Finite Group Databasebeta

← #62158

Subgroups — #62158

Order 256.

842 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3552C211yesmaximal, characteristic, complemented
2#3516C211yesmaximal, characteristic, complemented
3#3390C211yesmaximal, characteristic, complemented
4#3386C211yesmaximal, characteristic, complemented
5#3377C211yesmaximal, characteristic, complemented
6#3367C211yesmaximal, characteristic, complemented
7#3349C211yesmaximal, characteristic, complemented
8#3346C211yesmaximal, characteristic, complemented
9#3346C211yesmaximal, characteristic, complemented
10#3343C211yesmaximal, characteristic, complemented
11#3339C211yesmaximal, characteristic, complemented
12#3338C211yesmaximal, characteristic, complemented
13#3320C211yesmaximal, characteristic, complemented
14#3316C211yesmaximal, characteristic, complemented
15#3313C211yesmaximal, characteristic, complemented
16#3308C211yesmaximal, characteristic, complemented
17#3301C211yesmaximal, characteristic, complemented
18#3299C211yesmaximal, characteristic, complemented
19#3262C211yesmaximal, characteristic, complemented
20#3258C211yesmaximal, characteristic, complemented
21#3250C211yesmaximal, characteristic, complemented
22#3243C211yesmaximal, characteristic, complemented
23#3242C211yesmaximal, characteristic, complemented
24#3239C211yesmaximal, characteristic, complemented
25#3124C211yesmaximal, characteristic, complemented
26#3121C211yesmaximal, characteristic, complemented
27#3117C211yesmaximal, characteristic, complemented
28#3083C211yesmaximal, characteristic, complemented
29#3082C211yesmaximal, characteristic, complemented
30C2×#477C211yesmaximal, characteristic, complemented
31#2992C211yesmaximal, characteristic, complemented
32#563—21no—
33#563—21no—
34#557C2211yescharacteristic
35#557C2211yescharacteristic
36#556—21no—
37#556C2211yescharacteristic
38#556C2211yescharacteristic
39#554—21no—
40#554C2211yescharacteristic
41#554C2211yescharacteristic
42#554C2211yescharacteristic
43#553—21no—
44#553C2211yescharacteristic
45#553C2211yescharacteristic
46#553C2211yescharacteristic
47#552—21no—
48#552C2211yescharacteristic
49D4×Q8—21no—
50D4×Q8C2211yescharacteristic
51D4×Q8C2211yescharacteristic
52#548—21no—
53#548C2211yescharacteristic
54#548C2211yescharacteristic
55#547C2211yescharacteristic
56#544C2211yescharacteristic
57#544C2211yescharacteristic
58#542—21no—
59#542C2211yescharacteristic
60#542C2211yescharacteristic
61#542C2211yescharacteristic
62#541—21no—
63#541—21no—
64#541C2211yescharacteristic
65#539—21no—
66#539—21no—
67#536—21no—
68C2×C4⋊Q8C2211yescharacteristic
69#529—21no—
70#529—21no—
71#529C2211yescharacteristic
72#529C2211yescharacteristic
73#529C2211yescharacteristic
74#520C2211yescharacteristic
75#519C2211yescharacteristic
76C2×C4×Q8C2211yescharacteristic
77#501C2211yescharacteristic
78#501C2211yescharacteristic
79#501C2211yescharacteristic
80#501C2211yescharacteristic
81#500C2211yescharacteristic
82#499C2211yescharacteristic
83#491C2211yescharacteristic
84#489C2211yescharacteristic
85#489C2211yescharacteristic
86#489C2211yescharacteristic
87#488C2211yescharacteristic
88#487C2211yescharacteristic
89#485C2211yescharacteristic
90#485C2211yescharacteristic
91#485C2211yescharacteristic
92#485C2211yescharacteristic
93#484C2211yescharacteristic
94#484C2211yescharacteristic
95#484C2211yescharacteristic
96#484C2211yescharacteristic
97#484C2211yescharacteristic
