Finite Group Databasebeta

← #7712017

Subgroups — #7712017

Order 512.

5566 conjugacy classes of subgroups.

The subgroup lattice has 1335 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59654C212yesmaximal, complemented
2#59427C212yesmaximal, complemented
3#59233C212yesmaximal, complemented
4#59220C212yesmaximal, complemented
5#46043C214yesmaximal, complemented
6#45609C214yesmaximal, complemented
7#40142C214yesmaximal, complemented
8#39854C214yesmaximal, complemented
9#39608C212yesmaximal, complemented
10#39469C212yesmaximal, complemented
11#39191C212yesmaximal, complemented
12#39124C212yesmaximal, complemented
13#38964C212yesmaximal, complemented
14#38920C212yesmaximal, complemented
15#37969C214yesmaximal, complemented
16#37636C212yesmaximal, complemented
17#37350C214yesmaximal, complemented
18#36645C211yesmaximal, characteristic, complemented
19#36631C211yesmaximal, characteristic, complemented
20#36209C212yesmaximal, complemented
21#36194C211yesmaximal, characteristic, complemented
22#36187C211yesmaximal, characteristic, complemented
23#36127C211yesmaximal, characteristic, complemented
24#36122C212yesmaximal, complemented
25D4×C4⋊Q8C211yesmaximal, characteristic, complemented
26#35292C212yesmaximal, complemented
27#35279C212yesmaximal, complemented
28#34485C212yesmaximal, complemented
29C4×#532C211yesmaximal, characteristic, complemented
30C2×#555C2212yes—
31C2×D4×Q8C2212yes—
32C2×#548C2214yes—
33C2×#547C2212yes—
34C2×#533C2212yes—
35C2×#532C2211yescharacteristic
36C2×#532C2212yes—
37C22×C4⋊Q8C2212yes—
38C2×#529C2212yes—
39C2×C4×#41C2212yes—
40#2868C2211yescharacteristic
41#2868C2211yescharacteristic
42#2862C2212yes—
43#2861C2212yes—
44#2860C2212yes—
45#2860C2212yes—
46#2859C2211yescharacteristic
47#2859C2212yes—
48#2859C2212yes—
49#2858C2211yescharacteristic
50#2857C2212yes—
51#2857C2211yescharacteristic
52#2857C2212yes—
53#2857C2212yes—
54#2857C2212yes—
55#2857C2212yes—
56#2857C2212yes—
57#2857C2212yes—
58#2856C2211yescharacteristic
59#2856C2212yes—
60#2854C2212yes—
61#2854C2212yes—
62#2850C2212yes—
63#2832C2218yes—
64#2785C2218yes—
65#2783C2218yes—
66#2782C2218yes—
67#2763C2218yes—
68#2763C2218yes—
69#2753C2218yes—
70#2723C2218yes—
71#2720C2218yes—
72#2718C2218yes—
73#2712C2218yes—
74#2711C2218yes—
75#2706C2218yes—
76#2696C2218yes—
77#2692C2218yes—
78#2681C2218yes—
79#2676C2218yes—
80#2632C2218yes—
81#2628C2214yes—
82#2628C2214yes—
83#2628C2214yes—
84#2624C2214yes—
85#2624C2214yes—
86#2615C2214yes—
87#2610C2218yes—
88#2598C2218yes—
89#2592C2214yes—
90#2580C2214yes—
91#2571C2212yes—
92#2568C2214yes—
93#2567C2214yes—
94#2563C2212yes—
95#2563C2212yes—
96#2563C2214yes—
97#2563C2214yes—
98#2551C2212yes—
99#2551C2212yes—
100#2547C2212yes—
101#2546C2212yes—
102#2545C2214yes—
103#2542C2214yes—
104#2540C2214yes—
105#2538C2212yes—
106#2537C2212yes—
107#2537C2212yes—
108#2537C2212yes—
109#2537C2212yes—
110#2536C2214yes—
111#2535C2214yes—
112#2535C2214yes—
113#2532C2218yes—
114#2508C2214yes—
115#2508C2214yes—
116#2500C2214yes—
117#2497C2214yes—
118#2497C2214yes—
119#2495C2214yes—
120#2495C2214yes—
121#2495C2214yes—
122#2492C2214yes—
123#2491C2214yes—
124#2491C2214yes—
125#2491C2214yes—
126#2491C2214yes—
127#2491C2214yes—
128#2489C2214yes—
129#2489C2214yes—
