Finite Group Databasebeta

← #61855

Subgroups — #61855

Order 256.

840 conjugacy classes of subgroups.

The subgroup lattice has 809 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3557C211yesmaximal, characteristic, complemented
2#3501C211yesmaximal, characteristic, complemented
3#3389C211yesmaximal, characteristic, complemented
4#3389C211yesmaximal, characteristic, complemented
5#3388C211yesmaximal, characteristic, complemented
6#3388C211yesmaximal, characteristic, complemented
7#3386C211yesmaximal, characteristic, complemented
8#3384C211yesmaximal, characteristic, complemented
9#3381C211yesmaximal, characteristic, complemented
10#3380C211yesmaximal, characteristic, complemented
11#3376C211yesmaximal, characteristic, complemented
12#3376C211yesmaximal, characteristic, complemented
13#3373C211yesmaximal, characteristic, complemented
14#3370C211yesmaximal, characteristic, complemented
15#3370C211yesmaximal, characteristic, complemented
16#3367C211yesmaximal, characteristic, complemented
17#3361C211yesmaximal, characteristic, complemented
18#3360C211yesmaximal, characteristic, complemented
19#3244C211yesmaximal, characteristic, complemented
20#3243C211yesmaximal, characteristic, complemented
21#3242C211yesmaximal, characteristic, complemented
22#3241C211yesmaximal, characteristic, complemented
23#3240C211yesmaximal, characteristic, complemented
24#3233C211yesmaximal, characteristic, complemented
25#3123C211yesmaximal, characteristic, complemented
26#3122C211yesmaximal, characteristic
27#3118C211yesmaximal, characteristic, complemented
28#3118C211yesmaximal, characteristic, complemented
29#3114C211yesmaximal, characteristic, complemented
30#3105C211yesmaximal, characteristic, complemented
31#2985C211yesmaximal, characteristic, complemented
32#563—21no—
33#563—21no—
34#559C2211yescharacteristic, complemented
35#559C2211yescharacteristic, complemented
36#557C2211yescharacteristic, complemented
37#557C2211yescharacteristic, complemented
38#556C2211yescharacteristic, complemented
39#556C2211yescharacteristic, complemented
40#554—21no—
41#554—21no—
42#554—21no—
43#554C2211yescharacteristic
44#554C2211yescharacteristic
45#554C2211yescharacteristic
46#554C2211yescharacteristic
47#554C2211yescharacteristic
48#554C2211yescharacteristic
49#554C2211yescharacteristic, complemented
50#554C2211yescharacteristic, complemented
51#552—21no—
52#552—21no—
53D4×Q8—21no—
54D4×Q8C2211yescharacteristic
55D4×Q8C2211yescharacteristic
56#544C2211yescharacteristic
57#544C2211yescharacteristic
58#543—21no—
59#543—21no—
60#542—21no—
61#542—21no—
62#542C2211yescharacteristic
63#542C2211yescharacteristic
64#541C2211yescharacteristic
65#540C2211yescharacteristic
66#539—21no—
67#539—21no—
68#533C2211yescharacteristic
69#533C2211yescharacteristic
70#529C2211yescharacteristic
71#529C2211yescharacteristic
72C2×C22⋊Q8—21no—
73C2×C22⋊Q8—21no—
74#518C2211yescharacteristic
75#518C2211yescharacteristic
76C2×C4×D4C2211yescharacteristic
77#501C2211yescharacteristic, complemented
78#501C2211yescharacteristic, complemented
79#501C2211yescharacteristic, complemented
80#501C2211yescharacteristic, complemented
81#501C2211yescharacteristic, complemented
82#501C2211yescharacteristic, complemented
83#500C2211yescharacteristic, complemented
84#499C2211yescharacteristic, complemented
85#499C2211yescharacteristic, complemented
86#499C2211yescharacteristic, complemented
