Finite Group Databasebeta

← #61715

Subgroups — #61715

Order 256.

879 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3520C211yesmaximal, characteristic, complemented
2#3475C211yesmaximal, characteristic, complemented
3#3350C211yesmaximal, characteristic, complemented
4#3349C211yesmaximal, characteristic, complemented
5#3349C211yesmaximal, characteristic, complemented
6#3348C211yesmaximal, characteristic, complemented
7#3345C211yesmaximal, characteristic, complemented
8#3344C211yesmaximal, characteristic, complemented
9#3343C211yesmaximal, characteristic, complemented
10#3343C211yesmaximal, characteristic, complemented
11#3321C211yesmaximal, characteristic, complemented
12#3320C211yesmaximal, characteristic, complemented
13#3316C211yesmaximal, characteristic, complemented
14#3315C211yesmaximal, characteristic, complemented
15#3313C211yesmaximal, characteristic, complemented
16#3312C211yesmaximal, characteristic, complemented
17#3308C211yesmaximal, characteristic, complemented
18#3307C211yesmaximal, characteristic, complemented
19#3240C211yesmaximal, characteristic, complemented
20#3237C211yesmaximal, characteristic, complemented
21#3197C211yesmaximal, characteristic, complemented
22#3196C211yesmaximal, characteristic, complemented
23#3191C211yesmaximal, characteristic, complemented
24#3190C211yesmaximal, characteristic, complemented
25#3116C211yesmaximal, characteristic, complemented
26#3111C211yesmaximal, characteristic, complemented
27#3095C211yesmaximal, characteristic, complemented
28#3093C211yesmaximal, characteristic, complemented
29#3091C211yesmaximal, characteristic, complemented
30C2×#485C211yesmaximal, characteristic, complemented
31#2973C211yesmaximal, characteristic, complemented
32#556C2211yescharacteristic
33#556C2211yescharacteristic
34#555C2211yescharacteristic
35#554—21no—
36#554C2211yescharacteristic
37#553C2211yescharacteristic
38#553C2211yescharacteristic
39#552—21no—
40#552C2211yescharacteristic
41#552C2211yescharacteristic
42#552C2211yescharacteristic
43#552C2211yescharacteristic
44#551—21no—
45#551—21no—
46#551—21no—
47#551—21no—
48D4×Q8C2211yescharacteristic
49#548C2211yescharacteristic
50#548C2211yescharacteristic
51#547C2211yescharacteristic
52#547C2211yescharacteristic
53#547C2211yescharacteristic
54#546—21no—
55#546—21no—
56#542—21no—
57#539—21no—
58#539—21no—
59#533C2211yescharacteristic
60#533C2211yescharacteristic
61#529—21no—
62#529—21no—
63#529—21no—
64#529C2211yescharacteristic
65#525C2211yescharacteristic
66#525C2211yescharacteristic
67#525C2211yescharacteristic
68#525C2211yescharacteristic
69C2×C22⋊Q8C2211yescharacteristic
70C2×C22⋊Q8C2211yescharacteristic
71#520—21no—
72C4×#41—21no—
73C4×#41C2211yescharacteristic
74C2×C4×D4C2211yescharacteristic
75C2×#117C2211yescharacteristic
76C2×#117C2211yescharacteristic
77#501C2211yescharacteristic, complemented
78#501C2211yescharacteristic, complemented
79#501C2211yescharacteristic, complemented
80#501C2211yescharacteristic, complemented
81#491C2211yescharacteristic, complemented
82#491C2211yescharacteristic, complemented
83#489C2211yescharacteristic, complemented
84#489C2211yescharacteristic, complemented
85#485C2211yescharacteristic
86#485C2211yescharacteristic
87#485C2211yescharacteristic
88#485C2211yescharacteristic
89#485C2211yescharacteristic
90#485C2211yescharacteristic
91#485C2211yescharacteristic
92#485C2211yescharacteristic
93#485C2211yescharacteristic