130#2487C2214yes—
131#2487C2214yes—
132#2487C2214yes—
133#2485C2214yes—
134#2485C2214yes—
135#2461C2218yes—
136#2452C2214yes—
137#2452C2214yes—
138#2440C2214yes—
139#2440C2214yes—
140#2440C2214yes—
141#2439C2214yes—
142#2439C2214yes—
143#2436C2214yes—
144#2434C2214yes—
145#2432C2214yes—
146#2432C2214yes—
147#2428C2214yes—
148#2422C2214yes—
149#2422C2214yes—
150#2416C2214yes—
151#2416C2214yes—
152#2414C2214yes—
153#2414C2214yes—
154#2414C2214yes—
155#2409C2214yes—
156#2409C2214yes—
157#2407C2214yes—
158#2407C2214yes—
159#2379C2218yes—
160#2369C2212yes—
161#2361C2214yes—
162#2361C2214yes—
163#2361C2214yes—
164#2356C2214yes—
165#2355C2212yes—
166#2354C2212yes—
167#2354C2212yes—
168#2354C2212yes—
169D4×C4⋊C4C2212yes—
170D4×C4⋊C4C2212yes—
171D4×C4⋊C4C2212yes—
172D4×C4⋊C4C2212yes—
173#2346C2214yes—
174#2346C2214yes—
175#2346C2214yes—
176#2326C2218yes—
177#2324C2214yes—
178#2324C2214yes—
179#2324C2214yes—
180#2317C2214yes—
181#2317C2214yes—
182#2311C2214yes—
183C4×C4⋊Q8C2212yes—
184C4×C4⋊Q8C2212yes—
185C4×C4⋊Q8C2211yescharacteristic
186C4×C4⋊Q8C2212yes—
187C4×C4⋊Q8C2211yescharacteristic
188C4×C4⋊Q8C2212yes—
189C4×C4⋊Q8C2211yescharacteristic
190C4×#127C2211yescharacteristic
191C4×#127C2211yescharacteristic
192C4×#127C2211yescharacteristic
193C4×#124C2212yes—
194C4×#124C2212yes—
195C4×#124C2212yes—
196C4×#121C2211yescharacteristic
197C4×#121C2212yes—
198C4×#121C2212yes—
199C4×#121C2212yes—
200C4×#121C2211yescharacteristic
201C4×#121C2211yescharacteristic
202C4×#121C2212yes—
203C4×#121C2211yescharacteristic
204#2297C2212yes—
205#2293C2211yescharacteristic
206#2293C2212yes—
207#2293C2212yes—
208#2293C2211yescharacteristic
209#2293C2212yes—
210#2285C2212yes—
211#2285C2212yes—
212#2285C2212yes—
213#2285C2212yes—
214#2285C2211yescharacteristic
215C42×D4C2211yescharacteristic
216C42×D4C2212yes—
217C42×D4C2211yescharacteristic
218C2×C43C2211yescharacteristic
219C22×#41C2312yes—
220C22×#41C2314yes—
221C23×Q8C2314yes—
222#555—216no—
223D4×Q8—48no—
224#548—416no—
225#547—48no—
226#533—48no—
227#532—28no—
228#532—48no—
229C2×C4⋊Q8—48no—
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2314yes—
237C2×C4⋊Q8C2314yes—
238C2×C4⋊Q8C2314yes—
239C2×C4⋊Q8C2312yes—
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2314yes—
242C2×#127C2311yescharacteristic
243C2×#127C2311yescharacteristic
244#529—48no—
245C2×#126C2314yes—
246C2×#125C2314yes—
247C2×#125C2312yes—
248C2×#124C2318yes—
249C2×#124C2312yes—
250C2×#124C2312yes—
251C2×#124C2314yes—
252C2×#124C2312yes—
253C2×#124C2318yes—
254C2×#123C2314yes—
255C2×#123C2318yes—
256C2×C22⋊Q8C2312yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2318yes—
263C2×C22⋊Q8C2318yes—
264C2×#121C2312yes—
265C2×#121C2314yes—
266C2×#121C2314yes—
267C2×#121C2311yescharacteristic
268C2×#121C2312yes—
269C2×#121C2311yescharacteristic
270C2×#121C2312yes—
271C2×#121C2312yes—
272C2×#121C2314yes—
273C2×#121C2314yes—
274C2×#121C2314yes—
275C2×#121C2314yes—
276C2×#121C2314yes—
277C2×#121C2318yes—
278C4×#41—48no—
279C2×C4×Q8C2314yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2314yes—
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2312yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2311yescharacteristic
286C2×C4×D4C2312yes—
287C2×C4×D4C2311yescharacteristic
