Finite Group Databasebeta

← #62607

Subgroups — #62607

Order 256.

865 conjugacy classes of subgroups.

The subgroup lattice has 857 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3565C211yesmaximal, characteristic, complemented
2#3546C211yesmaximal, characteristic, complemented
3#3377C211yesmaximal, characteristic, complemented
4#3376C211yesmaximal, characteristic, complemented
5#3368C211yesmaximal, characteristic, complemented
6#3366C211yesmaximal, characteristic, complemented
7#3319C211yesmaximal, characteristic, complemented
8#3318C211yesmaximal, characteristic, complemented
9#3317C211yesmaximal, characteristic, complemented
10#3315C211yesmaximal, characteristic, complemented
11#3311C211yesmaximal, characteristic, complemented
12#3310C211yesmaximal, characteristic, complemented
13#3309C211yesmaximal, characteristic, complemented
14#3307C211yesmaximal, characteristic, complemented
15#3305C211yesmaximal, characteristic, complemented
16#3304C211yesmaximal, characteristic, complemented
17#3297C211yesmaximal, characteristic, complemented
18#3296C211yesmaximal, characteristic, complemented
19#3244C211yesmaximal, characteristic, complemented
20#3243C211yesmaximal, characteristic, complemented
21#3228C211yesmaximal, characteristic, complemented
22#3224C211yesmaximal, characteristic, complemented
23#3224C211yesmaximal, characteristic, complemented
24#3212C211yesmaximal, characteristic, complemented
25#3180C211yesmaximal, characteristic, complemented
26#3175C211yesmaximal, characteristic, complemented
27#3173C211yesmaximal, characteristic, complemented
28#3136C211yesmaximal, characteristic, complemented
29#3136C211yesmaximal, characteristic, complemented
30#3135C211yesmaximal, characteristic, complemented
31#2968C211yesmaximal, characteristic, complemented
32#563—21no—
33#562—21no—
34#560—21no—
35#560—21no—
36#557C2211yescharacteristic, complemented
37#556—21no—
38#556C2211yescharacteristic
39#556C2211yescharacteristic, complemented
40#555C2211yescharacteristic, complemented
41#554C2211yescharacteristic, complemented
42#553—21no—
43#553C2211yescharacteristic
44#553C2211yescharacteristic, complemented
45#552—21no—
46#552C2211yescharacteristic
47#552C2211yescharacteristic, complemented
48#550C2211yescharacteristic
49#550C2211yescharacteristic
50#550C2211yescharacteristic
51#547C2211yescharacteristic
52#546—21no—
53#546C2211yescharacteristic
54#546C2211yescharacteristic
55D42C2211yescharacteristic
56#544C2211yescharacteristic, complemented
57#544C2211yescharacteristic, complemented
58#542—21no—
59#542—21no—
60#542C2211yescharacteristic
61#542C2211yescharacteristic
62#542C2211yescharacteristic, complemented
63#542C2211yescharacteristic, complemented
64#541—21no—
65#539—21no—
66#538—21no—
67#538—21no—
68#537—21no—
69#535—21no—
70#535C2211yescharacteristic
71#535C2211yescharacteristic
72#533C2211yescharacteristic, complemented
73#532C2211yescharacteristic
74#532C2211yescharacteristic
75#529C2211yescharacteristic
76#529C2211yescharacteristic, complemented
77#501C2211yescharacteristic, complemented
78#500C2211yescharacteristic, complemented
79#498C2211yescharacteristic, complemented
80#496C2211yescharacteristic
81#495C2211yescharacteristic, complemented
82#495C2211yescharacteristic, complemented
83#491C2211yescharacteristic, complemented
84#491C2211yescharacteristic, complemented
85#490C2211yescharacteristic
86#490C2211yescharacteristic
87#490C2211yescharacteristic
88#490C2211yescharacteristic, complemented
