Finite Group Databasebeta

← #7656406

Subgroups — #7656406

Order 512.

4114 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42782C213yesmaximal, complemented
2#42774C213yesmaximal, complemented
3#42744C213yesmaximal, complemented
4#42733C213yesmaximal, complemented
5#42636C213yesmaximal
6#42623C213yesmaximal
7#42587C213yesmaximal
8#42573C213yesmaximal
9#40024C213yesmaximal, complemented
10#39999C213yesmaximal, complemented
11#39928C213yesmaximal
12#39907C213yesmaximal
13#37580C213yesmaximal, complemented
14#37580C213yesmaximal, complemented
15#36475C211yesmaximal, characteristic, complemented
16#36466C211yesmaximal, characteristic, complemented
17#36435C211yesmaximal, characteristic
18#36435C211yesmaximal, characteristic
19#35971C211yesmaximal, characteristic, complemented
20#35971C211yesmaximal, characteristic, complemented
21#35971C211yesmaximal, characteristic, complemented
22#35920C211yesmaximal, characteristic
23#35883C211yesmaximal, characteristic
24#35883C211yesmaximal, characteristic
25#35883C211yesmaximal, characteristic
26#35868C211yesmaximal, characteristic, complemented
27#35142C213yesmaximal
28#34629C213yesmaximal
29#34336C211yesmaximal, characteristic, complemented
30#34336C211yesmaximal, characteristic, complemented
31#34128C211yesmaximal, characteristic
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35#2864C2213yes—
36#2859C2213yes—
37#2851C2213yes—
38#2851C2213yes—
39#2839C2216yes—
40#2839C2216yes—
41#2833C2216yes—
42#2833C2216yes—
43#2802C2216yes—
44#2794C2216yes—
45#2789C2216yes—
46#2776C2216yes—
47#2776C2216yes—
48#2769C2216yes—
49#2766C2216yes—
50#2762C2216yes—
51#2758C2216yes—
52#2758C2216yes—
53#2744C2216yes—
54#2739C2216yes—
55#2719C2216yes—
56#2713C2216yes—
57#2698C2216yes—
58#2689C2216yes—
59#2666C2216yes—
60#2666C2216yes—
61#2655C2216yes—
62#2655C2216yes—
63#2655C2213yes—
64#2655C2213yes—
65#2655C2213yes—
66#2655C2213yes—
67#2655C2216yes—
68#2652C2211yescharacteristic
69#2652C2213yes—
70#2652C2213yes—
71#2652C2213yes—
72#2647C2213yes—
73#2647C2213yes—
74#2647C2213yes—
75#2647C2213yes—
76#2647C2213yes—
77#2645C2213yes—
78#2645C2213yes—
79#2645C2213yes—
80#2645C2213yes—
81#2645C2213yes—
82#2645C2213yes—
83#2642C2213yes—
84#2629C2213yes—
85#2625C2213yes—
86#2625C2213yes—
87#2621C2213yes—
88#2584C2213yes—
89#2584C2213yes—
90#2581C2213yes—
91#2581C2213yes—
92#2571C2213yes—
93#2571C2213yes—
94#2571C2213yes—
95#2570C2213yes—
96#2570C2213yes—
97#2570C2213yes—
98#2570C2213yes—
99#2570C2213yes—
100#2570C2213yes—
101#2565C2213yes—
102#2565C2213yes—
103#2552C2213yes—
104#2552C2213yes—
105#2551C2213yes—
106#2550C2213yes—
107#2550C2213yes—
108#2533C2216yes—
109#2533C2216yes—
110#2533C2216yes—
111#2528C2216yes—
112#2528C2216yes—
113#2528C2216yes—
114#2514C2213yes—
115#2514C2213yes—
116#2514C2213yes—