98#484C2211yescharacteristic
99#483C2211yescharacteristic
100#482C2211yescharacteristic
101#482C2211yescharacteristic
102#481C2211yescharacteristic
103#481C2211yescharacteristic
104#481C2211yescharacteristic
105#480C2211yescharacteristic
106#480C2211yescharacteristic
107#479C2211yescharacteristic
108#479C2211yescharacteristic
109#479C2211yescharacteristic
110#479C2211yescharacteristic
111#479C2211yescharacteristic
112#479C2211yescharacteristic
113#479C2211yescharacteristic
114#479C2211yescharacteristic
115#478C2211yescharacteristic
116#478C2211yescharacteristic
117#478C2211yescharacteristic
118#478C2211yescharacteristic
119#477C2211yescharacteristic
120#477C2211yescharacteristic
121#477C2211yescharacteristic
122#477C2211yescharacteristic
123#477C2211yescharacteristic
124#477C2211yescharacteristic
125#477C2211yescharacteristic
126#477C2211yescharacteristic
127#477C2211yescharacteristic
128#477C2211yescharacteristic
129#477C2211yescharacteristic
130#475C2211yescharacteristic
131#475C2211yescharacteristic
132#475C2211yescharacteristic
133#474C2211yescharacteristic
134#474C2211yescharacteristic
135#474C2211yescharacteristic
136#474C2211yescharacteristic
137#470C2211yescharacteristic
138#468C2211yescharacteristic
139#468C2211yescharacteristic
140#468C2211yescharacteristic
141#467C2211yescharacteristic
142#467C2211yescharacteristic
143#467C2211yescharacteristic
144#466C2211yescharacteristic
145#466C2211yescharacteristic
146#465C2211yescharacteristic
147#465C2211yescharacteristic
148#465C2211yescharacteristic
149#464C2211yescharacteristic
150#464C2211yescharacteristic
151#464C2211yescharacteristic
152#464C2211yescharacteristic
153#464C2211yescharacteristic
154#463C2211yescharacteristic
155#463C2211yescharacteristic
156#463C2211yescharacteristic
157#462C2211yescharacteristic
158#461C2211yescharacteristic
159#452C2211yescharacteristic
160#451C2211yescharacteristic
161#451C2211yescharacteristic
162#449C2211yescharacteristic
163#448C2211yescharacteristic
164#448C2211yescharacteristic
165#446C2211yescharacteristic
166#446C2211yescharacteristic
167#441C2211yescharacteristic
168#441C2211yescharacteristic
169#441C2211yescharacteristic
170#440C2211yescharacteristic
171#440C2211yescharacteristic
172#440C2211yescharacteristic
173#440C2211yescharacteristic
174#440C2211yescharacteristic
175C4×Q16C2211yescharacteristic
176C4×Q16C2211yescharacteristic
177C4×SD16C2211yescharacteristic
178C4×D8C2211yescharacteristic
179#435C2211yescharacteristic
180#435C2211yescharacteristic
181#435C2211yescharacteristic
182#435C2211yescharacteristic
183C8×D4C2211yescharacteristic
184C8×D4C2211yescharacteristic
185#433C2211yescharacteristic
186#433C2211yescharacteristic
187#432C2211yescharacteristic
188#428C2211yescharacteristic
189#428C2211yescharacteristic
190#427C2211yescharacteristic
191C2×#107C2211yescharacteristic
192C2×#107C2211yescharacteristic
193C2×#107C2211yescharacteristic
194#424C2211yescharacteristic
195#424C2211yescharacteristic
196C2×C4⋊C8C2211yescharacteristic
197#419C2211yescharacteristic
198#417C2211yescharacteristic
199#416C2211yescharacteristic
200C2×#103C2211yescharacteristic
201C2×#103C2211yescharacteristic
202C2×#103C2211yescharacteristic
203C2×#41—21no—
204C2×#41C2311yescharacteristic
205C22×Q8—21no—
206C22×Q8—21no—
207C22×Q8C2311yescharacteristic
208C22×Q8C2311yescharacteristic
209C2×Q16C2311yescharacteristic
210C2×Q16C2311yescharacteristic
211C2×Q16C2311yescharacteristic