288C2×C4×D4C2312yes—
289C2×C4×D4C2311yescharacteristic
290C2×C4×D4C2312yes—
291C2×C4×D4C2311yescharacteristic
292C2×C4×D4C2311yescharacteristic
293C2×C4×D4C2312yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2314yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2318yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2311yescharacteristic
307C2×#117C2314yes—
308C2×#117C2314yes—
309C2×#117C2312yes—
310C2×#117C2314yes—
311C2×#117C2312yes—
312C2×#117C2314yes—
313C2×#117C2314yes—
314C2×#117C2312yes—
315C22×C4⋊C4C2314yes—
316C22×C4⋊C4C2314yes—
317C22×C4⋊C4C2314yes—
318C22×C42C2311yescharacteristic
319C22×C42C2311yescharacteristic
320C22×C42C2311yescharacteristic
321C22×C42C2312yes—
322C22×C42C2312yes—
323C22×C42C2311yescharacteristic
324C22×C42C2311yescharacteristic
325C22×C42C2311yescharacteristic
326C22×C42C2311yescharacteristic
327#400C2318yes—
328#400C2318yes—
329#400C2318yes—
330#400C2318yes—
331#400C2318yes—
332#399C2318yes—
333#399C2318yes—
334#399C2318yes—
335#398C2318yes—
336#398C2318yes—
337#397C2318yes—
338#397C2318yes—
339#397C2318yes—
340#397C2318yes—
341#396C2318yes—
342#396C2318yes—
343#396C2318yes—
344#395C2318yes—
345#395C2318yes—
346#395C2318yes—
347#395C2318yes—
348#394C2318yes—
349#394C2318yes—
350#394C2318yes—
351#394C2318yes—
352#394C2318yes—
353#394C2318yes—
354#394C2318yes—
355#394C2318yes—
356#394C2318yes—
357#393C2318yes—
358#393C2318yes—
359#393C2318yes—
360#393C2318yes—
361#393C2318yes—
362#393C2318yes—
363#393C2318yes—
364#392C2318yes—
365#392C2318yes—
366#392C2318yes—
367#391C2314yes—
368#391C2314yes—
369#391C2312yes—
370#391C2314yes—
371#391C2314yes—
372#391C2312yes—
373#391C2312yes—
374#391C2318yes—
375#391C2312yes—
376#391C2314yes—
377#391C2314yes—
378#391C2318yes—
379#391C2314yes—
380#390C2311yescharacteristic
381#390C2312yes—
382#390C2312yes—
383#390C2312yes—
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2312yes—
387#390C2312yes—
388#390C2312yes—
389#390C2311yescharacteristic
390#390C2312yes—
391#390C2318yes—
392#390C2314yes—
393#390C2318yes—
394#390C2314yes—
395#390C2318yes—
396#390C2312yes—
397#390C2312yes—
398#390C2314yes—
399#390C2312yes—
400#390C2314yes—
401#390C2312yes—
402#390C2312yes—
403#390C2312yes—
404#390C2312yes—
405#389C2314yes—
406#389C2311yescharacteristic
407#389C2314yes—
408#389C2314yes—
409#389C2312yes—
410#389C2312yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2311yescharacteristic
417#389C2311yescharacteristic
418#389C2312yes—
419#389C2311yescharacteristic
420#389C2312yes—
421#389C2312yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2312yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2312yes—
432#389C2312yes—
433#389C2312yes—
434#389C2312yes—
435#389C2314yes—
436#388C2312yes—
437#388C2314yes—
438#388C2318yes—
439#388C2318yes—
440#388C2318yes—
441#388C2312yes—
442#388C2314yes—
443#388C2318yes—
444#388C2318yes—
445#388C2314yes—
446#388C2318yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2318yes—
451#388C2318yes—
452#388C2314yes—
453#388C2314yes—
454#388C2318yes—
455#388C2318yes—
456#388C2318yes—
457#388C2312yes—
458#388C2312yes—
459#388C2312yes—
460#388C2312yes—
461#388C2312yes—
462#388C2312yes—
463#387C2318yes—
464#387C2318yes—
465#387C2318yes—
466#386C2318yes—
