133205C2311yescharacteristic
275#13133203—21no—
276#13133203—21no—
277#13133202—21no—
278#13133202—21no—
279#13133196C2311yescharacteristic
280#13133196C2311yescharacteristic
281#13133195—21no—
282#13133195—21no—
283#13133193—21no—
284#13133192—21no—
285#13133192—21no—
286#13133192—21no—
287#13133192—21no—
288#13133191—21no—
289#13133191—21no—
290#13133191C2311yescharacteristic
291#13133191C2311yescharacteristic
292#13133191C2311yescharacteristic
293#13133191C2311yescharacteristic
294#13133191C2311yescharacteristic
295#13133191C2311yescharacteristic
296#13133190—21no—
297#13133190—21no—
298#13133190—21no—
299#13133190—21no—
300#13133190—21no—
301#13133190—21no—
302#13133189—21no—
303#13133189—21no—
304#13133189—21no—
305#13133189—21no—
306#13133188—21no—
307#13133187—21no—
308#13133187—21no—
309#13133187—21no—
310#13133187—21no—
311#13133187—21no—
312#13133187—21no—
313#13133185—21no—
314#13133185—21no—
315C4×Dic106C2311yescharacteristic
316C4×Dic106C2311yescharacteristic
317C4×D212C2311yescharacteristic
318C4×D212C2311yescharacteristic
319#13133179—21no—
320#13133179—21no—
321#13133177—21no—
322#13133177—21no—
323#13133177—21no—
324#13133177—21no—
325#13133175—21no—
326C2×C4⋊Dic53C2311yescharacteristic
327C4⋊C4×D53—21no—
328C2×#11719921—21no—
329C22⋊C4×D53—21no—
330C22⋊C4×D53—21no—
331#13133150C2311yescharacteristic
332#13133150C2311yescharacteristic
333#13133148C2311yescharacteristic
334#13133148C2311yescharacteristic
335#13133148C2311yescharacteristic
336#13133148C2311yescharacteristic
337#13133148C2311yescharacteristic
338#13133148C2311yescharacteristic
339C4⋊#88322C2311yescharacteristic
340C4⋊#88322C2311yescharacteristic
341C4⋊#88322C2311yescharacteristic
342C4⋊#88322C2311yescharacteristic
343#13133141C2311yescharacteristic
344#13133141C2311yescharacteristic
345#13133141C2311yescharacteristic
346#13133141C2311yescharacteristic
347#13133141C2311yescharacteristic
348#13133141C2311yescharacteristic
349#13133140C2311yescharacteristic
350#13133140C2311yescharacteristic
351#13133140C2311yescharacteristic
352#13133140C2311yescharacteristic
353#13133140C2311yescharacteristic
354#13133140C2311yescharacteristic
355#13133140C2311yescharacteristic
356#13133140C2311yescharacteristic
357#13133138C2311yescharacteristic
358#13133138C2311yescharacteristic
359#13133137C2311yescharacteristic
360#13133137C2311yescharacteristic
361#13133137C2311yescharacteristic
362#13133137C2311yescharacteristic
363#13133137C2311yescharacteristic
364#13133137C2311yescharacteristic
365#13133137C2311yescharacteristic
366#13133137C2311yescharacteristic
367#13133137C2311yescharacteristic
368#13133137C2311yescharacteristic
369#13133137C2311yescharacteristic
370#13133137C2311yescharacteristic
371#13133137C2311yescharacteristic
372#13133137C2311yescharacteristic
373#13133137C2311yescharacteristic
374#13133137C2311yescharacteristic
375C22⋊#88322C2311yescharacteristic
376C22⋊#88322C2311yescharacteristic
377C22⋊#88322C2311yescharacteristic
378C22⋊#88322C2311yescharacteristic
379C22⋊#88322C2311yescharacteristic
380C22⋊#88322C2311yescharacteristic
381C22⋊#88322C2311yescharacteristic
382C22⋊#88322C2311yescharacteristic
383C22⋊#88322C2311yescharacteristic
384C22⋊#88322C2311yescharacteristic
385C22⋊#88322C2311yescharacteristic
386C22⋊#88322C2311yescharacteristic
387#13133128C2311yescharacteristic
388#13133128C2311yescharacteristic
389C4×#88322C2311yescharacteristic
390C4×#88322C2311yescharacteristic
391C2×#41×C53C2311yescharacteristic
392C2×#41×C53C2311yescharacteristic
393C2×#41×C53C2311yescharacteristic
394C22×Q8×C53C2311yescharacteristic
395C22×Q8×C53C2311yescharacteristic
396C23×C4×C53C2311yescharacteristic
397C4⋊Q8×C53—21no—
398C4⋊Q8×C53—21no—
399C4⋊Q8×C53C2311yescharacteristic
400C4⋊Q8×C53C2311yescharacteristic
401#126×C53—21no—
402#126×C53—21no—
403#126×C53—21no—
404#126×C53—21no—
405#126×C53—21no—
406#126×C53—21no—
407#126×C53—21no—
408#125×C53—21no—
409#125×C53—21no—
410#125×C53—21no—
411#125×C53—21no—
412#125×C53C2311yescharacteristic
413#124×C53—21no—
414#124×C53—21no—
415#124×C53—21no—
416#124×C53—21no—
417#124×C53—21no—
418#124×C53C2311yescharacteristic
419#123×C53—21no—
420#123×C53—21no—
421#123×C53—21no—
422#123×C53—21no—
423#123×C53—21no—
424#123×C53—21no—
425#123×C53—21no—
426#123×C53—21no—
427#123×C53D411yescharacteristic
428#123×C53D411yescharacteristic
429C22⋊Q8×C53—21no—
430C22⋊Q8×C53—21no—
431C22⋊Q8×C53—21no—
432C22⋊Q8×C53—21no—
433C22⋊Q8×C53—21no—
434C22⋊Q8×C53—21no—
435C22⋊Q8×C53—21no—
436C22⋊Q8×C53—21no—
437C22⋊Q8×C53—21no—
438C22⋊Q8×C53—21no—
439C22⋊Q8×C53D411yescharacteristic
440C22⋊Q8×C53D411yescharacteristic
441C22⋊Q8×C53C2311yescharacteristic
442C22⋊Q8×C53C2311yescharacteristic
443C22⋊Q8×C53C2311yescharacteristic
444C22⋊Q8×C53C2311yescharacteristic
445C22⋊Q8×C53C2311yescharacteristic
446C22⋊Q8×C53C2311yescharacteristic
447C22⋊Q8×C53C2311yescharacteristic
448C22⋊Q8×C53C2311yescharacteristic
449C22⋊Q8×C53C2311yescharacteristic
450#121×C53—21no—
451#121×C53—21no—
452#121×C53—21no—
