Finite Group Databasebeta

← #28270652

Subgroups — #28270652

Order 13568.

2100 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#20289008C211yesmaximal, characteristic, complemented
2#20287053C211yesmaximal, characteristic, complemented
3#20286983C211yesmaximal, characteristic, complemented
4#20286946C211yesmaximal, characteristic, complemented
5#20286916C211yesmaximal, characteristic, complemented
6#20286796C211yesmaximal, characteristic, complemented
7#20286781C211yesmaximal, characteristic, complemented
8#20286736C211yesmaximal, characteristic, complemented
9#20286721C211yesmaximal, characteristic, complemented
10#20286381C211yesmaximal, characteristic, complemented
11#20286368C211yesmaximal, characteristic, complemented
12#20286342C211yesmaximal, characteristic, complemented
13#20286311C211yesmaximal, characteristic, complemented
14#20286296C211yesmaximal, characteristic, complemented
15#20286271C211yesmaximal, characteristic, complemented
16#20286221C211yesmaximal, characteristic, complemented
17#20286206C211yesmaximal, characteristic, complemented
18#20285809C211yesmaximal, characteristic, complemented
19#20285787C211yesmaximal, characteristic, complemented
20#20285612C211yesmaximal, characteristic, complemented
21#20285591C211yesmaximal, characteristic, complemented
22#20285529C211yesmaximal, characteristic, complemented
23#20285521C211yesmaximal, characteristic, complemented
24#20284977C211yesmaximal, characteristic, complemented
25#20284929C211yesmaximal, characteristic, complemented
26#20284019C211yesmaximal, characteristic, complemented
27#20283992C211yesmaximal, characteristic, complemented
28#20283975C211yesmaximal, characteristic, complemented
29#20283957C211yesmaximal, characteristic, complemented
30#20283777C211yesmaximal, characteristic, complemented
31C53×#3488C211yesmaximal, characteristic, complemented
32C2×#13133248C2211yescharacteristic, complemented
33C2×#13133247C2211yescharacteristic, complemented
34C2×#13133247C2211yescharacteristic, complemented
35C2×#13133247C2211yescharacteristic, complemented
36C2×#13133243C2211yescharacteristic, complemented
37C2×#13133243C2211yescharacteristic, complemented
38C2×#13133237C2211yescharacteristic, complemented
39C22×#11719923C2211yescharacteristic, complemented
40#16811374—21no—
41#16811368—21no—
42#16811343C2211yescharacteristic, complemented
43#16811330C2211yescharacteristic, complemented
44#16811327—21no—
45#16811319C2211yescharacteristic, complemented
46#16811316—21no—
47#16811313C2211yescharacteristic, complemented
48D4×Dic106C2211yescharacteristic, complemented
49#16811282C2211yescharacteristic, complemented
50#16811282C2211yescharacteristic, complemented
51#16811278C2211yescharacteristic, complemented
52#16811244C2211yescharacteristic, complemented
53#16811241—21no—
54#16811235C2211yescharacteristic, complemented
55#16811216—21no—
56#16811208—21no—
57#16811208—21no—
58#16811201C2211yescharacteristic, complemented
59#16811194C2211yescharacteristic, complemented
60#16811134C2211yescharacteristic, complemented
61C2×#13133196C2211yescharacteristic, complemented
62#16811018C2211yescharacteristic, complemented
63#16811010C2211yescharacteristic, complemented
64#16811005C2211yescharacteristic, complemented
65#16810995C2211yescharacteristic, complemented
66#16810987C2211yescharacteristic, complemented
67#16810982C2211yescharacteristic, complemented
68#16810977C2211yescharacteristic, complemented
69#16810969C2211yescharacteristic, complemented
70#16810961C2211yescharacteristic, complemented
71#16810958C2211yescharacteristic, complemented
72#16810958C2211yescharacteristic, complemented
73#16810956C2211yescharacteristic, complemented
74#16810953C2211yescharacteristic, complemented
75#16810944C2211yescharacteristic, complemented
76#16810944C2211yescharacteristic, complemented
77#16810944C2211yescharacteristic, complemented
78#16810936C2211yescharacteristic, complemented
79#16810934C2211yescharacteristic, complemented
80#16810934C2211yescharacteristic, complemented
81#16810934C2211yescharacteristic, complemented
82#16810930C2211yescharacteristic, complemented
83#16810923C2211yescharacteristic, complemented
84#16810918C2211yescharacteristic, complemented
85#16810903C2211yescharacteristic, complemented
86#16810879C2211yescharacteristic, complemented
87#16810874C2211yescharacteristic, complemented
88#16810874C2211yescharacteristic, complemented
89#16810871C2211yescharacteristic, complemented
90#16810867C2211yescharacteristic, complemented
91#16810867C2211yescharacteristic, complemented
92#16810867C2211yescharacteristic, complemented
93#16810867C2211yescharacteristic, complemented
94#16810867C2211yescharacteristic, complemented
95#16810867C2211yescharacteristic, complemented
96#16810867C2211yescharacteristic, complemented
97#16810867C2211yescharacteristic, complemented
98#16810862C2211yescharacteristic, complemented
99#16810862C2211yescharacteristic, complemented
100#16810857C2211yescharacteristic, complemented
101#16810850C2211yescharacteristic, complemented
102#16810845C2211yescharacteristic, complemented
103#16810842C2211yescharacteristic, complemented
104#16810842C2211yescharacteristic, complemented
105#16810842C2211yescharacteristic, complemented
106#16810838C2211yescharacteristic, complemented
107#16810835C2211yescharacteristic, complemented
108#16810833C2211yescharacteristic, complemented
109#16810828C2211yescharacteristic, complemented
