Finite Group Databasebeta

← #7656130

Subgroups — #7656130

Order 512.

4111 conjugacy classes of subgroups.

The subgroup lattice has 1185 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42765C213yesmaximal, complemented
2#42764C213yesmaximal
3#42703C213yesmaximal, complemented
4#42689C213yesmaximal, complemented
5#42667C213yesmaximal
6#42657C213yesmaximal
7#42600C213yesmaximal, complemented
8#42597C213yesmaximal
9#40155C213yesmaximal
10#40143C213yesmaximal, complemented
11#39011C213yesmaximal
12#39003C213yesmaximal, complemented
13#37597C213yesmaximal
14#37580C213yesmaximal, complemented
15#36475C211yesmaximal, characteristic, complemented
16#36475C211yesmaximal, characteristic, complemented
17#36448C211yesmaximal, characteristic
18#36448C211yesmaximal, characteristic
19#35971C211yesmaximal, characteristic, complemented
20#35971C211yesmaximal, characteristic, complemented
21#35971C211yesmaximal, characteristic, complemented
22#35937C211yesmaximal, characteristic, complemented
23#35883C211yesmaximal, characteristic
24#35883C211yesmaximal, characteristic
25#35786C211yesmaximal, characteristic
26#35711C211yesmaximal, characteristic
27#35187C213yesmaximal, complemented
28#34604C213yesmaximal
29#34335C211yesmaximal, characteristic, complemented
30#34262C211yesmaximal, characteristic
31C4×#557C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#519C2211yescharacteristic
35#2864C2213yes—
36#2864C2213yes—
37#2863C2213yes—
38#2863C2213yes—
39#2839C2216yes—
40#2833C2216yes—
41#2833C2216yes—
42#2831C2216yes—
43#2783C2216yes—
44#2776C2216yes—
45#2772C2216yes—
46#2769C2216yes—
47#2766C2216yes—
48#2766C2216yes—
49#2762C2216yes—
50#2762C2216yes—
51#2762C2216yes—
52#2762C2216yes—
53#2758C2216yes—
54#2758C2216yes—
55#2755C2216yes—
56#2754C2216yes—
57#2716C2216yes—
58#2713C2216yes—
59#2666C2213yes—
60#2666C2213yes—
61#2664C2213yes—
62#2664C2213yes—
63#2660C2213yes—
64#2655C2216yes—
65#2655C2213yes—
66#2655C2216yes—
67#2655C2213yes—
68#2655C2213yes—
69#2655C2213yes—
70#2655C2216yes—
71#2655C2216yes—
72#2654C2213yes—
73#2654C2213yes—
74#2654C2216yes—
75#2650C2211yescharacteristic
76#2650C2213yes—
77#2647C2213yes—
78#2647C2213yes—
79#2647C2213yes—
80#2645C2213yes—
81#2645C2213yes—
82#2637C2213yes—
83#2637C2213yes—
84#2634C2213yes—
85#2634C2213yes—
86#2629C2213yes—
87#2628C2213yes—
88#2584C2213yes—
89#2582C2213yes—
90#2581C2213yes—
91#2571C2213yes—
92#2571C2213yes—
93#2571C2213yes—
94#2570C2213yes—
95#2570C2213yes—
96#2570C2213yes—
97#2570C2213yes—
98#2570C2213yes—
99#2570C2213yes—
100#2570C2213yes—
101#2568C2213yes—
102#2565C2213yes—
103#2551C2213yes—
104#2551C2213yes—
105#2550C2213yes—
106#2550C2213yes—
107#2546C2213yes—
108#2533C2216yes—
109#2528C2216yes—
110#2524C2216yes—
111#2524C2216yes—
112#2514C2216yes—
113#2514C2213yes—
114#2514C2213yes—
115#2514C2213yes—
116#2514C2213yes—
117#2514C2213yes—
118#2514C2213yes—
119#2514C2213yes—
120#2514C2213yes—
121#2511C2213yes—
122#2511C2213yes—
123#2511C2213yes—
124#2511C2213yes—
125#2509C2213yes—
