Finite Group Databasebeta

← #62224

Subgroups — #62224

Order 256.

849 conjugacy classes of subgroups.

The subgroup lattice has 825 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3565C211yesmaximal, characteristic, complemented
2#3520C211yesmaximal, characteristic, complemented
3#3386C211yesmaximal, characteristic, complemented
4#3384C211yesmaximal, characteristic, complemented
5#3377C211yesmaximal, characteristic, complemented
6#3376C211yesmaximal, characteristic, complemented
7#3357C211yesmaximal, characteristic, complemented
8#3356C211yesmaximal, characteristic, complemented
9#3346C211yesmaximal, characteristic, complemented
10#3345C211yesmaximal, characteristic, complemented
11#3344C211yesmaximal, characteristic, complemented
12#3343C211yesmaximal, characteristic, complemented
13#3323C211yesmaximal, characteristic, complemented
14#3322C211yesmaximal, characteristic, complemented
15#3319C211yesmaximal, characteristic, complemented
16#3315C211yesmaximal, characteristic, complemented
17#3311C211yesmaximal, characteristic, complemented
18#3307C211yesmaximal, characteristic, complemented
19#3263C211yesmaximal, characteristic, complemented
20#3262C211yesmaximal, characteristic, complemented
21#3252C211yesmaximal, characteristic, complemented
22#3244C211yesmaximal, characteristic, complemented
23#3243C211yesmaximal, characteristic, complemented
24#3237C211yesmaximal, characteristic, complemented
25#3125C211yesmaximal, characteristic, complemented
26#3124C211yesmaximal, characteristic, complemented
27#3114C211yesmaximal, characteristic, complemented
28#3084C211yesmaximal, characteristic, complemented
29#3083C211yesmaximal, characteristic, complemented
30#3077C211yesmaximal, characteristic, complemented
31#2995C211yesmaximal, characteristic, complemented
32#563—21no—
33#562—21no—
34#557C2211yescharacteristic, complemented
35#556—21no—
36#556C2211yescharacteristic
37#556C2211yescharacteristic
38#555C2211yescharacteristic
39#554C2211yescharacteristic
40#554C2211yescharacteristic
41#554C2211yescharacteristic, complemented
42#553C2211yescharacteristic
43#553C2211yescharacteristic, complemented
44#552—21no—
45#552—21no—
46#552C2211yescharacteristic
47#552C2211yescharacteristic, complemented
48#551—21no—
49#551—21no—
50D4×Q8C2211yescharacteristic
51#548—21no—
52#547C2211yescharacteristic
53#547C2211yescharacteristic
54#546C2211yescharacteristic
55#546C2211yescharacteristic
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#539—21no—
67#539—21no—
68#533C2211yescharacteristic
69#533C2211yescharacteristic
70#529C2211yescharacteristic
71#529C2211yescharacteristic
72#525—21no—
73C2×C22⋊Q8—21no—
74#520C2211yescharacteristic
75#520C2211yescharacteristic
76C2×C4×D4C2211yescharacteristic
77#501C2211yescharacteristic, complemented
78#501C2211yescharacteristic, complemented
79#501C2211yescharacteristic, complemented
80#501C2211yescharacteristic, complemented
81#500C2211yescharacteristic, complemented
82#498C2211yescharacteristic, complemented
83#491C2211yescharacteristic, complemented
84#491C2211yescharacteristic, complemented
85#489C2211yescharacteristic
86#489C2211yescharacteristic
87#488C2211yescharacteristic
88#488C2211yescharacteristic
89#485C2211yescharacteristic
90#485C2211yescharacteristic
91#485C2211yescharacteristic
92#485C2211yescharacteristic
93#485C2211yescharacteristic, complemented
94#485C2211yescharacteristic, complemented
95#484C2211yescharacteristic, complemented
96#484C2211yescharacteristic, complemented
97#483C2211yescharacteristic