87#499C2211yescharacteristic, complemented
88#498C2211yescharacteristic, complemented
89#491C2211yescharacteristic, complemented
90#490C2211yescharacteristic, complemented
91#489C2211yescharacteristic, complemented
92#489C2211yescharacteristic, complemented
93#489C2211yescharacteristic, complemented
94#489C2211yescharacteristic, complemented
95#488C2211yescharacteristic, complemented
96#488C2211yescharacteristic, complemented
97#488C2211yescharacteristic, complemented
98#488C2211yescharacteristic, complemented
99#487C2211yescharacteristic, complemented
100#486C2211yescharacteristic, complemented
101#485C2211yescharacteristic
102#485C2211yescharacteristic
103#485C2211yescharacteristic
104#485C2211yescharacteristic
105#484C2211yescharacteristic
106#483C2211yescharacteristic
107#482C2211yescharacteristic
108#482C2211yescharacteristic
109#482C2211yescharacteristic
110#482C2211yescharacteristic
111#481C2211yescharacteristic
112#480C2211yescharacteristic
113#479C2211yescharacteristic, complemented
114#479C2211yescharacteristic, complemented
115#479C2211yescharacteristic, complemented
116#479C2211yescharacteristic, complemented
117#479C2211yescharacteristic, complemented
118#479C2211yescharacteristic, complemented
119#478C2211yescharacteristic
120#478C2211yescharacteristic
121#478C2211yescharacteristic
122#478C2211yescharacteristic
123#478C2211yescharacteristic
124#478C2211yescharacteristic
125#478C2211yescharacteristic
126#478C2211yescharacteristic
127#478C2211yescharacteristic, complemented
128#478C2211yescharacteristic, complemented
129#478C2211yescharacteristic, complemented
130#478C2211yescharacteristic, complemented
131#478C2211yescharacteristic, complemented
132#478C2211yescharacteristic, complemented
133#477C2211yescharacteristic, complemented
134#477C2211yescharacteristic, complemented
135#477C2211yescharacteristic, complemented
136#476C2211yescharacteristic
137#476C2211yescharacteristic
138#476C2211yescharacteristic, complemented
139#476C2211yescharacteristic, complemented
140#476C2211yescharacteristic, complemented
141#475C2211yescharacteristic, complemented
142#475C2211yescharacteristic, complemented
143#475C2211yescharacteristic, complemented
144#474C2211yescharacteristic
145#474C2211yescharacteristic
146#474C2211yescharacteristic, complemented
147#474C2211yescharacteristic, complemented
148#474C2211yescharacteristic, complemented
149#463C2211yescharacteristic
150#463C2211yescharacteristic
151#463C2211yescharacteristic
152#463C2211yescharacteristic
153#463C2211yescharacteristic
154#463C2211yescharacteristic
155#463C2211yescharacteristic
156#463C2211yescharacteristic
157#461C2211yescharacteristic
158#461C2211yescharacteristic
159#459C2211yescharacteristic
160#459C2211yescharacteristic
161#450C2211yescharacteristic
162#450C2211yescharacteristic
163#447C2211yescharacteristic
164#447C2211yescharacteristic
165#446C2211yescharacteristic, complemented
166#446C2211yescharacteristic, complemented
167#446C2211yescharacteristic, complemented
168#446C2211yescharacteristic, complemented
169#446C2211yescharacteristic, complemented
170#446C2211yescharacteristic, complemented
171C8×Q8C2211yescharacteristic, complemented
172C8×Q8C2211yescharacteristic, complemented
173#442C2211yescharacteristic
174#442C2211yescharacteristic
175#442C2211yescharacteristic
176#442C2211yescharacteristic
177#442C2211yescharacteristic
178#442C2211yescharacteristic
