Finite Group Databasebeta

← #7657075

Subgroups — #7657075

Order 512.

4167 conjugacy classes of subgroups.

The subgroup lattice has 1193 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42782C213yesmaximal, complemented
2#42780C213yesmaximal
3#42738C213yesmaximal
4#42733C213yesmaximal, complemented
5#42703C213yesmaximal, complemented
6#42667C213yesmaximal
7#42511C213yesmaximal, complemented
8#42455C213yesmaximal
9#40227C213yesmaximal
10#40189C213yesmaximal, complemented
11#39788C213yesmaximal
12#39653C213yesmaximal, complemented
13#37630C213yesmaximal, complemented
14#37597C213yesmaximal
15#36584C211yesmaximal, characteristic, complemented
16Q8×#126C211yesmaximal, characteristic
17#36475C211yesmaximal, characteristic, complemented
18#36448C211yesmaximal, characteristic
19#35937C211yesmaximal, characteristic, complemented
20#35920C211yesmaximal, characteristic
21#35883C211yesmaximal, characteristic
22#35868C211yesmaximal, characteristic, complemented
23#35868C211yesmaximal, characteristic, complemented
24#35868C211yesmaximal, characteristic, complemented
25#35786C211yesmaximal, characteristic
26#35711C211yesmaximal, characteristic
27#35115C213yesmaximal, complemented
28#34604C213yesmaximal
29#34336C211yesmaximal, characteristic, complemented
30#34262C211yesmaximal, characteristic
31C4×Q82C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#519C2211yescharacteristic
35#2864C2213yes—
36#2863C2213yes—
37#2863C2213yes—
38#2859C2213yes—
39#2839C2216yes—
40#2839C2216yes—
41#2833C2216yes—
42#2831C2216yes—
43#2802C2216yes—
44#2776C2216yes—
45#2762C2216yes—
46#2762C2216yes—
47#2758C2216yes—
48#2758C2216yes—
49#2758C2216yes—
50#2755C2216yes—
51#2755C2216yes—
52#2754C2216yes—
53#2725C2216yes—
54#2725C2216yes—
55#2719C2216yes—
56#2719C2216yes—
57#2716C2216yes—
58#2713C2216yes—
59#2666C2213yes—
60#2666C2213yes—
61#2664C2213yes—
62#2664C2213yes—
63#2664C2216yes—
64#2660C2213yes—
65#2655C2216yes—
66#2655C2213yes—
67#2655C2216yes—
68#2655C2213yes—
69#2655C2213yes—
70#2655C2213yes—
71#2654C2213yes—
72#2654C2213yes—
73#2650C2213yes—
74#2650C2213yes—
75#2647C2213yes—
76#2647C2213yes—
77#2647C2213yes—
78#2645C2216yes—
79#2645C2213yes—
80#2645C2213yes—
81#2642C2216yes—
82#2637C2211yescharacteristic
83#2637C2213yes—
84#2634C2213yes—
85#2634C2213yes—
86#2629C2213yes—
87#2628C2213yes—
88#2584C2213yes—
89#2582C2213yes—
90#2581C2213yes—
91#2571C2213yes—
92#2571C2213yes—
93#2570C2213yes—
94#2570C2213yes—
95#2570C2213yes—
96#2570C2213yes—
97#2570C2213yes—
98#2568C2213yes—
99#2565C2213yes—
100#2552C2213yes—
101#2552C2213yes—
102#2552C2213yes—
103#2551C2213yes—
104#2551C2213yes—
105#2550C2213yes—
106#2550C2213yes—
107#2546C2213yes—
108#2533C2216yes—
109#2528C2216yes—
110#2524C2216yes—
111#2514C2213yes—
112#2514C2213yes—
113#2514C2213yes—
114#2514C2213yes—
115#2511C2213yes—
116#2511C2213yes—
117#2511C2213yes—
118#2511C2213yes—
119#2511C2213yes—
120#2511C2213yes—
121#2511C2213yes—
122#2511C2213yes—
123#2509C2213yes—
124#2509C2213yes—
125#2509C2213yes—
126#2509C2213yes—
127#2509C2213yes—
128#2509C2213yes—
129#2509C2213yes—
130#2509C2213yes—
131#2508C2213yes—
132#2507C2213yes—
133#2507C2213yes—
134#2507C2213yes—
135#2507C2213yes—
136#2506C2213yes—
137#2506C2213yes—
138#2506C2213yes—
139#2506C2213yes—
140#2506C2213yes—
141#2506C2213yes—
142#2506C2213yes—
143#2497C2213yes—
144#2497C2213yes—
145#2497C2213yes—
146#2497C2213yes—
147#2496C2213yes—
148#2496C2213yes—
149#2496C2213yes—
150#2496C2213yes—
151#2495C2213yes—
152#2495C2213yes—
153#2494C2213yes—
154#2494C2213yes—
155#2469C2216yes—
156#2462C2216yes—
157#2462C2216yes—