117#2514C2213yes—
118#2514C2213yes—
119#2514C2213yes—
120#2511C2213yes—
121#2511C2213yes—
122#2511C2213yes—
123#2511C2213yes—
124#2511C2213yes—
125#2511C2213yes—
126#2509C2213yes—
127#2509C2213yes—
128#2509C2213yes—
129#2509C2213yes—
130#2509C2213yes—
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#2506C2213yes—
146#2497C2213yes—
147#2497C2213yes—
148#2497C2213yes—
149#2496C2213yes—
150#2496C2213yes—
151#2496C2213yes—
152#2495C2213yes—
153#2495C2213yes—
154#2495C2213yes—
155#2494C2213yes—
156#2494C2213yes—
157#2494C2213yes—
158#2478C2216yes—
159#2475C2216yes—
160#2453C2213yes—
161#2453C2213yes—
162#2451C2213yes—
163#2451C2213yes—
164#2442C2213yes—
165#2442C2213yes—
166#2440C2213yes—
167#2440C2213yes—
168#2402C2213yes—
169#2402C2213yes—
170#2402C2213yes—
171#2402C2213yes—
172#2401C2213yes—
173#2401C2213yes—
174#2401C2213yes—
175#2401C2213yes—
176#2370C2213yes—
177#2370C2213yes—
178#2370C2213yes—
179#2370C2213yes—
180#2369C2213yes—
181#2369C2213yes—
182#2356C2213yes—
183#2356C2213yes—
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
198Q8×C4⋊C4C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202Q8×C4⋊C4C2211yescharacteristic
203Q8×C4⋊C4C2211yescharacteristic
204Q8×C4⋊C4C2211yescharacteristic
205Q8×C4⋊C4C2211yescharacteristic
206#2344C2213yes—
207#2344C2213yes—
208Q8×C22⋊C4C2211yescharacteristic
209Q8×C22⋊C4C2211yescharacteristic
210Q8×C22⋊C4C2211yescharacteristic
211Q8×C22⋊C4C2211yescharacteristic
212Q8×C22⋊C4C2211yescharacteristic
213Q8×C22⋊C4C2211yescharacteristic
214#2336C2216yes—
215#2334C2216yes—
216#2331C2213yes—
217#2331C2213yes—
218#2330C2213yes—
219#2330C2213yes—
220C4×C4⋊Q8C2213yes—
221C4×#125C2213yes—
222C4×#125C2213yes—
223C4×#125C2213yes—
224C4×C22⋊Q8C2213yes—
225C4×C22⋊Q8C2213yes—
226#2295C2213yes—
227#2295C2213yes—
228#2295C2213yes—
229#2295C2213yes—
230#2283C2213yes—
231#2276C2211yescharacteristic
232#2276C2211yescharacteristic
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C4×#117C2213yes—
238C23×Q8C2311yescharacteristic
239#557—28no—
240#557—28no—
241C2×C4⋊Q8C2313yes—
242C2×C4⋊Q8C2313yes—
243C2×C4⋊Q8C2313yes—
244C2×#126C2316yes—
245C2×#125C2313yes—
246C2×#125C2313yes—
247C2×#125C2313yes—
248C2×#125C2313yes—
249C2×#125C2313yes—
250C2×#125C2316yes—
251C2×C22⋊Q8C2313yes—
252C2×C22⋊Q8C2313yes—
253C2×C4×Q8—28no—
254C2×C4×Q8C2313yes—
255C2×C4×Q8C2313yes—
256C2×C4×Q8C2313yes—
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×Q8C2311yescharacteristic
270C2×C4×Q8C2313yes—
271C2×C4×Q8C2311yescharacteristic
272C2×#117C2313yes—
273C2×#117C2313yes—
274C22×C4⋊C4C2313yes—
275C22×C42C2313yes—
276#401C2313yes—
277#401C2316yes—
278#401C2316yes—
279#401C2316yes—
280#401C2313yes—
281#401C2313yes—
282#401C2313yes—
283#400C2313yes—
284#400C2316yes—
285#400C2316yes—
286#400C2316yes—
287#400C2316yes—