98#483C2211yescharacteristic, complemented
99#483C2211yescharacteristic, complemented
100#482C2211yescharacteristic
101#482C2211yescharacteristic
102#481C2211yescharacteristic
103#481C2211yescharacteristic, complemented
104#480C2211yescharacteristic
105#480C2211yescharacteristic
106#480C2211yescharacteristic, complemented
107#479C2211yescharacteristic, complemented
108#479C2211yescharacteristic, complemented
109#479C2211yescharacteristic, complemented
110#479C2211yescharacteristic, complemented
111#478C2211yescharacteristic
112#478C2211yescharacteristic
113#478C2211yescharacteristic
114#478C2211yescharacteristic
115#478C2211yescharacteristic
116#478C2211yescharacteristic
117#478C2211yescharacteristic
118#478C2211yescharacteristic
119#477C2211yescharacteristic, complemented
120#477C2211yescharacteristic, complemented
121#477C2211yescharacteristic, complemented
122#477C2211yescharacteristic, complemented
123#477C2211yescharacteristic, complemented
124#476C2211yescharacteristic
125#476C2211yescharacteristic
126#476C2211yescharacteristic
127#476C2211yescharacteristic, complemented
128#476C2211yescharacteristic, complemented
129#475C2211yescharacteristic, complemented
130#475C2211yescharacteristic, complemented
131#475C2211yescharacteristic, complemented
132#475C2211yescharacteristic, complemented
133#474C2211yescharacteristic
134#474C2211yescharacteristic
135#474C2211yescharacteristic
136#474C2211yescharacteristic, complemented
137#470C2211yescharacteristic
138#470C2211yescharacteristic
139#470C2211yescharacteristic, complemented
140#469C2211yescharacteristic
141#468C2211yescharacteristic
142#468C2211yescharacteristic
143#468C2211yescharacteristic
144#468C2211yescharacteristic, complemented
145#467C2211yescharacteristic, complemented
146#466C2211yescharacteristic
147#465C2211yescharacteristic
148#465C2211yescharacteristic, complemented
149#464C2211yescharacteristic
150#464C2211yescharacteristic
151#464C2211yescharacteristic, complemented
152#464C2211yescharacteristic, complemented
153#463C2211yescharacteristic
154#463C2211yescharacteristic
155#463C2211yescharacteristic
156#463C2211yescharacteristic
157#462C2211yescharacteristic, complemented
158#461C2211yescharacteristic, complemented
159#452C2211yescharacteristic
160#452C2211yescharacteristic
161#450C2211yescharacteristic
162#449C2211yescharacteristic
163#449C2211yescharacteristic
164#447C2211yescharacteristic
165#446C2211yescharacteristic, complemented
166#446C2211yescharacteristic, complemented
167#442C2211yescharacteristic
168#442C2211yescharacteristic
169#442C2211yescharacteristic
170#441C2211yescharacteristic, complemented
171#440C2211yescharacteristic
172#440C2211yescharacteristic
173#440C2211yescharacteristic
174#440C2211yescharacteristic, complemented
175C4×Q16C2211yescharacteristic, complemented
176C4×SD16C2211yescharacteristic
177C4×SD16C2211yescharacteristic, complemented
178C4×D8C2211yescharacteristic
179#436C2211yescharacteristic
180#436C2211yescharacteristic
181#435C2211yescharacteristic
182#435C2211yescharacteristic
183#435C2211yescharacteristic, complemented
184#435C2211yescharacteristic, complemented
185#433C2211yescharacteristic, complemented
186#433C2211yescharacteristic, complemented
187#432C2211yescharacteristic
188#428C2211yescharacteristic
189#428C2211yescharacteristic
190#428C2211yescharacteristic, complemented
191#428C2211yescharacteristic, complemented
192C2×#107C2211yescharacteristic, complemented
193C2×#106C2211yescharacteristic, complemented
