Finite Group Databasebeta

← #61770

Subgroups — #61770

Order 256.

876 conjugacy classes of subgroups.

The subgroup lattice has 859 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3542C211yesmaximal, characteristic
2#3495C211yesmaximal, characteristic, complemented
3#3350C211yesmaximal, characteristic, complemented
4#3348C211yesmaximal, characteristic, complemented
5#3344C211yesmaximal, characteristic, complemented
6#3343C211yesmaximal, characteristic, complemented
7#3340C211yesmaximal, characteristic, complemented
8#3337C211yesmaximal, characteristic, complemented
9#3336C211yesmaximal, characteristic, complemented
10#3335C211yesmaximal, characteristic, complemented
11#3317C211yesmaximal, characteristic, complemented
12#3314C211yesmaximal, characteristic, complemented
13#3311C211yesmaximal, characteristic, complemented
14#3310C211yesmaximal, characteristic, complemented
15#3304C211yesmaximal, characteristic, complemented
16#3296C211yesmaximal, characteristic, complemented
17#3296C211yesmaximal, characteristic, complemented
18#3295C211yesmaximal, characteristic, complemented
19#3244C211yesmaximal, characteristic, complemented
20#3241C211yesmaximal, characteristic, complemented
21#3201C211yesmaximal, characteristic, complemented
22#3200C211yesmaximal, characteristic, complemented
23#3190C211yesmaximal, characteristic, complemented
24#3187C211yesmaximal, characteristic, complemented
25#3126C211yesmaximal, characteristic, complemented
26#3121C211yesmaximal, characteristic, complemented
27#3099C211yesmaximal, characteristic, complemented
28#3096C211yesmaximal, characteristic, complemented
29#3091C211yesmaximal, characteristic, complemented
30C2×#482C211yesmaximal, characteristic, complemented
31#2977C211yesmaximal, characteristic, complemented
32#562—21no—
33#560—21no—
34#556C2211yescharacteristic, complemented
35#556C2211yescharacteristic, complemented
36#555C2211yescharacteristic
37#554C2211yescharacteristic
38#554C2211yescharacteristic, complemented
39#553C2211yescharacteristic
40#552—21no—
41#552—21no—
42#552C2211yescharacteristic
43#552C2211yescharacteristic
44#552C2211yescharacteristic, complemented
45#552C2211yescharacteristic, complemented
46#552C2211yescharacteristic, complemented
47#551—21no—
48#551—21no—
49#551—21no—
50#550C2211yescharacteristic
51#547C2211yescharacteristic
52#546—21no—
53#546C2211yescharacteristic
54#546C2211yescharacteristic
55D42C2211yescharacteristic
56#544C2211yescharacteristic, complemented
57#542—21no—
58#542C2211yescharacteristic
59#541—21no—
60#540—21no—
61#540C2211yescharacteristic
62#538—21no—
63#537C2211yescharacteristic
64#536C2211yescharacteristic, complemented
65#535—21no—
66#535C2211yescharacteristic
67#534—21no—
68#533—21no—
69#529—21no—
70#525C2211yescharacteristic
71#525C2211yescharacteristic
72C2×C22⋊Q8C2211yescharacteristic, complemented
73C2×#121C2211yescharacteristic
74#520C2211yescharacteristic, complemented
75#519C2211yescharacteristic, complemented
76C2×#117C2211yescharacteristic, complemented
77#501C2211yescharacteristic, complemented
78#501C2211yescharacteristic, complemented
79#499C2211yescharacteristic, complemented
80#498C2211yescharacteristic, complemented
81#490C2211yescharacteristic, complemented
82#489C2211yescharacteristic, complemented
83#488C2211yescharacteristic, complemented
84#486C2211yescharacteristic, complemented
85#485C2211yescharacteristic, complemented
86#485C2211yescharacteristic, complemented
87#485C2211yescharacteristic, complemented
