Finite Group Databasebeta

← #7695807

Subgroups — #7695807

Order 512.

4317 conjugacy classes of subgroups.

The subgroup lattice has 1181 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59666C213yesmaximal
2#59464C213yesmaximal
3#59456C213yesmaximal
4#52274C213yesmaximal
5#45281C213yesmaximal
6#45280C213yesmaximal
7#44954C213yesmaximal
8#44953C213yesmaximal
9#44949C213yesmaximal
10#44949C213yesmaximal
11#39750C213yesmaximal
12#39681C213yesmaximal
13#39680C213yesmaximal
14#39643C213yesmaximal
15#39177C213yesmaximal
16#39176C213yesmaximal
17#36475C211yesmaximal, characteristic
18#36475C211yesmaximal, characteristic
19#36474C211yesmaximal, characteristic
20#35971C211yesmaximal, characteristic
21#35971C211yesmaximal, characteristic
22#35971C211yesmaximal, characteristic
23#35957C211yesmaximal, characteristic
24#35937C211yesmaximal, characteristic
25#35868C211yesmaximal, characteristic
26#34336C211yesmaximal, characteristic
27#34336C211yesmaximal, characteristic
28#34335C211yesmaximal, characteristic
29#34335C211yesmaximal, characteristic
30#34335C211yesmaximal, characteristic
31#34335C211yesmaximal, characteristic
32C2×Q82C2211yescharacteristic
33C2×Q82C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#557C2211yescharacteristic
36#2864C2213yes—
37#2864C2213yes—
38#2862C2213yes—
39#2809C2216yes—
40#2809C2213yes—
41#2806C2216yes—
42#2806C2213yes—
43#2805C2213yes—
44#2802C2216yes—
45#2802C2213yes—
46#2802C2213yes—
47#2799C2216yes—
48#2799C2216yes—
49#2799C2211yescharacteristic
50#2799C2213yes—
51#2799C2216yes—
52#2799C2216yes—
53#2799C2216yes—
54#2791C2213yes—
55#2791C2216yes—
56#2791C2213yes—
57#2774C2216yes—
58#2774C2213yes—
59#2774C2213yes—
60#2755C2213yes—
61#2755C2213yes—
62#2755C2216yes—
63#2755C2216yes—
64#2726C2213yes—
65#2713C2213yes—
66#2713C2216yes—
67#2713C2213yes—
68#2660C2213yes—
69#2660C2213yes—
70#2647C2213yes—
71#2647C2213yes—
72#2647C2213yes—
73#2647C2213yes—
74#2590C2216yes—
75#2588C2216yes—
76#2588C2216yes—
77#2588C2216yes—
78#2585C2216yes—
79#2585C2216yes—
80#2584C2213yes—
81#2584C2213yes—
82#2582C2216yes—
83#2581C2216yes—
84#2571C2213yes—
85#2571C2213yes—
86#2571C2213yes—
87#2570C2213yes—
88#2570C2213yes—
89#2570C2213yes—
90#2570C2213yes—
91#2570C2213yes—
92#2570C2213yes—
93#2570C2213yes—
94#2570C2213yes—
95#2568C2216yes—
96#2567C2213yes—
97#2567C2213yes—
98#2565C2216yes—
99#2565C2216yes—
100#2552C2213yes—
101#2552C2213yes—
102#2552C2213yes—
103#2551C2213yes—
104#2551C2213yes—
105#2550C2213yes—
106#2550C2213yes—
107#2550C2213yes—
108#2550C2213yes—
109#2550C2213yes—
110#2550C2213yes—
111#2550C2213yes—
112#2550C2213yes—
113#2546C2213yes—
114#2546C2213yes—
115#2520C2216yes—
116#2520C2216yes—
117#2520C2216yes—
118#2511C2216yes—
119#2509C2213yes—
120#2509C2213yes—
121#2509C2213yes—
122#2509C2213yes—
123#2509C2213yes—
124#2509C2213yes—
125#2508C2213yes—
126#2508C2213yes—
127#2508C2213yes—
128#2508C2213yes—
129#2508C2213yes—
130#2508C2213yes—
131#2508C2213yes—
132#2508C2213yes—
133#2507C2213yes—
134#2507C2213yes—
