Finite Group Databasebeta

← #7695717

Subgroups — #7695717

Order 512.

4949 conjugacy classes of subgroups.

The subgroup lattice has 1294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59919C213yesmaximal, complemented
2#59460C213yesmaximal, complemented
3#59322C213yesmaximal, complemented
4#52237C213yesmaximal, complemented
5#45359C213yesmaximal, complemented
6#45180C213yesmaximal, complemented
7#45086C213yesmaximal, complemented
8#44997C213yesmaximal, complemented
9#44966C213yesmaximal, complemented
10#44908C213yesmaximal, complemented
11#39688C213yesmaximal, complemented
12#39674C213yesmaximal, complemented
13#39603C213yesmaximal, complemented
14#38964C213yesmaximal, complemented
15#38104C213yesmaximal, complemented
16#37874C213yesmaximal, complemented
17Q8×#125C211yesmaximal, characteristic, complemented
18Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
19#36431C211yesmaximal, characteristic, complemented
20#35971C211yesmaximal, characteristic, complemented
21#35937C211yesmaximal, characteristic, complemented
22#35845C211yesmaximal, characteristic, complemented
23#35816C211yesmaximal, characteristic, complemented
24#35786C211yesmaximal, characteristic, complemented
25#35748C211yesmaximal, characteristic, complemented
26#34337C211yesmaximal, characteristic, complemented
27#34312C211yesmaximal, characteristic
28#34294C211yesmaximal, characteristic
29#34293C211yesmaximal, characteristic
30#34249C211yesmaximal, characteristic, complemented
31#34183C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C2×#520C2211yescharacteristic
38C2×#519C2211yescharacteristic
39C2×#519C2211yescharacteristic
40C2×C4×#41C2211yescharacteristic
41C22×C4×Q8C2211yescharacteristic
42#2859C2213yes—
43#2857C2213yes—
44#2851C2213yes—
45#2807C2216yes—
46#2792C2213yes—
47#2792C2216yes—
48#2791C2213yes—
49#2791C2216yes—
50#2790C2213yes—
51#2790C2216yes—
52#2788C2216yes—
53#2788C2213yes—
54#2784C2213yes—
55#2780C2216yes—
56#2780C2213yes—
57#2774C2213yes—
58#2768C2213yes—
59#2768C2213yes—
60#2768C2216yes—
61#2768C2216yes—
62#2763C2213yes—
63#2763C2216yes—
64#2755C2213yes—
65#2748C2213yes—
66#2742C2213yes—
67#2732C2216yes—
68#2729C2216yes—
69#2720C2211yescharacteristic
70#2720C2216yes—
71#2720C2216yes—
72#2704C2213yes—
73#2692C2213yes—
74#2660C2213yes—
75#2647C2213yes—
76#2629C2213yes—
77#2629C2213yes—
78#2628C2213yes—
79#2628C2213yes—
80#2589C2216yes—
81#2587C2216yes—
82#2587C2216yes—
83#2584C2213yes—
84#2583C2216yes—
85#2583C2216yes—
86#2583C2216yes—
87#2582C2213yes—
88#2582C2213yes—
89#2581C2213yes—
90#2580C2216yes—
91#2580C2213yes—
92#2580C2213yes—
93#2579C2216yes—
94#2574C2216yes—
95#2574C2216yes—
96#2571C2213yes—
97#2570C2213yes—
98#2567C2213yes—
99#2567C2216yes—
100#2567C2213yes—
101#2566C2213yes—
102#2566C2213yes—
103#2565C2213yes—
104#2556C2216yes—
105#2552C2213yes—
106#2552C2213yes—
107#2551C2213yes—
108#2551C2213yes—
109#2550C2213yes—
110#2550C2213yes—
111#2546C2213yes—
112#2542C2213yes—
113#2538C2213yes—
114#2522C2216yes—
115#2520C2216yes—
116#2509C2213yes—
117#2508C2213yes—
118#2508C2216yes—