158#2453C2213yes—
159#2453C2216yes—
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#2369C2213yes—
180#2369C2213yes—
181#2369C2213yes—
182#2356C2213yes—
183#2355C2213yes—
184#2355C2213yes—
185#2351C2211yescharacteristic
186#2351C2211yescharacteristic
187#2351C2211yescharacteristic
188#2351C2211yescharacteristic
189#2351C2211yescharacteristic
190#2351C2211yescharacteristic
191#2351C2211yescharacteristic
192#2351C2211yescharacteristic
193#2351C2211yescharacteristic
194Q8×C4⋊C4C2213yes—
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
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#2336C2216yes—
215#2336C2216yes—
216#2331C2213yes—
217#2330C2213yes—
218#2320C2213yes—
219#2314C2213yes—
220C4×C4⋊Q8C2213yes—
221C4×C4⋊Q8C2213yes—
222C4×C4⋊Q8C2213yes—
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×#126C2311yescharacteristic
247C2×#126C2313yes—
248C2×#126C2316yes—
249C2×#125C2313yes—
250C2×#125C2313yes—
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2316yes—
254C2×#125C2316yes—
255C2×#125C2316yes—
256#519—28no—
257C2×C4×Q8C2313yes—
258C2×C4×Q8C2313yes—
259C2×C4×Q8C2313yes—
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×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2313yes—
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2313yes—
276C2×C4×Q8C2316yes—
277C2×C4×Q8C2311yescharacteristic
278C2×#117C2313yes—
279C2×#117C2313yes—
280#401C2316yes—
281#401C2316yes—
282#401C2313yes—
283#401C2313yes—
284#400C2313yes—
285#400C2316yes—
286#400C2313yes—
287#400C2313yes—
288#400C2313yes—
289#400C2316yes—
290#400C2316yes—
291#400C2316yes—
292#400C2316yes—
293#400C2316yes—
294#400C2316yes—
295#400C2316yes—
296#400C2316yes—
297#400C2313yes—
298#400C2316yes—
299#400C2316yes—
300#400C2316yes—
301#400C2316yes—
302#400C2316yes—
303#400C2316yes—
304#400C2316yes—
305#400C2316yes—
306#400C2316yes—
307#400C2316yes—
308#400C2316yes—
309#400C2313yes—
310#400C2313yes—
311#400C2313yes—
312#400C2313yes—
313#400C2313yes—
314#400C2313yes—
315#400C2313yes—
316#400C2313yes—
317#400C2313yes—
318#400C2313yes—
319#400C2313yes—
320#400C2313yes—
321#400C2313yes—
322#400C2313yes—
323#400C2313yes—
324#399C2313yes—
325#399C2313yes—
326#398C2313yes—
327#398C2316yes—
328#398C2316yes—
329#398C2316yes—
330#398C2316yes—
331#398C2316yes—
332#398C2316yes—
333#398C2316yes—
334#398C2313yes—
335#398C2316yes—
336#398C2313yes—
337#398C2313yes—
338#398C2313yes—
339#398C2316yes—
340#398C2316yes—
341#398C2316yes—
342#398C2313yes—
343#398C2313yes—
344#398C2311yescharacteristic
345#398C2311yescharacteristic
346#398C2313yes—
347#398C2311yescharacteristic
348#398C2313yes—
349#398C2313yes—
350#398C2313yes—
351#398C2313yes—
352#398C2313yes—
353#398C2313yes—
354#398C2313yes—
355#398C2313yes—
356#398C2313yes—
357#397C2313yes—
358#397C2313yes—
359#397C2316yes—
360#397C2311yescharacteristic
361#397C2313yes—
362#397C2313yes—
363#397C2313yes—
364#396C2316yes—
365#396C2316yes—
366#396C2313yes—
367#396C2311yescharacteristic
368#396C2311yescharacteristic
369#396C2313yes—
370#396C2313yes—
371#396C2313yes—
372#395C2316yes—
373#395C2316yes—
374#395C2316yes—
375#395C2313yes—
376#395C2313yes—
377#395C2311yescharacteristic
378#395C2313yes—
379#395C2313yes—
380#395C2313yes—
381#393C2316yes—
382#393C2311yescharacteristic
383#393C2313yes—
384#391C2316yes—
385#391C2316yes—
386#391C2316yes—
387#391C2313yes—
388#391C2313yes—
389#391C2313yes—
390#391C2313yes—
391#391C2316yes—
392#391C2316yes—
393#391C2313yes—
394#391C2313yes—
395#391C2313yes—
396#391C2313yes—
397#391C2313yes—
398#391C2313yes—
399#391C2316yes—
400#391C2313yes—
401#391C2316yes—
402#391C2313yes—