88#485C2211yescharacteristic, complemented
89#485C2211yescharacteristic, complemented
90#485C2211yescharacteristic, complemented
91#485C2211yescharacteristic, complemented
92#484C2211yescharacteristic, complemented
93#484C2211yescharacteristic, complemented
94#483C2211yescharacteristic, complemented
95#483C2211yescharacteristic, complemented
96#483C2211yescharacteristic, complemented
97#483C2211yescharacteristic, complemented
98#483C2211yescharacteristic, complemented
99#483C2211yescharacteristic, complemented
100#482C2211yescharacteristic
101#482C2211yescharacteristic
102#482C2211yescharacteristic
103#482C2211yescharacteristic
104#482C2211yescharacteristic, complemented
105#482C2211yescharacteristic, complemented
106#482C2211yescharacteristic, complemented
107#482C2211yescharacteristic, complemented
108#482C2211yescharacteristic, complemented
109#482C2211yescharacteristic, complemented
110#482C2211yescharacteristic, complemented
111#482C2211yescharacteristic, complemented
112#482C2211yescharacteristic, complemented
113#481C2211yescharacteristic
114#481C2211yescharacteristic
115#481C2211yescharacteristic, complemented
116#481C2211yescharacteristic, complemented
117#481C2211yescharacteristic, complemented
118#480C2211yescharacteristic
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#476C2211yescharacteristic, complemented
129#476C2211yescharacteristic, complemented
130#475C2211yescharacteristic, complemented
131#475C2211yescharacteristic, complemented
132#474C2211yescharacteristic, complemented
133#470C2211yescharacteristic, complemented
134#468C2211yescharacteristic, complemented
135#468C2211yescharacteristic, complemented
136#468C2211yescharacteristic, complemented
137#467C2211yescharacteristic, complemented
138#467C2211yescharacteristic, complemented
139#467C2211yescharacteristic, complemented
140#465C2211yescharacteristic
141#465C2211yescharacteristic
142#465C2211yescharacteristic
143#465C2211yescharacteristic
144#465C2211yescharacteristic, complemented
145#465C2211yescharacteristic, complemented
146#465C2211yescharacteristic, complemented
147#465C2211yescharacteristic, complemented
148#465C2211yescharacteristic, complemented
149#464C2211yescharacteristic, complemented
150#464C2211yescharacteristic, complemented
151#460C2211yescharacteristic, complemented
152#460C2211yescharacteristic, complemented
153#452C2211yescharacteristic, complemented
154#452C2211yescharacteristic, complemented
155#452C2211yescharacteristic, complemented
156#452C2211yescharacteristic, complemented
157#451C2211yescharacteristic, complemented
158#450C2211yescharacteristic
159#450C2211yescharacteristic
160#450C2211yescharacteristic, complemented
161#450C2211yescharacteristic, complemented
162#448C2211yescharacteristic
163#448C2211yescharacteristic, complemented
164#448C2211yescharacteristic, complemented
165#441C2211yescharacteristic, complemented
166#440C2211yescharacteristic, complemented
167#440C2211yescharacteristic, complemented
168#440C2211yescharacteristic, complemented
169C4×Q16C2211yescharacteristic, complemented
170C4×SD16C2211yescharacteristic, complemented
171C4×SD16C2211yescharacteristic, complemented
172C4×SD16C2211yescharacteristic, complemented
173#435C2211yescharacteristic
174#435C2211yescharacteristic, complemented
175#435C2211yescharacteristic, complemented
176#435C2211yescharacteristic, complemented
177C8×D4C2211yescharacteristic
178C8×D4C2211yescharacteristic, complemented
179C8×D4C2211yescharacteristic, complemented