119#2508C2213yes—
120#2507C2213yes—
121#2507C2213yes—
122#2507C2213yes—
123#2507C2213yes—
124#2507C2213yes—
125#2507C2216yes—
126#2473C2216yes—
127#2465C2216yes—
128#2454C2213yes—
129#2454C2213yes—
130#2453C2213yes—
131#2453C2213yes—
132#2453C2213yes—
133#2452C2213yes—
134#2452C2216yes—
135#2452C2213yes—
136#2452C2213yes—
137#2452C2213yes—
138#2451C2213yes—
139#2451C2213yes—
140#2451C2213yes—
141#2449C2216yes—
142#2442C2213yes—
143#2441C2213yes—
144#2441C2213yes—
145#2441C2213yes—
146#2441C2213yes—
147#2440C2216yes—
148#2440C2213yes—
149#2440C2213yes—
150#2440C2213yes—
151#2440C2213yes—
152#2440C2213yes—
153#2439C2213yes—
154#2439C2213yes—
155#2402C2213yes—
156#2399C2213yes—
157#2396C2213yes—
158#2396C2213yes—
159#2396C2213yes—
160#2396C2213yes—
161#2370C2213yes—
162#2370C2213yes—
163#2367C2213yes—
164#2367C2213yes—
165#2367C2213yes—
166#2365C2213yes—
167#2363C2213yes—
168#2363C2213yes—
169#2362C2213yes—
170#2361C2213yes—
171#2360C2213yes—
172#2360C2216yes—
173#2360C2213yes—
174#2354C2213yes—
175#2352C2213yes—
176#2351C2211yescharacteristic
177#2351C2211yescharacteristic
178#2351C2213yes—
179#2351C2211yescharacteristic
180#2351C2211yescharacteristic
181#2351C2211yescharacteristic
182#2351C2213yes—
183Q8×C4⋊C4C2211yescharacteristic
184Q8×C4⋊C4C2211yescharacteristic
185Q8×C4⋊C4C2213yes—
186Q8×C4⋊C4C2213yes—
187Q8×C4⋊C4C2211yescharacteristic
188Q8×C4⋊C4C2211yescharacteristic
189Q8×C4⋊C4C2211yescharacteristic
190Q8×C4⋊C4C2211yescharacteristic
191Q8×C4⋊C4C2211yescharacteristic
192Q8×C4⋊C4C2211yescharacteristic
193Q8×C4⋊C4C2211yescharacteristic
194Q8×C4⋊C4C2211yescharacteristic
195Q8×C4⋊C4C2213yes—
196Q8×C4⋊C4C2211yescharacteristic
197D4×C4⋊C4C2213yes—
198D4×C4⋊C4C2213yes—
199D4×C4⋊C4C2213yes—
200D4×C4⋊C4C2213yes—
201D4×C4⋊C4C2213yes—
202#2341C2211yescharacteristic
203#2341C2211yescharacteristic
204#2341C2211yescharacteristic
205Q8×C22⋊C4C2211yescharacteristic
206Q8×C22⋊C4C2211yescharacteristic
207Q8×C22⋊C4C2211yescharacteristic
208#2330C2213yes—
209#2330C2213yes—
210#2326C2213yes—
211#2326C2213yes—
212#2324C2213yes—
213#2324C2213yes—
214#2323C2213yes—
215#2323C2213yes—
216#2317C2213yes—
217#2317C2213yes—
218#2317C2213yes—
219#2317C2213yes—
220C4×C4⋊Q8C2213yes—
221C4×#125C2213yes—
222C4×#124C2213yes—
223C4×C22⋊Q8C2213yes—
224C4×C22⋊Q8C2213yes—
225C4×C22⋊Q8C2213yes—
226C4×#121C2213yes—
227#2296C2213yes—
228#2296C2213yes—
229#2295C2213yes—
230#2293C2213yes—
231#2290C2213yes—
232#2290C2213yes—
233#2285C2213yes—
234C2×#384C2213yes—
235#2276C2211yescharacteristic
236#2276C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240Q82—44no—
241#557—28no—
242#557—44no—
243#548Q8116yescomplemented
244C2×C4⋊Q8C2313yes—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2316yes—
250C2×#125C2311yescharacteristic
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2316yes—
256C2×#124C2313yes—
257C2×C22⋊Q8C2313yes—
258C2×C22⋊Q8C2311yescharacteristic
259C2×C22⋊Q8C2316yes—
260C2×C22⋊Q8C2316yes—
261C2×C22⋊Q8C2316yes—
262C2×C22⋊Q8C2316yes—
263C2×C22⋊Q8C2313yes—
264C2×#121C2313yes—
265#520—44no—
266#520—44no—