467#386C2318yes—
468#386C2318yes—
469#386C2318yes—
470#386C2318yes—
471#386C2314yes—
472#386C2314yes—
473#386C2312yes—
474#386C2312yes—
475#386C2318yes—
476#386C2312yes—
477#386C2312yes—
478#385C2318yes—
479#385C2318yes—
480#385C2318yes—
481#385C2318yes—
482#385C2318yes—
483#385C2318yes—
484#385C2318yes—
485#385C2318yes—
486#385C2318yes—
487#385C2318yes—
488#384C2311yescharacteristic
489#384C2311yescharacteristic
490#384C2311yescharacteristic
491#384C2311yescharacteristic
492#384C2312yes—
493#384C2312yes—
494#384C2312yes—
495#384C2312yes—
496#384C2318yes—
497#384C2312yes—
498#384C2312yes—
499#384C2312yes—
500#384C2312yes—
501#383C2318yes—
502#382C2318yes—
503#382C2314yes—
504#382C2318yes—
505#382C2314yes—
506#382C2314yes—
507#382C2318yes—
508#382C2312yes—
509#382C2314yes—
510#382C2314yes—
511#382C2312yes—
512#380C2311yescharacteristic
513#380C2312yes—
514#380C2314yes—
515#380C2314yes—
516#380C2314yes—
517#380C2314yes—
518#380C2314yes—
519#380C2314yes—
520#380C2314yes—
521#380C2314yes—
522#380C2314yes—
523#380C2312yes—
524#380C2314yes—
525#380C2314yes—
526#380C2314yes—
527#380C2314yes—
528#380C2314yes—
529#380C2314yes—
530#380C2314yes—
531#380C2314yes—
532#380C2312yes—
533#380C2314yes—
534#380C2311yescharacteristic
535C4×C4⋊C4C2314yes—
536C4×C4⋊C4C2314yes—
537C4×C4⋊C4C2314yes—
538C4×C4⋊C4C2314yes—
539C4×C4⋊C4C2312yes—
540C4×C4⋊C4C2311yescharacteristic
541C4×C4⋊C4C2312yes—
542C4×C4⋊C4C2311yescharacteristic
543C4×C4⋊C4C2311yescharacteristic
544C4×C4⋊C4C2311yescharacteristic
545C4×C4⋊C4C2312yes—
546C4×C4⋊C4C2312yes—
547C4×C4⋊C4C2311yescharacteristic
548C4×C4⋊C4C2314yes—
549C4×C4⋊C4C2314yes—
550C4×C4⋊C4C2314yes—
551C4×C4⋊C4C2314yes—
552C4×C4⋊C4C2314yes—
553C4×C4⋊C4C2311yescharacteristic
554C4×C4⋊C4C2312yes—
555C4×C22⋊C4C2312yes—
556C4×C22⋊C4C2312yes—
557C4×C22⋊C4C2314yes—
558C4×C22⋊C4C2312yes—
559C4×C22⋊C4C2312yes—
560C4×C22⋊C4C2312yes—
561C4×C22⋊C4C2314yes—
562C4×C22⋊C4C2312yes—
563C4×C22⋊C4C2312yes—
564C4×C22⋊C4C2312yes—
565C4×C22⋊C4C2312yes—
566C4×C22⋊C4C2312yes—
567C4×C22⋊C4C2312yes—
568C4×C22⋊C4C2312yes—
569#376C2318yes—
570C43C2311yescharacteristic
571C43C2311yescharacteristic
572C43C2311yescharacteristic
573C43C2311yescharacteristic
574C43C2311yescharacteristic
575C43C2311yescharacteristic
576C43C2311yescharacteristic
577C43C2311yescharacteristic
578C2×#41—28no—
579C2×#41—28no—
580C2×#41—44no—
581C2×#41—48no—
582C2×#41—48no—
583C2×#41—48no—
584C22×Q8—48no—
585C22×Q8—48no—
586C22×Q8—48no—
587C22×Q8C2412yes—
588C22×Q8C2414yes—
589C22×Q8C2412yes—
590C22×Q8C2414yes—
591C22×Q8C2418yes—
592C22×D4C2412yes—
593C22×D4C2411yescharacteristic
594C22×D4C2412yes—
595C22×D4C2412yes—
596C22×D4C2412yes—
597C22×D4C2412yes—
598C22×D4C2412yes—
599C22×D4C2412yes—
600C22×D4C2411yescharacteristic
601C22×D4C2418yes—
602C22×D4C2414yes—
603C22×D4C2418yes—
604C23×C4C2412yes—
605C23×C4C2414yes—
606C23×C4C2411yescharacteristic
607C23×C4C2412yes—
608C23×C4C2412yes—
609C23×C4C2411yescharacteristic
610C23×C4C2412yes—
611C23×C4C2411yescharacteristic
612C23×C4C2411yescharacteristic
613C23×C4C2412yes—
614C23×C4C2411yescharacteristic
615C23×C4C2411yescharacteristic
616C23×C4C2412yes—
617C23×C4C2411yescharacteristic
618C23×C4C2418yes—
619C23×C4C2418yes—
620C4⋊Q8—24no—
621C4⋊Q8—28no—
622C4⋊Q8—24no—