110#16810820C2211yescharacteristic, complemented
111#16810820C2211yescharacteristic, complemented
112#16810820C2211yescharacteristic, complemented
113#16810815C2211yescharacteristic, complemented
114#16810785C2211yescharacteristic
115#16810785C2211yescharacteristic
116#16810785C2211yescharacteristic
117#16810785C2211yescharacteristic, complemented
118#16810785C2211yescharacteristic, complemented
119#16810785C2211yescharacteristic, complemented
120#16810785C2211yescharacteristic, complemented
121#16810785C2211yescharacteristic, complemented
122#16810785C2211yescharacteristic, complemented
123#16810785C2211yescharacteristic, complemented
124#16810785C2211yescharacteristic, complemented
125#16810783C2211yescharacteristic, complemented
126#16810779C2211yescharacteristic, complemented
127#16810779C2211yescharacteristic, complemented
128#16810778C2211yescharacteristic, complemented
129#16810774C2211yescharacteristic, complemented
130#16810774C2211yescharacteristic, complemented
131#16810774C2211yescharacteristic, complemented
132#16810774C2211yescharacteristic, complemented
133#16810774C2211yescharacteristic, complemented
134#16810774C2211yescharacteristic, complemented
135#16810774C2211yescharacteristic, complemented
136#16810774C2211yescharacteristic, complemented
137#16810768C2211yescharacteristic
138#16810768C2211yescharacteristic, complemented
139#16810768C2211yescharacteristic, complemented
140#16810768C2211yescharacteristic, complemented
141#16810768C2211yescharacteristic, complemented
142#16810766C2211yescharacteristic, complemented
143#16810766C2211yescharacteristic, complemented
144#16810766C2211yescharacteristic, complemented
145#16810761C2211yescharacteristic, complemented
146#16810761C2211yescharacteristic, complemented
147#16810761C2211yescharacteristic, complemented
148#16810757C2211yescharacteristic, complemented
149#16810757C2211yescharacteristic, complemented
150#16810728C2211yescharacteristic, complemented
151#16810723C2211yescharacteristic, complemented
152#16810723C2211yescharacteristic, complemented
153#16810721C2211yescharacteristic, complemented
154C4×#11719925C2211yescharacteristic, complemented
155C4×#11719925C2211yescharacteristic, complemented
156C4×#11719923C2211yescharacteristic, complemented
157C4×#11719922C2211yescharacteristic, complemented
158#16810701C2211yescharacteristic, complemented
159#16810701C2211yescharacteristic, complemented
160#16810701C2211yescharacteristic, complemented
161#16810701C2211yescharacteristic, complemented
162#16810695C2211yescharacteristic, complemented
163#16810695C2211yescharacteristic, complemented
164#16810695C2211yescharacteristic, complemented
165#16810695C2211yescharacteristic, complemented
166#16810684C2211yescharacteristic, complemented
167#16810684C2211yescharacteristic, complemented
168#16810632C2211yescharacteristic, complemented
169#16810628C2211yescharacteristic, complemented
170#16810628C2211yescharacteristic, complemented
171#16810624C2211yescharacteristic, complemented
172#16810624C2211yescharacteristic, complemented
173#16810624C2211yescharacteristic, complemented
174#16810619C2211yescharacteristic, complemented
175C2×#13133138C2211yescharacteristic, complemented
176#16810590C2211yescharacteristic, complemented
177#16810590C2211yescharacteristic, complemented
178#16810587C2211yescharacteristic, complemented
179#16810587C2211yescharacteristic, complemented
180C2×H(5,𝔽2)×C53C2211yescharacteristic
181C22×#41×C53C2211yescharacteristic
182C53×#550C2211yescharacteristic
183C53×#550C2211yescharacteristic
184C53×#548C2211yescharacteristic
185C53×#548C2211yescharacteristic
186C53×#546—21no—
187C53×#546—21no—
188C53×#546C2211yescharacteristic
189C53×#546C2211yescharacteristic
190D42×C53—21no—
191D42×C53—21no—
192D42×C53C2211yescharacteristic
193D42×C53C2211yescharacteristic
194C53×#537—21no—
195C53×#537C2211yescharacteristic
196C53×#535—21no—
197C53×#535C2211yescharacteristic
198C53×#525—21no—
199C53×#525C2211yescharacteristic
200C2×#121×C53—21no—
201C2×#121×C53C2211yescharacteristic
202C53×#520C2211yescharacteristic
203C2×#11719945C2311yescharacteristic
204C2×#11719945C2311yescharacteristic
205C22×Dic106C2311yescharacteristic
206C22×Dic106C2311yescharacteristic
207#13133248—42no—
208#13133247—42no—
209#13133247—42no—
210#13133247—42no—
211#13133243—42no—
212#13133243—42no—
213#13133237—42no—
214C2×#11719925C2311yescharacteristic
215C2×#11719925C2311yescharacteristic
216C2×#11719925C2311yescharacteristic
217C2×#11719925C2311yescharacteristic
218C2×#11719925C2311yescharacteristic
219C2×#11719925C2311yescharacteristic
220C2×#11719923—42no—
221C2×#11719923C2311yescharacteristic
222C2×#11719923C2311yescharacteristic
223C2×#11719923C2311yescharacteristic
224C2×#11719923C2311yescharacteristic
225C2×#11719923C2311yescharacteristic
226C2×#11719923C2311yescharacteristic
227C2×#11719923C2311yescharacteristic
228C2×#11719923C2311yescharacteristic
229C2×#11719923C2311yescharacteristic
230C2×#11719923C2311yescharacteristic
231C2×#11719923C2311yescharacteristic
232C2×#11719923C2311yescharacteristic
233C2×#11719924C2311yescharacteristic
234C2×#11719924C2311yescharacteristic
235C2×#11719922C2311yescharacteristic
236C2×#11719922C2311yescharacteristic
237C2×#11719922C2311yescharacteristic
238C2×#11719922C2311yescharacteristic
239C2×#11719917C2311yescharacteristic
240C2×#11719917C2311yescharacteristic
241C2×#11719917C2311yescharacteristic