453#121×C53—21no—
454#121×C53—21no—
455#121×C53—21no—
456#121×C53—21no—
457#121×C53D411yescharacteristic
458#121×C53D411yescharacteristic
459#121×C53C2311yescharacteristic
460#121×C53C2311yescharacteristic
461#121×C53C2311yescharacteristic
462#120×C53—21no—
463#120×C53D411yescharacteristic
464#120×C53D411yescharacteristic
465C4×Q8×C53—21no—
466C4×Q8×C53C2311yescharacteristic
467C4×Q8×C53C2311yescharacteristic
468C4×Q8×C53C2311yescharacteristic
469C4×D4×C53—21no—
470C4×D4×C53—21no—
471C4×D4×C53—21no—
472C4×D4×C53—21no—
473C4×D4×C53—21no—
474C4×D4×C53—21no—
475C4×D4×C53—21no—
476C4×D4×C53C2311yescharacteristic
477C4×D4×C53C2311yescharacteristic
478C4×D4×C53C2311yescharacteristic
479C4×D4×C53C2311yescharacteristic
480C4×D4×C53C2311yescharacteristic
481#117×C53—21no—
482#117×C53C2311yescharacteristic
483#117×C53C2311yescharacteristic
484#117×C53C2311yescharacteristic
485C2×C4⋊C4×C53—21no—
486C2×C4⋊C4×C53—21no—
487C2×C4⋊C4×C53C2311yescharacteristic
488C2×C4⋊C4×C53C2311yescharacteristic
489C2×C22⋊C4×C53—21no—
490C24×C53C2×D411yescharacteristic
491C23×D53—21no—
492C23×D53—21no—
493C23×D53—21no—
494C23×D53—21no—
495#41×C53—41no—
496#41×C53—41no—
497#41×C53—41no—
498#41×C53—41no—
499#41×C53—41no—
500#41×C53—41no—
501C2×Q8×C53—21no—
502C2×Q8×C53—21no—
503C2×Q8×C53—21no—
504C2×Q8×C53—41no—
505C2×Q8×C53—41no—
506C2×Q8×C53—41no—
507C2×Q8×C53—41no—
508C2×Q8×C53C2×D411yescharacteristic
509C2×Q8×C53C2411yescharacteristic
510C2×Q8×C53C2411yescharacteristic
511C2×Q8×C53C2411yescharacteristic
512C2×D4×C53—21no—
513C2×D4×C53—21no—
514C2×D4×C53—21no—
515C2×D4×C53—21no—
516C2×D4×C53—21no—
517C2×D4×C53C2×D411yescharacteristic
518C2×D4×C53C2×D411yescharacteristic
519C2×D4×C53C2×D411yescharacteristic
520C2×D4×C53C2×D411yescharacteristic
521C2×D4×C53C2×D411yescharacteristic
522C2×D4×C53C2×D411yescharacteristic
523C2×D4×C53C2×D411yescharacteristic
524C2×D4×C53C2411yescharacteristic
525C22×C4×C53—21no—
526C22×C4×C53—21no—
527C22×C4×C53—21no—
528C22×C4×C53—21no—
529C22×C4×C53—21no—
530C22×C4×C53—21no—
531C22×C4×C53—21no—
532C22×C4×C53—41no—
533C22×C4×C53—41no—
534C22×C4×C53C2×D411yescharacteristic
535C22×C4×C53C2×D411yescharacteristic
536C22×C4×C53C2×D411yescharacteristic
537C22×C4×C53C2411yescharacteristic
538C22×C4×C53C2411yescharacteristic
539C22×C4×C53C2411yescharacteristic
540C22×C4×C53C2411yescharacteristic
541C22×C4×C53C2411yescharacteristic
542C2×C22⋊D53—21no—
543C2×C22⋊D53—21no—
544C2×C22⋊D53—21no—
545C2×C22⋊D53—21no—
546C2×C22⋊D53—21no—
547C2×C22⋊D53—21no—
548C2×C22⋊D53—21no—
549C2×C22⋊D53—21no—
550C2×C22⋊D53—21no—
551C2×C22⋊D53—21no—
552C2×C22⋊D53—21no—
553C2×C22⋊D53—21no—
554C2×C22⋊D53—44no—
555C2×C22⋊D53—82no—
556C22×Dic53—21no—
557C22×Dic53—21no—
558#11719949—44no—
559D4×D53—44no—
560D4×D53—44no—
561D4×D53—44no—
562D4×D53—82no—
563D4×D53—82no—
564#11719945—22no—
565#11719945—22no—
566#11719945—22no—
567#11719945—22no—
568#11719945—22no—
569#11719945—22no—
570#11719945—41no—
571#11719945—41no—
572#11719945—41no—
573#11719945—41no—
574#11719945—41no—
575#11719945—41no—
576#11719945—44no—
577#11719945—44no—
578C2×D212—22no—
579C2×D212—22no—
580C2×D212—22no—
581C2×D212—21no—
582C2×D212—21no—
583C2×D212—21no—
584C2×D212—21no—
585C2×D212—21no—
586C2×D212—21no—
587C2×D212—21no—
588C2×D212—21no—
589C2×D212—41no—
590C2×D212—41no—
591C2×D212—41no—
592C2×D212—41no—
593C2×D212—41no—
594C2×D212C2411yescharacteristic
595C2×D212C2411yescharacteristic
596C2×D212C2411yescharacteristic
597C2×D212C2411yescharacteristic
598C2×C4×D53—21no—
599C2×C4×D53—21no—
600C2×C4×D53—21no—
601C2×C4×D53—21no—
602C2×C4×D53—21no—
603C2×C4×D53—21no—
604C2×C4×D53—21no—
605C2×C4×D53—21no—
606C2×C4×D53—44no—
607C2×Dic106—22no—
608C2×Dic106—21no—
609C2×Dic106—41no—
610C2×Dic106C2411yescharacteristic
611C2×Dic106C2411yescharacteristic
612C4⋊C4×C53—21no—
613C4⋊C4×C53—21no—
614C4⋊C4×C53—21no—
615C4⋊C4×C53—21no—
616C4⋊C4×C53—21no—
617C4⋊C4×C53—21no—
618C4⋊C4×C53—21no—
619C4⋊C4×C53—21no—
620C4⋊C4×C53—21no—
621C4⋊C4×C53—21no—
622C4⋊C4×C53—21no—
623C4⋊C4×C53—21no—
624C4⋊C4×C53—21no—
625C4⋊C4×C53—21no—
626C4⋊C4×C53—21no—
627C4⋊C4×C53—21no—
628C4⋊C4×C53—21no—
629C4⋊C4×C53—21no—
630C4⋊C4×C53—21no—
631C4⋊C4×C53C2×D411yescharacteristic
632C4⋊C4×C53C2×D411yescharacteristic
633C4⋊C4×C53C2×D411yescharacteristic
634C4⋊C4×C53C2×D411yescharacteristic
635C4⋊C4×C53C2×D411yescharacteristic
636C4⋊C4×C53C2×D411yescharacteristic
637C4⋊C4×C53C2411yescharacteristic
638C4⋊C4×C53C2411yescharacteristic
639C4⋊C4×C53C2411yescharacteristic
640C4⋊C4×C53C2411yescharacteristic
641C22⋊C4×C53—21no—
642C22⋊C4×C53—21no—
643C22⋊C4×C53—21no—
644C22⋊C4×C53—21no—
645C22⋊C4×C53—21no—
646C22⋊C4×C53—21no—
647C22⋊C4×C53—21no—
648C22⋊C4×C53—21no—
649C22⋊C4×C53—21no—
650C22⋊C4×C53—21no—
651C22⋊C4×C53—21no—
652C22⋊C4×C53—21no—
653C22⋊C4×C53—21no—
654C22⋊C4×C53—21no—
655C22⋊C4×C53—21no—
656C22⋊C4×C53—21no—
657C22⋊C4×C53—21no—
658C22⋊C4×C53C2×D411yescharacteristic
659C22⋊C4×C53C2×D411yescharacteristic
660C22⋊C4×C53C2×D411yescharacteristic
661C22⋊C4×C53C2×D411yescharacteristic
