Finite Group Databasebeta

← #62232

Subgroups — #62232

Order 256.

851 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3555C211yesmaximal, characteristic, complemented
2#3513C211yesmaximal, characteristic
3#3388C211yesmaximal, characteristic, complemented
4#3385C211yesmaximal, characteristic, complemented
5#3375C211yesmaximal, characteristic, complemented
6#3371C211yesmaximal, characteristic, complemented
7#3353C211yesmaximal, characteristic, complemented
8#3352C211yesmaximal, characteristic, complemented
9#3350C211yesmaximal, characteristic, complemented
10#3349C211yesmaximal, characteristic, complemented
11#3346C211yesmaximal, characteristic, complemented
12#3343C211yesmaximal, characteristic, complemented
13#3324C211yesmaximal, characteristic, complemented
14#3323C211yesmaximal, characteristic, complemented
15#3314C211yesmaximal, characteristic, complemented
16#3311C211yesmaximal, characteristic, complemented
17#3311C211yesmaximal, characteristic, complemented
18#3310C211yesmaximal, characteristic, complemented
19#3260C211yesmaximal, characteristic, complemented
20#3258C211yesmaximal, characteristic, complemented
21#3252C211yesmaximal, characteristic, complemented
22#3243C211yesmaximal, characteristic, complemented
23#3241C211yesmaximal, characteristic, complemented
24#3240C211yesmaximal, characteristic, complemented
25#3123C211yesmaximal, characteristic, complemented
26#3120C211yesmaximal, characteristic, complemented
27#3110C211yesmaximal, characteristic, complemented
28#3083C211yesmaximal, characteristic, complemented
29#3081C211yesmaximal, characteristic, complemented
30#3077C211yesmaximal, characteristic, complemented
31#2995C211yesmaximal, characteristic, complemented
32#563—21no—
33#563—21no—
34#559C2211yescharacteristic
35Q82C2211yescharacteristic, complemented
36#557—21no—
37#557C2211yescharacteristic, complemented
38#556—21no—
39#556C2211yescharacteristic
40#556C2211yescharacteristic, complemented
41#556C2211yescharacteristic, complemented
42#554C2211yescharacteristic
43#554C2211yescharacteristic, complemented
44#553—21no—
45#553C2211yescharacteristic
46#552C2211yescharacteristic
47#552C2211yescharacteristic
48#552C2211yescharacteristic, complemented
49#551—21no—
50#551—21no—
51#547C2211yescharacteristic
52#546—21no—
53#546C2211yescharacteristic
54#546C2211yescharacteristic
55D42C2211yescharacteristic
56#544C2211yescharacteristic, complemented
57#544C2211yescharacteristic, complemented
58#542—21no—
59#542C2211yescharacteristic
60#541—21no—
61#541—21no—
62#541—21no—
63#541C2211yescharacteristic, complemented
64#541C2211yescharacteristic, complemented
65#540C2211yescharacteristic
66#539—21no—
67#538—21no—
68#533C2211yescharacteristic, complemented
69#533C2211yescharacteristic, complemented
70#529C2211yescharacteristic
71#529C2211yescharacteristic
72#525—21no—
73C2×#123—21no—
74#520C2211yescharacteristic
75#518C2211yescharacteristic
76C2×C4×D4C2211yescharacteristic
77#501C2211yescharacteristic, complemented
78#501C2211yescharacteristic, complemented
79#501C2211yescharacteristic, complemented
80#501C2211yescharacteristic, complemented
81#500C2211yescharacteristic, complemented
82#499C2211yescharacteristic, complemented
83#490C2211yescharacteristic
84#489C2211yescharacteristic, complemented
85#489C2211yescharacteristic, complemented
86#489C2211yescharacteristic, complemented
87#488C2211yescharacteristic, complemented
88#486C2211yescharacteristic
89#485C2211yescharacteristic, complemented
