Finite Group Databasebeta

← #7660837

Subgroups — #7660837

Order 512.

4176 conjugacy classes of subgroups.

The subgroup lattice has 1195 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52251C213yesmaximal
2#42753C213yesmaximal
3#42733C213yesmaximal, complemented
4#42733C213yesmaximal, complemented
5#42689C213yesmaximal, complemented
6#42610C213yesmaximal
7#42527C213yesmaximal, complemented
8#40096C213yesmaximal
9#39928C213yesmaximal
10#39661C213yesmaximal
11#39526C213yesmaximal, complemented
12#39003C213yesmaximal, complemented
13#38943C213yesmaximal
14#37359C213yesmaximal, complemented
15#37344C213yesmaximal, complemented
16#37291C213yesmaximal
17Q8×#126C211yesmaximal, characteristic
18Q8×C22⋊Q8C211yesmaximal, characteristic
19#36448C211yesmaximal, characteristic
20#36447C211yesmaximal, characteristic, complemented
21#36447C211yesmaximal, characteristic, complemented
22#36435C211yesmaximal, characteristic
23#35971C211yesmaximal, characteristic, complemented
24#35971C211yesmaximal, characteristic, complemented
25#35937C211yesmaximal, characteristic, complemented
26#35883C211yesmaximal, characteristic
27#35883C211yesmaximal, characteristic
28#35868C211yesmaximal, characteristic, complemented
29#34336C211yesmaximal, characteristic, complemented
30#34335C211yesmaximal, characteristic, complemented
31#34192C211yesmaximal, characteristic
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35#2863C2213yes—
36#2863C2213yes—
37#2859C2213yes—
38#2859C2213yes—
39#2857C2213yes—
40#2851C2213yes—
41#2833C2216yes—
42#2833C2216yes—
43#2802C2216yes—
44#2789C2216yes—
45#2776C2213yes—
46#2776C2216yes—
47#2776C2216yes—
48#2769C2213yes—
49#2769C2216yes—
50#2769C2216yes—
51#2766C2213yes—
52#2766C2216yes—
53#2762C2213yes—
54#2762C2213yes—
55#2762C2216yes—
56#2762C2216yes—
57#2758C2213yes—
58#2758C2216yes—
59#2758C2216yes—
60#2755C2213yes—
61#2747C2213yes—
62#2744C2213yes—
63#2744C2216yes—
64#2739C2213yes—
65#2722C2213yes—
66#2719C2216yes—
67#2719C2213yes—
68#2719C2216yes—
69#2719C2216yes—
70#2713C2216yes—
71#2713C2216yes—
72#2704C2216yes—
73#2704C2213yes—
74#2698C2213yes—
75#2690C2213yes—
76#2690C2216yes—
77#2689C2211yescharacteristic
78#2666C2216yes—
79#2666C2216yes—
80#2660C2213yes—
81#2655C2216yes—
82#2652C2216yes—
83#2647C2213yes—
84#2647C2213yes—
85#2647C2213yes—
86#2645C2213yes—
87#2645C2213yes—
88#2642C2216yes—
89#2634C2216yes—
90#2584C2213yes—
91#2582C2213yes—
92#2581C2213yes—
93#2571C2213yes—
94#2571C2213yes—
95#2571C2213yes—
96#2571C2213yes—
97#2570C2213yes—
98#2570C2213yes—
99#2570C2213yes—
100#2567C2213yes—
101#2565C2213yes—
102#2552C2213yes—
103#2552C2213yes—
104#2552C2213yes—
105#2551C2213yes—
106#2551C2213yes—
107#2550C2213yes—
108#2550C2213yes—
109#2546C2213yes—
110#2528C2216yes—
111#2528C2216yes—
112#2524C2216yes—
113#2514C2213yes—
114#2514C2213yes—
115#2514C2213yes—
116#2514C2213yes—
117#2514C2213yes—
118#2514C2213yes—
119#2511C2213yes—
120#2511C2213yes—
121#2511C2213yes—
