Finite Group Databasebeta

← #7710069

Subgroups — #7710069

Order 512.

5274 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59644C214yesmaximal, complemented
2#59639C212yesmaximal, complemented
3#59410C212yesmaximal, complemented
4#46024C214yesmaximal, complemented
5#46023C212yesmaximal, complemented
6#46016C212yesmaximal, complemented
7#39830C214yesmaximal, complemented
8#39783C214yesmaximal, complemented
9#39632C212yesmaximal, complemented
10#39555C214yesmaximal, complemented
11#39505C212yesmaximal, complemented
12#39503C212yesmaximal, complemented
13#39488C212yesmaximal, complemented
14#37895C214yesmaximal, complemented
15#37546C212yesmaximal, complemented
16#36765C214yesmaximal, complemented
17#36645C211yesmaximal, characteristic, complemented
18#36631C211yesmaximal, characteristic, complemented
19#36579C212yesmaximal, complemented
20#36148C214yesmaximal, complemented
21#36100C212yesmaximal, complemented
22#35032C212yesmaximal, complemented
23#35014C212yesmaximal, complemented
24#34382C212yesmaximal, complemented
25C2×C4×#124C211yesmaximal, characteristic, complemented
26C2×#556C2212yescomplemented
27C2×#547C2212yes—
28C2×#533C2212yes—
29C2×#529C2212yes—
30C22×#124C2211yescharacteristic
31C2×#525C2214yes—
32C22×C4×Q8C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34#2868C2211yescharacteristic, complemented
35#2868C2211yescharacteristic, complemented
36#2862C2212yescomplemented
37#2861C2212yescomplemented
38#2860C2212yescomplemented
39#2860C2212yescomplemented
40#2859C2211yescharacteristic, complemented
41#2859C2212yescomplemented
42#2859C2212yescomplemented
43#2858C2211yescharacteristic, complemented
44#2857C2212yes—
45#2857C2211yescharacteristic
46#2857C2212yes—
47#2857C2212yes—
48#2857C2212yes—
49#2856C2211yescharacteristic
50#2854C2212yes—
51#2854C2212yes—
52#2850C2212yes—
53#2850C2214yes—
54#2848C2214yes—
55#2820C2214yes—
56#2819C2214yes—
57#2808C2214yes—
58#2806C2214yescomplemented
59#2804C2214yescomplemented
60#2803C2218yes—
61#2800C2218yescomplemented
62#2798C2218yescomplemented
63#2795C2218yescomplemented
64#2788C2218yescomplemented
65#2779C2218yescomplemented
66#2772C2218yescomplemented
67#2754C2218yescomplemented
68#2753C2218yescomplemented
69#2733C2214yes—
70#2731C2218yescomplemented
71#2718C2218yescomplemented
72#2718C2218yescomplemented
73#2712C2218yescomplemented
74#2705C2218yescomplemented
75#2662C2218yes—
76#2646C2214yes—
77#2626C2214yes—
78#2620C2214yes—
79#2620C2214yes—
80#2617C2214yes—
81#2617C2214yes—
82#2602C2218yescomplemented
83#2602C2218yescomplemented
84#2596C2218yescomplemented
85#2595C2218yescomplemented
86#2593C2218yescomplemented
87#2592C2214yes—
88#2592C2214yescomplemented
89#2589C2218yescomplemented
90#2587C2218yescomplemented
91#2581C2214yescomplemented
92#2568C2212yescomplemented
93#2558C2218yescomplemented
94#2554C2218yescomplemented
95#2542C2212yes—
96#2540C2214yes—
97#2538C2212yescomplemented
98#2537C2212yes—
99#2513C2214yes—
100#2511C2214yescomplemented
101#2502C2214yescomplemented
102#2500C2214yes—
103#2500C2214yescomplemented
104#2499C2214yescomplemented
105#2497C2214yescomplemented
