Finite Group Databasebeta

← #28271173

Subgroups — #28271173

Order 13568.

2036 conjugacy classes of subgroups.

The subgroup lattice has 1864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289142C211yesmaximal, characteristic, complemented
2#20286983C211yesmaximal, characteristic, complemented
3#20286968C211yesmaximal, characteristic, complemented
4#20286886C211yesmaximal, characteristic, complemented
5#20286841C211yesmaximal, characteristic, complemented
6#20286766C211yesmaximal, characteristic, complemented
7#20286721C211yesmaximal, characteristic, complemented
8#20286617C211yesmaximal, characteristic, complemented
9#20286602C211yesmaximal, characteristic, complemented
10#20286452C211yesmaximal, characteristic, complemented
11#20286423C211yesmaximal, characteristic, complemented
12#20286368C211yesmaximal, characteristic, complemented
13#20286347C211yesmaximal, characteristic, complemented
14#20286296C211yesmaximal, characteristic, complemented
15#20286286C211yesmaximal, characteristic, complemented
16#20286256C211yesmaximal, characteristic, complemented
17#20286226C211yesmaximal, characteristic, complemented
18#20285752C211yesmaximal, characteristic, complemented
19#20285691C211yesmaximal, characteristic, complemented
20#20285621C211yesmaximal, characteristic, complemented
21#20285612C211yesmaximal, characteristic, complemented
22#20285591C211yesmaximal, characteristic, complemented
23#20285561C211yesmaximal, characteristic, complemented
24#20284886C211yesmaximal, characteristic, complemented
25#20284795C211yesmaximal, characteristic, complemented
26#20284030C211yesmaximal, characteristic, complemented
27#20284030C211yesmaximal, characteristic, complemented
28#20284010C211yesmaximal, characteristic, complemented
29#20284001C211yesmaximal, characteristic, complemented
30#20283791C211yesmaximal, characteristic, complemented
31C53×#3497C211yesmaximal, characteristic, complemented
32C2×#13133248C2211yescharacteristic
33C2×#13133248C2211yescharacteristic
34C2×#13133247C2211yescharacteristic, complemented
35C2×#13133242C2211yescharacteristic
36C2×#13133237C2211yescharacteristic
37C2×#13133237C2211yescharacteristic
38C22×#11719925C2211yescharacteristic, complemented
39C22×#11719924C2211yescharacteristic
40#16811372—21no—
41#16811360—21no—
42#16811335—21no—
43#16811319C2211yescharacteristic
44#16811319C2211yescharacteristic
45#16811313C2211yescharacteristic
46#16811313C2211yescharacteristic
47#16811303—21no—
48#16811282C2211yescharacteristic
49#16811282C2211yescharacteristic
50#16811269C2211yescharacteristic
51#16811269C2211yescharacteristic
52#16811223—21no—
53#16811223—21no—
54#16811205—21no—
55#16811205—21no—
56#16811201C2211yescharacteristic
57#16811201C2211yescharacteristic
58#16811194C2211yescharacteristic
59#16811187C2211yescharacteristic
60#16811157C2211yescharacteristic
61#16811157C2211yescharacteristic
62#16811015C2211yescharacteristic
63#16811010C2211yescharacteristic
64#16811005C2211yescharacteristic
65#16811005C2211yescharacteristic
66#16810991C2211yescharacteristic, complemented
67#16810987C2211yescharacteristic, complemented
68#16810977C2211yescharacteristic, complemented
69#16810977C2211yescharacteristic, complemented
70#16810961C2211yescharacteristic
71#16810961C2211yescharacteristic, complemented
72#16810958C2211yescharacteristic, complemented
73#16810956C2211yescharacteristic, complemented
74#16810953C2211yescharacteristic, complemented
75#16810951C2211yescharacteristic, complemented
76#16810944C2211yescharacteristic
77#16810944C2211yescharacteristic, complemented
78#16810941C2211yescharacteristic
79#16810939C2211yescharacteristic, complemented
80#16810936C2211yescharacteristic
81#16810934C2211yescharacteristic, complemented
82#16810930C2211yescharacteristic, complemented
83#16810930C2211yescharacteristic, complemented
84#16810930C2211yescharacteristic, complemented
85#16810930C2211yescharacteristic, complemented
86#16810879C2211yescharacteristic
87#16810879C2211yescharacteristic, complemented
88#16810874C2211yescharacteristic
89#16810874C2211yescharacteristic
90#16810871C2211yescharacteristic
91#16810871C2211yescharacteristic
92#16810867C2211yescharacteristic
93#16810867C2211yescharacteristic, complemented
94#16810862C2211yescharacteristic
95#16810862C2211yescharacteristic, complemented
96#16810857C2211yescharacteristic
97#16810857C2211yescharacteristic
98#16810854C2211yescharacteristic
99#16810854C2211yescharacteristic
100#16810850C2211yescharacteristic
101#16810850C2211yescharacteristic, complemented
102#16810845C2211yescharacteristic
103#16810845C2211yescharacteristic
104#16810845C2211yescharacteristic
105#16810845C2211yescharacteristic
106#16810842C2211yescharacteristic, complemented
107#16810842C2211yescharacteristic, complemented
108#16810835C2211yescharacteristic
109#16810835C2211yescharacteristic
110#16810830C2211yescharacteristic, complemented
111#16810825C2211yescharacteristic
112#16810820C2211yescharacteristic, complemented
113#16810815C2211yescharacteristic
114#16810785C2211yescharacteristic
115#16810785C2211yescharacteristic
116#16810785C2211yescharacteristic, complemented
117#16810785C2211yescharacteristic, complemented
118#16810785C2211yescharacteristic, complemented
119#16810785C2211yescharacteristic, complemented
120#16810785C2211yescharacteristic, complemented
121#16810785C2211yescharacteristic, complemented
122#16810783C2211yescharacteristic
123#16810783C2211yescharacteristic
124#16810779C2211yescharacteristic
125#16810779C2211yescharacteristic
126#16810779C2211yescharacteristic, complemented
127#16810779C2211yescharacteristic, complemented
128#16810779C2211yescharacteristic, complemented
129#16810779C2211yescharacteristic, complemented
130#16810778C2211yescharacteristic, complemented
131#16810773C2211yescharacteristic
132#16810768C2211yescharacteristic
133#16810768C2211yescharacteristic