135#2507C2213yes—
136#2507C2213yes—
137#2507C2213yes—
138#2507C2213yes—
139#2506C2213yes—
140#2506C2213yes—
141#2506C2213yes—
142#2506C2213yes—
143#2462C2216yes—
144#2453C2216yes—
145#2453C2216yes—
146#2451C2216yes—
147#2451C2216yes—
148#2446C2216yes—
149#2402C2213yes—
150#2402C2213yes—
151#2402C2213yes—
152#2402C2213yes—
153#2399C2213yes—
154#2399C2213yes—
155#2370C2213yes—
156#2370C2213yes—
157#2370C2213yes—
158#2370C2213yes—
159#2369C2213yes—
160#2369C2213yes—
161#2369C2213yes—
162#2369C2213yes—
163#2369C2213yes—
164#2369C2213yes—
165#2365C2213yes—
166#2365C2213yes—
167#2365C2213yes—
168#2365C2213yes—
169#2365C2213yes—
170#2365C2213yes—
171#2365C2213yes—
172#2365C2213yes—
173#2355C2213yes—
174#2355C2213yes—
175#2355C2213yes—
176#2355C2213yes—
177#2355C2213yes—
178#2355C2213yes—
179#2351C2216yes—
180#2351C2211yescharacteristic
181#2351C2211yescharacteristic
182#2351C2211yescharacteristic
183#2351C2211yescharacteristic
184#2351C2211yescharacteristic
185#2351C2211yescharacteristic
186#2351C2211yescharacteristic
187#2351C2211yescharacteristic
188#2351C2211yescharacteristic
189#2351C2211yescharacteristic
190#2351C2211yescharacteristic
191#2351C2211yescharacteristic
192#2351C2211yescharacteristic
193#2351C2211yescharacteristic
194Q8×C4⋊C4C2211yescharacteristic
195Q8×C4⋊C4C2211yescharacteristic
196Q8×C4⋊C4C2211yescharacteristic
197Q8×C4⋊C4C2211yescharacteristic
198Q8×C4⋊C4C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202#2331C2213yes—
203#2331C2213yes—
204#2331C2213yes—
205#2331C2213yes—
206#2331C2213yes—
207#2331C2213yes—
208#2331C2213yes—
209#2331C2213yes—
210#2331C2213yes—
211#2331C2213yes—
212#2330C2213yes—
213#2330C2213yes—
214C4×C4⋊Q8C2213yes—
215C4×C4⋊Q8C2213yes—
216C4×C4⋊Q8C2213yes—
217C4×C4⋊Q8C2213yes—
218C4×C4⋊Q8C2213yes—
219C4×#125C2213yes—
220C4×#125C2213yes—
221C4×#125C2213yes—
222C4×#125C2213yes—
223#2295C2213yes—
224#2295C2213yes—
225#2295C2213yes—
226#2295C2213yes—
227#2295C2213yes—
228#2295C2213yes—
229#2276C2211yescharacteristic
230#2276C2211yescharacteristic
231#2276C2211yescharacteristic
232#2276C2211yescharacteristic
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238Q82—28no—
239Q82Q8116yescomplemented
240#557—28no—
241#557—28no—
242C2×C4⋊Q8C2313yes—
243C2×C4⋊Q8C2313yes—
244C2×C4⋊Q8C2313yes—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2316yes—
249C2×C4⋊Q8C2313yes—
250C2×C4⋊Q8C2313yes—
251C2×C4⋊Q8C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2313yes—
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#125C2316yes—
259C2×C4×Q8C2313yes—
260C2×C4×Q8C2313yes—
261C2×C4×Q8C2313yes—
262C2×C4×Q8C2311yescharacteristic
263C2×C4×Q8C2311yescharacteristic
264C2×C4×Q8C2311yescharacteristic
265C2×C4×Q8C2311yescharacteristic
266C2×C4×Q8C2311yescharacteristic
267C2×C4×Q8C2311yescharacteristic
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2316yes—
274C2×C4×Q8C2316yes—
275C2×C4×Q8C2316yes—
276C2×C4×Q8C2316yes—
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2313yes—
281C2×C4×Q8C2311yescharacteristic