180C8×D4C2211yescharacteristic, complemented
181#433C2211yescharacteristic, complemented
182#433C2211yescharacteristic, complemented
183#428C2211yescharacteristic, complemented
184#428C2211yescharacteristic, complemented
185#427C2211yescharacteristic, complemented
186#427C2211yescharacteristic, complemented
187#427C2211yescharacteristic, complemented
188C2×#107C2211yescharacteristic, complemented
189C2×#106C2211yescharacteristic, complemented
190C2×#106C2211yescharacteristic, complemented
191#418C2211yescharacteristic, complemented
192#417C2211yescharacteristic, complemented
193#416C2211yescharacteristic, complemented
194#416C2211yescharacteristic, complemented
195#416C2211yescharacteristic, complemented
196C2×#102C2211yescharacteristic
197C2×#102C2211yescharacteristic
198C2×#102C2211yescharacteristic, complemented
199#408C2211yescharacteristic, complemented
200#408C2211yescharacteristic, complemented
201C2×C22⋊C8C2211yescharacteristic, complemented
202C2×C22⋊C8C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C22×Q8C2311yescharacteristic
208C22×D4—21no—
209C22×D4—21no—
210C22×D4C2311yescharacteristic
211C22×D4C2311yescharacteristic
212C23×C4C2311yescharacteristic
213C2×Q16C2311yescharacteristic
214C2×Q16C2311yescharacteristic
215C2×SD16C2311yescharacteristic
216C2×SD16C2311yescharacteristic
217C2×SD16C2311yescharacteristic
218C2×SD16C2311yescharacteristic
219C2×SD16C2311yescharacteristic
220C2×SD16C2311yescharacteristic
221C2×M16C2311yescharacteristic
222C2×M16C2311yescharacteristic
223C22×C8C2311yescharacteristic
224C22×C8C2311yescharacteristic
225C22×C8C2311yescharacteristic
226C22×C8C2311yescharacteristic
227C22×C8C2311yescharacteristic
228C22×C8C2311yescharacteristic
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8C2311yescharacteristic
232C4⋊Q8C2311yescharacteristic
233C4⋊Q8C2311yescharacteristic
234#127—21no—
235#127—21no—
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#125—21no—
249#125—21no—
250#125—21no—
251#125—21no—
252#125—21no—
253#125—21no—
254#125—21no—
255#125—21no—
256#125C2311yescharacteristic
257#125C2311yescharacteristic
258#125C2311yescharacteristic
259#124—21no—
260#124—21no—
261#124—21no—
262#124—21no—
263#124—21no—
264#124—21no—
265#124—21no—
266#124C2311yescharacteristic
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—
278#123—21no—
279#123—21no—
280#123—21no—
281#123—21no—
282#123—21no—
283#123D411yescharacteristic
284#123D411yescharacteristic
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⋊Q8D411yescharacteristic
297C22⋊Q8D411yescharacteristic
298C22⋊Q8C2311yescharacteristic
299C22⋊Q8C2311yescharacteristic
300C22⋊Q8C2311yescharacteristic
301C22⋊Q8C2311yescharacteristic
302C22⋊Q8C2311yescharacteristic
303C22⋊Q8C2311yescharacteristic
304C22⋊Q8C2311yescharacteristic
305C22⋊Q8C2311yescharacteristic
306C22⋊Q8C2311yescharacteristic
307C22⋊Q8C2311yescharacteristic
308C22⋊Q8C2311yescharacteristic
309#121—21no—
310#121—21no—
311#121—21no—
312#121—21no—
313#121—21no—
314#121—21no—
315#121—21no—
316#121—21no—
317#121—21no—
318#121—21no—
319#121—21no—
320#121—21no—
321#121—21no—
322#121—21no—
323#121D411yescharacteristic
324#121D411yescharacteristic
325#121C2311yescharacteristic
326#121C2311yescharacteristic
327#121C2311yescharacteristic
328#121C2311yescharacteristic
329#121C2311yescharacteristic
330#121C2311yescharacteristic
331#121C2311yescharacteristic
332#121C2311yescharacteristic
333#121C2311yescharacteristic
334#120—21no—
335#120—21no—
336#120—21no—
337#120—21no—
338#120—21no—
339#120—21no—