89#490C2211yescharacteristic, complemented
90#489C2211yescharacteristic
91#489C2211yescharacteristic
92#489C2211yescharacteristic, complemented
93#489C2211yescharacteristic, complemented
94#489C2211yescharacteristic, complemented
95#489C2211yescharacteristic, complemented
96#489C2211yescharacteristic, complemented
97#488C2211yescharacteristic
98#488C2211yescharacteristic
99#488C2211yescharacteristic, complemented
100#488C2211yescharacteristic, complemented
101#486C2211yescharacteristic
102#486C2211yescharacteristic
103#486C2211yescharacteristic, complemented
104#486C2211yescharacteristic, complemented
105#485C2211yescharacteristic, complemented
106#485C2211yescharacteristic, complemented
107#484C2211yescharacteristic, complemented
108#483C2211yescharacteristic, complemented
109#482C2211yescharacteristic
110#482C2211yescharacteristic
111#482C2211yescharacteristic
112#482C2211yescharacteristic
113#482C2211yescharacteristic, complemented
114#482C2211yescharacteristic, complemented
115#481C2211yescharacteristic
116#480C2211yescharacteristic
117#479C2211yescharacteristic, complemented
118#479C2211yescharacteristic, complemented
119#478C2211yescharacteristic
120#478C2211yescharacteristic
121#478C2211yescharacteristic, complemented
122#478C2211yescharacteristic, complemented
123#478C2211yescharacteristic, complemented
124#478C2211yescharacteristic, complemented
125#477C2211yescharacteristic, complemented
126#476C2211yescharacteristic, complemented
127#475C2211yescharacteristic, complemented
128#474C2211yescharacteristic, complemented
129#470C2211yescharacteristic, complemented
130#469C2211yescharacteristic
131#468C2211yescharacteristic
132#468C2211yescharacteristic, complemented
133#467C2211yescharacteristic, complemented
134#466C2211yescharacteristic
135#466C2211yescharacteristic
136#466C2211yescharacteristic, complemented
137#465C2211yescharacteristic
138#465C2211yescharacteristic
139#465C2211yescharacteristic, complemented
140#465C2211yescharacteristic, complemented
141#464C2211yescharacteristic
142#464C2211yescharacteristic
143#463C2211yescharacteristic
144#463C2211yescharacteristic
145#462C2211yescharacteristic, complemented
146#461C2211yescharacteristic, complemented
147#460C2211yescharacteristic
148#460C2211yescharacteristic, complemented
149#460C2211yescharacteristic, complemented
150#459C2211yescharacteristic
151#459C2211yescharacteristic, complemented
152#459C2211yescharacteristic, complemented
153#452C2211yescharacteristic, complemented
154#452C2211yescharacteristic, complemented
155#452C2211yescharacteristic, complemented
156#452C2211yescharacteristic, complemented
157#450C2211yescharacteristic
158#450C2211yescharacteristic
159#449C2211yescharacteristic, complemented
160#449C2211yescharacteristic, complemented
161#449C2211yescharacteristic, complemented
162#449C2211yescharacteristic, complemented
163#447C2211yescharacteristic
164#447C2211yescharacteristic
165#446C2211yescharacteristic, complemented
166#446C2211yescharacteristic, complemented
167#442C2211yescharacteristic
168#442C2211yescharacteristic, complemented
169#442C2211yescharacteristic, complemented
170#441C2211yescharacteristic, complemented
171#440C2211yescharacteristic
172#440C2211yescharacteristic, complemented
173#440C2211yescharacteristic, complemented
174#440C2211yescharacteristic, complemented
175C4×Q16C2211yescharacteristic, complemented
176C4×SD16C2211yescharacteristic, complemented
177C4×SD16C2211yescharacteristic, complemented