282#400C2313yes—
283#400C2316yes—
284#400C2316yes—
285#400C2316yes—
286#400C2313yes—
287#400C2316yes—
288#400C2316yes—
289#400C2316yes—
290#400C2316yes—
291#400C2316yes—
292#400C2316yes—
293#400C2313yes—
294#400C2313yes—
295#400C2313yes—
296#400C2313yes—
297#400C2316yes—
298#400C2313yes—
299#400C2316yes—
300#400C2311yescharacteristic
301#400C2311yescharacteristic
302#400C2311yescharacteristic
303#400C2313yes—
304#400C2313yes—
305#400C2313yes—
306#400C2313yes—
307#400C2313yes—
308#400C2313yes—
309#398C2313yes—
310#398C2313yes—
311#398C2313yes—
312#398C2316yes—
313#398C2316yes—
314#398C2316yes—
315#398C2316yes—
316#398C2316yes—
317#398C2313yes—
318#398C2313yes—
319#398C2313yes—
320#398C2316yes—
321#398C2316yes—
322#398C2316yes—
323#398C2313yes—
324#398C2316yes—
325#398C2316yes—
326#398C2313yes—
327#398C2316yes—
328#398C2316yes—
329#398C2313yes—
330#398C2316yes—
331#398C2316yes—
332#398C2313yes—
333#398C2313yes—
334#398C2311yescharacteristic
335#398C2313yes—
336#398C2313yes—
337#398C2313yes—
338#398C2313yes—
339#398C2313yes—
340#398C2311yescharacteristic
341#398C2313yes—
342#398C2313yes—
343#398C2313yes—
344#398C2313yes—
345#398C2313yes—
346#398C2313yes—
347#395C2313yes—
348#395C2316yes—
349#395C2316yes—
350#395C2316yes—
351#395C2316yes—
352#395C2313yes—
353#395C2313yes—
354#395C2313yes—
355#395C2316yes—
356#395C2311yescharacteristic
357#395C2313yes—
358#395C2313yes—
359#395C2313yes—
360#391C2311yescharacteristic
361#391C2316yes—
362#391C2316yes—
363#391C2316yes—
364#391C2316yes—
365#391C2313yes—
366#391C2316yes—
367#391C2316yes—
368#391C2316yes—
369#391C2316yes—
370#391C2316yes—
371#391C2313yes—
372#391C2316yes—
373#391C2316yes—
374#391C2316yes—
375#391C2316yes—
376#391C2313yes—
377#391C2313yes—
378#391C2316yes—
379#391C2316yes—
380#391C2316yes—
381#391C2316yes—
382#391C2316yes—
383#391C2316yes—
384#391C2313yes—
385#391C2313yes—
386#391C2313yes—
387#391C2313yes—
388#391C2313yes—
389#391C2311yescharacteristic
390#391C2311yescharacteristic
391#391C2311yescharacteristic
392#391C2311yescharacteristic
393#389C2313yes—
394#389C2313yes—
395#389C2313yes—
396#389C2313yes—
397#389C2313yes—
398#389C2313yes—
399#389C2313yes—
400#389C2313yes—
401#389C2313yes—
402#389C2313yes—
403#389C2313yes—
404#389C2313yes—
405#389C2313yes—
406#389C2313yes—
407#389C2313yes—
408#389C2313yes—
409#389C2313yes—
410#389C2313yes—
411#389C2313yes—
412#389C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2313yes—
422#389C2313yes—
423#389C2313yes—
424#389C2313yes—
425#389C2313yes—
426#389C2313yes—
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2316yes—
433#389C2313yes—
434#389C2313yes—
435#389C2316yes—
436#389C2316yes—
437#389C2316yes—
438#389C2313yes—
439#389C2316yes—
440#389C2316yes—
441#389C2316yes—
442#389C2316yes—
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#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2316yes—
462#389C2313yes—
463#389C2313yes—
464#389C2313yes—
465#389C2313yes—
466#389C2313yes—
467#387C2311yescharacteristic
468#387C2311yescharacteristic