623C4⋊Q8—28no—
624C4⋊Q8—28no—
625C4⋊Q8—48no—
626C4⋊Q8—48no—
627C4⋊Q8—44no—
628C4⋊Q8—44no—
629C4⋊Q8—48no—
630C4⋊Q8—48no—
631C4⋊Q8—44no—
632#127—24no—
633#127—24no—
634#126—48no—
635#125—44no—
636#125—48no—
637#124—28no—
638#124—232no—
639#124—28no—
640#124—416no—
641#124—44no—
642#124—48no—
643#123—416no—
644#123—48no—
645C22⋊Q8—416no—
646C22⋊Q8—416no—
647C22⋊Q8—48no—
648C22⋊Q8—44no—
649C22⋊Q8—48no—
650C22⋊Q8—48no—
651C22⋊Q8—48no—
652C22⋊Q8—48no—
653#121—24no—
654#121—216no—
655#121—216no—
656#121—28no—
657#121—24no—
658#121—28no—
659#121—416no—
660#121—44no—
661#121—48no—
662#121—44no—
663#121—48no—
664#121—48no—
665#121—48no—
666#121—48no—
667C4×Q8—28no—
668C4×Q8—216no—
669C4×Q8—44no—
670C4×Q8—44no—
671C4×Q8—48no—
672C4×D4—28no—
673C4×D4—24no—
674C4×D4—28no—
675C4×D4—28no—
676C4×D4—24no—
677C4×D4—28no—
678C4×D4—24no—
679C4×D4—24no—
680C4×D4—28no—
681C4×D4—24no—
682C4×D4—416no—
683C4×D4—48no—
684C4×D4—48no—
685C4×D4—48no—
686C4×D4—44no—
687C4×D4—44no—
688C4×D4—44no—
689C4×D4—44no—
690C4×D4—44no—
691C4×D4—44no—
692C4×D4—44no—
693C4×D4—48no—
694C4×D4#4118yescomplemented
695#117—216no—
696#117—216no—
697#117—44no—
698#117—44no—
699#117—44no—
700#117—48no—
701#117—48no—
702#117—48no—
703C2×C4⋊C4—48no—
704C2×C4⋊C4—48no—
705C2×C4⋊C4—48no—
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2411yescharacteristic
723C2×C4⋊C4C2411yescharacteristic
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2418yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2418yes—
732C2×C4⋊C4C2418yes—
733C2×C4⋊C4C2418yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2418yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2418yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2418yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2411yescharacteristic
752C2×C22⋊C4C2418yes—
753C2×C22⋊C4C2418yes—
754C2×C22⋊C4C2412yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2412yes—
757C2×C22⋊C4C2412yes—
758C2×C22⋊C4C2412yes—
759C2×C22⋊C4C2412yes—
760C2×C22⋊C4C2412yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2412yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2412yes—
765C2×C22⋊C4C2412yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2412yes—
770C2×C22⋊C4C2412yes—
771C2×C22⋊C4C2412yes—
772C2×C22⋊C4C2412yes—
773C2×C22⋊C4C2412yes—
774C2×C22⋊C4C2412yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2418yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2418yes—
779C2×C22⋊C4C2418yes—
780C2×C22⋊C4C2418yes—
781C2×C22⋊C4C2418yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2412yes—
785C2×C22⋊C4C2412yes—
786C2×C22⋊C4C2418yes—
787C2×C22⋊C4C2418yes—
788C2×C22⋊C4C2418yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2418yes—
791C2×C22⋊C4C2412yes—
792C2×C42—24no—
793C2×C42—24no—
794C2×C42—24no—
795C2×C42—28no—
796C2×C42—28no—
797C2×C42—24no—
798C2×C42—24no—
799C2×C42—24no—
800C2×C42—42no—
801C2×C42C2411yescharacteristic
802C2×C42C2411yescharacteristic
803C2×C42C2412yes—
804C2×C42C2418yes—
805C2×C42C2412yes—
806C2×C42C2414yes—
807C2×C42C2418yes—
808C2×C42C2412yes—
809C2×C42C2411yescharacteristic
810C2×C42C2411yescharacteristic
811C2×C42C2411yescharacteristic
812C2×C42C2411yescharacteristic
813C2×C42C2412yes—
814C2×C42C2412yes—
815C2×C42C2412yes—