179#440C2211yescharacteristic
180#440C2211yescharacteristic
181#440C2211yescharacteristic
182#440C2211yescharacteristic
183#440C2211yescharacteristic
184#440C2211yescharacteristic
185C4×SD16C2211yescharacteristic
186C4×SD16C2211yescharacteristic
187C4×SD16C2211yescharacteristic
188C4×SD16C2211yescharacteristic
189C4×SD16C2211yescharacteristic
190C4×SD16C2211yescharacteristic
191C4×D8C2211yescharacteristic
192C4×D8C2211yescharacteristic
193C4×D8C2211yescharacteristic
194C4×D8C2211yescharacteristic
195C4×D8C2211yescharacteristic
196C4×D8C2211yescharacteristic
197#433C2211yescharacteristic
198#433C2211yescharacteristic
199#433C2211yescharacteristic
200#433C2211yescharacteristic
201#432C2211yescharacteristic
202#431C2211yescharacteristic
203C22×Q8—21no—
204C22×Q8—21no—
205C22×D4C2311yescharacteristic
206C23×C4—21no—
207C2×SD16C2311yescharacteristic
208C2×SD16C2311yescharacteristic
209C2×SD16C2311yescharacteristic
210C2×SD16C2311yescharacteristic
211C2×D8C2311yescharacteristic
212C2×D8C2311yescharacteristic
213C2×D8C2311yescharacteristic
214C2×D8C2311yescharacteristic
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8—21no—
218C4⋊Q8—21no—
219C4⋊Q8D411yescharacteristic
220C4⋊Q8D411yescharacteristic
221C4⋊Q8C2311yescharacteristic
222C4⋊Q8C2311yescharacteristic
223C4⋊Q8C2311yescharacteristic
224C4⋊Q8C2311yescharacteristic
225C4⋊Q8C2311yescharacteristic
226C4⋊Q8C2311yescharacteristic
227C4⋊Q8C2311yescharacteristic
228C4⋊Q8C2311yescharacteristic
229C4⋊Q8C2311yescharacteristic
230#127C2311yescharacteristic
231#126—21no—
232#126—21no—
233#126—21no—
234#126—21no—
235#126—21no—
236#126—21no—
237#126—21no—
238#126—21no—
239#126—21no—
240#126—21no—
241#125—21no—
242#125—21no—
243#125—21no—
244#125—21no—
245#125—21no—
246#125—21no—
247#125—21no—
248#125—21no—
249#125D411yescharacteristic
250#125D411yescharacteristic
251#125C2311yescharacteristic
252#125C2311yescharacteristic
253#125C2311yescharacteristic
254#125C2311yescharacteristic
255#125C2311yescharacteristic
256#125C2311yescharacteristic
257#125C2311yescharacteristic
258#125C2311yescharacteristic
259#125C2311yescharacteristic
260#125C2311yescharacteristic
261#124—21no—
262#124—21no—
263#124—21no—
264#124—21no—
265#124C2311yescharacteristic
266#124C2311yescharacteristic
267#124C2311yescharacteristic
268#124C2311yescharacteristic
269#123—21no—
270#123—21no—
271#123—21no—
272#123—21no—
273#123—21no—
274#123—21no—
275#123—21no—
276#123—21no—
277#123—21no—
278#123—21no—
279C22⋊Q8—21no—
280C22⋊Q8—21no—
281C22⋊Q8—21no—
282C22⋊Q8—21no—
283C22⋊Q8—21no—
284C22⋊Q8—21no—
285C22⋊Q8—21no—
286C22⋊Q8—21no—
287C22⋊Q8—21no—
288C22⋊Q8—21no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
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⋊Q8—21no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C22⋊Q8—21no—
319C22⋊Q8D411yescharacteristic
320C22⋊Q8D411yescharacteristic
321C22⋊Q8D411yescharacteristic
322C22⋊Q8D411yescharacteristic
323C22⋊Q8C2311yescharacteristic
324C22⋊Q8C2311yescharacteristic
325#121—21no—
326#121—21no—
327#121C2311yescharacteristic
328#121C2311yescharacteristic
329C4×Q8—21no—
330C4×Q8—21no—
331C4×Q8—21no—
332C4×Q8—21no—
333C4×Q8C2311yescharacteristic
334C4×Q8C2311yescharacteristic
335C4×Q8C2311yescharacteristic
336C4×Q8C2311yescharacteristic
337C4×Q8C2311yescharacteristic
338C4×Q8C2311yescharacteristic
339C4×Q8C2311yescharacteristic
340C4×Q8C2311yescharacteristic
341C4×Q8C2311yescharacteristic