288#400C2316yes—
289#400C2313yes—
290#400C2313yes—
291#400C2313yes—
292#400C2313yes—
293#400C2313yes—
294#400C2316yes—
295#400C2316yes—
296#400C2316yes—
297#400C2316yes—
298#400C2316yes—
299#400C2316yes—
300#400C2316yes—
301#400C2313yes—
302#400C2313yes—
303#400C2316yes—
304#400C2316yes—
305#400C2316yes—
306#400C2316yes—
307#400C2316yes—
308#400C2316yes—
309#400C2316yes—
310#400C2316yes—
311#400C2313yes—
312#400C2313yes—
313#400C2311yescharacteristic
314#400C2313yes—
315#400C2313yes—
316#400C2313yes—
317#400C2313yes—
318#400C2313yes—
319#400C2311yescharacteristic
320#400C2311yescharacteristic
321#400C2313yes—
322#400C2313yes—
323#400C2313yes—
324#400C2313yes—
325#400C2313yes—
326#400C2313yes—
327#400C2313yes—
328#400C2313yes—
329#400C2313yes—
330#400C2313yes—
331#398C2316yes—
332#398C2316yes—
333#398C2316yes—
334#398C2316yes—
335#398C2313yes—
336#398C2313yes—
337#398C2313yes—
338#398C2316yes—
339#398C2316yes—
340#398C2316yes—
341#398C2313yes—
342#398C2316yes—
343#398C2316yes—
344#398C2313yes—
345#398C2313yes—
346#398C2316yes—
347#398C2316yes—
348#398C2316yes—
349#398C2316yes—
350#398C2313yes—
351#398C2313yes—
352#398C2313yes—
353#398C2313yes—
354#398C2313yes—
355#398C2313yes—
356#398C2313yes—
357#398C2311yescharacteristic
358#398C2313yes—
359#398C2313yes—
360#397C2311yescharacteristic
361#397C2313yes—
362#397C2313yes—
363#397C2313yes—
364#397C2311yescharacteristic
365#397C2311yescharacteristic
366#397C2313yes—
367#397C2313yes—
368#397C2313yes—
369#397C2313yes—
370#397C2313yes—
371#397C2313yes—
372#396C2311yescharacteristic
373#396C2313yes—
374#396C2313yes—
375#396C2313yes—
376#395C2316yes—
377#395C2316yes—
378#395C2316yes—
379#395C2316yes—
380#391C2313yes—
381#391C2313yes—
382#391C2313yes—
383#391C2313yes—
384#391C2313yes—
385#391C2313yes—
386#391C2313yes—
387#391C2313yes—
388#391C2313yes—
389#391C2313yes—
390#391C2313yes—
391#391C2313yes—
392#391C2313yes—
393#391C2313yes—
394#391C2316yes—
395#391C2316yes—
396#391C2313yes—
397#391C2313yes—
398#391C2313yes—
399#391C2313yes—
400#391C2313yes—
401#391C2313yes—
402#389C2313yes—
403#389C2313yes—
404#389C2313yes—
405#389C2313yes—
406#389C2313yes—
407#389C2313yes—
408#389C2311yescharacteristic
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#389C2316yes—
428#389C2316yes—
429#389C2313yes—
430#389C2313yes—
431#389C2316yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2316yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2316yes—
448#389C2316yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2316yes—
455#389C2316yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2316yes—
463#388C2316yes—
464#388C2316yes—
465#388C2316yes—
466#387C2311yescharacteristic
467#387C2313yes—
468#387C2313yes—
469#387C2313yes—
470#387C2313yes—
471#387C2316yes—
472#387C2316yes—
473#387C2313yes—