212C2×SD16C2311yescharacteristic
213C2×SD16C2311yescharacteristic
214C2×SD16C2311yescharacteristic
215C2×SD16C2311yescharacteristic
216C2×D8C2311yescharacteristic
217C2×M16C2311yescharacteristic
218C2×M16C2311yescharacteristic
219C22×C8C2311yescharacteristic
220C22×C8C2311yescharacteristic
221C22×C8C2311yescharacteristic
222C22×C8C2311yescharacteristic
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8C2311yescharacteristic
231C4⋊Q8C2311yescharacteristic
232C4⋊Q8C2311yescharacteristic
233C4⋊Q8C2311yescharacteristic
234C4⋊Q8C2311yescharacteristic
235C4⋊Q8C2311yescharacteristic
236C4⋊Q8C2311yescharacteristic
237C4⋊Q8C2311yescharacteristic
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#126—21no—
251#126—21no—
252#126—21no—
253#126D411yescharacteristic
254#126D411yescharacteristic
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#125—21no—
264#125—21no—
265#125—21no—
266#125—21no—
267#125D411yescharacteristic
268#125C2311yescharacteristic
269#125C2311yescharacteristic
270#125C2311yescharacteristic
271#125C2311yescharacteristic
272#125C2311yescharacteristic
273#124—21no—
274#124—21no—
275#124—21no—
276#124—21no—
277#124—21no—
278#124—21no—
279#124D411yescharacteristic
280#124C2311yescharacteristic
281#124C2311yescharacteristic
282#124C2311yescharacteristic
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#123—21no—
294#123D411yescharacteristic
295#123D411yescharacteristic
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
322C22⋊Q8C2311yescharacteristic
323C22⋊Q8C2311yescharacteristic
324C22⋊Q8C2311yescharacteristic
325C22⋊Q8C2311yescharacteristic
326#121—21no—
327#121—21no—
328#121—21no—
329#121—21no—
330#121—21no—
331#121D411yescharacteristic
332#121C2311yescharacteristic
333#121C2311yescharacteristic
334#121C2311yescharacteristic
335#121C2311yescharacteristic
336#121C2311yescharacteristic
337C4×Q8—21no—
338C4×Q8—21no—
339C4×Q8—21no—
340C4×Q8—21no—
341C4×Q8—21no—
342C4×Q8—21no—
343C4×Q8—21no—
344C4×Q8C2311yescharacteristic
345C4×Q8C2311yescharacteristic
346C4×Q8C2311yescharacteristic
347C4×Q8C2311yescharacteristic
348C4×Q8C2311yescharacteristic
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×D4—21no—
362C4×D4—21no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4—21no—
367C4×D4—21no—
368C4×D4—21no—
369C4×D4C2311yescharacteristic
370C4×D4C2311yescharacteristic
371C4×D4C2311yescharacteristic
372C4×D4C2311yescharacteristic
373C4×D4C2311yescharacteristic
374C4×D4C2311yescharacteristic
375C4×D4C2311yescharacteristic
376C4×D4C2311yescharacteristic
377#117—21no—
378#117—21no—
379#117—21no—
380#117—21no—
381#117—21no—
382#117—21no—
383#117—21no—
384#117C2311yescharacteristic
385#117C2311yescharacteristic
386#117C2311yescharacteristic
387#117C2311yescharacteristic
388#117C2311yescharacteristic
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4C2311yescharacteristic
393C2×C4⋊C4C2311yescharacteristic
394C2×C4⋊C4C2311yescharacteristic
395C2×C4⋊C4C2311yescharacteristic
396C2×C4⋊C4C2311yescharacteristic
397C2×C4⋊C4C2311yescharacteristic
398C2×C42—21no—
399C2×C42C2311yescharacteristic
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#107C2311yescharacteristic
415#107C2311yescharacteristic
416#106C2311yescharacteristic
417#106C2311yescharacteristic
418#106C2311yescharacteristic
419#106C2311yescharacteristic
420#106C2311yescharacteristic
421#106C2311yescharacteristic
422#106C2311yescharacteristic
423#106C2311yescharacteristic