242C2×#11719917C2311yescharacteristic
243C2×#11719917C2311yescharacteristic
244C2×#11719917C2311yescharacteristic
245C22×#88322C2311yescharacteristic
246C22×#88322C2311yescharacteristic
247#13133217C2311yescharacteristic
248#13133217C2311yescharacteristic
249#13133216—21no—
250#13133215—21no—
251#13133212—21no—
252#13133212—21no—
253#13133210—21no—
254#13133210—21no—
255#13133210—21no—
256#13133210—21no—
257#13133210—21no—
258#13133209C2311yescharacteristic
259#13133208—21no—
260#13133207—21no—
261#13133207—21no—
262#13133207—21no—
263#13133205C2311yescharacteristic
264#13133204—21no—
265#13133204—21no—
266#13133203—21no—
267#13133203—21no—
268#13133203—21no—
269#13133200—21no—
270#13133199—21no—
271#13133199—21no—
272#13133199—21no—
273#13133199—21no—
274#13133198—21no—
275#13133198—21no—
276#13133198—21no—
277#13133196—21no—
278#13133196—21no—
279#13133196C2311yescharacteristic
280#13133196C2311yescharacteristic
281#13133196C2311yescharacteristic
282#13133196C2311yescharacteristic
283#13133196C2311yescharacteristic
284#13133196C2311yescharacteristic
285#13133196C2311yescharacteristic
286#13133196C2311yescharacteristic
287#13133196C2311yescharacteristic
288#13133195—21no—
289#13133195—21no—
290#13133195—21no—
291#13133194—21no—
292#13133194—21no—
293#13133194—21no—
294#13133194—21no—
295#13133193—21no—
296#13133191C2311yescharacteristic
297#13133191C2311yescharacteristic
298#13133191C2311yescharacteristic
299#13133189—21no—
300#13133189—21no—
301#13133189—21no—
302#13133189—21no—
303#13133189—21no—
304#13133188—21no—
305#13133188—21no—
306#13133186—21no—
307C4×Dic106C2311yescharacteristic
308C4×Dic106C2311yescharacteristic
309C4×Dic106C2311yescharacteristic
310#13133182—21no—
311C4×D212C2311yescharacteristic
312D4×Dic53—21no—
313D4×Dic53—21no—
314C4×C22⋊D53—21no—
315C4×C22⋊D53—21no—
316#13133177—21no—
317#13133177—21no—
318#13133177—21no—
319#13133176C2311yescharacteristic
320#13133176C2311yescharacteristic
321#13133173—21no—
322C2×C4⋊Dic53C2311yescharacteristic
323C2×C4⋊Dic53C2311yescharacteristic
324C2×#11719919—21no—
325C4⋊C4×D53—21no—
326C2×C22⋊Dic53—21no—
327#13133150C2311yescharacteristic
328#13133150C2311yescharacteristic
329#13133150C2311yescharacteristic
330#13133150C2311yescharacteristic
331#13133150C2311yescharacteristic
332#13133150C2311yescharacteristic
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#13133140C2311yescharacteristic
348#13133140C2311yescharacteristic
349#13133140C2311yescharacteristic
350#13133140C2311yescharacteristic
351#13133140C2311yescharacteristic
352#13133140C2311yescharacteristic
353#13133138C2311yescharacteristic
354#13133138C2311yescharacteristic
355#13133138C2311yescharacteristic
356#13133138C2311yescharacteristic
357#13133138C2311yescharacteristic
358#13133138C2311yescharacteristic
359#13133138C2311yescharacteristic
360#13133138C2311yescharacteristic
361#13133138C2311yescharacteristic
362#13133138C2311yescharacteristic
363#13133138C2311yescharacteristic
364#13133138C2311yescharacteristic
365#13133138C2311yescharacteristic
366#13133138C2311yescharacteristic
367#13133138C2311yescharacteristic
368#13133138C2311yescharacteristic
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
387H(5,𝔽2)×C53—42no—
388H(5,𝔽2)×C53—42no—
389C2×#41×C53—21no—
390C2×#41×C53—21no—
391C2×#41×C53—21no—
392C2×#41×C53—42no—
393C2×#41×C53—42no—
394C2×#41×C53C2311yescharacteristic
395C2×#41×C53C2311yescharacteristic
396C2×#41×C53C2311yescharacteristic
397C2×#41×C53C2311yescharacteristic
398C2×#41×C53C2311yescharacteristic
399C2×#41×C53C2311yescharacteristic
400C2×#41×C53C2311yescharacteristic
401C22×Q8×C53C2311yescharacteristic
402C22×D4×C53—21no—
403C22×D4×C53—21no—
404C22×D4×C53—21no—
405C22×D4×C53—21no—
406C22×D4×C53—21no—
407C22×D4×C53—21no—
408C22×D4×C53—21no—
409C22×D4×C53C2311yescharacteristic
410C22×D4×C53C2311yescharacteristic
411C22×D4×C53C2311yescharacteristic
412C22×D4×C53C2311yescharacteristic
413C23×C4×C53—21no—
414C23×C4×C53C2311yescharacteristic
415#127×C53—21no—
416#127×C53—21no—
417#127×C53C2311yescharacteristic
418#127×C53C2311yescharacteristic
419#124×C53—21no—
420#124×C53—21no—
421#124×C53C2311yescharacteristic
422#124×C53C2311yescharacteristic
423#123×C53—21no—
424#123×C53—21no—
425#123×C53D411yescharacteristic
426#123×C53D411yescharacteristic
427C22⋊Q8×C53—21no—
428C22⋊Q8×C53—21no—
429C22⋊Q8×C53—21no—
430C22⋊Q8×C53D411yescharacteristic
431C22⋊Q8×C53D411yescharacteristic
432C22⋊Q8×C53C2311yescharacteristic
433C22⋊Q8×C53C2311yescharacteristic
434#121×C53—21no—
435#121×C53—21no—
436#121×C53—21no—
437#121×C53—21no—
438#121×C53—21no—
439#121×C53—21no—
440#121×C53—21no—
441#121×C53—21no—
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×C53D411yescharacteristic
452#121×C53D411yescharacteristic
453#121×C53C2311yescharacteristic
454#121×C53C2311yescharacteristic
455#121×C53C2311yescharacteristic
456#121×C53C2311yescharacteristic
457#121×C53C2311yescharacteristic
458#121×C53C2311yescharacteristic
459#120×C53—21no—
460#120×C53—21no—
461#120×C53—21no—
462#120×C53—21no—
463#120×C53—21no—
464#120×C53—21no—
465#120×C53—21no—
466#120×C53—21no—
467#120×C53D411yescharacteristic
468#120×C53D411yescharacteristic
469C4×Q8×C53C2311yescharacteristic
470C4×Q8×C53C2311yescharacteristic
471C4×D4×C53—21no—
472C4×D4×C53—21no—
473C4×D4×C53—21no—
474C4×D4×C53—21no—
475C4×D4×C53—21no—
476C4×D4×C53—21no—
477C4×D4×C53C2311yescharacteristic
478C4×D4×C53C2311yescharacteristic
479C4×D4×C53C2311yescharacteristic