134#16810768C2211yescharacteristic
135#16810768C2211yescharacteristic
136#16810768C2211yescharacteristic
137#16810768C2211yescharacteristic
138#16810768C2211yescharacteristic
139#16810768C2211yescharacteristic
140#16810766C2211yescharacteristic
141#16810766C2211yescharacteristic
142#16810762C2211yescharacteristic
143#16810762C2211yescharacteristic
144#16810762C2211yescharacteristic
145#16810762C2211yescharacteristic
146#16810762C2211yescharacteristic
147#16810762C2211yescharacteristic
148#16810761C2211yescharacteristic, complemented
149#16810756C2211yescharacteristic
150#16810728C2211yescharacteristic, complemented
151#16810728C2211yescharacteristic, complemented
152#16810721C2211yescharacteristic
153#16810721C2211yescharacteristic
154C4×#11719925C2211yescharacteristic, complemented
155C4×#11719925C2211yescharacteristic, complemented
156C4×#11719924C2211yescharacteristic
157C4×#11719924C2211yescharacteristic
158#16810701C2211yescharacteristic
159#16810701C2211yescharacteristic, complemented
160#16810695C2211yescharacteristic
161#16810695C2211yescharacteristic
162#16810695C2211yescharacteristic, complemented
163#16810695C2211yescharacteristic, complemented
164D4×#88322C2211yescharacteristic
165D4×#88322C2211yescharacteristic, complemented
166#16810680C2211yescharacteristic, complemented
167#16810676C2211yescharacteristic, complemented
168#16810632C2211yescharacteristic
169#16810632C2211yescharacteristic, complemented
170#16810624C2211yescharacteristic, complemented
171#16810624C2211yescharacteristic, complemented
172#16810619C2211yescharacteristic
173#16810619C2211yescharacteristic, complemented
174C2×#13133141C2211yescharacteristic, complemented
175C2×#13133141C2211yescharacteristic, complemented
176#16810590C2211yescharacteristic
177#16810590C2211yescharacteristic
178#16810590C2211yescharacteristic, complemented
179#16810590C2211yescharacteristic, complemented
180C2×2−1+4×C53C2211yescharacteristic
181C2×2−1+4×C53C2211yescharacteristic, complemented
182C53×#550—21no—
183C53×#550C2211yescharacteristic
184C53×#550C2211yescharacteristic, complemented
185D4×Q8×C53—21no—
186D4×Q8×C53C2211yescharacteristic
187D4×Q8×C53C2211yescharacteristic, complemented
188C53×#548—21no—
189C53×#548—21no—
190C53×#548C2211yescharacteristic
191C53×#548C2211yescharacteristic
192C53×#548C2211yescharacteristic, complemented
193C53×#548C2211yescharacteristic, complemented
194C53×#537—21no—
195C53×#537—21no—
196C53×#537C2211yescharacteristic
197C53×#537C2211yescharacteristic, complemented
198C53×#532—21no—
199C53×#532—21no—
200C53×#532C2211yescharacteristic
201C53×#532C2211yescharacteristic, complemented
202C2×C4×Q8×C53C2211yescharacteristic, complemented
203C2×#11719945C2311yescharacteristic
204C2×#11719945C2311yescharacteristic
205C22×Dic106C2311yescharacteristic
206C22×D212C2311yescharacteristic
207#13133248—42no—
208#13133248—42no—
209#13133247—42no—
210#13133242—42no—
211#13133237—42no—
212#13133237—42no—
213C2×#11719925—42no—
214C2×#11719925C2311yescharacteristic
215C2×#11719925C2311yescharacteristic
216C2×#11719925C2311yescharacteristic
217C2×#11719925C2311yescharacteristic
218C2×#11719925C2311yescharacteristic
219C2×#11719925C2311yescharacteristic
220C2×#11719925C2311yescharacteristic
221C2×#11719925C2311yescharacteristic
222C2×#11719923C2311yescharacteristic
223C2×#11719923C2311yescharacteristic
224C2×#11719923C2311yescharacteristic
225C2×#11719923C2311yescharacteristic
226C2×#11719924—42no—
227C2×#11719924C2311yescharacteristic
228C2×#11719924C2311yescharacteristic
229C2×#11719924C2311yescharacteristic
230C2×#11719924C2311yescharacteristic
231C2×#11719924C2311yescharacteristic
232C2×#11719924C2311yescharacteristic
233C2×#11719924C2311yescharacteristic
234C2×#11719924C2311yescharacteristic
235C2×#11719922C2311yescharacteristic
236C2×#11719922C2311yescharacteristic
237C2×#11719922C2311yescharacteristic
238C2×#11719922C2311yescharacteristic
239C2×#11719917C2311yescharacteristic
240C2×#11719917C2311yescharacteristic
241C2×#11719917C2311yescharacteristic
242C2×#11719917C2311yescharacteristic
243C22×#88322C2311yescharacteristic
244C22×#88322C2311yescharacteristic
245C22×#88322C2311yescharacteristic
246C22×#88322C2311yescharacteristic
247#13133215—21no—
248#13133213—21no—
249#13133212—21no—
250#13133212—21no—
251#13133211—21no—
252#13133211—21no—
253#13133210—21no—
254#13133210—21no—
255#13133209C2311yescharacteristic
256#13133209C2311yescharacteristic
257#13133207—21no—
258#13133207—21no—
259#13133206—21no—
260#13133205C2311yescharacteristic
261#13133205C2311yescharacteristic
262#13133204—21no—
263#13133203—21no—
264#13133203—21no—
265#13133202—21no—
266#13133202—21no—
267#13133200—21no—
268#13133200—21no—
269#13133199—21no—
270#13133199—21no—
271#13133198—21no—
272#13133198—21no—
273#13133198—21no—
274#13133198—21no—
275#13133196C2311yescharacteristic
276#13133196C2311yescharacteristic
277#13133196C2311yescharacteristic
278#13133196C2311yescharacteristic
279#13133196C2311yescharacteristic
280#13133196C2311yescharacteristic
281#13133195—21no—
282#13133195—21no—
283#13133193—21no—
284#13133193—21no—
285#13133191C2311yescharacteristic
286#13133191C2311yescharacteristic
287#13133191C2311yescharacteristic
288#13133191C2311yescharacteristic
289#13133191C2311yescharacteristic
290#13133191C2311yescharacteristic
291#13133190—21no—
292#13133190—21no—
293#13133189—21no—
294#13133189—21no—
295#13133189—21no—
296#13133189—21no—
297#13133189—21no—
298#13133189—21no—
299#13133189—21no—
300#13133189—21no—
301#13133188—21no—
302#13133188—21no—
303#13133185—21no—
304#13133185—21no—
305#13133185—21no—
306#13133185—21no—
307C4×Dic106C2311yescharacteristic
308C4×Dic106C2311yescharacteristic
309C4×D212C2311yescharacteristic
310C4×D212C2311yescharacteristic
311C4×C22⋊D53—21no—
312C4×C22⋊D53—21no—
313#13133177—21no—
314#13133177—21no—
315#13133177—21no—
316#13133177—21no—