90#485C2211yescharacteristic, complemented
91#485C2211yescharacteristic, complemented
92#485C2211yescharacteristic, complemented
93#485C2211yescharacteristic, complemented
94#484C2211yescharacteristic, complemented
95#484C2211yescharacteristic, complemented
96#484C2211yescharacteristic, complemented
97#484C2211yescharacteristic, complemented
98#483C2211yescharacteristic, complemented
99#482C2211yescharacteristic
100#482C2211yescharacteristic
101#482C2211yescharacteristic
102#482C2211yescharacteristic, complemented
103#482C2211yescharacteristic, complemented
104#481C2211yescharacteristic, complemented
105#480C2211yescharacteristic
106#480C2211yescharacteristic, complemented
107#479C2211yescharacteristic, complemented
108#479C2211yescharacteristic, complemented
109#479C2211yescharacteristic, complemented
110#479C2211yescharacteristic, complemented
111#479C2211yescharacteristic, complemented
112#479C2211yescharacteristic, complemented
113#479C2211yescharacteristic, complemented
114#478C2211yescharacteristic
115#478C2211yescharacteristic
116#478C2211yescharacteristic
117#478C2211yescharacteristic
118#478C2211yescharacteristic, complemented
119#478C2211yescharacteristic, complemented
120#478C2211yescharacteristic, complemented
121#478C2211yescharacteristic, complemented
122#478C2211yescharacteristic, complemented
123#477C2211yescharacteristic, complemented
124#477C2211yescharacteristic, complemented
125#477C2211yescharacteristic, complemented
126#476C2211yescharacteristic
127#476C2211yescharacteristic
128#476C2211yescharacteristic, complemented
129#476C2211yescharacteristic, complemented
130#475C2211yescharacteristic, complemented
131#474C2211yescharacteristic
132#474C2211yescharacteristic
133#474C2211yescharacteristic
134#474C2211yescharacteristic, complemented
135#474C2211yescharacteristic, complemented
136#474C2211yescharacteristic, complemented
137#470C2211yescharacteristic, complemented
138#470C2211yescharacteristic, complemented
139#470C2211yescharacteristic, complemented
140#468C2211yescharacteristic
141#468C2211yescharacteristic
142#468C2211yescharacteristic
143#468C2211yescharacteristic, complemented
144#468C2211yescharacteristic, complemented
145#467C2211yescharacteristic, complemented
146#465C2211yescharacteristic
147#465C2211yescharacteristic, complemented
148#465C2211yescharacteristic, complemented
149#464C2211yescharacteristic, complemented
150#464C2211yescharacteristic, complemented
151#464C2211yescharacteristic, complemented
152#464C2211yescharacteristic, complemented
153#462C2211yescharacteristic, complemented
154#461C2211yescharacteristic
155#461C2211yescharacteristic, complemented
156#461C2211yescharacteristic, complemented
157#460C2211yescharacteristic
158#460C2211yescharacteristic
159#452C2211yescharacteristic
160#452C2211yescharacteristic
161#450C2211yescharacteristic
162#450C2211yescharacteristic
163#450C2211yescharacteristic
164#450C2211yescharacteristic
165#446C2211yescharacteristic, complemented
166#446C2211yescharacteristic, complemented
167#441C2211yescharacteristic, complemented
168#440C2211yescharacteristic
169#440C2211yescharacteristic
170#440C2211yescharacteristic
171#440C2211yescharacteristic
172#440C2211yescharacteristic, complemented
173#440C2211yescharacteristic, complemented
174#440C2211yescharacteristic, complemented
175C4×Q16C2211yescharacteristic, complemented
176C4×SD16C2211yescharacteristic
177C4×SD16C2211yescharacteristic
178C4×SD16C2211yescharacteristic, complemented