340#120—21no—
341#120D411yescharacteristic
342#120D411yescharacteristic
343C4×Q8—21no—
344C4×Q8—21no—
345C4×Q8—21no—
346C4×Q8—21no—
347C4×Q8—21no—
348C4×Q8C2311yescharacteristic
349C4×Q8C2311yescharacteristic
350C4×Q8C2311yescharacteristic
351C4×Q8C2311yescharacteristic
352C4×Q8C2311yescharacteristic
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
369#117—21no—
370#117—21no—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117—21no—
379#117C2311yescharacteristic
380#117C2311yescharacteristic
381#117C2311yescharacteristic
382#117C2311yescharacteristic
383#117C2311yescharacteristic
384#117C2311yescharacteristic
385#117C2311yescharacteristic
386#117C2311yescharacteristic
387#117C2311yescharacteristic
388C2×C4⋊C4—21no—
389C2×C4⋊C4C2311yescharacteristic
390C2×C4⋊C4C2311yescharacteristic
391C2×C4⋊C4C2311yescharacteristic
392C2×C4⋊C4C2311yescharacteristic
393C2×C4⋊C4C2311yescharacteristic
394C2×C4⋊C4C2311yescharacteristic
395C2×C4⋊C4C2311yescharacteristic
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C42—21no—
402#107C2311yescharacteristic
403#107C2311yescharacteristic
404#107C2311yescharacteristic
405#107C2311yescharacteristic
406#107C2311yescharacteristic
407#107C2311yescharacteristic
408#107C2311yescharacteristic
409#107C2311yescharacteristic
410#107C2311yescharacteristic
411#107C2311yescharacteristic
412#106C2311yescharacteristic
413#106C2311yescharacteristic
414#106C2311yescharacteristic
415#106C2311yescharacteristic
416#106C2311yescharacteristic
417#106C2311yescharacteristic
418#106C2311yescharacteristic
419#106C2311yescharacteristic
420#106C2311yescharacteristic
421#106C2311yescharacteristic
422#106C2311yescharacteristic
423#106C2311yescharacteristic
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#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
466C22⋊C8C2311yescharacteristic
467C22⋊C8C2311yescharacteristic
468C22⋊C8C2311yescharacteristic
469C22⋊C8C2311yescharacteristic
470C22⋊C8C2311yescharacteristic
471C22⋊C8C2311yescharacteristic
472C22⋊C8C2311yescharacteristic
473C22⋊C8C2311yescharacteristic
474#97C2311yescharacteristic
475#97C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478C24—21no—
479C24—21no—
480C24C2×D411yescharacteristic
481#41—41no—
482#41—41no—
483#41—41no—
484#41—41no—
485#41—41no—
486#41—41no—
487#41—82no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—41no—
493C2×Q8—41no—
494C2×Q8C2×D411yescharacteristic
495C2×Q8C2411yescharacteristic
496C2×Q8C2411yescharacteristic
497C2×Q8C2411yescharacteristic
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—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—41no—
514C2×D4—41no—
515C2×D4—41no—
516C2×D4—41no—
517C2×D4—82no—
518C2×D4—82no—
519C2×D4C2×D411yescharacteristic
520C2×D4C2×D411yescharacteristic
521C2×D4C2×D411yescharacteristic
522C2×D4C2×D411yescharacteristic
523C2×D4C2×D411yescharacteristic
524C2×D4C2×D411yescharacteristic
525C2×D4C2×D411yescharacteristic
526C2×D4C2411yescharacteristic
527C2×D4C2411yescharacteristic
528C2×D4C2411yescharacteristic
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—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4C2×D411yescharacteristic
545C22×C4C2×D411yescharacteristic
546C22×C4C2×D411yescharacteristic
547C22×C4C2411yescharacteristic
548C22×C4C2411yescharacteristic
549C22×C4C2411yescharacteristic
550C22×C4C2411yescharacteristic
551C22×C4C2411yescharacteristic
552Q16—41no—
553Q16—41no—
554SD16—41no—
555SD16—41no—
556SD16—41no—
557SD16—41no—
558SD16—41no—
559SD16—41no—