317#13133176C2311yescharacteristic
318#13133176C2311yescharacteristic
319#13133174—21no—
320#13133174—21no—
321#13133173—21no—
322#13133173—21no—
323C2×C4⋊Dic53C2311yescharacteristic
324C2×C4⋊Dic53C2311yescharacteristic
325C22⋊C4×D53—21no—
326C22⋊C4×D53—21no—
327#13133150C2311yescharacteristic
328#13133150C2311yescharacteristic
329#13133150C2311yescharacteristic
330#13133150C2311yescharacteristic
331#13133148C2311yescharacteristic
332#13133148C2311yescharacteristic
333#13133148C2311yescharacteristic
334#13133148C2311yescharacteristic
335C4⋊#88322C2311yescharacteristic
336C4⋊#88322C2311yescharacteristic
337C4⋊#88322C2311yescharacteristic
338C4⋊#88322C2311yescharacteristic
339#13133141C2311yescharacteristic
340#13133141C2311yescharacteristic
341#13133141C2311yescharacteristic
342#13133141C2311yescharacteristic
343#13133141C2311yescharacteristic
344#13133141C2311yescharacteristic
345#13133141C2311yescharacteristic
346#13133141C2311yescharacteristic
347#13133141C2311yescharacteristic
348#13133141C2311yescharacteristic
349#13133141C2311yescharacteristic
350#13133141C2311yescharacteristic
351#13133141C2311yescharacteristic
352#13133141C2311yescharacteristic
353#13133141C2311yescharacteristic
354#13133141C2311yescharacteristic
355#13133140C2311yescharacteristic
356#13133140C2311yescharacteristic
357#13133140C2311yescharacteristic
358#13133140C2311yescharacteristic
359#13133138C2311yescharacteristic
360#13133138C2311yescharacteristic
361#13133138C2311yescharacteristic
362#13133138C2311yescharacteristic
363#13133138C2311yescharacteristic
364#13133138C2311yescharacteristic
365#13133138C2311yescharacteristic
366#13133138C2311yescharacteristic
367#13133137C2311yescharacteristic
368#13133137C2311yescharacteristic
369#13133137C2311yescharacteristic
370#13133137C2311yescharacteristic
371C22⋊#88322C2311yescharacteristic
372C22⋊#88322C2311yescharacteristic
373C22⋊#88322C2311yescharacteristic
374C22⋊#88322C2311yescharacteristic
375C22⋊#88322C2311yescharacteristic
376C22⋊#88322C2311yescharacteristic
377C22⋊#88322C2311yescharacteristic
378C22⋊#88322C2311yescharacteristic
379C22⋊#88322C2311yescharacteristic
380C22⋊#88322C2311yescharacteristic
381C22⋊#88322C2311yescharacteristic
382C22⋊#88322C2311yescharacteristic
383#13133128C2311yescharacteristic
384#13133128C2311yescharacteristic
385C4×#88322C2311yescharacteristic
386C4×#88322C2311yescharacteristic
3872−1+4×C53—42no—
3882−1+4×C53—42no—
3892−1+4×C53—42no—
3902−1+4×C53—42no—
391C2×#41×C53—21no—
392C2×#41×C53—21no—
393C2×#41×C53—21no—
394C2×#41×C53—21no—
395C2×#41×C53—21no—
396C2×#41×C53—21no—
397C2×#41×C53C2311yescharacteristic
398C2×#41×C53C2311yescharacteristic
399C2×#41×C53C2311yescharacteristic
400C2×#41×C53C2311yescharacteristic
401C2×#41×C53C2311yescharacteristic
402C2×#41×C53C2311yescharacteristic
403C2×#41×C53C2311yescharacteristic
404C2×#41×C53C2311yescharacteristic
405C22×Q8×C53—21no—
406C22×Q8×C53—21no—
407C22×Q8×C53C2311yescharacteristic
408C22×Q8×C53C2311yescharacteristic
409C22×Q8×C53C2311yescharacteristic
410C22×Q8×C53C2311yescharacteristic
411C22×Q8×C53C2311yescharacteristic
412C4⋊Q8×C53—21no—
413C4⋊Q8×C53—21no—
414C4⋊Q8×C53D411yescharacteristic
415C4⋊Q8×C53C2311yescharacteristic
416#127×C53—21no—
417#127×C53—21no—
418#127×C53D411yescharacteristic
419#127×C53C2311yescharacteristic
420#124×C53—21no—
421#124×C53—21no—
422#124×C53—21no—
423#124×C53—21no—
424#124×C53D411yescharacteristic
425#124×C53D411yescharacteristic
426#124×C53C2311yescharacteristic
427#124×C53C2311yescharacteristic
428C22⋊Q8×C53—21no—
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×C53C2311yescharacteristic
439C22⋊Q8×C53C2311yescharacteristic
440C22⋊Q8×C53C2311yescharacteristic
441C22⋊Q8×C53C2311yescharacteristic
442#121×C53—21no—
443#121×C53—21no—
444#121×C53—21no—
445#121×C53—21no—
446#121×C53—21no—
447#121×C53—21no—
448#121×C53—21no—
449#121×C53—21no—
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×C53—21no—
458#121×C53D411yescharacteristic
459#121×C53D411yescharacteristic
460#121×C53D411yescharacteristic
461#121×C53D411yescharacteristic
462#121×C53C2311yescharacteristic
463#121×C53C2311yescharacteristic
464#121×C53C2311yescharacteristic
465#121×C53C2311yescharacteristic
466C4×Q8×C53—21no—
467C4×Q8×C53—21no—
468C4×Q8×C53C2311yescharacteristic
469C4×Q8×C53C2311yescharacteristic
470C4×Q8×C53C2311yescharacteristic
471C4×Q8×C53C2311yescharacteristic
472C4×D4×C53—21no—
473C4×D4×C53—21no—
474C4×D4×C53—21no—
475C4×D4×C53—21no—
476C4×D4×C53—21no—
477C4×D4×C53—21no—
478C4×D4×C53—21no—
479C4×D4×C53—21no—
480C4×D4×C53—21no—
481C4×D4×C53—21no—
482C4×D4×C53C2311yescharacteristic
483C4×D4×C53C2311yescharacteristic
484C4×D4×C53C2311yescharacteristic
485C4×D4×C53C2311yescharacteristic
486C2×C4⋊C4×C53—21no—
487C2×C4⋊C4×C53C2311yescharacteristic
488C2×C42×C53—21no—
489C2×C42×C53C2311yescharacteristic
490C23×D53—21no—
491#41×C53—22no—
492#41×C53—22no—
493#41×C53—22no—
494#41×C53—22no—
495#41×C53—41no—
496#41×C53—41no—
497#41×C53—41no—
498#41×C53—41no—
499#41×C53—41no—
500#41×C53—41no—
501#41×C53—41no—
502#41×C53—41no—
503#41×C53—41no—
504#41×C53—41no—
505#41×C53—41no—
506#41×C53—41no—
507#41×C53—44no—
508#41×C53—44no—
509#41×C53—44no—
510#41×C53—44no—
511#41×C53—44no—
512#41×C53—44no—
513C2×Q8×C53—22no—
514C2×Q8×C53—22no—
515C2×Q8×C53—21no—
516C2×Q8×C53—21no—
517C2×Q8×C53—21no—
518C2×Q8×C53—21no—
519C2×Q8×C53—21no—
520C2×Q8×C53—22no—
521C2×Q8×C53—22no—
522C2×Q8×C53—22no—
523C2×Q8×C53—22no—
524C2×Q8×C53—41no—
525C2×Q8×C53—41no—
526C2×Q8×C53—41no—
527C2×Q8×C53—41no—
528C2×Q8×C53—44no—
529C2×Q8×C53—44no—
530C2×Q8×C53C2×D411yescharacteristic
531C2×Q8×C53C2×D411yescharacteristic
532C2×Q8×C53C2411yescharacteristic
533C2×Q8×C53C2411yescharacteristic
534C2×Q8×C53C2411yescharacteristic
535C2×Q8×C53C2411yescharacteristic
536C2×D4×C53—21no—
537C2×D4×C53—21no—
538C2×D4×C53—21no—
539C2×D4×C53—21no—
540C2×D4×C53—21no—
541C2×D4×C53—21no—
542C2×D4×C53—21no—