179#436C2211yescharacteristic
180#436C2211yescharacteristic, complemented
181#435C2211yescharacteristic
182#435C2211yescharacteristic, complemented
183#435C2211yescharacteristic, complemented
184#435C2211yescharacteristic, complemented
185#433C2211yescharacteristic, complemented
186#433C2211yescharacteristic, complemented
187#432C2211yescharacteristic, complemented
188#428C2211yescharacteristic, complemented
189#428C2211yescharacteristic, complemented
190#428C2211yescharacteristic, complemented
191#428C2211yescharacteristic, complemented
192#427C2211yescharacteristic, complemented
193C2×#107C2211yescharacteristic, complemented
194#424C2211yescharacteristic, complemented
195#424C2211yescharacteristic, complemented
196#423C2211yescharacteristic, complemented
197#418C2211yescharacteristic
198#418C2211yescharacteristic
199#418C2211yescharacteristic
200#417C2211yescharacteristic
201#416C2211yescharacteristic
202C2×#102C2211yescharacteristic
203C2×#41—21no—
204C2×#41C2311yescharacteristic
205C22×D4—21no—
206C22×D4C2311yescharacteristic
207C22×D4C2311yescharacteristic
208C23×C4—21no—
209C2×Q16C2311yescharacteristic
210C2×Q16C2311yescharacteristic
211C2×SD16C2311yescharacteristic
212C2×SD16C2311yescharacteristic
213C2×SD16C2311yescharacteristic
214C2×SD16C2311yescharacteristic
215C2×SD16C2311yescharacteristic
216C2×SD16C2311yescharacteristic
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⋊Q8C2311yescharacteristic
230C4⋊Q8C2311yescharacteristic
231C4⋊Q8C2311yescharacteristic
232C4⋊Q8C2311yescharacteristic
233C4⋊Q8C2311yescharacteristic
234C4⋊Q8C2311yescharacteristic
235C4⋊Q8C2311yescharacteristic
236#127C2311yescharacteristic
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#126—21no—
249#126—21no—
250#126—21no—
251#126—21no—
252#126—21no—
253#126D411yescharacteristic
254#126D411yescharacteristic
255#125—21no—
256#125—21no—
257#125—21no—
258#125—21no—
259#125—21no—
260#125—21no—
261#125—21no—
262#125—21no—
263#125—21no—
264#125—21no—
265#125—21no—
266#125—21no—
267#125—21no—
268#125D411yescharacteristic
269#125C2311yescharacteristic
270#125C2311yescharacteristic
271#125C2311yescharacteristic
272#125C2311yescharacteristic
273#125C2311yescharacteristic
274#125C2311yescharacteristic
275#124—21no—
276#124—21no—
277#124—21no—
278#124—21no—
279#124—21no—
280#124D411yescharacteristic
281#124C2311yescharacteristic
282#124C2311yescharacteristic
283#123—21no—
284#123—21no—
285#123—21no—
286#123—21no—
287#123—21no—
288#123—21no—
289#123—21no—
290#123—21no—
291#123—21no—
292#123—21no—
293#123—21no—
294#123—21no—
295#123—21no—
296#123—21no—
297#123D411yescharacteristic
298#123D411yescharacteristic
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⋊Q8D411yescharacteristic
314C22⋊Q8C2311yescharacteristic
315C22⋊Q8C2311yescharacteristic
316C22⋊Q8C2311yescharacteristic
317C22⋊Q8C2311yescharacteristic
318C22⋊Q8C2311yescharacteristic
319C22⋊Q8C2311yescharacteristic
320C22⋊Q8C2311yescharacteristic
321C22⋊Q8C2311yescharacteristic
322#121—21no—
323#121—21no—
324#121—21no—
325#121—21no—
326#121—21no—
327#121—21no—
328#121D411yescharacteristic
329#121C2311yescharacteristic
330#121C2311yescharacteristic
331#121C2311yescharacteristic
332#121C2311yescharacteristic
333#120—21no—
334#120—21no—
335#120—21no—
336#120—21no—
337C4×Q8—21no—
338C4×Q8—21no—
339C4×Q8—21no—
340C4×Q8—21no—
341C4×Q8—21no—
342C4×Q8—21no—
343C4×Q8—21no—
344C4×Q8—21no—
345C4×Q8C2311yescharacteristic
346C4×Q8C2311yescharacteristic
347C4×Q8C2311yescharacteristic