106#2492C2214yescomplemented
107#2492C2214yescomplemented
108#2491C2214yes—
109#2491C2214yescomplemented
110#2481C2218yes—
111#2472C2218yes—
112#2469C2218yescomplemented
113#2460C2218yescomplemented
114#2458C2218yescomplemented
115#2455C2218yes—
116#2450C2218yes—
117#2439C2214yescomplemented
118#2432C2214yescomplemented
119#2432C2214yescomplemented
120#2431C2214yescomplemented
121#2429C2214yescomplemented
122#2429C2214yescomplemented
123#2426C2214yescomplemented
124#2423C2214yescomplemented
125#2422C2214yes—
126#2421C2214yescomplemented
127#2421C2214yescomplemented
128#2418C2218yes—
129#2417C2214yescomplemented
130#2415C2214yes—
131#2414C2214yes—
132#2411C2218yes—
133#2409C2214yes—
134#2408C2214yes—
135#2407C2214yes—
136#2382C2214yescomplemented
137#2379C2214yescomplemented
138#2367C2218yescomplemented
139#2362C2214yescomplemented
140#2362C2214yescomplemented
141#2361C2214yes—
142#2359C2218yes—
143#2355C2214yescomplemented
144#2355C2212yescomplemented
145#2354C2212yes—
146#2352C2214yes—
147#2352C2214yescomplemented
148D4×C4⋊C4C2214yes—
149#2341C2214yescomplemented
150#2334C2218yescomplemented
151#2329C2214yes—
152#2325C2214yes—
153#2325C2214yes—
154#2317C2214yescomplemented
155#2314C2214yescomplemented
156#2312C2214yes—
157C4×C4⋊Q8C2212yescomplemented
158C4×C4⋊Q8C2211yescharacteristic, complemented
159C4×C4⋊Q8C2212yescomplemented
160C4×C4⋊Q8C2212yescomplemented
161C4×C4⋊Q8C2212yescomplemented
162C4×#127C2211yescharacteristic, complemented
163C4×#124C2212yes—
164C4×#124C2212yes—
165C4×#124C2212yes—
166C4×#124C2212yes—
167C4×#124C2212yes—
168C4×#124C2212yes—
169C4×#124C2212yes—
170C4×#124C2212yes—
171C4×#124C2212yescomplemented
172C4×C22⋊Q8C2214yes—
173C4×#121C2212yes—
174C4×#121C2212yes—
175C2×#391C2211yescharacteristic
176#2293C2212yescomplemented
177#2293C2212yescomplemented
178C2×#390C2211yescharacteristic
179C2×#388C2212yes—
180C2×#388C2212yes—
181#2285C2212yes—
182#2285C2212yes—
183C2×#382C2211yescharacteristic
184C2×C4×C22⋊C4C2212yes—
185C2×C4×C22⋊C4C2212yes—
186C2×C43C2211yescharacteristic
187C22×#41C2314yes—
188C23×Q8C2311yescharacteristic
189C23×D4C2311yescharacteristic
190C24×C4C2312yes—
191#556—48no—
192#547—48no—
193#533—48no—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2311yescharacteristic
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2312yes—
201C2×#127C2311yescharacteristic
202#529—216no—
203C2×#126C2314yes—
204C2×#126C2318yes—
205C2×#125C2312yes—
206C2×#125C2314yes—
207C2×#124—28no—
208C2×#124C2312yes—
209C2×#124C2312yes—
210C2×#124C2312yes—
211C2×#124C2312yes—
212C2×#124C2312yes—
213C2×#124C2314yes—
214C2×#124C2312yes—
215C2×#124C2318yes—
216#525—416no—
217C2×#123C2314yes—
218C2×#123C2318yes—
219C2×#123C2318yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×#121C2312yes—
229C2×#121C2312yes—
230C2×#121C2312yes—
231C2×#121C2314yes—
232C2×#121C2314yes—
233C2×#121C2314yes—
234C2×#120C2318yes—
235C2×C4×Q8—44no—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2312yes—
244C2×C4×D4—44no—
245C2×C4×D4C2312yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C2312yes—
250C2×C4×D4C2318yes—