122#2511C2213yes—
123#2511C2213yes—
124#2511C2213yes—
125#2509C2213yes—
126#2509C2213yes—
127#2509C2213yes—
128#2508C2213yes—
129#2508C2213yes—
130#2508C2213yes—
131#2508C2213yes—
132#2508C2213yes—
133#2508C2213yes—
134#2508C2213yes—
135#2508C2213yes—
136#2507C2213yes—
137#2507C2213yes—
138#2507C2213yes—
139#2506C2213yes—
140#2506C2213yes—
141#2506C2213yes—
142#2506C2213yes—
143#2506C2213yes—
144#2506C2213yes—
145#2497C2213yes—
146#2497C2213yes—
147#2497C2213yes—
148#2497C2213yes—
149#2497C2213yes—
150#2496C2213yes—
151#2495C2213yes—
152#2495C2213yes—
153#2495C2213yes—
154#2494C2213yes—
155#2494C2213yes—
156#2494C2213yes—
157#2489C2216yes—
158#2462C2216yes—
159#2453C2213yes—
160#2451C2213yes—
161#2451C2213yes—
162#2451C2213yes—
163#2442C2213yes—
164#2440C2213yes—
165#2440C2213yes—
166#2440C2213yes—
167#2429C2216yes—
168#2402C2213yes—
169#2402C2213yes—
170#2402C2213yes—
171#2401C2213yes—
172#2401C2213yes—
173#2399C2213yes—
174#2370C2213yes—
175#2370C2213yes—
176#2369C2213yes—
177#2369C2213yes—
178#2365C2213yes—
179#2365C2213yes—
180#2356C2213yes—
181#2356C2213yes—
182#2355C2213yes—
183#2355C2213yes—
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
202Q8×C4⋊C4C2211yescharacteristic
203Q8×C4⋊C4C2211yescharacteristic
204#2345C2213yes—
205#2345C2213yes—
206Q8×C22⋊C4C2211yescharacteristic
207Q8×C22⋊C4C2211yescharacteristic
208Q8×C22⋊C4C2211yescharacteristic
209Q8×C22⋊C4C2211yescharacteristic
210Q8×C22⋊C4C2211yescharacteristic
211Q8×C22⋊C4C2211yescharacteristic
212#2334C2216yes—
213#2331C2213yes—
214#2331C2213yes—
215#2331C2213yes—
216#2330C2213yes—
217#2320C2216yes—
218#2320C2213yes—
219#2320C2213yes—
220C4×C4⋊Q8C2213yes—
221C4×#125C2213yes—
222C4×#125C2213yes—
223C4×#125C2213yes—
224C4×#126C2213yes—
225C4×#126C2213yes—
226C4×C22⋊Q8C2213yes—
227C4×C22⋊Q8C2213yes—
228#2295C2213yes—
229#2295C2213yes—
230#2283C2213yes—
231#2283C2213yes—
232#2276C2211yescharacteristic
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C23×Q8C2311yescharacteristic
239Q82—28no—
240#557—28no—
241C2×C4⋊Q8C2313yes—
242C2×C4⋊Q8C2313yes—
243C2×C4⋊Q8C2313yes—
244C2×C4⋊Q8C2313yes—
245C2×C4⋊Q8C2316yes—
246C2×#126C2311yescharacteristic
247C2×#126C2313yes—
248C2×#125C2313yes—
249C2×#125C2313yes—
250C2×#125C2313yes—
251C2×#125C2313yes—
252C2×#125C2316yes—
253C2×#125C2316yes—
254C2×#125C2316yes—
255C2×C22⋊Q8C2311yescharacteristic
256C2×C22⋊Q8C2313yes—
257C2×C22⋊Q8C2316yes—
258C2×C4×Q8—28no—
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×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2313yes—
276C2×C4×Q8C2316yes—
277C2×C4×Q8C2311yescharacteristic
278C22×C4⋊C4C2313yes—
279C22×C42C2313yes—
280#401C2313yes—
281#401C2316yes—
282#401C2316yes—
283#401C2316yes—
284#401C2313yes—
285#400C2313yes—
286#400C2316yes—
287#400C2316yes—
288#400C2313yes—
289#400C2313yes—
290#400C2316yes—
291#400C2316yes—
292#400C2316yes—
293#400C2316yes—
294#400C2313yes—
295#400C2313yes—
296#400C2313yes—
297#400C2316yes—