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×D4C2311yescharacteristic
365C4×D4C2311yescharacteristic
366C4×D4C2311yescharacteristic
367C4×D4C2311yescharacteristic
368C4×D4C2311yescharacteristic
369C4×D4C2311yescharacteristic
370C4×D4C2311yescharacteristic
371C4×D4C2311yescharacteristic
372C4×D4C2311yescharacteristic
373C4×D4C2311yescharacteristic
374C4×D4C2311yescharacteristic
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
387#117C2311yescharacteristic
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
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×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#107C2311yescharacteristic
413#107C2311yescharacteristic
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#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
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—
479C24—21no—
480#41—22no—
481#41—41no—
482#41—82no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8C2×D411yescharacteristic
490C2×Q8C2411yescharacteristic
491C2×Q8C2411yescharacteristic
492C2×Q8C2411yescharacteristic
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—41no—
505C2×D4—41no—
506C2×D4—82no—
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—82no—
527C22×C4C2×D411yescharacteristic
528C22×C4C2×D411yescharacteristic
529C22×C4C2411yescharacteristic
530C22×C4C2411yescharacteristic
531C22×C4C2411yescharacteristic
532Q16—41no—
533Q16—41no—
534SD16—22no—
535SD16—22no—
536SD16—41no—
537SD16—41no—
538SD16—41no—
539SD16—41no—
540M16—41no—
541M16—41no—
542M16—41no—
543M16—41no—
544C2×C8—41no—
545C2×C8—41no—
546C2×C8C2411yescharacteristic
547C2×C8C2411yescharacteristic
548C2×C8C2411yescharacteristic
549C2×C8C2411yescharacteristic
550C2×C8C2411yescharacteristic
551C2×C8C2411yescharacteristic
552C2×C8C2411yescharacteristic
553C2×C8C2411yescharacteristic
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊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⋊C4C2×D411yescharacteristic
644C22⋊C4C2×D411yescharacteristic
645C22⋊C4C2×D411yescharacteristic
646C22⋊C4C2×D411yescharacteristic
647C22⋊C4C2×D411yescharacteristic
648C22⋊C4C2×D411yescharacteristic
649C22⋊C4C2×D411yescharacteristic
650C22⋊C4C2×D411yescharacteristic
651C22⋊C4C2×D411yescharacteristic
652C22⋊C4C2×D411yescharacteristic
653C42—21no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42C2×D411yescharacteristic
667C42C2×D411yescharacteristic
668C42C2411yescharacteristic
669C42C2411yescharacteristic
670C42C2411yescharacteristic
671C42C2411yescharacteristic
672C23—21no—
673C23—21no—
674C23—21no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—81no—
679C23—81no—
680C23—81no—
681C23C22×D411yescharacteristic
682C23C22×D411yescharacteristic
683C23C22×D411yescharacteristic
684Q8—21no—
685Q8—21no—
686Q8—21no—
687Q8—21no—
688Q8—21no—
689Q8—21no—
690Q8—41no—
691Q8—42no—
692Q8—81no—
693Q8—81no—
694Q8—81no—
695Q8—81no—
696Q8—81no—
697D4—21no—
698D4—21no—
699D4—21no—
700D4—21no—
701D4—21no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—42no—
706D4—42no—
707D4—42no—
708D4—42no—
709D4—81no—
710D4—81no—
711D4—81no—
712D4—81no—
713D4—81no—
714D42−1+412yes—
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—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—41no—
735C2×C4—41no—
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—84no—
788C22—162no—
789C22C23×D411yescharacteristic
790C4—21no—
791C4—21no—
792C4—21no—
793C4—21no—
794C4—21no—
795C4—21no—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4C2×2−1+411yescharacteristic