267#519—28no—
268#519—44no—
269C4×#41—28no—
270C2×C4×Q8—44no—
271C2×C4×Q8C2313yes—
272C2×C4×Q8C2313yes—
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2313yes—
285C2×C4×Q8C2313yes—
286C2×C4×Q8C2313yes—
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2313yes—
289C2×C4×Q8C2313yes—
290C2×C4×Q8C2313yes—
291C2×C4×Q8C2316yes—
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2311yescharacteristic
294C2×C4×D4C2313yes—
295C2×C4×D4C2313yes—
296C2×C4×D4C2313yes—
297C2×C4×D4C2313yes—
298C2×C4×D4C2313yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2316yes—
301C2×C4×D4C2313yes—
302C2×#117C2313yes—
303C2×#117C2313yes—
304C2×#117C2313yes—
305C2×#117C2313yes—
306C2×#117C2313yes—
307C2×#117C2313yes—
308C2×#117C2313yes—
309C22×C4⋊C4C2313yes—
310C22×C4⋊C4C2313yes—
311C22×C4⋊C4C2313yes—
312C22×C4⋊C4C2316yes—
313C22×C4⋊C4C2316yes—
314C22×C42C2313yes—
315C22×C42C2313yes—
316#400C2316yes—
317#400C2313yes—
318#400C2313yes—
319#400C2316yes—
320#400C2316yes—
321#400C2313yes—
322#400C2313yes—
323#400C2313yes—
324#400C2311yescharacteristic
325#400C2313yes—
326#400C2313yes—
327#399C2316yes—
328#399C2316yes—
329#399C2316yes—
330#399C2313yes—
331#399C2311yescharacteristic
332#399C2313yes—
333#399C2313yes—
334#398C2313yes—
335#398C2316yes—
336#398C2313yes—
337#398C2313yes—
338#398C2316yes—
339#398C2316yes—
340#398C2316yes—
341#398C2313yes—
342#398C2316yes—
343#398C2316yes—
344#398C2316yes—
345#398C2316yes—
346#398C2313yes—
347#398C2313yes—
348#398C2316yes—
349#398C2313yes—
350#398C2311yescharacteristic
351#398C2313yes—
352#398C2313yes—
353#398C2313yes—
354#398C2313yes—
355#398C2313yes—
356#398C2313yes—
357#398C2313yes—
358#398C2313yes—
359#398C2316yes—
360#398C2316yes—
361#396C2313yes—
362#396C2316yes—
363#396C2316yes—
364#396C2316yes—
365#396C2313yes—
366#396C2316yes—
367#396C2313yes—
368#396C2313yes—
369#396C2316yes—
370#396C2311yescharacteristic
371#396C2313yes—
372#396C2313yes—
373#396C2313yes—
374#395C2316yes—
375#395C2316yes—
376#395C2313yes—
377#395C2313yes—
378#395C2316yes—
379#395C2316yes—
380#395C2313yes—
381#395C2313yes—
382#395C2316yes—
383#395C2316yes—
384#395C2311yescharacteristic
385#395C2313yes—
386#395C2311yescharacteristic
387#395C2313yes—
388#393C2313yes—
389#393C2316yes—
390#393C2316yes—
391#393C2313yes—
392#393C2313yes—
393#393C2313yes—
394#391C2313yes—
395#391C2313yes—
396#391C2313yes—
397#391C2313yes—
398#391C2313yes—
399#391C2313yes—
400#391C2316yes—
401#391C2313yes—
402#391C2313yes—
403#391C2316yes—
404#391C2313yes—
405#391C2313yes—
406#391C2316yes—
407#390C2313yes—
408#390C2313yes—
409#390C2313yes—
410#390C2313yes—
411#390C2313yes—
412#390C2316yes—
413#390C2313yes—
414#390C2313yes—
415#390C2313yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2316yes—
420#389C2313yes—
421#389C2313yes—
422#389C2313yes—
423#389C2316yes—
424#389C2316yes—
425#389C2316yes—
426#389C2316yes—
427#389C2316yes—
428#389C2316yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2316yes—
435#389C2316yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2316yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2316yes—