662C22⋊C4×C53C2×D411yescharacteristic
663C22⋊C4×C53C2×D411yescharacteristic
664C22⋊C4×C53C2×D411yescharacteristic
665C22⋊C4×C53C2×D411yescharacteristic
666C22⋊C4×C53C2×D411yescharacteristic
667C22⋊C4×C53C2×D411yescharacteristic
668C42×C53—21no—
669C42×C53—21no—
670C42×C53—21no—
671C42×C53—21no—
672C42×C53—21no—
673C42×C53C2411yescharacteristic
674C42×C53C2411yescharacteristic
675C22⋊Dic53—21no—
676C22⋊Dic53—21no—
677#11719925—22no—
678#11719925—22no—
679#11719925—22no—
680#11719925—41no—
681#11719925—41no—
682#11719925—41no—
683#11719924—22no—
684#11719924—22no—
685#11719924—22no—
686#11719924—41no—
687#11719924—41no—
688#11719924—41no—
689#11719924—41no—
690#11719924—41no—
691#11719924—41no—
692#11719924—41no—
693#11719924—41no—
694#11719924—41no—
695#11719923—22no—
696#11719923—41no—
697#11719922—22no—
698#11719922—41no—
699#11719922—41no—
700#11719922—41no—
701#11719921—21no—
702#11719921—21no—
703#11719921—21no—
704#11719921—21no—
705#11719921—21no—
706#11719921—21no—
707#11719921—21no—
708#11719921—21no—
709#11719921—21no—
710#11719921—21no—
711#11719921—21no—
712#11719921—21no—
713C4⋊Dic53—21no—
714C4⋊Dic53C2411yescharacteristic
715C4⋊Dic53C2411yescharacteristic
716#11719919—21no—
717#11719919—21no—
718#11719919—21no—
719#11719919—21no—
720C4×Dic53—21no—
721C4×Dic53—21no—
722#11719917—41no—
723#11719917—41no—
724C2×#88322—41no—
725C2×#88322—41no—
726C2×#88322—41no—
727C2×#88322—41no—
728C2×#88322—41no—
729C2×#88322—41no—
730C2×#88322C2411yescharacteristic
731C2×#88322C2411yescharacteristic
732C2×#88322C2411yescharacteristic
733C2×#88322C2411yescharacteristic
734C2×#88322C2411yescharacteristic
735C2×#88322C2411yescharacteristic
736C2×#88322C2411yescharacteristic
737C2×#88322C2411yescharacteristic
738C23×C53—22no—
739C23×C53—21no—
740C23×C53—41no—
741C23×C53—41no—
742C23×C53C22×D411yescharacteristic
743C23×C53C22×D411yescharacteristic
744C23×C53C22×D411yescharacteristic
745C23×C53C22×D411yescharacteristic
746C23×C53C22×D411yescharacteristic
747C22×D53—21no—
748C22×D53—21no—
749C22×D53—21no—
750C22×D53—21no—
751C22×D53—42no—
752C22×D53—42no—
753C22×D53—42no—
754C22×D53—42no—
755C22×D53—42no—
756C22×D53—81no—
757C22×D53—81no—
758C22×D53—81no—
759C22×D53—81no—
760C22×D53—81no—
761C22×D53—81no—
762C22×D53—81no—
763Q8×C53—21no—
764Q8×C53—21no—
765Q8×C53—21no—
766Q8×C53—21no—
767Q8×C53—21no—
768Q8×C53—21no—
769Q8×C53—41no—
770Q8×C53—81no—
771Q8×C53—81no—
772Q8×C53—81no—
773D4×C53—22no—
774D4×C53—22no—
775D4×C53—21no—
776D4×C53—21no—
777D4×C53—41no—
778D4×C53—41no—
779D4×C53—41no—
780D4×C53—41no—
781D4×C53—41no—
782D4×C53—42no—
783D4×C53—81no—
784D4×C53—81no—
785D4×C53—81no—
786D4×C53—81no—
787C2×C4×C53—21no—
788C2×C4×C53—21no—
789C2×C4×C53—21no—
790C2×C4×C53—21no—
791C2×C4×C53—21no—
792C2×C4×C53—21no—
793C2×C4×C53—21no—
794C2×C4×C53—21no—
795C2×C4×C53—21no—
796C2×C4×C53—21no—
797C2×C4×C53—21no—
798C2×C4×C53—21no—
799C2×C4×C53—21no—
800C2×C4×C53—21no—
801C2×C4×C53—21no—
802C2×C4×C53—21no—
803C2×C4×C53—21no—
804C2×C4×C53—41no—
805C2×C4×C53—41no—
806C2×C4×C53—41no—
807C2×C4×C53—81no—
808C2×C4×C53—81no—
809C2×C4×C53—81no—
810C2×C4×C53—81no—
811C2×C4×C53—81no—
812C2×C4×C53—81no—
813C2×C4×C53—81no—
814C2×C4×C53C22×D411yescharacteristic
815C2×C4×C53C22×D411yescharacteristic
816C2×C4×C53C22×D411yescharacteristic
817C2×C4×C53C22×D411yescharacteristic
818C2×C4×C53C22×D411yescharacteristic
819C2×C4×C53C22×D411yescharacteristic
820C2×C4×C53C22×D411yescharacteristic
821C2×C4×C53C22×D411yescharacteristic
822C2×C4×C53C22×D411yescharacteristic
823C2×C4×C53C2511yescharacteristic
824C22⋊D53—24no—
825C22⋊D53—42no—
826C22⋊D53—42no—
827C22⋊D53—42no—
828C22⋊D53—42no—
829C22⋊D53—42no—
830C22⋊D53—42no—
831C22⋊D53—42no—
832C22⋊D53—81no—
833C22⋊D53—81no—
834C22⋊D53—81no—
835C22⋊D53—81no—
836C2×Dic53—21no—
837C2×Dic53—21no—
838C2×Dic53—21no—
839C2×Dic53—21no—
840C2×Dic53—42no—
841C2×Dic53—81no—
842D212—21no—
843D212—21no—
844D212—21no—
845D212—21no—
846D212—21no—
847D212—21no—
848D212—21no—
849D212—42no—
850D212—42no—
851D212—42no—
852D212—42no—
853D212—81no—
854D212—81no—
855D212—81no—
856D212—81no—
857D212H(5,𝔽2)12yes—
858C4×D53—24no—
859C4×D53—42no—
860C4×D53—42no—
861C4×D53—42no—
862C4×D53—42no—
863C4×D53—42no—
864C4×D53—81no—
865C4×D53—81no—
866Dic106—21no—
867Dic106—21no—
868Dic106—21no—
869Dic106—42no—
870Dic106H(5,𝔽2)12yes—
871#88322—21no—
872#88322—21no—
873#88322—21no—
874#88322—21no—
875#88322—21no—
876#88322—21no—
877#88322—21no—
878#88322—21no—
879#61640—531nomaximal, Sylow
880C22×C53—21no—
881C22×C53—21no—
882C22×C53—21no—
883C22×C53—21no—
884C22×C53—21no—
885C22×C53—21no—
886C22×C53—21no—
887C22×C53—21no—
888C22×C53—21no—
889C22×C53—21no—
890C22×C53—21no—
891C22×C53—21no—
892C22×C53—21no—
893C22×C53—21no—
894C22×C53—41no—
895C22×C53—41no—
896C22×C53—41no—
897C22×C53—82no—
898C22×C53#57712yes—
899C22×C53C23×D411yescharacteristic
900C2×D53—22no—
901C2×D53—41no—
902C2×D53—41no—
903C2×D53—41no—
904C2×D53—41no—
905C2×D53—41no—
906C2×D53—41no—
907C2×D53—41no—
908C2×D53—41no—