474#387C2313yes—
475#387C2313yes—
476#387C2316yes—
477#387C2316yes—
478#387C2316yes—
479#387C2316yes—
480#387C2316yes—
481#387C2316yes—
482#387C2316yes—
483#387C2316yes—
484#387C2316yes—
485#387C2316yes—
486#387C2316yes—
487#387C2316yes—
488#387C2316yes—
489#387C2313yes—
490#387C2313yes—
491#387C2316yes—
492#387C2316yes—
493#387C2316yes—
494#387C2316yes—
495#387C2316yes—
496#387C2316yes—
497#387C2316yes—
498#387C2316yes—
499#387C2316yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2316yes—
504#387C2313yes—
505#387C2313yes—
506#387C2313yes—
507#387C2313yes—
508#387C2311yescharacteristic
509#387C2311yescharacteristic
510#387C2316yes—
511#387C2316yes—
512#387C2316yes—
513#387C2316yes—
514#387C2316yes—
515#387C2316yes—
516#385C2313yes—
517#385C2313yes—
518#385C2316yes—
519#385C2316yes—
520#385C2311yescharacteristic
521#385C2311yescharacteristic
522#384C2313yes—
523#384C2313yes—
524#384C2313yes—
525#384C2313yes—
526#384C2313yes—
527#384C2313yes—
528#384C2313yes—
529#384C2313yes—
530#384C2313yes—
531#383C2316yes—
532#383C2316yes—
533#383C2316yes—
534#383C2316yes—
535#382C2313yes—
536#382C2313yes—
537#382C2313yes—
538#382C2313yes—
539#382C2313yes—
540#382C2313yes—
541#382C2313yes—
542#382C2313yes—
543#382C2313yes—
544#382C2313yes—
545#382C2313yes—
546#382C2313yes—
547#382C2316yes—
548#382C2313yes—
549#382C2316yes—
550#382C2316yes—
551#381C2316yes—
552#380C2313yes—
553#380C2313yes—
554#380C2313yes—
555#380C2313yes—
556#380C2313yes—
557#380C2313yes—
558#380C2313yes—
559#380C2313yes—
560C4×C4⋊C4C2313yes—
561C4×C4⋊C4C2313yes—
562C4×C4⋊C4C2313yes—
563C4×C4⋊C4C2313yes—
564C4×C4⋊C4C2313yes—
565C4×C4⋊C4C2313yes—
566C4×C4⋊C4C2313yes—
567C4×C4⋊C4C2313yes—
568C4×C4⋊C4C2313yes—
569C4×C4⋊C4C2316yes—
570C4×C4⋊C4C2316yes—
571C4×C4⋊C4C2313yes—
572C4×C4⋊C4C2316yes—
573C4×C4⋊C4C2316yes—
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⋊C4C2313yes—
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⋊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×C22⋊C4C2313yes—
605C4×C22⋊C4C2313yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2311yescharacteristic
612#376C2313yes—
613#376C2313yes—
614#376C2313yes—
615#376C2313yes—
616#376C2313yes—
617#376C2313yes—
618#376C2316yes—
619C43C2313yes—
620C43C2313yes—
621C22×Q8—24no—
622C22×Q8—24no—
623C22×Q8—24no—
624C22×Q8C2413yes—
625C22×Q8C2413yes—
626C22×Q8C2413yes—
627C22×Q8C2411yescharacteristic
628C23×C4C2413yes—
629C23×C4C2413yes—
630C23×C4C2411yescharacteristic
631C4⋊Q8—212no—
632C4⋊Q8—212no—
633C4⋊Q8—46no—
634#126—412no—
635#125—212no—
636#125—212no—
637#125—212no—
638#125—212no—
639#125—46no—
640#125—412no—
641C22⋊Q8—46no—
642C22⋊Q8—46no—
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—24no—
655C4×Q8—24no—
656C4×Q8—212no—
657C4×Q8—212no—
658C4×Q8—212no—
659C4×Q8—212no—
660C4×Q8#4118yes—
