Finite Group Databasebeta

← #62497

Subgroups — #62497

Order 256.

820 conjugacy classes of subgroups.

The subgroup lattice has 801 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3565C211yesmaximal, characteristic, complemented
2#3544C211yesmaximal, characteristic, complemented
3#3389C211yesmaximal, characteristic, complemented
4#3388C211yesmaximal, characteristic, complemented
5#3387C211yesmaximal, characteristic, complemented
6#3385C211yesmaximal, characteristic, complemented
7#3354C211yesmaximal, characteristic, complemented
8#3353C211yesmaximal, characteristic, complemented
9#3352C211yesmaximal, characteristic, complemented
10#3351C211yesmaximal, characteristic, complemented
11#3349C211yesmaximal, characteristic, complemented
12#3348C211yesmaximal, characteristic, complemented
13#3348C211yesmaximal, characteristic, complemented
14#3347C211yesmaximal, characteristic, complemented
15#3346C211yesmaximal, characteristic, complemented
16#3345C211yesmaximal, characteristic, complemented
17#3344C211yesmaximal, characteristic, complemented
18#3343C211yesmaximal, characteristic, complemented
19#3244C211yesmaximal, characteristic, complemented
20#3244C211yesmaximal, characteristic, complemented
21#3243C211yesmaximal, characteristic, complemented
22#3243C211yesmaximal, characteristic, complemented
23#3240C211yesmaximal, characteristic, complemented
24#3239C211yesmaximal, characteristic, complemented
25#3183C211yesmaximal, characteristic, complemented
26#3175C211yesmaximal, characteristic, complemented
27#3173C211yesmaximal, characteristic, complemented
28#3165C211yesmaximal, characteristic, complemented
29#3164C211yesmaximal, characteristic, complemented
30#3163C211yesmaximal, characteristic, complemented
31#2967C211yesmaximal, characteristic, complemented
32#563—21no—
33#563—21no—
34#563—21no—
35#562—21no—
36Q82C2211yescharacteristic
37#557C2211yescharacteristic
38#556—21no—
39#556C2211yescharacteristic
40#555C2211yescharacteristic
41#555C2211yescharacteristic
42#554C2211yescharacteristic
43#554C2211yescharacteristic
44#554C2211yescharacteristic
45#553C2211yescharacteristic
46#553C2211yescharacteristic
47#552—21no—
48#552—21no—
49#552C2211yescharacteristic
50#552C2211yescharacteristic
51#552C2211yescharacteristic
52#552C2211yescharacteristic
53#547—21no—
54#547C2211yescharacteristic
55#547C2211yescharacteristic
56#544—21no—
57#544C2211yescharacteristic
58#544C2211yescharacteristic
59#544C2211yescharacteristic
60#544C2211yescharacteristic
61#542—21no—
62#542—21no—
63#542—21no—
64#542C2211yescharacteristic
65#542C2211yescharacteristic
66#542C2211yescharacteristic
67#542C2211yescharacteristic
68#541—21no—
69#539—21no—
70#536—21no—
71#536—21no—
72#533C2211yescharacteristic
73C2×C4⋊Q8C2211yescharacteristic
74#529C2211yescharacteristic
75#529C2211yescharacteristic
76#529C2211yescharacteristic
77#501C2211yescharacteristic
78#501C2211yescharacteristic
79#501C2211yescharacteristic
80#501C2211yescharacteristic
81#501C2211yescharacteristic
82#501C2211yescharacteristic
83#501C2211yescharacteristic
84#501C2211yescharacteristic
85#501C2211yescharacteristic
86#501C2211yescharacteristic
87#501C2211yescharacteristic
88#501C2211yescharacteristic
89#500C2211yescharacteristic
90#500C2211yescharacteristic
91#500C2211yescharacteristic
92#499C2211yescharacteristic
93#499C2211yescharacteristic
94#499C2211yescharacteristic
95#498C2211yescharacteristic
96#498C2211yescharacteristic
97#498C2211yescharacteristic
98#495C2211yescharacteristic
99#489C2211yescharacteristic
100#489C2211yescharacteristic
101#489C2211yescharacteristic
102#489C2211yescharacteristic
103#488C2211yescharacteristic
104#488C2211yescharacteristic
