Finite Group Databasebeta

← #62156

Subgroups — #62156

Order 256.

877 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3552C211yesmaximal, characteristic, complemented
2#3513C211yesmaximal, characteristic, complemented
3#3388C211yesmaximal, characteristic, complemented
4#3384C211yesmaximal, characteristic, complemented
5#3373C211yesmaximal, characteristic, complemented
6#3371C211yesmaximal, characteristic, complemented
7#3350C211yesmaximal, characteristic, complemented
8#3345C211yesmaximal, characteristic, complemented
9#3345C211yesmaximal, characteristic, complemented
10#3344C211yesmaximal, characteristic, complemented
11#3337C211yesmaximal, characteristic, complemented
12#3335C211yesmaximal, characteristic, complemented
13#3318C211yesmaximal, characteristic, complemented
14#3314C211yesmaximal, characteristic, complemented
15#3311C211yesmaximal, characteristic, complemented
16#3306C211yesmaximal, characteristic, complemented
17#3297C211yesmaximal, characteristic, complemented
18#3295C211yesmaximal, characteristic, complemented
19#3263C211yesmaximal, characteristic, complemented
20#3257C211yesmaximal, characteristic, complemented
21#3250C211yesmaximal, characteristic, complemented
22#3244C211yesmaximal, characteristic, complemented
23#3241C211yesmaximal, characteristic, complemented
24#3239C211yesmaximal, characteristic, complemented
25#3125C211yesmaximal, characteristic, complemented
26#3118C211yesmaximal, characteristic, complemented
27#3114C211yesmaximal, characteristic, complemented
28#3084C211yesmaximal, characteristic, complemented
29#3081C211yesmaximal, characteristic, complemented
30C2×#476C211yesmaximal, characteristic, complemented
31#2992C211yesmaximal, characteristic, complemented
32#563—21no—
33#563—21no—
34#559C2211yescharacteristic
35#557C2211yescharacteristic, complemented
36#556C2211yescharacteristic, complemented
37#554C2211yescharacteristic
38#554C2211yescharacteristic
39#554C2211yescharacteristic, complemented
40#553—21no—
41#553C2211yescharacteristic
42#553C2211yescharacteristic
43#553C2211yescharacteristic, complemented
44#552C2211yescharacteristic
45#551—21no—
46#551—21no—
47D4×Q8—21no—
48D4×Q8C2211yescharacteristic, complemented
49#548—21no—
50#547C2211yescharacteristic
51#547C2211yescharacteristic, complemented
52#546—21no—
53#546C2211yescharacteristic
54#546C2211yescharacteristic
55D42C2211yescharacteristic
56#544C2211yescharacteristic, complemented
57#544C2211yescharacteristic, complemented
58#542C2211yescharacteristic
59#542C2211yescharacteristic, complemented
60#542C2211yescharacteristic, complemented
61#541—21no—
62#540C2211yescharacteristic
63#539—21no—
64#539—21no—
65#539—21no—
66#538—21no—
67#536—21no—
68C2×C4⋊Q8C2211yescharacteristic, complemented
69#529C2211yescharacteristic
70#529C2211yescharacteristic
71#529C2211yescharacteristic, complemented
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#499C2211yescharacteristic, complemented
82#498C2211yescharacteristic, complemented
83#490C2211yescharacteristic
84#489C2211yescharacteristic, complemented
85#489C2211yescharacteristic, complemented
86#489C2211yescharacteristic, complemented
87#488C2211yescharacteristic, complemented
88#486C2211yescharacteristic
89#485C2211yescharacteristic, complemented
90#485C2211yescharacteristic, complemented
91#484C2211yescharacteristic, complemented
92#484C2211yescharacteristic, complemented
93#483C2211yescharacteristic, complemented
94#483C2211yescharacteristic, complemented
95#483C2211yescharacteristic, complemented
96#482C2211yescharacteristic
97#482C2211yescharacteristic, complemented
98#482C2211yescharacteristic, complemented
99#482C2211yescharacteristic, complemented
100#481C2211yescharacteristic
101#481C2211yescharacteristic
102#481C2211yescharacteristic
103#481C2211yescharacteristic, complemented
104#481C2211yescharacteristic, complemented
105#480C2211yescharacteristic, complemented