909C2×D53—41no—
910C2×D53—41no—
911C2×D53—41no—
912C2×D53—84no—
913C2×D53—162no—
914C2×D53—162no—
915C2×D53—162no—
916C4×C53—21no—
917C4×C53—21no—
918C4×C53—21no—
919C4×C53—21no—
920C4×C53—21no—
921C4×C53—21no—
922C4×C53—21no—
923C4×C53—21no—
924C4×C53—21no—
925C4×C53—41no—
926C4×C53—41no—
927C4×C53—41no—
928C4×C53—41no—
929C4×C53—41no—
930C4×C53—41no—
931C4×C53—41no—
932C4×C53C2×H(5,𝔽2)11yescharacteristic
933C4×C53C2×H(5,𝔽2)11yescharacteristic
934Dic53—22no—
935Dic53—41no—
936Dic53—41no—
937Dic53—41no—
938#3541D5311yescharacteristic, complemented
939#3488—531no—
940#3318—531no—
941#3317—531no—
942#3316—531no—
943#3311—531no—
944#3304—531no—
945#3301—531no—
946#3296—531no—
947#3295—531no—
948#3285—531no—
949#3284—531no—
950#3282—531no—
951D4×SD16—531no—
952#3271—531no—
953#3270—531no—
954#3267—531no—
955#3265—531no—
956#3224—531no—
957#3222—531no—
958#3204—531no—
959#3201—531no—
960#3188—531no—
961#3187—531no—
962#3125—531no—
963#3120—531no—
964#3012—531no—
965#3009—531no—
966#3002—531no—
967C2×#452—531no—
968#2977—531no—
969C2×C53—22no—
970C2×C53—41no—
971C2×C53—41no—
972C2×C53—41no—
973C2×C53—41no—
974C2×C53—81no—
975C2×C53#348411yescharacteristic
976C2×C53C2×#57711yescharacteristic
977C2×C53#358411yescharacteristic
978D53—42no—
979D53—81no—
980D53—81no—
981D53—81no—
982C2×H(5,𝔽2)—531no—
983C22×#41—531no—
984C2×#137—531no—
985C2×AGL(1,ℤ/8)—531no—
986C2×#135—531no—
987C2×#135—531no—
988C2×#135—531no—
989C22×Q16—531no—
990C22×SD16—531no—
991C22×SD16—531no—
992#563—21no—
993#562—21no—
994#556C2×D5311yescharacteristic, complemented
995#554—21no—
996#554C2×D5311yescharacteristic, complemented
997#553—21no—
998#553C2×D5311yescharacteristic, complemented
999#552C2×D5311yescharacteristic, complemented
1000#550—531no—
1001#550—531no—
1002D4×Q8C2×D5311yescharacteristic, complemented
1003#548—531no—
1004#548—531no—
1005#548C2×D5311yescharacteristic, complemented
1006#548C2×D5311yescharacteristic, complemented
1007#547C2×D5311yescharacteristic, complemented
1008#546—531no—
1009#546—531no—
1010#546—1061no—
1011#546—1061no—
1012D42—531no—
1013D42—531no—
1014D42—1061no—
1015D42—1061no—
1016#542—21no—
1017#542C2×D5311yescharacteristic, complemented
1018#541C2×D5311yescharacteristic, complemented
1019#539—21no—
1020#538—21no—
1021#538—21no—
1022#537—531no—
1023#537—1061no—
1024#537C2×D5311yescharacteristic, complemented
1025#536C2×D5311yescharacteristic, complemented
1026#535—531no—
1027#535—1061no—
1028#525—1061no—
1029#525C2×D5311yescharacteristic
1030#525C2×D5311yescharacteristic, complemented
1031C2×C22⋊Q8C2×D5311yescharacteristic, complemented
1032C2×#121—531no—
1033C2×#121—1061no—
1034#520—531no—
1035#497—531no—
1036#496—531no—
1037#495—531no—
1038#492—531no—
1039#490—531no—
1040#489—531no—
1041#488—531no—
1042#486—531no—
1043#485—531no—
1044#484—531no—
1045#483—531no—
1046#483—531no—
1047#483—531no—
1048#482—531no—
1049#482—531no—
1050#482—531no—
1051#481—531no—
1052#481—531no—
1053#481—531no—
1054#481—531no—
1055#479—531no—
1056#478—531no—
1057#476—531no—
1058#475—531no—
1059#470—531no—
1060#470—531no—
1061#469—531no—
1062#468—531no—
1063#467—531no—
1064#466—531no—
1065#466—531no—
1066#465—531no—
1067#465—531no—
1068#465—531no—
1069#465—531no—
1070#465—531no—
1071#465—531no—
1072#465—531no—
1073#465—531no—
1074#465—531no—
1075#464—531no—
1076#464—531no—
1077#464—531no—
1078#464—531no—
1079#463—531no—
1080#463—531no—
1081#462—531no—
1082#461—531no—
1083#460—531no—
1084#460—531no—
1085#460—531no—
1086#459—531no—
1087#452—531no—
1088#452—531no—
1089#452—531no—
1090#452—531no—
1091#452—531no—
1092#452—531no—
1093#452—531no—
1094#452—531no—
1095#452—531no—
1096#452—531no—
1097#452—531no—
1098#452—531no—
1099#452—531no—
1100#452—531no—
1101#451—531no—
1102#451—531no—
1103#450—531no—
1104#450—531no—
1105#450—531no—
1106#450—531no—
1107#450—531no—
1108#450—531no—
1109#450—531no—
1110#449—531no—
1111#449—531no—
1112#449—531no—
1113#449—531no—
1114#449—531no—
1115#449—531no—
1116#448—531no—
1117#448—531no—
1118#448—531no—
1119#448—531no—
1120#447—531no—
1121#447—531no—
1122#447—531no—
1123#442—531no—
1124#441—531no—
1125#441—531no—
1126#440—531no—
1127C4×Q16—531no—
1128C4×SD16—531no—
1129C4×SD16—531no—
1130C4×SD16—531no—
1131#435—531no—
1132#435—531no—
1133#435—531no—
1134#435—531no—
1135C8×D4—531no—
1136C8×D4—531no—
1137C8×D4—531no—
1138C8×D4—531no—
1139#433—531no—
1140#433—531no—
1141#418—531no—
1142#417—531no—
1143#416—531no—
1144#416—531no—
1145#416—531no—
1146C2×#103—531no—
1147C2×#102—531no—
1148C2×#102—531no—
1149#408—531no—
1150#408—531no—
1151C2×C22⋊C8—531no—
1152C2×C22⋊C8—531no—
1153C53#6164011yescharacteristic, complemented, Sylow
1154H(5,𝔽2)—2122no—
1155H(5,𝔽2)—2122no—
1156C2×#41—531no—
1157C2×#41—531no—
1158C2×#41—531no—
1159C2×#41—531no—
1160C2×#41—531no—
1161C2×#41—531no—
1162C2×#41—1061no—
1163C2×#41—1061no—
1164C2×#41—1061no—
1165C2×#41—2122no—
1166C2×#41—2122no—
1167C2×#41C22×D5311yescharacteristic
1168C2×#41C22×D5311yescharacteristic
1169C2×#41C22×D5311yescharacteristic