457#389C2313yes—
458#389C2313yes—
459#389C2316yes—
460#389C2316yes—
461#389C2313yes—
462#389C2313yes—
463#389C2313yes—
464#389C2316yes—
465#389C2313yes—
466#389C2313yes—
467#389C2316yes—
468#389C2313yes—
469#389C2313yes—
470#389C2313yes—
471#389C2313yes—
472#389C2313yes—
473#389C2313yes—
474#389C2311yescharacteristic
475#388C2316yes—
476#388C2316yes—
477#388C2316yes—
478#388C2316yes—
479#388C2316yes—
480#388C2316yes—
481#388C2313yes—
482#388C2316yes—
483#388C2313yes—
484#388C2313yes—
485#388C2313yes—
486#388C2313yes—
487#388C2313yes—
488#388C2311yescharacteristic
489#388C2311yescharacteristic
490#387C2313yes—
491#387C2313yes—
492#387C2313yes—
493#387C2313yes—
494#387C2316yes—
495#387C2316yes—
496#387C2316yes—
497#387C2316yes—
498#387C2316yes—
499#387C2316yes—
500#387C2313yes—
501#387C2316yes—
502#387C2316yes—
503#387C2313yes—
504#387C2313yes—
505#387C2316yes—
506#387C2313yes—
507#387C2313yes—
508#387C2316yes—
509#387C2313yes—
510#387C2313yes—
511#387C2313yes—
512#387C2313yes—
513#387C2313yes—
514#387C2311yescharacteristic
515#387C2313yes—
516#386C2313yes—
517#386C2316yes—
518#386C2313yes—
519#386C2313yes—
520#386C2313yes—
521#385C2313yes—
522#385C2316yes—
523#385C2316yes—
524#385C2316yes—
525#385C2316yes—
526#385C2313yes—
527#385C2313yes—
528#385C2316yes—
529#385C2316yes—
530#385C2316yes—
531#385C2316yes—
532#385C2316yes—
533#385C2313yes—
534#385C2316yes—
535#385C2316yes—
536#385C2316yes—
537#385C2313yes—
538#385C2313yes—
539#385C2316yes—
540#385C2313yes—
541#385C2316yes—
542#385C2316yes—
543#385C2313yes—
544#385C2313yes—
545#385C2313yes—
546#385C2311yescharacteristic
547#385C2311yescharacteristic
548#384C2313yes—
549#384C2313yes—
550#384C2313yes—
551#384C2313yes—
552#384C2316yes—
553#384C2316yes—
554#384C2313yes—
555#384C2313yes—
556#384C2313yes—
557#384C2313yes—
558#384C2313yes—
559#384C2313yes—
560#384C2313yes—
561#384C2311yescharacteristic
562#384C2313yes—
563#382C2313yes—
564#382C2313yes—
565#382C2313yes—
566#382C2313yes—
567#382C2313yes—
568#382C2316yes—
569#382C2313yes—
570#382C2313yes—
571#382C2316yes—
572#382C2313yes—
573#380C2313yes—
574#380C2316yes—
575#380C2313yes—
576#380C2313yes—
577#380C2313yes—
578#380C2313yes—
579#380C2313yes—
580#380C2313yes—
581#380C2313yes—
582#380C2313yes—
583#380C2313yes—
584#380C2313yes—
585#380C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2316yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2316yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2316yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2316yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C4⋊C4C2313yes—
610C4×C4⋊C4C2313yes—
611C4×C4⋊C4C2313yes—
612C4×C4⋊C4C2313yes—
613C4×C4⋊C4C2313yes—
614C4×C4⋊C4C2313yes—
615C4×C22⋊C4C2316yes—
616C4×C22⋊C4C2316yes—
617C4×C22⋊C4C2316yes—
618C4×C22⋊C4C2316yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624C4×C22⋊C4C2313yes—
625#376C2313yes—
626#376C2313yes—
627C43C2313yes—
628C2×#41—24no—
629C2×#41—24no—
630C2×#41C2×Q818yes—
631C22×Q8—24no—
632C22×Q8—24no—
633C22×Q8C2×Q818yes—
634C22×Q8C2413yes—