816C2×C42C2411yescharacteristic
817C2×C42C2411yescharacteristic
818C2×C42C2411yescharacteristic
819C2×C42C2411yescharacteristic
820C2×C42C2411yescharacteristic
821C2×C42C2411yescharacteristic
822C2×C42C2411yescharacteristic
823C2×C42C2411yescharacteristic
824C2×C42C2411yescharacteristic
825C2×C42C2411yescharacteristic
826C2×C42C2411yescharacteristic
827C2×C42C2411yescharacteristic
828C2×C42C2411yescharacteristic
829C2×C42C2411yescharacteristic
830C2×C42C2411yescharacteristic
831C2×C42C2418yes—
832C2×C42C2411yescharacteristic
833C2×C42C2411yescharacteristic
834C2×C42C2411yescharacteristic
835C2×C42C2411yescharacteristic
836C2×C42C2411yescharacteristic
837C2×C42C2411yescharacteristic
838C2×C42C2411yescharacteristic
839#95C2412yes—
840#95C2414yes—
841#95C2418yes—
842#95C2418yes—
843#95C2412yes—
844#95C2412yes—
845#95C2412yes—
846#95C2412yes—
847#95C2412yes—
848#95C2412yes—
849#95C2412yes—
850#95C2412yes—
851#95C2412yes—
852#95C2412yes—
853#95C2412yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2418yes—
858#95C2418yes—
859#95C2418yes—
860#95C2418yes—
861#95C2418yes—
862#95C2418yes—
863#95C2418yes—
864#95C2418yes—
865#95C2418yes—
866#95C2414yes—
867#95C2414yes—
868#95C2418yes—
869#95C2418yes—
870#95C2418yes—
871C24C2514yes—
872C24C2512yes—
873C24C2512yes—
874C24C2511yescharacteristic
875#41—432no—
876#41—832no—
877C2×Q8—24no—
878C2×Q8—28no—
879C2×Q8—24no—
880C2×Q8—28no—
881C2×Q8—24no—
882C2×Q8—28no—
883C2×Q8—28no—
884C2×Q8—24no—
885C2×Q8—24no—
886C2×Q8—42no—
887C2×Q8—44no—
888C2×Q8—48no—
889C2×Q8—48no—
890C2×Q8—48no—
891C2×Q8—44no—
892C2×Q8—832no—
893C2×D4—24no—
894C2×D4—24no—
895C2×D4—24no—
896C2×D4—24no—
897C2×D4—24no—
898C2×D4—216no—
899C2×D4—28no—
900C2×D4—24no—
901C2×D4—22no—
902C2×D4—24no—
903C2×D4—22no—
904C2×D4—24no—
905C2×D4—22no—
906C2×D4—24no—
907C2×D4—24no—
908C2×D4—24no—
909C2×D4—24no—
910C2×D4—24no—
911C2×D4—22no—
912C2×D4—22no—
913C2×D4—24no—
914C2×D4—24no—
915C2×D4—24no—
916C2×D4—24no—
917C2×D4—42no—
918C2×D4—42no—
919C2×D4—42no—
920C2×D4—42no—
921C2×D4—48no—
922C2×D4—44no—
923C2×D4—48no—
924C2×D4—48no—
925C2×D4—48no—
926C2×D4—44no—
927C2×D4—48no—
928C2×D4C2×#4114yes—
929C22×C4—22no—
930C22×C4—22no—
931C22×C4—24no—
932C22×C4—22no—
933C22×C4—22no—
934C22×C4—22no—
935C22×C4—24no—
936C22×C4—22no—
937C22×C4—22no—
938C22×C4—22no—
939C22×C4—28no—
940C22×C4—24no—
941C22×C4—24no—
942C22×C4—24no—
943C22×C4—22no—
944C22×C4—22no—
945C22×C4—22no—
946C22×C4—24no—
947C22×C4—24no—
948C22×C4—24no—
949C22×C4—22no—
950C22×C4—22no—
951C22×C4—22no—
952C22×C4—22no—
953C22×C4—28no—
954C22×C4—24no—
955C22×C4—24no—
956C22×C4—24no—
957C22×C4—24no—
958C22×C4—22no—
959C22×C4—22no—
960C22×C4—28no—
961C22×C4—24no—
962C22×C4—24no—
963C22×C4—24no—
964C22×C4—22no—
965C22×C4—24no—
966C22×C4—24no—
967C22×C4—41no—
968C22×C4—41no—
969C22×C4—48no—
970C22×C4—48no—
971C22×C4—48no—
972C22×C4—48no—
973C22×C4—48no—
974C22×C4—48no—
975C22×C4C2×#4118yes—
976C22×C42−1+414yes—
977C22×C4C2512yes—
978C22×C4C2511yescharacteristic
979C22×C4C2512yes—
980C22×C4C2511yescharacteristic
981C22×C4C2511yescharacteristic
982C22×C4C2514yes—
983C22×C4C2514yes—
984C22×C4C2512yes—
985C22×C4C2518yes—
986C22×C4C2512yes—
987C22×C4C2512yes—
988C22×C4C2514yes—
989C22×C4C2518yes—
990C22×C4C2511yescharacteristic