1170C22×Q8—531no—
1171C22×Q8C22×D5311yescharacteristic
1172C22×Q8C22×D5311yescharacteristic
1173C22×D4—531no—
1174C22×D4—531no—
1175C22×D4—531no—
1176C22×D4—531no—
1177C22×D4—1061no—
1178C22×D4—1061no—
1179C22×D4—1061no—
1180C22×D4—1061no—
1181C22×D4—1061no—
1182C22×D4—1061no—
1183C22×D4—1061no—
1184C23×C4—1061no—
1185C23×C4C22×D5311yescharacteristic
1186#137—2122no—
1187AGL(1,ℤ/8)—2122no—
1188#135—2122no—
1189#135—2122no—
1190#135—2122no—
1191C2×Q16—531no—
1192C2×Q16—531no—
1193C2×Q16—531no—
1194C2×Q16—531no—
1195C2×Q16—531no—
1196C2×Q16—531no—
1197C2×Q16—2122no—
1198C2×SD16—531no—
1199C2×SD16—531no—
1200C2×SD16—531no—
1201C2×SD16—531no—
1202C2×SD16—531no—
1203C2×SD16—531no—
1204C2×SD16—531no—
1205C2×SD16—531no—
1206C2×SD16—531no—
1207C2×SD16—531no—
1208C2×SD16—531no—
1209C2×SD16—531no—
1210C2×SD16—531no—
1211C2×SD16—531no—
1212C2×SD16—2122no—
1213C2×SD16—2122no—
1214C2×D8—531no—
1215C2×D8—531no—
1216C2×D8—531no—
1217C2×D8—531no—
1218C2×M16—531no—
1219C2×M16—531no—
1220C22×C8—531no—
1221C22×C8—531no—
1222C22×C8—531no—
1223C22×C8—531no—
1224C22×C8—531no—
1225C22×C8—531no—
1226C4⋊Q8—21no—
1227C4⋊Q8—21no—
1228C4⋊Q8C22×D5311yescharacteristic
1229C4⋊Q8C22×D5311yescharacteristic
1230#127—531no—
1231#127—531no—
1232#127—1061no—
1233#127—1061no—
1234#126—21no—
1235#126—21no—
1236#126—21no—
1237#126—21no—
1238#126—21no—
1239#126—21no—
1240#126—21no—
1241#125—21no—
1242#125—21no—
1243#125—21no—
1244#125—21no—
1245#125C22×D5311yescharacteristic
1246#124—21no—
1247#124—21no—
1248#124—21no—
1249#124—21no—
1250#124—21no—
1251#124—531no—
1252#124—531no—
1253#124—1061no—
1254#124—1061no—
1255#124C22×D5311yescharacteristic
1256#123—21no—
1257#123—21no—
1258#123—21no—
1259#123—21no—
1260#123—21no—
1261#123—21no—
1262#123—21no—
1263#123—21no—
1264#123—1061no—
1265#123—1061no—
1266#123C22⋊D5311yescharacteristic
1267#123C22⋊D5311yescharacteristic
1268C22⋊Q8—21no—
1269C22⋊Q8—21no—
1270C22⋊Q8—21no—
1271C22⋊Q8—21no—
1272C22⋊Q8—21no—
1273C22⋊Q8—21no—
1274C22⋊Q8—21no—
1275C22⋊Q8—21no—
1276C22⋊Q8—21no—
1277C22⋊Q8—21no—
1278C22⋊Q8—531no—
1279C22⋊Q8—531no—
1280C22⋊Q8—1061no—
1281C22⋊Q8—1061no—
1282C22⋊Q8—1061no—
1283C22⋊Q8C22⋊D5311yescharacteristic
1284C22⋊Q8C22⋊D5311yescharacteristic
1285C22⋊Q8C22×D5311yescharacteristic
1286C22⋊Q8C22×D5311yescharacteristic
1287C22⋊Q8C22×D5311yescharacteristic
1288C22⋊Q8C22×D5311yescharacteristic
1289C22⋊Q8C22×D5311yescharacteristic
1290C22⋊Q8C22×D5311yescharacteristic
1291C22⋊Q8C22×D5311yescharacteristic
1292C22⋊Q8C22×D5311yescharacteristic
1293C22⋊Q8C22×D5311yescharacteristic
1294#121—21no—
1295#121—21no—
1296#121—21no—
1297#121—21no—
1298#121—21no—
1299#121—21no—
1300#121—21no—
1301#121—531no—
1302#121—531no—
1303#121—531no—
1304#121—531no—
1305#121—531no—
1306#121—531no—
1307#121—1061no—
1308#121—1061no—
1309#121—1061no—
1310#121—1061no—
1311#121—1061no—
1312#121—1061no—
1313#121—1061no—
1314#121—1061no—
1315#121—1061no—
1316#121—1061no—
1317#121—1061no—
1318#121—1061no—
1319#121—1061no—
1320#121—1061no—
1321#121—1061no—
1322#121—1061no—
1323#121—1061no—
1324#121C22⋊D5311yescharacteristic
1325#121C22⋊D5311yescharacteristic
1326#121C22×D5311yescharacteristic
1327#121C22×D5311yescharacteristic
1328#121C22×D5311yescharacteristic
1329#120—21no—
1330#120—1061no—
1331#120—1061no—
1332#120—1061no—
1333#120—1061no—
1334#120—1061no—
1335#120—1061no—
1336#120—1061no—
1337#120—1061no—
1338#120C22⋊D5311yescharacteristic
1339#120C22⋊D5311yescharacteristic
1340C4×Q8—21no—
1341C4×Q8—531no—
1342C4×Q8—531no—
1343C4×Q8C22×D5311yescharacteristic
1344C4×Q8C22×D5311yescharacteristic
1345C4×Q8C22×D5311yescharacteristic
1346C4×D4—21no—
1347C4×D4—21no—
1348C4×D4—21no—
1349C4×D4—21no—
1350C4×D4—21no—
1351C4×D4—21no—
1352C4×D4—21no—
1353C4×D4—531no—
1354C4×D4—531no—
1355C4×D4—1061no—
1356C4×D4—1061no—
1357C4×D4—1061no—
1358C4×D4—1061no—
1359C4×D4—1061no—
1360C4×D4—1061no—
1361C4×D4C22×D5311yescharacteristic
1362C4×D4C22×D5311yescharacteristic
1363C4×D4C22×D5311yescharacteristic
1364C4×D4C22×D5311yescharacteristic
1365C4×D4C22×D5311yescharacteristic
1366#117—21no—
1367#117—1061no—
1368#117C22×D5311yescharacteristic
1369#117C22×D5311yescharacteristic
1370#117C22×D5311yescharacteristic
1371C2×C4⋊C4—21no—
1372C2×C4⋊C4—21no—
1373C2×C4⋊C4—531no—
1374C2×C4⋊C4—1061no—
1375C2×C4⋊C4C22×D5311yescharacteristic
1376C2×C4⋊C4C22×D5311yescharacteristic
1377C2×C22⋊C4—21no—
1378C2×C22⋊C4—1061no—
1379C2×C22⋊C4—1061no—
1380C2×C22⋊C4—1061no—
1381#107—531no—
1382#107—531no—
1383#106—531no—
1384#106—531no—
1385#106—531no—
1386#106—531no—
1387#106—531no—
1388#106—531no—
1389C4⋊C8—531no—
1390C4⋊C8—531no—
1391C4⋊C8—531no—
1392C4⋊C8—531no—
1393#103—531no—
1394#103—531no—
1395#103—531no—
1396#103—531no—
1397#103—531no—
1398#103—531no—
1399#103—531no—
1400#103—531no—
1401#103—531no—
1402#103—531no—
1403#103—531no—
1404#103—531no—
1405#103—531no—
1406#103—531no—
1407#102—531no—
1408#102—531no—
1409#102—531no—
1410#102—531no—
1411#102—531no—
1412#102—531no—
1413#102—531no—
1414#102—531no—
1415#102—531no—