298#400C2316yes—
299#400C2316yes—
300#400C2316yes—
301#400C2316yes—
302#400C2313yes—
303#400C2313yes—
304#400C2313yes—
305#400C2316yes—
306#400C2316yes—
307#400C2313yes—
308#400C2313yes—
309#400C2316yes—
310#400C2316yes—
311#400C2313yes—
312#400C2316yes—
313#400C2316yes—
314#400C2313yes—
315#400C2313yes—
316#400C2311yescharacteristic
317#400C2311yescharacteristic
318#400C2313yes—
319#400C2313yes—
320#400C2316yes—
321#400C2316yes—
322#398C2316yes—
323#398C2316yes—
324#398C2313yes—
325#398C2313yes—
326#398C2316yes—
327#398C2316yes—
328#398C2316yes—
329#398C2316yes—
330#398C2316yes—
331#398C2316yes—
332#398C2316yes—
333#398C2316yes—
334#398C2316yes—
335#398C2313yes—
336#398C2313yes—
337#398C2316yes—
338#398C2316yes—
339#398C2313yes—
340#398C2313yes—
341#398C2313yes—
342#398C2313yes—
343#398C2311yescharacteristic
344#398C2313yes—
345#398C2313yes—
346#398C2313yes—
347#398C2313yes—
348#398C2313yes—
349#398C2313yes—
350#398C2313yes—
351#397C2313yes—
352#397C2313yes—
353#397C2316yes—
354#397C2311yescharacteristic
355#397C2311yescharacteristic
356#397C2313yes—
357#397C2313yes—
358#396C2316yes—
359#396C2313yes—
360#396C2313yes—
361#395C2316yes—
362#395C2316yes—
363#395C2313yes—
364#395C2316yes—
365#395C2316yes—
366#395C2313yes—
367#395C2316yes—
368#395C2311yescharacteristic
369#395C2313yes—
370#391C2316yes—
371#391C2313yes—
372#391C2313yes—
373#391C2313yes—
374#391C2313yes—
375#391C2313yes—
376#391C2313yes—
377#391C2313yes—
378#391C2313yes—
379#391C2316yes—
380#391C2316yes—
381#391C2316yes—
382#391C2316yes—
383#391C2313yes—
384#391C2313yes—
385#391C2313yes—
386#391C2313yes—
387#391C2313yes—
388#391C2313yes—
389#391C2316yes—
390#391C2313yes—
391#391C2313yes—
392#391C2313yes—
393#391C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2313yes—
397#389C2313yes—
398#389C2313yes—
399#389C2313yes—
400#389C2313yes—
401#389C2313yes—
402#389C2313yes—
403#389C2313yes—
404#389C2316yes—
405#389C2313yes—
406#389C2313yes—
407#389C2313yes—
408#389C2313yes—
409#389C2313yes—
410#389C2313yes—
411#389C2313yes—
412#389C2313yes—
413#389C2316yes—
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2316yes—
418#389C2313yes—
419#389C2313yes—
420#389C2316yes—
421#389C2316yes—
422#389C2313yes—
423#389C2313yes—
424#389C2313yes—
425#389C2316yes—
426#389C2313yes—
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2316yes—
431#389C2313yes—
432#389C2313yes—
433#389C2316yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2316yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#388C2311yescharacteristic
454#388C2313yes—
455#388C2313yes—
456#388C2313yes—
457#388C2313yes—
458#388C2313yes—
459#388C2316yes—
460#388C2316yes—
461#387C2313yes—
462#387C2313yes—
463#387C2313yes—
464#387C2313yes—
465#387C2313yes—
466#387C2313yes—
467#387C2313yes—
468#387C2313yes—
469#387C2316yes—
470#387C2313yes—
471#387C2313yes—
472#387C2313yes—
473#387C2313yes—
474#387C2313yes—
475#387C2313yes—
476#387C2313yes—
477#387C2313yes—
