Finite Group Databasebeta

← #61744

Subgroups — #61744

Order 256.

899 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3542C211yesmaximal, characteristic, complemented
2#3492C211yesmaximal, characteristic, complemented
3#3357C211yesmaximal, characteristic, complemented
4#3355C211yesmaximal, characteristic, complemented
5#3347C211yesmaximal, characteristic, complemented
6#3346C211yesmaximal, characteristic, complemented
7#3343C211yesmaximal, characteristic, complemented
8#3343C211yesmaximal, characteristic, complemented
9#3336C211yesmaximal, characteristic, complemented
10#3334C211yesmaximal, characteristic, complemented
11#3333C211yesmaximal, characteristic, complemented
12#3322C211yesmaximal, characteristic, complemented
13#3314C211yesmaximal, characteristic, complemented
14#3310C211yesmaximal, characteristic, complemented
15#3309C211yesmaximal, characteristic, complemented
16#3306C211yesmaximal, characteristic, complemented
17#3296C211yesmaximal, characteristic, complemented
18#3294C211yesmaximal, characteristic, complemented
19#3243C211yesmaximal, characteristic, complemented
20#3241C211yesmaximal, characteristic, complemented
21#3203C211yesmaximal, characteristic, complemented
22#3198C211yesmaximal, characteristic, complemented
23#3194C211yesmaximal, characteristic, complemented
24#3191C211yesmaximal, characteristic, complemented
25#3124C211yesmaximal, characteristic, complemented
26#3119C211yesmaximal, characteristic, complemented
27#3098C211yesmaximal, characteristic, complemented
28#3096C211yesmaximal, characteristic, complemented
29#3092C211yesmaximal, characteristic, complemented
30C2×#480C211yesmaximal, characteristic, complemented
31#2976C211yesmaximal, characteristic, complemented
32#562—21no—
33#560—21no—
34#555C2211yescharacteristic
35#554—21no—
36#554C2211yescharacteristic, complemented
37#554C2211yescharacteristic, complemented
38#553—21no—
39#553C2211yescharacteristic
40#553C2211yescharacteristic, complemented
41#553C2211yescharacteristic, complemented
42#552—21no—
43#552C2211yescharacteristic
44#552C2211yescharacteristic
45#552C2211yescharacteristic, complemented
46#551—21no—
47#550C2211yescharacteristic
48#547—21no—
49#547C2211yescharacteristic
50#547C2211yescharacteristic
51#547C2211yescharacteristic, complemented
52#546—21no—
53#546C2211yescharacteristic
54#546C2211yescharacteristic
55D42C2211yescharacteristic
56#544C2211yescharacteristic, complemented
57#542C2211yescharacteristic
58#540—21no—
59#540C2211yescharacteristic
60#539—21no—
61#539—21no—
62#538—21no—
63#537C2211yescharacteristic
64#537C2211yescharacteristic, complemented
65#535—21no—
66#535C2211yescharacteristic
67#534—21no—
68#525—21no—
69#525—21no—
70#525C2211yescharacteristic
71#525C2211yescharacteristic
72#525C2211yescharacteristic, complemented
73C2×#121C2211yescharacteristic
74#520C2211yescharacteristic, complemented
75#520C2211yescharacteristic, complemented
76C22×C4⋊C4C2211yescharacteristic, complemented
77#501C2211yescharacteristic, complemented
78#501C2211yescharacteristic, complemented
79#500C2211yescharacteristic, complemented
80#499C2211yescharacteristic, 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#484C2211yescharacteristic, complemented
90#484C2211yescharacteristic, 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#482C2211yescharacteristic, complemented
101#482C2211yescharacteristic, complemented
102#482C2211yescharacteristic, complemented
103#482C2211yescharacteristic, complemented
104#481C2211yescharacteristic, complemented
105#481C2211yescharacteristic, complemented
106#481C2211yescharacteristic, complemented
107#480C2211yescharacteristic
108#480C2211yescharacteristic
109#480C2211yescharacteristic
110#480C2211yescharacteristic
111#480C2211yescharacteristic
112#480C2211yescharacteristic
113#480C2211yescharacteristic, complemented
114#480C2211yescharacteristic, complemented
115#480C2211yescharacteristic, complemented
116#480C2211yescharacteristic, complemented