480C4×D4×C53C2311yescharacteristic
481C4×D4×C53C2311yescharacteristic
482C4×D4×C53C2311yescharacteristic
483#117×C53—21no—
484#117×C53C2311yescharacteristic
485C2×C4⋊C4×C53—21no—
486C2×C4⋊C4×C53C2311yescharacteristic
487C2×C22⋊C4×C53—21no—
488C2×C22⋊C4×C53—21no—
489C2×C22⋊C4×C53—21no—
490C24×C53—21no—
491C24×C53—21no—
492C24×C53—21no—
493C24×C53—21no—
494C24×C53C2×D411yescharacteristic
495#41×C53—22no—
496#41×C53—22no—
497#41×C53—22no—
498#41×C53—22no—
499#41×C53—22no—
500#41×C53—22no—
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—41no—
508#41×C53—41no—
509#41×C53—44no—
510#41×C53—44no—
511#41×C53—44no—
512C2×Q8×C53—21no—
513C2×Q8×C53—22no—
514C2×Q8×C53—41no—
515C2×Q8×C53C2×D411yescharacteristic
516C2×Q8×C53C2411yescharacteristic
517C2×Q8×C53C2411yescharacteristic
518C2×D4×C53—21no—
519C2×D4×C53—22no—
520C2×D4×C53—22no—
521C2×D4×C53—22no—
522C2×D4×C53—21no—
523C2×D4×C53—21no—
524C2×D4×C53—21no—
525C2×D4×C53—21no—
526C2×D4×C53—21no—
527C2×D4×C53—21no—
528C2×D4×C53—21no—
529C2×D4×C53—21no—
530C2×D4×C53—21no—
531C2×D4×C53—21no—
532C2×D4×C53—21no—
533C2×D4×C53—21no—
534C2×D4×C53—21no—
535C2×D4×C53—21no—
536C2×D4×C53—21no—
537C2×D4×C53—21no—
538C2×D4×C53—21no—
539C2×D4×C53—21no—
540C2×D4×C53—21no—
541C2×D4×C53—41no—
542C2×D4×C53—41no—
543C2×D4×C53—41no—
544C2×D4×C53—41no—
545C2×D4×C53—41no—
546C2×D4×C53—44no—
547C2×D4×C53—44no—
548C2×D4×C53—44no—
549C2×D4×C53—44no—
550C2×D4×C53—82no—
551C2×D4×C53—82no—
552C2×D4×C53—82no—
553C2×D4×C53C2×D411yescharacteristic
554C2×D4×C53C2×D411yescharacteristic
555C2×D4×C53C2×D411yescharacteristic
556C2×D4×C53C2×D411yescharacteristic
557C2×D4×C53C2×D411yescharacteristic
558C2×D4×C53C2×D411yescharacteristic
559C2×D4×C53C2×D411yescharacteristic
560C2×D4×C53C2411yescharacteristic
561C2×D4×C53C2411yescharacteristic
562C2×D4×C53C2411yescharacteristic
563C2×D4×C53C2411yescharacteristic
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×C53—21no—
573C22×C4×C53—21no—
574C22×C4×C53—41no—
575C22×C4×C53—41no—
576C22×C4×C53—44no—
577C22×C4×C53C2×D411yescharacteristic
578C22×C4×C53C2×D411yescharacteristic
579C22×C4×C53C2×D411yescharacteristic
580C22×C4×C53C2411yescharacteristic
581C22×C4×C53C2411yescharacteristic
582C22×C4×C53C2411yescharacteristic
583C22×C4×C53C2411yescharacteristic
584C22×C4×C53C2411yescharacteristic
585C2×C22⋊D53—21no—
586C2×C22⋊D53—21no—
587C2×C22⋊D53—21no—
588C2×C22⋊D53—21no—
589C2×C22⋊D53—21no—
590C22×Dic53—21no—
591C22×Dic53—21no—
592C22×Dic53—21no—
593C22×Dic53—21no—
594#11719945—41no—
595#11719945—41no—
596#11719945—41no—
597#11719945—41no—
598C2×D212C2411yescharacteristic
599C2×C4×D53—21no—
600C2×C4×D53—21no—
601C2×C4×D53—21no—
602C2×Dic106—21no—
603C2×Dic106—21no—
604C2×Dic106—21no—
605C2×Dic106—41no—
606C2×Dic106—41no—
607C2×Dic106—41no—
608C2×Dic106—41no—
609C2×Dic106C2411yescharacteristic
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×C53C2×D411yescharacteristic
618C4⋊C4×C53C2×D411yescharacteristic
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×C53—21no—
638C22⋊C4×C53—21no—
639C22⋊C4×C53C2×D411yescharacteristic
640C22⋊C4×C53C2×D411yescharacteristic
641C22⋊C4×C53C2×D411yescharacteristic
642C22⋊C4×C53C2×D411yescharacteristic
643C22⋊C4×C53C2×D411yescharacteristic
644C22⋊C4×C53C2×D411yescharacteristic
645C22⋊C4×C53C2×D411yescharacteristic
646C22⋊C4×C53C2×D411yescharacteristic
647C22⋊C4×C53C2×D411yescharacteristic
648C22⋊C4×C53C2×D411yescharacteristic
649C42×C53—21no—
650C42×C53—21no—
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—
661C22⋊Dic53—21no—
662C22⋊Dic53—21no—
663C22⋊Dic53—21no—
664#11719925—22no—
665#11719925—22no—
666#11719925—22no—
667#11719925—41no—
668#11719925—41no—
669#11719925—41no—
670#11719924—22no—
671#11719924—41no—
672#11719923—22no—
673#11719923—22no—
674#11719923—22no—
675#11719923—41no—
676#11719923—41no—
677#11719923—41no—
678#11719923—41no—
679#11719923—41no—
680#11719923—41no—
681#11719923—41no—
682#11719923—41no—
683#11719923—41no—
684#11719922—22no—
685#11719922—41no—
686#11719922—41no—
687#11719922—41no—
688#11719921—21no—
689#11719921—21no—
690#11719921—21no—
691#11719921—21no—
692#11719921—21no—
693#11719921—21no—
694C4⋊Dic53—21no—
695C4⋊Dic53—21no—
696C4⋊Dic53—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—
715#11719919—21no—
716#11719919—21no—
717C4×Dic53—21no—
718C4×Dic53—21no—
719C4×Dic53—21no—
720C4×Dic53—21no—
721C4×Dic53—21no—
722#11719917—41no—
723#11719917—41no—
724#11719917—41no—
725#11719917—41no—
726#11719917—41no—
727#11719917—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—21no—
739C23×C53—21no—
740C23×C53—21no—
741C23×C53—21no—
742C23×C53—41no—
743C23×C53—41no—
744C23×C53—41no—
745C23×C53—42no—
746C23×C53—42no—
747C23×C53—42no—
748C23×C53—42no—
749C23×C53—42no—
750C23×C53—81no—
751C23×C53—81no—
752C23×C53—81no—
753C23×C53—81no—
754C23×C53—81no—
755C23×C53—81no—
756C23×C53—81no—
757C23×C53C22×D411yescharacteristic
758C23×C53C22×D411yescharacteristic
759C23×C53C22×D411yescharacteristic
760C23×C53C22×D411yescharacteristic
761C23×C53C22×D411yescharacteristic
762C22×D53—21no—
763Q8×C53—21no—
764Q8×C53—21no—
765Q8×C53—21no—
766Q8×C53—41no—
767Q8×C53—42no—
768Q8×C53H(5,𝔽2)12yes—
769D4×C53—24no—
770D4×C53—21no—
771D4×C53—21no—
772D4×C53—21no—
773D4×C53—21no—
774D4×C53—21no—
775D4×C53—21no—
776D4×C53—21no—
777D4×C53—41no—
778D4×C53—41no—
779D4×C53—41no—
780D4×C53—41no—
781D4×C53—41no—
782D4×C53—41no—
783D4×C53—41no—
784D4×C53—42no—
785D4×C53—42no—
786D4×C53—42no—
787D4×C53—42no—
