Finite Group Databasebeta

← #62524

Subgroups — #62524

Order 256.

827 conjugacy classes of subgroups.

The subgroup lattice has 809 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3565C211yesmaximal, characteristic, complemented
2#3559C211yesmaximal, characteristic, complemented
3#3389C211yesmaximal, characteristic, complemented
4#3388C211yesmaximal, characteristic, complemented
5#3381C211yesmaximal, characteristic, complemented
6#3380C211yesmaximal, characteristic, complemented
7#3355C211yesmaximal, characteristic, complemented
8#3355C211yesmaximal, characteristic, complemented
9#3354C211yesmaximal, characteristic, complemented
10#3353C211yesmaximal, characteristic, complemented
11#3351C211yesmaximal, characteristic, complemented
12#3351C211yesmaximal, characteristic, complemented
13#3350C211yesmaximal, characteristic, complemented
14#3347C211yesmaximal, characteristic, complemented
15#3345C211yesmaximal, characteristic, complemented
16#3343C211yesmaximal, characteristic, complemented
17#3339C211yesmaximal, characteristic, complemented
18#3337C211yesmaximal, characteristic, complemented
19#3244C211yesmaximal, characteristic, complemented
20#3243C211yesmaximal, characteristic, complemented
21#3241C211yesmaximal, characteristic, complemented
22#3241C211yesmaximal, characteristic, complemented
23#3232C211yesmaximal, characteristic, complemented
24#3228C211yesmaximal, characteristic, complemented
25#3179C211yesmaximal, characteristic, complemented
26#3179C211yesmaximal, characteristic, complemented
27#3171C211yesmaximal, characteristic, complemented
28#3166C211yesmaximal, characteristic, complemented
29#3164C211yesmaximal, characteristic, complemented
30#3163C211yesmaximal, characteristic, complemented
31#2969C211yesmaximal, characteristic, complemented
32#563—21no—
33#563—21no—
34#562—21no—
35#562—21no—
36#557C2211yescharacteristic
37#556—21no—
38#556C2211yescharacteristic
39#555C2211yescharacteristic
40#554C2211yescharacteristic
41#554C2211yescharacteristic
42#554C2211yescharacteristic
43#553C2211yescharacteristic
44#553C2211yescharacteristic
45#553C2211yescharacteristic
46#553C2211yescharacteristic
47#553C2211yescharacteristic
48#553C2211yescharacteristic
49#552—21no—
50#552C2211yescharacteristic
51#552C2211yescharacteristic
52#547—21no—
53#547—21no—
54#547C2211yescharacteristic
55#547C2211yescharacteristic
56#544C2211yescharacteristic
57#544C2211yescharacteristic
58#544C2211yescharacteristic
59#544C2211yescharacteristic
60#542—21no—
61#542—21no—
62#542C2211yescharacteristic
63#542C2211yescharacteristic
64#541—21no—
65#540C2211yescharacteristic
66#540C2211yescharacteristic
67#539—21no—
68#539—21no—
69#539—21no—
70#539—21no—
71#537—21no—
72#533C2211yescharacteristic
73#532C2211yescharacteristic
74#529C2211yescharacteristic
75#529C2211yescharacteristic
76C2×#125C2211yescharacteristic
77#501C2211yescharacteristic
78#501C2211yescharacteristic
79#501C2211yescharacteristic
80#501C2211yescharacteristic
81#501C2211yescharacteristic
82#501C2211yescharacteristic
83#501C2211yescharacteristic
84#501C2211yescharacteristic
85#501C2211yescharacteristic
86#500C2211yescharacteristic
87#500C2211yescharacteristic
88#499C2211yescharacteristic
89#499C2211yescharacteristic
90#499C2211yescharacteristic
91#499C2211yescharacteristic
92#499C2211yescharacteristic
93#499C2211yescharacteristic
94#499C2211yescharacteristic
95#499C2211yescharacteristic
96#498C2211yescharacteristic
97#498C2211yescharacteristic
98#496C2211yescharacteristic
99#490C2211yescharacteristic
100#489C2211yescharacteristic
101#488C2211yescharacteristic
102#488C2211yescharacteristic
103#486C2211yescharacteristic