117#480C2211yescharacteristic, complemented
118#480C2211yescharacteristic, complemented
119#480C2211yescharacteristic, complemented
120#480C2211yescharacteristic, complemented
121#479C2211yescharacteristic, complemented
122#479C2211yescharacteristic, complemented
123#478C2211yescharacteristic, complemented
124#478C2211yescharacteristic, complemented
125#478C2211yescharacteristic, complemented
126#478C2211yescharacteristic, complemented
127#477C2211yescharacteristic, complemented
128#477C2211yescharacteristic, complemented
129#476C2211yescharacteristic, complemented
130#474C2211yescharacteristic, complemented
131#474C2211yescharacteristic, complemented
132#474C2211yescharacteristic, complemented
133#469C2211yescharacteristic
134#469C2211yescharacteristic, complemented
135#469C2211yescharacteristic, complemented
136#468C2211yescharacteristic
137#468C2211yescharacteristic, complemented
138#468C2211yescharacteristic, complemented
139#468C2211yescharacteristic, complemented
140#468C2211yescharacteristic, complemented
141#467C2211yescharacteristic, complemented
142#467C2211yescharacteristic, complemented
143#466C2211yescharacteristic
144#466C2211yescharacteristic, complemented
145#466C2211yescharacteristic, complemented
146#465C2211yescharacteristic
147#465C2211yescharacteristic, complemented
148#465C2211yescharacteristic, complemented
149#464C2211yescharacteristic, complemented
150#463C2211yescharacteristic, complemented
151#460C2211yescharacteristic, complemented
152#459C2211yescharacteristic, complemented
153#452C2211yescharacteristic, complemented
154#452C2211yescharacteristic, complemented
155#452C2211yescharacteristic, complemented
156#450C2211yescharacteristic
157#450C2211yescharacteristic, complemented
158#449C2211yescharacteristic
159#449C2211yescharacteristic, complemented
160#449C2211yescharacteristic, complemented
161#449C2211yescharacteristic, complemented
162#449C2211yescharacteristic, complemented
163#447C2211yescharacteristic
164#447C2211yescharacteristic, complemented
165#442C2211yescharacteristic, complemented
166#440C2211yescharacteristic, complemented
167#440C2211yescharacteristic, complemented
168#440C2211yescharacteristic, complemented
169C4×Q16C2211yescharacteristic, complemented
170C4×SD16C2211yescharacteristic, complemented
171C4×D8C2211yescharacteristic, complemented
172C4×D8C2211yescharacteristic, complemented
173#436C2211yescharacteristic, complemented
174#436C2211yescharacteristic, complemented
175#435C2211yescharacteristic
176#435C2211yescharacteristic, complemented
177#435C2211yescharacteristic, complemented
178#435C2211yescharacteristic, complemented
179C8×D4C2211yescharacteristic
180C8×D4C2211yescharacteristic, complemented
181#433C2211yescharacteristic, complemented
182#433C2211yescharacteristic, complemented
183#428C2211yescharacteristic, complemented
184#428C2211yescharacteristic, complemented
185#428C2211yescharacteristic, complemented
186#428C2211yescharacteristic, complemented
187#427C2211yescharacteristic, complemented
188C2×#107C2211yescharacteristic, complemented
189C2×#107C2211yescharacteristic, complemented
190C2×#107C2211yescharacteristic, complemented
191#418C2211yescharacteristic, complemented
192#417C2211yescharacteristic, complemented
193#417C2211yescharacteristic, complemented
194#417C2211yescharacteristic, complemented
195#416C2211yescharacteristic, complemented
196C2×#102C2211yescharacteristic
197C2×#102C2211yescharacteristic
198C2×#102C2211yescharacteristic, complemented
199#408C2211yescharacteristic, complemented
200#408C2211yescharacteristic, complemented
201#407C2211yescharacteristic, complemented
202C2×C22⋊C8C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41—21no—
205C2×#41—21no—
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C2×#41C2311yescharacteristic
209C2×#41C2311yescharacteristic
210C22×D4—21no—
211C22×D4—21no—
212C22×D4C2311yescharacteristic
213C22×D4C2311yescharacteristic
