Finite Group Databasebeta

← #62228

Subgroups — #62228

Order 256.

847 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#3544C211yesmaximal, characteristic, complemented
2#3521C211yesmaximal, characteristic, complemented
3#3389C211yesmaximal, characteristic, complemented
4#3385C211yesmaximal, characteristic, complemented
5#3376C211yesmaximal, characteristic, complemented
6#3369C211yesmaximal, characteristic, complemented
7#3353C211yesmaximal, characteristic, complemented
8#3351C211yesmaximal, characteristic, complemented
9#3349C211yesmaximal, characteristic, complemented
10#3348C211yesmaximal, characteristic, complemented
11#3345C211yesmaximal, characteristic, complemented
12#3344C211yesmaximal, characteristic, complemented
13#3330C211yesmaximal, characteristic, complemented
14#3323C211yesmaximal, characteristic, complemented
15#3319C211yesmaximal, characteristic, complemented
16#3315C211yesmaximal, characteristic, complemented
17#3314C211yesmaximal, characteristic, complemented
18#3306C211yesmaximal, characteristic, complemented
19#3262C211yesmaximal, characteristic, complemented
20#3258C211yesmaximal, characteristic, complemented
21#3256C211yesmaximal, characteristic, complemented
22#3243C211yesmaximal, characteristic, complemented
23#3242C211yesmaximal, characteristic, complemented
24#3239C211yesmaximal, characteristic, complemented
25#3125C211yesmaximal, characteristic, complemented
26#3118C211yesmaximal, characteristic, complemented
27#3111C211yesmaximal, characteristic, complemented
28#3084C211yesmaximal, characteristic, complemented
29#3081C211yesmaximal, characteristic, complemented
30#3079C211yesmaximal, characteristic, complemented
31#2995C211yesmaximal, characteristic, complemented
32#563—21no—
33#563—21no—
34Q82C2211yescharacteristic, complemented
35#556C2211yescharacteristic
36#556C2211yescharacteristic
37#555C2211yescharacteristic
38#554C2211yescharacteristic
39#554C2211yescharacteristic
40#554C2211yescharacteristic, complemented
41#553—21no—
42#553C2211yescharacteristic
43#552—21no—
44#552—21no—
45#552C2211yescharacteristic
46#552C2211yescharacteristic
47#552C2211yescharacteristic, complemented
48#551—21no—
49#551—21no—
50#547—21no—
51#547C2211yescharacteristic
52#547C2211yescharacteristic
53#547C2211yescharacteristic, complemented
54#546C2211yescharacteristic
55#546C2211yescharacteristic
56#544—21no—
57#544C2211yescharacteristic
58#544C2211yescharacteristic, complemented
59#542—21no—
60#542C2211yescharacteristic
61#542C2211yescharacteristic
62#542C2211yescharacteristic, complemented
63#541C2211yescharacteristic
64#539—21no—
65#538—21no—
66#536—21no—
67#536—21no—
68C2×C4⋊Q8C2211yescharacteristic, complemented
69#529—21no—
70#529C2211yescharacteristic
71#529C2211yescharacteristic
72#529C2211yescharacteristic, complemented
73C2×#126—21no—
74#520C2211yescharacteristic
75#518C2211yescharacteristic
76C4×#41C2211yescharacteristic
77#501C2211yescharacteristic, complemented
78#501C2211yescharacteristic, complemented
79#501C2211yescharacteristic, complemented
80#501C2211yescharacteristic, complemented
81#500C2211yescharacteristic, complemented
82#499C2211yescharacteristic, complemented
83#491C2211yescharacteristic, complemented
84#489C2211yescharacteristic
85#489C2211yescharacteristic
86#489C2211yescharacteristic
87#488C2211yescharacteristic
88#487C2211yescharacteristic, complemented
89#485C2211yescharacteristic
90#485C2211yescharacteristic
91#485C2211yescharacteristic
92#485C2211yescharacteristic, complemented
93#485C2211yescharacteristic, complemented
94#484C2211yescharacteristic
95#484C2211yescharacteristic, complemented
96#484C2211yescharacteristic, complemented
97#484C2211yescharacteristic, complemented
98#483C2211yescharacteristic
99#483C2211yescharacteristic, complemented
100#482C2211yescharacteristic
101#482C2211yescharacteristic
102#482C2211yescharacteristic, complemented
103#481C2211yescharacteristic
104#481C2211yescharacteristic
105#481C2211yescharacteristic, complemented
106#480C2211yescharacteristic
107#479C2211yescharacteristic, complemented
108#479C2211yescharacteristic, complemented
109#479C2211yescharacteristic, complemented
110#479C2211yescharacteristic, complemented
111#479C2211yescharacteristic, complemented
112#478C2211yescharacteristic
113#478C2211yescharacteristic