104#486C2211yescharacteristic
105#485C2211yescharacteristic
106#485C2211yescharacteristic
107#484C2211yescharacteristic
108#484C2211yescharacteristic
109#483C2211yescharacteristic
110#483C2211yescharacteristic
111#482C2211yescharacteristic
112#482C2211yescharacteristic
113#482C2211yescharacteristic
114#482C2211yescharacteristic
115#482C2211yescharacteristic
116#482C2211yescharacteristic
117#482C2211yescharacteristic
118#482C2211yescharacteristic
119#482C2211yescharacteristic
120#482C2211yescharacteristic
121#481C2211yescharacteristic
122#481C2211yescharacteristic
123#481C2211yescharacteristic
124#481C2211yescharacteristic
125#480C2211yescharacteristic
126#480C2211yescharacteristic
127#480C2211yescharacteristic
128#480C2211yescharacteristic
129#479C2211yescharacteristic
130#479C2211yescharacteristic
131#479C2211yescharacteristic
132#479C2211yescharacteristic
133#478C2211yescharacteristic
134#478C2211yescharacteristic
135#478C2211yescharacteristic
136#478C2211yescharacteristic
137#478C2211yescharacteristic
138#478C2211yescharacteristic
139#478C2211yescharacteristic
140#478C2211yescharacteristic
141#478C2211yescharacteristic
142#478C2211yescharacteristic
143#478C2211yescharacteristic
144#478C2211yescharacteristic
145#477C2211yescharacteristic
146#476C2211yescharacteristic
147#476C2211yescharacteristic
148#476C2211yescharacteristic
149#475C2211yescharacteristic
150#474C2211yescharacteristic
151#474C2211yescharacteristic
152#474C2211yescharacteristic
153#469C2211yescharacteristic
154#469C2211yescharacteristic
155#469C2211yescharacteristic
156#469C2211yescharacteristic
157#468C2211yescharacteristic
158#468C2211yescharacteristic
159#468C2211yescharacteristic
160#468C2211yescharacteristic
161#466C2211yescharacteristic
162#466C2211yescharacteristic
163#465C2211yescharacteristic
164#465C2211yescharacteristic
165#446C2211yescharacteristic
166C8×Q8C2211yescharacteristic
167#442C2211yescharacteristic
168#442C2211yescharacteristic
169#440C2211yescharacteristic
170#440C2211yescharacteristic
171C4×SD16C2211yescharacteristic
172C4×SD16C2211yescharacteristic
173C4×SD16C2211yescharacteristic
174C4×SD16C2211yescharacteristic
175C4×D8C2211yescharacteristic
176C4×D8C2211yescharacteristic
177C4×D8C2211yescharacteristic
178C4×D8C2211yescharacteristic
179#436C2211yescharacteristic
180#436C2211yescharacteristic
181#436C2211yescharacteristic
182#435C2211yescharacteristic
183#435C2211yescharacteristic
184C8×D4C2211yescharacteristic
185#433C2211yescharacteristic
186#433C2211yescharacteristic
187#431C2211yescharacteristic
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—
205C2×#41—21no—
206C2×SD16C2311yescharacteristic
207C2×SD16C2311yescharacteristic
208C2×D8C2311yescharacteristic
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⋊Q8C2311yescharacteristic
222C4⋊Q8C2311yescharacteristic
223C4⋊Q8C2311yescharacteristic
224C4⋊Q8C2311yescharacteristic
225C4⋊Q8C2311yescharacteristic
226C4⋊Q8C2311yescharacteristic
227C4⋊Q8C2311yescharacteristic
228#127C2311yescharacteristic
229#126—21no—
230#126—21no—
231#126—21no—
232#126—21no—
233#126—21no—
234#126—21no—
235#126—21no—
236#126—21no—
237#126—21no—
238#126—21no—
239#126—21no—
240#126—21no—
241#126—21no—
242#126D411yescharacteristic
243#126D411yescharacteristic
244#125—21no—
245#125—21no—
246#125—21no—
247#125—21no—
248#125—21no—
249#125—21no—
250#125—21no—
251#125—21no—
252#125—21no—
253#125—21no—
254#125D411yescharacteristic
255#125C2311yescharacteristic
256#125C2311yescharacteristic
257#125C2311yescharacteristic
258#125C2311yescharacteristic
259#125C2311yescharacteristic
260#125C2311yescharacteristic
