Finite Group Databasebeta

← #61801

Subgroups — #61801

Order 256.

846 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3551C211yesmaximal, characteristic
2#3507C211yesmaximal, characteristic, complemented
3#3352C211yesmaximal, characteristic, complemented
4#3351C211yesmaximal, characteristic, complemented
5#3350C211yesmaximal, characteristic, complemented
6#3349C211yesmaximal, characteristic, complemented
7#3346C211yesmaximal, characteristic, complemented
8#3344C211yesmaximal, characteristic, complemented
9#3337C211yesmaximal, characteristic, complemented
10#3336C211yesmaximal, characteristic, complemented
11#3327C211yesmaximal, characteristic, complemented
12#3323C211yesmaximal, characteristic, complemented
13#3316C211yesmaximal, characteristic, complemented
14#3314C211yesmaximal, characteristic, complemented
15#3313C211yesmaximal, characteristic, complemented
16#3311C211yesmaximal, characteristic, complemented
17#3300C211yesmaximal, characteristic, complemented
18#3296C211yesmaximal, characteristic, complemented
19#3240C211yesmaximal, characteristic, complemented
20#3233C211yesmaximal, characteristic, complemented
21#3202C211yesmaximal, characteristic, complemented
22#3201C211yesmaximal, characteristic, complemented
23#3201C211yesmaximal, characteristic, complemented
24#3200C211yesmaximal, characteristic, complemented
25#3117C211yesmaximal, characteristic, complemented
26#3108C211yesmaximal, characteristic, complemented
27#3099C211yesmaximal, characteristic, complemented
28#3098C211yesmaximal, characteristic, complemented
29#3097C211yesmaximal, characteristic, complemented
30#3096C211yesmaximal, characteristic, complemented
31#2981C211yesmaximal, characteristic, complemented
32#563—21no—
33#560—21no—
34#559—21no—
35#557—21no—
36#556—21no—
37#556—21no—
38#556C2211yescharacteristic
39#556C2211yescharacteristic, complemented
40#555—21no—
41#554C2211yescharacteristic
42#554C2211yescharacteristic, complemented
43#553C2211yescharacteristic
44#553C2211yescharacteristic
45#552C2211yescharacteristic
46#552C2211yescharacteristic
47#552C2211yescharacteristic
48#552C2211yescharacteristic
49#552C2211yescharacteristic, complemented
50#552C2211yescharacteristic, complemented
51#551—21no—
52#548C2211yescharacteristic
53#548C2211yescharacteristic
54#546C2211yescharacteristic
55#546C2211yescharacteristic
56#540—21no—
57#540—21no—
58#539—21no—
59#539—21no—
60#538—21no—
61#538—21no—
62#537C2211yescharacteristic
63#537C2211yescharacteristic
64#536C2211yescharacteristic
65#536C2211yescharacteristic
66#536C2211yescharacteristic, complemented
67#535C2211yescharacteristic
68#533C2211yescharacteristic, complemented
69#532C2211yescharacteristic
70#529—21no—
71#529—21no—
72#529C2211yescharacteristic
73#529C2211yescharacteristic
74#520C2211yescharacteristic
75#520C2211yescharacteristic, complemented
76C2×C4×Q8C2211yescharacteristic, complemented
77#501C2211yescharacteristic, complemented
78#501C2211yescharacteristic, complemented
79#499C2211yescharacteristic, complemented
80#499C2211yescharacteristic, complemented
81#489C2211yescharacteristic
82#489C2211yescharacteristic
83#488C2211yescharacteristic
84#488C2211yescharacteristic
85#485C2211yescharacteristic
86#485C2211yescharacteristic
87#485C2211yescharacteristic
88#485C2211yescharacteristic
89#485C2211yescharacteristic, complemented
90#485C2211yescharacteristic, complemented
91#485C2211yescharacteristic, complemented
92#485C2211yescharacteristic, complemented
93#485C2211yescharacteristic, complemented
94#485C2211yescharacteristic, complemented
95#485C2211yescharacteristic, complemented
96#485C2211yescharacteristic, complemented
97#484C2211yescharacteristic
98#484C2211yescharacteristic, complemented
99#484C2211yescharacteristic, complemented
100#484C2211yescharacteristic, complemented