788D4×C53—42no—
789D4×C53—42no—
790D4×C53—42no—
791D4×C53—42no—
792D4×C53—42no—
793D4×C53—42no—
794D4×C53—42no—
795D4×C53—81no—
796D4×C53—81no—
797D4×C53—81no—
798D4×C53—81no—
799D4×C53—81no—
800D4×C53—81no—
801D4×C53—81no—
802D4×C53—81no—
803D4×C53H(5,𝔽2)12yes—
804C2×C4×C53—24no—
805C2×C4×C53—21no—
806C2×C4×C53—21no—
807C2×C4×C53—21no—
808C2×C4×C53—21no—
809C2×C4×C53—21no—
810C2×C4×C53—21no—
811C2×C4×C53—21no—
812C2×C4×C53—21no—
813C2×C4×C53—21no—
814C2×C4×C53—21no—
815C2×C4×C53—21no—
816C2×C4×C53—21no—
817C2×C4×C53—21no—
818C2×C4×C53—21no—
819C2×C4×C53—41no—
820C2×C4×C53—41no—
821C2×C4×C53—41no—
822C2×C4×C53—42no—
823C2×C4×C53—42no—
824C2×C4×C53—42no—
825C2×C4×C53—42no—
826C2×C4×C53—42no—
827C2×C4×C53—42no—
828C2×C4×C53—81no—
829C2×C4×C53—81no—
830C2×C4×C53—81no—
831C2×C4×C53C22×D411yescharacteristic
832C2×C4×C53C22×D411yescharacteristic
833C2×C4×C53C22×D411yescharacteristic
834C2×C4×C53C22×D411yescharacteristic
835C2×C4×C53C22×D411yescharacteristic
836C2×C4×C53C22×D411yescharacteristic
837C2×C4×C53C22×D411yescharacteristic
838C2×C4×C53C22×D411yescharacteristic
839C2×C4×C53C22×D411yescharacteristic
840C2×C4×C53C2511yescharacteristic
841C22⋊D53—42no—
842C22⋊D53—81no—
843C22⋊D53—81no—
844C22⋊D53—81no—
845C22⋊D53—81no—
846C2×Dic53—21no—
847C2×Dic53—21no—
848C2×Dic53—21no—
849C2×Dic53—21no—
850C2×Dic53—21no—
851C2×Dic53—21no—
852C2×Dic53—21no—
853C2×Dic53—81no—
854C2×Dic53—81no—
855C2×Dic53—81no—
856C2×Dic53—81no—
857D212—21no—
858D212—21no—
859C4×D53—81no—
860C4×D53—81no—
861C4×D53—81no—
862Dic106—21no—
863Dic106—21no—
864Dic106—21no—
865Dic106—21no—
866Dic106—21no—
867Dic106—21no—
868Dic106—81no—
869Dic106—81no—
870Dic106—81no—
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#61654—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—21no—
895C22×C53—22no—
896C22×C53—41no—
897C22×C53—41no—
898C22×C53—41no—
899C22×C53—41no—
900C22×C53—41no—
901C22×C53—41no—
902C22×C53—41no—
903C22×C53—41no—
904C22×C53—41no—
905C22×C53—41no—
906C22×C53—41no—
907C22×C53—82no—
908C22×C53—84no—
909C22×C53—162no—
910C22×C53—162no—
911C22×C53—162no—
912C22×C53C23×D411yescharacteristic
913C2×D53—41no—
914C2×D53—41no—
915C2×D53—41no—
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—22no—
926C4×C53—41no—
927C4×C53—41no—
928C4×C53—41no—
929C4×C53C2×H(5,𝔽2)11yescharacteristic
930C4×C53C2×H(5,𝔽2)11yescharacteristic
931Dic53—41no—
932Dic53—41no—
933Dic53—41no—
934Dic53—41no—
935Dic53—41no—
936Dic53—41no—
937Dic53—41no—
938#3541—531no—
939#3488D5311yescharacteristic, complemented
940#3333—531no—
941#3327—531no—
942#3324—531no—
943#3322—531no—
944#3314—531no—
945#3313—531no—
946#3310—531no—
947#3309—531no—
948#3278—531no—
949#3277—531no—
950#3275—531no—
951#3272—531no—
952#3271—531no—
953#3269—531no—
954#3266—531no—
955#3265—531no—
956#3224—531no—
957#3222—531no—
958#3203—531no—
959#3201—531no—
960#3194—531no—
961#3193—531no—
962#3124—531no—
963#3120—531no—
964#3012—531no—
965#3009—531no—
966#3007—531no—
967#3005—531no—
968#2978—531no—
969C2×C53—41no—
970C2×C53—41no—
971C2×C53—41no—
972C2×C53—41no—
973C2×C53—41no—
974C2×C53—42no—
975C2×C53—81no—
976C2×C53—81no—
977C2×C53—81no—
978C2×C53#348411yescharacteristic
979C2×C53#358511yescharacteristic
980C2×C53#358611yescharacteristic
981D53—81no—
982C2×H(5,𝔽2)C2×D5311yescharacteristic
983C22×#41C2×D5311yescharacteristic
984C2×#137—531no—
985C2×#137—531no—
986C2×#137—531no—
987C2×#137—531no—
988C2×AGL(1,ℤ/8)—531no—
989C2×AGL(1,ℤ/8)—531no—
990C2×#135—531no—
991C22×SD16—531no—
992#563—1061no—
993#562—1061no—
994#556—531no—
995#554—531no—
996#554—1061no—
997#553—531no—
998#553—1061no—
999#552—531no—
1000#550C2×D5311yescharacteristic
1001#550C2×D5311yescharacteristic
1002D4×Q8—531no—
1003#548—531no—
1004#548—531no—
1005#548C2×D5311yescharacteristic
1006#548C2×D5311yescharacteristic
1007#547—531no—
1008#546—21no—
1009#546—21no—
1010#546C2×D5311yescharacteristic
1011#546C2×D5311yescharacteristic
1012D42—21no—
1013D42—21no—
1014D42C2×D5311yescharacteristic
1015D42C2×D5311yescharacteristic
1016#542—531no—
1017#542—1061no—
1018#541—531no—
1019#539—1061no—
1020#538—1061no—
1021#538—1061no—
1022#537—21no—
1023#537—531no—
1024#537C2×D5311yescharacteristic
1025#536—531no—
1026#535—21no—
1027#535C2×D5311yescharacteristic
1028#525—21no—
1029#525—531no—
1030#525C2×D5311yescharacteristic
1031C2×C22⋊Q8—531no—
1032C2×#121—21no—
1033C2×#121C2×D5311yescharacteristic
1034#520C2×D5311yescharacteristic
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#484—531no—
1046#484—531no—
1047#483—531no—
1048#482—531no—
1049#482—531no—
1050#482—531no—
1051#480—531no—
1052#480—531no—
1053#480—531no—
1054#480—531no—
1055#479—531no—
1056#478—531no—
1057#477—531no—
1058#474—531no—
1059#470—531no—
1060#469—531no—
1061#469—531no—
1062#468—531no—
1063#468—531no—
1064#468—531no—
1065#468—531no—
1066#468—531no—
1067#468—531no—
1068#468—531no—
1069#468—531no—
1070#468—531no—
1071#467—531no—
1072#467—531no—
1073#466—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#451—531no—
1100#451—531no—
1101#451—531no—
1102#450—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#449—531no—
1117#449—531no—
1118#448—531no—
1119#448—531no—
1120#448—531no—
1121#447—531no—
1122#447—531no—
1123#441—531no—
1124#440—531no—
1125#440—531no—
1126#440—531no—
1127C4×Q16—531no—
1128C4×Q16—531no—
1129C4×SD16—531no—
1130C4×D8—531no—
1131#436—531no—
1132#436—531no—
1133#436—531no—
1134#436—531no—
1135#435—531no—
1136#435—531no—
1137#435—531no—