560M16—41no—
561M16—41no—
562C2×C8—41no—
563C2×C8—41no—
564C2×C8—41no—
565C2×C8—41no—
566C2×C8—41no—
567C2×C8—41no—
568C2×C8C2411yescharacteristic
569C2×C8C2411yescharacteristic
570C2×C8C2411yescharacteristic
571C2×C8C2411yescharacteristic
572C2×C8C2411yescharacteristic
573C2×C8C2411yescharacteristic
574C2×C8C2411yescharacteristic
575C2×C8C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
613C4⋊C4C2×D411yescharacteristic
614C4⋊C4C2411yescharacteristic
615C4⋊C4C2411yescharacteristic
616C4⋊C4C2411yescharacteristic
617C4⋊C4C2411yescharacteristic
618C4⋊C4C2411yescharacteristic
619C4⋊C4C2411yescharacteristic
620C4⋊C4C2411yescharacteristic
621C4⋊C4C2411yescharacteristic
622C4⋊C4C2411yescharacteristic
623C4⋊C4C2411yescharacteristic
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⋊C4—21no—
657C22⋊C4C2×D411yescharacteristic
658C22⋊C4C2×D411yescharacteristic
659C22⋊C4C2×D411yescharacteristic
660C22⋊C4C2×D411yescharacteristic
661C22⋊C4C2×D411yescharacteristic
662C22⋊C4C2×D411yescharacteristic
663C22⋊C4C2×D411yescharacteristic
664C22⋊C4C2×D411yescharacteristic
665C22⋊C4C2×D411yescharacteristic
666C22⋊C4C2×D411yescharacteristic
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—21no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42C2411yescharacteristic
681C42C2411yescharacteristic
682C23—22no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—41no—
687C23—41no—
688C23—42no—
689C23—81no—
690C23—81no—
691C23—81no—
692C23—81no—
693C23—81no—
694C23C22×D411yescharacteristic
695C23C22×D411yescharacteristic
696C23C22×D411yescharacteristic
697C23C22×D411yescharacteristic
698C23C22×D411yescharacteristic
699Q8—21no—
700Q8—21no—
701Q8—21no—
702Q8—21no—
703Q8—21no—
704Q8—21no—
705Q8—41no—
706Q8—42no—
707Q8—81no—
708Q8—81no—
709Q8—81no—
710D4—22no—
711D4—22no—
712D4—21no—
713D4—21no—
714D4—21no—
715D4—21no—
716D4—21no—
717D4—21no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—42no—
724D4—81no—
725D4—81no—
726D4—81no—
727D4—81no—
728D4—81no—
729D4—81no—
730D4—81no—
731D4—81no—
732D4—81no—
733D4—81no—
734D4—81no—
735D4—81no—
736D4—81no—
737D4—81no—
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—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—81no—
776C2×C4—81no—
777C2×C4C22×D411yescharacteristic
778C2×C4C22×D411yescharacteristic
779C2×C4C22×D411yescharacteristic
780C2×C4C22×D411yescharacteristic
781C2×C4C22×D411yescharacteristic
782C2×C4C22×D411yescharacteristic
783C2×C4C22×D411yescharacteristic
784C2×C4C22×D411yescharacteristic
785C2×C4C22×D411yescharacteristic
786C2×C4C2511yescharacteristic
787C8—21no—
788C8—21no—
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—21no—
794C8—21no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—82no—
819C22—162no—
820C22—162no—
821C22#57712yes—
822C22C23×D411yescharacteristic
823C4—21no—
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—41no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4#58511yescharacteristic
846C4#58511yescharacteristic
847C2—22no—
848C2—41no—
849C2—41no—
850C2—41no—
851C2—41no—
852C2—81no—
853C2—81no—
854C2—81no—
855C2#348511yescharacteristic
856C2C2×#57711yescharacteristic
857C2#358411yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
prime radical#3542C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #525 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #3495C2semidirect
3. #3350C2semidirect
4. #3348C2semidirect
5. #3344C2semidirect
6. #3343C2semidirect
7. #3340C2semidirect
8. #3337C2semidirect
9. #3336C2semidirect
10. #3335C2semidirect