178C4×D8C2211yescharacteristic, complemented
179#435C2211yescharacteristic
180#435C2211yescharacteristic
181#435C2211yescharacteristic, complemented
182#435C2211yescharacteristic, complemented
183C8×D4C2211yescharacteristic, complemented
184C8×D4C2211yescharacteristic, complemented
185#433C2211yescharacteristic, complemented
186#433C2211yescharacteristic, complemented
187#431C2211yescharacteristic, complemented
188#418C2211yescharacteristic
189#418C2211yescharacteristic
190#417C2211yescharacteristic, complemented
191#417C2211yescharacteristic, complemented
192#416C2211yescharacteristic, complemented
193#416C2211yescharacteristic, complemented
194#416C2211yescharacteristic, complemented
195#416C2211yescharacteristic, complemented
196#416C2211yescharacteristic, complemented
197#416C2211yescharacteristic, complemented
198C2×#102C2211yescharacteristic
199C2×#102C2211yescharacteristic
200#405C2211yescharacteristic, complemented
201#405C2211yescharacteristic, complemented
202C2×#97C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41—21no—
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C2×#41C2311yescharacteristic
209C22×D4—21no—
210C22×D4C2311yescharacteristic
211C22×D4C2311yescharacteristic
212C2×Q16C2311yescharacteristic
213C2×Q16C2311yescharacteristic
214C2×SD16C2311yescharacteristic
215C2×SD16C2311yescharacteristic
216C2×SD16C2311yescharacteristic
217C2×SD16C2311yescharacteristic
218C2×SD16C2311yescharacteristic
219C2×SD16C2311yescharacteristic
220C2×D8C2311yescharacteristic
221C2×D8C2311yescharacteristic
222C2×D8C2311yescharacteristic
223C2×D8C2311yescharacteristic
224C2×M16C2311yescharacteristic
225C2×M16C2311yescharacteristic
226C22×C8C2311yescharacteristic
227C22×C8C2311yescharacteristic
228C22×C8C2311yescharacteristic
229C22×C8C2311yescharacteristic
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8C2311yescharacteristic
234C4⋊Q8C2311yescharacteristic
235C4⋊Q8C2311yescharacteristic
236C4⋊Q8C2311yescharacteristic
237C4⋊Q8C2311yescharacteristic
238C4⋊Q8C2311yescharacteristic
239#127—21no—
240#127—21no—
241#127C2311yescharacteristic
242#127C2311yescharacteristic
243#127C2311yescharacteristic
244#127C2311yescharacteristic
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#126—21no—
254#126—21no—
255#126—21no—
256#126—21no—
257#126—21no—
258#126D411yescharacteristic
259#126D411yescharacteristic
260#125—21no—
261#125—21no—
262#125—21no—
263#125—21no—
264#125—21no—
265#125—21no—
266#125D411yescharacteristic
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#124D411yescharacteristic
281#124C2311yescharacteristic
282#124C2311yescharacteristic
283#124C2311yescharacteristic
284#124C2311yescharacteristic
285#124C2311yescharacteristic
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#123D411yescharacteristic
300#123D411yescharacteristic
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⋊Q8D411yescharacteristic
316C22⋊Q8C2311yescharacteristic
317C22⋊Q8C2311yescharacteristic
318C22⋊Q8C2311yescharacteristic
319C22⋊Q8C2311yescharacteristic
320C22⋊Q8C2311yescharacteristic
321#121—21no—
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#121—21no—
335#121—21no—
336#121—21no—
337#121—21no—
338#121—21no—
339#121—21no—
340#121—21no—
341#121—21no—
342#121D411yescharacteristic
343#121C2311yescharacteristic
344#121C2311yescharacteristic
345#121C2311yescharacteristic
346#121C2311yescharacteristic
347#121C2311yescharacteristic
348#121C2311yescharacteristic
349#121C2311yescharacteristic
350#120—21no—
351#120—21no—