543C2×D4×C53—21no—
544C2×D4×C53—21no—
545C2×D4×C53—21no—
546C2×D4×C53—21no—
547C2×D4×C53—21no—
548C2×D4×C53C2×D411yescharacteristic
549C2×D4×C53C2×D411yescharacteristic
550C2×D4×C53C2×D411yescharacteristic
551C2×D4×C53C2×D411yescharacteristic
552C2×D4×C53C2×D411yescharacteristic
553C2×D4×C53C2×D411yescharacteristic
554C2×D4×C53C2×D411yescharacteristic
555C2×D4×C53C2×D411yescharacteristic
556C2×D4×C53C2×D411yescharacteristic
557C2×D4×C53C2×D411yescharacteristic
558C2×D4×C53C2411yescharacteristic
559C2×D4×C53C2411yescharacteristic
560C22×C4×C53—21no—
561C22×C4×C53—21no—
562C22×C4×C53—21no—
563C22×C4×C53—21no—
564C22×C4×C53—21no—
565C22×C4×C53—21no—
566C22×C4×C53—21no—
567C22×C4×C53—21no—
568C22×C4×C53—21no—
569C22×C4×C53—21no—
570C22×C4×C53—21no—
571C22×C4×C53—21no—
572C22×C4×C53C2×D411yescharacteristic
573C22×C4×C53C2×D411yescharacteristic
574C22×C4×C53C2411yescharacteristic
575C22×C4×C53C2411yescharacteristic
576C22×C4×C53C2411yescharacteristic
577C22×C4×C53C2411yescharacteristic
578C22×C4×C53C2411yescharacteristic
579C2×C22⋊D53—21no—
580C2×C22⋊D53—21no—
581C2×C22⋊D53—21no—
582C2×C22⋊D53—21no—
583C2×C22⋊D53—21no—
584C2×C22⋊D53—21no—
585C2×C22⋊D53—21no—
586C2×C22⋊D53—21no—
587C22×Dic53—21no—
588C22×Dic53—21no—
589C22×Dic53—21no—
590#11719945—41no—
591#11719945—41no—
592#11719945—41no—
593#11719945—41no—
594C2×D212—21no—
595C2×D212—41no—
596C2×D212—41no—
597C2×D212C2411yescharacteristic
598C2×D212C2411yescharacteristic
599C2×C4×D53—21no—
600C2×C4×D53—21no—
601C2×C4×D53—21no—
602C2×C4×D53—21no—
603C2×Dic106—21no—
604C2×Dic106—41no—
605C2×Dic106—41no—
606C2×Dic106C2411yescharacteristic
607C2×Dic106C2411yescharacteristic
608C4⋊C4×C53—21no—
609C4⋊C4×C53—21no—
610C4⋊C4×C53—21no—
611C4⋊C4×C53—21no—
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×C53C2×D411yescharacteristic
620C4⋊C4×C53C2×D411yescharacteristic
621C4⋊C4×C53C2×D411yescharacteristic
622C4⋊C4×C53C2×D411yescharacteristic
623C4⋊C4×C53C2411yescharacteristic
624C4⋊C4×C53C2411yescharacteristic
625C22⋊C4×C53—21no—
626C22⋊C4×C53—21no—
627C22⋊C4×C53—21no—
628C22⋊C4×C53—21no—
629C22⋊C4×C53—21no—
630C22⋊C4×C53—21no—
631C22⋊C4×C53—21no—
632C22⋊C4×C53—21no—
633C22⋊C4×C53—21no—
634C22⋊C4×C53—21no—
635C22⋊C4×C53—21no—
636C22⋊C4×C53—21no—
637C22⋊C4×C53C2×D411yescharacteristic
638C22⋊C4×C53C2×D411yescharacteristic
639C22⋊C4×C53C2×D411yescharacteristic
640C22⋊C4×C53C2×D411yescharacteristic
641C22⋊C4×C53C2×D411yescharacteristic
642C22⋊C4×C53C2×D411yescharacteristic
643C22⋊C4×C53C2×D411yescharacteristic
644C22⋊C4×C53C2×D411yescharacteristic
645C42×C53—21no—
646C42×C53—21no—
647C42×C53—21no—
648C42×C53—21no—
649C42×C53C2×D411yescharacteristic
650C42×C53C2×D411yescharacteristic
651C42×C53C2411yescharacteristic
652C42×C53C2411yescharacteristic
653C22⋊Dic53—21no—
654C22⋊Dic53—21no—
655C22⋊Dic53—21no—
656C22⋊Dic53—21no—
657C22⋊Dic53—21no—
658C22⋊Dic53—21no—
659C22⋊Dic53—21no—
660C22⋊Dic53—21no—
661#11719925—22no—
662#11719925—22no—
663#11719925—22no—
664#11719925—22no—
665#11719925—41no—
666#11719925—41no—
667#11719925—41no—
668#11719925—41no—
669#11719924—22no—
670#11719924—22no—
671#11719924—22no—
672#11719924—22no—
673#11719924—41no—
674#11719924—41no—
675#11719924—41no—
676#11719924—41no—
677#11719923—41no—
678#11719923—41no—
679#11719923—41no—
680#11719923—41no—
681#11719922—41no—
682#11719922—41no—
683#11719922—41no—
684#11719922—41no—
685#11719921—21no—
686#11719921—21no—
687#11719921—21no—
688#11719921—21no—
689#11719921—21no—
690#11719921—21no—
691#11719921—21no—
692#11719921—21no—
693#11719921—21no—
694#11719921—21no—
695#11719921—21no—
696#11719921—21no—
697C4⋊Dic53—21no—
698C4⋊Dic53—21no—
699C4⋊Dic53C2411yescharacteristic
700C4⋊Dic53C2411yescharacteristic
701C4⋊Dic53C2411yescharacteristic
702C4⋊Dic53C2411yescharacteristic
703#11719919—21no—
704#11719919—21no—
705#11719919—21no—
706#11719919—21no—
707#11719919—21no—
708#11719919—21no—
709#11719919—21no—
710#11719919—21no—
711#11719919—21no—
712#11719919—21no—
713#11719919—21no—
714#11719919—21no—
715C4×Dic53—21no—
716C4×Dic53—21no—
717C4×Dic53—21no—
718C4×Dic53—21no—
719#11719917—41no—
720#11719917—41no—
721#11719917—41no—
722#11719917—41no—
723C2×#88322—41no—
724C2×#88322—41no—
725C2×#88322—41no—
726C2×#88322—41no—
727C2×#88322C2411yescharacteristic
728C2×#88322C2411yescharacteristic
729C2×#88322C2411yescharacteristic
730C2×#88322C2411yescharacteristic
731C2×#88322C2411yescharacteristic
732C2×#88322C2411yescharacteristic
733C2×#88322C2411yescharacteristic
734C2×#88322C2411yescharacteristic
735C23×C53—21no—
736C23×C53—21no—
737C23×C53C22×D411yescharacteristic
738C23×C53C22×D411yescharacteristic
739C23×C53C22×D411yescharacteristic
740C23×C53C22×D411yescharacteristic
741C23×C53C22×D411yescharacteristic
742C22×D53—21no—
743C22×D53—21no—
744C22×D53—81no—
745C22×D53—81no—
746C22×D53—81no—
747Q8×C53—24no—
748Q8×C53—21no—
749Q8×C53—21no—
750Q8×C53—21no—
751Q8×C53—21no—
752Q8×C53—21no—
753Q8×C53—21no—
754Q8×C53—41no—
755Q8×C53—41no—
756Q8×C53—42no—
757Q8×C53—42no—
758Q8×C53—42no—
759Q8×C53—42no—
760Q8×C53H(5,𝔽2)12yes—
761Q8×C53H(5,𝔽2)12yes—
762D4×C53—21no—
763D4×C53—21no—
764D4×C53—21no—
765D4×C53—21no—
766D4×C53—41no—
767D4×C53—41no—
768D4×C53—41no—
769D4×C53—41no—
770D4×C53—41no—
771D4×C53—41no—
772D4×C53—41no—
773D4×C53—41no—
774D4×C53—41no—
775D4×C53—41no—
776D4×C53—42no—
777D4×C53—42no—
778D4×C53—42no—
779D4×C53—42no—
780D4×C53—42no—
781D4×C53—42no—
782D4×C53—42no—
783D4×C53—81no—
784D4×C53—81no—
785D4×C53—81no—
786D4×C53—81no—
787D4×C53—81no—
788C2×C4×C53—24no—
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—21no—
805C2×C4×C53—41no—
806C2×C4×C53—41no—
807C2×C4×C53—42no—
808C2×C4×C53—42no—
809C2×C4×C53—42no—
810C2×C4×C53—42no—
811C2×C4×C53—42no—
812C2×C4×C53—42no—
813C2×C4×C53—42no—
814C2×C4×C53—42no—
815C2×C4×C53—42no—
816C2×C4×C53—42no—
817C2×C4×C53—81no—
818C2×C4×C53C22×D411yescharacteristic
819C2×C4×C53C22×D411yescharacteristic