251C2×C4×D4C2318yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2312yes—
255C2×#117C2314yes—
256C2×#117C2314yes—
257C2×#117C2314yes—
258C2×#117C2314yes—
259C22×C4⋊C4C2314yes—
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2312yes—
263C22×C22⋊C4C2312yes—
264C22×C22⋊C4C2312yes—
265C22×C22⋊C4C2312yes—
266C22×C22⋊C4C2312yes—
267C22×C22⋊C4C2312yes—
268C22×C42C2311yescharacteristic
269C22×C42C2311yescharacteristic
270C22×C42C2311yescharacteristic
271C22×C42C2311yescharacteristic
272C22×C42C2312yes—
273C22×C42C2311yescharacteristic
274C22×C42C2311yescharacteristic
275C22×C42C2311yescharacteristic
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#399C2318yes—
282#399C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#397C2318yes—
287#397C2318yes—
288#397C2318yes—
289#397C2318yes—
290#397C2318yes—
291#396C2318yes—
292#396C2318yes—
293#396C2318yes—
294#396C2318yes—
295#396C2318yes—
296#396C2318yes—
297#395C2318yes—
298#394C2318yes—
299#394C2318yes—
300#394C2318yes—
301#394C2318yes—
302#394C2318yes—
303#394C2318yes—
304#394C2318yes—
305#394C2318yes—
306#394C2318yes—
307#394C2318yes—
308#394C2318yes—
309#393C2318yes—
310#393C2318yes—
311#393C2318yes—
312#393C2318yes—
313#392C2318yes—
314#392C2318yes—
315#392C2318yes—
316#391C2314yes—
317#391C2312yes—
318#391C2314yes—
319#391C2314yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2318yes—
325#391C2312yes—
326#391C2314yes—
327#391C2318yes—
328#391C2312yes—
329#391C2312yes—
330#391C2312yes—
331#391C2312yes—
332#390C2312yes—
333#390C2312yes—
334#390C2312yes—
335#390C2314yes—
336#390C2314yes—
337#390C2312yes—
338#390C2314yes—
339#390C2318yes—
340#390C2318yes—
341#390C2318yes—
342#390C2312yes—
343#390C2312yes—
344#390C2312yes—
345#390C2312yes—
346#390C2312yes—
347#390C2312yes—
348#390C2312yes—
349#390C2312yes—
350#390C2312yes—
351#390C2312yes—
352#389C2314yes—
353#389C2314yes—
354#389C2312yes—
355#389C2312yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2318yes—
363#389C2318yes—
364#389C2312yes—
365#389C2314yes—
366#389C2312yes—
367#389C2318yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2314yes—
385#388C2314yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2314yes—
390#388C2314yes—
391#388C2314yes—
392#388C2318yes—
393#388C2314yes—
394#388C2314yes—
395#388C2314yes—
396#388C2314yes—
397#388C2314yes—
398#388C2318yes—
399#388C2318yes—
400#388C2314yes—
401#388C2314yes—
402#388C2314yes—
403#388C2314yes—
404#388C2314yes—
405#388C2314yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#386C2318yes—
418#386C2318yes—
419#386C2318yes—
420#386C2318yes—
421#386C2314yes—
422#386C2314yes—
423#386C2318yes—
424#385C2318yes—
425#385C2318yes—
426#385C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2318yes—
432#385C2318yes—
433#384C2311yescharacteristic
434#384C2311yescharacteristic
435#384C2312yes—
436#384C2312yes—
437#384C2312yes—
438#384C2312yes—
439#384C2312yes—
440#384C2312yes—
441#384C2314yes—
442#384C2312yes—
443#384C2312yes—
444#382C2314yes—
445#382C2314yes—
446#382C2312yes—
447#382C2314yes—
448#382C2312yes—
449#382C2312yes—
450#382C2314yes—
451#382C2312yes—
452#382C2312yes—
453#380C2312yes—
454#380C2314yes—