478#387C2316yes—
479#387C2316yes—
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#387C2313yes—
494#387C2316yes—
495#387C2313yes—
496#387C2313yes—
497#387C2316yes—
498#387C2316yes—
499#387C2316yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2313yes—
504#387C2313yes—
505#387C2313yes—
506#387C2313yes—
507#387C2316yes—
508#387C2316yes—
509#387C2316yes—
510#387C2311yescharacteristic
511#387C2313yes—
512#387C2313yes—
513#385C2313yes—
514#385C2316yes—
515#385C2313yes—
516#385C2313yes—
517#385C2311yescharacteristic
518#384C2313yes—
519#384C2313yes—
520#384C2313yes—
521#384C2313yes—
522#384C2313yes—
523#384C2313yes—
524#384C2313yes—
525#384C2313yes—
526#384C2313yes—
527#384C2313yes—
528#383C2313yes—
529#383C2313yes—
530#383C2316yes—
531#383C2316yes—
532#383C2316yes—
533#383C2313yes—
534#383C2313yes—
535#383C2316yes—
536#382C2313yes—
537#382C2313yes—
538#382C2313yes—
539#382C2313yes—
540#382C2313yes—
541#382C2313yes—
542#382C2313yes—
543#382C2313yes—
544#382C2313yes—
545#382C2316yes—
546#382C2313yes—
547#382C2313yes—
548#382C2313yes—
549#382C2316yes—
550#382C2313yes—
551#382C2313yes—
552#382C2316yes—
553#382C2316yes—
554#381C2311yescharacteristic
555#381C2313yes—
556#380C2313yes—
557#380C2313yes—
558#380C2313yes—
559#380C2313yes—
560#380C2313yes—
561#380C2313yes—
562#380C2313yes—
563#380C2313yes—
564#380C2313yes—
565#380C2313yes—
566C4×C4⋊C4C2313yes—
567C4×C4⋊C4C2313yes—
568C4×C4⋊C4C2313yes—
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⋊C4C2316yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
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×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2316yes—
613C4×C22⋊C4C2313yes—
614#376C2313yes—
615#376C2316yes—
616#376C2313yes—
617#376C2313yes—
618#376C2313yes—
619C43C2313yes—
620C43C2313yes—
621C22×Q8—24no—
622C22×Q8—24no—
623C22×Q8—24no—
624C22×Q8C2413yes—
625C22×Q8C2411yescharacteristic
626C22×Q8C2413yes—
627C22×Q8C2416yes—
628C22×Q8C2411yescharacteristic
629C23×C4C2413yes—
630C23×C4C2411yescharacteristic
631C23×C4C2413yes—
632C4⋊Q8—212no—
633C4⋊Q8—212no—
634C4⋊Q8—212no—
635C4⋊Q8—212no—
636C4⋊Q8—86no—
637#126—24no—
638#126—212no—
639#125—212no—
640#125—212no—
641#125—46no—
642#125—46no—
643#125—86no—
644#125—86no—
645#125—86no—
646C22⋊Q8—24no—
647C22⋊Q8—46no—
648C22⋊Q8—86no—
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—24no—
658C4×Q8—24no—
659C4×Q8—24no—
660C4×Q8—24no—
661C4×Q8—24no—
662C4×Q8—212no—
663C4×Q8—212no—
664C4×Q8—212no—
665C4×Q8—212no—
666C4×Q8—412no—
667C4×Q8#4118yes—
668C2×C4⋊C4—212no—
669C2×C4⋊C4C2413yes—
670C2×C4⋊C4C2416yes—
671C2×C4⋊C4C2411yescharacteristic
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⋊C4C2413yes—
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2411yescharacteristic
694C2×C4⋊C4C2411yescharacteristic
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2411yescharacteristic
697C2×C4⋊C4C2416yes—
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2411yescharacteristic