105#485C2211yescharacteristic
106#485C2211yescharacteristic
107#485C2211yescharacteristic
108#485C2211yescharacteristic
109#485C2211yescharacteristic
110#485C2211yescharacteristic
111#484C2211yescharacteristic
112#484C2211yescharacteristic
113#484C2211yescharacteristic
114#484C2211yescharacteristic
115#483C2211yescharacteristic
116#483C2211yescharacteristic
117#482C2211yescharacteristic
118#482C2211yescharacteristic
119#482C2211yescharacteristic
120#482C2211yescharacteristic
121#482C2211yescharacteristic
122#482C2211yescharacteristic
123#481C2211yescharacteristic
124#481C2211yescharacteristic
125#481C2211yescharacteristic
126#481C2211yescharacteristic
127#480C2211yescharacteristic
128#480C2211yescharacteristic
129#479C2211yescharacteristic
130#479C2211yescharacteristic
131#479C2211yescharacteristic
132#479C2211yescharacteristic
133#479C2211yescharacteristic
134#479C2211yescharacteristic
135#478C2211yescharacteristic
136#478C2211yescharacteristic
137#478C2211yescharacteristic
138#478C2211yescharacteristic
139#478C2211yescharacteristic
140#478C2211yescharacteristic
141#477C2211yescharacteristic
142#477C2211yescharacteristic
143#476C2211yescharacteristic
144#476C2211yescharacteristic
145#475C2211yescharacteristic
146#475C2211yescharacteristic
147#475C2211yescharacteristic
148#475C2211yescharacteristic
149#474C2211yescharacteristic
150#474C2211yescharacteristic
151#474C2211yescharacteristic
152#474C2211yescharacteristic
153#470C2211yescharacteristic
154#470C2211yescharacteristic
155#469C2211yescharacteristic
156#469C2211yescharacteristic
157#468C2211yescharacteristic
158#468C2211yescharacteristic
159#468C2211yescharacteristic
160#468C2211yescharacteristic
161#467C2211yescharacteristic
162#466C2211yescharacteristic
163#465C2211yescharacteristic
164#465C2211yescharacteristic
165#446C2211yescharacteristic
166#446C2211yescharacteristic
167#442C2211yescharacteristic
168#442C2211yescharacteristic
169#441C2211yescharacteristic
170#441C2211yescharacteristic
171#440C2211yescharacteristic
172#440C2211yescharacteristic
173#440C2211yescharacteristic
174#440C2211yescharacteristic
175C4×Q16C2211yescharacteristic
176C4×SD16C2211yescharacteristic
177C4×SD16C2211yescharacteristic
178C4×D8C2211yescharacteristic
179#436C2211yescharacteristic
180#436C2211yescharacteristic
181#435C2211yescharacteristic
182#435C2211yescharacteristic
183#435C2211yescharacteristic
184#435C2211yescharacteristic
185#433C2211yescharacteristic
186#433C2211yescharacteristic
187#432C2211yescharacteristic
188#428C2211yescharacteristic
189#428C2211yescharacteristic
190#428C2211yescharacteristic
191#428C2211yescharacteristic
192#428C2211yescharacteristic
193#428C2211yescharacteristic
194#428C2211yescharacteristic
195#428C2211yescharacteristic
196#427C2211yescharacteristic
197#427C2211yescharacteristic
198C2×#107C2211yescharacteristic
199C2×#106C2211yescharacteristic
200#405C2211yescharacteristic
201#405C2211yescharacteristic
202C4×M16C2211yescharacteristic
203C2×#41—21no—
204C2×#41—21no—
205C22×Q8—21no—
206C2×Q16C2311yescharacteristic
207C2×SD16C2311yescharacteristic
208C2×SD16C2311yescharacteristic
209C2×D8C2311yescharacteristic
210C2×M16C2311yescharacteristic
211C2×M16C2311yescharacteristic
212C2×M16C2311yescharacteristic
213C2×M16C2311yescharacteristic
214C22×C8C2311yescharacteristic
215C22×C8C2311yescharacteristic
216C4⋊Q8—21no—
217C4⋊Q8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8C2311yescharacteristic
227C4⋊Q8C2311yescharacteristic
228C4⋊Q8C2311yescharacteristic
229C4⋊Q8C2311yescharacteristic
230C4⋊Q8C2311yescharacteristic
231C4⋊Q8C2311yescharacteristic
232C4⋊Q8C2311yescharacteristic
233C4⋊Q8C2311yescharacteristic
234C4⋊Q8C2311yescharacteristic