94#485C2211yescharacteristic, complemented
95#485C2211yescharacteristic, complemented
96#485C2211yescharacteristic, complemented
97#485C2211yescharacteristic, complemented
98#485C2211yescharacteristic, complemented
99#485C2211yescharacteristic, complemented
100#485C2211yescharacteristic, complemented
101#485C2211yescharacteristic, complemented
102#484C2211yescharacteristic, complemented
103#484C2211yescharacteristic, complemented
104#484C2211yescharacteristic, complemented
105#484C2211yescharacteristic, complemented
106#483C2211yescharacteristic, complemented
107#483C2211yescharacteristic, complemented
108#483C2211yescharacteristic, complemented
109#483C2211yescharacteristic, complemented
110#482C2211yescharacteristic
111#482C2211yescharacteristic
112#482C2211yescharacteristic
113#482C2211yescharacteristic, complemented
114#482C2211yescharacteristic, complemented
115#482C2211yescharacteristic, complemented
116#482C2211yescharacteristic, complemented
117#481C2211yescharacteristic, complemented
118#481C2211yescharacteristic, complemented
119#480C2211yescharacteristic, complemented
120#480C2211yescharacteristic, complemented
121#479C2211yescharacteristic, complemented
122#479C2211yescharacteristic, complemented
123#479C2211yescharacteristic, complemented
124#478C2211yescharacteristic, complemented
125#478C2211yescharacteristic, complemented
126#478C2211yescharacteristic, complemented
127#477C2211yescharacteristic, complemented
128#477C2211yescharacteristic, complemented
129#477C2211yescharacteristic, complemented
130#476C2211yescharacteristic, complemented
131#475C2211yescharacteristic, complemented
132#475C2211yescharacteristic, complemented
133#470C2211yescharacteristic, complemented
134#470C2211yescharacteristic, complemented
135#470C2211yescharacteristic, complemented
136#469C2211yescharacteristic, complemented
137#468C2211yescharacteristic, complemented
138#468C2211yescharacteristic, complemented
139#468C2211yescharacteristic, complemented
140#468C2211yescharacteristic, complemented
141#467C2211yescharacteristic, complemented
142#467C2211yescharacteristic, complemented
143#467C2211yescharacteristic, complemented
144#466C2211yescharacteristic, complemented
145#465C2211yescharacteristic, complemented
146#465C2211yescharacteristic, complemented
147#465C2211yescharacteristic, complemented
148#465C2211yescharacteristic, complemented
149#464C2211yescharacteristic, complemented
150#463C2211yescharacteristic, complemented
151#462C2211yescharacteristic, complemented
152#461C2211yescharacteristic, complemented
153#452C2211yescharacteristic
154#452C2211yescharacteristic
155#452C2211yescharacteristic
156#452C2211yescharacteristic, complemented
157#452C2211yescharacteristic, complemented
158#451C2211yescharacteristic, complemented
159#451C2211yescharacteristic, complemented
160#449C2211yescharacteristic
161#449C2211yescharacteristic, complemented
162#449C2211yescharacteristic, complemented
163#448C2211yescharacteristic, complemented
164#448C2211yescharacteristic, complemented
165#442C2211yescharacteristic, complemented
166#441C2211yescharacteristic, complemented
167#441C2211yescharacteristic, complemented
168#441C2211yescharacteristic, complemented
169#440C2211yescharacteristic, complemented
170#440C2211yescharacteristic, complemented
171#440C2211yescharacteristic, complemented
172#440C2211yescharacteristic, complemented
173#435C2211yescharacteristic
174#435C2211yescharacteristic