1416#102—531no—
1417#102—531no—
1418#102—531no—
1419#102—531no—
1420#102—531no—
1421#102—531no—
1422#102—531no—
1423#102—531no—
1424#102—531no—
1425C22⋊C8—531no—
1426C22⋊C8—531no—
1427C22⋊C8—531no—
1428C22⋊C8—531no—
1429C22⋊C8—531no—
1430C22⋊C8—531no—
1431C22⋊C8—531no—
1432C22⋊C8—531no—
1433C22⋊C8—531no—
1434C22⋊C8—531no—
1435C22⋊C8—531no—
1436C22⋊C8—531no—
1437#97—531no—
1438#97—531no—
1439C4×C8—531no—
1440C4×C8—531no—
1441C24—1061no—
1442C24—1061no—
1443C24—1061no—
1444C24—1061no—
1445C24C2×C22⋊D5311yescharacteristic
1446#41—41no—
1447#41—41no—
1448#41—41no—
1449#41—41no—
1450#41—41no—
1451#41—41no—
1452#41—1062no—
1453#41—1062no—
1454#41—1062no—
1455#41—1062no—
1456#41—1062no—
1457#41—1062no—
1458#41—2121no—
1459#41—2121no—
1460#41—2121no—
1461#41—2121no—
1462#41—2121no—
1463#41—2121no—
1464#41—2124no—
1465#41—2124no—
1466#41—2124no—
1467C2×Q8—21no—
1468C2×Q8—21no—
1469C2×Q8—21no—
1470C2×Q8—41no—
1471C2×Q8—41no—
1472C2×Q8—41no—
1473C2×Q8—41no—
1474C2×Q8—531no—
1475C2×Q8—531no—
1476C2×Q8—1062no—
1477C2×Q8—1061no—
1478C2×Q8—2121no—
1479C2×Q8C2×C22⋊D5311yescharacteristic
1480C2×Q8C23×D5311yescharacteristic
1481C2×Q8C23×D5311yescharacteristic
1482C2×Q8C23×D5311yescharacteristic
1483C2×D4—21no—
1484C2×D4—21no—
1485C2×D4—21no—
1486C2×D4—21no—
1487C2×D4—21no—
1488C2×D4—531no—
1489C2×D4—531no—
1490C2×D4—531no—
1491C2×D4—531no—
1492C2×D4—1062no—
1493C2×D4—1062no—
1494C2×D4—1062no—
1495C2×D4—1061no—
1496C2×D4—1061no—
1497C2×D4—1061no—
1498C2×D4—1061no—
1499C2×D4—1061no—
1500C2×D4—1061no—
1501C2×D4—1061no—
1502C2×D4—1061no—
1503C2×D4—1061no—
1504C2×D4—1061no—
1505C2×D4—1061no—
1506C2×D4—1061no—
1507C2×D4—1061no—
1508C2×D4—1061no—
1509C2×D4—1061no—
1510C2×D4—1061no—
1511C2×D4—1061no—
1512C2×D4—1061no—
1513C2×D4—1061no—
1514C2×D4—1061no—
1515C2×D4—4242no—
1516C2×D4—4242no—
1517C2×D4—4242no—
1518C2×D4—2121no—
1519C2×D4—2121no—
1520C2×D4—2121no—
1521C2×D4—2121no—
1522C2×D4—2121no—
1523C2×D4—2124no—
1524C2×D4—2124no—
1525C2×D4—2124no—
1526C2×D4—2124no—
1527C2×D4C2×C22⋊D5311yescharacteristic
1528C2×D4C2×C22⋊D5311yescharacteristic
1529C2×D4C2×C22⋊D5311yescharacteristic
1530C2×D4C2×C22⋊D5311yescharacteristic
1531C2×D4C2×C22⋊D5311yescharacteristic
1532C2×D4C2×C22⋊D5311yescharacteristic
1533C2×D4C2×C22⋊D5311yescharacteristic
1534C2×D4C23×D5311yescharacteristic
1535C22×C4—21no—
1536C22×C4—21no—
1537C22×C4—21no—
1538C22×C4—21no—
1539C22×C4—21no—
1540C22×C4—21no—
1541C22×C4—21no—
1542C22×C4—41no—
1543C22×C4—41no—
1544C22×C4—1061no—
1545C22×C4—1061no—
1546C22×C4—1061no—
1547C22×C4—1061no—
1548C22×C4—1061no—
1549C22×C4—1061no—
1550C22×C4—1061no—
1551C22×C4—1061no—
1552C22×C4—1061no—
1553C22×C4—1061no—
1554C22×C4—2124no—
1555C22×C4C2×C22⋊D5311yescharacteristic
1556C22×C4C2×C22⋊D5311yescharacteristic
1557C22×C4C2×C22⋊D5311yescharacteristic
1558C22×C4C23×D5311yescharacteristic
1559C22×C4C23×D5311yescharacteristic
1560C22×C4C23×D5311yescharacteristic
1561C22×C4C23×D5311yescharacteristic
1562C22×C4C23×D5311yescharacteristic
1563Q16—1062no—
1564Q16—1062no—
1565Q16—1062no—
1566Q16—2121no—
1567Q16—2121no—
1568Q16—2121no—
1569SD16—1062no—
1570SD16—1062no—
1571SD16—1062no—
1572SD16—1062no—
1573SD16—2121no—
1574SD16—2121no—
1575SD16—2121no—
1576SD16—2121no—
1577SD16—2121no—
1578SD16—2121no—
1579SD16—2121no—
1580SD16—2121no—
1581SD16—2121no—
1582SD16—2121no—
1583D8—1062no—
1584D8—2121no—
1585D8—2121no—
1586D8—2121no—
1587M16—2121no—
1588M16—2121no—
1589C2×C8—531no—
1590C2×C8—531no—
1591C2×C8—531no—
1592C2×C8—531no—
1593C2×C8—531no—
1594C2×C8—531no—
1595C2×C8—531no—
1596C2×C8—531no—
1597C2×C8—2121no—
1598C2×C8—2121no—
1599C2×C8—2121no—
1600C2×C8—2121no—
1601C2×C8—2121no—
1602C2×C8—2121no—
1603C4⋊C4—21no—
1604C4⋊C4—21no—
1605C4⋊C4—21no—
1606C4⋊C4—21no—
1607C4⋊C4—21no—
1608C4⋊C4—21no—
1609C4⋊C4—21no—
1610C4⋊C4—21no—
1611C4⋊C4—21no—
1612C4⋊C4—21no—
1613C4⋊C4—21no—
1614C4⋊C4—21no—
1615C4⋊C4—21no—
1616C4⋊C4—21no—
1617C4⋊C4—21no—
1618C4⋊C4—21no—
1619C4⋊C4—21no—
1620C4⋊C4—21no—
1621C4⋊C4—21no—
1622C4⋊C4—531no—
1623C4⋊C4—531no—
1624C4⋊C4—1061no—
1625C4⋊C4—1061no—
1626C4⋊C4—1061no—
1627C4⋊C4—1061no—
1628C4⋊C4—1061no—
1629C4⋊C4C2×C22⋊D5311yescharacteristic
1630C4⋊C4C2×C22⋊D5311yescharacteristic
1631C4⋊C4C2×C22⋊D5311yescharacteristic
1632C4⋊C4C2×C22⋊D5311yescharacteristic
1633C4⋊C4C2×C22⋊D5311yescharacteristic
1634C4⋊C4C2×C22⋊D5311yescharacteristic
1635C4⋊C4C23×D5311yescharacteristic
1636C4⋊C4C23×D5311yescharacteristic
1637C4⋊C4C23×D5311yescharacteristic
1638C4⋊C4C23×D5311yescharacteristic
1639C22⋊C4—21no—
1640C22⋊C4—21no—
1641C22⋊C4—21no—
1642C22⋊C4—21no—
1643C22⋊C4—21no—
1644C22⋊C4—21no—
1645C22⋊C4—21no—
1646C22⋊C4—21no—
1647C22⋊C4—21no—
1648C22⋊C4—21no—
1649C22⋊C4—21no—
1650C22⋊C4—21no—
1651C22⋊C4—21no—
1652C22⋊C4—21no—
1653C22⋊C4—21no—
1654C22⋊C4—21no—
1655C22⋊C4—21no—
1656C22⋊C4—1061no—
1657C22⋊C4—1061no—
1658C22⋊C4—1061no—
1659C22⋊C4—1061no—
1660C22⋊C4—1061no—
1661C22⋊C4—1061no—
1662C22⋊C4—1061no—
1663C22⋊C4—1061no—
1664C22⋊C4—1061no—
1665C22⋊C4—1061no—
1666C22⋊C4—1061no—
1667C22⋊C4—1061no—
1668C22⋊C4—1061no—