455#380C2314yes—
456#380C2314yes—
457#380C2314yes—
458#380C2312yes—
459#380C2314yes—
460#380C2314yes—
461#380C2318yes—
462#380C2314yes—
463#380C2314yes—
464#379C2318yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2318yes—
474C4×C4⋊C4C2318yes—
475C4×C4⋊C4C2314yes—
476C4×C22⋊C4C2318yes—
477C4×C22⋊C4C2314yes—
478C4×C22⋊C4C2314yes—
479C4×C22⋊C4C2318yes—
480C4×C22⋊C4C2314yes—
481C4×C22⋊C4C2314yes—
482C4×C22⋊C4C2314yes—
483C4×C22⋊C4C2314yes—
484C4×C22⋊C4C2314yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2314yes—
488C2×#95C2312yes—
489C2×#95C2312yes—
490C2×#95C2312yes—
491C2×#95C2312yes—
492C43C2311yescharacteristic
493C43C2311yescharacteristic
494C43C2311yescharacteristic
495C43C2311yescharacteristic
496C43C2311yescharacteristic
497C43C2311yescharacteristic
498C43C2311yescharacteristic
499C43C2311yescharacteristic
500C25C2412yes—
501C2×#41—48no—
502C2×#41—48no—
503C2×#41—48no—
504C22×Q8—24no—
505C22×Q8—42no—
506C22×Q8—42no—
507C22×Q8C2412yes—
508C22×Q8C2414yes—
509C22×Q8C2412yes—
510C22×Q8C2414yes—
511C22×Q8C2412yes—
512C22×D4—24no—
513C22×D4—42no—
514C22×D4—42no—
515C22×D4C2414yes—
516C22×D4C2412yes—
517C22×D4C2412yes—
518C22×D4C2412yes—
519C22×D4C2412yes—
520C22×D4C2412yes—
521C22×D4C2418yes—
522C22×D4C2418yes—
523C23×C4—28no—
524C23×C4—44no—
525C23×C4—44no—
526C23×C4C2414yes—
527C23×C4C2414yes—
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C23×C4C2412yes—
534C23×C4C2412yes—
535C23×C4C2412yes—
536C23×C4C2414yes—
537C23×C4C2418yes—
538C23×C4C2411yescharacteristic
539C23×C4C2411yescharacteristic
540C4⋊Q8—28no—
541C4⋊Q8—42no—
542C4⋊Q8—44no—
543C4⋊Q8—44no—
544C4⋊Q8—44no—
545C4⋊Q8—44no—
546C4⋊Q8—44no—
547#127—42no—
548#126—216no—
549#126—416no—
550#125—28no—
551#125—48no—
552#124—28no—
553#124—28no—
554#124—28no—
555#124—28no—
556#124—28no—
557#124—44no—
558#124—48no—
559#124—416no—
560#123—216no—
561#123—416no—
562#123—416no—
563C22⋊Q8—28no—
564C22⋊Q8—216no—
565C22⋊Q8—48no—
566C22⋊Q8—48no—
567C22⋊Q8—48no—
568C22⋊Q8—48no—
569C22⋊Q8—48no—
570C22⋊Q8—48no—
571#121—28no—
572#121—28no—
573#121—28no—
574#121—48no—
575#121—48no—
576#121—48no—
577#120—416no—
578C4×Q8—28no—
579C4×Q8—28no—
580C4×Q8—44no—
581C4×Q8—44no—
582C4×Q8—48no—
583C4×Q8—44no—
584C4×Q8—48no—
585C4×Q8—48no—
586C4×D4—216no—
587C4×D4—28no—
588C4×D4—28no—
589C4×D4—28no—
590C4×D4—44no—
591C4×D4—44no—
592C4×D4—44no—
593C4×D4—44no—
594C4×D4—416no—
595C4×D4—416no—
596#117—216no—
597#117—48no—
598#117—48no—
599#117—48no—
600C2×C4⋊C4—42no—
601C2×C4⋊C4—42no—
602C2×C4⋊C4—44no—
603C2×C4⋊C4—48no—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2412yes—
641C2×C22⋊C4—28no—
642C2×C22⋊C4—28no—
643C2×C22⋊C4—28no—
644C2×C22⋊C4—44no—
645C2×C22⋊C4—44no—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2418yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2418yes—
679C2×C42—24no—
680C2×C42—24no—
681C2×C42—24no—
682C2×C42—44no—
683C2×C42—42no—
684C2×C42—42no—
685C2×C42—42no—
686C2×C42#4118yescomplemented
687C2×C42C2414yes—
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2414yes—
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2418yes—
707C2×C42C2418yes—
708C2×C42C2418yes—