342C4×Q8C2311yescharacteristic
343C4×D4—21no—
344C4×D4—21no—
345C4×D4—21no—
346C4×D4—21no—
347C4×D4—21no—
348C4×D4—21no—
349C4×D4—21no—
350C4×D4—21no—
351C4×D4—21no—
352C4×D4—21no—
353C4×D4C2311yescharacteristic
354C4×D4C2311yescharacteristic
355C4×D4C2311yescharacteristic
356C4×D4C2311yescharacteristic
357C4×D4C2311yescharacteristic
358C4×D4C2311yescharacteristic
359C4×D4C2311yescharacteristic
360C4×D4C2311yescharacteristic
361C4×D4C2311yescharacteristic
362C4×D4C2311yescharacteristic
363C4×D4C2311yescharacteristic
364C4×D4C2311yescharacteristic
365C4×D4C2311yescharacteristic
366C4×D4C2311yescharacteristic
367C4×D4C2311yescharacteristic
368C4×D4C2311yescharacteristic
369C4×D4C2311yescharacteristic
370C4×D4C2311yescharacteristic
371#117—21no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117C2311yescharacteristic
376#117C2311yescharacteristic
377#117C2311yescharacteristic
378#117C2311yescharacteristic
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4C2311yescharacteristic
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C42C2311yescharacteristic
394#107C2311yescharacteristic
395#107C2311yescharacteristic
396#107C2311yescharacteristic
397#107C2311yescharacteristic
398#107C2311yescharacteristic
399#107C2311yescharacteristic
400#107C2311yescharacteristic
401#107C2311yescharacteristic
402#107C2311yescharacteristic
403#107C2311yescharacteristic
404#107C2311yescharacteristic
405#107C2311yescharacteristic
406#106C2311yescharacteristic
407#106C2311yescharacteristic
408#106C2311yescharacteristic
409#106C2311yescharacteristic
410#106C2311yescharacteristic
411#106C2311yescharacteristic
412#106C2311yescharacteristic
413#106C2311yescharacteristic
414#106C2311yescharacteristic
415#106C2311yescharacteristic
416#106C2311yescharacteristic
417#106C2311yescharacteristic
418C4⋊C8C2311yescharacteristic
419C4⋊C8C2311yescharacteristic
420C4⋊C8C2311yescharacteristic
421C4⋊C8C2311yescharacteristic
422C4⋊C8C2311yescharacteristic
423C4⋊C8C2311yescharacteristic
424C4⋊C8C2311yescharacteristic
425C4⋊C8C2311yescharacteristic
426C4⋊C8C2311yescharacteristic
427C4⋊C8C2311yescharacteristic
428C4⋊C8C2311yescharacteristic
429C4⋊C8C2311yescharacteristic
430#103C2311yescharacteristic
431#103C2311yescharacteristic
432#103C2311yescharacteristic
433#103C2311yescharacteristic
434#103C2311yescharacteristic
435#103C2311yescharacteristic
436#103C2311yescharacteristic
437#103C2311yescharacteristic
438#103C2311yescharacteristic
439#103C2311yescharacteristic
440#103C2311yescharacteristic
441#103C2311yescharacteristic
442#102C2311yescharacteristic
443#102C2311yescharacteristic
444#102C2311yescharacteristic
445#102C2311yescharacteristic
446#102C2311yescharacteristic
447#102C2311yescharacteristic
448#102C2311yescharacteristic
449#102C2311yescharacteristic
450#102C2311yescharacteristic
451#102C2311yescharacteristic
452#102C2311yescharacteristic
453#102C2311yescharacteristic
454#102C2311yescharacteristic
455#102C2311yescharacteristic
456#102C2311yescharacteristic
457#102C2311yescharacteristic
458#102C2311yescharacteristic
459#102C2311yescharacteristic
460#102C2311yescharacteristic
461#102C2311yescharacteristic
462C22⋊C8C2311yescharacteristic
463C22⋊C8C2311yescharacteristic
464C22⋊C8C2311yescharacteristic
465C22⋊C8C2311yescharacteristic
466#97C2311yescharacteristic
467#97C2311yescharacteristic
468#97C2311yescharacteristic
469#97C2311yescharacteristic