106#480C2211yescharacteristic, complemented
107#479C2211yescharacteristic, complemented
108#479C2211yescharacteristic, complemented
109#479C2211yescharacteristic, complemented
110#479C2211yescharacteristic, complemented
111#478C2211yescharacteristic
112#478C2211yescharacteristic
113#478C2211yescharacteristic
114#478C2211yescharacteristic, complemented
115#478C2211yescharacteristic, complemented
116#478C2211yescharacteristic, complemented
117#478C2211yescharacteristic, complemented
118#478C2211yescharacteristic, complemented
119#476C2211yescharacteristic
120#476C2211yescharacteristic
121#476C2211yescharacteristic
122#476C2211yescharacteristic
123#476C2211yescharacteristic
124#476C2211yescharacteristic, complemented
125#476C2211yescharacteristic, complemented
126#476C2211yescharacteristic, complemented
127#476C2211yescharacteristic, complemented
128#476C2211yescharacteristic, complemented
129#476C2211yescharacteristic, complemented
130#475C2211yescharacteristic, complemented
131#475C2211yescharacteristic, complemented
132#475C2211yescharacteristic, complemented
133#475C2211yescharacteristic, complemented
134#474C2211yescharacteristic
135#474C2211yescharacteristic, complemented
136#474C2211yescharacteristic, complemented
137#470C2211yescharacteristic, complemented
138#469C2211yescharacteristic
139#469C2211yescharacteristic, complemented
140#468C2211yescharacteristic, complemented
141#467C2211yescharacteristic, complemented
142#466C2211yescharacteristic
143#466C2211yescharacteristic, complemented
144#465C2211yescharacteristic
145#465C2211yescharacteristic
146#465C2211yescharacteristic, complemented
147#465C2211yescharacteristic, complemented
148#465C2211yescharacteristic, complemented
149#464C2211yescharacteristic, complemented
150#464C2211yescharacteristic, complemented
151#464C2211yescharacteristic, complemented
152#463C2211yescharacteristic
153#463C2211yescharacteristic, complemented
154#463C2211yescharacteristic, complemented
155#463C2211yescharacteristic, complemented
156#463C2211yescharacteristic, complemented
157#460C2211yescharacteristic
158#459C2211yescharacteristic
159#452C2211yescharacteristic
160#450C2211yescharacteristic
161#450C2211yescharacteristic
162#449C2211yescharacteristic
163#447C2211yescharacteristic
164#447C2211yescharacteristic
165#446C2211yescharacteristic, complemented
166#446C2211yescharacteristic, complemented
167#442C2211yescharacteristic
168#442C2211yescharacteristic
169#442C2211yescharacteristic, complemented
170#442C2211yescharacteristic, complemented
171#441C2211yescharacteristic, complemented
172#440C2211yescharacteristic
173#440C2211yescharacteristic
174#440C2211yescharacteristic, complemented
175C4×SD16C2211yescharacteristic
176C4×SD16C2211yescharacteristic, complemented
177C4×SD16C2211yescharacteristic, complemented
178C4×D8C2211yescharacteristic
179#435C2211yescharacteristic
180#435C2211yescharacteristic, complemented
181#435C2211yescharacteristic, complemented
182#435C2211yescharacteristic, complemented
183C8×D4C2211yescharacteristic
184C8×D4C2211yescharacteristic, complemented
185#433C2211yescharacteristic, complemented
186#433C2211yescharacteristic, complemented
187#432C2211yescharacteristic, complemented
188#428C2211yescharacteristic, complemented
189#428C2211yescharacteristic, complemented
190#427C2211yescharacteristic, complemented
191C2×#106C2211yescharacteristic, complemented
192C2×#106C2211yescharacteristic, complemented
193C2×#106C2211yescharacteristic, complemented
194#424C2211yescharacteristic, complemented
195#424C2211yescharacteristic, complemented
196C2×C4⋊C8C2211yescharacteristic, complemented
197#418C2211yescharacteristic
198#417C2211yescharacteristic
199#416C2211yescharacteristic
200C2×#102C2211yescharacteristic
201C2×#102C2211yescharacteristic
202C2×#102C2211yescharacteristic
203C2×#41—21no—
204C2×#41—21no—
205C2×#41C2311yescharacteristic
206C22×Q8—21no—
207C22×Q8—21no—
208C22×D4—21no—
209C22×D4C2311yescharacteristic