469#387C2313yes—
470#387C2313yes—
471#387C2313yes—
472#387C2313yes—
473#387C2313yes—
474#387C2313yes—
475#387C2316yes—
476#387C2316yes—
477#387C2313yes—
478#387C2313yes—
479#387C2313yes—
480#387C2316yes—
481#387C2316yes—
482#387C2316yes—
483#387C2316yes—
484#387C2316yes—
485#387C2316yes—
486#387C2316yes—
487#387C2316yes—
488#387C2316yes—
489#387C2316yes—
490#387C2316yes—
491#387C2316yes—
492#387C2316yes—
493#387C2316yes—
494#387C2313yes—
495#387C2316yes—
496#387C2313yes—
497#387C2313yes—
498#387C2316yes—
499#387C2316yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2313yes—
504#387C2313yes—
505#387C2313yes—
506#387C2313yes—
507#387C2313yes—
508#387C2313yes—
509#387C2313yes—
510#387C2313yes—
511#387C2316yes—
512#387C2316yes—
513#387C2316yes—
514#387C2316yes—
515#387C2313yes—
516#387C2313yes—
517#387C2316yes—
518#387C2316yes—
519#387C2313yes—
520#387C2313yes—
521#387C2313yes—
522#387C2313yes—
523#387C2313yes—
524#387C2313yes—
525#387C2311yescharacteristic
526#387C2311yescharacteristic
527#384C2313yes—
528#384C2313yes—
529#384C2313yes—
530#384C2313yes—
531#384C2313yes—
532#384C2316yes—
533#384C2313yes—
534#384C2313yes—
535#384C2313yes—
536#384C2313yes—
537#382C2313yes—
538#382C2313yes—
539#382C2313yes—
540#382C2313yes—
541#382C2316yes—
542#382C2316yes—
543#382C2316yes—
544#382C2313yes—
545#382C2313yes—
546#382C2313yes—
547#382C2313yes—
548#382C2313yes—
549#382C2313yes—
550#382C2313yes—
551#382C2313yes—
552#382C2313yes—
553#382C2313yes—
554#382C2313yes—
555#382C2313yes—
556C4×C4⋊C4C2313yes—
557C4×C4⋊C4C2316yes—
558C4×C4⋊C4C2316yes—
559C4×C4⋊C4C2313yes—
560C4×C4⋊C4C2313yes—
561C4×C4⋊C4C2313yes—
562C4×C4⋊C4C2313yes—
563C4×C4⋊C4C2313yes—
564C4×C4⋊C4C2313yes—
565C4×C4⋊C4C2313yes—
566C4×C4⋊C4C2316yes—
567C4×C4⋊C4C2313yes—
568C4×C4⋊C4C2316yes—
569C4×C4⋊C4C2313yes—
570C4×C4⋊C4C2313yes—
571C4×C4⋊C4C2313yes—
572C4×C4⋊C4C2313yes—
573C4×C4⋊C4C2313yes—
574C4×C4⋊C4C2313yes—
575C4×C4⋊C4C2316yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2316yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2316yes—
587C4×C4⋊C4C2316yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C4⋊C4C2313yes—
610C4×C4⋊C4C2313yes—
611C4×C4⋊C4C2313yes—
612C4×C4⋊C4C2313yes—
613#376C2313yes—
614#376C2313yes—
615#376C2313yes—
616#376C2313yes—
617#376C2313yes—
618#376C2313yes—
619C43C2313yes—
620C43C2313yes—
621C43C2313yes—
622C22×Q8C2411yescharacteristic
623C22×Q8C2413yes—
624C22×Q8C2416yes—
625C22×Q8C2413yes—
626C22×Q8C2416yes—
627C22×Q8C2411yescharacteristic
628C22×Q8C2411yescharacteristic
629C4⋊Q8—212no—
630C4⋊Q8—212no—
631C4⋊Q8—212no—
632C4⋊Q8—212no—
633C4⋊Q8—212no—
634C4⋊Q8—46no—
635C4⋊Q8—86no—
636C4⋊Q8C2×Q8124yes—
637C4⋊Q8C2×Q8124yes—
638C4⋊Q8C2×Q8124yes—
639#125—212no—
640#125—212no—
641#125—212no—
642#125—212no—
643#125—46no—
644#125—46no—
645#125—86no—
646C4×Q8—24no—
647C4×Q8—24no—
648C4×Q8—24no—
649C4×Q8—24no—
650C4×Q8—24no—
651C4×Q8—24no—
652C4×Q8—24no—
653C4×Q8—24no—
654C4×Q8—24no—
655C4×Q8—24no—
656C4×Q8—24no—
657C4×Q8—212no—
658C4×Q8—212no—
659C4×Q8—212no—