635C22×Q8C2413yes—
636C22×Q8C2411yescharacteristic
637C22×Q8C2413yes—
638C22×Q8C2416yes—
639C22×Q8C2411yescharacteristic
640C22×D4C2413yes—
641C22×D4C2413yes—
642C23×C4C2413yes—
643C23×C4C2413yes—
644C23×C4C2413yes—
645C23×C4C2413yes—
646C23×C4C2411yescharacteristic
647C23×C4C2416yes—
648C23×C4C2416yes—
649C23×C4C2413yes—
650C4⋊Q8—212no—
651C4⋊Q8—46no—
652C4⋊Q8—46no—
653C4⋊Q8—46no—
654C4⋊Q8—46no—
655C4⋊Q8—86no—
656#125—212no—
657#125—24no—
658#125—212no—
659#125—46no—
660#125—46no—
661#125—86no—
662#124C2×Q8124yes—
663C22⋊Q8—212no—
664C22⋊Q8—24no—
665C22⋊Q8—86no—
666C22⋊Q8—86no—
667C22⋊Q8—86no—
668C22⋊Q8—86no—
669C22⋊Q8C2×Q8124yes—
670#121C2×Q8124yes—
671C4×Q8—24no—
672C4×Q8—24no—
673C4×Q8—24no—
674C4×Q8—24no—
675C4×Q8—24no—
676C4×Q8—24no—
677C4×Q8—24no—
678C4×Q8—24no—
679C4×Q8—24no—
680C4×Q8—24no—
681C4×Q8—24no—
682C4×Q8—212no—
683C4×Q8—212no—
684C4×Q8—212no—
685C4×Q8—46no—
686C4×Q8—46no—
687C4×Q8—46no—
688C4×Q8—46no—
689C4×Q8—46no—
690C4×Q8—46no—
691C4×Q8—86no—
692C4×Q8C2×Q818yes—
693C4×Q8#4118yes—
694C4×D4—212no—
695C4×D4—212no—
696C4×D4—46no—
697C4×D4—46no—
698C4×D4—46no—
699C4×D4—46no—
700C4×D4—86no—
701C4×D4C2×Q8124yes—
702#117—212no—
703#117—212no—
704#117—212no—
705#117—46no—
706#117—46no—
707#117—46no—
708#117—46no—
709C2×C4⋊C4—46no—
710C2×C4⋊C4—46no—
711C2×C4⋊C4—46no—
712C2×C4⋊C4—86no—
713C2×C4⋊C4—86no—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2411yescharacteristic
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2416yes—
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2416yes—
747C2×C4⋊C4C2416yes—
748C2×C4⋊C4C2416yes—
749C2×C4⋊C4C2416yes—
750C2×C4⋊C4C2416yes—
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2411yescharacteristic
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2416yes—
756C2×C4⋊C4C2411yescharacteristic
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2416yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2416yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2416yes—
771C2×C4⋊C4C2416yes—
772C2×C4⋊C4C2416yes—
773C2×C4⋊C4C2416yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2413yes—
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2413yes—
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2416yes—
785C2×C4⋊C4C2413yes—
786C2×C4⋊C4C2413yes—
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2413yes—
790C2×C4⋊C4C2411yescharacteristic
791C2×C22⋊C4C2411yescharacteristic
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2416yes—
794C2×C22⋊C4C2411yescharacteristic
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2411yescharacteristic
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2411yescharacteristic
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2416yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2416yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2411yescharacteristic
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2416yes—
815C2×C22⋊C4C2411yescharacteristic
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2416yes—
818C2×C42—212no—
819C2×C42—46no—
820C2×C42C2413yes—
821C2×C42C2413yes—