991C22×C4C2511yescharacteristic
992C22×C4C2512yes—
993C22×C4C2511yescharacteristic
994C22×C4C2511yescharacteristic
995C22×C4C2511yescharacteristic
996C22×C4C2511yescharacteristic
997C22×C4C2511yescharacteristic
998C22×C4C2511yescharacteristic
999C22×C4C2511yescharacteristic
1000C22×C4C2511yescharacteristic
1001C22×C4C2511yescharacteristic
1002C4⋊C4—24no—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—24no—
1006C4⋊C4—22no—
1007C4⋊C4—22no—
1008C4⋊C4—24no—
1009C4⋊C4—24no—
1010C4⋊C4—28no—
1011C4⋊C4—28no—
1012C4⋊C4—28no—
1013C4⋊C4—24no—
1014C4⋊C4—24no—
1015C4⋊C4—22no—
1016C4⋊C4—24no—
1017C4⋊C4—216no—
1018C4⋊C4—28no—
1019C4⋊C4—28no—
1020C4⋊C4—28no—
1021C4⋊C4—22no—
1022C4⋊C4—22no—
1023C4⋊C4—24no—
1024C4⋊C4—24no—
1025C4⋊C4—24no—
1026C4⋊C4—28no—
1027C4⋊C4—48no—
1028C4⋊C4—48no—
1029C4⋊C4—48no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—42no—
1041C4⋊C4—48no—
1042C4⋊C4—44no—
1043C4⋊C4—48no—
1044C4⋊C4—44no—
1045C4⋊C4—48no—
1046C4⋊C4—44no—
1047C4⋊C4C2×#4114yes—
1048C22⋊C4—216no—
1049C22⋊C4—24no—
1050C22⋊C4—216no—
1051C22⋊C4—24no—
1052C22⋊C4—24no—
1053C22⋊C4—28no—
1054C22⋊C4—24no—
1055C22⋊C4—24no—
1056C22⋊C4—24no—
1057C22⋊C4—28no—
1058C22⋊C4—24no—
1059C22⋊C4—28no—
1060C22⋊C4—28no—
1061C22⋊C4—24no—
1062C22⋊C4—24no—
1063C22⋊C4—28no—
1064C22⋊C4—28no—
1065C22⋊C4—48no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—44no—
1073C22⋊C4—48no—
1074C22⋊C4—44no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—48no—
1078C22⋊C4—48no—
1079C22⋊C4—48no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—48no—
1084C22⋊C4—48no—
1085C22⋊C4—48no—
1086C22⋊C4—48no—
1087C22⋊C4C2×#4118yes—
1088C42—22no—
1089C42—22no—
1090C42—22no—
1091C42—216no—
1092C42—22no—
1093C42—22no—
1094C42—24no—
1095C42—24no—
1096C42—24no—
1097C42—22no—
1098C42—22no—
1099C42—24no—
1100C42—24no—
1101C42—24no—
1102C42—22no—
1103C42—22no—
1104C42—22no—
1105C42—22no—
1106C42—22no—
1107C42—28no—
1108C42—216no—
1109C42—22no—
1110C42—22no—
1111C42—22no—
1112C42—22no—
1113C42—22no—
1114C42—22no—
1115C42—22no—
1116C42—22no—
1117C42—22no—
1118C42—41no—
1119C42—41no—
1120C42—48no—
1121C42C2×#4114yes—
1122C42H(5,𝔽2)14yes—
1123C42H(5,𝔽2)14yes—
1124C42H(5,𝔽2)14yes—
1125C422−1+414yes—
1126C23—21no—
1127C23—22no—
1128C23—22no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—22no—
1133C23—22no—
1134C23—21no—
1135C23—22no—
1136C23—22no—
1137C23—21no—
1138C23—24no—
1139C23—22no—
1140C23—24no—
1141C23—22no—
1142C23—22no—
1143C23—24no—
1144C23—24no—
1145C23—22no—
1146C23—22no—
1147C23—24no—
1148C23—24no—
1149C23—22no—
1150C23—22no—
1151C23—24no—
1152C23C22×#4114yes—
1153C23C2×2−1+412yes—
1154C23C2611yescharacteristic
1155Q8—48no—
1156Q8—48no—
1157Q8—416no—
1158Q8—88no—
1159Q8—816no—
1160D4—28no—
1161D4—48no—
1162D4—48no—
1163D4—48no—
1164D4—48no—
1165D4—44no—
1166D4—48no—
1167D4—48no—
1168D4—48no—
1169D4—816no—
1170D4—88no—
1171D4—816no—
1172C2×C4—28no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—22no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—22no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—216no—
1188C2×C4—28no—
1189C2×C4—21no—
1190C2×C4—24no—
1191C2×C4—28no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—21no—
1204C2×C4—24no—
1205C2×C4—28no—
1206C2×C4—24no—
1207C2×C4—28no—
1208C2×C4—24no—