114#478C2211yescharacteristic
115#478C2211yescharacteristic
116#478C2211yescharacteristic
117#478C2211yescharacteristic, complemented
118#478C2211yescharacteristic, complemented
119#477C2211yescharacteristic, complemented
120#477C2211yescharacteristic, complemented
121#477C2211yescharacteristic, complemented
122#476C2211yescharacteristic
123#476C2211yescharacteristic
124#476C2211yescharacteristic
125#476C2211yescharacteristic
126#475C2211yescharacteristic, complemented
127#475C2211yescharacteristic, complemented
128#475C2211yescharacteristic, complemented
129#475C2211yescharacteristic, complemented
130#475C2211yescharacteristic, complemented
131#474C2211yescharacteristic
132#474C2211yescharacteristic
133#474C2211yescharacteristic
134#474C2211yescharacteristic
135#474C2211yescharacteristic
136#474C2211yescharacteristic, complemented
137#470C2211yescharacteristic
138#470C2211yescharacteristic, complemented
139#469C2211yescharacteristic
140#468C2211yescharacteristic
141#468C2211yescharacteristic
142#468C2211yescharacteristic
143#468C2211yescharacteristic, complemented
144#468C2211yescharacteristic, complemented
145#467C2211yescharacteristic
146#467C2211yescharacteristic, complemented
147#466C2211yescharacteristic
148#465C2211yescharacteristic
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#441C2211yescharacteristic, complemented
172#440C2211yescharacteristic
173#440C2211yescharacteristic
174#440C2211yescharacteristic, complemented
175C4×SD16C2211yescharacteristic
176C4×SD16C2211yescharacteristic
177C4×SD16C2211yescharacteristic, complemented
178C4×D8C2211yescharacteristic
179#436C2211yescharacteristic
180#436C2211yescharacteristic, complemented
181#435C2211yescharacteristic
182#435C2211yescharacteristic
183#435C2211yescharacteristic
184#435C2211yescharacteristic, complemented
185#433C2211yescharacteristic
186#433C2211yescharacteristic, complemented
187#432C2211yescharacteristic, complemented
188#428C2211yescharacteristic
189#428C2211yescharacteristic, complemented
190#428C2211yescharacteristic, complemented
191#428C2211yescharacteristic, complemented
192#427C2211yescharacteristic
193C2×#106C2211yescharacteristic, complemented
194#424C2211yescharacteristic
195#424C2211yescharacteristic, complemented
196#423C2211yescharacteristic, complemented
197#418C2211yescharacteristic
198#417C2211yescharacteristic
199#417C2211yescharacteristic
200#417C2211yescharacteristic
201#416C2211yescharacteristic
202C2×#102C2211yescharacteristic
203C2×#41—21no—
204C2×#41—21no—
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C22×Q8—21no—
208C22×D4C2311yescharacteristic
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⋊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#125D411yescharacteristic
264#125C2311yescharacteristic
265#125C2311yescharacteristic
266#125C2311yescharacteristic
267#125C2311yescharacteristic
268#125C2311yescharacteristic
269#124—21no—
270#124—21no—
271#124—21no—
272#124—21no—
273#124—21no—
274#124—21no—
275#124D411yescharacteristic
276#124C2311yescharacteristic
277#124C2311yescharacteristic
278#124C2311yescharacteristic
279#123—21no—
280#123—21no—
281#123—21no—
282#123—21no—
283#123—21no—
284#123—21no—
285#123—21no—
286#123—21no—
287#123—21no—
288#123—21no—
289#123—21no—
290#123—21no—
291#123—21no—
292#123—21no—
293#123—21no—
294#123—21no—
295#123—21no—
296#123D411yescharacteristic
297#123D411yescharacteristic
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⋊Q8D411yescharacteristic
317C22⋊Q8C2311yescharacteristic
318C22⋊Q8C2311yescharacteristic
319C22⋊Q8C2311yescharacteristic
320C22⋊Q8C2311yescharacteristic
321C22⋊Q8C2311yescharacteristic
322C22⋊Q8C2311yescharacteristic
323C22⋊Q8C2311yescharacteristic
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×Q8C2311yescharacteristic
340C4×Q8C2311yescharacteristic
341C4×Q8C2311yescharacteristic
342C4×Q8C2311yescharacteristic
343C4×Q8C2311yescharacteristic
344C4×Q8C2311yescharacteristic
345C4×Q8C2311yescharacteristic
346C4×Q8C2311yescharacteristic
347C4×D4—21no—
348C4×D4—21no—
349C4×D4—21no—
350C4×D4—21no—
351C4×D4—21no—
352C4×D4—21no—
353C4×D4—21no—
354C4×D4—21no—
355C4×D4—21no—
356C4×D4—21no—
357C4×D4C2311yescharacteristic
358C4×D4C2311yescharacteristic
359C4×D4C2311yescharacteristic
360C4×D4C2311yescharacteristic
361C4×D4C2311yescharacteristic