822C2×C42C2413yes—
823C2×C42C2413yes—
824C2×C42C2413yes—
825C2×C42C2413yes—
826C2×C42C2413yes—
827C2×C42C2416yes—
828C2×C42C2413yes—
829C2×C42C2413yes—
830C2×C42C2413yes—
831C2×C42C2413yes—
832C2×C42C2413yes—
833C2×C42C2411yescharacteristic
834C2×C42C2411yescharacteristic
835C2×C42C2416yes—
836C2×C42C2416yes—
837C2×C42C2413yes—
838C2×C42C2413yes—
839C2×C42C2413yes—
840C2×C42C2416yes—
841C2×C42C2413yes—
842C2×C42C2413yes—
843C2×C42C2413yes—
844C2×C42C2413yes—
845#95C2411yescharacteristic
846#95C2411yescharacteristic
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2411yescharacteristic
854#95C2413yes—
855#95C2411yescharacteristic
856#95C2411yescharacteristic
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2416yes—
865#95C2416yes—
866#95C2416yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2411yescharacteristic
872#95C2413yes—
873#95C2413yes—
874#95C2411yescharacteristic
875#95C2413yes—
876#95C2416yes—
877#95C2411yescharacteristic
878#95C2413yes—
879#95C2411yescharacteristic
880#95C2411yescharacteristic
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2416yes—
885#95C2413yes—
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2416yes—
891#95C2413yes—
892#95C2413yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2416yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2416yes—
905#95C2416yes—
906C24C2511yescharacteristic
907C24C2513yes—
908#41—232no—
909C2×Q8—232no—
910C2×Q8—26no—
911C2×Q8—26no—
912C2×Q8—26no—
913C2×Q8—26no—
914C2×Q8—22no—
915C2×Q8—41no—
916C2×Q8—43no—
917C2×Q8—41no—
918C2×Q8—43no—
919C2×Q8—43no—
920C2×Q8—43no—
921C2×Q8—46no—
922C2×Q8—46no—
923C2×Q8—46no—
924C2×Q8C22×Q8112yes—
925C2×Q8C22×Q814yes—
926C2×Q8C2×#4114yes—
927C2×Q8H(5,𝔽2)14yes—
928C2×D4—26no—
929C2×D4—26no—
930C2×D4—43no—
931C2×D4—43no—
932C2×D4C22×Q8112yes—
933C2×D4C22×Q8112yes—
934C22×C4—26no—
935C22×C4—26no—
936C22×C4—26no—
937C22×C4—26no—
938C22×C4—26no—
939C22×C4—26no—
940C22×C4—26no—
941C22×C4—22no—
942C22×C4—41no—
943C22×C4—43no—
944C22×C4—43no—
945C22×C4—41no—
946C22×C4—43no—
947C22×C4—43no—
948C22×C4—43no—
949C22×C4—43no—
950C22×C4—46no—
951C22×C4—46no—
952C22×C4—46no—
953C22×C4—46no—
954C22×C4—46no—
955C22×C4—46no—
956C22×C4C22×Q8112yes—
957C22×C4C22×Q8112yes—
958C22×C4C2511yescharacteristic
959C22×C4C2513yes—
960C22×C4C2511yescharacteristic
961C22×C4C2511yescharacteristic
962C22×C4C2511yescharacteristic
963C22×C4C2511yescharacteristic
964C22×C4C2511yescharacteristic
965C22×C4C2513yes—
966C22×C4C2513yes—
967C22×C4C2513yes—
968C22×C4C2511yescharacteristic
969C22×C4C2513yes—
970C22×C4C2513yes—
971C22×C4C2513yes—
972C22×C4C2511yescharacteristic
973C22×C4C2513yes—
974C22×C4C2513yes—
975C22×C4C2513yes—
976C22×C4C2513yes—
977C22×C4C2511yescharacteristic
978C22×C4C2513yes—
979C22×C4C2513yes—
980C22×C4C2511yescharacteristic
981C22×C4C2513yes—
982C22×C4C2511yescharacteristic
983C22×C4C2511yescharacteristic
984C22×C4C2511yescharacteristic
985C22×C4C2511yescharacteristic
986C22×C4C2513yes—
987C4⋊C4—26no—
988C4⋊C4—26no—
989C4⋊C4—26no—
990C4⋊C4—26no—
991C4⋊C4—22no—
992C4⋊C4—26no—