1138#435—531no—
1139#433—531no—
1140#433—531no—
1141#419—531no—
1142#418—531no—
1143#418—531no—
1144#417—531no—
1145#417—531no—
1146#417—531no—
1147#416—531no—
1148C2×#102—531no—
1149#408—531no—
1150#408—531no—
1151#407—531no—
1152#407—531no—
1153C53#6165411yescharacteristic, complemented, Sylow
1154H(5,𝔽2)—42no—
1155H(5,𝔽2)—42no—
1156C2×#41—21no—
1157C2×#41—21no—
1158C2×#41—21no—
1159C2×#41—42no—
1160C2×#41—42no—
1161C2×#41—531no—
1162C2×#41—531no—
1163C2×#41C22×D5311yescharacteristic
1164C2×#41C22×D5311yescharacteristic
1165C2×#41C22×D5311yescharacteristic
1166C2×#41C22×D5311yescharacteristic
1167C2×#41C22×D5311yescharacteristic
1168C2×#41C22×D5311yescharacteristic
1169C2×#41C22×D5311yescharacteristic
1170C22×Q8—531no—
1171C22×Q8—531no—
1172C22×Q8C22×D5311yescharacteristic
1173C22×D4—21no—
1174C22×D4—21no—
1175C22×D4—21no—
1176C22×D4—21no—
1177C22×D4—21no—
1178C22×D4—21no—
1179C22×D4—21no—
1180C22×D4C22×D5311yescharacteristic
1181C22×D4C22×D5311yescharacteristic
1182C22×D4C22×D5311yescharacteristic
1183C22×D4C22×D5311yescharacteristic
1184C23×C4—21no—
1185C23×C4C22×D5311yescharacteristic
1186#137—2122no—
1187#137—2122no—
1188#137—2122no—
1189#137—2122no—
1190AGL(1,ℤ/8)—2122no—
1191AGL(1,ℤ/8)—2122no—
1192#135—2122no—
1193C2×Q16—531no—
1194C2×Q16—531no—
1195C2×Q16—531no—
1196C2×Q16—531no—
1197C2×Q16—531no—
1198C2×Q16—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—531no—
1213C2×SD16—2122no—
1214C2×D8—531no—
1215C2×D8—531no—
1216C2×D8—531no—
1217C2×D8—531no—
1218C2×M16—531no—
1219C2×M16—531no—
1220C2×M16—531no—
1221C2×M16—531no—
1222C2×M16—531no—
1223C2×M16—531no—
1224C22×C8—531no—
1225C22×C8—531no—
1226C4⋊Q8—531no—
1227C4⋊Q8—531no—
1228C4⋊Q8—1061no—
1229C4⋊Q8—1061no—
1230#127—21no—
1231#127—21no—
1232#127C22×D5311yescharacteristic
1233#127C22×D5311yescharacteristic
1234#126—1061no—
1235#126—1061no—
1236#126—1061no—
1237#126—1061no—
1238#126—1061no—
1239#126—1061no—
1240#126—1061no—
1241#125—531no—
1242#125—1061no—
1243#125—1061no—
1244#125—1061no—
1245#125—1061no—
1246#124—21no—
1247#124—21no—
1248#124—531no—
1249#124—1061no—
1250#124—1061no—
1251#124—1061no—
1252#124—1061no—
1253#124—1061no—
1254#124C22×D5311yescharacteristic
1255#124C22×D5311yescharacteristic
1256#123—21no—
1257#123—21no—
1258#123—1061no—
1259#123—1061no—
1260#123—1061no—
1261#123—1061no—
1262#123—1061no—
1263#123—1061no—
1264#123—1061no—
1265#123—1061no—
1266#123C22⋊D5311yescharacteristic
1267#123C22⋊D5311yescharacteristic
1268C22⋊Q8—21no—
1269C22⋊Q8—21no—
1270C22⋊Q8—21no—
1271C22⋊Q8—531no—
1272C22⋊Q8—531no—
1273C22⋊Q8—531no—
1274C22⋊Q8—531no—
1275C22⋊Q8—531no—
1276C22⋊Q8—531no—
1277C22⋊Q8—531no—
1278C22⋊Q8—531no—
1279C22⋊Q8—531no—
1280C22⋊Q8—1061no—
1281C22⋊Q8—1061no—
1282C22⋊Q8—1061no—
1283C22⋊Q8—1061no—
1284C22⋊Q8—1061no—
1285C22⋊Q8—1061no—
1286C22⋊Q8—1061no—
1287C22⋊Q8—1061no—
1288C22⋊Q8—1061no—
1289C22⋊Q8—1061no—
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—21no—
1302#121—21no—
1303#121—21no—
1304#121—21no—
1305#121—21no—
1306#121—21no—
1307#121—21no—
1308#121—21no—
1309#121—21no—
1310#121—21no—
1311#121—531no—
1312#121—531no—
1313#121—531no—
1314#121—1061no—
1315#121—1061no—
1316#121—1061no—
1317#121—1061no—
1318#121—1061no—
1319#121—1061no—
1320#121—1061no—
1321#121C22⋊D5311yescharacteristic
1322#121C22⋊D5311yescharacteristic
1323#121C22×D5311yescharacteristic
1324#121C22×D5311yescharacteristic
1325#121C22×D5311yescharacteristic
1326#121C22×D5311yescharacteristic
1327#121C22×D5311yescharacteristic
1328#121C22×D5311yescharacteristic
1329#120—21no—
1330#120—21no—
1331#120—21no—
1332#120—21no—
1333#120—21no—
1334#120—21no—
1335#120—21no—
1336#120—21no—
1337#120—1061no—
1338#120C22⋊D5311yescharacteristic
1339#120C22⋊D5311yescharacteristic
1340C4×Q8—531no—
1341C4×Q8—531no—
1342C4×Q8—531no—
1343C4×Q8—1061no—
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—531no—
1353C4×D4—1061no—
1354C4×D4—1061no—
1355C4×D4—1061no—
1356C4×D4—1061no—
1357C4×D4—1061no—
1358C4×D4—1061no—
1359C4×D4—1061no—
1360C4×D4C22×D5311yescharacteristic
1361C4×D4C22×D5311yescharacteristic
1362C4×D4C22×D5311yescharacteristic
1363C4×D4C22×D5311yescharacteristic
1364C4×D4C22×D5311yescharacteristic
1365C4×D4C22×D5311yescharacteristic
1366#117—21no—
1367#117—531no—
1368#117—531no—
1369#117—1061no—
1370#117C22×D5311yescharacteristic
1371C2×C4⋊C4—21no—
1372C2×C4⋊C4—531no—
1373C2×C4⋊C4—531no—
1374C2×C4⋊C4—1061no—
1375C2×C4⋊C4—1061no—
1376C2×C4⋊C4C22×D5311yescharacteristic
1377C2×C22⋊C4—21no—
1378C2×C22⋊C4—21no—
1379C2×C22⋊C4—21no—
1380C2×C22⋊C4—1061no—
1381#107—531no—
1382#107—531no—
1383#107—531no—
1384#107—531no—
1385#107—531no—
1386#107—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—21no—
1442C24—21no—
1443C24—21no—
1444C24—21no—
1445C24C2×C22⋊D5311yescharacteristic
1446#41—22no—
1447#41—22no—
1448#41—22no—
1449#41—22no—
1450#41—22no—
1451#41—22no—
1452#41—41no—
1453#41—41no—
1454#41—41no—
1455#41—41no—
1456#41—41no—
1457#41—41no—
1458#41—41no—
1459#41—41no—
1460#41—44no—
1461#41—44no—
1462#41—44no—
1463#41—2121no—
1464#41—2121no—
1465#41—2121no—
1466#41—2121no—
1467C2×Q8—21no—
1468C2×Q8—22no—
1469C2×Q8—41no—
1470C2×Q8—531no—
1471C2×Q8—531no—
1472C2×Q8—531no—
1473C2×Q8—1061no—
1474C2×Q8—1061no—
1475C2×Q8—1061no—
1476C2×Q8—2121no—
1477C2×Q8—2121no—
1478C2×Q8—2121no—
1479C2×Q8—2121no—
1480C2×Q8C2×C22⋊D5311yescharacteristic
1481C2×Q8C23×D5311yescharacteristic
1482C2×Q8C23×D5311yescharacteristic
1483C2×D4—21no—
1484C2×D4—22no—
1485C2×D4—22no—