261#125C2311yescharacteristic
262#125C2311yescharacteristic
263#125C2311yescharacteristic
264#125C2311yescharacteristic
265#125C2311yescharacteristic
266#124—21no—
267#124—21no—
268#124—21no—
269#124—21no—
270#124—21no—
271#124—21no—
272#124D411yescharacteristic
273#124C2311yescharacteristic
274#123—21no—
275#123—21no—
276#123—21no—
277#123—21no—
278#123—21no—
279#123—21no—
280#123—21no—
281#123—21no—
282#123—21no—
283#123—21no—
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#123D411yescharacteristic
294#123D411yescharacteristic
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C22⋊Q8—21no—
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⋊Q8D411yescharacteristic
319C22⋊Q8C2311yescharacteristic
320C22⋊Q8C2311yescharacteristic
321C22⋊Q8C2311yescharacteristic
322#121—21no—
323#121—21no—
324#121—21no—
325#121—21no—
326#121—21no—
327#121—21no—
328#121—21no—
329#121—21no—
330#121—21no—
331#121—21no—
332#121—21no—
333#121—21no—
334#121D411yescharacteristic
335#121C2311yescharacteristic
336#121C2311yescharacteristic
337#121C2311yescharacteristic
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×Q8C2311yescharacteristic
349C4×Q8C2311yescharacteristic
350C4×Q8C2311yescharacteristic
351C4×Q8C2311yescharacteristic
352C4×D4—21no—
353C4×D4—21no—
354C4×D4—21no—
355C4×D4—21no—
356C4×D4—21no—
357C4×D4—21no—
358C4×D4—21no—
359C4×D4—21no—
360C4×D4C2311yescharacteristic
361C4×D4C2311yescharacteristic
362C4×D4C2311yescharacteristic
363C4×D4C2311yescharacteristic
364C4×D4C2311yescharacteristic
365C4×D4C2311yescharacteristic
366C4×D4C2311yescharacteristic
367C4×D4C2311yescharacteristic
368C4×D4C2311yescharacteristic
369C4×D4C2311yescharacteristic
370C4×D4C2311yescharacteristic
371C4×D4C2311yescharacteristic
372#117—21no—
373#117—21no—
374#117—21no—
375#117—21no—
376#117C2311yescharacteristic
377#117C2311yescharacteristic
378#117C2311yescharacteristic
379#117C2311yescharacteristic
380#117C2311yescharacteristic
381#117C2311yescharacteristic
382#117C2311yescharacteristic
383#117C2311yescharacteristic
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
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#102C2311yescharacteristic
445#102C2311yescharacteristic
446#102C2311yescharacteristic
447#102C2311yescharacteristic
448#102C2311yescharacteristic
449#102C2311yescharacteristic
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
472C4×C8C2311yescharacteristic
473C4×C8C2311yescharacteristic
474C4×C8C2311yescharacteristic
475C4×C8C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478#41—82no—
479#41—82no—
480#41—82no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8C2×D411yescharacteristic
489C2×Q8C2411yescharacteristic
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4C2×D411yescharacteristic
502C2×D4C2×D411yescharacteristic
503C2×D4C2×D411yescharacteristic
504C2×D4C2411yescharacteristic
505C2×D4C2411yescharacteristic
506C2×D4C2411yescharacteristic
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×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4C2×D411yescharacteristic
523C22×C4C2×D411yescharacteristic
524C22×C4C2411yescharacteristic
525C22×C4C2411yescharacteristic
526C22×C4C2411yescharacteristic
527SD16—22no—
528SD16—22no—
529D8—22no—
530D8—22no—
531M16—22no—
532M16—22no—
533M16—22no—
534M16—22no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8C2411yescharacteristic
538C2×C8C2411yescharacteristic
539C2×C8C2411yescharacteristic
540C2×C8C2411yescharacteristic
541C2×C8C2411yescharacteristic
542C2×C8C2411yescharacteristic
543C2×C8C2411yescharacteristic
544C2×C8C2411yescharacteristic
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⋊C4—21no—