126#2509C2213yes—
127#2509C2213yes—
128#2509C2213yes—
129#2509C2213yes—
130#2508C2213yes—
131#2508C2213yes—
132#2508C2213yes—
133#2508C2213yes—
134#2508C2213yes—
135#2508C2213yes—
136#2508C2213yes—
137#2508C2213yes—
138#2507C2213yes—
139#2507C2213yes—
140#2507C2213yes—
141#2507C2213yes—
142#2507C2213yes—
143#2506C2213yes—
144#2506C2213yes—
145#2497C2213yes—
146#2497C2213yes—
147#2496C2213yes—
148#2496C2213yes—
149#2495C2213yes—
150#2495C2213yes—
151#2495C2213yes—
152#2495C2213yes—
153#2494C2213yes—
154#2494C2213yes—
155#2494C2213yes—
156#2494C2213yes—
157#2469C2216yes—
158#2462C2216yes—
159#2453C2213yes—
160#2451C2213yes—
161#2451C2213yes—
162#2451C2213yes—
163#2446C2216yes—
164#2441C2213yes—
165#2439C2213yes—
166#2439C2213yes—
167#2439C2213yes—
168#2402C2213yes—
169#2402C2213yes—
170#2402C2213yes—
171#2401C2213yes—
172#2401C2213yes—
173#2399C2213yes—
174#2396C2213yes—
175#2396C2213yes—
176#2370C2213yes—
177#2370C2213yes—
178#2369C2213yes—
179#2365C2213yes—
180#2365C2213yes—
181#2365C2213yes—
182#2356C2213yes—
183#2355C2213yes—
184#2355C2213yes—
185#2355C2213yes—
186#2351C2211yescharacteristic
187#2351C2211yescharacteristic
188#2351C2211yescharacteristic
189#2351C2211yescharacteristic
190#2351C2211yescharacteristic
191#2351C2211yescharacteristic
192#2351C2211yescharacteristic
193#2351C2211yescharacteristic
194#2351C2211yescharacteristic
195#2351C2211yescharacteristic
196#2351C2211yescharacteristic
197#2351C2211yescharacteristic
198#2351C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202Q8×C4⋊C4C2211yescharacteristic
203Q8×C4⋊C4C2211yescharacteristic
204Q8×C4⋊C4C2211yescharacteristic
205Q8×C4⋊C4C2211yescharacteristic
206#2347C2213yes—
207#2346C2213yes—
208Q8×C22⋊C4C2211yescharacteristic
209Q8×C22⋊C4C2211yescharacteristic
210Q8×C22⋊C4C2211yescharacteristic
211Q8×C22⋊C4C2211yescharacteristic
212Q8×C22⋊C4C2211yescharacteristic
213Q8×C22⋊C4C2211yescharacteristic
214#2331C2213yes—
215#2331C2213yes—
216#2327C2216yes—
217#2320C2216yes—
218#2320C2213yes—
219#2314C2213yes—
220C4×C4⋊Q8C2213yes—
221C4×C4⋊Q8C2213yes—
222C4×#125C2213yes—
223C4×#125C2213yes—
224C4×#125C2213yes—
225C4×#125C2213yes—
226C4×#126C2213yes—
227C4×#126C2213yes—
228#2298C2213yes—
229#2295C2213yes—
230#2295C2213yes—
231#2276C2211yescharacteristic
232#2276C2211yescharacteristic
233#2276C2211yescharacteristic
234C42×Q8C2211yescharacteristic
235C42×Q8C2213yes—
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×#126C2313yes—
247C2×#126C2313yes—
248C2×#125C2313yes—
249C2×#125C2313yes—
250C2×#125C2313yes—
251C2×#125C2313yes—
252#519—28no—
253C2×C4×Q8C2313yes—
254C2×C4×Q8C2313yes—
255C2×C4×Q8C2313yes—
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2311yescharacteristic
261C2×C4×Q8C2311yescharacteristic
262C2×C4×Q8C2311yescharacteristic
263C2×C4×Q8C2311yescharacteristic
264C2×C4×Q8C2311yescharacteristic
265C2×C4×Q8C2311yescharacteristic
266C2×C4×Q8C2311yescharacteristic
267C2×C4×Q8C2311yescharacteristic
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2313yes—