403#391C2313yes—
404#391C2313yes—
405#391C2316yes—
406#389C2313yes—
407#389C2313yes—
408#389C2313yes—
409#389C2313yes—
410#389C2313yes—
411#389C2313yes—
412#389C2313yes—
413#389C2313yes—
414#389C2316yes—
415#389C2313yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2316yes—
420#389C2316yes—
421#389C2313yes—
422#389C2313yes—
423#389C2313yes—
424#389C2313yes—
425#389C2313yes—
426#389C2313yes—
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2316yes—
436#389C2316yes—
437#389C2316yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2316yes—
445#389C2313yes—
446#389C2316yes—
447#389C2316yes—
448#389C2313yes—
449#389C2313yes—
450#389C2316yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2316yes—
463#389C2316yes—
464#388C2311yescharacteristic
465#388C2313yes—
466#388C2313yes—
467#388C2313yes—
468#388C2313yes—
469#388C2313yes—
470#388C2313yes—
471#388C2316yes—
472#388C2313yes—
473#388C2313yes—
474#388C2311yescharacteristic
475#388C2316yes—
476#387C2313yes—
477#387C2313yes—
478#387C2313yes—
479#387C2313yes—
480#387C2313yes—
481#387C2313yes—
482#387C2311yescharacteristic
483#387C2313yes—
484#387C2313yes—
485#387C2313yes—
486#387C2316yes—
487#387C2313yes—
488#387C2313yes—
489#387C2313yes—
490#387C2313yes—
491#387C2313yes—
492#387C2316yes—
493#387C2316yes—
494#387C2316yes—
495#387C2316yes—
496#387C2316yes—
497#387C2316yes—
498#387C2316yes—
499#387C2316yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2313yes—
504#387C2313yes—
505#387C2316yes—
506#387C2316yes—
507#387C2313yes—
508#387C2313yes—
509#387C2316yes—
510#387C2316yes—
511#387C2316yes—
512#387C2316yes—
513#387C2316yes—
514#387C2316yes—
515#387C2316yes—
516#387C2316yes—
517#387C2316yes—
518#387C2316yes—
519#387C2316yes—
520#387C2316yes—
521#387C2313yes—
522#387C2313yes—
523#387C2311yescharacteristic
524#387C2316yes—
525#387C2316yes—
526#384C2313yes—
527#384C2313yes—
528#384C2313yes—
529#384C2313yes—
530#384C2313yes—
531#384C2313yes—
532#384C2313yes—
533#384C2313yes—
534#384C2313yes—
535#384C2313yes—
536#384C2313yes—
537#383C2313yes—
538#383C2313yes—
539#383C2316yes—
540#383C2316yes—
541#383C2316yes—
542#382C2311yescharacteristic
543#382C2313yes—
544#382C2313yes—
545#382C2313yes—
546#382C2313yes—
547#382C2313yes—
548#382C2313yes—
549#382C2313yes—
550#382C2313yes—
551#382C2316yes—
552#382C2313yes—
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⋊C4C2313yes—
568C4×C4⋊C4C2313yes—
569C4×C4⋊C4C2313yes—
570C4×C4⋊C4C2313yes—
571C4×C4⋊C4C2313yes—
572C4×C4⋊C4C2313yes—
573C4×C4⋊C4C2313yes—
574C4×C4⋊C4C2316yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2316yes—
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⋊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⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614#376C2313yes—
615#376C2313yes—
616#376C2313yes—
617#376C2316yes—
618C43C2313yes—
619C43C2313yes—
620C43C2313yes—
621C22×Q8—24no—
622C22×Q8—24no—
623C22×Q8—24no—
624C22×Q8C2411yescharacteristic
625C22×Q8C2413yes—
626C22×Q8C2413yes—
627C22×Q8C2416yes—
628C22×Q8C2411yescharacteristic
629C23×C4C2413yes—
630C4⋊Q8—212no—
631C4⋊Q8—212no—
632C4⋊Q8—212no—
633C4⋊Q8—212no—
634C4⋊Q8—86no—
635#126—24no—
636#126—46no—
637#126—86no—
638#125—212no—
639#125—212no—
640#125—212no—
641#125—46no—
642#125—412no—
643#125—86no—
644#125—86no—
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—24no—
657C4×Q8—24no—
658C4×Q8—212no—
659C4×Q8—212no—
660C4×Q8—212no—
661C4×Q8—212no—
662C4×Q8—24no—
663C4×Q8—46no—
664C4×Q8—86no—
665C4×Q8#4118yes—
666#117—212no—
667#117—212no—
668C2×C4⋊C4C2413yes—
669C2×C4⋊C4C2413yes—
670C2×C4⋊C4C2413yes—