210C22×D4C2311yescharacteristic
211C23×C4—21no—
212C2×Q16C2311yescharacteristic
213C2×SD16C2311yescharacteristic
214C2×SD16C2311yescharacteristic
215C2×SD16C2311yescharacteristic
216C2×SD16C2311yescharacteristic
217C2×D8C2311yescharacteristic
218C2×D8C2311yescharacteristic
219C2×D8C2311yescharacteristic
220C2×M16C2311yescharacteristic
221C2×M16C2311yescharacteristic
222C22×C8C2311yescharacteristic
223C22×C8C2311yescharacteristic
224C22×C8C2311yescharacteristic
225C22×C8C2311yescharacteristic
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8C2311yescharacteristic
232C4⋊Q8C2311yescharacteristic
233C4⋊Q8C2311yescharacteristic
234C4⋊Q8C2311yescharacteristic
235C4⋊Q8C2311yescharacteristic
236C4⋊Q8C2311yescharacteristic
237C4⋊Q8C2311yescharacteristic
238#127C2311yescharacteristic
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#126D411yescharacteristic
251#126D411yescharacteristic
252#125—21no—
253#125—21no—
254#125—21no—
255#125—21no—
256#125—21no—
257#125—21no—
258#125—21no—
259#125D411yescharacteristic
260#125C2311yescharacteristic
261#125C2311yescharacteristic
262#125C2311yescharacteristic
263#125C2311yescharacteristic
264#125C2311yescharacteristic
265#124—21no—
266#124—21no—
267#124—21no—
268#124—21no—
269#124—21no—
270#124D411yescharacteristic
271#124C2311yescharacteristic
272#124C2311yescharacteristic
273#124C2311yescharacteristic
274#123—21no—
275#123—21no—
276#123—21no—
277#123—21no—
278#123—21no—
279#123—21no—
280#123—21no—
281#123—21no—
282#123—21no—
283#123—21no—
284#123—21no—
285#123—21no—
286#123—21no—
287#123—21no—
288#123—21no—
289#123—21no—
290#123—21no—
291#123—21no—
292#123—21no—
293#123D411yescharacteristic
294#123D411yescharacteristic
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⋊Q8D411yescharacteristic
315C22⋊Q8C2311yescharacteristic
316C22⋊Q8C2311yescharacteristic
317C22⋊Q8C2311yescharacteristic
318C22⋊Q8C2311yescharacteristic
319C22⋊Q8C2311yescharacteristic
320#121—21no—
321#121—21no—
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#121C2311yescharacteristic
334#121C2311yescharacteristic
335#121C2311yescharacteristic
336#120—21no—
337#120—21no—
338#120—21no—
339#120—21no—
340C4×Q8—21no—
341C4×Q8—21no—
342C4×Q8C2311yescharacteristic
343C4×Q8C2311yescharacteristic
344C4×Q8C2311yescharacteristic
345C4×Q8C2311yescharacteristic
346C4×Q8C2311yescharacteristic
347C4×Q8C2311yescharacteristic
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×D4—21no—
358C4×D4—21no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4C2311yescharacteristic
363C4×D4C2311yescharacteristic
364C4×D4C2311yescharacteristic
365C4×D4C2311yescharacteristic
366C4×D4C2311yescharacteristic
367C4×D4C2311yescharacteristic
368C4×D4C2311yescharacteristic
369C4×D4C2311yescharacteristic
370C4×D4C2311yescharacteristic
371C4×D4C2311yescharacteristic
372C4×D4C2311yescharacteristic
373C4×D4C2311yescharacteristic
374C4×D4C2311yescharacteristic
375C4×D4C2311yescharacteristic
376#117—21no—
377#117—21no—
378#117—21no—
379#117—21no—
380#117C2311yescharacteristic
381#117C2311yescharacteristic
382#117C2311yescharacteristic
383#117C2311yescharacteristic
384#117C2311yescharacteristic
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4C2311yescharacteristic
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×C22⋊C4—21no—
399C2×C42C2311yescharacteristic
400#107C2311yescharacteristic
401#107C2311yescharacteristic
402#107C2311yescharacteristic
403#107C2311yescharacteristic
404#107C2311yescharacteristic
405#107C2311yescharacteristic
406#107C2311yescharacteristic
407#107C2311yescharacteristic
408#106C2311yescharacteristic
409#106C2311yescharacteristic
410#106C2311yescharacteristic
411#106C2311yescharacteristic
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#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
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—
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×Q8—82no—