101#484C2211yescharacteristic, complemented
102#483C2211yescharacteristic
103#483C2211yescharacteristic, complemented
104#483C2211yescharacteristic, complemented
105#483C2211yescharacteristic, complemented
106#483C2211yescharacteristic, complemented
107#482C2211yescharacteristic
108#482C2211yescharacteristic
109#482C2211yescharacteristic
110#482C2211yescharacteristic
111#482C2211yescharacteristic
112#482C2211yescharacteristic
113#482C2211yescharacteristic
114#482C2211yescharacteristic
115#481C2211yescharacteristic
116#481C2211yescharacteristic
117#481C2211yescharacteristic
118#480C2211yescharacteristic
119#480C2211yescharacteristic
120#480C2211yescharacteristic
121#479C2211yescharacteristic, complemented
122#479C2211yescharacteristic, complemented
123#479C2211yescharacteristic, complemented
124#479C2211yescharacteristic, complemented
125#479C2211yescharacteristic, complemented
126#479C2211yescharacteristic, complemented
127#478C2211yescharacteristic
128#478C2211yescharacteristic
129#477C2211yescharacteristic, complemented
130#476C2211yescharacteristic
131#475C2211yescharacteristic, complemented
132#474C2211yescharacteristic
133#470C2211yescharacteristic
134#470C2211yescharacteristic
135#470C2211yescharacteristic, complemented
136#470C2211yescharacteristic, complemented
137#468C2211yescharacteristic
138#468C2211yescharacteristic
139#468C2211yescharacteristic
140#468C2211yescharacteristic
141#467C2211yescharacteristic
142#467C2211yescharacteristic
143#467C2211yescharacteristic, complemented
144#467C2211yescharacteristic, complemented
145#465C2211yescharacteristic
146#465C2211yescharacteristic
147#465C2211yescharacteristic
148#465C2211yescharacteristic
149#464C2211yescharacteristic
150#464C2211yescharacteristic
151#464C2211yescharacteristic
152#464C2211yescharacteristic
153#452C2211yescharacteristic
154#452C2211yescharacteristic
155#452C2211yescharacteristic
156#452C2211yescharacteristic
157#451C2211yescharacteristic, complemented
158#451C2211yescharacteristic, complemented
159#451C2211yescharacteristic, complemented
160#451C2211yescharacteristic, complemented
161#450C2211yescharacteristic
162#450C2211yescharacteristic
163#448C2211yescharacteristic
164#448C2211yescharacteristic
165#441C2211yescharacteristic, complemented
166#441C2211yescharacteristic, complemented
167#440C2211yescharacteristic
168#440C2211yescharacteristic
169C4×Q16C2211yescharacteristic, complemented
170C4×Q16C2211yescharacteristic, complemented
171C4×SD16C2211yescharacteristic
172C4×SD16C2211yescharacteristic
173#436C2211yescharacteristic
174#436C2211yescharacteristic, complemented
175#435C2211yescharacteristic
176#435C2211yescharacteristic
177#435C2211yescharacteristic, complemented
178#435C2211yescharacteristic, complemented
179C8×D4C2211yescharacteristic
180C8×D4C2211yescharacteristic, complemented
181#432C2211yescharacteristic, complemented
182#431C2211yescharacteristic, complemented
183#428C2211yescharacteristic
184#428C2211yescharacteristic, complemented
185#428C2211yescharacteristic, complemented
186#428C2211yescharacteristic, complemented
187#427C2211yescharacteristic
188#427C2211yescharacteristic, complemented
189C2×#107C2211yescharacteristic, complemented
190C2×#106C2211yescharacteristic, complemented
191#419C2211yescharacteristic, complemented
192#418C2211yescharacteristic
193#417C2211yescharacteristic
194#417C2211yescharacteristic
195#416C2211yescharacteristic
196#416C2211yescharacteristic
197C2×#103C2211yescharacteristic, complemented
198C2×#102C2211yescharacteristic
199#408C2211yescharacteristic
200#408C2211yescharacteristic
201#408C2211yescharacteristic, complemented
202#408C2211yescharacteristic, complemented
203C2×#41C2311yescharacteristic
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C22×Q8C2311yescharacteristic