270C2×C4×Q8C2313yes—
271C2×C4×Q8C2316yes—
272C2×C4×Q8C2313yes—
273C2×C4×Q8C2311yescharacteristic
274C2×#117C2313yes—
275C2×#117C2313yes—
276#401C2316yes—
277#401C2316yes—
278#401C2316yes—
279#401C2316yes—
280#401C2313yes—
281#401C2313yes—
282#400C2313yes—
283#400C2316yes—
284#400C2316yes—
285#400C2316yes—
286#400C2316yes—
287#400C2316yes—
288#400C2316yes—
289#400C2316yes—
290#400C2316yes—
291#400C2313yes—
292#400C2313yes—
293#400C2313yes—
294#400C2316yes—
295#400C2313yes—
296#400C2316yes—
297#400C2316yes—
298#400C2316yes—
299#400C2316yes—
300#400C2316yes—
301#400C2316yes—
302#400C2316yes—
303#400C2316yes—
304#400C2316yes—
305#400C2316yes—
306#400C2311yescharacteristic
307#400C2313yes—
308#400C2313yes—
309#400C2313yes—
310#400C2313yes—
311#400C2313yes—
312#400C2313yes—
313#400C2313yes—
314#400C2313yes—
315#400C2311yescharacteristic
316#400C2311yescharacteristic
317#400C2313yes—
318#400C2313yes—
319#400C2313yes—
320#400C2313yes—
321#399C2313yes—
322#399C2313yes—
323#398C2313yes—
324#398C2316yes—
325#398C2313yes—
326#398C2313yes—
327#398C2313yes—
328#398C2316yes—
329#398C2316yes—
330#398C2316yes—
331#398C2316yes—
332#398C2316yes—
333#398C2316yes—
334#398C2313yes—
335#398C2316yes—
336#398C2316yes—
337#398C2313yes—
338#398C2316yes—
339#398C2313yes—
340#398C2313yes—
341#398C2313yes—
342#398C2313yes—
343#398C2313yes—
344#398C2313yes—
345#398C2313yes—
346#398C2313yes—
347#398C2313yes—
348#398C2313yes—
349#398C2313yes—
350#398C2313yes—
351#398C2313yes—
352#398C2313yes—
353#397C2313yes—
354#397C2316yes—
355#397C2316yes—
356#397C2311yescharacteristic
357#397C2313yes—
358#397C2311yescharacteristic
359#397C2313yes—
360#397C2313yes—
361#396C2313yes—
362#396C2316yes—
363#396C2313yes—
364#396C2313yes—
365#396C2313yes—
366#396C2313yes—
367#396C2311yescharacteristic
368#395C2316yes—
369#395C2313yes—
370#395C2313yes—
371#395C2316yes—
372#395C2316yes—
373#395C2313yes—
374#395C2313yes—
375#395C2313yes—
376#395C2311yescharacteristic
377#393C2316yes—
378#393C2313yes—
379#393C2311yescharacteristic
380#391C2316yes—
381#391C2316yes—
382#391C2313yes—
383#391C2313yes—
384#391C2316yes—
385#391C2316yes—
386#391C2313yes—
387#391C2313yes—
388#391C2313yes—
389#391C2313yes—
390#391C2316yes—
391#391C2313yes—
392#391C2313yes—
393#391C2313yes—
394#391C2316yes—
395#391C2313yes—
396#391C2313yes—
397#391C2316yes—
398#391C2316yes—
399#391C2313yes—
400#391C2313yes—
401#391C2311yescharacteristic
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#389C2316yes—
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#389C2316yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2316yes—
434#389C2316yes—
435#389C2316yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2316yes—
444#389C2316yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#388C2311yescharacteristic
456#388C2311yescharacteristic
457#388C2313yes—
458#388C2313yes—
459#388C2313yes—
460#388C2313yes—
461#388C2313yes—
462#388C2316yes—
463#388C2313yes—
464#388C2313yes—
465#388C2311yescharacteristic
466#388C2316yes—