235C4⋊Q8C2311yescharacteristic
236#126—21no—
237#126—21no—
238#126—21no—
239#126—21no—
240#126—21no—
241#126—21no—
242#126—21no—
243#126—21no—
244#126—21no—
245#126—21no—
246#126—21no—
247#126—21no—
248#126—21no—
249#126—21no—
250#126D411yescharacteristic
251#126D411yescharacteristic
252#125—21no—
253#125—21no—
254#125—21no—
255#125—21no—
256#125—21no—
257#125—21no—
258#125—21no—
259#125—21no—
260#125—21no—
261#125—21no—
262#125—21no—
263#125D411yescharacteristic
264#125C2311yescharacteristic
265#125C2311yescharacteristic
266#125C2311yescharacteristic
267#125C2311yescharacteristic
268#125C2311yescharacteristic
269#125C2311yescharacteristic
270#125C2311yescharacteristic
271#125C2311yescharacteristic
272#124—21no—
273#124—21no—
274#124—21no—
275#124—21no—
276#124—21no—
277#124—21no—
278#124—21no—
279#124—21no—
280#124—21no—
281#124D411yescharacteristic
282#124C2311yescharacteristic
283#124C2311yescharacteristic
284#123—21no—
285#123—21no—
286#123—21no—
287#123—21no—
288#123—21no—
289#123—21no—
290#123—21no—
291#123—21no—
292#123—21no—
293#123—21no—
294#123—21no—
295#123—21no—
296#123—21no—
297#123—21no—
298#123—21no—
299#123—21no—
300#123D411yescharacteristic
301#123D411yescharacteristic
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—21no—
305C22⋊Q8—21no—
306C22⋊Q8—21no—
307C22⋊Q8—21no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310C22⋊Q8—21no—
311C22⋊Q8—21no—
312C22⋊Q8—21no—
313C22⋊Q8—21no—
314C22⋊Q8—21no—
315C22⋊Q8—21no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C22⋊Q8—21no—
323C22⋊Q8—21no—
324C22⋊Q8—21no—
325C22⋊Q8—21no—
326C22⋊Q8D411yescharacteristic
327C22⋊Q8C2311yescharacteristic
328C22⋊Q8C2311yescharacteristic
329C22⋊Q8C2311yescharacteristic
330C22⋊Q8C2311yescharacteristic
331C22⋊Q8C2311yescharacteristic
332C22⋊Q8C2311yescharacteristic
333#121—21no—
334#121—21no—
335#121—21no—
336#121—21no—
337#121D411yescharacteristic
338#121C2311yescharacteristic
339#121C2311yescharacteristic
340#121C2311yescharacteristic
341#121C2311yescharacteristic
342#121C2311yescharacteristic
343#121C2311yescharacteristic
344C4×Q8—21no—
345C4×Q8—21no—
346C4×Q8—21no—
347C4×Q8—21no—
348C4×Q8—21no—
349C4×Q8C2311yescharacteristic
350C4×Q8C2311yescharacteristic
351C4×Q8C2311yescharacteristic
352C4×Q8C2311yescharacteristic
353C4×Q8C2311yescharacteristic
354C4×Q8C2311yescharacteristic
355C4×Q8C2311yescharacteristic
356C4×D4—21no—
357C4×D4—21no—
358C4×D4—21no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4C2311yescharacteristic
362C4×D4C2311yescharacteristic
363C4×D4C2311yescharacteristic
364C4×D4C2311yescharacteristic
365C4×D4C2311yescharacteristic
366C4×D4C2311yescharacteristic
367C4×D4C2311yescharacteristic
368C4×D4C2311yescharacteristic
369C4×D4C2311yescharacteristic
370#117—21no—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117C2311yescharacteristic
379#117C2311yescharacteristic
380#117C2311yescharacteristic
381#117C2311yescharacteristic
382#117C2311yescharacteristic
383#117C2311yescharacteristic
384#117C2311yescharacteristic
385#117C2311yescharacteristic
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4C2311yescharacteristic
390C2×C4⋊C4C2311yescharacteristic
391C2×C4⋊C4C2311yescharacteristic
392C2×C4⋊C4C2311yescharacteristic
393C2×C4⋊C4C2311yescharacteristic
394C2×C4⋊C4C2311yescharacteristic
395C2×C42C2311yescharacteristic
396#107C2311yescharacteristic
397#107C2311yescharacteristic
398#107C2311yescharacteristic
399#107C2311yescharacteristic
400#107C2311yescharacteristic
401#107C2311yescharacteristic
402#107C2311yescharacteristic
403#107C2311yescharacteristic
404#107C2311yescharacteristic
405#107C2311yescharacteristic
406#107C2311yescharacteristic
407#107C2311yescharacteristic