352#120—21no—
353#120—21no—
354#120—21no—
355#120—21no—
356#120—21no—
357#120—21no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8C2311yescharacteristic
363C4×Q8C2311yescharacteristic
364C4×Q8C2311yescharacteristic
365C4×Q8C2311yescharacteristic
366C4×Q8C2311yescharacteristic
367C4×Q8C2311yescharacteristic
368C4×D4—21no—
369C4×D4—21no—
370C4×D4—21no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4C2311yescharacteristic
377C4×D4C2311yescharacteristic
378C4×D4C2311yescharacteristic
379C4×D4C2311yescharacteristic
380C4×D4C2311yescharacteristic
381C4×D4C2311yescharacteristic
382C4×D4C2311yescharacteristic
383C4×D4C2311yescharacteristic
384C4×D4C2311yescharacteristic
385C4×D4C2311yescharacteristic
386#117—21no—
387#117—21no—
388#117—21no—
389#117—21no—
390#117—21no—
391#117C2311yescharacteristic
392#117C2311yescharacteristic
393#117C2311yescharacteristic
394#117C2311yescharacteristic
395#117C2311yescharacteristic
396#117C2311yescharacteristic
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4C2311yescharacteristic
400C2×C4⋊C4C2311yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C42C2311yescharacteristic
404#107C2311yescharacteristic
405#107C2311yescharacteristic
406#107C2311yescharacteristic
407#107C2311yescharacteristic
408#107C2311yescharacteristic
409#107C2311yescharacteristic
410#106C2311yescharacteristic
411#106C2311yescharacteristic
412#106C2311yescharacteristic
413#106C2311yescharacteristic
414#106C2311yescharacteristic
415#106C2311yescharacteristic
416C4⋊C8C2311yescharacteristic
417C4⋊C8C2311yescharacteristic
418C4⋊C8C2311yescharacteristic
419C4⋊C8C2311yescharacteristic
420C4⋊C8C2311yescharacteristic
421C4⋊C8C2311yescharacteristic
422#103C2311yescharacteristic
423#103C2311yescharacteristic
424#103C2311yescharacteristic
425#103C2311yescharacteristic
426#103C2311yescharacteristic
427#103C2311yescharacteristic
428#103C2311yescharacteristic
429#103C2311yescharacteristic
430#103C2311yescharacteristic
431#103C2311yescharacteristic
432#103C2311yescharacteristic
433#103C2311yescharacteristic
434#103C2311yescharacteristic
435#103C2311yescharacteristic
436#102C2311yescharacteristic
437#102C2311yescharacteristic
438#102C2311yescharacteristic
439#102C2311yescharacteristic
440#102C2311yescharacteristic
441#102C2311yescharacteristic
442#102C2311yescharacteristic
443#102C2311yescharacteristic
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
472#97C2311yescharacteristic
473#97C2311yescharacteristic
474C4×C8C2311yescharacteristic
475C4×C8C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478C24—21no—
479C24—21no—
480#41—41no—
481#41—41no—
482#41—41no—
483#41—41no—
484#41—41no—
485#41—41no—
486#41—41no—
487#41—41no—
488#41—82no—
489#41—82no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8C2×D411yescharacteristic
496C2×Q8C2411yescharacteristic
497C2×Q8C2411yescharacteristic
498C2×Q8C2411yescharacteristic
499C2×D4—21no—
500C2×D4—21no—
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—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—41no—
521C2×D4—41no—
522C2×D4—41no—
523C2×D4—41no—
524C2×D4—82no—
525C2×D4C2×D411yescharacteristic
526C2×D4C2×D411yescharacteristic
527C2×D4C2×D411yescharacteristic
528C2×D4C2411yescharacteristic
529C2×D4C2411yescharacteristic
530C2×D4C2411yescharacteristic
531C2×D4C2411yescharacteristic
532C2×D4C2411yescharacteristic
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4C2×D411yescharacteristic
547C22×C4C2×D411yescharacteristic
548C22×C4C2411yescharacteristic