702C2×C4⋊C4C2413yes—
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2416yes—
705C2×C4⋊C4C2416yes—
706C2×C4⋊C4C2416yes—
707C2×C4⋊C4C2416yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2416yes—
717C2×C4⋊C4C2416yes—
718C2×C4⋊C4C2416yes—
719C2×C4⋊C4C2416yes—
720C2×C4⋊C4C2416yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
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⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2413yes—
741C2×C22⋊C4C2411yescharacteristic
742C2×C22⋊C4C2411yescharacteristic
743C2×C22⋊C4C2413yes—
744C2×C22⋊C4C2411yescharacteristic
745C2×C22⋊C4C2411yescharacteristic
746C2×C22⋊C4C2413yes—
747C2×C22⋊C4C2413yes—
748C2×C22⋊C4C2413yes—
749C2×C22⋊C4C2413yes—
750C2×C22⋊C4C2413yes—
751C2×C22⋊C4C2411yescharacteristic
752C2×C22⋊C4C2411yescharacteristic
753C2×C42—212no—
754C2×C42C2413yes—
755C2×C42C2413yes—
756C2×C42C2413yes—
757C2×C42C2413yes—
758C2×C42C2413yes—
759C2×C42C2413yes—
760C2×C42C2413yes—
761C2×C42C2413yes—
762C2×C42C2413yes—
763C2×C42C2413yes—
764C2×C42C2413yes—
765C2×C42C2413yes—
766C2×C42C2413yes—
767C2×C42C2413yes—
768C2×C42C2413yes—
769C2×C42C2413yes—
770C2×C42C2411yescharacteristic
771C2×C42C2413yes—
772C2×C42C2416yes—
773C2×C42C2416yes—
774C2×C42C2413yes—
775C2×C42C2413yes—
776C2×C42C2416yes—
777C2×C42C2413yes—
778C2×C42C2411yescharacteristic
779C2×C42C2413yes—
780C2×C42C2416yes—
781C2×C42C2413yes—
782#95C2411yescharacteristic
783#95C2411yescharacteristic
784#95C2411yescharacteristic
785#95C2411yescharacteristic
786#95C2413yes—
787#95C2413yes—
788#95C2413yes—
789#95C2413yes—
790#95C2413yes—
791#95C2413yes—
792#95C2413yes—
793#95C2413yes—
794#95C2413yes—
795#95C2413yes—
796#95C2413yes—
797#95C2413yes—
798#95C2413yes—
799#95C2413yes—
800#95C2416yes—
801#95C2416yes—
802#95C2416yes—
803#95C2416yes—
804#95C2413yes—
805#95C2413yes—
806#95C2413yes—
807#95C2413yes—
808#95C2413yes—
809#95C2413yes—
810#95C2413yes—
811#95C2413yes—
812#95C2413yes—
813#95C2413yes—
814#95C2413yes—
815#95C2413yes—
816#95C2411yescharacteristic
817#95C2411yescharacteristic
818#95C2413yes—
819#95C2411yescharacteristic
820#95C2411yescharacteristic
821#95C2413yes—
822#95C2411yescharacteristic
823#95C2411yescharacteristic
824#95C2411yescharacteristic
825#95C2411yescharacteristic
826#95C2416yes—
827#95C2416yes—
828#95C2411yescharacteristic
829#95C2411yescharacteristic
830#95C2413yes—
831#95C2413yes—
832#95C2413yes—
833#95C2413yes—
834#95C2413yes—
835#95C2413yes—
836#95C2413yes—
837#95C2416yes—
838#95C2416yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2416yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2416yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2416yes—
861#95C2416yes—
862#95C2416yes—
863#95C2416yes—
864#95C2416yes—
865#95C2416yes—
866#95C2416yes—
867#95C2416yes—
868C24C2511yescharacteristic
869C2×Q8—22no—
870C2×Q8—26no—
871C2×Q8—26no—
872C2×Q8—212no—
873C2×Q8—22no—
874C2×Q8—26no—
875C2×Q8—26no—
876C2×Q8—41no—
877C2×Q8—46no—