194#424C2211yescharacteristic, complemented
195#424C2211yescharacteristic, complemented
196#423C2211yescharacteristic
197#418C2211yescharacteristic
198#418C2211yescharacteristic
199#417C2211yescharacteristic
200#417C2211yescharacteristic
201#416C2211yescharacteristic
202#416C2211yescharacteristic
203C2×#41—21no—
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C22×Q8—21no—
207C22×D4C2311yescharacteristic
208C23×C4—21no—
209C2×Q16C2311yescharacteristic
210C2×Q16C2311yescharacteristic
211C2×SD16C2311yescharacteristic
212C2×SD16C2311yescharacteristic
213C2×SD16C2311yescharacteristic
214C2×SD16C2311yescharacteristic
215C2×D8C2311yescharacteristic
216C2×D8C2311yescharacteristic
217C2×M16C2311yescharacteristic
218C2×M16C2311yescharacteristic
219C2×M16C2311yescharacteristic
220C2×M16C2311yescharacteristic
221C22×C8C2311yescharacteristic
222C22×C8C2311yescharacteristic
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
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#126D411yescharacteristic
248#126D411yescharacteristic
249#125—21no—
250#125—21no—
251#125—21no—
252#125—21no—
253#125—21no—
254#125—21no—
255#125—21no—
256#125—21no—
257#125—21no—
258#125D411yescharacteristic
259#125C2311yescharacteristic
260#125C2311yescharacteristic
261#125C2311yescharacteristic
262#125C2311yescharacteristic
263#125C2311yescharacteristic
264#124—21no—
265#124—21no—
266#124—21no—
267#124—21no—
268#124—21no—
269#124—21no—
270#124—21no—
271#124D411yescharacteristic
272#124C2311yescharacteristic
273#124C2311yescharacteristic
274#124C2311yescharacteristic
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#123D411yescharacteristic
291#123D411yescharacteristic
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⋊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⋊Q8D411yescharacteristic
316C22⋊Q8C2311yescharacteristic
317C22⋊Q8C2311yescharacteristic
318C22⋊Q8C2311yescharacteristic
319C22⋊Q8C2311yescharacteristic
320C22⋊Q8C2311yescharacteristic
321C22⋊Q8C2311yescharacteristic
322C22⋊Q8C2311yescharacteristic
323#121—21no—
324#121—21no—
325#121—21no—
326#121—21no—
327#121—21no—
328#121—21no—
329#121D411yescharacteristic
330#121C2311yescharacteristic
331#121C2311yescharacteristic
332#121C2311yescharacteristic
333#121C2311yescharacteristic
334#121C2311yescharacteristic
335#120—21no—
336#120—21no—
337C4×Q8—21no—
338C4×Q8—21no—
339C4×Q8—21no—
340C4×Q8—21no—
341C4×Q8—21no—
342C4×Q8C2311yescharacteristic
343C4×Q8C2311yescharacteristic
344C4×Q8C2311yescharacteristic
345C4×Q8C2311yescharacteristic
346C4×Q8C2311yescharacteristic
347C4×Q8C2311yescharacteristic
348C4×Q8C2311yescharacteristic
349C4×Q8C2311yescharacteristic
350C4×D4—21no—
351C4×D4—21no—
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×D4—21no—
361C4×D4C2311yescharacteristic
362C4×D4C2311yescharacteristic
363C4×D4C2311yescharacteristic
364C4×D4C2311yescharacteristic
365C4×D4C2311yescharacteristic
366C4×D4C2311yescharacteristic
367C4×D4C2311yescharacteristic
368C4×D4C2311yescharacteristic
369C4×D4C2311yescharacteristic
370C4×D4C2311yescharacteristic
371C4×D4C2311yescharacteristic
372C4×D4C2311yescharacteristic
373#117—21no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117—21no—
379#117—21no—
380#117—21no—
381#117C2311yescharacteristic
382#117C2311yescharacteristic
383#117C2311yescharacteristic
384#117C2311yescharacteristic
385#117C2311yescharacteristic
386#117C2311yescharacteristic
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4C2311yescharacteristic
392C2×C4⋊C4C2311yescharacteristic
393C2×C4⋊C4C2311yescharacteristic