815C4#58511yescharacteristic
816C2—41no—
817C2—41no—
818C2—41no—
819C2—42no—
820C2—81no—
821C2—81no—
822C2#348911yescharacteristic
823C2#358511yescharacteristic
824C2#358611yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
prime radical#3513C2
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. #3555C2semidirect
3. #3388C2semidirect
4. #3385C2semidirect
5. #3375C2semidirect
6. #3371C2semidirect
7. #3353C2semidirect
8. #3352C2semidirect
9. #3350C2semidirect
10. #3349C2semidirect
11. #3346C2semidirect
12. #3343C2semidirect
13. #3324C2semidirect
14. #3323C2semidirect
15. #3314C2semidirect
16. #3311C2semidirect
17. #3311C2semidirect
18. #3310C2semidirect
19. #3260C2semidirect
20. #3258C2semidirect
21. #3252C2semidirect
22. #3243C2semidirect
23. #3241C2semidirect
24. #3240C2semidirect
25. #3123C2semidirect
26. #3120C2semidirect
27. #3110C2semidirect
28. #3083C2semidirect
29. #3081C2semidirect
30. #3077C2semidirect
31. #2995C2semidirect
35. Q82C22semidirect
37. #557C22semidirect
40. #556C22semidirect
41. #556C22semidirect
43. #554C22semidirect
48. #552C22semidirect
56. #544C22semidirect
57. #544C22semidirect
63. #541C22semidirect
64. #541C22semidirect
68. #533C22semidirect
69. #533C22semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #501C22semidirect
80. #501C22semidirect
81. #500C22semidirect
82. #499C22semidirect
84. #489C22semidirect
85. #489C22semidirect
86. #489C22semidirect
87. #488C22semidirect
89. #485C22semidirect
90. #485C22semidirect
91. #485C22semidirect
92. #485C22semidirect
93. #485C22semidirect
94. #484C22semidirect
95. #484C22semidirect
96. #484C22semidirect
97. #484C22semidirect
98. #483C22semidirect
102. #482C22semidirect
103. #482C22semidirect
104. #481C22semidirect
106. #480C22semidirect
107. #479C22semidirect
108. #479C22semidirect
109. #479C22semidirect
110. #479C22semidirect
111. #479C22semidirect
112. #479C22semidirect
113. #479C22semidirect
118. #478C22semidirect
119. #478C22semidirect
120. #478C22semidirect
121. #478C22semidirect
122. #478C22semidirect
123. #477C22semidirect
124. #477C22semidirect
125. #477C22semidirect
128. #476C22semidirect
129. #476C22semidirect
130. #475C22semidirect
134. #474C22semidirect
135. #474C22semidirect
136. #474C22semidirect
137. #470C22semidirect
138. #470C22semidirect
139. #470C22semidirect
143. #468C22semidirect
144. #468C22semidirect
145. #467C22semidirect
147. #465C22semidirect
148. #465C22semidirect
149. #464C22semidirect
150. #464C22semidirect
151. #464C22semidirect
152. #464C22semidirect
153. #462C22semidirect
155. #461C22semidirect
156. #461C22semidirect
165. #446C22semidirect
166. #446C22semidirect
167. #441C22semidirect
172. #440C22semidirect
173. #440C22semidirect
174. #440C22semidirect
175. C4×Q16C22semidirect
178. C4×SD16C22semidirect
180. #436C22semidirect
182. #435C22semidirect
183. #435C22semidirect
184. #435C22semidirect
185. #433C22semidirect
186. #433C22semidirect
187. #432C22semidirect
188. #428C22semidirect
189. #428C22semidirect
190. #428C22semidirect
191. #428C22semidirect
192. #427C22semidirect
193. C2×#107C22semidirect
194. #424C22semidirect
195. #424C22semidirect
196. #423C22semidirect

Maximal subgroups

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

subgroupindex
#35552
#35132
#33882
#33852
#33752
#33712
#33532
#33522
#33502
#33492
#33462
#33432
#33242
#33232
#33142
#33112
#33102
#32602
#32582
#32522
#32432
#32412
#32402
#31232
#31202
#31102
#30832
#30812
#30772
#29952