878C2×Q8—43no—
879C2×Q8—46no—
880C2×Q8—43no—
881C2×Q8—416no—
882C2×Q8C2×#4114yes—
883C2×Q82−1+414yes—
884C2×Q82−1+414yes—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—26no—
888C22×C4—26no—
889C22×C4—26no—
890C22×C4—26no—
891C22×C4—41no—
892C22×C4—43no—
893C22×C4—43no—
894C22×C4C2513yes—
895C22×C4C2513yes—
896C22×C4C2511yescharacteristic
897C22×C4C2511yescharacteristic
898C22×C4C2511yescharacteristic
899C22×C4C2511yescharacteristic
900C22×C4C2511yescharacteristic
901C22×C4C2511yescharacteristic
902C22×C4C2513yes—
903C22×C4C2513yes—
904C22×C4C2511yescharacteristic
905C22×C4C2511yescharacteristic
906C22×C4C2513yes—
907C22×C4C2513yes—
908C22×C4C2513yes—
909C22×C4C2511yescharacteristic
910C22×C4C2513yes—
911C22×C4C2513yes—
912C22×C4C2513yes—
913C22×C4C2511yescharacteristic
914C22×C4C2513yes—
915C22×C4C2513yes—
916C22×C4C2513yes—
917C22×C4C2513yes—
918C22×C4C2511yescharacteristic
919C22×C4C2513yes—
920C22×C4C2511yescharacteristic
921C22×C4C2511yescharacteristic
922C22×C4C2511yescharacteristic
923C22×C4C2513yes—
924C4⋊C4—26no—
925C4⋊C4—212no—
926C4⋊C4—22no—
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—26no—
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—26no—
945C4⋊C4—22no—
946C4⋊C4—22no—
947C4⋊C4—22no—
948C4⋊C4—22no—
949C4⋊C4—22no—
950C4⋊C4—26no—
951C4⋊C4—26no—
952C4⋊C4—26no—
953C4⋊C4—22no—
954C4⋊C4—26no—
955C4⋊C4—26no—
956C4⋊C4—26no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—41no—
960C4⋊C4—43no—
961C4⋊C4—43no—
962C4⋊C4—43no—
963C4⋊C4—41no—
964C4⋊C4—43no—
965C4⋊C4—43no—
966C4⋊C4—43no—
967C4⋊C4—43no—
968C4⋊C4—46no—
969C4⋊C4—46no—
970C4⋊C4—43no—
971C4⋊C4—46no—
972C4⋊C4—46no—
973C4⋊C4—46no—
974C4⋊C4—43no—
975C4⋊C4—43no—
976C4⋊C4—43no—
977C4⋊C4—43no—
978C4⋊C4—43no—
979C4⋊C4—43no—
980C4⋊C4—43no—
981C4⋊C4—43no—
982C4⋊C4—43no—
983C4⋊C4—43no—
984C4⋊C4—43no—
985C4⋊C4—43no—
986C4⋊C4—46no—
987C4⋊C4—43no—
988C4⋊C4—46no—
989C4⋊C4—43no—
990C4⋊C4—46no—
991C4⋊C4—46no—
992C4⋊C4—46no—
993C4⋊C4—43no—
994C4⋊C4—43no—
995C4⋊C4C2×#41112yes—
996C22⋊C4—22no—
997C22⋊C4—26no—
998C22⋊C4—22no—
999C22⋊C4—22no—
1000C22⋊C4—26no—
1001C22⋊C4—22no—
1002C22⋊C4—43no—
1003C22⋊C4—41no—
1004C22⋊C4—43no—
1005C22⋊C4—43no—
1006C22⋊C4—43no—
1007C22⋊C42−1+414yes—
1008C42—26no—
1009C42—26no—
1010C42—26no—
1011C42—26no—
1012C42—26no—
1013C42—26no—
1014C42—26no—
1015C42—26no—
1016C42—26no—
1017C42—26no—
1018C42—26no—
1019C42—26no—
1020C42—26no—
1021C42—26no—
1022C42—26no—
1023C42—26no—
1024C42—22no—
1025C42—26no—
1026C42—41no—
1027C42—43no—
1028C42—46no—
1029C42—46no—
1030C42—46no—
1031C42—43no—
1032C42—43no—
1033C42—43no—
1034C42—46no—
1035C42C2×#41112yes—
1036C23—21no—
1037C23—21no—
1038C23—21no—
1039C23—21no—
1040C23—21no—
1041C23—21no—
1042C23C2×2−1+412yes—
1043C23C2611yescharacteristic
1044Q8—44no—
1045Q8—412no—
1046Q8—86no—
1047Q8—812no—
1048Q8#541116yes—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—23no—
1055C2×C4—23no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—23no—