660C4×Q8—412no—
661C4×Q8—86no—
662C4×Q8—86no—
663C4×Q8—86no—
664C4×Q8C2×Q8124yes—
665C4×Q8C2×Q818yes—
666C4×Q8C2×Q818yes—
667C4×Q8C2×Q818yes—
668C4×Q8#4118yes—
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2413yes—
672C2×C4⋊C4C2413yes—
673C2×C4⋊C4C2413yes—
674C2×C4⋊C4C2413yes—
675C2×C4⋊C4C2413yes—
676C2×C4⋊C4C2413yes—
677C2×C4⋊C4C2413yes—
678C2×C4⋊C4C2413yes—
679C2×C4⋊C4C2413yes—
680C2×C4⋊C4C2413yes—
681C2×C4⋊C4C2413yes—
682C2×C4⋊C4C2413yes—
683C2×C4⋊C4C2413yes—
684C2×C4⋊C4C2413yes—
685C2×C4⋊C4C2413yes—
686C2×C4⋊C4C2413yes—
687C2×C4⋊C4C2413yes—
688C2×C4⋊C4C2413yes—
689C2×C4⋊C4C2413yes—
690C2×C4⋊C4C2413yes—
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2416yes—
694C2×C4⋊C4C2413yes—
695C2×C4⋊C4C2416yes—
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2416yes—
703C2×C4⋊C4C2416yes—
704C2×C4⋊C4C2416yes—
705C2×C4⋊C4C2416yes—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2416yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2413yes—
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⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2411yescharacteristic
731C2×C4⋊C4C2411yescharacteristic
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2416yes—
737C2×C4⋊C4C2416yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2416yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C42C2413yes—
751C2×C42C2413yes—
752C2×C42C2413yes—
753C2×C42C2413yes—
754C2×C42C2413yes—
755C2×C42C2413yes—
756C2×C42C2413yes—
757C2×C42C2413yes—
758C2×C42C2413yes—
759C2×C42C2413yes—
760C2×C42C2413yes—
761C2×C42C2413yes—
762C2×C42C2413yes—
763C2×C42C2413yes—
764C2×C42C2413yes—
765C2×C42C2416yes—
766C2×C42C2416yes—
767C2×C42C2416yes—
768C2×C42C2416yes—
769C2×C42C2416yes—
770C2×C42C2416yes—
771C2×C42C2413yes—
772C2×C42C2413yes—
773C2×C42C2411yescharacteristic
774C2×C42C2411yescharacteristic
775C2×C42C2411yescharacteristic
776C2×C42C2413yes—
777C2×C42C2413yes—
778C2×C42C2413yes—
779C2×C42C2413yes—
780C2×C42C2413yes—
781C2×C42C2413yes—
782C2×C42C2413yes—
783#95C2411yescharacteristic
784#95C2411yescharacteristic
785#95C2411yescharacteristic
786#95C2411yescharacteristic
787#95C2411yescharacteristic
788#95C2411yescharacteristic
789#95C2413yes—
790#95C2413yes—
791#95C2413yes—
792#95C2413yes—
793#95C2413yes—
794#95C2413yes—
795#95C2413yes—
796#95C2413yes—
797#95C2413yes—
798#95C2413yes—
799#95C2413yes—
800#95C2413yes—
801#95C2413yes—
802#95C2413yes—
803#95C2413yes—
804#95C2413yes—
805#95C2413yes—
806#95C2413yes—
807#95C2413yes—
808#95C2411yescharacteristic
809#95C2413yes—
810#95C2411yescharacteristic
811#95C2413yes—
812#95C2416yes—
813#95C2411yescharacteristic
814#95C2411yescharacteristic
815#95C2411yescharacteristic
816#95C2411yescharacteristic
817#95C2411yescharacteristic
818#95C2411yescharacteristic
819#95C2416yes—
820#95C2416yes—
821#95C2416yes—
822#95C2411yescharacteristic
823#95C2411yescharacteristic
824#95C2411yescharacteristic
825#95C2413yes—
826#95C2411yescharacteristic
827#95C2411yescharacteristic
828#95C2411yescharacteristic
829#95C2413yes—