585C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
595C4⋊C4C2×D411yescharacteristic
596C4⋊C4C2411yescharacteristic
597C4⋊C4C2411yescharacteristic
598C4⋊C4C2411yescharacteristic
599C4⋊C4C2411yescharacteristic
600C4⋊C4C2411yescharacteristic
601C4⋊C4C2411yescharacteristic
602C4⋊C4C2411yescharacteristic
603C4⋊C4C2411yescharacteristic
604C4⋊C4C2411yescharacteristic
605C4⋊C4C2411yescharacteristic
606C4⋊C4C2411yescharacteristic
607C4⋊C4C2411yescharacteristic
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⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4C2×D411yescharacteristic
638C22⋊C4C2×D411yescharacteristic
639C22⋊C4C2×D411yescharacteristic
640C22⋊C4C2×D411yescharacteristic
641C22⋊C4C2×D411yescharacteristic
642C22⋊C4C2×D411yescharacteristic
643C22⋊C4C2×D411yescharacteristic
644C22⋊C4C2×D411yescharacteristic
645C22⋊C4C2×D411yescharacteristic
646C22⋊C4C2×D411yescharacteristic
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—
664C23—21no—
665C23C22×D411yescharacteristic
666C23C22×D411yescharacteristic
667C23C22×D411yescharacteristic
668Q8—21no—
669Q8—21no—
670Q8—41no—
671Q8—81no—
672Q8—81no—
673Q8—81no—
674Q8—81no—
675Q8—81no—
676Q8—81no—
677Q8—81no—
678D4—21no—
679D4—21no—
680D4—21no—
681D4—21no—
682D4—21no—
683D4—21no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—42no—
688D4—42no—
689D4—81no—
690D4—81no—
691D4—81no—
692D4—81no—
693D4—81no—
694D4—81no—
695D4—81no—
696D4—81no—
697D4—81no—
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—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
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×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4C22×D411yescharacteristic
735C2×C4C22×D411yescharacteristic
736C2×C4C22×D411yescharacteristic
737C2×C4C22×D411yescharacteristic
738C2×C4C22×D411yescharacteristic
739C2×C4C22×D411yescharacteristic
740C2×C4C22×D411yescharacteristic
741C2×C4C22×D411yescharacteristic
742C2×C4C22×D411yescharacteristic
743C2×C4C22×D411yescharacteristic
744C2×C4C22×D411yescharacteristic
745C2×C4C2511yescharacteristic
746C8—21no—
747C8—21no—
748C8—21no—
749C8—21no—
750C8—21no—
751C8—21no—
752C82−1+412yes—
753C82−1+412yes—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22C23×D411yescharacteristic
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—21no—
780C4—21no—
781C4—21no—
782C4—21no—
783C4—21no—
784C4—41no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4C2×2−1+411yescharacteristic
798C4C2×2−1+411yescharacteristic
799C2—41no—
800C2—41no—
801C2—41no—
802C2—81no—
803C2—81no—
804C2—81no—
805C2#349911yescharacteristic
806C2#358411yescharacteristic
807C2#358511yescharacteristic
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. #3559C2semidirect
3. #3389C2semidirect
4. #3388C2semidirect
5. #3381C2semidirect
6. #3380C2semidirect
7. #3355C2semidirect
8. #3355C2semidirect
9. #3354C2semidirect
10. #3353C2semidirect
11. #3351C2semidirect
12. #3351C2semidirect
13. #3350C2semidirect
14. #3347C2semidirect
15. #3345C2semidirect
16. #3343C2semidirect
17. #3339C2semidirect
18. #3337C2semidirect
19. #3244C2semidirect
20. #3243C2semidirect
21. #3241C2semidirect
22. #3241C2semidirect
23. #3232C2semidirect
24. #3228C2semidirect
25. #3179C2semidirect
26. #3179C2semidirect
27. #3171C2semidirect
28. #3166C2semidirect
29. #3164C2semidirect
30. #3163C2semidirect
31. #2969C2semidirect

Maximal subgroups

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

subgroupindex
#35652
#35592
#33892
#33882
#33812
#33802
#33552
#33542
#33532
#33512
#33502
#33472
#33452
#33432
#33392
#33372
#32442
#32432
#32412
#32322
#32282
#31792
#31712
#31662
#31642
#31632
#29692