208C22×Q8C2311yescharacteristic
209C22×D4C2311yescharacteristic
210C2×Q16C2311yescharacteristic
211C2×Q16C2311yescharacteristic
212C2×Q16C2311yescharacteristic
213C2×Q16C2311yescharacteristic
214C2×SD16C2311yescharacteristic
215C2×SD16C2311yescharacteristic
216C2×SD16C2311yescharacteristic
217C2×SD16C2311yescharacteristic
218C2×M16C2311yescharacteristic
219C2×M16C2311yescharacteristic
220C2×M16C2311yescharacteristic
221C2×M16C2311yescharacteristic
222C22×C8C2311yescharacteristic
223C22×C8C2311yescharacteristic
224C22×C8C2311yescharacteristic
225C22×C8C2311yescharacteristic
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8D411yescharacteristic
230C4⋊Q8C2311yescharacteristic
231C4⋊Q8C2311yescharacteristic
232#127—21no—
233#127D411yescharacteristic
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#126—21no—
243#126—21no—
244#126—21no—
245#126—21no—
246#126—21no—
247#126—21no—
248#125—21no—
249#125—21no—
250#125—21no—
251#125—21no—
252#125—21no—
253#125—21no—
254#125—21no—
255#125—21no—
256#125C2311yescharacteristic
257#125C2311yescharacteristic
258#125C2311yescharacteristic
259#125C2311yescharacteristic
260#124—21no—
261#124—21no—
262#124—21no—
263#124—21no—
264#124—21no—
265#124—21no—
266#124—21no—
267#124—21no—
268#124D411yescharacteristic
269#124D411yescharacteristic
270#124C2311yescharacteristic
271#124C2311yescharacteristic
272#123—21no—
273#123—21no—
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—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C22⋊Q8C2311yescharacteristic
301C22⋊Q8C2311yescharacteristic
302C22⋊Q8C2311yescharacteristic
303C22⋊Q8C2311yescharacteristic
304C22⋊Q8C2311yescharacteristic
305C22⋊Q8C2311yescharacteristic
306C22⋊Q8C2311yescharacteristic
307C22⋊Q8C2311yescharacteristic
308C22⋊Q8C2311yescharacteristic
309C22⋊Q8C2311yescharacteristic
310C22⋊Q8C2311yescharacteristic
311C22⋊Q8C2311yescharacteristic
312C22⋊Q8C2311yescharacteristic
313C22⋊Q8C2311yescharacteristic
314#121—21no—
315#121—21no—
316#121—21no—
317#121—21no—
318#121—21no—
319#121—21no—
320#121—21no—
321#121—21no—
322#121—21no—
323#121—21no—
324#121—21no—
325#121—21no—
326#121D411yescharacteristic
327#121D411yescharacteristic
328#121D411yescharacteristic
329#121D411yescharacteristic
330#121C2311yescharacteristic
331#121C2311yescharacteristic
332#121C2311yescharacteristic
333#121C2311yescharacteristic
334#121C2311yescharacteristic
335#121C2311yescharacteristic
336#120—21no—
337#120—21no—
338#120—21no—
339#120—21no—
340C4×Q8—21no—
341C4×Q8—21no—
342C4×Q8—21no—
343C4×Q8—21no—
344C4×Q8—21no—
345C4×Q8—21no—
346C4×Q8—21no—
347C4×Q8—21no—
348C4×Q8C2311yescharacteristic
349C4×Q8C2311yescharacteristic
350C4×Q8C2311yescharacteristic
351C4×Q8C2311yescharacteristic
352C4×Q8C2311yescharacteristic
353C4×Q8C2311yescharacteristic
354C4×D4—21no—
355C4×D4—21no—
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×D4C2311yescharacteristic
369C4×D4C2311yescharacteristic
370C4×D4C2311yescharacteristic
371C4×D4C2311yescharacteristic
372C4×D4C2311yescharacteristic
373C4×D4C2311yescharacteristic
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117—21no—
379#117—21no—
380#117—21no—
381#117—21no—
382#117C2311yescharacteristic
383#117C2311yescharacteristic
384#117C2311yescharacteristic
385#117C2311yescharacteristic
386#117C2311yescharacteristic
387#117C2311yescharacteristic
388#117C2311yescharacteristic
389#117C2311yescharacteristic
390C2×C4⋊C4—21no—
391C2×C4⋊C4C2311yescharacteristic
392C2×C4⋊C4C2311yescharacteristic
393C2×C4⋊C4C2311yescharacteristic
394C2×C4⋊C4C2311yescharacteristic
395C2×C4⋊C4C2311yescharacteristic
396C2×C4⋊C4C2311yescharacteristic
397C2×C4⋊C4C2311yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C42—21no—
401C2×C42C2311yescharacteristic
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