820C2×C4×C53C22×D411yescharacteristic
821C2×C4×C53C22×D411yescharacteristic
822C2×C4×C53C22×D411yescharacteristic
823C2×C4×C53C22×D411yescharacteristic
824C2×C4×C53C22×D411yescharacteristic
825C2×C4×C53C22×D411yescharacteristic
826C2×C4×C53C22×D411yescharacteristic
827C2×C4×C53C2511yescharacteristic
828C22⋊D53—81no—
829C22⋊D53—81no—
830C22⋊D53—81no—
831C22⋊D53—81no—
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—21no—
841C2×Dic53—21no—
842C2×Dic53—81no—
843C2×Dic53—81no—
844C2×Dic53—81no—
845D212—21no—
846D212—21no—
847D212—21no—
848D212—21no—
849D212—81no—
850C4×D53—81no—
851C4×D53—81no—
852C4×D53—81no—
853C4×D53—81no—
854Dic106—21no—
855Dic106—21no—
856Dic106—21no—
857Dic106—21no—
858Dic106—81no—
859#88322—21no—
860#88322—21no—
861#88322—21no—
862#88322—21no—
863#88322—21no—
864#88322—21no—
865#88322—21no—
866#88322—21no—
867#61681—531nomaximal, Sylow
868C22×C53—21no—
869C22×C53—21no—
870C22×C53—21no—
871C22×C53—21no—
872C22×C53—21no—
873C22×C53—21no—
874C22×C53—21no—
875C22×C53—21no—
876C22×C53—21no—
877C22×C53—21no—
878C22×C53—21no—
879C22×C53—21no—
880C22×C53—21no—
881C22×C53—21no—
882C22×C53—21no—
883C22×C53—41no—
884C22×C53—41no—
885C22×C53—41no—
886C22×C53—41no—
887C22×C53—41no—
888C22×C53—41no—
889C22×C53C23×D411yescharacteristic
890C2×D53—41no—
891C2×D53—41no—
892C2×D53—41no—
893C2×D53—41no—
894C2×D53—41no—
895C2×D53—41no—
896C2×D53—162no—
897C4×C53—21no—
898C4×C53—21no—
899C4×C53—21no—
900C4×C53—21no—
901C4×C53—21no—
902C4×C53—21no—
903C4×C53—21no—
904C4×C53—21no—
905C4×C53—22no—
906C4×C53—22no—
907C4×C53—21no—
908C4×C53—41no—
909C4×C53—41no—
910C4×C53—41no—
911C4×C53—41no—
912C4×C53C2×H(5,𝔽2)11yescharacteristic
913C4×C53C2×H(5,𝔽2)11yescharacteristic
914Dic53—41no—
915Dic53—41no—
916Dic53—41no—
917Dic53—41no—
918Dic53—41no—
919Dic53—41no—
920#3551—531no—
921#3497D5311yescharacteristic, complemented
922#3327—531no—
923#3326—531no—
924#3320—531no—
925#3317—531no—
926#3312—531no—
927#3309—531no—
928#3301—531no—
929#3300—531no—
930#3285—531no—
931#3282—531no—
932#3277—531no—
933#3275—531no—
934#3271—531no—
935#3270—531no—
936#3268—531no—
937#3266—531no—
938#3219—531no—
939#3212—531no—
940#3204—531no—
941#3203—531no—
942#3201—531no—
943#3198—531no—
944#3117—531no—
945#3108—531no—
946#3013—531no—
947#3013—531no—
948#3011—531no—
949#3010—531no—
950#2981—531no—
951C2×C53—41no—
952C2×C53—41no—
953C2×C53—41no—
954C2×C53—41no—
955C2×C53—41no—
956C2×C53—81no—
957C2×C53—81no—
958C2×C53#348411yescharacteristic
959C2×C53#358411yescharacteristic
960C2×C53#358611yescharacteristic
961D53—81no—
962D53—81no—
963C2×2−1+4C2×D5311yescharacteristic
964C2×2−1+4C2×D5311yescharacteristic, complemented
965C2×#137—531no—
966C2×#137—531no—
967C2×#137—531no—
968C2×AGL(1,ℤ/8)—531no—
969C2×#135—531no—
970C2×#135—531no—
971C22×Q16—531no—
972C22×SD16—531no—
973#563—1061no—
974#560—1061no—
975#555—1061no—
976#553—531no—
977#553—531no—
978#552—531no—
979#552—531no—
980#551—1061no—
981#550—21no—
982#550C2×D5311yescharacteristic
983#550C2×D5311yescharacteristic, complemented
984D4×Q8—21no—
985D4×Q8C2×D5311yescharacteristic
986D4×Q8C2×D5311yescharacteristic, complemented
987#548—21no—
988#548—21no—
989#548—531no—
990#548—531no—
991#548C2×D5311yescharacteristic
992#548C2×D5311yescharacteristic
993#548C2×D5311yescharacteristic, complemented
994#548C2×D5311yescharacteristic, complemented
995#546—531no—
996#546—531no—
997#540—1061no—
998#540—1061no—
999#538—1061no—
1000#538—1061no—
1001#537—21no—
1002#537—21no—
1003#537—531no—
1004#537—531no—
1005#537C2×D5311yescharacteristic
1006#537C2×D5311yescharacteristic, complemented
1007#536—531no—
1008#535—531no—
1009#532—21no—
1010#532—21no—
1011#532C2×D5311yescharacteristic
1012#532C2×D5311yescharacteristic, complemented
1013#529—531no—
1014#529—531no—
1015C2×C4×Q8C2×D5311yescharacteristic, complemented
1016#497—531no—
1017#496—531no—
1018#495—531no—
1019#495—531no—
1020#491—531no—
1021#490—531no—
1022#488—531no—
1023#488—531no—
1024#485—531no—
1025#485—531no—
1026#484—531no—
1027#484—531no—
1028#483—531no—
1029#483—531no—
1030#482—531no—
1031#482—531no—
1032#481—531no—
1033#481—531no—
1034#480—531no—
1035#480—531no—
1036#479—531no—
1037#479—531no—
1038#479—531no—
1039#479—531no—
1040#470—531no—
1041#470—531no—
1042#469—531no—
1043#469—531no—
1044#468—531no—
1045#468—531no—
1046#468—531no—
1047#468—531no—
1048#467—531no—
1049#467—531no—
1050#466—531no—
1051#466—531no—
1052#465—531no—
1053#465—531no—
1054#465—531no—
1055#465—531no—
1056#464—531no—
1057#464—531no—
1058#464—531no—
1059#464—531no—
1060#464—531no—
1061#464—531no—
1062#463—531no—
1063#463—531no—
1064#462—531no—
1065#461—531no—
1066#460—531no—
1067#459—531no—
1068#452—531no—
1069#452—531no—
1070#452—531no—
1071#452—531no—
1072#452—531no—
1073#452—531no—
1074#452—531no—
1075#452—531no—
1076#452—531no—
1077#452—531no—
1078#451—531no—
1079#451—531no—
1080#451—531no—
1081#451—531no—
1082#451—531no—
1083#451—531no—
1084#451—531no—
1085#450—531no—
1086#449—531no—
1087#449—531no—
1088#449—531no—
1089#449—531no—
1090#449—531no—
1091#449—531no—
1092#449—531no—
1093#449—531no—
1094#449—531no—
1095#449—531no—
1096#448—531no—
1097#448—531no—
1098#448—531no—
1099#448—531no—
1100#448—531no—
1101#448—531no—
1102#448—531no—
1103#447—531no—
1104#441—531no—
1105#441—531no—
1106#440—531no—
1107#440—531no—
1108C4×Q16—531no—
1109C4×Q16—531no—
1110C4×SD16—531no—
1111C4×SD16—531no—
1112#436—531no—
1113#436—531no—
1114#435—531no—
1115#435—531no—
1116#435—531no—
1117#435—531no—
1118C8×D4—531no—
1119C8×D4—531no—
1120#432—531no—
1121#431—531no—
1122#419—531no—
1123#419—531no—
1124#417—531no—
1125#417—531no—
1126#416—531no—
1127#416—531no—
1128C2×#103—531no—
1129C2×#103—531no—
1130#408—531no—
1131#408—531no—
1132#408—531no—
1133#408—531no—
1134C53#6168111yescharacteristic, complemented, Sylow
11352−1+4—42no—
11362−1+4—42no—
11372−1+4—42no—
11382−1+4—42no—
1139C2×#41—21no—