993C4⋊C4—26no—
994C4⋊C4—26no—
995C4⋊C4—26no—
996C4⋊C4—212no—
997C4⋊C4—26no—
998C4⋊C4—26no—
999C4⋊C4—26no—
1000C4⋊C4—26no—
1001C4⋊C4—26no—
1002C4⋊C4—26no—
1003C4⋊C4—26no—
1004C4⋊C4—26no—
1005C4⋊C4—26no—
1006C4⋊C4—22no—
1007C4⋊C4—22no—
1008C4⋊C4—22no—
1009C4⋊C4—22no—
1010C4⋊C4—22no—
1011C4⋊C4—22no—
1012C4⋊C4—22no—
1013C4⋊C4—43no—
1014C4⋊C4—43no—
1015C4⋊C4—46no—
1016C4⋊C4—43no—
1017C4⋊C4—43no—
1018C4⋊C4—43no—
1019C4⋊C4—43no—
1020C4⋊C4—46no—
1021C4⋊C4—46no—
1022C4⋊C4—46no—
1023C4⋊C4—46no—
1024C4⋊C4—43no—
1025C4⋊C4—46no—
1026C4⋊C4—43no—
1027C4⋊C4—41no—
1028C4⋊C4—41no—
1029C4⋊C4—41no—
1030C4⋊C4—43no—
1031C4⋊C4—43no—
1032C4⋊C4—43no—
1033C4⋊C4—41no—
1034C4⋊C4—41no—
1035C4⋊C4—43no—
1036C4⋊C4—43no—
1037C4⋊C4—46no—
1038C4⋊C4—41no—
1039C4⋊C4—43no—
1040C4⋊C4—43no—
1041C4⋊C4—43no—
1042C4⋊C4—43no—
1043C4⋊C4—43no—
1044C4⋊C4—43no—
1045C4⋊C4—46no—
1046C4⋊C4—43no—
1047C4⋊C4—46no—
1048C4⋊C4—43no—
1049C4⋊C4—43no—
1050C4⋊C4—43no—
1051C4⋊C4—43no—
1052C4⋊C4—46no—
1053C4⋊C4—46no—
1054C4⋊C4—46no—
1055C4⋊C4—46no—
1056C4⋊C4—43no—
1057C4⋊C4—43no—
1058C4⋊C4—43no—
1059C4⋊C4—43no—
1060C4⋊C4C22×Q8112yes—
1061C4⋊C4C22×Q8112yes—
1062C4⋊C4C2×#41112yes—
1063C4⋊C42−1+414yes—
1064C22⋊C4—26no—
1065C22⋊C4—22no—
1066C22⋊C4—212no—
1067C22⋊C4—26no—
1068C22⋊C4—22no—
1069C22⋊C4—26no—
1070C22⋊C4—22no—
1071C22⋊C4—46no—
1072C22⋊C4—43no—
1073C22⋊C4—41no—
1074C22⋊C4—41no—
1075C22⋊C4—43no—
1076C22⋊C4—43no—
1077C22⋊C4—43no—
1078C22⋊C4—43no—
1079C22⋊C4—43no—
1080C22⋊C4—43no—
1081C22⋊C4—46no—
1082C22⋊C4—43no—
1083C22⋊C4—43no—
1084C22⋊C4—43no—
1085C22⋊C4—43no—
1086C22⋊C4—46no—
1087C22⋊C4—43no—
1088C22⋊C4C22×Q814yes—
1089C22⋊C4C22×Q8112yes—
1090C22⋊C4C22×Q8124yes—
1091C42—22no—
1092C42—26no—
1093C42—26no—
1094C42—212no—
1095C42—26no—
1096C42—26no—
1097C42—26no—
1098C42—26no—
1099C42—26no—
1100C42—26no—
1101C42—26no—
1102C42—26no—
1103C42—26no—
1104C42—26no—
1105C42—22no—
1106C42—43no—
1107C42—43no—
1108C42—43no—
1109C42—46no—
1110C42—46no—
1111C42—43no—
1112C42—46no—
1113C42—43no—
1114C42C22×Q8112yes—
1115C42C2×#41112yes—
1116C23—21no—
1117C23—23no—
1118C23—21no—
1119C23—23no—
1120C23—23no—
1121C23—21no—
1122C23—21no—
1123C23—23no—
1124C23—23no—
1125C23—21no—
1126C23—23no—
1127C23—21no—
1128C23C23×Q816yes—
1129C23C23×Q812yes—
1130C23C2611yescharacteristic
1131Q8—224no—
1132Q8—412no—
1133Q8—44no—
1134Q8—86no—
1135Q8—166no—
1136Q8#554116yes—
1137D4—224no—
1138D4—412no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—23no—
1143C2×C4—21no—
1144C2×C4—23no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—23no—
1148C2×C4—23no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—23no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—23no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—224no—
1158C2×C4—224no—
1159C2×C4—21no—
1160C2×C4—23no—
1161C2×C4—21no—
1162C2×C4—23no—
1163C2×C4—23no—
1164C2×C4—23no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—23no—
1172C2×C4—23no—
1173C2×C4—23no—
1174C2×C4—23no—
1175C2×C4—23no—
1176C2×C4—23no—
1177C2×C4—23no—
1178C2×C4—21no—
1179C2×C4—23no—
1180C2×C4—23no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—23no—