661#117—46no—
662#117—46no—
663C2×C4⋊C4—212no—
664C2×C4⋊C4C2413yes—
665C2×C4⋊C4C2416yes—
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⋊C4C2411yescharacteristic
686C2×C4⋊C4C2413yes—
687C2×C4⋊C4C2413yes—
688C2×C4⋊C4C2416yes—
689C2×C4⋊C4C2416yes—
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2413yes—
692C2×C4⋊C4C2413yes—
693C2×C4⋊C4C2413yes—
694C2×C4⋊C4C2413yes—
695C2×C4⋊C4C2413yes—
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2413yes—
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2416yes—
705C2×C4⋊C4C2416yes—
706C2×C4⋊C4C2416yes—
707C2×C4⋊C4C2416yes—
708C2×C4⋊C4C2416yes—
709C2×C4⋊C4C2416yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2413yes—
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⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2416yes—
733C2×C4⋊C4C2416yes—
734C2×C4⋊C4C2413yes—
735C2×C22⋊C4C2411yescharacteristic
736C2×C22⋊C4C2411yescharacteristic
737C2×C22⋊C4C2413yes—
738C2×C22⋊C4C2411yescharacteristic
739C2×C22⋊C4C2411yescharacteristic
740C2×C22⋊C4C2413yes—
741C2×C22⋊C4C2413yes—
742C2×C22⋊C4C2413yes—
743C2×C22⋊C4C2411yescharacteristic
744C2×C22⋊C4C2411yescharacteristic
745C2×C22⋊C4C2413yes—
746C2×C22⋊C4C2413yes—
747C2×C42—212no—
748C2×C42C2413yes—
749C2×C42C2413yes—
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×C42C2413yes—
766C2×C42C2413yes—
767C2×C42C2416yes—
768C2×C42C2416yes—
769C2×C42C2411yescharacteristic
770C2×C42C2411yescharacteristic
771C2×C42C2413yes—
772C2×C42C2413yes—
773C2×C42C2416yes—
774C2×C42C2416yes—
775C2×C42C2413yes—
776#95C2411yescharacteristic
777#95C2411yescharacteristic
778#95C2411yescharacteristic
779#95C2411yescharacteristic
780#95C2411yescharacteristic
781#95C2411yescharacteristic
782#95C2413yes—
783#95C2413yes—
784#95C2413yes—
785#95C2413yes—
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#95C2416yes—
813#95C2416yes—
814#95C2411yescharacteristic
815#95C2413yes—
816#95C2413yes—
817#95C2411yescharacteristic
818#95C2411yescharacteristic
819#95C2411yescharacteristic
820#95C2411yescharacteristic
821#95C2411yescharacteristic
822#95C2413yes—
823#95C2413yes—
824#95C2411yescharacteristic
825#95C2411yescharacteristic
826#95C2411yescharacteristic
827#95C2411yescharacteristic
828#95C2413yes—
829#95C2413yes—
830#95C2413yes—
831#95C2413yes—
832#95C2413yes—
833#95C2413yes—
834#95C2413yes—
835#95C2413yes—
836#95C2413yes—
837#95C2416yes—
838#95C2413yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2416yes—
843#95C2416yes—
844#95C2416yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2416yes—
855#95C2416yes—
856#95C2416yes—
857#95C2416yes—
858#95C2416yes—
859#95C2416yes—
860#95C2416yes—
861#95C2416yes—
862#95C2416yes—
863#95C2416yes—
864C24C2511yescharacteristic
865C2×Q8—26no—
866C2×Q8—26no—
867C2×Q8—26no—
868C2×Q8—26no—
869C2×Q8—26no—
870C2×Q8—43no—