709C2×C42C2414yes—
710C2×C42C2418yes—
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2418yes—
732#95C2418yes—
733#95C2414yes—
734#95C2418yes—
735#95C2414yes—
736#95C2414yes—
737#95C2418yes—
738#95C2418yes—
739#95C2418yes—
740#95C2418yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2414yes—
747#95C2414yes—
748#95C2418yes—
749#95C2418yes—
750C24—24no—
751C24—24no—
752C24—24no—
753C24—42no—
754C24—42no—
755C24—42no—
756C24—42no—
757C24C2514yes—
758C24C2514yes—
759C24C2511yescharacteristic
760#41—832no—
761C2×Q8—24no—
762C2×Q8—24no—
763C2×Q8—24no—
764C2×Q8—24no—
765C2×Q8—28no—
766C2×Q8—28no—
767C2×Q8—24no—
768C2×Q8—28no—
769C2×Q8—28no—
770C2×Q8—42no—
771C2×Q8—42no—
772C2×Q8—44no—
773C2×Q8—42no—
774C2×Q8—42no—
775C2×Q8—44no—
776C2×Q8—416no—
777C2×D4—28no—
778C2×D4—28no—
779C2×D4—28no—
780C2×D4—24no—
781C2×D4—24no—
782C2×D4—24no—
783C2×D4—24no—
784C2×D4—24no—
785C2×D4—24no—
786C2×D4—24no—
787C2×D4—24no—
788C2×D4—24no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—416no—
792C2×D4—48no—
793C2×D4—42no—
794C2×D4—48no—
795C2×D4—48no—
796C2×D4—48no—
797C2×D4—42no—
798C2×D4—48no—
799C2×D4—42no—
800C2×D4—42no—
801C2×D4—48no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—24no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—28no—
814C22×C4—22no—
815C22×C4—28no—
816C22×C4—28no—
817C22×C4—28no—
818C22×C4—22no—
819C22×C4—28no—
820C22×C4—28no—
821C22×C4—28no—
822C22×C4—42no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—41no—
826C22×C4—41no—
827C22×C4—41no—
828C22×C4—41no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—48no—
834C22×C4—44no—
835C22×C4—48no—
836C22×C4—44no—
837C22×C4—42no—
838C22×C4—48no—
839C22×C4—816no—
840C22×C4C2×#4114yes—
841C22×C4C2×#4114yes—
842C22×C4C2×#4114yes—
843C22×C4H(5,𝔽2)14yes—
844C22×C42−1+414yes—
845C22×C4C2511yescharacteristic
846C22×C4C2514yes—
847C22×C4C2514yes—
848C22×C4C2514yes—
849C22×C4C2514yes—
850C22×C4C2514yes—
851C22×C4C2518yes—
852C22×C4C2511yescharacteristic
853C22×C4C2514yes—
854C22×C4C2518yes—
855C22×C4C2511yescharacteristic
856C22×C4C2511yescharacteristic
857C22×C4C2511yescharacteristic
858C22×C4C2511yescharacteristic
859C22×C4C2511yescharacteristic
860C22×C4C2511yescharacteristic
861C22×C4C2511yescharacteristic
862C22×C4C2511yescharacteristic
863C22×C4C2511yescharacteristic
864C22×C4C2511yescharacteristic
865C22×C4C2511yescharacteristic
866C22×C4C2511yescharacteristic
867C4⋊C4—28no—
868C4⋊C4—28no—
869C4⋊C4—24no—
870C4⋊C4—28no—
871C4⋊C4—24no—
872C4⋊C4—28no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—24no—
878C4⋊C4—28no—
879C4⋊C4—24no—
880C4⋊C4—216no—
881C4⋊C4—28no—
882C4⋊C4—24no—
883C4⋊C4—28no—
884C4⋊C4—24no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—44no—
888C4⋊C4—48no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—42no—
892C4⋊C4—48no—
893C4⋊C4—48no—
894C4⋊C4—48no—
895C4⋊C4—44no—
896C4⋊C4—48no—
897C4⋊C4—48no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—42no—
904C22⋊C4—28no—
905C22⋊C4—216no—
906C22⋊C4—28no—
907C22⋊C4—28no—
908C22⋊C4—28no—
909C22⋊C4—28no—
910C22⋊C4—28no—
911C22⋊C4—28no—
912C22⋊C4—28no—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—28no—