424C4⋊C8C2311yescharacteristic
425C4⋊C8C2311yescharacteristic
426C4⋊C8C2311yescharacteristic
427C4⋊C8C2311yescharacteristic
428C4⋊C8C2311yescharacteristic
429C4⋊C8C2311yescharacteristic
430C4⋊C8C2311yescharacteristic
431C4⋊C8C2311yescharacteristic
432C4⋊C8C2311yescharacteristic
433C4⋊C8C2311yescharacteristic
434#103C2311yescharacteristic
435#103C2311yescharacteristic
436#103C2311yescharacteristic
437#103C2311yescharacteristic
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#103C2311yescharacteristic
451#103C2311yescharacteristic
452#103C2311yescharacteristic
453#103C2311yescharacteristic
454#103C2311yescharacteristic
455#103C2311yescharacteristic
456#102C2311yescharacteristic
457#102C2311yescharacteristic
458#102C2311yescharacteristic
459#102C2311yescharacteristic
460#102C2311yescharacteristic
461#102C2311yescharacteristic
462#102C2311yescharacteristic
463#102C2311yescharacteristic
464#102C2311yescharacteristic
465#102C2311yescharacteristic
466C22⋊C8C2311yescharacteristic
467C22⋊C8C2311yescharacteristic
468C22⋊C8C2311yescharacteristic
469C22⋊C8C2311yescharacteristic
470C22⋊C8C2311yescharacteristic
471C22⋊C8C2311yescharacteristic
472#97C2311yescharacteristic
473#97C2311yescharacteristic
474#97C2311yescharacteristic
475#97C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478#41—22no—
479#41—41no—
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×Q8—21no—
489C2×Q8—21no—
490C2×Q8—22no—
491C2×Q8—22no—
492C2×Q8—41no—
493C2×Q8—41no—
494C2×Q8—82no—
495C2×Q8—82no—
496C2×Q8C2×D411yescharacteristic
497C2×Q8C2411yescharacteristic
498C2×Q8C2411yescharacteristic
499C2×Q8C2411yescharacteristic
500C2×Q8C2411yescharacteristic
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4C2×D411yescharacteristic
508C2×D4C2×D411yescharacteristic
509C2×D4C2×D411yescharacteristic
510C2×D4C2411yescharacteristic
511C2×D4C2411yescharacteristic
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×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4C2×D411yescharacteristic
527C22×C4C2×D411yescharacteristic
528C22×C4C2411yescharacteristic
529C22×C4C2411yescharacteristic
530C22×C4C2411yescharacteristic
531Q16—22no—
532Q16—41no—
533Q16—41no—
534SD16—22no—
535SD16—41no—
536SD16—41no—
537SD16—41no—
538D8—41no—
539M16—41no—
540M16—41no—
541C2×C8—41no—
542C2×C8—41no—
543C2×C8—41no—
544C2×C8—41no—
545C2×C8C2411yescharacteristic
546C2×C8C2411yescharacteristic
547C2×C8C2411yescharacteristic
548C2×C8C2411yescharacteristic
549C2×C8C2411yescharacteristic
550C2×C8C2411yescharacteristic
551C2×C8C2411yescharacteristic
552C2×C8C2411yescharacteristic
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⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4C2×D411yescharacteristic
597C4⋊C4C2×D411yescharacteristic
598C4⋊C4C2×D411yescharacteristic
599C4⋊C4C2×D411yescharacteristic
600C4⋊C4C2×D411yescharacteristic
601C4⋊C4C2×D411yescharacteristic
602C4⋊C4C2×D411yescharacteristic
603C4⋊C4C2×D411yescharacteristic
604C4⋊C4C2×D411yescharacteristic
605C4⋊C4C2×D411yescharacteristic
606C4⋊C4C2411yescharacteristic
607C4⋊C4C2411yescharacteristic
608C4⋊C4C2411yescharacteristic
609C4⋊C4C2411yescharacteristic
610C4⋊C4C2411yescharacteristic
611C4⋊C4C2411yescharacteristic
612C4⋊C4C2411yescharacteristic
613C4⋊C4C2411yescharacteristic
614C4⋊C4C2411yescharacteristic
615C4⋊C4C2411yescharacteristic
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⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4C2×D411yescharacteristic