493C2×Q8C2×D411yescharacteristic
494C2×Q8C2411yescharacteristic
495C2×Q8C2411yescharacteristic
496C2×D4—22no—
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—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—41no—
511C2×D4—41no—
512C2×D4—82no—
513C2×D4C2×D411yescharacteristic
514C2×D4C2×D411yescharacteristic
515C2×D4C2×D411yescharacteristic
516C2×D4C2411yescharacteristic
517C2×D4C2411yescharacteristic
518C2×D4C2411yescharacteristic
519C2×D4C2411yescharacteristic
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×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—82no—
539C22×C4C2×D411yescharacteristic
540C22×C4C2×D411yescharacteristic
541C22×C4C2411yescharacteristic
542C22×C4C2411yescharacteristic
543C22×C4C2411yescharacteristic
544Q16—41no—
545SD16—22no—
546SD16—41no—
547SD16—41no—
548SD16—41no—
549D8—22no—
550D8—41no—
551D8—41no—
552M16—41no—
553M16—41no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8C2411yescharacteristic
559C2×C8C2411yescharacteristic
560C2×C8C2411yescharacteristic
561C2×C8C2411yescharacteristic
562C2×C8C2411yescharacteristic
563C2×C8C2411yescharacteristic
564C2×C8C2411yescharacteristic
565C2×C8C2411yescharacteristic
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⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4C2×D411yescharacteristic
600C4⋊C4C2×D411yescharacteristic
601C4⋊C4C2×D411yescharacteristic
602C4⋊C4C2×D411yescharacteristic
603C4⋊C4C2×D411yescharacteristic
604C4⋊C4C2×D411yescharacteristic
605C4⋊C4C2×D411yescharacteristic
606C4⋊C4C2×D411yescharacteristic
607C4⋊C4C2×D411yescharacteristic
608C4⋊C4C2×D411yescharacteristic
609C4⋊C4C2411yescharacteristic
610C4⋊C4C2411yescharacteristic
611C4⋊C4C2411yescharacteristic
612C4⋊C4C2411yescharacteristic
613C4⋊C4C2411yescharacteristic
614C4⋊C4C2411yescharacteristic
615C4⋊C4C2411yescharacteristic
616C4⋊C4C2411yescharacteristic
617C4⋊C4C2411yescharacteristic
618C4⋊C4C2411yescharacteristic
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—21no—
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4C2×D411yescharacteristic
652C22⋊C4C2×D411yescharacteristic
653C22⋊C4C2×D411yescharacteristic
654C22⋊C4C2×D411yescharacteristic
655C22⋊C4C2×D411yescharacteristic
656C22⋊C4C2×D411yescharacteristic
657C22⋊C4C2×D411yescharacteristic
658C22⋊C4C2×D411yescharacteristic
659C22⋊C4C2×D411yescharacteristic
660C22⋊C4C2×D411yescharacteristic
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42C2×D411yescharacteristic
670C42C2×D411yescharacteristic
671C42C2411yescharacteristic
672C42C2411yescharacteristic
673C42C2411yescharacteristic
674C42C2411yescharacteristic
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—81no—
683C23—81no—
684C23—81no—
685C23C22×D411yescharacteristic
686C23C22×D411yescharacteristic
687C23C22×D411yescharacteristic
688Q8—21no—
689Q8—21no—
690Q8—21no—
691Q8—21no—
692Q8—41no—
693Q8—42no—
694Q8—42no—
695Q8—81no—
696Q8—81no—
697Q8—81no—
698Q8—81no—
699Q8—81no—
700D4—22no—
701D4—22no—
702D4—21no—
703D4—21no—
704D4—21no—
705D4—21no—
706D4—21no—
707D4—21no—
708D4—21no—
709D4—41no—
710D4—42no—
711D4—42no—
712D4—42no—
713D4—42no—
714D4—42no—
715D4—81no—
716D4—81no—
717D4—81no—
718D4—81no—
719D4—81no—
720D4—81no—
721D4—81no—
722D42−1+412yes—
723C2×C4—22no—
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—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—81no—
747C2×C4—81no—
748C2×C4—81no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—81no—
752C2×C4—81no—
753C2×C4—81no—
754C2×C4—81no—
755C2×C4—81no—
756C2×C4—81no—
757C2×C4—81no—
758C2×C4—81no—
759C2×C4—81no—
760C2×C4—81no—
761C2×C4C22×D411yescharacteristic
762C2×C4C22×D411yescharacteristic
763C2×C4C22×D411yescharacteristic
764C2×C4C22×D411yescharacteristic
765C2×C4C22×D411yescharacteristic
766C2×C4C22×D411yescharacteristic
767C2×C4C22×D411yescharacteristic
768C2×C4C22×D411yescharacteristic
769C2×C4C22×D411yescharacteristic
770C2×C4C22×D411yescharacteristic
771C2×C4C22×D411yescharacteristic