408#107C2311yescharacteristic
409#107C2311yescharacteristic
410#107C2311yescharacteristic
411#107C2311yescharacteristic
412#107C2311yescharacteristic
413#107C2311yescharacteristic
414#106C2311yescharacteristic
415#106C2311yescharacteristic
416#106C2311yescharacteristic
417#106C2311yescharacteristic
418#106C2311yescharacteristic
419#106C2311yescharacteristic
420#106C2311yescharacteristic
421#106C2311yescharacteristic
422#106C2311yescharacteristic
423#106C2311yescharacteristic
424#106C2311yescharacteristic
425#106C2311yescharacteristic
426#106C2311yescharacteristic
427#106C2311yescharacteristic
428#106C2311yescharacteristic
429#106C2311yescharacteristic
430#106C2311yescharacteristic
431#106C2311yescharacteristic
432C4⋊C8C2311yescharacteristic
433C4⋊C8C2311yescharacteristic
434C4⋊C8C2311yescharacteristic
435C4⋊C8C2311yescharacteristic
436C4⋊C8C2311yescharacteristic
437C4⋊C8C2311yescharacteristic
438#103C2311yescharacteristic
439#103C2311yescharacteristic
440#103C2311yescharacteristic
441#103C2311yescharacteristic
442#103C2311yescharacteristic
443#103C2311yescharacteristic
444#103C2311yescharacteristic
445#103C2311yescharacteristic
446#103C2311yescharacteristic
447#103C2311yescharacteristic
448#103C2311yescharacteristic
449#103C2311yescharacteristic
450#102C2311yescharacteristic
451#102C2311yescharacteristic
452#102C2311yescharacteristic
453#102C2311yescharacteristic
454#102C2311yescharacteristic
455#102C2311yescharacteristic
456#102C2311yescharacteristic
457#102C2311yescharacteristic
458#102C2311yescharacteristic
459#102C2311yescharacteristic
460#102C2311yescharacteristic
461#102C2311yescharacteristic
462C22⋊C8C2311yescharacteristic
463C22⋊C8C2311yescharacteristic
464C22⋊C8C2311yescharacteristic
465C22⋊C8C2311yescharacteristic
466C22⋊C8C2311yescharacteristic
467C22⋊C8C2311yescharacteristic
468#97C2311yescharacteristic
469#97C2311yescharacteristic
470#97C2311yescharacteristic
471#97C2311yescharacteristic
472#97C2311yescharacteristic
473#97C2311yescharacteristic
474C4×C8C2311yescharacteristic
475C4×C8C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478#41—82no—
479#41—82no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—82no—
491C2×Q8C2×D411yescharacteristic
492C2×Q8C2411yescharacteristic
493C2×Q8C2411yescharacteristic
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4C2×D411yescharacteristic
501C2×D4C2×D411yescharacteristic
502C2×D4C2×D411yescharacteristic
503C2×D4C2411yescharacteristic
504C2×D4C2411yescharacteristic
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4C2×D411yescharacteristic
518C22×C4C2×D411yescharacteristic
519C22×C4C2411yescharacteristic
520C22×C4C2411yescharacteristic
521C22×C4C2411yescharacteristic
522Q16—22no—
523SD16—22no—
524SD16—22no—
525D8—22no—
526M16—22no—
527M16—22no—
528M16—22no—
529M16—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8C2411yescharacteristic
533C2×C8C2411yescharacteristic
534C2×C8C2411yescharacteristic
535C2×C8C2411yescharacteristic
536C2×C8C2411yescharacteristic
537C2×C8C2411yescharacteristic
538C2×C8C2411yescharacteristic
539C2×C8C2411yescharacteristic
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4C2×D411yescharacteristic
585C4⋊C4C2×D411yescharacteristic
586C4⋊C4C2×D411yescharacteristic
587C4⋊C4C2×D411yescharacteristic
588C4⋊C4C2×D411yescharacteristic
589C4⋊C4C2×D411yescharacteristic
590C4⋊C4C2×D411yescharacteristic
591C4⋊C4C2×D411yescharacteristic
592C4⋊C4C2×D411yescharacteristic
593C4⋊C4C2×D411yescharacteristic
594C4⋊C4C2411yescharacteristic
595C4⋊C4C2411yescharacteristic
596C4⋊C4C2411yescharacteristic
597C4⋊C4C2411yescharacteristic
598C4⋊C4C2411yescharacteristic
599C4⋊C4C2411yescharacteristic
600C4⋊C4C2411yescharacteristic