362C4×D4C2311yescharacteristic
363C4×D4C2311yescharacteristic
364C4×D4C2311yescharacteristic
365C4×D4C2311yescharacteristic
366C4×D4C2311yescharacteristic
367C4×D4C2311yescharacteristic
368C4×D4C2311yescharacteristic
369#117—21no—
370#117—21no—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117C2311yescharacteristic
379#117C2311yescharacteristic
380#117C2311yescharacteristic
381#117C2311yescharacteristic
382#117C2311yescharacteristic
383#117C2311yescharacteristic
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4C2311yescharacteristic
390C2×C4⋊C4C2311yescharacteristic
391C2×C4⋊C4C2311yescharacteristic
392C2×C4⋊C4C2311yescharacteristic
393C2×C4⋊C4C2311yescharacteristic
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
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#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—
484#41—82no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—82no—
493C2×Q8C2×D411yescharacteristic
494C2×Q8C2411yescharacteristic
495C2×Q8C2411yescharacteristic
496C2×Q8C2411yescharacteristic
497C2×D4—22no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—41no—
507C2×D4C2×D411yescharacteristic
508C2×D4C2×D411yescharacteristic
509C2×D4C2×D411yescharacteristic
510C2×D4C2411yescharacteristic
511C2×D4C2411yescharacteristic
512C2×D4C2411yescharacteristic
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—21no—
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—81no—
677C23—81no—
678C23C22×D411yescharacteristic
679C23C22×D411yescharacteristic
680C23C22×D411yescharacteristic
681Q8—21no—
682Q8—21no—
683Q8—21no—
684Q8—21no—
685Q8—21no—
686Q8—21no—
687Q8—41no—
688Q8—81no—
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—42no—
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—42no—
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—162no—
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. #3544C2semidirect
2. #3521C2semidirect
3. #3389C2semidirect
4. #3385C2semidirect
5. #3376C2semidirect
6. #3369C2semidirect
7. #3353C2semidirect
8. #3351C2semidirect
9. #3349C2semidirect
10. #3348C2semidirect
11. #3345C2semidirect
12. #3344C2semidirect
13. #3330C2semidirect
14. #3323C2semidirect
15. #3319C2semidirect
16. #3315C2semidirect
17. #3314C2semidirect
18. #3306C2semidirect
19. #3262C2semidirect
20. #3258C2semidirect
21. #3256C2semidirect
22. #3243C2semidirect
23. #3242C2semidirect
24. #3239C2semidirect
25. #3125C2semidirect
26. #3118C2semidirect
27. #3111C2semidirect
28. #3084C2semidirect
29. #3081C2semidirect
30. #3079C2semidirect
31. #2995C2semidirect
34. Q82C22semidirect
40. #554C22semidirect
47. #552C22semidirect
53. #547C22semidirect
58. #544C22semidirect
62. #542C22semidirect
68. C2×C4⋊Q8C22semidirect
72. #529C22semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #501C22semidirect
80. #501C22semidirect
81. #500C22semidirect
82. #499C22semidirect
83. #491C22semidirect
88. #487C22semidirect
92. #485C22semidirect
93. #485C22semidirect
95. #484C22semidirect
96. #484C22semidirect
97. #484C22semidirect
99. #483C22semidirect
102. #482C22semidirect
105. #481C22semidirect
107. #479C22semidirect
108. #479C22semidirect
109. #479C22semidirect
110. #479C22semidirect
111. #479C22semidirect
117. #478C22semidirect
118. #478C22semidirect
119. #477C22semidirect
120. #477C22semidirect
121. #477C22semidirect
126. #475C22semidirect
127. #475C22semidirect
128. #475C22semidirect
129. #475C22semidirect
130. #475C22semidirect
136. #474C22semidirect
138. #470C22semidirect
143. #468C22semidirect
144. #468C22semidirect
146. #467C22semidirect
151. #464C22semidirect
152. #464C22semidirect
157. #462C22semidirect
158. #461C22semidirect
165. #446C22semidirect
166. #446C22semidirect
170. #441C22semidirect
171. #441C22semidirect
174. #440C22semidirect
177. C4×SD16C22semidirect
180. #436C22semidirect
184. #435C22semidirect
186. #433C22semidirect
187. #432C22semidirect
189. #428C22semidirect
190. #428C22semidirect
191. #428C22semidirect
193. C2×#106C22semidirect
195. #424C22semidirect
196. #423C22semidirect

Maximal subgroups

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

subgroupindex
#35442
#35212
#33892
#33852
#33762
#33692
#33532
#33512
#33492
#33482
#33452
#33442
#33302
#33232
#33192
#33152
#33142
#33062
#32622
#32582
#32562
#32432
#32422
#32392
#31252
#31182
#31112
#30842
#30812
#30792
#29952