470#97C2311yescharacteristic
471#97C2311yescharacteristic
472C4×C8C2311yescharacteristic
473C4×C8C2311yescharacteristic
474C4×C8C2311yescharacteristic
475C4×C8C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478C24—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—82no—
488C2×Q8—82no—
489C2×Q8C2×D411yescharacteristic
490C2×Q8C2×D411yescharacteristic
491C2×Q8C2×D411yescharacteristic
492C2×Q8C2×D411yescharacteristic
493C2×Q8C2411yescharacteristic
494C2×Q8C2411yescharacteristic
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4C2411yescharacteristic
503C2×D4C2411yescharacteristic
504C2×D4C2411yescharacteristic
505C2×D4C2411yescharacteristic
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
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—82no—
526C22×C4C2×D411yescharacteristic
527C22×C4C2×D411yescharacteristic
528C22×C4C2411yescharacteristic
529SD16—22no—
530SD16—22no—
531SD16—22no—
532SD16—22no—
533D8—22no—
534D8—22no—
535D8—22no—
536D8—22no—
537C2×C8C2411yescharacteristic
538C2×C8C2411yescharacteristic
539C2×C8C2411yescharacteristic
540C2×C8C2411yescharacteristic
541C2×C8C2411yescharacteristic
542C2×C8C2411yescharacteristic
543C2×C8C2411yescharacteristic
544C2×C8C2411yescharacteristic
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
585C4⋊C4C2×D411yescharacteristic
586C4⋊C4C2×D411yescharacteristic
587C4⋊C4C2×D411yescharacteristic
588C4⋊C4C2×D411yescharacteristic
589C4⋊C4C2×D411yescharacteristic
590C4⋊C4C2×D411yescharacteristic
591C4⋊C4C2×D411yescharacteristic
592C4⋊C4C2×D411yescharacteristic
593C4⋊C4C2×D411yescharacteristic
594C4⋊C4C2×D411yescharacteristic
595C4⋊C4C2×D411yescharacteristic
596C4⋊C4C2×D411yescharacteristic
597C4⋊C4C2×D411yescharacteristic
598C4⋊C4C2×D411yescharacteristic
599C4⋊C4C2×D411yescharacteristic
600C4⋊C4C2411yescharacteristic
601C4⋊C4C2411yescharacteristic
602C4⋊C4C2411yescharacteristic
603C4⋊C4C2411yescharacteristic
604C4⋊C4C2411yescharacteristic
605C4⋊C4C2411yescharacteristic
606C4⋊C4C2411yescharacteristic
607C4⋊C4C2411yescharacteristic
608C4⋊C4C2411yescharacteristic
609C4⋊C4C2411yescharacteristic
610C22⋊C4—21no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
643C22⋊C4C2×D411yescharacteristic
644C22⋊C4C2×D411yescharacteristic
645C22⋊C4C2×D411yescharacteristic
646C42—21no—
647C42—21no—
648C42—21no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42—21no—
654C42C2×D411yescharacteristic
655C42C2×D411yescharacteristic
656C42C2411yescharacteristic
657C42C2411yescharacteristic
658C42C2411yescharacteristic
659C42C2411yescharacteristic
660C42C2411yescharacteristic
661C42C2411yescharacteristic
662C23—24no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—81no—
668C23—81no—
669C23C22×D411yescharacteristic
670Q8—21no—
671Q8—21no—
672Q8—21no—
673Q8—21no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—42no—
679Q8—81no—
680Q8—81no—
681Q8—81no—
682Q8—81no—
683Q8—81no—
684Q8—81no—
685Q8—81no—
686D4—24no—
687D4—21no—
688D4—21no—
689D4—21no—
690D4—21no—
691D4—21no—
692D4—21no—
693D4—81no—
694D4—81no—
695D4—81no—
696D4—81no—
697D42−1+412yes—
698D42−1+412yes—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—81no—
724C2×C4—81no—
725C2×C4—81no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4C22×D411yescharacteristic
735C2×C4C22×D411yescharacteristic
736C2×C4C22×D411yescharacteristic
737C2×C4C22×D411yescharacteristic
738C2×C4C22×D411yescharacteristic
739C2×C4C22×D411yescharacteristic