467#388C2316yes—
468#387C2313yes—
469#387C2313yes—
470#387C2313yes—
471#387C2313yes—
472#387C2313yes—
473#387C2313yes—
474#387C2311yescharacteristic
475#387C2311yescharacteristic
476#387C2313yes—
477#387C2313yes—
478#387C2313yes—
479#387C2313yes—
480#387C2316yes—
481#387C2313yes—
482#387C2316yes—
483#387C2313yes—
484#387C2316yes—
485#387C2316yes—
486#387C2316yes—
487#387C2316yes—
488#387C2316yes—
489#387C2316yes—
490#387C2316yes—
491#387C2316yes—
492#387C2316yes—
493#387C2316yes—
494#387C2316yes—
495#387C2316yes—
496#387C2316yes—
497#387C2316yes—
498#387C2313yes—
499#387C2316yes—
500#387C2316yes—
501#387C2313yes—
502#387C2316yes—
503#387C2316yes—
504#387C2316yes—
505#387C2316yes—
506#387C2316yes—
507#387C2316yes—
508#387C2313yes—
509#387C2313yes—
510#387C2316yes—
511#387C2316yes—
512#387C2316yes—
513#387C2316yes—
514#387C2316yes—
515#387C2316yes—
516#387C2313yes—
517#387C2313yes—
518#387C2313yes—
519#387C2313yes—
520#387C2316yes—
521#387C2316yes—
522#384C2313yes—
523#384C2313yes—
524#384C2313yes—
525#384C2313yes—
526#384C2313yes—
527#384C2313yes—
528#384C2313yes—
529#383C2313yes—
530#383C2313yes—
531#383C2316yes—
532#383C2316yes—
533#383C2316yes—
534#383C2316yes—
535#383C2316yes—
536#382C2313yes—
537#382C2313yes—
538#382C2313yes—
539#382C2313yes—
540#382C2313yes—
541#382C2313yes—
542#382C2313yes—
543#382C2313yes—
544#382C2313yes—
545#382C2313yes—
546#382C2313yes—
547#382C2313yes—
548#382C2313yes—
549#382C2313yes—
550#382C2316yes—
551#382C2316yes—
552#382C2316yes—
553#382C2313yes—
554#382C2316yes—
555#380C2313yes—
556#380C2313yes—
557#380C2313yes—
558#380C2313yes—
559#380C2313yes—
560#380C2313yes—
561C4×C4⋊C4C2313yes—
562C4×C4⋊C4C2313yes—
563C4×C4⋊C4C2313yes—
564C4×C4⋊C4C2313yes—
565C4×C4⋊C4C2313yes—
566C4×C4⋊C4C2313yes—
567C4×C4⋊C4C2316yes—
568C4×C4⋊C4C2313yes—
569C4×C4⋊C4C2313yes—
570C4×C4⋊C4C2313yes—
571C4×C4⋊C4C2313yes—
572C4×C4⋊C4C2313yes—
573C4×C4⋊C4C2313yes—
574C4×C4⋊C4C2313yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2316yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2316yes—
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⋊C4C2311yescharacteristic
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614#376C2316yes—
615#376C2313yes—
616#376C2313yes—
617#376C2313yes—
618C43C2313yes—
619C43C2313yes—
620C43C2313yes—
621C22×Q8—24no—
622C22×Q8—24no—
623C22×Q8—24no—
624C22×Q8C2413yes—
625C22×Q8C2413yes—
626C22×Q8C2411yescharacteristic
627C22×Q8C2416yes—
628C22×Q8C2411yescharacteristic
629C23×C4C2413yes—
630C4⋊Q8—212no—
631C4⋊Q8—212no—
632C4⋊Q8—212no—
633C4⋊Q8—212no—
634C4⋊Q8—412no—
635#126—46no—
636#126—46no—
637#125—212no—
638#125—212no—
639#125—46no—
640#125—46no—
641C4×Q8—24no—
642C4×Q8—24no—
643C4×Q8—24no—
644C4×Q8—24no—
645C4×Q8—24no—
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—212no—
655C4×Q8—212no—
656C4×Q8—212no—
657C4×Q8—212no—
658C4×Q8—46no—
659C4×Q8—412no—
660C4×Q8—46no—
661C4×Q8#4118yes—
662#117—212no—
663#117—212no—
664C2×C4⋊C4C2413yes—
665C2×C4⋊C4C2413yes—
666C2×C4⋊C4C2413yes—