871C2×Q8—43no—
872C2×Q8—43no—
873C2×Q8—43no—
874C2×Q8—416no—
875C2×Q8C2×#4114yes—
876C2×Q82−1+414yes—
877C2×Q82−1+414yes—
878C22×C4—26no—
879C22×C4—22no—
880C22×C4—26no—
881C22×C4—26no—
882C22×C4—26no—
883C22×C4—26no—
884C22×C4—43no—
885C22×C4—41no—
886C22×C4—41no—
887C22×C4C2513yes—
888C22×C4C2511yescharacteristic
889C22×C4C2511yescharacteristic
890C22×C4C2511yescharacteristic
891C22×C4C2513yes—
892C22×C4C2513yes—
893C22×C4C2511yescharacteristic
894C22×C4C2511yescharacteristic
895C22×C4C2511yescharacteristic
896C22×C4C2511yescharacteristic
897C22×C4C2511yescharacteristic
898C22×C4C2513yes—
899C22×C4C2513yes—
900C22×C4C2513yes—
901C22×C4C2513yes—
902C22×C4C2513yes—
903C22×C4C2513yes—
904C22×C4C2511yescharacteristic
905C22×C4C2511yescharacteristic
906C22×C4C2511yescharacteristic
907C22×C4C2511yescharacteristic
908C22×C4C2513yes—
909C22×C4C2513yes—
910C22×C4C2513yes—
911C22×C4C2513yes—
912C22×C4C2513yes—
913C22×C4C2511yescharacteristic
914C22×C4C2513yes—
915C22×C4C2511yescharacteristic
916C22×C4C2513yes—
917C4⋊C4—26no—
918C4⋊C4—212no—
919C4⋊C4—22no—
920C4⋊C4—22no—
921C4⋊C4—26no—
922C4⋊C4—26no—
923C4⋊C4—26no—
924C4⋊C4—26no—
925C4⋊C4—26no—
926C4⋊C4—26no—
927C4⋊C4—26no—
928C4⋊C4—26no—
929C4⋊C4—212no—
930C4⋊C4—212no—
931C4⋊C4—26no—
932C4⋊C4—26no—
933C4⋊C4—26no—
934C4⋊C4—26no—
935C4⋊C4—26no—
936C4⋊C4—26no—
937C4⋊C4—26no—
938C4⋊C4—26no—
939C4⋊C4—26no—
940C4⋊C4—26no—
941C4⋊C4—22no—
942C4⋊C4—26no—
943C4⋊C4—22no—
944C4⋊C4—43no—
945C4⋊C4—41no—
946C4⋊C4—43no—
947C4⋊C4—43no—
948C4⋊C4—43no—
949C4⋊C4—43no—
950C4⋊C4—43no—
951C4⋊C4—43no—
952C4⋊C4—43no—
953C4⋊C4—41no—
954C4⋊C4—43no—
955C4⋊C4—41no—
956C4⋊C4—41no—
957C4⋊C4—43no—
958C4⋊C4—43no—
959C4⋊C4—43no—
960C4⋊C4—43no—
961C4⋊C4—46no—
962C4⋊C4—46no—
963C4⋊C4—41no—
964C4⋊C4—41no—
965C4⋊C4—43no—
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—46no—
980C4⋊C4—46no—
981C4⋊C4—46no—
982C4⋊C4—46no—
983C4⋊C4—46no—
984C4⋊C4—46no—
985C4⋊C4—43no—
986C4⋊C4—43no—
987C4⋊C4C2×#41112yes—
988C22⋊C4—22no—
989C22⋊C4—26no—
990C22⋊C4—22no—
991C22⋊C4—22no—
992C22⋊C4—26no—
993C22⋊C4—26no—
994C22⋊C4—22no—
995C22⋊C4—43no—
996C22⋊C4—41no—
997C22⋊C4—41no—
998C22⋊C4—43no—
999C22⋊C4—43no—
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—26no—
1014C42—26no—
1015C42—26no—
1016C42—41no—
1017C42—43no—
1018C42—41no—
1019C42—43no—
1020C42—46no—
1021C42—46no—
1022C42—43no—
1023C42—43no—
1024C42—43no—
1025C42—46no—
1026C42—46no—
1027C42C2×#41112yes—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23#58512yes—
1035C23C2611yescharacteristic
1036Q8—412no—
1037Q8—86no—
1038Q8—86no—
1039Q8#541116yes—
1040C2×C4—21no—
1041C2×C4—23no—
1042C2×C4—23no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—23no—
1052C2×C4—23no—
1053C2×C4—23no—
1054C2×C4—23no—
1055C2×C4—23no—
1056C2×C4—23no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—23no—