1064C2×C4—23no—
1065C2×C4—23no—
1066C2×C4—23no—
1067C2×C4—23no—
1068C2×C4—23no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—23no—
1077C2×C4—21no—
1078C2×C4—23no—
1079C2×C4—23no—
1080C2×C4—23no—
1081C2×C4—23no—
1082C2×C4—23no—
1083C2×C4—23no—
1084C2×C4—23no—
1085C2×C4—23no—
1086C2×C4—23no—
1087C2×C4—23no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—23no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—23no—
1095C2×C4—23no—
1096C2×C4—23no—
1097C2×C4—23no—
1098C2×C4—23no—
1099C2×C4—23no—
1100C2×C4—23no—
1101C2×C4—23no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—23no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—23no—
1110C2×C4—23no—
1111C2×C4—23no—
1112C2×C4—23no—
1113C2×C4—23no—
1114C2×C4—23no—
1115C2×C4—23no—
1116C2×C4—23no—
1117C2×C4—21no—
1118C2×C4—23no—
1119C2×C4—21no—
1120C2×C4—23no—
1121C2×C4—21no—
1122C2×C4—23no—
1123C2×C4—23no—
1124C2×C4—21no—
1125C2×C4—23no—
1126C2×C4—23no—
1127C2×C4—21no—
1128C2×C4—23no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—44no—
1132C2×C4—412no—
1133C2×C4—86no—
1134C2×C4C22×#4112yes—
1135C2×C4C22×#4116yes—
1136C2×C4C22×#4116yes—
1137C2×C4C2×2−1+412yes—
1138C2×C4C2×2−1+412yes—
1139C2×C4C2×2−1+416yes—
1140C2×C4C2×2−1+416yes—
1141C2×C4#58512yes—
1142C22—22no—
1143C22—22no—
1144C22—22no—
1145C22—41no—
1146C22—41no—
1147C22—41no—
1148C22—41no—
1149C22C23×#4111yescharacteristic
1150C22C22×2−1+411yescharacteristic
1151C22C22×2−1+411yescharacteristic
1152C22C22×2−1+411yescharacteristic
1153C22C2×#58511yescharacteristic
1154C22H(7,𝔽2)11yescharacteristic
1155C222−1+611yescharacteristic
1156C4—26no—
1157C4—22no—
1158C4—22no—
1159C4—22no—
1160C4—22no—
1161C4—43no—
1162C4—43no—
1163C4—43no—
1164C4—43no—
1165C4—41no—
1166C4—41no—
1167C4—43no—
1168C4—41no—
1169C4—41no—
1170C4—41no—
1171C4—41no—
1172C4—43no—
1173C4—41no—
1174C4—43no—
1175C4—43no—
1176C4—43no—
1177C4—43no—
1178C4—41no—
1179C4—41no—
1180C4—43no—
1181C4—43no—
1182C4—41no—
1183C4—43no—
1184C4—43no—
1185C4C2×#541112yes—
1186C2—42no—
1187C2C22×#54111yescharacteristic
1188C2#6294311yescharacteristic
1189C2#6294911yescharacteristic
1190C2#6299411yescharacteristic
1191C2#6299811yescharacteristic
1192C2#6303211yescharacteristic
1193C2#6306111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #42733C2semidirect
4. #42733C2semidirect
5. #42689C2semidirect
7. #42527C2semidirect
11. #39526C2semidirect
12. #39003C2semidirect
14. #37359C2semidirect
15. #37344C2semidirect
20. #36447C2semidirect
21. #36447C2semidirect
23. #35971C2semidirect
24. #35971C2semidirect
25. #35937C2semidirect
28. #35868C2semidirect
29. #34336C2semidirect
30. #34335C2semidirect

Maximal subgroups

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

subgroupindex
#522512
#427532
#427332
#426892
#426102
#425272
#400962
#399282
#396612
#395262
#390032
#389432
#373592
#373442
#372912
Q8×#1262
Q8×C22⋊Q82
#364482
#364472
#364352
#359712
#359372
#358832
#358682
#343362
#343352
#341922