394C2×C4⋊C4C2311yescharacteristic
395C2×C4⋊C4C2311yescharacteristic
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—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#106C2311yescharacteristic
413#106C2311yescharacteristic
414#106C2311yescharacteristic
415#106C2311yescharacteristic
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#102C2311yescharacteristic
451#102C2311yescharacteristic
452#102C2311yescharacteristic
453#102C2311yescharacteristic
454#102C2311yescharacteristic
455#102C2311yescharacteristic
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
478C24—21no—
479#41—22no—
480#41—22no—
481#41—41no—
482#41—41no—
483#41—82no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—82no—
492C2×Q8C2×D411yescharacteristic
493C2×Q8C2411yescharacteristic
494C2×Q8C2411yescharacteristic
495C2×Q8C2411yescharacteristic
496C2×D4—22no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—41no—
506C2×D4C2×D411yescharacteristic
507C2×D4C2×D411yescharacteristic
508C2×D4C2×D411yescharacteristic
509C2×D4C2411yescharacteristic
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×C4—21no—
527C22×C4—21no—
528C22×C4—82no—
529C22×C4C2×D411yescharacteristic
530C22×C4C2×D411yescharacteristic
531C22×C4C2411yescharacteristic
532C22×C4C2411yescharacteristic
533C22×C4C2411yescharacteristic
534Q16—41no—
535Q16—41no—
536SD16—22no—
537SD16—41no—
538SD16—41no—
539SD16—41no—
540D8—22no—
541D8—41no—
542M16—41no—
543M16—41no—
544M16—41no—
545M16—41no—
546C2×C8—41no—
547C2×C8—41no—
548C2×C8C2411yescharacteristic
549C2×C8C2411yescharacteristic
550C2×C8C2411yescharacteristic
551C2×C8C2411yescharacteristic
552C2×C8C2411yescharacteristic
553C2×C8C2411yescharacteristic
554C2×C8C2411yescharacteristic
555C2×C8C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
595C4⋊C4C2×D411yescharacteristic
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⋊C4C2411yescharacteristic
605C4⋊C4C2411yescharacteristic
606C4⋊C4C2411yescharacteristic
607C4⋊C4C2411yescharacteristic
608C4⋊C4C2411yescharacteristic
609C4⋊C4C2411yescharacteristic
610C4⋊C4C2411yescharacteristic
611C4⋊C4C2411yescharacteristic
612C4⋊C4C2411yescharacteristic
613C4⋊C4C2411yescharacteristic
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⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4C2×D411yescharacteristic
646C22⋊C4C2×D411yescharacteristic
647C22⋊C4C2×D411yescharacteristic
648C22⋊C4C2×D411yescharacteristic
649C22⋊C4C2×D411yescharacteristic
650C22⋊C4C2×D411yescharacteristic
651C22⋊C4C2×D411yescharacteristic
652C22⋊C4C2×D411yescharacteristic
653C22⋊C4C2×D411yescharacteristic
654C22⋊C4C2×D411yescharacteristic
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—
674C23—21no—
675C23—42no—
676C23—42no—
677C23—81no—
678C23C22×D411yescharacteristic
679C23C22×D411yescharacteristic
680C23C22×D411yescharacteristic
681Q8—21no—
682Q8—21no—
683Q8—21no—
684Q8—21no—
685Q8—21no—
686Q8—21no—
687Q8—41no—
688Q8—42no—
689Q8—81no—
690Q8—81no—
691Q8—81no—
692Q8—81no—
693Q8—81no—
694Q8—81no—
695D4—21no—
696D4—21no—
697D4—21no—
698D4—21no—
699D4—21no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—42no—
704D4—42no—
705D4—42no—
706D4—81no—
707D4—81no—
708D4—81no—
709D4—81no—
710D4—81no—
711D42−1+412yes—
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—21no—
730C2×C4—21no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—81no—
738C2×C4—81no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4—81no—
742C2×C4—81no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4—81no—
748C2×C4—81no—