426C4⋊C8C2311yescharacteristic
427C4⋊C8C2311yescharacteristic
428C4⋊C8C2311yescharacteristic
429C4⋊C8C2311yescharacteristic
430#103C2311yescharacteristic
431#103C2311yescharacteristic
432#103C2311yescharacteristic
433#103C2311yescharacteristic
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#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
468C22⋊C8C2311yescharacteristic
469C22⋊C8C2311yescharacteristic
470C22⋊C8C2311yescharacteristic
471C22⋊C8C2311yescharacteristic
472C22⋊C8C2311yescharacteristic
473C22⋊C8C2311yescharacteristic
474#97C2311yescharacteristic
475#97C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478C24—21no—
479#41—41no—
480#41—41no—
481#41—41no—
482#41—41no—
483#41—41no—
484#41—41no—
485#41—41no—
486#41—41no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—41no—
492C2×Q8—41no—
493C2×Q8—41no—
494C2×Q8—41no—
495C2×Q8C2×D411yescharacteristic
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×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—41no—
511C2×D4—41no—
512C2×D4C2×D411yescharacteristic
513C2×D4C2×D411yescharacteristic
514C2×D4C2×D411yescharacteristic
515C2×D4C2×D411yescharacteristic
516C2×D4C2×D411yescharacteristic
517C2×D4C2×D411yescharacteristic
518C2×D4C2×D411yescharacteristic
519C2×D4C2×D411yescharacteristic
520C2×D4C2×D411yescharacteristic
521C2×D4C2×D411yescharacteristic
522C2×D4C2411yescharacteristic
523C2×D4C2411yescharacteristic
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4C2×D411yescharacteristic
538C22×C4C2×D411yescharacteristic
539C22×C4C2411yescharacteristic
540C22×C4C2411yescharacteristic
541C22×C4C2411yescharacteristic
542C22×C4C2411yescharacteristic
543C22×C4C2411yescharacteristic
544Q16—41no—
545Q16—41no—
546Q16—41no—
547Q16—41no—
548SD16—41no—
549SD16—41no—
550SD16—41no—
551SD16—41no—
552M16—41no—
553M16—41no—
554M16—41no—
555M16—41no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8C2411yescharacteristic
561C2×C8C2411yescharacteristic
562C2×C8C2411yescharacteristic
563C2×C8C2411yescharacteristic
564C2×C8C2411yescharacteristic
565C2×C8C2411yescharacteristic
566C2×C8C2411yescharacteristic
567C2×C8C2411yescharacteristic
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⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4C2×D411yescharacteristic
606C4⋊C4C2×D411yescharacteristic
607C4⋊C4C2×D411yescharacteristic
608C4⋊C4C2×D411yescharacteristic
609C4⋊C4C2411yescharacteristic
610C4⋊C4C2411yescharacteristic
611C4⋊C4C2411yescharacteristic
612C4⋊C4C2411yescharacteristic
613C4⋊C4C2411yescharacteristic
614C4⋊C4C2411yescharacteristic
615C4⋊C4C2411yescharacteristic
616C4⋊C4C2411yescharacteristic
617C4⋊C4C2411yescharacteristic
618C4⋊C4C2411yescharacteristic
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⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4C2×D411yescharacteristic
654C22⋊C4C2×D411yescharacteristic
655C22⋊C4C2×D411yescharacteristic
656C22⋊C4C2×D411yescharacteristic
657C22⋊C4C2×D411yescharacteristic
658C22⋊C4C2×D411yescharacteristic
659C22⋊C4C2×D411yescharacteristic
660C22⋊C4C2×D411yescharacteristic
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42C2×D411yescharacteristic
676C42C2×D411yescharacteristic
677C42C2411yescharacteristic
678C42C2411yescharacteristic
679C23—21no—
680C23—21no—
681C23—81no—
682C23—81no—
683C23—81no—
684C23C22×D411yescharacteristic
685C23C22×D411yescharacteristic
686C23C22×D411yescharacteristic
687C23C22×D411yescharacteristic
688C23C22×D411yescharacteristic
689Q8—21no—
690Q8—21no—
691Q8—21no—
692Q8—21no—
693Q8—21no—
694Q8—21no—
695Q8—21no—
696Q8—21no—
697Q8—41no—
698Q8—41no—
699Q8—42no—
700Q8—42no—
701Q8—81no—
702Q8—81no—
703D4—21no—
704D4—21no—
705D4—21no—
706D4—21no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—81no—
718D4—81no—
719D4—81no—
720D4—81no—
721D4—81no—