175#435C2211yescharacteristic
176#435C2211yescharacteristic
177#435C2211yescharacteristic
178#435C2211yescharacteristic
179#435C2211yescharacteristic
180#435C2211yescharacteristic
181#432C2211yescharacteristic
182#432C2211yescharacteristic
183#428C2211yescharacteristic, complemented
184#428C2211yescharacteristic, complemented
185#428C2211yescharacteristic, complemented
186#428C2211yescharacteristic, complemented
187#427C2211yescharacteristic, complemented
188#427C2211yescharacteristic, complemented
189C2×#107C2211yescharacteristic, complemented
190C2×#106C2211yescharacteristic, complemented
191#419C2211yescharacteristic, complemented
192#419C2211yescharacteristic, complemented
193#417C2211yescharacteristic, complemented
194#417C2211yescharacteristic, complemented
195#416C2211yescharacteristic, complemented
196#416C2211yescharacteristic, complemented
197C2×#103C2211yescharacteristic, complemented
198C2×#103C2211yescharacteristic, complemented
199#407C2211yescharacteristic
200#407C2211yescharacteristic
201C2×C22⋊C8C2211yescharacteristic
202C2×C22⋊C8C2211yescharacteristic
203C2×#41—21no—
204C2×#41—21no—
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C22×Q8C2311yescharacteristic
209C22×Q8C2311yescharacteristic
210C22×D4D411yescharacteristic
211C23×C4C2311yescharacteristic
212C23×C4C2311yescharacteristic
213C2×Q16C2311yescharacteristic
214C2×Q16C2311yescharacteristic
215C2×Q16C2311yescharacteristic
216C2×SD16C2311yescharacteristic
217C2×SD16C2311yescharacteristic
218C2×SD16C2311yescharacteristic
219C2×SD16C2311yescharacteristic
220C2×D8C2311yescharacteristic
221C2×M16C2311yescharacteristic
222C2×M16C2311yescharacteristic
223C2×M16C2311yescharacteristic
224C2×M16C2311yescharacteristic
225C22×C8C2311yescharacteristic
226C22×C8C2311yescharacteristic
227C22×C8C2311yescharacteristic
228C22×C8C2311yescharacteristic
229C4⋊Q8—21no—
230C4⋊Q8C2311yescharacteristic
231C4⋊Q8C2311yescharacteristic
232C4⋊Q8C2311yescharacteristic
233C4⋊Q8C2311yescharacteristic
234#126—21no—
235#126—21no—
236#126—21no—
237#126—21no—
238#126—21no—
239#126—21no—
240#126—21no—
241#126—21no—
242#126—21no—
243#126—21no—
244#126—21no—
245#125—21no—
246#125—21no—
247#125—21no—
248#125—21no—
249#125—21no—
250#125—21no—
251#125C2311yescharacteristic
252#125C2311yescharacteristic
253#125C2311yescharacteristic
254#124—21no—
255#124—21no—
256#124—21no—
257#124—21no—
258#124—21no—
259#124—21no—
260#124C2311yescharacteristic
261#123—21no—
262#123—21no—
263#123—21no—
264#123—21no—
265#123—21no—
266#123—21no—
267#123—21no—
268#123—21no—
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—
278C22⋊Q8—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⋊Q8C2311yescharacteristic
294C22⋊Q8C2311yescharacteristic
295C22⋊Q8C2311yescharacteristic
296C22⋊Q8C2311yescharacteristic
297C22⋊Q8C2311yescharacteristic
298C22⋊Q8C2311yescharacteristic
299C22⋊Q8C2311yescharacteristic
300C22⋊Q8C2311yescharacteristic
301C22⋊Q8C2311yescharacteristic
302C22⋊Q8C2311yescharacteristic
303C22⋊Q8C2311yescharacteristic
304C22⋊Q8C2311yescharacteristic
305C22⋊Q8C2311yescharacteristic
306#121—21no—
307#121—21no—
308#121—21no—
309#121—21no—
310#121—21no—
311#121—21no—
312#121C2311yescharacteristic
313#121C2311yescharacteristic
314#121C2311yescharacteristic
315#121C2311yescharacteristic
316#121C2311yescharacteristic
317#121C2311yescharacteristic
318#121C2311yescharacteristic
319#120—21no—
320#120—21no—
321#120—21no—
322#120—21no—