1209C2×C4—22no—
1210C2×C4—24no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—28no—
1215C2×C4—28no—
1216C2×C4—24no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—22no—
1225C2×C4—21no—
1226C2×C4—22no—
1227C2×C4—21no—
1228C2×C4—24no—
1229C2×C4—28no—
1230C2×C4—22no—
1231C2×C4—44no—
1232C2×C4—44no—
1233C2×C4—44no—
1234C2×C4—416no—
1235C2×C4—48no—
1236C2×C4—48no—
1237C2×C4—44no—
1238C2×C4—48no—
1239C2×C4—44no—
1240C2×C4—48no—
1241C2×C4—48no—
1242C2×C4—816no—
1243C2×C4—816no—
1244C2×C4C22×#4114yes—
1245C2×C4C22×#4112yes—
1246C2×C4C22×#4112yes—
1247C2×C4C22×#4112yes—
1248C2×C4C2×H(5,𝔽2)12yes—
1249C2×C4C2×H(5,𝔽2)12yes—
1250C2×C4C2×H(5,𝔽2)12yes—
1251C2×C4C2×H(5,𝔽2)12yes—
1252C2×C4C2×H(5,𝔽2)12yes—
1253C2×C4C2×H(5,𝔽2)12yes—
1254C2×C4C2×H(5,𝔽2)12yes—
1255C2×C4C2×H(5,𝔽2)12yes—
1256C2×C4C2×H(5,𝔽2)12yes—
1257C2×C4C2×2−1+412yes—
1258C2×C4C2×2−1+412yes—
1259C2×C4C2×2−1+412yes—
1260C2×C4C2×2−1+412yes—
1261C2×C4C2×2−1+412yes—
1262C2×C4#58512yes—
1263C22—22no—
1264C22—24no—
1265C22—24no—
1266C22—24no—
1267C22—22no—
1268C22—22no—
1269C22—41no—
1270C22—42no—
1271C22—42no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—44no—
1279C22—42no—
1280C22—44no—
1281C22—42no—
1282C22—44no—
1283C22—44no—
1284C22—42no—
1285C22—42no—
1286C22—44no—
1287C22—44no—
1288C22—42no—
1289C22—44no—
1290C22—42no—
1291C22C23×#4111yescharacteristic
1292C22C22×H(5,𝔽2)11yescharacteristic
1293C22C22×H(5,𝔽2)11yescharacteristic
1294C22C22×H(5,𝔽2)11yescharacteristic
1295C22C22×2−1+411yescharacteristic
1296C22C22×2−1+411yescharacteristic
1297C22C2×#58511yescharacteristic
1298C4—24no—
1299C4—22no—
1300C4—22no—
1301C4—22no—
1302C4—22no—
1303C4—22no—
1304C4—22no—
1305C4—42no—
1306C4—41no—
1307C4—42no—
1308C4—41no—
1309C4—42no—
1310C4—42no—
1311C4—48no—
1312C4—44no—
1313C4—42no—
1314C4—41no—
1315C4—44no—
1316C4—48no—
1317C4—41no—
1318C4—44no—
1319C4#351114yes—
1320C4#352014yes—
1321C4#354714yes—
1322C4#354914yes—
1323C2—42no—
1324C2—44no—
1325C2—82no—
1326C2—84no—
1327C2C2×#354711yescharacteristic
1328C2C2×#354911yescharacteristic
1329C2C2×#352011yescharacteristic
1330C2C2×#351111yescharacteristic
1331C2#6280011yescharacteristic
1332C2#6283311yescharacteristic
1333C2#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. #59654C2semidirect
2. #59427C2semidirect
3. #59233C2semidirect
4. #59220C2semidirect
5. #46043C2semidirect
6. #45609C2semidirect
7. #40142C2semidirect
8. #39854C2semidirect
9. #39608C2semidirect
10. #39469C2semidirect
11. #39191C2semidirect
12. #39124C2semidirect
13. #38964C2semidirect
14. #38920C2semidirect
15. #37969C2semidirect
16. #37636C2semidirect
17. #37350C2semidirect
18. #36645C2semidirect
19. #36631C2semidirect
20. #36209C2semidirect
21. #36194C2semidirect
22. #36187C2semidirect
23. #36127C2semidirect
24. #36122C2semidirect
25. D4×C4⋊Q8C2semidirect
26. #35292C2semidirect
27. #35279C2semidirect
28. #34485C2semidirect
29. C4×#532C2semidirect
694. C4×D4#41semidirect

Maximal subgroups

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

subgroupindex
#596542
#594272
#592332
#592202
#460432
#456092
#401422
#398542
#396082
#394692
#391912
#391242
#389642
#389202
#379692
#376362
#373502
#366452
#366312
#362092
#361942
#361872
#361272
#361222
D4×C4⋊Q82
#352922
#352792
#344852
C4×#5322