1140C2×#41—21no—
1141C2×#41—21no—
1142C2×#41—21no—
1143C2×#41—21no—
1144C2×#41—21no—
1145C2×#41—531no—
1146C2×#41—531no—
1147C2×#41C22×D5311yescharacteristic
1148C2×#41C22×D5311yescharacteristic
1149C2×#41C22×D5311yescharacteristic
1150C2×#41C22×D5311yescharacteristic
1151C2×#41C22×D5311yescharacteristic
1152C2×#41C22×D5311yescharacteristic
1153C2×#41C22×D5311yescharacteristic
1154C2×#41C22×D5311yescharacteristic
1155C22×Q8—21no—
1156C22×Q8—21no—
1157C22×Q8—531no—
1158C22×Q8C22×D5311yescharacteristic
1159C22×Q8C22×D5311yescharacteristic
1160C22×Q8C22×D5311yescharacteristic
1161C22×Q8C22×D5311yescharacteristic
1162C22×Q8C22×D5311yescharacteristic
1163C22×D4—531no—
1164#137—2122no—
1165#137—2122no—
1166#137—2122no—
1167AGL(1,ℤ/8)—2122no—
1168#135—2122no—
1169#135—2122no—
1170C2×Q16—531no—
1171C2×Q16—531no—
1172C2×Q16—531no—
1173C2×Q16—531no—
1174C2×Q16—531no—
1175C2×Q16—531no—
1176C2×Q16—531no—
1177C2×Q16—531no—
1178C2×Q16—2122no—
1179C2×SD16—531no—
1180C2×SD16—531no—
1181C2×SD16—531no—
1182C2×SD16—531no—
1183C2×SD16—531no—
1184C2×SD16—531no—
1185C2×SD16—531no—
1186C2×SD16—531no—
1187C2×SD16—531no—
1188C2×SD16—531no—
1189C2×SD16—531no—
1190C2×SD16—531no—
1191C2×SD16—2122no—
1192C2×D8—531no—
1193C2×D8—531no—
1194C2×D8—531no—
1195C2×D8—531no—
1196C2×M16—531no—
1197C2×M16—531no—
1198C2×M16—531no—
1199C2×M16—531no—
1200C22×C8—531no—
1201C22×C8—531no—
1202C22×C8—531no—
1203C22×C8—531no—
1204C4⋊Q8—21no—
1205C4⋊Q8—21no—
1206C4⋊Q8—1061no—
1207C4⋊Q8C22⋊D5311yescharacteristic
1208C4⋊Q8C22×D5311yescharacteristic
1209#127—21no—
1210#127—21no—
1211#127—1061no—
1212#127C22⋊D5311yescharacteristic
1213#127C22×D5311yescharacteristic
1214#126—1061no—
1215#126—1061no—
1216#126—1061no—
1217#126—1061no—
1218#126—1061no—
1219#126—1061no—
1220#125—531no—
1221#125—531no—
1222#125—1061no—
1223#125—1061no—
1224#124—21no—
1225#124—21no—
1226#124—21no—
1227#124—21no—
1228#124—531no—
1229#124—531no—
1230#124—1061no—
1231#124—1061no—
1232#124—1061no—
1233#124—1061no—
1234#124C22⋊D5311yescharacteristic
1235#124C22⋊D5311yescharacteristic
1236#124C22×D5311yescharacteristic
1237#124C22×D5311yescharacteristic
1238#123—1061no—
1239#123—1061no—
1240#123—1061no—
1241#123—1061no—
1242#123—1061no—
1243#123—1061no—
1244#123—1061no—
1245#123—1061no—
1246#123—1061no—
1247#123—1061no—
1248C22⋊Q8—21no—
1249C22⋊Q8—21no—
1250C22⋊Q8—21no—
1251C22⋊Q8—21no—
1252C22⋊Q8—21no—
1253C22⋊Q8—21no—
1254C22⋊Q8—21no—
1255C22⋊Q8—21no—
1256C22⋊Q8—21no—
1257C22⋊Q8—21no—
1258C22⋊Q8—531no—
1259C22⋊Q8—531no—
1260C22⋊Q8—531no—
1261C22⋊Q8—531no—
1262C22⋊Q8—531no—
1263C22⋊Q8—531no—
1264C22⋊Q8—1061no—
1265C22⋊Q8—1061no—
1266C22⋊Q8—1061no—
1267C22⋊Q8—1061no—
1268C22⋊Q8C22×D5311yescharacteristic
1269C22⋊Q8C22×D5311yescharacteristic
1270C22⋊Q8C22×D5311yescharacteristic
1271C22⋊Q8C22×D5311yescharacteristic
1272#121—21no—
1273#121—21no—
1274#121—21no—
1275#121—21no—
1276#121—21no—
1277#121—21no—
1278#121—21no—
1279#121—21no—
1280#121—21no—
1281#121—21no—
1282#121—21no—
1283#121—21no—
1284#121—21no—
1285#121—21no—
1286#121—21no—
1287#121—21no—
1288#121—531no—
1289#121—531no—
1290#121—531no—
1291#121—531no—
1292#121—531no—
1293#121—531no—
1294#121—1061no—
1295#121—1061no—
1296#121—1061no—
1297#121—1061no—
1298#121—1061no—
1299#121—1061no—
1300#121—1061no—
1301#121—1061no—
1302#121—1061no—
1303#121—1061no—
1304#121—1061no—
1305#121—1061no—
1306#121C22⋊D5311yescharacteristic
1307#121C22⋊D5311yescharacteristic
1308#121C22⋊D5311yescharacteristic
1309#121C22⋊D5311yescharacteristic
1310#121C22×D5311yescharacteristic
1311#121C22×D5311yescharacteristic
1312#121C22×D5311yescharacteristic
1313#121C22×D5311yescharacteristic
1314#120—1061no—
1315#120—1061no—
1316#120—1061no—
1317#120—1061no—
1318C4×Q8—21no—
1319C4×Q8—21no—
1320C4×Q8—531no—
1321C4×Q8—531no—
1322C4×Q8C22×D5311yescharacteristic
1323C4×Q8C22×D5311yescharacteristic
1324C4×Q8C22×D5311yescharacteristic
1325C4×Q8C22×D5311yescharacteristic
1326C4×D4—21no—
1327C4×D4—21no—
1328C4×D4—21no—
1329C4×D4—21no—
1330C4×D4—21no—
1331C4×D4—21no—
1332C4×D4—21no—
1333C4×D4—21no—
1334C4×D4—21no—
1335C4×D4—21no—
1336C4×D4—531no—
1337C4×D4—531no—
1338C4×D4—1061no—
1339C4×D4—1061no—
1340C4×D4—1061no—
1341C4×D4—1061no—
1342C4×D4—1061no—
1343C4×D4—1061no—
1344C4×D4C22×D5311yescharacteristic
1345C4×D4C22×D5311yescharacteristic
1346C4×D4C22×D5311yescharacteristic
1347C4×D4C22×D5311yescharacteristic
1348#117—531no—
1349#117—531no—
1350#117—1061no—
1351#117—1061no—
1352#117—1061no—
1353#117—1061no—
1354C2×C4⋊C4—21no—
1355C2×C4⋊C4—531no—
1356C2×C4⋊C4—531no—
1357C2×C4⋊C4C22×D5311yescharacteristic
1358C2×C22⋊C4—1061no—
1359C2×C22⋊C4—1061no—
1360C2×C42—21no—
1361C2×C42C22×D5311yescharacteristic
1362#107—531no—
1363#107—531no—
1364#107—531no—
1365#107—531no—
1366#106—531no—
1367#106—531no—
1368#106—531no—
1369#106—531no—
1370C4⋊C8—531no—
1371C4⋊C8—531no—
1372C4⋊C8—531no—
1373C4⋊C8—531no—
1374#103—531no—
1375#103—531no—
1376#103—531no—
1377#103—531no—
1378#103—531no—
1379#103—531no—
1380#103—531no—
1381#103—531no—
1382#103—531no—
1383#103—531no—
1384#103—531no—
1385#103—531no—
1386#103—531no—
1387#103—531no—
1388#103—531no—
1389#103—531no—
1390#103—531no—
1391#103—531no—
1392#103—531no—
1393#103—531no—
1394#102—531no—
1395#102—531no—
1396#102—531no—
1397#102—531no—
1398#102—531no—
1399#102—531no—
1400#102—531no—
1401#102—531no—
1402#102—531no—
1403#102—531no—
1404#102—531no—
1405#102—531no—
1406C22⋊C8—531no—
1407C22⋊C8—531no—
1408C22⋊C8—531no—
1409C22⋊C8—531no—
1410C22⋊C8—531no—
1411C22⋊C8—531no—
1412C22⋊C8—531no—
1413C22⋊C8—531no—
1414C22⋊C8—531no—
1415C22⋊C8—531no—
1416C22⋊C8—531no—
1417C22⋊C8—531no—
1418#97—531no—
1419#97—531no—
1420C4×C8—531no—
1421C4×C8—531no—
1422C24—1061no—
1423#41—22no—
1424#41—22no—
1425#41—22no—
1426#41—22no—
1427#41—41no—
1428#41—41no—
1429#41—41no—
1430#41—41no—
1431#41—41no—
1432#41—41no—
1433#41—41no—
1434#41—41no—
1435#41—41no—
1436#41—41no—
1437#41—41no—
1438#41—41no—