323C4×Q8—21no—
324C4×Q8—21no—
325C4×Q8—21no—
326C4×Q8—21no—
327C4×Q8—21no—
328C4×Q8C2311yescharacteristic
329C4×Q8C2311yescharacteristic
330C4×Q8C2311yescharacteristic
331C4×Q8C2311yescharacteristic
332C4×Q8C2311yescharacteristic
333C4×D4—21no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4—21no—
337C4×D4—21no—
338C4×D4—21no—
339C4×D4—21no—
340C4×D4—21no—
341C4×D4—21no—
342C4×D4—21no—
343C4×D4—21no—
344C4×D4—21no—
345C4×D4—21no—
346C4×D4—21no—
347C4×D4—21no—
348C4×D4—21no—
349C4×D4—21no—
350C4×D4D411yescharacteristic
351C4×D4D411yescharacteristic
352C4×D4D411yescharacteristic
353C4×D4D411yescharacteristic
354C4×D4C2311yescharacteristic
355C4×D4C2311yescharacteristic
356C4×D4C2311yescharacteristic
357C4×D4C2311yescharacteristic
358C4×D4C2311yescharacteristic
359C4×D4C2311yescharacteristic
360C4×D4C2311yescharacteristic
361#117—21no—
362#117—21no—
363#117—21no—
364#117—21no—
365#117—21no—
366#117—21no—
367#117—21no—
368#117—21no—
369#117—21no—
370#117—21no—
371#117—21no—
372#117—21no—
373#117C2311yescharacteristic
374#117C2311yescharacteristic
375#117C2311yescharacteristic
376#117C2311yescharacteristic
377#117C2311yescharacteristic
378#117C2311yescharacteristic
379#117C2311yescharacteristic
380#117C2311yescharacteristic
381#117C2311yescharacteristic
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4D411yescharacteristic
386C2×C4⋊C4C2311yescharacteristic
387C2×C4⋊C4C2311yescharacteristic
388C2×C4⋊C4C2311yescharacteristic
389C2×C4⋊C4C2311yescharacteristic
390C2×C4⋊C4C2311yescharacteristic
391C2×C4⋊C4C2311yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4D411yescharacteristic
397C2×C22⋊C4D411yescharacteristic
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42C2311yescharacteristic
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
424#106C2311yescharacteristic
425#106C2311yescharacteristic
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#103C2311yescharacteristic
443#103C2311yescharacteristic
444#103C2311yescharacteristic
445#103C2311yescharacteristic
446#103C2311yescharacteristic
447#103C2311yescharacteristic
448#103C2311yescharacteristic
449#103C2311yescharacteristic
450#103C2311yescharacteristic
451#103C2311yescharacteristic
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
466C22⋊C8C2311yescharacteristic
467C22⋊C8C2311yescharacteristic
468C22⋊C8C2311yescharacteristic
469C22⋊C8C2311yescharacteristic
470C22⋊C8C2311yescharacteristic
471C22⋊C8C2311yescharacteristic
472C22⋊C8C2311yescharacteristic
473C22⋊C8C2311yescharacteristic
474#97C2311yescharacteristic
475#97C2311yescharacteristic
476#97C2311yescharacteristic
477#97C2311yescharacteristic
478C24C2×D411yescharacteristic
479C24C2×D411yescharacteristic
480#41—41no—
481#41—41no—
482#41—41no—
483#41—41no—
484#41—41no—
485#41—41no—
486#41—44no—
487#41—44no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—41no—
494C2×Q8—41no—
495C2×Q8—41no—
496C2×Q8—41no—
497C2×Q8C2411yescharacteristic
498C2×Q8C2411yescharacteristic
499C2×Q8C2411yescharacteristic
500C2×Q8C2411yescharacteristic
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—21no—
511C2×D4—42no—
512C2×D4C2×D411yescharacteristic
513C2×D4C2×D411yescharacteristic
514C2×D4C2×D411yescharacteristic
515C2×D4C2×D411yescharacteristic
516C2×D4C2411yescharacteristic
517C2×D4C2411yescharacteristic
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×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4C2×D411yescharacteristic