1486C2×D4—22no—
1487C2×D4—21no—
1488C2×D4—21no—
1489C2×D4—21no—
1490C2×D4—21no—
1491C2×D4—21no—
1492C2×D4—21no—
1493C2×D4—21no—
1494C2×D4—21no—
1495C2×D4—21no—
1496C2×D4—21no—
1497C2×D4—21no—
1498C2×D4—21no—
1499C2×D4—21no—
1500C2×D4—21no—
1501C2×D4—21no—
1502C2×D4—21no—
1503C2×D4—21no—
1504C2×D4—21no—
1505C2×D4—21no—
1506C2×D4—41no—
1507C2×D4—41no—
1508C2×D4—41no—
1509C2×D4—41no—
1510C2×D4—41no—
1511C2×D4—44no—
1512C2×D4—44no—
1513C2×D4—44no—
1514C2×D4—44no—
1515C2×D4—82no—
1516C2×D4—82no—
1517C2×D4—82no—
1518C2×D4—531no—
1519C2×D4—1061no—
1520C2×D4—1061no—
1521C2×D4—1061no—
1522C2×D4—1061no—
1523C2×D4—1061no—
1524C2×D4C2×C22⋊D5311yescharacteristic
1525C2×D4C2×C22⋊D5311yescharacteristic
1526C2×D4C2×C22⋊D5311yescharacteristic
1527C2×D4C2×C22⋊D5311yescharacteristic
1528C2×D4C2×C22⋊D5311yescharacteristic
1529C2×D4C2×C22⋊D5311yescharacteristic
1530C2×D4C2×C22⋊D5311yescharacteristic
1531C2×D4C23×D5311yescharacteristic
1532C2×D4C23×D5311yescharacteristic
1533C2×D4C23×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—21no—
1543C22×C4—21no—
1544C22×C4—21no—
1545C22×C4—41no—
1546C22×C4—41no—
1547C22×C4—44no—
1548C22×C4—1061no—
1549C22×C4—1061no—
1550C22×C4—1061no—
1551C22×C4—1061no—
1552C22×C4—1061no—
1553C22×C4—1061no—
1554C22×C4—1061no—
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—
1589M16—2121no—
1590M16—2121no—
1591M16—2121no—
1592M16—2121no—
1593C2×C8—531no—
1594C2×C8—531no—
1595C2×C8—531no—
1596C2×C8—531no—
1597C2×C8—531no—
1598C2×C8—531no—
1599C2×C8—531no—
1600C2×C8—531no—
1601C2×C8—2121no—
1602C2×C8—2121no—
1603C4⋊C4—21no—
1604C4⋊C4—21no—
1605C4⋊C4—21no—
1606C4⋊C4—21no—
1607C4⋊C4—21no—
1608C4⋊C4—531no—
1609C4⋊C4—531no—
1610C4⋊C4—531no—
1611C4⋊C4—531no—
1612C4⋊C4—1061no—
1613C4⋊C4—1061no—
1614C4⋊C4—1061no—
1615C4⋊C4—1061no—
1616C4⋊C4—1061no—
1617C4⋊C4—1061no—
1618C4⋊C4—1061no—
1619C4⋊C4—1061no—
1620C4⋊C4—1061no—
1621C4⋊C4—1061no—
1622C4⋊C4—1061no—
1623C4⋊C4—1061no—
1624C4⋊C4—1061no—
1625C4⋊C4—1061no—
1626C4⋊C4—1061no—
1627C4⋊C4—1061no—
1628C4⋊C4—1061no—
1629C4⋊C4—1061no—
1630C4⋊C4—1061no—
1631C4⋊C4C2×C22⋊D5311yescharacteristic
1632C4⋊C4C2×C22⋊D5311yescharacteristic
1633C4⋊C4C2×C22⋊D5311yescharacteristic
1634C4⋊C4C2×C22⋊D5311yescharacteristic
1635C4⋊C4C2×C22⋊D5311yescharacteristic
1636C4⋊C4C2×C22⋊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—1061no—
1654C22⋊C4—1061no—
1655C22⋊C4—1061no—
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—1061no—
1683C42—1061no—
1684C42—1061no—
1685C42—1061no—
1686C42—1061no—
1687C42C23×D5311yescharacteristic
1688C42C23×D5311yescharacteristic
1689C23—21no—
1690C23—21no—
1691C23—21no—
1692C23—21no—
1693C23—41no—
1694C23—41no—
1695C23—41no—
1696C23—42no—
1697C23—42no—
1698C23—42no—
1699C23—42no—
1700C23—42no—
1701C23—81no—
1702C23—81no—
1703C23—81no—
1704C23—81no—
1705C23—81no—
1706C23—81no—
1707C23—81no—
1708C23—1061no—
1709C23C22×C22⋊D5311yescharacteristic
1710C23C22×C22⋊D5311yescharacteristic
1711C23C22×C22⋊D5311yescharacteristic
1712C23C22×C22⋊D5311yescharacteristic
1713C23C22×C22⋊D5311yescharacteristic
1714Q8—21no—
1715Q8—21no—
1716Q8—21no—
1717Q8—41no—
1718Q8—42no—
1719Q8—1061no—
1720Q8—1061no—
1721Q8—1061no—
1722Q8—1061no—
1723Q8—1061no—
1724Q8—1061no—
1725Q8—4241no—
1726Q8—4241no—
1727Q8—4241no—
1728Q8#1313326212yes—
1729D4—24no—
1730D4—21no—
1731D4—21no—
1732D4—21no—
1733D4—21no—
1734D4—21no—
1735D4—21no—
1736D4—21no—
1737D4—41no—
1738D4—41no—
1739D4—41no—
1740D4—41no—
1741D4—41no—
1742D4—41no—
1743D4—41no—
1744D4—42no—
1745D4—42no—
1746D4—42no—
1747D4—42no—
1748D4—42no—
1749D4—42no—
1750D4—42no—
1751D4—42no—
1752D4—42no—
1753D4—42no—
1754D4—42no—
1755D4—81no—
1756D4—81no—
1757D4—81no—
1758D4—81no—
1759D4—81no—
1760D4—81no—
1761D4—81no—
1762D4—81no—
1763D4—1061no—
1764D4—1061no—
1765D4—4241no—
1766D4—4241no—
1767D4—4241no—
1768D4—4241no—
1769D4—2122no—
1770D4#1313326212yes—
1771C2×C4—24no—
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—41no—
1787C2×C4—41no—
1788C2×C4—41no—
1789C2×C4—42no—
1790C2×C4—42no—
1791C2×C4—42no—
1792C2×C4—42no—
1793C2×C4—42no—
1794C2×C4—42no—
1795C2×C4—81no—
1796C2×C4—81no—
1797C2×C4—81no—
1798C2×C4—1061no—
1799C2×C4—1061no—
1800C2×C4—1061no—
1801C2×C4—1061no—
1802C2×C4—1061no—
1803C2×C4—1061no—
1804C2×C4—1061no—
1805C2×C4—4241no—
1806C2×C4—4241no—
1807C2×C4—4241no—
1808C2×C4—4241no—
1809C2×C4—4241no—
1810C2×C4—4241no—
1811C2×C4—4241no—
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—22no—
1834C22—21no—
1835C22—21no—
1836C22—21no—
1837C22—21no—
1838C22—21no—
1839C22—21no—
1840C22—21no—
1841C22—21no—
1842C22—21no—
1843C22—21no—
1844C22—21no—
1845C22—21no—
1846C22—41no—
1847C22—41no—
1848C22—41no—
1849C22—41no—
1850C22—41no—
1851C22—41no—
1852C22—41no—
1853C22—41no—
1854C22—41no—
1855C22—41no—
1856C22—41no—
1857C22—82no—
1858C22—84no—
1859C22—162no—
1860C22—162no—
1861C22—162no—
1862C22—2121no—
1863C22—2121no—
1864C22—2121no—
1865C22C23×C22⋊D5311yescharacteristic
1866C4—21no—
1867C4—22no—
1868C4—21no—
1869C4—21no—
1870C4—21no—
1871C4—21no—
1872C4—21no—
1873C4—21no—
1874C4—21no—
1875C4—21no—
1876C4—41no—
1877C4—41no—
1878C4—41no—
1879C4—2121no—
1880C4—2121no—
1881C4—2121no—
1882C4—2121no—
1883C4—2121no—
1884C4—2121no—
1885C4—2121no—
1886C4C2×#1313326211yescharacteristic
1887C4C2×#1313326211yescharacteristic
1888C2—41no—
1889C2—41no—
1890C2—41no—
1891C2—41no—
1892C2—41no—
1893C2—42no—
1894C2—81no—
1895C2—81no—
1896C2—81no—
1897C2—4241no—
1898C2#2028835011yescharacteristic
1899C2#2028949511yescharacteristic