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2413yes—
670C2×C4⋊C4C2413yes—
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⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2416yes—
691C2×C4⋊C4C2413yes—
692C2×C4⋊C4C2413yes—
693C2×C4⋊C4C2413yes—
694C2×C4⋊C4C2413yes—
695C2×C4⋊C4C2413yes—
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2416yes—
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2413yes—
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2416yes—
712C2×C4⋊C4C2416yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2411yescharacteristic
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2416yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2416yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2416yes—
732C2×C4⋊C4C2416yes—
733C2×C4⋊C4C2413yes—
734C2×C22⋊C4C2413yes—
735C2×C22⋊C4C2411yescharacteristic
736C2×C22⋊C4C2411yescharacteristic
737C2×C22⋊C4C2411yescharacteristic
738C2×C22⋊C4C2413yes—
739C2×C22⋊C4C2413yes—
740C2×C22⋊C4C2413yes—
741C2×C22⋊C4C2413yes—
742C2×C22⋊C4C2411yescharacteristic
743C2×C22⋊C4C2411yescharacteristic
744C2×C22⋊C4C2411yescharacteristic
745C2×C22⋊C4C2411yescharacteristic
746C2×C22⋊C4C2413yes—
747C2×C22⋊C4C2413yes—
748C2×C42C2416yes—
749C2×C42C2413yes—
750C2×C42C2411yescharacteristic
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×C42C2413yes—
766C2×C42C2413yes—
767C2×C42C2413yes—
768C2×C42C2416yes—
769C2×C42C2416yes—
770C2×C42C2416yes—
771C2×C42C2411yescharacteristic
772C2×C42C2411yescharacteristic
773C2×C42C2413yes—
774C2×C42C2413yes—
775C2×C42C2413yes—
776C2×C42C2413yes—
777C2×C42C2413yes—
778#95C2411yescharacteristic
779#95C2411yescharacteristic
780#95C2411yescharacteristic
781#95C2413yes—
782#95C2413yes—
783#95C2413yes—
784#95C2413yes—
785#95C2413yes—
786#95C2413yes—
787#95C2413yes—
788#95C2413yes—
789#95C2413yes—
790#95C2413yes—
791#95C2413yes—
792#95C2416yes—
793#95C2416yes—
794#95C2413yes—
795#95C2413yes—
796#95C2413yes—
797#95C2413yes—
798#95C2413yes—
799#95C2413yes—
800#95C2413yes—
801#95C2413yes—
802#95C2413yes—
803#95C2413yes—
804#95C2413yes—
805#95C2411yescharacteristic
806#95C2411yescharacteristic
807#95C2413yes—
808#95C2411yescharacteristic
809#95C2411yescharacteristic
810#95C2413yes—
811#95C2413yes—
812#95C2416yes—
813#95C2411yescharacteristic
814#95C2411yescharacteristic
815#95C2411yescharacteristic
816#95C2411yescharacteristic
817#95C2411yescharacteristic
818#95C2416yes—
819#95C2411yescharacteristic
820#95C2411yescharacteristic
821#95C2411yescharacteristic
822#95C2413yes—
823#95C2416yes—
824#95C2411yescharacteristic
825#95C2416yes—
826#95C2413yes—
827#95C2413yes—
828#95C2413yes—
829#95C2413yes—
830#95C2413yes—
831#95C2413yes—
832#95C2413yes—
833#95C2413yes—
834#95C2413yes—
835#95C2413yes—
836#95C2413yes—
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2416yes—
841#95C2416yes—
842#95C2416yes—
843#95C2413yes—
844#95C2416yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2416yes—
853#95C2416yes—
854#95C2416yes—
855#95C2416yes—
856#95C2416yes—