722D4—81no—
723D4—81no—
724D4—81no—
725D4—81no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—81no—
754C2×C4—81no—
755C2×C4—81no—
756C2×C4—81no—
757C2×C4—81no—
758C2×C4—81no—
759C2×C4—81no—
760C2×C4—81no—
761C2×C4—81no—
762C2×C4—81no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4C22×D411yescharacteristic
766C2×C4C22×D411yescharacteristic
767C2×C4C22×D411yescharacteristic
768C2×C4C22×D411yescharacteristic
769C2×C4C22×D411yescharacteristic
770C2×C4C22×D411yescharacteristic
771C2×C4C22×D411yescharacteristic
772C2×C4C22×D411yescharacteristic
773C2×C4C22×D411yescharacteristic
774C2×C4C2511yescharacteristic
775C8—21no—
776C8—21no—
777C8—21no—
778C8—21no—
779C8—21no—
780C8—21no—
781C8—21no—
782C8—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—162no—
805C22C23×D411yescharacteristic
806C4—21no—
807C4—21no—
808C4—21no—
809C4—21no—
810C4—21no—
811C4—21no—
812C4—21no—
813C4—21no—
814C4—21no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4#58511yescharacteristic
830C4#58511yescharacteristic
831C2—41no—
832C2—41no—
833C2—41no—
834C2—41no—
835C2—41no—
836C2—81no—
837C2—81no—
838C2#348511yescharacteristic
839C2#358411yescharacteristic
840C2#358611yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
prime radical#3551C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #532 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #3507C2semidirect
3. #3352C2semidirect
4. #3351C2semidirect
5. #3350C2semidirect
6. #3349C2semidirect
7. #3346C2semidirect
8. #3344C2semidirect
9. #3337C2semidirect
10. #3336C2semidirect
11. #3327C2semidirect
12. #3323C2semidirect
13. #3316C2semidirect
14. #3314C2semidirect
15. #3313C2semidirect
16. #3311C2semidirect
17. #3300C2semidirect
18. #3296C2semidirect
19. #3240C2semidirect
20. #3233C2semidirect
21. #3202C2semidirect
22. #3201C2semidirect
23. #3201C2semidirect
24. #3200C2semidirect
25. #3117C2semidirect
26. #3108C2semidirect
27. #3099C2semidirect
28. #3098C2semidirect
29. #3097C2semidirect
30. #3096C2semidirect
31. #2981C2semidirect
39. #556C22semidirect
42. #554C22semidirect
49. #552C22semidirect
50. #552C22semidirect
66. #536C22semidirect
68. #533C22semidirect
75. #520C22semidirect
76. C2×C4×Q8C22semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #499C22semidirect
80. #499C22semidirect
89. #485C22semidirect
90. #485C22semidirect
91. #485C22semidirect
92. #485C22semidirect
93. #485C22semidirect
94. #485C22semidirect
95. #485C22semidirect
96. #485C22semidirect
98. #484C22semidirect
99. #484C22semidirect
100. #484C22semidirect
101. #484C22semidirect
103. #483C22semidirect
104. #483C22semidirect
105. #483C22semidirect
106. #483C22semidirect
121. #479C22semidirect
122. #479C22semidirect
123. #479C22semidirect
124. #479C22semidirect
125. #479C22semidirect
126. #479C22semidirect
129. #477C22semidirect
131. #475C22semidirect
135. #470C22semidirect
136. #470C22semidirect
143. #467C22semidirect
144. #467C22semidirect
157. #451C22semidirect
158. #451C22semidirect
159. #451C22semidirect
160. #451C22semidirect
165. #441C22semidirect
166. #441C22semidirect
169. C4×Q16C22semidirect
170. C4×Q16C22semidirect
174. #436C22semidirect
177. #435C22semidirect
178. #435C22semidirect
180. C8×D4C22semidirect
181. #432C22semidirect
182. #431C22semidirect
184. #428C22semidirect
185. #428C22semidirect
186. #428C22semidirect
188. #427C22semidirect
189. C2×#107C22semidirect
190. C2×#106C22semidirect
191. #419C22semidirect
197. C2×#103C22semidirect
201. #408C22semidirect
202. #408C22semidirect

Maximal subgroups

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

subgroupindex
#35512
#35072
#33522
#33512
#33502
#33492
#33462
#33442
#33372
#33362
#33272
#33232
#33162
#33142
#33132
#33112
#33002
#32962
#32402
#32332
#32022
#32012
#32002
#31172
#31082
#30992
#30982
#30972
#30962
#29812