1669C22⋊C4—1061no—
1670C22⋊C4C2×C22⋊D5311yescharacteristic
1671C22⋊C4C2×C22⋊D5311yescharacteristic
1672C22⋊C4C2×C22⋊D5311yescharacteristic
1673C22⋊C4C2×C22⋊D5311yescharacteristic
1674C22⋊C4C2×C22⋊D5311yescharacteristic
1675C22⋊C4C2×C22⋊D5311yescharacteristic
1676C22⋊C4C2×C22⋊D5311yescharacteristic
1677C22⋊C4C2×C22⋊D5311yescharacteristic
1678C22⋊C4C2×C22⋊D5311yescharacteristic
1679C22⋊C4C2×C22⋊D5311yescharacteristic
1680C42—21no—
1681C42—21no—
1682C42—21no—
1683C42—21no—
1684C42—21no—
1685C42—1061no—
1686C42—1061no—
1687C42C23×D5311yescharacteristic
1688C42C23×D5311yescharacteristic
1689C23—22no—
1690C23—21no—
1691C23—41no—
1692C23—41no—
1693C23—1061no—
1694C23—1061no—
1695C23—1061no—
1696C23—1061no—
1697C23—4241no—
1698C23—4241no—
1699C23—4241no—
1700C23—4241no—
1701C23—4241no—
1702C23—4241no—
1703C23—4241no—
1704C23—2122no—
1705C23—2122no—
1706C23—2122no—
1707C23—2122no—
1708C23—2122no—
1709C23C22×C22⋊D5311yescharacteristic
1710C23C22×C22⋊D5311yescharacteristic
1711C23C22×C22⋊D5311yescharacteristic
1712C23C22×C22⋊D5311yescharacteristic
1713C23C22×C22⋊D5311yescharacteristic
1714Q8—21no—
1715Q8—21no—
1716Q8—21no—
1717Q8—21no—
1718Q8—21no—
1719Q8—21no—
1720Q8—41no—
1721Q8—81no—
1722Q8—81no—
1723Q8—81no—
1724Q8—532no—
1725Q8—1061no—
1726Q8—1061no—
1727Q8—1061no—
1728Q8—2122no—
1729D4—22no—
1730D4—22no—
1731D4—21no—
1732D4—21no—
1733D4—41no—
1734D4—41no—
1735D4—41no—
1736D4—41no—
1737D4—41no—
1738D4—42no—
1739D4—81no—
1740D4—81no—
1741D4—81no—
1742D4—81no—
1743D4—532no—
1744D4—1064no—
1745D4—1061no—
1746D4—1061no—
1747D4—1061no—
1748D4—1061no—
1749D4—1061no—
1750D4—1061no—
1751D4—1061no—
1752D4—4241no—
1753D4—4241no—
1754D4—4241no—
1755D4—4241no—
1756D4—4241no—
1757D4—4241no—
1758D4—4241no—
1759D4—4241no—
1760D4—2122no—
1761D4—2122no—
1762D4—2122no—
1763D4—2122no—
1764D4—2122no—
1765D4—2122no—
1766D4—2122no—
1767D4—2122no—
1768D4—2122no—
1769D4—2122no—
1770D4—2122no—
1771C2×C4—21no—
1772C2×C4—21no—
1773C2×C4—21no—
1774C2×C4—21no—
1775C2×C4—21no—
1776C2×C4—21no—
1777C2×C4—21no—
1778C2×C4—21no—
1779C2×C4—21no—
1780C2×C4—21no—
1781C2×C4—21no—
1782C2×C4—21no—
1783C2×C4—21no—
1784C2×C4—21no—
1785C2×C4—21no—
1786C2×C4—21no—
1787C2×C4—21no—
1788C2×C4—41no—
1789C2×C4—41no—
1790C2×C4—41no—
1791C2×C4—81no—
1792C2×C4—81no—
1793C2×C4—81no—
1794C2×C4—81no—
1795C2×C4—81no—
1796C2×C4—81no—
1797C2×C4—81no—
1798C2×C4—1064no—
1799C2×C4—1061no—
1800C2×C4—1061no—
1801C2×C4—1061no—
1802C2×C4—1061no—
1803C2×C4—4241no—
1804C2×C4—4241no—
1805C2×C4—4241no—
1806C2×C4—2122no—
1807C2×C4—2122no—
1808C2×C4—2122no—
1809C2×C4—2122no—
1810C2×C4—2122no—
1811C2×C4—2122no—
1812C2×C4C22×C22⋊D5311yescharacteristic
1813C2×C4C22×C22⋊D5311yescharacteristic
1814C2×C4C22×C22⋊D5311yescharacteristic
1815C2×C4C22×C22⋊D5311yescharacteristic
1816C2×C4C22×C22⋊D5311yescharacteristic
1817C2×C4C22×C22⋊D5311yescharacteristic
1818C2×C4C22×C22⋊D5311yescharacteristic
1819C2×C4C22×C22⋊D5311yescharacteristic
1820C2×C4C22×C22⋊D5311yescharacteristic
1821C2×C4C24×D5311yescharacteristic
1822C8—1061no—
1823C8—1061no—
1824C8—1061no—
1825C8—1061no—
1826C8—1061no—
1827C8—1061no—
1828C8—1061no—
1829C8—1061no—
1830C22—21no—
1831C22—21no—
1832C22—21no—
1833C22—21no—
1834C22—21no—
1835C22—21no—
1836C22—21no—
1837C22—21no—
1838C22—21no—
1839C22—21no—
1840C22—21no—
1841C22—21no—
1842C22—21no—
1843C22—21no—
1844C22—41no—
1845C22—41no—
1846C22—41no—
1847C22—82no—
1848C22—8482no—
1849C22—8482no—
1850C22—8482no—
1851C22—1062no—
1852C22—4244no—
1853C22—2121no—
1854C22—2121no—
1855C22—2121no—
1856C22—2121no—
1857C22—2121no—
1858C22—2121no—
1859C22—2121no—
1860C22—2121no—
1861C22—2121no—
1862C22—2121no—
1863C22—2121no—
1864C22#1681143112yes—
1865C22C23×C22⋊D5311yescharacteristic
1866C4—21no—
1867C4—21no—
1868C4—21no—
1869C4—21no—
1870C4—21no—
1871C4—21no—
1872C4—21no—
1873C4—21no—
1874C4—21no—
1875C4—41no—
1876C4—41no—
1877C4—41no—
1878C4—41no—
1879C4—41no—
1880C4—41no—
1881C4—41no—
1882C4—1062no—
1883C4—2121no—
1884C4—2121no—
1885C4—2121no—
1886C4H(5,𝔽2)×D5311yescharacteristic
1887C4H(5,𝔽2)×D5311yescharacteristic
1888C2—22no—
1889C2—41no—
1890C2—41no—
1891C2—41no—
1892C2—41no—
1893C2—81no—
1894C2—4241no—
1895C2—4241no—
1896C2—4241no—
1897C2—2122no—
1898C2#2028834611yescharacteristic
1899C2C2×#1681143111yescharacteristic
1900C2#2028948611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3541C2
socleC22×C53C23×D4
hypercenter#3541D53
hypocenterC53#61640
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ #525 ◁ #3541

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20288376C2semidirect
2. #20286850C2semidirect
3. #20286835C2semidirect
4. #20286820C2semidirect
5. #20286745C2semidirect
6. #20286648C2semidirect
7. #20286611C2semidirect
8. #20286544C2semidirect
9. #20286533C2semidirect
10. #20286452C2semidirect
11. #20286441C2semidirect
12. #20286423C2semidirect
13. D4×#11719924C2semidirect
14. #20286301C2semidirect
15. #20286286C2semidirect
16. #20286241C2semidirect
17. #20286211C2semidirect
18. #20285803C2semidirect
19. #20285781C2semidirect