918C22⋊C4—28no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—28no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—44no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4—48no—
931C22⋊C4—48no—
932C22⋊C4—48no—
933C22⋊C4—48no—
934C22⋊C4—44no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C42—28no—
938C42—22no—
939C42—22no—
940C42—22no—
941C42—22no—
942C42—22no—
943C42—22no—
944C42—22no—
945C42—28no—
946C42—22no—
947C42—22no—
948C42—22no—
949C42—22no—
950C42—22no—
951C42—22no—
952C42—22no—
953C42—22no—
954C42—22no—
955C42—22no—
956C42—41no—
957C42—41no—
958C42—41no—
959C42—41no—
960C42—41no—
961C42—41no—
962C42—44no—
963C42—48no—
964C42—48no—
965C42—48no—
966C42—48no—
967C42C2×#4114yes—
968C42C2×#4114yes—
969C42C2×#4114yes—
970C42C2×#4114yes—
971C42H(5,𝔽2)14yes—
972C23—21no—
973C23—21no—
974C23—21no—
975C23—21no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—48no—
991C23—48no—
992C23—48no—
993C23—84no—
994C23—84no—
995C23—84no—
996C23—84no—
997C23C22×#4112yes—
998C23C2×H(5,𝔽2)12yes—
999C23C2×2−1+412yes—
1000C23C2611yescharacteristic
1001Q8—48no—
1002Q8—48no—
1003Q8—416no—
1004Q8—88no—
1005Q8—84no—
1006D4—48no—
1007D4—416no—
1008D4—48no—
1009D4—48no—
1010D4—84no—
1011D4—84no—
1012D4—816no—
1013D4—816no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—28no—
1035C2×C4—28no—
1036C2×C4—28no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—28no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—28no—
1050C2×C4—28no—
1051C2×C4—24no—
1052C2×C4—21no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—21no—
1060C2×C4—28no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—28no—
1064C2×C4—24no—
1065C2×C4—28no—
1066C2×C4—24no—
1067C2×C4—44no—
1068C2×C4—44no—
1069C2×C4—44no—
1070C2×C4—44no—
1071C2×C4—48no—
1072C2×C4—416no—
1073C2×C4—416no—
1074C2×C4—88no—
1075C2×C4—84no—
1076C2×C4—84no—
1077C2×C4—816no—
1078C2×C4C22×#4112yes—
1079C2×C4C22×#4112yes—
1080C2×C4C22×#4112yes—
1081C2×C4C22×#4112yes—
1082C2×C4C22×#4112yes—
1083C2×C4C22×#4112yes—
1084C2×C4C2×H(5,𝔽2)12yes—
1085C2×C4C2×H(5,𝔽2)12yes—
1086C2×C4C2×H(5,𝔽2)12yes—
1087C2×C4C2×H(5,𝔽2)12yes—
1088C2×C4C2×H(5,𝔽2)12yes—
1089C2×C4C2×2−1+412yes—
1090C2×C4C2×2−1+412yes—
1091C2×C4#58512yes—
1092C2×C4#58512yes—
1093C2×C4#58512yes—
1094C22—22no—
1095C22—22no—
1096C22—22no—
1097C22—22no—
1098C22—22no—
1099C22—22no—
1100C22—44no—
1101C22—44no—
1102C22—44no—
1103C22—44no—
1104C22—44no—
1105C22—44no—
1106C22—44no—
1107C22—44no—
1108C22—44no—
1109C22—44no—
1110C22—44no—
1111C22—44no—
1112C22—44no—
1113C22—44no—
1114C22—816no—
1115C22#351114yes—
1116C22C23×#4111yescharacteristic
1117C22C22×H(5,𝔽2)11yescharacteristic
1118C22C22×H(5,𝔽2)11yescharacteristic
1119C22C22×2−1+411yescharacteristic
1120C22C2×#58511yescharacteristic
1121C22C2×#58511yescharacteristic
1122C22C2×#58511yescharacteristic
1123C4—22no—
1124C4—22no—
1125C4—22no—
1126C4—22no—
1127C4—22no—
1128C4—22no—
1129C4—22no—
1130C4—22no—
1131C4—22no—
1132C4—22no—
1133C4—44no—
1134C4—48no—
1135C4—41no—
1136C4—48no—
1137C4—44no—
1138C4—44no—
1139C4—44no—
1140C4—44no—
1141C4—41no—
1142C4—44no—
1143C4#350614yes—