1065C2×C4—23no—
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—21no—
1076C2×C4—21no—
1077C2×C4—23no—
1078C2×C4—21no—
1079C2×C4—23no—
1080C2×C4—23no—
1081C2×C4—23no—
1082C2×C4—23no—
1083C2×C4—23no—
1084C2×C4—23no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—23no—
1088C2×C4—23no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—23no—
1093C2×C4—21no—
1094C2×C4—23no—
1095C2×C4—23no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—23no—
1099C2×C4—23no—
1100C2×C4—23no—
1101C2×C4—23no—
1102C2×C4—23no—
1103C2×C4—23no—
1104C2×C4—23no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—23no—
1108C2×C4—21no—
1109C2×C4—23no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—23no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—23no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—23no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—23no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—412no—
1125C2×C4—44no—
1126C2×C4—412no—
1127C2×C4C22×#4112yes—
1128C2×C4C22×#4116yes—
1129C2×C4C22×#4116yes—
1130C2×C4C2×2−1+416yes—
1131C2×C4C2×2−1+416yes—
1132C2×C4#58512yes—
1133C22—22no—
1134C22—22no—
1135C22—22no—
1136C22—41no—
1137C22—41no—
1138C22—41no—
1139C22—41no—
1140C22C23×#4111yescharacteristic
1141C22C22×2−1+411yescharacteristic
1142C22C22×2−1+411yescharacteristic
1143C22C2×#58511yescharacteristic
1144C22C2×#58511yescharacteristic
1145C222−1+611yescharacteristic
1146C222−1+611yescharacteristic
1147C4—26no—
1148C4—22no—
1149C4—22no—
1150C4—43no—
1151C4—43no—
1152C4—43no—
1153C4—41no—
1154C4—41no—
1155C4—41no—
1156C4—41no—
1157C4—43no—
1158C4—43no—
1159C4—41no—
1160C4—43no—
1161C4—41no—
1162C4—43no—
1163C4—43no—
1164C4—41no—
1165C4—41no—
1166C4—41no—
1167C4—41no—
1168C4—43no—
1169C4—43no—
1170C4—43no—
1171C4—43no—
1172C4—41no—
1173C4—41no—
1174C4—43no—
1175C4—43no—
1176C4C2×#541112yes—
1177C2—42no—
1178C2C22×#54111yescharacteristic
1179C2#6281611yescharacteristic
1180C2#6285011yescharacteristic
1181C2#6294911yescharacteristic
1182C2#6294911yescharacteristic
1183C2#6294911yescharacteristic
1184C2#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. #42782C2semidirect
2. #42774C2semidirect
3. #42744C2semidirect
4. #42733C2semidirect
9. #40024C2semidirect
10. #39999C2semidirect
13. #37580C2semidirect
14. #37580C2semidirect
15. #36475C2semidirect
16. #36466C2semidirect
19. #35971C2semidirect
20. #35971C2semidirect
21. #35971C2semidirect
26. #35868C2semidirect
29. #34336C2semidirect
30. #34336C2semidirect

Maximal subgroups

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

subgroupindex
#427822
#427742
#427442
#427332
#426362
#426232
#425872
#425732
#400242
#399992
#399282
#399072
#375802
#364752
#364662
#364352
#359712
#359202
#358832
#358682
#351422
#346292
#343362
#341282