214C23×C4—21no—
215C23×C4C2311yescharacteristic
216C2×Q16C2311yescharacteristic
217C2×SD16C2311yescharacteristic
218C2×SD16C2311yescharacteristic
219C2×SD16C2311yescharacteristic
220C2×SD16C2311yescharacteristic
221C2×D8C2311yescharacteristic
222C2×D8C2311yescharacteristic
223C2×D8C2311yescharacteristic
224C2×M16C2311yescharacteristic
225C2×M16C2311yescharacteristic
226C2×M16C2311yescharacteristic
227C2×M16C2311yescharacteristic
228C22×C8C2311yescharacteristic
229C22×C8C2311yescharacteristic
230C22×C8C2311yescharacteristic
231C22×C8C2311yescharacteristic
232C4⋊Q8—21no—
233C4⋊Q8C2311yescharacteristic
234C4⋊Q8C2311yescharacteristic
235C4⋊Q8C2311yescharacteristic
236#127—21no—
237#127—21no—
238#127C2311yescharacteristic
239#126—21no—
240#126—21no—
241#126—21no—
242#126—21no—
243#126—21no—
244#126—21no—
245#126—21no—
246#125—21no—
247#125—21no—
248#125—21no—
249#125—21no—
250#125—21no—
251#125—21no—
252#125C2311yescharacteristic
253#125C2311yescharacteristic
254#125C2311yescharacteristic
255#124—21no—
256#124—21no—
257#124—21no—
258#124—21no—
259#124C2311yescharacteristic
260#123—21no—
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—
278#123—21no—
279#123D411yescharacteristic
280#123D411yescharacteristic
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⋊Q8D411yescharacteristic
294C22⋊Q8D411yescharacteristic
295C22⋊Q8C2311yescharacteristic
296C22⋊Q8C2311yescharacteristic
297C22⋊Q8C2311yescharacteristic
298C22⋊Q8C2311yescharacteristic
299C22⋊Q8C2311yescharacteristic
300C22⋊Q8C2311yescharacteristic
301C22⋊Q8C2311yescharacteristic
302#121—21no—
303#121—21no—
304#121—21no—
305#121—21no—
306#121—21no—
307#121—21no—
308#121—21no—
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#121D411yescharacteristic
322#121D411yescharacteristic
323#121C2311yescharacteristic
324#121C2311yescharacteristic
325#121C2311yescharacteristic
326#121C2311yescharacteristic
327#121C2311yescharacteristic
328#121C2311yescharacteristic
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—
340#120—21no—
341#120—21no—
342#120—21no—
343#120—21no—
344#120D411yescharacteristic
345#120D411yescharacteristic
346C4×Q8—21no—
347C4×Q8C2311yescharacteristic
348C4×Q8C2311yescharacteristic
349C4×Q8C2311yescharacteristic
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×D4—21no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4C2311yescharacteristic
366C4×D4C2311yescharacteristic
367C4×D4C2311yescharacteristic
368C4×D4C2311yescharacteristic
369C4×D4C2311yescharacteristic
370C4×D4C2311yescharacteristic
371C4×D4C2311yescharacteristic
372C4×D4C2311yescharacteristic
373C4×D4C2311yescharacteristic
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
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
397C2×C4⋊C4C2311yescharacteristic
398C2×C4⋊C4C2311yescharacteristic
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
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#107C2311yescharacteristic
415#107C2311yescharacteristic
416#107C2311yescharacteristic
417#107C2311yescharacteristic
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#102C2311yescharacteristic
441#102C2311yescharacteristic
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
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—41no—
488#41—41no—
489#41—82no—
490#41—82no—
491#41—82no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8C2×D411yescharacteristic
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—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—41no—
521C2×D4—41no—
522C2×D4—82no—
523C2×D4—82no—
524C2×D4C2×D411yescharacteristic
525C2×D4C2×D411yescharacteristic
526C2×D4C2×D411yescharacteristic
527C2×D4C2×D411yescharacteristic
528C2×D4C2×D411yescharacteristic
529C2×D4C2×D411yescharacteristic
530C2×D4C2×D411yescharacteristic
531C2×D4C2411yescharacteristic
532C2×D4C2411yescharacteristic
533C2×D4C2411yescharacteristic
534C2×D4C2411yescharacteristic
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—82no—