1900C2#2028950111yescharacteristic
subgroupG/H
centerC22C23×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3488C2
socleC22×C53C23×D4
hypercenter#3488D53
hypocenterC53#61654
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ #525 ◁ #3488

Complements

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

NH ≅ G/Ntype
1. #20289008C2semidirect
2. #20287053C2semidirect
3. #20286983C2semidirect
4. #20286946C2semidirect
5. #20286916C2semidirect
6. #20286796C2semidirect
7. #20286781C2semidirect
8. #20286736C2semidirect
9. #20286721C2semidirect
10. #20286381C2semidirect
11. #20286368C2semidirect
12. #20286342C2semidirect
13. #20286311C2semidirect
14. #20286296C2semidirect
15. #20286271C2semidirect
16. #20286221C2semidirect
17. #20286206C2semidirect
18. #20285809C2semidirect
19. #20285787C2semidirect
20. #20285612C2semidirect
21. #20285591C2semidirect
22. #20285529C2semidirect
23. #20285521C2semidirect
24. #20284977C2semidirect
25. #20284929C2semidirect
26. #20284019C2semidirect
27. #20283992C2semidirect
28. #20283975C2semidirect
29. #20283957C2semidirect
30. #20283777C2semidirect
31. C53×#3488C2semidirect
32. C2×#13133248C22semidirect
33. C2×#13133247C22semidirect
34. C2×#13133247C22semidirect
35. C2×#13133247C22semidirect
36. C2×#13133243C22semidirect
37. C2×#13133243C22semidirect
38. C2×#13133237C22semidirect
39. C22×#11719923C22semidirect
42. #16811343C22semidirect
43. #16811330C22semidirect
45. #16811319C22semidirect
47. #16811313C22semidirect
48. D4×Dic106C22semidirect
49. #16811282C22semidirect
50. #16811282C22semidirect
51. #16811278C22semidirect
52. #16811244C22semidirect
54. #16811235C22semidirect
58. #16811201C22semidirect
59. #16811194C22semidirect
60. #16811134C22semidirect
61. C2×#13133196C22semidirect
62. #16811018C22semidirect
63. #16811010C22semidirect
64. #16811005C22semidirect
65. #16810995C22semidirect
66. #16810987C22semidirect
67. #16810982C22semidirect
68. #16810977C22semidirect
69. #16810969C22semidirect
70. #16810961C22semidirect
71. #16810958C22semidirect
72. #16810958C22semidirect
73. #16810956C22semidirect
74. #16810953C22semidirect
75. #16810944C22semidirect
76. #16810944C22semidirect
77. #16810944C22semidirect
78. #16810936C22semidirect
79. #16810934C22semidirect
80. #16810934C22semidirect
81. #16810934C22semidirect
82. #16810930C22semidirect
83. #16810923C22semidirect
84. #16810918C22semidirect
85. #16810903C22semidirect
86. #16810879C22semidirect
87. #16810874C22semidirect
88. #16810874C22semidirect
89. #16810871C22semidirect
90. #16810867C22semidirect
91. #16810867C22semidirect
92. #16810867C22semidirect
93. #16810867C22semidirect
94. #16810867C22semidirect
95. #16810867C22semidirect
96. #16810867C22semidirect
97. #16810867C22semidirect
98. #16810862C22semidirect
99. #16810862C22semidirect
100. #16810857C22semidirect
101. #16810850C22semidirect
102. #16810845C22semidirect
103. #16810842C22semidirect
104. #16810842C22semidirect
105. #16810842C22semidirect
106. #16810838C22semidirect
107. #16810835C22semidirect
108. #16810833C22semidirect
109. #16810828C22semidirect
110. #16810820C22semidirect
111. #16810820C22semidirect
112. #16810820C22semidirect
113. #16810815C22semidirect
117. #16810785C22semidirect
118. #16810785C22semidirect
119. #16810785C22semidirect
120. #16810785C22semidirect
121. #16810785C22semidirect
122. #16810785C22semidirect
123. #16810785C22semidirect
124. #16810785C22semidirect
125. #16810783C22semidirect
126. #16810779C22semidirect
127. #16810779C22semidirect
128. #16810778C22semidirect
129. #16810774C22semidirect
130. #16810774C22semidirect
131. #16810774C22semidirect
132. #16810774C22semidirect
133. #16810774C22semidirect
134. #16810774C22semidirect
135. #16810774C22semidirect
136. #16810774C22semidirect
138. #16810768C22semidirect
139. #16810768C22semidirect
140. #16810768C22semidirect
141. #16810768C22semidirect
142. #16810766C22semidirect
143. #16810766C22semidirect
144. #16810766C22semidirect
145. #16810761C22semidirect
146. #16810761C22semidirect
147. #16810761C22semidirect
148. #16810757C22semidirect
149. #16810757C22semidirect
150. #16810728C22semidirect
151. #16810723C22semidirect
152. #16810723C22semidirect
153. #16810721C22semidirect
154. C4×#11719925C22semidirect
155. C4×#11719925C22semidirect
156. C4×#11719923C22semidirect
157. C4×#11719922C22semidirect
158. #16810701C22semidirect
159. #16810701C22semidirect
160. #16810701C22semidirect
161. #16810701C22semidirect
162. #16810695C22semidirect
163. #16810695C22semidirect
164. #16810695C22semidirect
165. #16810695C22semidirect
166. #16810684C22semidirect
167. #16810684C22semidirect
168. #16810632C22semidirect
169. #16810628C22semidirect
170. #16810628C22semidirect
171. #16810624C22semidirect
172. #16810624C22semidirect
173. #16810624C22semidirect
174. #16810619C22semidirect
175. C2×#13133138C22semidirect
176. #16810590C22semidirect
177. #16810590C22semidirect
178. #16810587C22semidirect
179. #16810587C22semidirect
939. #3488D53semidirect
1153. C53#61654semidirect

Maximal subgroups

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

subgroupindex
#202890082
#202870532
#202869832
#202869462
#202869162
#202867962
#202867812
#202867362
#202867212
#202863812
#202863682
#202863422
#202863112
#202862962
#202862712
#202862212
#202862062
#202858092
#202857872
#202856122
#202855912
#202855292
#202855212
#202849772
#202849292
#202840192
#202839922
#202839752
#202839572
#202837772
C53×#34882
#6165453