857#95C2416yes—
858#95C2416yes—
859#95C2416yes—
860#95C2416yes—
861#95C2416yes—
862#95C2416yes—
863#95C2416yes—
864C24C2511yescharacteristic
865C2×Q8—22no—
866C2×Q8—26no—
867C2×Q8—26no—
868C2×Q8—212no—
869C2×Q8—26no—
870C2×Q8—26no—
871C2×Q8—26no—
872C2×Q8—43no—
873C2×Q8—41no—
874C2×Q8—41no—
875C2×Q8—46no—
876C2×Q8—46no—
877C2×Q8—416no—
878C2×Q8C2×#4114yes—
879C2×Q82−1+414yes—
880C2×Q82−1+414yes—
881C22×C4—26no—
882C22×C4—26no—
883C22×C4—26no—
884C22×C4C2513yes—
885C22×C4C2511yescharacteristic
886C22×C4C2511yescharacteristic
887C22×C4C2511yescharacteristic
888C22×C4C2513yes—
889C22×C4C2513yes—
890C22×C4C2511yescharacteristic
891C22×C4C2511yescharacteristic
892C22×C4C2511yescharacteristic
893C22×C4C2511yescharacteristic
894C22×C4C2513yes—
895C22×C4C2513yes—
896C22×C4C2513yes—
897C22×C4C2513yes—
898C22×C4C2513yes—
899C22×C4C2513yes—
900C22×C4C2511yescharacteristic
901C22×C4C2511yescharacteristic
902C22×C4C2511yescharacteristic
903C22×C4C2513yes—
904C22×C4C2513yes—
905C22×C4C2513yes—
906C22×C4C2513yes—
907C22×C4C2513yes—
908C22×C4C2511yescharacteristic
909C22×C4C2511yescharacteristic
910C22×C4C2513yes—
911C22×C4C2511yescharacteristic
912C22×C4C2511yescharacteristic
913C22×C4C2513yes—
914C4⋊C4—26no—
915C4⋊C4—26no—
916C4⋊C4—26no—
917C4⋊C4—22no—
918C4⋊C4—26no—
919C4⋊C4—26no—
920C4⋊C4—26no—
921C4⋊C4—26no—
922C4⋊C4—26no—
923C4⋊C4—26no—
924C4⋊C4—26no—
925C4⋊C4—26no—
926C4⋊C4—26no—
927C4⋊C4—212no—
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—22no—
937C4⋊C4—26no—
938C4⋊C4—26no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—26no—
942C4⋊C4—26no—
943C4⋊C4—41no—
944C4⋊C4—43no—
945C4⋊C4—41no—
946C4⋊C4—41no—
947C4⋊C4—46no—
948C4⋊C4—46no—
949C4⋊C4—43no—
950C4⋊C4—43no—
951C4⋊C4—43no—
952C4⋊C4—46no—
953C4⋊C4—43no—
954C4⋊C4—43no—
955C4⋊C4—43no—
956C4⋊C4—43no—
957C4⋊C4—43no—
958C4⋊C4—46no—
959C4⋊C4—41no—
960C4⋊C4—43no—
961C4⋊C4—43no—
962C4⋊C4—43no—
963C4⋊C4—43no—
964C4⋊C4—43no—
965C4⋊C4—46no—
966C4⋊C4—43no—
967C4⋊C4—43no—
968C4⋊C4—43no—
969C4⋊C4—43no—
970C4⋊C4—43no—
971C4⋊C4—43no—
972C4⋊C4—43no—
973C4⋊C4—43no—
974C4⋊C4—43no—
975C4⋊C4—43no—
976C4⋊C4—43no—
977C4⋊C4—43no—
978C4⋊C4—43no—
979C4⋊C4—43no—
980C4⋊C4—43no—
981C4⋊C4—46no—
982C4⋊C4—46no—
983C4⋊C4C2×#41112yes—
984C22⋊C4—26no—
985C22⋊C4—22no—
986C22⋊C4—22no—
987C22⋊C4—22no—
988C22⋊C4—41no—
989C22⋊C4—41no—
990C22⋊C4—41no—
991C22⋊C4—43no—
992C22⋊C4—43no—
993C22⋊C4—41no—
994C22⋊C4—43no—
995C22⋊C4—43no—
996C22⋊C4—43no—
997C22⋊C4—43no—
998C42—26no—
999C42—212no—
1000C42—26no—
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—22no—
1014C42—26no—
1015C42—26no—
1016C42—41no—
1017C42—41no—
1018C42—43no—
1019C42—43no—
1020C42—43no—
1021C42—43no—
1022C42—43no—
1023C42—46no—
1024C42—46no—
1025C42—43no—
1026C42—46no—
1027C42C2×#41112yes—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—21no—
1035C23C2611yescharacteristic
1036Q8—412no—
1037Q8—44no—
1038Q8—412no—
1039Q8—812no—
1040Q8#541116yes—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—23no—
1044C2×C4—21no—