830#95C2413yes—
831#95C2416yes—
832#95C2413yes—
833#95C2413yes—
834#95C2413yes—
835#95C2413yes—
836#95C2413yes—
837#95C2416yes—
838#95C2413yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2416yes—
846#95C2416yes—
847#95C2416yes—
848#95C2413yes—
849#95C2413yes—
850#95C2416yes—
851#95C2416yes—
852#95C2416yes—
853#95C2416yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2416yes—
865#95C2416yes—
866#95C2416yes—
867#95C2416yes—
868C2×Q8—22no—
869C2×Q8—26no—
870C2×Q8—26no—
871C2×Q8—212no—
872C2×Q8—22no—
873C2×Q8—46no—
874C2×Q8—46no—
875C2×Q8—41no—
876C2×Q8—41no—
877C2×Q8—41no—
878C2×Q8—46no—
879C2×Q8—43no—
880C2×Q8—43no—
881C2×Q8—46no—
882C2×Q8—43no—
883C2×Q8—43no—
884C2×Q8C22×Q814yes—
885C2×Q8C22×Q8124yes—
886C2×Q8C22×Q814yes—
887C2×Q8C2×#4114yes—
888C2×Q82−1+414yes—
889C22×C4C2511yescharacteristic
890C22×C4C2513yes—
891C22×C4C2511yescharacteristic
892C22×C4C2511yescharacteristic
893C22×C4C2513yes—
894C22×C4C2511yescharacteristic
895C22×C4C2511yescharacteristic
896C22×C4C2511yescharacteristic
897C22×C4C2513yes—
898C22×C4C2513yes—
899C22×C4C2513yes—
900C22×C4C2511yescharacteristic
901C22×C4C2513yes—
902C22×C4C2513yes—
903C22×C4C2513yes—
904C22×C4C2513yes—
905C22×C4C2511yescharacteristic
906C22×C4C2513yes—
907C22×C4C2513yes—
908C22×C4C2511yescharacteristic
909C22×C4C2511yescharacteristic
910C22×C4C2511yescharacteristic
911C22×C4C2511yescharacteristic
912C22×C4C2511yescharacteristic
913C22×C4C2513yes—
914C22×C4C2513yes—
915C22×C4C2513yes—
916C22×C4C2511yescharacteristic
917C22×C4C2513yes—
918C22×C4C2511yescharacteristic
919C22×C4C2513yes—
920C4⋊C4—22no—
921C4⋊C4—22no—
922C4⋊C4—26no—
923C4⋊C4—26no—
924C4⋊C4—26no—
925C4⋊C4—26no—
926C4⋊C4—26no—
927C4⋊C4—26no—
928C4⋊C4—26no—
929C4⋊C4—26no—
930C4⋊C4—26no—
931C4⋊C4—26no—
932C4⋊C4—26no—
933C4⋊C4—26no—
934C4⋊C4—26no—
935C4⋊C4—212no—
936C4⋊C4—212no—
937C4⋊C4—26no—
938C4⋊C4—26no—
939C4⋊C4—26no—
940C4⋊C4—26no—
941C4⋊C4—26no—
942C4⋊C4—26no—
943C4⋊C4—26no—
944C4⋊C4—22no—
945C4⋊C4—22no—
946C4⋊C4—26no—
947C4⋊C4—41no—
948C4⋊C4—41no—
949C4⋊C4—41no—
950C4⋊C4—43no—
951C4⋊C4—43no—
952C4⋊C4—43no—
953C4⋊C4—43no—
954C4⋊C4—43no—
955C4⋊C4—43no—
956C4⋊C4—43no—
957C4⋊C4—41no—
958C4⋊C4—46no—
959C4⋊C4—43no—
960C4⋊C4—41no—
961C4⋊C4—46no—
962C4⋊C4—43no—
963C4⋊C4—43no—
964C4⋊C4—41no—
965C4⋊C4—46no—
966C4⋊C4—43no—
967C4⋊C4—43no—
968C4⋊C4—43no—
969C4⋊C4—46no—
970C4⋊C4—43no—
971C4⋊C4—43no—
972C4⋊C4—43no—
973C4⋊C4—43no—
974C4⋊C4—43no—
975C4⋊C4—43no—
976C4⋊C4—46no—
977C4⋊C4—46no—
978C4⋊C4—46no—
979C4⋊C4—43no—
980C4⋊C4—43no—
981C4⋊C4—43no—
982C4⋊C4—43no—
983C4⋊C4—43no—
984C4⋊C4—43no—
985C4⋊C4—43no—
986C4⋊C4—43no—
987C4⋊C4—43no—
988C4⋊C4—43no—
989C4⋊C4—46no—
990C4⋊C4—43no—
991C4⋊C4—43no—
992C4⋊C4—43no—
993C4⋊C4—43no—
994C4⋊C4C22×Q8112yes—
995C4⋊C4C22×Q8112yes—
996C4⋊C4C22×Q8112yes—
997C4⋊C4C22×Q8112yes—
998C4⋊C4C22×Q8112yes—
999C4⋊C4C22×Q8112yes—
1000C4⋊C4C2×#41112yes—
1001C42—26no—
1002C42—26no—
1003C42—26no—
1004C42—26no—
1005C42—26no—
1006C42—26no—
1007C42—26no—
1008C42—26no—
1009C42—26no—
1010C42—26no—
1011C42—26no—
1012C42—26no—