772C2×C4C2511yescharacteristic
773C8—21no—
774C8—21no—
775C8—21no—
776C8—21no—
777C8—21no—
778C8—21no—
779C8—21no—
780C8—21no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—22no—
788C22—21no—
789C22—21no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—84no—
802C22—162no—
803C22#57712yes—
804C22C23×D411yescharacteristic
805C4—21no—
806C4—21no—
807C4—21no—
808C4—21no—
809C4—21no—
810C4—21no—
811C4—21no—
812C4—21no—
813C4—21no—
814C4—21no—
815C4—21no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4C2×2−1+411yescharacteristic
829C4#58511yescharacteristic
830C2—22no—
831C2—41no—
832C2—41no—
833C2—42no—
834C2—81no—
835C2—81no—
836C2—81no—
837C2#348911yescharacteristic
838C2C2×#57711yescharacteristic
839C2#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. #3552C2semidirect
2. #3513C2semidirect
3. #3388C2semidirect
4. #3384C2semidirect
5. #3373C2semidirect
6. #3371C2semidirect
7. #3350C2semidirect
8. #3345C2semidirect
9. #3345C2semidirect
10. #3344C2semidirect
11. #3337C2semidirect
12. #3335C2semidirect
13. #3318C2semidirect
14. #3314C2semidirect
15. #3311C2semidirect
16. #3306C2semidirect
17. #3297C2semidirect
18. #3295C2semidirect
19. #3263C2semidirect
20. #3257C2semidirect
21. #3250C2semidirect
22. #3244C2semidirect
23. #3241C2semidirect
24. #3239C2semidirect
25. #3125C2semidirect
26. #3118C2semidirect
27. #3114C2semidirect
28. #3084C2semidirect
29. #3081C2semidirect
30. C2×#476C2semidirect
31. #2992C2semidirect
35. #557C22semidirect
36. #556C22semidirect
39. #554C22semidirect
43. #553C22semidirect
48. D4×Q8C22semidirect
51. #547C22semidirect
56. #544C22semidirect
57. #544C22semidirect
59. #542C22semidirect
60. #542C22semidirect
68. C2×C4⋊Q8C22semidirect
71. #529C22semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #501C22semidirect
80. #501C22semidirect
81. #499C22semidirect
82. #498C22semidirect
84. #489C22semidirect
85. #489C22semidirect
86. #489C22semidirect
87. #488C22semidirect
89. #485C22semidirect
90. #485C22semidirect
91. #484C22semidirect
92. #484C22semidirect
93. #483C22semidirect
94. #483C22semidirect
95. #483C22semidirect
97. #482C22semidirect
98. #482C22semidirect
99. #482C22semidirect
103. #481C22semidirect
104. #481C22semidirect
105. #480C22semidirect
106. #480C22semidirect
107. #479C22semidirect
108. #479C22semidirect
109. #479C22semidirect
110. #479C22semidirect
114. #478C22semidirect
115. #478C22semidirect
116. #478C22semidirect
117. #478C22semidirect
118. #478C22semidirect
124. #476C22semidirect
125. #476C22semidirect
126. #476C22semidirect
127. #476C22semidirect
128. #476C22semidirect
129. #476C22semidirect
130. #475C22semidirect
131. #475C22semidirect
132. #475C22semidirect
133. #475C22semidirect
135. #474C22semidirect
136. #474C22semidirect
137. #470C22semidirect
139. #469C22semidirect
140. #468C22semidirect
141. #467C22semidirect
143. #466C22semidirect
146. #465C22semidirect
147. #465C22semidirect
148. #465C22semidirect
149. #464C22semidirect
150. #464C22semidirect
151. #464C22semidirect
153. #463C22semidirect
154. #463C22semidirect
155. #463C22semidirect
156. #463C22semidirect
165. #446C22semidirect
166. #446C22semidirect
169. #442C22semidirect
170. #442C22semidirect
171. #441C22semidirect
174. #440C22semidirect
176. C4×SD16C22semidirect
177. C4×SD16C22semidirect
180. #435C22semidirect
181. #435C22semidirect
182. #435C22semidirect
184. C8×D4C22semidirect
185. #433C22semidirect
186. #433C22semidirect
187. #432C22semidirect
188. #428C22semidirect
189. #428C22semidirect
190. #427C22semidirect
191. C2×#106C22semidirect
192. C2×#106C22semidirect
193. C2×#106C22semidirect
194. #424C22semidirect
195. #424C22semidirect
196. C2×C4⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
#35522
#35132
#33882
#33842
#33732
#33712
#33502
#33452
#33442
#33372
#33352
#33182
#33142
#33112
#33062
#32972
#32952
#32632
#32572
#32502
#32442
#32412
#32392
#31252
#31182
#31142
#30842
#30812
C2×#4762
#29922