601C4⋊C4C2411yescharacteristic
602C4⋊C4C2411yescharacteristic
603C4⋊C4C2411yescharacteristic
604C4⋊C4C2411yescharacteristic
605C4⋊C4C2411yescharacteristic
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—21no—
609C22⋊C4—21no—
610C22⋊C4—21no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—21no—
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4C2×D411yescharacteristic
635C22⋊C4C2×D411yescharacteristic
636C22⋊C4C2×D411yescharacteristic
637C22⋊C4C2×D411yescharacteristic
638C22⋊C4C2×D411yescharacteristic
639C22⋊C4C2×D411yescharacteristic
640C22⋊C4C2×D411yescharacteristic
641C22⋊C4C2×D411yescharacteristic
642C22⋊C4C2×D411yescharacteristic
643C22⋊C4C2×D411yescharacteristic
644C42—21no—
645C42—21no—
646C42—21no—
647C42—21no—
648C42—21no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42—21no—
654C42—21no—
655C42—21no—
656C42C2×D411yescharacteristic
657C42C2×D411yescharacteristic
658C42C2411yescharacteristic
659C42C2411yescharacteristic
660C42C2411yescharacteristic
661C42C2411yescharacteristic
662C23—21no—
663C23—21no—
664C23C22×D411yescharacteristic
665C23C22×D411yescharacteristic
666C23C22×D411yescharacteristic
667Q8—21no—
668Q8—21no—
669Q8—21no—
670Q8—21no—
671Q8—41no—
672Q8—81no—
673Q8—81no—
674Q8—81no—
675Q8—81no—
676Q8—81no—
677Q8—81no—
678Q8—81no—
679Q8—81no—
680Q8—81no—
681Q8—81no—
682D4—21no—
683D4—21no—
684D4—21no—
685D4—21no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—42no—
690D4—81no—
691D4—81no—
692D4—81no—
693D4—81no—
694D4—81no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—81no—
724C2×C4—81no—
725C2×C4—81no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4C22×D411yescharacteristic
730C2×C4C22×D411yescharacteristic
731C2×C4C22×D411yescharacteristic
732C2×C4C22×D411yescharacteristic
733C2×C4C22×D411yescharacteristic
734C2×C4C22×D411yescharacteristic
735C2×C4C22×D411yescharacteristic
736C2×C4C22×D411yescharacteristic
737C2×C4C22×D411yescharacteristic
738C2×C4C22×D411yescharacteristic
739C2×C4C22×D411yescharacteristic
740C2×C4C2511yescharacteristic
741C8—21no—
742C8—21no—
743C8—21no—
744C8—21no—
745C8—21no—
746C8—21no—
747C82−1+412yes—
748C82−1+412yes—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22C23×D411yescharacteristic
765C4—21no—
766C4—21no—
767C4—21no—
768C4—21no—
769C4—21no—
770C4—21no—
771C4—21no—
772C4—21no—
773C4—21no—
774C4—21no—
775C4—21no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4C2×2−1+411yescharacteristic
791C4C2×2−1+411yescharacteristic
792C2—41no—
793C2—41no—
794C2—41no—
795C2—81no—
796C2—81no—
797C2#349911yescharacteristic
798C2#358511yescharacteristic
799C2#358611yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #529 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3565C2semidirect
2. #3544C2semidirect
3. #3389C2semidirect
4. #3388C2semidirect
5. #3387C2semidirect
6. #3385C2semidirect
7. #3354C2semidirect
8. #3353C2semidirect
9. #3352C2semidirect
10. #3351C2semidirect
11. #3349C2semidirect
12. #3348C2semidirect
13. #3348C2semidirect
14. #3347C2semidirect
15. #3346C2semidirect
16. #3345C2semidirect
17. #3344C2semidirect
18. #3343C2semidirect
19. #3244C2semidirect
20. #3244C2semidirect
21. #3243C2semidirect
22. #3243C2semidirect
23. #3240C2semidirect
24. #3239C2semidirect
25. #3183C2semidirect
26. #3175C2semidirect
27. #3173C2semidirect
28. #3165C2semidirect
29. #3164C2semidirect
30. #3163C2semidirect
31. #2967C2semidirect

Maximal subgroups

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

subgroupindex
#35652
#35442
#33892
#33882
#33872
#33852
#33542
#33532
#33522
#33512
#33492
#33482
#33472
#33462
#33452
#33442
#33432
#32442
#32432
#32402
#32392
#31832
#31752
#31732
#31652
#31642
#31632
#29672