643C22⋊C4C2×D411yescharacteristic
644C22⋊C4C2×D411yescharacteristic
645C22⋊C4C2×D411yescharacteristic
646C22⋊C4C2×D411yescharacteristic
647C22⋊C4C2×D411yescharacteristic
648C22⋊C4C2×D411yescharacteristic
649C22⋊C4C2×D411yescharacteristic
650C22⋊C4C2×D411yescharacteristic
651C22⋊C4C2×D411yescharacteristic
652C42—21no—
653C42—21no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42C2×D411yescharacteristic
667C42C2×D411yescharacteristic
668C42C2411yescharacteristic
669C42C2411yescharacteristic
670C42C2411yescharacteristic
671C42C2411yescharacteristic
672C23—21no—
673C23—21no—
674C23C22×D411yescharacteristic
675C23C22×D411yescharacteristic
676C23C22×D411yescharacteristic
677Q8—21no—
678Q8—21no—
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—21no—
683Q8—21no—
684Q8—41no—
685Q8—42no—
686Q8—42no—
687Q8—42no—
688Q8—42no—
689Q8—81no—
690Q8—81no—
691Q8—81no—
692Q8—81no—
693Q8—81no—
694Q82−1+412yes—
695D4—22no—
696D4—22no—
697D4—21no—
698D4—21no—
699D4—21no—
700D4—21no—
701D4—41no—
702D4—42no—
703D4—42no—
704D4—42no—
705D4—81no—
706D4—81no—
707D4—81no—
708C2×C4—22no—
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—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4—81no—
737C2×C4—81no—
738C2×C4—81no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4—81no—
742C2×C4—81no—
743C2×C4—81no—
744C2×C4C22×D411yescharacteristic
745C2×C4C22×D411yescharacteristic
746C2×C4C22×D411yescharacteristic
747C2×C4C22×D411yescharacteristic
748C2×C4C22×D411yescharacteristic
749C2×C4C22×D411yescharacteristic
750C2×C4C22×D411yescharacteristic
751C2×C4C22×D411yescharacteristic
752C2×C4C22×D411yescharacteristic
753C2×C4C22×D411yescharacteristic
754C2×C4C22×D411yescharacteristic
755C2×C4C2511yescharacteristic
756C8—21no—
757C8—21no—
758C8—21no—
759C8—21no—
760C8—21no—
761C8—21no—
762C8—21no—
763C8—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22#57812yes—
779C22C23×D411yescharacteristic
780C4—21no—
781C4—21no—
782C4—21no—
783C4—21no—
784C4—21no—
785C4—21no—
786C4—21no—
787C4—22no—
788C4—21no—
789C4—21no—
790C4—21no—
791C4—21no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—41no—
799C4—41no—
800C4—41no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4C2×2−1+411yescharacteristic
806C4#58511yescharacteristic
807C2—22no—
808C2—41no—
809C2—41no—
810C2—81no—
811C2—81no—
812C2#348911yescharacteristic
813C2C2×#57811yescharacteristic
814C2#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. #3552C2semidirect
2. #3516C2semidirect
3. #3390C2semidirect
4. #3386C2semidirect
5. #3377C2semidirect
6. #3367C2semidirect
7. #3349C2semidirect
8. #3346C2semidirect
9. #3346C2semidirect
10. #3343C2semidirect
11. #3339C2semidirect
12. #3338C2semidirect
13. #3320C2semidirect
14. #3316C2semidirect
15. #3313C2semidirect
16. #3308C2semidirect
17. #3301C2semidirect
18. #3299C2semidirect
19. #3262C2semidirect
20. #3258C2semidirect
21. #3250C2semidirect
22. #3243C2semidirect
23. #3242C2semidirect
24. #3239C2semidirect
25. #3124C2semidirect
26. #3121C2semidirect
27. #3117C2semidirect
28. #3083C2semidirect
29. #3082C2semidirect
30. C2×#477C2semidirect
31. #2992C2semidirect

Maximal subgroups

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

subgroupindex
#35522
#35162
#33902
#33862
#33772
#33672
#33492
#33462
#33432
#33392
#33382
#33202
#33162
#33132
#33082
#33012
#32992
#32622
#32582
#32502
#32432
#32422
#32392
#31242
#31212
#31172
#30832
#30822
C2×#4772
#29922