1013C42—43no—
1014C42—43no—
1015C42—43no—
1016C42—41no—
1017C42—41no—
1018C42—41no—
1019C42—46no—
1020C42—46no—
1021C42—46no—
1022C42—46no—
1023C42—43no—
1024C42—43no—
1025C42—43no—
1026C42—46no—
1027C42—46no—
1028C42—43no—
1029C42—43no—
1030C42C22×Q8112yes—
1031C42C22×Q8112yes—
1032C42C22×Q8112yes—
1033C42C2×#41112yes—
1034C23C2611yescharacteristic
1035Q8—424no—
1036Q8—44no—
1037Q8—44no—
1038Q8—86no—
1039Q8—86no—
1040Q8—812no—
1041Q8#557116yes—
1042C2×C4—21no—
1043C2×C4—23no—
1044C2×C4—23no—
1045C2×C4—23no—
1046C2×C4—21no—
1047C2×C4—23no—
1048C2×C4—23no—
1049C2×C4—23no—
1050C2×C4—23no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—23no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—23no—
1066C2×C4—23no—
1067C2×C4—23no—
1068C2×C4—23no—
1069C2×C4—23no—
1070C2×C4—23no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—23no—
1077C2×C4—23no—
1078C2×C4—23no—
1079C2×C4—23no—
1080C2×C4—23no—
1081C2×C4—23no—
1082C2×C4—21no—
1083C2×C4—23no—
1084C2×C4—23no—
1085C2×C4—23no—
1086C2×C4—23no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—23no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—23no—
1096C2×C4—23no—
1097C2×C4—23no—
1098C2×C4—23no—
1099C2×C4—23no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—23no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—23no—
1108C2×C4—23no—
1109C2×C4—23no—
1110C2×C4—23no—
1111C2×C4—21no—
1112C2×C4—23no—
1113C2×C4—23no—
1114C2×C4—23no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—23no—
1120C2×C4—23no—
1121C2×C4—23no—
1122C2×C4—21no—
1123C2×C4C23×Q812yes—
1124C2×C4C23×Q812yes—
1125C2×C4C23×Q812yes—
1126C2×C4C23×Q816yes—
1127C2×C4C23×Q816yes—
1128C2×C4C23×Q816yes—
1129C2×C4C23×Q816yes—
1130C2×C4C22×#4112yes—
1131C2×C4C22×#4116yes—
1132C2×C4C22×#4116yes—
1133C2×C4C2×2−1+416yes—
1134C2×C4#58512yes—
1135C22C24×Q811yescharacteristic
1136C22C23×#4111yescharacteristic
1137C22C22×2−1+411yescharacteristic
1138C22C2×#58511yescharacteristic
1139C22H(7,𝔽2)11yescharacteristic
1140C222−1+611yescharacteristic
1141C222−1+611yescharacteristic
1142C4—26no—
1143C4—26no—
1144C4—26no—
1145C4—22no—
1146C4—22no—
1147C4—22no—
1148C4—22no—
1149C4—22no—
1150C4—26no—
1151C4—41no—
1152C4—43no—
1153C4—41no—
1154C4—43no—
1155C4—43no—
1156C4—41no—
1157C4—41no—
1158C4—43no—
1159C4—43no—
1160C4—43no—
1161C4—41no—
1162C4—41no—
1163C4—43no—
1164C4—43no—
1165C4—43no—
1166C4—41no—
1167C4—41no—
1168C4—41no—
1169C4—41no—
1170C4—43no—
1171C4—43no—
1172C4C2×#557112yes—
1173C2C22×#55711yescharacteristic
1174C2#6284911yescharacteristic
1175C2#6285711yescharacteristic
1176C2#6295311yescharacteristic
1177C2#6298911yescharacteristic
1178C2#6300511yescharacteristic
1179C2#6306111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
239. Q82Q8semidirect

Maximal subgroups

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

subgroupindex
#596662
#594642
#594562
#522742
#452812
#452802
#449542
#449532
#449492
#397502
#396812
#396802
#396432
#391772
#391762
#364752
#364742
#359712
#359572
#359372
#358682
#343362
#343352