549C22×C4C2411yescharacteristic
550C22×C4C2411yescharacteristic
551Q16—41no—
552Q16—41no—
553SD16—41no—
554SD16—41no—
555SD16—41no—
556SD16—41no—
557SD16—41no—
558SD16—41no—
559D8—41no—
560D8—41no—
561D8—41no—
562D8—41no—
563M16—41no—
564M16—41no—
565C2×C8—41no—
566C2×C8—41no—
567C2×C8—41no—
568C2×C8—41no—
569C2×C8C2411yescharacteristic
570C2×C8C2411yescharacteristic
571C2×C8C2411yescharacteristic
572C2×C8C2411yescharacteristic
573C2×C8C2411yescharacteristic
574C2×C8C2411yescharacteristic
575C2×C8C2411yescharacteristic
576C2×C8C2411yescharacteristic
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⋊C4—21no—
606C4⋊C4C2×D411yescharacteristic
607C4⋊C4C2×D411yescharacteristic
608C4⋊C4C2×D411yescharacteristic
609C4⋊C4C2×D411yescharacteristic
610C4⋊C4C2×D411yescharacteristic
611C4⋊C4C2×D411yescharacteristic
612C4⋊C4C2×D411yescharacteristic
613C4⋊C4C2×D411yescharacteristic
614C4⋊C4C2×D411yescharacteristic
615C4⋊C4C2×D411yescharacteristic
616C4⋊C4C2411yescharacteristic
617C4⋊C4C2411yescharacteristic
618C4⋊C4C2411yescharacteristic
619C4⋊C4C2411yescharacteristic
620C4⋊C4C2411yescharacteristic
621C4⋊C4C2411yescharacteristic
622C4⋊C4C2411yescharacteristic
623C4⋊C4C2411yescharacteristic
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⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4C2×D411yescharacteristic
658C22⋊C4C2×D411yescharacteristic
659C22⋊C4C2×D411yescharacteristic
660C22⋊C4C2×D411yescharacteristic
661C22⋊C4C2×D411yescharacteristic
662C22⋊C4C2×D411yescharacteristic
663C22⋊C4C2×D411yescharacteristic
664C22⋊C4C2×D411yescharacteristic
665C22⋊C4C2×D411yescharacteristic
666C22⋊C4C2×D411yescharacteristic
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—21no—
676C42C2×D411yescharacteristic
677C42C2×D411yescharacteristic
678C42C2411yescharacteristic
679C42C2411yescharacteristic
680C42C2411yescharacteristic
681C42C2411yescharacteristic
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—81no—
688C23—81no—
689C23—81no—
690C23—81no—
691C23—81no—
692C23—81no—
693C23C22×D411yescharacteristic
694C23C22×D411yescharacteristic
695C23C22×D411yescharacteristic
696Q8—21no—
697Q8—21no—
698Q8—21no—
699Q8—21no—
700Q8—21no—
701Q8—21no—
702Q8—41no—
703Q8—81no—
704Q8—81no—
705Q8—81no—
706Q8—81no—
707Q8—81no—
708D4—21no—
709D4—21no—
710D4—21no—
711D4—21no—
712D4—21no—
713D4—21no—
714D4—21no—
715D4—21no—
716D4—21no—
717D4—21no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—42no—
722D4—81no—
723D4—81no—
724D4—81no—
725D4—81no—
726D4—81no—
727D4—81no—
728D4—81no—
729D4—81no—
730D4—81no—
731D4—81no—
732D4—81no—
733D4—81no—
734D4—81no—
735D4—81no—
736D4—81no—
737D4—81no—
738D4—81no—
739D4—81no—
740D4—81no—
741D4—81no—
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—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4C22×D411yescharacteristic
775C2×C4C22×D411yescharacteristic
776C2×C4C22×D411yescharacteristic
777C2×C4C22×D411yescharacteristic
778C2×C4C22×D411yescharacteristic
779C2×C4C22×D411yescharacteristic
780C2×C4C22×D411yescharacteristic
781C2×C4C22×D411yescharacteristic
782C2×C4C22×D411yescharacteristic
783C2×C4C22×D411yescharacteristic
784C2×C4C22×D411yescharacteristic
785C2×C4C2511yescharacteristic
786C8—21no—
787C8—21no—
788C8—21no—
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—21no—
794C22—21no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—162no—
819C22—162no—
820C22C23×D411yescharacteristic
821C4—21no—
822C4—21no—
823C4—21no—