11. #3317C2semidirect
12. #3314C2semidirect
13. #3311C2semidirect
14. #3310C2semidirect
15. #3304C2semidirect
16. #3296C2semidirect
17. #3296C2semidirect
18. #3295C2semidirect
19. #3244C2semidirect
20. #3241C2semidirect
21. #3201C2semidirect
22. #3200C2semidirect
23. #3190C2semidirect
24. #3187C2semidirect
25. #3126C2semidirect
26. #3121C2semidirect
27. #3099C2semidirect
28. #3096C2semidirect
29. #3091C2semidirect
30. C2×#482C2semidirect
31. #2977C2semidirect
34. #556C22semidirect
35. #556C22semidirect
38. #554C22semidirect
44. #552C22semidirect
45. #552C22semidirect
46. #552C22semidirect
56. #544C22semidirect
64. #536C22semidirect
72. C2×C22⋊Q8C22semidirect
74. #520C22semidirect
75. #519C22semidirect
76. C2×#117C22semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #499C22semidirect
80. #498C22semidirect
81. #490C22semidirect
82. #489C22semidirect
83. #488C22semidirect
84. #486C22semidirect
85. #485C22semidirect
86. #485C22semidirect
87. #485C22semidirect
88. #485C22semidirect
89. #485C22semidirect
90. #485C22semidirect
91. #485C22semidirect
92. #484C22semidirect
93. #484C22semidirect
94. #483C22semidirect
95. #483C22semidirect
96. #483C22semidirect
97. #483C22semidirect
98. #483C22semidirect
99. #483C22semidirect
104. #482C22semidirect
105. #482C22semidirect
106. #482C22semidirect
107. #482C22semidirect
108. #482C22semidirect
109. #482C22semidirect
110. #482C22semidirect
111. #482C22semidirect
112. #482C22semidirect
115. #481C22semidirect
116. #481C22semidirect
117. #481C22semidirect
119. #480C22semidirect
120. #480C22semidirect
121. #479C22semidirect
122. #479C22semidirect
123. #479C22semidirect
124. #478C22semidirect
125. #478C22semidirect
126. #478C22semidirect
127. #477C22semidirect
128. #476C22semidirect
129. #476C22semidirect
130. #475C22semidirect
131. #475C22semidirect
132. #474C22semidirect
133. #470C22semidirect
134. #468C22semidirect
135. #468C22semidirect
136. #468C22semidirect
137. #467C22semidirect
138. #467C22semidirect
139. #467C22semidirect
144. #465C22semidirect
145. #465C22semidirect
146. #465C22semidirect
147. #465C22semidirect
148. #465C22semidirect
149. #464C22semidirect
150. #464C22semidirect
151. #460C22semidirect
152. #460C22semidirect
153. #452C22semidirect
154. #452C22semidirect
155. #452C22semidirect
156. #452C22semidirect
157. #451C22semidirect
160. #450C22semidirect
161. #450C22semidirect
163. #448C22semidirect
164. #448C22semidirect
165. #441C22semidirect
166. #440C22semidirect
167. #440C22semidirect
168. #440C22semidirect
169. C4×Q16C22semidirect
170. C4×SD16C22semidirect
171. C4×SD16C22semidirect
172. C4×SD16C22semidirect
174. #435C22semidirect
175. #435C22semidirect
176. #435C22semidirect
178. C8×D4C22semidirect
179. C8×D4C22semidirect
180. C8×D4C22semidirect
181. #433C22semidirect
182. #433C22semidirect
183. #428C22semidirect
184. #428C22semidirect
185. #427C22semidirect
186. #427C22semidirect
187. #427C22semidirect
188. C2×#107C22semidirect
189. C2×#106C22semidirect
190. C2×#106C22semidirect
191. #418C22semidirect
192. #417C22semidirect
193. #416C22semidirect
194. #416C22semidirect
195. #416C22semidirect
198. C2×#102C22semidirect
199. #408C22semidirect
200. #408C22semidirect
201. C2×C22⋊C8C22semidirect
202. C2×C22⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
#35422
#34952
#33502
#33482
#33442
#33432
#33402
#33372
#33362
#33352
#33172
#33142
#33112
#33102
#33042
#32962
#32952
#32442
#32412
#32012
#32002
#31902
#31872
#31262
#31212
#30992
#30962
#30912
C2×#4822
#29772