1187C2×C4—23no—
1188C2×C4—23no—
1189C2×C4—23no—
1190C2×C4—23no—
1191C2×C4—23no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—23no—
1196C2×C4—23no—
1197C2×C4—23no—
1198C2×C4—23no—
1199C2×C4—23no—
1200C2×C4—23no—
1201C2×C4—23no—
1202C2×C4—23no—
1203C2×C4—23no—
1204C2×C4—21no—
1205C2×C4—23no—
1206C2×C4—21no—
1207C2×C4—23no—
1208C2×C4—21no—
1209C2×C4—23no—
1210C2×C4—23no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—23no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—412no—
1217C2×C4—412no—
1218C2×C4—44no—
1219C2×C4—86no—
1220C2×C4—166no—
1221C2×C4—166no—
1222C2×C4C23×Q812yes—
1223C2×C4C23×Q816yes—
1224C2×C4C23×Q816yes—
1225C2×C4C23×Q812yes—
1226C2×C4C23×Q816yes—
1227C2×C4C22×#4116yes—
1228C2×C4C22×#4112yes—
1229C2×C4C22×#4116yes—
1230C2×C4C2×H(5,𝔽2)16yes—
1231C2×C4C2×2−1+412yes—
1232C2×C4C2×2−1+412yes—
1233C2×C4C2×2−1+412yes—
1234C22—22no—
1235C22—26no—
1236C22—22no—
1237C22—26no—
1238C22—22no—
1239C22—26no—
1240C22—43no—
1241C22—41no—
1242C22—41no—
1243C22—43no—
1244C22—43no—
1245C22—41no—
1246C22—41no—
1247C22—43no—
1248C22C24×Q811yescharacteristic
1249C22C23×#4111yescharacteristic
1250C22C22×H(5,𝔽2)11yescharacteristic
1251C22C22×2−1+411yescharacteristic
1252C22H(7,𝔽2)11yescharacteristic
1253C22H(7,𝔽2)11yescharacteristic
1254C222−1+611yescharacteristic
1255C4—22no—
1256C4—22no—
1257C4—26no—
1258C4—22no—
1259C4—22no—
1260C4—26no—
1261C4—22no—
1262C4—22no—
1263C4—26no—
1264C4—41no—
1265C4—43no—
1266C4—43no—
1267C4—43no—
1268C4—43no—
1269C4—43no—
1270C4—43no—
1271C4—41no—
1272C4—43no—
1273C4—43no—
1274C4—41no—
1275C4—43no—
1276C4—43no—
1277C4—41no—
1278C4—41no—
1279C4—43no—
1280C4—41no—
1281C4—41no—
1282C4—41no—
1283C4C2×#554112yes—
1284C2—42no—
1285C2—46no—
1286C2C22×#55411yescharacteristic
1287C2#6285111yescharacteristic
1288C2#6285411yescharacteristic
1289C2#6291311yescharacteristic
1290C2Q8×2−1+411yescharacteristic
1291C2#6300011yescharacteristic
1292C2#6306611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#548C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59919C2semidirect
2. #59460C2semidirect
3. #59322C2semidirect
4. #52237C2semidirect
5. #45359C2semidirect
6. #45180C2semidirect
7. #45086C2semidirect
8. #44997C2semidirect
9. #44966C2semidirect
10. #44908C2semidirect
11. #39688C2semidirect
12. #39674C2semidirect
13. #39603C2semidirect
14. #38964C2semidirect
15. #38104C2semidirect
16. #37874C2semidirect
17. Q8×#125C2semidirect
18. Q8×C22⋊Q8C2semidirect
19. #36431C2semidirect
20. #35971C2semidirect
21. #35937C2semidirect
22. #35845C2semidirect
23. #35816C2semidirect
24. #35786C2semidirect
25. #35748C2semidirect
26. #34337C2semidirect
30. #34249C2semidirect
31. #34183C2semidirect
243. #548Q8semidirect

Maximal subgroups

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

subgroupindex
#599192
#594602
#593222
#522372
#453592
#451802
#450862
#449972
#449662
#449082
#396882
#396742
#396032
#389642
#381042
#378742
Q8×#1252
Q8×C22⋊Q82
#364312
#359712
#359372
#358452
#358162
#357862
#357482
#343372
#343122
#342942
#342932
#342492
#341832