1045C2×C4—23no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—23no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—23no—
1055C2×C4—23no—
1056C2×C4—23no—
1057C2×C4—23no—
1058C2×C4—23no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—23no—
1067C2×C4—23no—
1068C2×C4—23no—
1069C2×C4—23no—
1070C2×C4—23no—
1071C2×C4—23no—
1072C2×C4—23no—
1073C2×C4—23no—
1074C2×C4—23no—
1075C2×C4—23no—
1076C2×C4—23no—
1077C2×C4—23no—
1078C2×C4—23no—
1079C2×C4—23no—
1080C2×C4—23no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—23no—
1085C2×C4—23no—
1086C2×C4—23no—
1087C2×C4—23no—
1088C2×C4—23no—
1089C2×C4—23no—
1090C2×C4—23no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—23no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—23no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—23no—
1102C2×C4—23no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—23no—
1106C2×C4—21no—
1107C2×C4—23no—
1108C2×C4—23no—
1109C2×C4—23no—
1110C2×C4—21no—
1111C2×C4—23no—
1112C2×C4—21no—
1113C2×C4—23no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—23no—
1117C2×C4—23no—
1118C2×C4—23no—
1119C2×C4—23no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—412no—
1125C2×C4C22×#4116yes—
1126C2×C4C22×#4112yes—
1127C2×C4C22×#4116yes—
1128C2×C4C2×2−1+416yes—
1129C2×C4C2×2−1+416yes—
1130C2×C4#58512yes—
1131C2×C4#58512yes—
1132C22—41no—
1133C22—41no—
1134C22—41no—
1135C22—41no—
1136C22—41no—
1137C22—41no—
1138C22—41no—
1139C22C23×#4111yescharacteristic
1140C22C22×2−1+411yescharacteristic
1141C22C22×2−1+411yescharacteristic
1142C22C2×#58511yescharacteristic
1143C22C2×#58511yescharacteristic
1144C222−1+611yescharacteristic
1145C222−1+611yescharacteristic
1146C4—26no—
1147C4—22no—
1148C4—22no—
1149C4—22no—
1150C4—41no—
1151C4—43no—
1152C4—43no—
1153C4—43no—
1154C4—43no—
1155C4—41no—
1156C4—43no—
1157C4—41no—
1158C4—41no—
1159C4—43no—
1160C4—41no—
1161C4—43no—
1162C4—43no—
1163C4—41no—
1164C4—41no—
1165C4—41no—
1166C4—41no—
1167C4—41no—
1168C4—41no—
1169C4—43no—
1170C4—43no—
1171C4—43no—
1172C4—43no—
1173C4—43no—
1174C4—43no—
1175C4C2×#541112yes—
1176C2—81no—
1177C2C22×#54111yescharacteristic
1178C2#6281011yescharacteristic
1179C2#6285011yescharacteristic
1180C2#6294911yescharacteristic
1181C2#6295311yescharacteristic
1182C2#6295311yescharacteristic
1183C2#6295311yescharacteristic
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
1. #42765C2semidirect
3. #42703C2semidirect
4. #42689C2semidirect
7. #42600C2semidirect
10. #40143C2semidirect
12. #39003C2semidirect
14. #37580C2semidirect
15. #36475C2semidirect
16. #36475C2semidirect
19. #35971C2semidirect
20. #35971C2semidirect
21. #35971C2semidirect
22. #35937C2semidirect
27. #35187C2semidirect
29. #34335C2semidirect
31. C4×#557C2semidirect

Maximal subgroups

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

subgroupindex
#427652
#427642
#427032
#426892
#426672
#426572
#426002
#425972
#401552
#401432
#390112
#390032
#375972
#375802
#364752
#364482
#359712
#359372
#358832
#357862
#357112
#351872
#346042
#343352
#342622
C4×#5572