1439#41—44no—
1440#41—44no—
1441#41—44no—
1442#41—44no—
1443#41—44no—
1444#41—44no—
1445#41—2121no—
1446#41—2121no—
1447#41—2121no—
1448#41—2121no—
1449C2×Q8—22no—
1450C2×Q8—22no—
1451C2×Q8—21no—
1452C2×Q8—21no—
1453C2×Q8—21no—
1454C2×Q8—21no—
1455C2×Q8—21no—
1456C2×Q8—22no—
1457C2×Q8—22no—
1458C2×Q8—22no—
1459C2×Q8—22no—
1460C2×Q8—41no—
1461C2×Q8—41no—
1462C2×Q8—41no—
1463C2×Q8—41no—
1464C2×Q8—44no—
1465C2×Q8—44no—
1466C2×Q8—531no—
1467C2×Q8—531no—
1468C2×Q8—1061no—
1469C2×Q8—2121no—
1470C2×Q8—2121no—
1471C2×Q8C2×C22⋊D5311yescharacteristic
1472C2×Q8C2×C22⋊D5311yescharacteristic
1473C2×Q8C23×D5311yescharacteristic
1474C2×Q8C23×D5311yescharacteristic
1475C2×Q8C23×D5311yescharacteristic
1476C2×Q8C23×D5311yescharacteristic
1477C2×D4—21no—
1478C2×D4—21no—
1479C2×D4—21no—
1480C2×D4—21no—
1481C2×D4—21no—
1482C2×D4—21no—
1483C2×D4—21no—
1484C2×D4—21no—
1485C2×D4—21no—
1486C2×D4—21no—
1487C2×D4—21no—
1488C2×D4—21no—
1489C2×D4—531no—
1490C2×D4—531no—
1491C2×D4—1061no—
1492C2×D4—1061no—
1493C2×D4—1061no—
1494C2×D4—1061no—
1495C2×D4—1061no—
1496C2×D4—1061no—
1497C2×D4—1061no—
1498C2×D4—1061no—
1499C2×D4—1061no—
1500C2×D4—2121no—
1501C2×D4—2121no—
1502C2×D4C2×C22⋊D5311yescharacteristic
1503C2×D4C2×C22⋊D5311yescharacteristic
1504C2×D4C2×C22⋊D5311yescharacteristic
1505C2×D4C2×C22⋊D5311yescharacteristic
1506C2×D4C2×C22⋊D5311yescharacteristic
1507C2×D4C2×C22⋊D5311yescharacteristic
1508C2×D4C2×C22⋊D5311yescharacteristic
1509C2×D4C2×C22⋊D5311yescharacteristic
1510C2×D4C2×C22⋊D5311yescharacteristic
1511C2×D4C2×C22⋊D5311yescharacteristic
1512C2×D4C23×D5311yescharacteristic
1513C2×D4C23×D5311yescharacteristic
1514C22×C4—21no—
1515C22×C4—21no—
1516C22×C4—21no—
1517C22×C4—21no—
1518C22×C4—21no—
1519C22×C4—21no—
1520C22×C4—21no—
1521C22×C4—21no—
1522C22×C4—21no—
1523C22×C4—21no—
1524C22×C4—21no—
1525C22×C4—21no—
1526C22×C4—1061no—
1527C22×C4—1061no—
1528C22×C4—1061no—
1529C22×C4—1061no—
1530C22×C4—1061no—
1531C22×C4—1061no—
1532C22×C4—1061no—
1533C22×C4C2×C22⋊D5311yescharacteristic
1534C22×C4C2×C22⋊D5311yescharacteristic
1535C22×C4C23×D5311yescharacteristic
1536C22×C4C23×D5311yescharacteristic
1537C22×C4C23×D5311yescharacteristic
1538C22×C4C23×D5311yescharacteristic
1539C22×C4C23×D5311yescharacteristic
1540Q16—1062no—
1541Q16—1062no—
1542Q16—1062no—
1543Q16—1062no—
1544Q16—2121no—
1545Q16—2121no—
1546Q16—2121no—
1547Q16—2121no—
1548SD16—1062no—
1549SD16—1062no—
1550SD16—1062no—
1551SD16—1062no—
1552SD16—2121no—
1553SD16—2121no—
1554SD16—2121no—
1555SD16—2121no—
1556SD16—2121no—
1557SD16—2121no—
1558SD16—2121no—
1559SD16—2121no—
1560D8—2121no—
1561D8—2121no—
1562D8—2121no—
1563D8—2121no—
1564M16—2121no—
1565M16—2121no—
1566M16—2121no—
1567M16—2121no—
1568C2×C8—531no—
1569C2×C8—531no—
1570C2×C8—531no—
1571C2×C8—531no—
1572C2×C8—531no—
1573C2×C8—531no—
1574C2×C8—531no—
1575C2×C8—531no—
1576C2×C8—2121no—
1577C2×C8—2121no—
1578C2×C8—2121no—
1579C2×C8—2121no—
1580C4⋊C4—21no—
1581C4⋊C4—21no—
1582C4⋊C4—21no—
1583C4⋊C4—21no—
1584C4⋊C4—21no—
1585C4⋊C4—21no—
1586C4⋊C4—21no—
1587C4⋊C4—21no—
1588C4⋊C4—21no—
1589C4⋊C4—21no—
1590C4⋊C4—21no—
1591C4⋊C4—531no—
1592C4⋊C4—531no—
1593C4⋊C4—531no—
1594C4⋊C4—531no—
1595C4⋊C4—1061no—
1596C4⋊C4—1061no—
1597C4⋊C4—1061no—
1598C4⋊C4—1061no—
1599C4⋊C4—1061no—
1600C4⋊C4—1061no—
1601C4⋊C4—1061no—
1602C4⋊C4—1061no—
1603C4⋊C4—1061no—
1604C4⋊C4—1061no—
1605C4⋊C4—1061no—
1606C4⋊C4—1061no—
1607C4⋊C4—1061no—
1608C4⋊C4—1061no—
1609C4⋊C4C2×C22⋊D5311yescharacteristic
1610C4⋊C4C2×C22⋊D5311yescharacteristic
1611C4⋊C4C2×C22⋊D5311yescharacteristic
1612C4⋊C4C2×C22⋊D5311yescharacteristic
1613C4⋊C4C23×D5311yescharacteristic
1614C4⋊C4C23×D5311yescharacteristic
1615C22⋊C4—21no—
1616C22⋊C4—21no—
1617C22⋊C4—21no—
1618C22⋊C4—21no—
1619C22⋊C4—21no—
1620C22⋊C4—21no—
1621C22⋊C4—21no—
1622C22⋊C4—21no—
1623C22⋊C4—21no—
1624C22⋊C4—21no—
1625C22⋊C4—21no—
1626C22⋊C4—21no—
1627C22⋊C4—1061no—
1628C22⋊C4—1061no—
1629C22⋊C4—1061no—
1630C22⋊C4—1061no—
1631C22⋊C4—1061no—
1632C22⋊C4—1061no—
1633C22⋊C4—1061no—
1634C22⋊C4—1061no—
1635C22⋊C4—1061no—
1636C22⋊C4—1061no—
1637C22⋊C4—1061no—
1638C22⋊C4—1061no—
1639C22⋊C4—1061no—
1640C22⋊C4—1061no—
1641C22⋊C4—1061no—
1642C22⋊C4—1061no—
1643C22⋊C4—1061no—
1644C22⋊C4—1061no—
1645C22⋊C4—1061no—
1646C22⋊C4—1061no—
1647C22⋊C4C2×C22⋊D5311yescharacteristic
1648C22⋊C4C2×C22⋊D5311yescharacteristic
1649C22⋊C4C2×C22⋊D5311yescharacteristic
1650C22⋊C4C2×C22⋊D5311yescharacteristic
1651C22⋊C4C2×C22⋊D5311yescharacteristic
1652C22⋊C4C2×C22⋊D5311yescharacteristic
1653C22⋊C4C2×C22⋊D5311yescharacteristic
1654C22⋊C4C2×C22⋊D5311yescharacteristic
1655C42—21no—
1656C42—21no—
1657C42—21no—
1658C42—21no—
1659C42—1061no—
1660C42—1061no—
1661C42—1061no—
1662C42—1061no—
1663C42C2×C22⋊D5311yescharacteristic
1664C42C2×C22⋊D5311yescharacteristic
1665C42C23×D5311yescharacteristic
1666C42C23×D5311yescharacteristic
1667C23—21no—
1668C23—21no—
1669C23—1061no—
1670C23—1061no—
1671C23—4241no—
1672C23—4241no—
1673C23—4241no—
1674C23C22×C22⋊D5311yescharacteristic
1675C23C22×C22⋊D5311yescharacteristic
1676C23C22×C22⋊D5311yescharacteristic
1677C23C22×C22⋊D5311yescharacteristic
1678C23C22×C22⋊D5311yescharacteristic
1679Q8—24no—
1680Q8—21no—
1681Q8—21no—
1682Q8—21no—
1683Q8—21no—
1684Q8—21no—
1685Q8—21no—
1686Q8—41no—
1687Q8—41no—
1688Q8—42no—
1689Q8—42no—
1690Q8—42no—
1691Q8—42no—
1692Q8—1061no—
1693Q8—1061no—
1694Q8—1061no—
1695Q8—1061no—
1696Q8—4241no—
1697Q8#1313326212yes—
1698Q8#1313326212yes—
1699D4—21no—
1700D4—21no—
1701D4—21no—
1702D4—21no—
1703D4—41no—
1704D4—41no—
1705D4—41no—
1706D4—41no—
1707D4—41no—
1708D4—41no—
1709D4—41no—
1710D4—41no—
1711D4—41no—
1712D4—41no—
1713D4—42no—
1714D4—42no—
1715D4—42no—
1716D4—42no—
1717D4—42no—
1718D4—42no—
1719D4—42no—
1720D4—81no—
1721D4—81no—
1722D4—81no—
1723D4—81no—
1724D4—81no—
1725D4—1061no—
1726D4—1061no—
1727D4—1061no—
1728D4—1061no—
1729D4—4241no—
1730D4—4241no—
1731D4—4241no—
1732D4—4241no—
1733D4—4241no—
1734D4—4241no—