556C22×C4C2×D411yescharacteristic
557C22×C4C2×D411yescharacteristic
558C22×C4C2×D411yescharacteristic
559C22×C4C2411yescharacteristic
560C22×C4C2411yescharacteristic
561C22×C4C2411yescharacteristic
562C22×C4C2411yescharacteristic
563C22×C4C2411yescharacteristic
564Q16—41no—
565SD16—41no—
566SD16—41no—
567SD16—41no—
568SD16—41no—
569D8—41no—
570D8—41no—
571D8—41no—
572M16—41no—
573M16—41no—
574M16—41no—
575M16—41no—
576C2×C8—41no—
577C2×C8—41no—
578C2×C8—41no—
579C2×C8—41no—
580C2×C8C2411yescharacteristic
581C2×C8C2411yescharacteristic
582C2×C8C2411yescharacteristic
583C2×C8C2411yescharacteristic
584C2×C8C2411yescharacteristic
585C2×C8C2411yescharacteristic
586C2×C8C2411yescharacteristic
587C2×C8C2411yescharacteristic
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⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4C2×D411yescharacteristic
618C4⋊C4C2×D411yescharacteristic
619C4⋊C4C2×D411yescharacteristic
620C4⋊C4C2×D411yescharacteristic
621C4⋊C4C2×D411yescharacteristic
622C4⋊C4C2×D411yescharacteristic
623C4⋊C4C2411yescharacteristic
624C4⋊C4C2411yescharacteristic
625C4⋊C4C2411yescharacteristic
626C4⋊C4C2411yescharacteristic
627C4⋊C4C2411yescharacteristic
628C4⋊C4C2411yescharacteristic
629C4⋊C4C2411yescharacteristic
630C4⋊C4C2411yescharacteristic
631C4⋊C4C2411yescharacteristic
632C4⋊C4C2411yescharacteristic
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⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4C2×D411yescharacteristic
666C22⋊C4C2×D411yescharacteristic
667C22⋊C4C2×D411yescharacteristic
668C22⋊C4C2×D411yescharacteristic
669C22⋊C4C2×D411yescharacteristic
670C22⋊C4C2×D411yescharacteristic
671C22⋊C4C2×D411yescharacteristic
672C22⋊C4C2×D411yescharacteristic
673C22⋊C4C2×D411yescharacteristic
674C22⋊C4C2×D411yescharacteristic
675C42—21no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42C2411yescharacteristic
684C42C2411yescharacteristic
685C23—22no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—41no—
691C23—41no—
692C23—42no—
693C23—81no—
694C23—81no—
695C23—81no—
696C23—81no—
697C23—81no—
698C23C22×D411yescharacteristic
699C23C22×D411yescharacteristic
700C23C22×D411yescharacteristic
701C23C22×D411yescharacteristic
702C23C22×D411yescharacteristic
703Q8—21no—
704Q8—21no—
705Q8—21no—
706Q8—21no—
707Q8—41no—
708Q8—81no—
709Q8—81no—
710Q8—81no—
711D4—22no—
712D4—22no—
713D4—21no—
714D4—21no—
715D4—21no—
716D4—21no—
717D4—21no—
718D4—21no—
719D4—21no—
720D4—21no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—42no—
727D4—42no—
728D4—42no—
729D4—42no—
730D4—81no—
731D4—81no—
732D4—81no—
733D4—81no—
734D4—81no—
735D4—81no—
736D4—81no—
737D4—81no—
738D4—81no—
739D4—81no—
740D4—81no—
741D4—81no—
742D4—81no—
743D4—81no—
744D4—81no—
745D4—81no—
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—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—81no—
776C2×C4—81no—
777C2×C4—81no—
778C2×C4—81no—
779C2×C4—81no—
780C2×C4—81no—
781C2×C4—81no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—81no—
786C2×C4—81no—
787C2×C4—81no—
788C2×C4—81no—
789C2×C4C22×D411yescharacteristic
790C2×C4C22×D411yescharacteristic
791C2×C4C22×D411yescharacteristic
792C2×C4C22×D411yescharacteristic
793C2×C4C22×D411yescharacteristic
794C2×C4C22×D411yescharacteristic
795C2×C4C22×D411yescharacteristic
796C2×C4C22×D411yescharacteristic
797C2×C4C22×D411yescharacteristic
798C2×C4C2511yescharacteristic
799C8—21no—
800C8—21no—
801C8—21no—
802C8—21no—
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—44no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—162no—
835C22—162no—
836C22#57612yes—
837C22C23×D411yescharacteristic
838C4—21no—
839C4—21no—
840C4—21no—
841C4—21no—
842C4—21no—
843C4—21no—
844C4—21no—
845C4—21no—
846C4—21no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—41no—
852C4—41no—
853C4—41no—
854C4—41no—
855C4—41no—
856C4—41no—
857C4—41no—
858C4—41no—
859C4#58511yescharacteristic
860C4#58511yescharacteristic
861C2—22no—
862C2—41no—