749C2×C4C22×D411yescharacteristic
750C2×C4C22×D411yescharacteristic
751C2×C4C22×D411yescharacteristic
752C2×C4C22×D411yescharacteristic
753C2×C4C22×D411yescharacteristic
754C2×C4C22×D411yescharacteristic
755C2×C4C22×D411yescharacteristic
756C2×C4C22×D411yescharacteristic
757C2×C4C22×D411yescharacteristic
758C2×C4C22×D411yescharacteristic
759C2×C4C22×D411yescharacteristic
760C2×C4C2511yescharacteristic
761C8—21no—
762C8—21no—
763C8—21no—
764C8—21no—
765C8—21no—
766C8—21no—
767C8—21no—
768C8—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—21no—
778C22—22no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—84no—
788C22C23×D411yescharacteristic
789C4—21no—
790C4—21no—
791C4—21no—
792C4—21no—
793C4—21no—
794C4—21no—
795C4—21no—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—41no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4C2×2−1+411yescharacteristic
814C4#58511yescharacteristic
815C2—41no—
816C2—41no—
817C2—41no—
818C2—42no—
819C2—81no—
820C2—81no—
821C2#348911yescharacteristic
822C2#358511yescharacteristic
823C2#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. #3520C2semidirect
3. #3386C2semidirect
4. #3384C2semidirect
5. #3377C2semidirect
6. #3376C2semidirect
7. #3357C2semidirect
8. #3356C2semidirect
9. #3346C2semidirect
10. #3345C2semidirect
11. #3344C2semidirect
12. #3343C2semidirect
13. #3323C2semidirect
14. #3322C2semidirect
15. #3319C2semidirect
16. #3315C2semidirect
17. #3311C2semidirect
18. #3307C2semidirect
19. #3263C2semidirect
20. #3262C2semidirect
21. #3252C2semidirect
22. #3244C2semidirect
23. #3243C2semidirect
24. #3237C2semidirect
25. #3125C2semidirect
26. #3124C2semidirect
27. #3114C2semidirect
28. #3084C2semidirect
29. #3083C2semidirect
30. #3077C2semidirect
31. #2995C2semidirect
34. #557C22semidirect
41. #554C22semidirect
43. #553C22semidirect
47. #552C22semidirect
56. #544C22semidirect
57. #544C22semidirect
62. #542C22semidirect
63. #542C22semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #501C22semidirect
80. #501C22semidirect
81. #500C22semidirect
82. #498C22semidirect
83. #491C22semidirect
84. #491C22semidirect
93. #485C22semidirect
94. #485C22semidirect
95. #484C22semidirect
96. #484C22semidirect
98. #483C22semidirect
99. #483C22semidirect
103. #481C22semidirect
106. #480C22semidirect
107. #479C22semidirect
108. #479C22semidirect
109. #479C22semidirect
110. #479C22semidirect
119. #477C22semidirect
120. #477C22semidirect
121. #477C22semidirect
122. #477C22semidirect
123. #477C22semidirect
127. #476C22semidirect
128. #476C22semidirect
129. #475C22semidirect
130. #475C22semidirect
131. #475C22semidirect
132. #475C22semidirect
136. #474C22semidirect
139. #470C22semidirect
144. #468C22semidirect
145. #467C22semidirect
148. #465C22semidirect
151. #464C22semidirect
152. #464C22semidirect
157. #462C22semidirect
158. #461C22semidirect
165. #446C22semidirect
166. #446C22semidirect
170. #441C22semidirect
174. #440C22semidirect
175. C4×Q16C22semidirect
177. C4×SD16C22semidirect
183. #435C22semidirect
184. #435C22semidirect
185. #433C22semidirect
186. #433C22semidirect
190. #428C22semidirect
191. #428C22semidirect
192. C2×#107C22semidirect
193. C2×#106C22semidirect
194. #424C22semidirect
195. #424C22semidirect

Maximal subgroups

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

subgroupindex
#35652
#35202
#33862
#33842
#33772
#33762
#33572
#33562
#33462
#33452
#33442
#33432
#33232
#33222
#33192
#33152
#33112
#33072
#32632
#32622
#32522
#32442
#32432
#32372
#31252
#31242
#31142
#30842
#30832
#30772
#29952