537C22×C4C2×D411yescharacteristic
538C22×C4C2×D411yescharacteristic
539C22×C4C2×D411yescharacteristic
540C22×C4C2×D411yescharacteristic
541C22×C4C2×D411yescharacteristic
542C22×C4C2×D411yescharacteristic
543C22×C4C2×D411yescharacteristic
544C22×C4C2411yescharacteristic
545C22×C4C2411yescharacteristic
546C22×C4C2411yescharacteristic
547C22×C4C2411yescharacteristic
548C22×C4C2411yescharacteristic
549Q16—41no—
550Q16—41no—
551Q16—41no—
552SD16—41no—
553SD16—41no—
554SD16—41no—
555SD16—41no—
556D8—41no—
557M16—41no—
558M16—41no—
559M16—41no—
560M16—41no—
561C2×C8—41no—
562C2×C8—41no—
563C2×C8—41no—
564C2×C8—41no—
565C2×C8C2411yescharacteristic
566C2×C8C2411yescharacteristic
567C2×C8C2411yescharacteristic
568C2×C8C2411yescharacteristic
569C2×C8C2411yescharacteristic
570C2×C8C2411yescharacteristic
571C2×C8C2411yescharacteristic
572C2×C8C2411yescharacteristic
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⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4C2×D411yescharacteristic
609C4⋊C4C2×D411yescharacteristic
610C4⋊C4C2×D411yescharacteristic
611C4⋊C4C2×D411yescharacteristic
612C4⋊C4C2411yescharacteristic
613C4⋊C4C2411yescharacteristic
614C4⋊C4C2411yescharacteristic
615C4⋊C4C2411yescharacteristic
616C4⋊C4C2411yescharacteristic
617C4⋊C4C2411yescharacteristic
618C4⋊C4C2411yescharacteristic
619C4⋊C4C2411yescharacteristic
620C4⋊C4C2411yescharacteristic
621C4⋊C4C2411yescharacteristic
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⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4C2×D411yescharacteristic
657C22⋊C4C2×D411yescharacteristic
658C22⋊C4C2×D411yescharacteristic
659C22⋊C4C2×D411yescharacteristic
660C22⋊C4C2×D411yescharacteristic
661C22⋊C4C2×D411yescharacteristic
662C22⋊C4C2×D411yescharacteristic
663C22⋊C4C2×D411yescharacteristic
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—21no—
676C42—21no—
677C42—21no—
678C42C2×D411yescharacteristic
679C42C2×D411yescharacteristic
680C42C2411yescharacteristic
681C42C2411yescharacteristic
682C23—22no—
683C23—21no—
684C23—21no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23C22×D411yescharacteristic
691C23C22×D411yescharacteristic
692C23C22×D411yescharacteristic
693C23C22×D411yescharacteristic
694C23C22×D411yescharacteristic
695Q8—21no—
696Q8—21no—
697Q8—21no—
698Q8—21no—
699Q8—21no—
700Q8—21no—
701Q8—21no—
702Q8—21no—
703Q8—42no—
704Q8—42no—
705Q8—81no—
706Q8—81no—
707Q8—81no—
708D4—22no—
709D4—22no—
710D4—21no—
711D4—21no—
712D4—21no—
713D4—21no—
714D4—41no—
715D4—41no—
716D4—42no—
717D4—42no—
718D4—42no—
719D4—42no—
720D4—42no—
721D4—42no—
722D4—81no—
723D4—81no—
724D4—81no—
725D4—81no—
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—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4C22×D411yescharacteristic
773C2×C4C22×D411yescharacteristic
774C2×C4C22×D411yescharacteristic
775C2×C4C22×D411yescharacteristic
776C2×C4C22×D411yescharacteristic
777C2×C4C22×D411yescharacteristic
778C2×C4C22×D411yescharacteristic
779C2×C4C22×D411yescharacteristic
780C2×C4C22×D411yescharacteristic
781C2×C4C2511yescharacteristic
782C8—21no—
783C8—21no—
784C8—21no—
785C8—21no—
786C8—21no—
787C8—21no—
788C8—21no—
789C8—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—82no—
811C22—82no—
812C22#57512yes—
813C22C23×D411yescharacteristic
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—21no—
820C4—21no—
821C4—21no—
822C4—21no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4#58511yescharacteristic