20. #20285621C2semidirect
21. #20285597C2semidirect
22. #20285476C2semidirect
23. #20285468C2semidirect
24. #20284986C2semidirect
25. #20284923C2semidirect
26. #20284016C2semidirect
27. #20283990C2semidirect
28. #20283931C2semidirect
29. C2×#16810783C2semidirect
30. #20283771C2semidirect
31. C53×#3541C2semidirect
34. C2×#13133248C22semidirect
35. C2×#13133242C22semidirect
36. C2×#13133237C22semidirect
37. C2×#13133237C22semidirect
38. C2×#13133237C22semidirect
39. C22×#11719925C22semidirect
40. C22×#11719924C22semidirect
41. C22×#11719924C22semidirect
62. #16811015C22semidirect
63. #16811013C22semidirect
64. #16811005C22semidirect
65. #16810997C22semidirect
66. #16810989C22semidirect
67. #16810985C22semidirect
68. #16810980C22semidirect
69. #16810971C22semidirect
70. #16810964C22semidirect
71. #16810956C22semidirect
72. #16810953C22semidirect
73. #16810951C22semidirect
74. #16810951C22semidirect
75. #16810947C22semidirect
76. #16810947C22semidirect
77. #16810947C22semidirect
78. #16810941C22semidirect
79. #16810941C22semidirect
80. #16810941C22semidirect
81. #16810939C22semidirect
82. #16810927C22semidirect
83. #16810920C22semidirect
84. #16810910C22semidirect
85. #16810905C22semidirect
86. #16810879C22semidirect
87. #16810879C22semidirect
88. #16810874C22semidirect
89. #16810871C22semidirect
90. #16810862C22semidirect
91. #16810857C22semidirect
92. #16810857C22semidirect
93. #16810854C22semidirect
94. #16810854C22semidirect
95. #16810854C22semidirect
96. #16810854C22semidirect
97. #16810854C22semidirect
98. #16810854C22semidirect
99. #16810854C22semidirect
100. #16810854C22semidirect
101. #16810850C22semidirect
102. #16810845C22semidirect
103. #16810845C22semidirect
104. #16810845C22semidirect
105. #16810842C22semidirect
106. #16810838C22semidirect
107. #16810835C22semidirect
108. #16810830C22semidirect
109. #16810825C22semidirect
110. #16810823C22semidirect
111. #16810823C22semidirect
112. #16810823C22semidirect
113. #16810818C22semidirect
114. #16810785C22semidirect
118. #16810783C22semidirect
119. #16810783C22semidirect
120. #16810783C22semidirect
121. #16810783C22semidirect
122. #16810783C22semidirect
123. #16810783C22semidirect
124. #16810783C22semidirect
125. #16810783C22semidirect
126. #16810783C22semidirect
127. #16810783C22semidirect
128. #16810779C22semidirect
129. #16810778C22semidirect
130. #16810773C22semidirect
131. #16810773C22semidirect
132. #16810773C22semidirect
133. #16810773C22semidirect
134. #16810773C22semidirect
135. #16810773C22semidirect
136. #16810773C22semidirect
137. #16810768C22semidirect
138. #16810768C22semidirect
139. #16810768C22semidirect
141. #16810766C22semidirect
142. #16810766C22semidirect
143. #16810762C22semidirect
144. #16810762C22semidirect
145. #16810762C22semidirect
146. #16810761C22semidirect
147. #16810756C22semidirect
148. #16810756C22semidirect
149. #16810756C22semidirect
150. #16810733C22semidirect
151. #16810728C22semidirect
152. #16810728C22semidirect
153. #16810721C22semidirect
154. C4×#11719925C22semidirect
155. C4×#11719924C22semidirect
156. C4×#11719924C22semidirect
157. C4×#11719923C22semidirect
158. #16810695C22semidirect
159. #16810695C22semidirect
160. #16810695C22semidirect
161. #16810695C22semidirect
162. D4×#88322C22semidirect
163. D4×#88322C22semidirect
164. D4×#88322C22semidirect
165. D4×#88322C22semidirect
166. #16810684C22semidirect
167. #16810684C22semidirect
168. #16810627C22semidirect
169. #16810622C22semidirect
170. #16810617C22semidirect
171. #16810617C22semidirect
172. #16810617C22semidirect
173. C2×#13133140C22semidirect
174. C2×#13133137C22semidirect
175. C2×#13133137C22semidirect
176. #16810590C22semidirect
177. #16810590C22semidirect
178. C2×C22⋊#88322C22semidirect
179. C2×C22⋊#88322C22semidirect
182. C53×#556C22semidirect
184. C53×#554C22semidirect
186. C53×#553C22semidirect
187. C53×#552C22semidirect
188. D4×Q8×C53C22semidirect
189. C53×#548C22semidirect
190. C53×#548C22semidirect
191. C53×#547C22semidirect
193. C53×#542C22semidirect
194. C53×#541C22semidirect
198. C53×#537C22semidirect
199. C53×#536C22semidirect
201. C53×#525C22semidirect
202. C2×C22⋊Q8×C53C22semidirect
938. #3541D53semidirect
994. #556C2×D53semidirect
996. #554C2×D53semidirect
998. #553C2×D53semidirect
999. #552C2×D53semidirect
1002. D4×Q8C2×D53semidirect
1005. #548C2×D53semidirect
1006. #548C2×D53semidirect
1007. #547C2×D53semidirect
1017. #542C2×D53semidirect
1018. #541C2×D53semidirect
1024. #537C2×D53semidirect
1025. #536C2×D53semidirect
1030. #525C2×D53semidirect
1031. C2×C22⋊Q8C2×D53semidirect
1153. C53#61640semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202883762
#202868502
#202868352
#202868202
#202867452
#202866482
#202866112
#202865442
#202865332
#202864522
#202864412
#202864232
D4×#117199242
#202863012
#202862862
#202862412
#202862112
#202858032
#202857812
#202856212
#202855972
#202854762
#202854682
#202849862
#202849232
#202840162
#202839902
#202839312
C2×#168107832
#202837712
C53×#35412
#6164053