863C2—41no—
864C2—41no—
865C2—41no—
866C2—81no—
867C2—81no—
868C2—81no—
869C2—81no—
870C2#348511yescharacteristic
871C2C2×#57611yescharacteristic
872C2#358611yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
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
1. #3542C2semidirect
2. #3492C2semidirect
3. #3357C2semidirect
4. #3355C2semidirect
5. #3347C2semidirect
6. #3346C2semidirect
7. #3343C2semidirect
8. #3343C2semidirect
9. #3336C2semidirect
10. #3334C2semidirect
11. #3333C2semidirect
12. #3322C2semidirect
13. #3314C2semidirect
14. #3310C2semidirect
15. #3309C2semidirect
16. #3306C2semidirect
17. #3296C2semidirect
18. #3294C2semidirect
19. #3243C2semidirect
20. #3241C2semidirect
21. #3203C2semidirect
22. #3198C2semidirect
23. #3194C2semidirect
24. #3191C2semidirect
25. #3124C2semidirect
26. #3119C2semidirect
27. #3098C2semidirect
28. #3096C2semidirect
29. #3092C2semidirect
30. C2×#480C2semidirect
31. #2976C2semidirect
36. #554C22semidirect
37. #554C22semidirect
40. #553C22semidirect
41. #553C22semidirect
45. #552C22semidirect
51. #547C22semidirect
56. #544C22semidirect
64. #537C22semidirect
72. #525C22semidirect
74. #520C22semidirect
75. #520C22semidirect
76. C22×C4⋊C4C22semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #500C22semidirect
80. #499C22semidirect
81. #490C22semidirect
82. #489C22semidirect
83. #488C22semidirect
84. #486C22semidirect
85. #485C22semidirect
86. #485C22semidirect
87. #485C22semidirect
88. #485C22semidirect
89. #484C22semidirect
90. #484C22semidirect
91. #484C22semidirect
92. #484C22semidirect
93. #483C22semidirect
94. #483C22semidirect
95. #483C22semidirect
97. #482C22semidirect
98. #482C22semidirect
99. #482C22semidirect
100. #482C22semidirect
101. #482C22semidirect
102. #482C22semidirect
103. #482C22semidirect
104. #481C22semidirect
105. #481C22semidirect
106. #481C22semidirect
113. #480C22semidirect
114. #480C22semidirect
115. #480C22semidirect
116. #480C22semidirect
117. #480C22semidirect
118. #480C22semidirect
119. #480C22semidirect
120. #480C22semidirect
121. #479C22semidirect
122. #479C22semidirect
123. #478C22semidirect
124. #478C22semidirect
125. #478C22semidirect
126. #478C22semidirect
127. #477C22semidirect
128. #477C22semidirect
129. #476C22semidirect
130. #474C22semidirect
131. #474C22semidirect
132. #474C22semidirect
134. #469C22semidirect
135. #469C22semidirect
137. #468C22semidirect
138. #468C22semidirect
139. #468C22semidirect
140. #468C22semidirect
141. #467C22semidirect
142. #467C22semidirect
144. #466C22semidirect
145. #466C22semidirect
147. #465C22semidirect
148. #465C22semidirect
149. #464C22semidirect
150. #463C22semidirect
151. #460C22semidirect
152. #459C22semidirect
153. #452C22semidirect
154. #452C22semidirect
155. #452C22semidirect
157. #450C22semidirect
159. #449C22semidirect
160. #449C22semidirect
161. #449C22semidirect
162. #449C22semidirect
164. #447C22semidirect
165. #442C22semidirect
166. #440C22semidirect
167. #440C22semidirect
168. #440C22semidirect
169. C4×Q16C22semidirect
170. C4×SD16C22semidirect
171. C4×D8C22semidirect
172. C4×D8C22semidirect
173. #436C22semidirect
174. #436C22semidirect
176. #435C22semidirect
177. #435C22semidirect
178. #435C22semidirect
180. C8×D4C22semidirect
181. #433C22semidirect
182. #433C22semidirect
183. #428C22semidirect
184. #428C22semidirect
185. #428C22semidirect
186. #428C22semidirect
187. #427C22semidirect
188. C2×#107C22semidirect
189. C2×#107C22semidirect
190. C2×#107C22semidirect
191. #418C22semidirect
192. #417C22semidirect
193. #417C22semidirect
194. #417C22semidirect
195. #416C22semidirect
198. C2×#102C22semidirect
199. #408C22semidirect
200. #408C22semidirect
201. #407C22semidirect
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
#34922
#33572
#33552
#33472
#33462
#33432
#33362
#33342
#33332
#33222
#33142
#33102
#33092
#33062
#32962
#32942
#32432
#32412
#32032
#31982
#31942
#31912
#31242
#31192
#30982
#30962
#30922
C2×#4802
#29762