838C4#58511yescharacteristic
839C2—22no—
840C2—41no—
841C2—41no—
842C2—41no—
843C2—41no—
844C2—81no—
845C2—81no—
846C2#348511yescharacteristic
847C2C2×#57511yescharacteristic
848C2#358611yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3520C2semidirect
2. #3475C2semidirect
3. #3350C2semidirect
4. #3349C2semidirect
5. #3349C2semidirect
6. #3348C2semidirect
7. #3345C2semidirect
8. #3344C2semidirect
9. #3343C2semidirect
10. #3343C2semidirect
11. #3321C2semidirect
12. #3320C2semidirect
13. #3316C2semidirect
14. #3315C2semidirect
15. #3313C2semidirect
16. #3312C2semidirect
17. #3308C2semidirect
18. #3307C2semidirect
19. #3240C2semidirect
20. #3237C2semidirect
21. #3197C2semidirect
22. #3196C2semidirect
23. #3191C2semidirect
24. #3190C2semidirect
25. #3116C2semidirect
26. #3111C2semidirect
27. #3095C2semidirect
28. #3093C2semidirect
29. #3091C2semidirect
30. C2×#485C2semidirect
31. #2973C2semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #501C22semidirect
80. #501C22semidirect
81. #491C22semidirect
82. #491C22semidirect
83. #489C22semidirect
84. #489C22semidirect
94. #485C22semidirect
95. #485C22semidirect
96. #485C22semidirect
97. #485C22semidirect
98. #485C22semidirect
99. #485C22semidirect
100. #485C22semidirect
101. #485C22semidirect
102. #484C22semidirect
103. #484C22semidirect
104. #484C22semidirect
105. #484C22semidirect
106. #483C22semidirect
107. #483C22semidirect
108. #483C22semidirect
109. #483C22semidirect
113. #482C22semidirect
114. #482C22semidirect
115. #482C22semidirect
116. #482C22semidirect
117. #481C22semidirect
118. #481C22semidirect
119. #480C22semidirect
120. #480C22semidirect
121. #479C22semidirect
122. #479C22semidirect
123. #479C22semidirect
124. #478C22semidirect
125. #478C22semidirect
126. #478C22semidirect
127. #477C22semidirect
128. #477C22semidirect
129. #477C22semidirect
130. #476C22semidirect
131. #475C22semidirect
132. #475C22semidirect
133. #470C22semidirect
134. #470C22semidirect
135. #470C22semidirect
136. #469C22semidirect
137. #468C22semidirect
138. #468C22semidirect
139. #468C22semidirect
140. #468C22semidirect
141. #467C22semidirect
142. #467C22semidirect
143. #467C22semidirect
144. #466C22semidirect
145. #465C22semidirect
146. #465C22semidirect
147. #465C22semidirect
148. #465C22semidirect
149. #464C22semidirect
150. #463C22semidirect
151. #462C22semidirect
152. #461C22semidirect
156. #452C22semidirect
157. #452C22semidirect
158. #451C22semidirect
159. #451C22semidirect
161. #449C22semidirect
162. #449C22semidirect
163. #448C22semidirect
164. #448C22semidirect
165. #442C22semidirect
166. #441C22semidirect
167. #441C22semidirect
168. #441C22semidirect
169. #440C22semidirect
170. #440C22semidirect
171. #440C22semidirect
172. #440C22semidirect
183. #428C22semidirect
184. #428C22semidirect
185. #428C22semidirect
186. #428C22semidirect
187. #427C22semidirect
188. #427C22semidirect
189. C2×#107C22semidirect
190. C2×#106C22semidirect
191. #419C22semidirect
192. #419C22semidirect
193. #417C22semidirect
194. #417C22semidirect
195. #416C22semidirect
196. #416C22semidirect
197. C2×#103C22semidirect
198. C2×#103C22semidirect

Maximal subgroups

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

subgroupindex
#35202
#34752
#33502
#33492
#33482
#33452
#33442
#33432
#33212
#33202
#33162
#33152
#33132
#33122
#33082
#33072
#32402
#32372
#31972
#31962
#31912
#31902
#31162
#31112
#30952
#30932
#30912
C2×#4852
#29732