740C2×C4C22×D411yescharacteristic
741C2×C4C22×D411yescharacteristic
742C2×C4C22×D411yescharacteristic
743C2×C4C22×D411yescharacteristic
744C2×C4C22×D411yescharacteristic
745C2×C4C22×D411yescharacteristic
746C2×C4C22×D411yescharacteristic
747C2×C4C2511yescharacteristic
748C8—21no—
749C8—21no—
750C8—21no—
751C8—21no—
752C8—21no—
753C8—21no—
754C8—21no—
755C8—21no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—22no—
760C22—22no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—84no—
772C22C23×D411yescharacteristic
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—21no—
780C4—21no—
781C4—21no—
782C4—21no—
783C4—21no—
784C4—21no—
785C4—21no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4C2×2−1+411yescharacteristic
799C4C2×2−1+411yescharacteristic
800C2—41no—
801C2—42no—
802C2—42no—
803C2—81no—
804C2—81no—
805C2#348611yescharacteristic
806C2#358411yescharacteristic
807C2#358511yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
prime radical#3122C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #533 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #3557C2semidirect
2. #3501C2semidirect
3. #3389C2semidirect
4. #3389C2semidirect
5. #3388C2semidirect
6. #3388C2semidirect
7. #3386C2semidirect
8. #3384C2semidirect
9. #3381C2semidirect
10. #3380C2semidirect
11. #3376C2semidirect
12. #3376C2semidirect
13. #3373C2semidirect
14. #3370C2semidirect
15. #3370C2semidirect
16. #3367C2semidirect
17. #3361C2semidirect
18. #3360C2semidirect
19. #3244C2semidirect
20. #3243C2semidirect
21. #3242C2semidirect
22. #3241C2semidirect
23. #3240C2semidirect
24. #3233C2semidirect
25. #3123C2semidirect
27. #3118C2semidirect
28. #3118C2semidirect
29. #3114C2semidirect
30. #3105C2semidirect
31. #2985C2semidirect
34. #559C22semidirect
35. #559C22semidirect
36. #557C22semidirect
37. #557C22semidirect
38. #556C22semidirect
39. #556C22semidirect
49. #554C22semidirect
50. #554C22semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #501C22semidirect
80. #501C22semidirect
81. #501C22semidirect
82. #501C22semidirect
83. #500C22semidirect
84. #499C22semidirect
85. #499C22semidirect
86. #499C22semidirect
87. #499C22semidirect
88. #498C22semidirect
89. #491C22semidirect
90. #490C22semidirect
91. #489C22semidirect
92. #489C22semidirect
93. #489C22semidirect
94. #489C22semidirect
95. #488C22semidirect
96. #488C22semidirect
97. #488C22semidirect
98. #488C22semidirect
99. #487C22semidirect
100. #486C22semidirect
113. #479C22semidirect
114. #479C22semidirect
115. #479C22semidirect
116. #479C22semidirect
117. #479C22semidirect
118. #479C22semidirect
127. #478C22semidirect
128. #478C22semidirect
129. #478C22semidirect
130. #478C22semidirect
131. #478C22semidirect
132. #478C22semidirect
133. #477C22semidirect
134. #477C22semidirect
135. #477C22semidirect
138. #476C22semidirect
139. #476C22semidirect
140. #476C22semidirect
141. #475C22semidirect
142. #475C22semidirect
143. #475C22semidirect
146. #474C22semidirect
147. #474C22semidirect
148. #474C22semidirect
165. #446C22semidirect
166. #446C22semidirect
167. #446C22semidirect
168. #446C22semidirect
169. #446C22semidirect
170. #446C22semidirect
171. C8×Q8C22semidirect
172. C8×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#35572
#35012
#33892
#33882
#33862
#33842
#33812
#33802
#33762
#33732
#33702
#33672
#33612
#33602
#32442
#32432
#32422
#32412
#32402
#32332
#31232
#31222
#31182
#31142
#31052
#29852