1144C4#355814yes—
1145C2—24no—
1146C2—84no—
1147C2—84no—
1148C2C2×#355811yescharacteristic
1149C2#6274811yescharacteristic
1150C2C2×#350611yescharacteristic
1151C2C2×#351111yescharacteristic
1152C2#6281511yescharacteristic
1153C2#6282311yescharacteristic
1154C2#6283511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59644C2semidirect
2. #59639C2semidirect
3. #59410C2semidirect
4. #46024C2semidirect
5. #46023C2semidirect
6. #46016C2semidirect
7. #39830C2semidirect
8. #39783C2semidirect
9. #39632C2semidirect
10. #39555C2semidirect
11. #39505C2semidirect
12. #39503C2semidirect
13. #39488C2semidirect
14. #37895C2semidirect
15. #37546C2semidirect
16. #36765C2semidirect
17. #36645C2semidirect
18. #36631C2semidirect
19. #36579C2semidirect
20. #36148C2semidirect
21. #36100C2semidirect
22. #35032C2semidirect
23. #35014C2semidirect
24. #34382C2semidirect
25. C2×C4×#124C2semidirect
26. C2×#556C22semidirect
34. #2868C22semidirect
35. #2868C22semidirect
36. #2862C22semidirect
37. #2861C22semidirect
38. #2860C22semidirect
39. #2860C22semidirect
40. #2859C22semidirect
41. #2859C22semidirect
42. #2859C22semidirect
43. #2858C22semidirect
58. #2806C22semidirect
59. #2804C22semidirect
61. #2800C22semidirect
62. #2798C22semidirect
63. #2795C22semidirect
64. #2788C22semidirect
65. #2779C22semidirect
66. #2772C22semidirect
67. #2754C22semidirect
68. #2753C22semidirect
70. #2731C22semidirect
71. #2718C22semidirect
72. #2718C22semidirect
73. #2712C22semidirect
74. #2705C22semidirect
82. #2602C22semidirect
83. #2602C22semidirect
84. #2596C22semidirect
85. #2595C22semidirect
86. #2593C22semidirect
88. #2592C22semidirect
89. #2589C22semidirect
90. #2587C22semidirect
91. #2581C22semidirect
92. #2568C22semidirect
93. #2558C22semidirect
94. #2554C22semidirect
97. #2538C22semidirect
100. #2511C22semidirect
101. #2502C22semidirect
103. #2500C22semidirect
104. #2499C22semidirect
105. #2497C22semidirect
106. #2492C22semidirect
107. #2492C22semidirect
109. #2491C22semidirect
112. #2469C22semidirect
113. #2460C22semidirect
114. #2458C22semidirect
117. #2439C22semidirect
118. #2432C22semidirect
119. #2432C22semidirect
120. #2431C22semidirect
121. #2429C22semidirect
122. #2429C22semidirect
123. #2426C22semidirect
124. #2423C22semidirect
126. #2421C22semidirect
127. #2421C22semidirect
129. #2417C22semidirect
136. #2382C22semidirect
137. #2379C22semidirect
138. #2367C22semidirect
139. #2362C22semidirect
140. #2362C22semidirect
143. #2355C22semidirect
144. #2355C22semidirect
147. #2352C22semidirect
149. #2341C22semidirect
150. #2334C22semidirect
154. #2317C22semidirect
155. #2314C22semidirect
157. C4×C4⋊Q8C22semidirect
158. C4×C4⋊Q8C22semidirect
159. C4×C4⋊Q8C22semidirect
160. C4×C4⋊Q8C22semidirect
161. C4×C4⋊Q8C22semidirect
162. C4×#127C22semidirect
171. C4×#124C22semidirect
176. #2293C22semidirect
177. #2293C22semidirect
686. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
#596442
#596392
#594102
#460242
#460232
#460162
#398302
#397832
#396322
#395552
#395052
#395032
#394882
#378952
#375462
#367652
#366452
#366312
#365792
#361482
#361002
#350322
#350142
#343822
C2×C4×#1242