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—41no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4#58511yescharacteristic
844C4#58511yescharacteristic
845C2—41no—
846C2—41no—
847C2—41no—
848C2—81no—
849C2—81no—
850C2—81no—
851C2—81no—
852C2—81no—
853C2#350011yescharacteristic
854C2#358411yescharacteristic
855C2#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. #3546C2semidirect
3. #3377C2semidirect
4. #3376C2semidirect
5. #3368C2semidirect
6. #3366C2semidirect
7. #3319C2semidirect
8. #3318C2semidirect
9. #3317C2semidirect
10. #3315C2semidirect
11. #3311C2semidirect
12. #3310C2semidirect
13. #3309C2semidirect
14. #3307C2semidirect
15. #3305C2semidirect
16. #3304C2semidirect
17. #3297C2semidirect
18. #3296C2semidirect
19. #3244C2semidirect
20. #3243C2semidirect
21. #3228C2semidirect
22. #3224C2semidirect
23. #3224C2semidirect
24. #3212C2semidirect
25. #3180C2semidirect
26. #3175C2semidirect
27. #3173C2semidirect
28. #3136C2semidirect
29. #3136C2semidirect
30. #3135C2semidirect
31. #2968C2semidirect
36. #557C22semidirect
39. #556C22semidirect
40. #555C22semidirect
41. #554C22semidirect
44. #553C22semidirect
47. #552C22semidirect
56. #544C22semidirect
57. #544C22semidirect
62. #542C22semidirect
63. #542C22semidirect
72. #533C22semidirect
76. #529C22semidirect
77. #501C22semidirect
78. #500C22semidirect
79. #498C22semidirect
81. #495C22semidirect
82. #495C22semidirect
83. #491C22semidirect
84. #491C22semidirect
88. #490C22semidirect
89. #490C22semidirect
92. #489C22semidirect
93. #489C22semidirect
94. #489C22semidirect
95. #489C22semidirect
96. #489C22semidirect
99. #488C22semidirect
100. #488C22semidirect
103. #486C22semidirect
104. #486C22semidirect
105. #485C22semidirect
106. #485C22semidirect
107. #484C22semidirect
108. #483C22semidirect
113. #482C22semidirect
114. #482C22semidirect
117. #479C22semidirect
118. #479C22semidirect
121. #478C22semidirect
122. #478C22semidirect
123. #478C22semidirect
124. #478C22semidirect
125. #477C22semidirect
126. #476C22semidirect
127. #475C22semidirect
128. #474C22semidirect
129. #470C22semidirect
132. #468C22semidirect
133. #467C22semidirect
136. #466C22semidirect
139. #465C22semidirect
140. #465C22semidirect
145. #462C22semidirect
146. #461C22semidirect
148. #460C22semidirect
149. #460C22semidirect
151. #459C22semidirect
152. #459C22semidirect
153. #452C22semidirect
154. #452C22semidirect
155. #452C22semidirect
156. #452C22semidirect
159. #449C22semidirect
160. #449C22semidirect
161. #449C22semidirect
162. #449C22semidirect
165. #446C22semidirect
166. #446C22semidirect
168. #442C22semidirect
169. #442C22semidirect
170. #441C22semidirect
172. #440C22semidirect
173. #440C22semidirect
174. #440C22semidirect
175. C4×Q16C22semidirect
176. C4×SD16C22semidirect
177. C4×SD16C22semidirect
178. C4×D8C22semidirect
181. #435C22semidirect
182. #435C22semidirect
183. C8×D4C22semidirect
184. C8×D4C22semidirect
185. #433C22semidirect
186. #433C22semidirect
187. #431C22semidirect
190. #417C22semidirect
191. #417C22semidirect
192. #416C22semidirect
193. #416C22semidirect
194. #416C22semidirect
195. #416C22semidirect
196. #416C22semidirect
197. #416C22semidirect
200. #405C22semidirect
201. #405C22semidirect
202. C2×#97C22semidirect

Maximal subgroups

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

subgroupindex
#35652
#35462
#33772
#33762
#33682
#33662
#33192
#33182
#33172
#33152
#33112
#33102
#33092
#33072
#33052
#33042
#32972
#32962
#32442
#32432
#32282
#32242
#32122
#31802
#31752
#31732
#31362
#31352
#29682