1735D4—4241no—
1736D4—4241no—
1737D4—4241no—
1738C2×C4—24no—
1739C2×C4—21no—
1740C2×C4—21no—
1741C2×C4—21no—
1742C2×C4—21no—
1743C2×C4—21no—
1744C2×C4—21no—
1745C2×C4—21no—
1746C2×C4—21no—
1747C2×C4—21no—
1748C2×C4—21no—
1749C2×C4—21no—
1750C2×C4—21no—
1751C2×C4—21no—
1752C2×C4—21no—
1753C2×C4—21no—
1754C2×C4—21no—
1755C2×C4—41no—
1756C2×C4—41no—
1757C2×C4—42no—
1758C2×C4—42no—
1759C2×C4—42no—
1760C2×C4—42no—
1761C2×C4—42no—
1762C2×C4—42no—
1763C2×C4—42no—
1764C2×C4—42no—
1765C2×C4—42no—
1766C2×C4—42no—
1767C2×C4—81no—
1768C2×C4—1061no—
1769C2×C4—1061no—
1770C2×C4—1061no—
1771C2×C4—1061no—
1772C2×C4—1061no—
1773C2×C4—1061no—
1774C2×C4—4241no—
1775C2×C4—4241no—
1776C2×C4—4241no—
1777C2×C4—4241no—
1778C2×C4—4241no—
1779C2×C4—4241no—
1780C2×C4—4241no—
1781C2×C4C22×C22⋊D5311yescharacteristic
1782C2×C4C22×C22⋊D5311yescharacteristic
1783C2×C4C22×C22⋊D5311yescharacteristic
1784C2×C4C22×C22⋊D5311yescharacteristic
1785C2×C4C22×C22⋊D5311yescharacteristic
1786C2×C4C22×C22⋊D5311yescharacteristic
1787C2×C4C22×C22⋊D5311yescharacteristic
1788C2×C4C22×C22⋊D5311yescharacteristic
1789C2×C4C22×C22⋊D5311yescharacteristic
1790C2×C4C24×D5311yescharacteristic
1791C8—1061no—
1792C8—1061no—
1793C8—1061no—
1794C8—1061no—
1795C8—1061no—
1796C8—1061no—
1797C8—1061no—
1798C8—1061no—
1799C22—21no—
1800C22—21no—
1801C22—21no—
1802C22—21no—
1803C22—21no—
1804C22—21no—
1805C22—21no—
1806C22—21no—
1807C22—21no—
1808C22—21no—
1809C22—21no—
1810C22—21no—
1811C22—21no—
1812C22—21no—
1813C22—21no—
1814C22—41no—
1815C22—41no—
1816C22—41no—
1817C22—41no—
1818C22—41no—
1819C22—41no—
1820C22—8482no—
1821C22—2121no—
1822C22—2121no—
1823C22—2121no—
1824C22—2121no—
1825C22—2121no—
1826C22—2121no—
1827C22C23×C22⋊D5311yescharacteristic
1828C4—22no—
1829C4—22no—
1830C4—21no—
1831C4—21no—
1832C4—21no—
1833C4—21no—
1834C4—21no—
1835C4—21no—
1836C4—21no—
1837C4—21no—
1838C4—21no—
1839C4—41no—
1840C4—41no—
1841C4—41no—
1842C4—41no—
1843C4—2121no—
1844C4—2121no—
1845C4—2121no—
1846C4—2121no—
1847C4—2121no—
1848C4—2121no—
1849C4C2×#1313326211yescharacteristic
1850C4C2×#1313326211yescharacteristic
1851C2—41no—
1852C2—41no—
1853C2—41no—
1854C2—41no—
1855C2—41no—
1856C2—81no—
1857C2—81no—
1858C2—4241no—
1859C2—4241no—
1860C2#2028835011yescharacteristic
1861C2#2028948611yescharacteristic
1862C2#2028950211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3497C2
socleC22×C53C23×D4
hypercenter#3497D53
hypocenterC53#61681
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ #532 ◁ #3497

Complements

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

NH ≅ G/Ntype
1. #20289142C2semidirect
2. #20286983C2semidirect
3. #20286968C2semidirect
4. #20286886C2semidirect
5. #20286841C2semidirect
6. #20286766C2semidirect
7. #20286721C2semidirect
8. #20286617C2semidirect
9. #20286602C2semidirect
10. #20286452C2semidirect
11. #20286423C2semidirect
12. #20286368C2semidirect
13. #20286347C2semidirect
14. #20286296C2semidirect
15. #20286286C2semidirect
16. #20286256C2semidirect
17. #20286226C2semidirect
18. #20285752C2semidirect
19. #20285691C2semidirect
20. #20285621C2semidirect
21. #20285612C2semidirect
22. #20285591C2semidirect
23. #20285561C2semidirect
24. #20284886C2semidirect
25. #20284795C2semidirect
26. #20284030C2semidirect
27. #20284030C2semidirect
28. #20284010C2semidirect
29. #20284001C2semidirect
30. #20283791C2semidirect
31. C53×#3497C2semidirect
34. C2×#13133247C22semidirect
38. C22×#11719925C22semidirect
66. #16810991C22semidirect
67. #16810987C22semidirect
68. #16810977C22semidirect
69. #16810977C22semidirect
71. #16810961C22semidirect
72. #16810958C22semidirect
73. #16810956C22semidirect
74. #16810953C22semidirect
75. #16810951C22semidirect
77. #16810944C22semidirect
79. #16810939C22semidirect
81. #16810934C22semidirect
82. #16810930C22semidirect
83. #16810930C22semidirect
84. #16810930C22semidirect
85. #16810930C22semidirect
87. #16810879C22semidirect
93. #16810867C22semidirect
95. #16810862C22semidirect
101. #16810850C22semidirect
106. #16810842C22semidirect
107. #16810842C22semidirect
110. #16810830C22semidirect
112. #16810820C22semidirect
116. #16810785C22semidirect
117. #16810785C22semidirect
118. #16810785C22semidirect
119. #16810785C22semidirect
120. #16810785C22semidirect
121. #16810785C22semidirect
126. #16810779C22semidirect
127. #16810779C22semidirect
128. #16810779C22semidirect
129. #16810779C22semidirect
130. #16810778C22semidirect
148. #16810761C22semidirect
150. #16810728C22semidirect
151. #16810728C22semidirect
154. C4×#11719925C22semidirect
155. C4×#11719925C22semidirect
159. #16810701C22semidirect
162. #16810695C22semidirect
163. #16810695C22semidirect
165. D4×#88322C22semidirect
166. #16810680C22semidirect
167. #16810676C22semidirect
169. #16810632C22semidirect
170. #16810624C22semidirect
171. #16810624C22semidirect
173. #16810619C22semidirect
174. C2×#13133141C22semidirect
175. C2×#13133141C22semidirect
178. #16810590C22semidirect
179. #16810590C22semidirect
181. C2×2−1+4×C53C22semidirect
184. C53×#550C22semidirect
187. D4×Q8×C53C22semidirect
192. C53×#548C22semidirect
193. C53×#548C22semidirect
197. C53×#537C22semidirect
201. C53×#532C22semidirect
202. C2×C4×Q8×C53C22semidirect
921. #3497D53semidirect
964. C2×2−1+4C2×D53semidirect
983. #550C2×D53semidirect
986. D4×Q8C2×D53semidirect
993. #548C2×D53semidirect
994. #548C2×D53semidirect
1006. #537C2×D53semidirect
1012. #532C2×D53semidirect
1015. C2×C4×Q8C2×D53semidirect
1134. C53#61681semidirect

Maximal subgroups

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

subgroupindex
#202891422
#202869832
#202869682
#202868862
#202868412
#202867662
#202867212
#202866172
#202866022
#202864522
#202864232
#202863682
#202863472
#202862962
#202862862
#202862562
#202862262
#202857522
#202856912
#202856212
#202856122
#202855912
#202855612
#202848862
#202847952
#202840302
#202840102
#202840012
#202837912
C53×#34972
#6168153