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⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2413yes—
688C2×C4⋊C4C2413yes—
689C2×C4⋊C4C2413yes—
690C2×C4⋊C4C2413yes—
691C2×C4⋊C4C2413yes—
692C2×C4⋊C4C2413yes—
693C2×C4⋊C4C2411yescharacteristic
694C2×C4⋊C4C2413yes—
695C2×C4⋊C4C2413yes—
696C2×C4⋊C4C2416yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2413yes—
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2416yes—
707C2×C4⋊C4C2416yes—
708C2×C4⋊C4C2416yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2416yes—
718C2×C4⋊C4C2416yes—
719C2×C4⋊C4C2416yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2416yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2416yes—
726C2×C4⋊C4C2416yes—
727C2×C4⋊C4C2416yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2416yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C22⋊C4C2413yes—
743C2×C22⋊C4C2411yescharacteristic
744C2×C22⋊C4C2411yescharacteristic
745C2×C22⋊C4C2411yescharacteristic
746C2×C22⋊C4C2411yescharacteristic
747C2×C22⋊C4C2411yescharacteristic
748C2×C22⋊C4C2413yes—
749C2×C22⋊C4C2413yes—
750C2×C22⋊C4C2413yes—
751C2×C22⋊C4C2413yes—
752C2×C22⋊C4C2413yes—
753C2×C22⋊C4C2411yescharacteristic
754C2×C22⋊C4C2411yescharacteristic
755C2×C22⋊C4C2413yes—
756C2×C42C2416yes—
757C2×C42C2413yes—
758C2×C42C2413yes—
759C2×C42C2413yes—
760C2×C42C2413yes—
761C2×C42C2413yes—
762C2×C42C2413yes—
763C2×C42C2413yes—
764C2×C42C2411yescharacteristic
765C2×C42C2411yescharacteristic
766C2×C42C2413yes—
767C2×C42C2413yes—
768C2×C42C2413yes—
769C2×C42C2413yes—
770C2×C42C2413yes—
771C2×C42C2413yes—
772C2×C42C2413yes—
773C2×C42C2413yes—
774C2×C42C2413yes—
775C2×C42C2413yes—
776C2×C42C2413yes—
777C2×C42C2413yes—
778C2×C42C2416yes—
779C2×C42C2416yes—
780C2×C42C2416yes—
781C2×C42C2413yes—
782C2×C42C2413yes—
783C2×C42C2413yes—
784C2×C42C2413yes—
785C2×C42C2411yescharacteristic
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#95C2416yes—
801#95C2416yes—
802#95C2413yes—
803#95C2413yes—
804#95C2413yes—
805#95C2413yes—
806#95C2413yes—
807#95C2413yes—
808#95C2413yes—
809#95C2413yes—
810#95C2413yes—
811#95C2413yes—
812#95C2413yes—
813#95C2411yescharacteristic
814#95C2413yes—
815#95C2416yes—
816#95C2411yescharacteristic
817#95C2411yescharacteristic
818#95C2411yescharacteristic
819#95C2411yescharacteristic
820#95C2411yescharacteristic
821#95C2413yes—
822#95C2413yes—
823#95C2413yes—
824#95C2413yes—
825#95C2413yes—
826#95C2411yescharacteristic
827#95C2411yescharacteristic
828#95C2411yescharacteristic
829#95C2416yes—
830#95C2416yes—
831#95C2413yes—
832#95C2413yes—
833#95C2416yes—
834#95C2413yes—
835#95C2413yes—
836#95C2416yes—
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2416yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2416yes—
859#95C2416yes—
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—22no—
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—26no—
886C22×C4—26no—
887C22×C4—26no—
888C22×C4C2513yes—
889C22×C4C2511yescharacteristic
890C22×C4C2511yescharacteristic
891C22×C4C2511yescharacteristic
892C22×C4C2513yes—
893C22×C4C2511yescharacteristic
894C22×C4C2511yescharacteristic
895C22×C4C2511yescharacteristic
896C22×C4C2513yes—
897C22×C4C2513yes—
898C22×C4C2513yes—
899C22×C4C2511yescharacteristic
900C22×C4C2513yes—
901C22×C4C2511yescharacteristic
902C22×C4C2513yes—
903C22×C4C2513yes—
904C22×C4C2513yes—
905C22×C4C2513yes—
906C22×C4C2513yes—
907C22×C4C2513yes—
908C22×C4C2513yes—
909C22×C4C2513yes—
910C22×C4C2511yescharacteristic
911C22×C4C2511yescharacteristic
912C22×C4C2513yes—
913C22×C4C2511yescharacteristic
914C22×C4C2511yescharacteristic
915C22×C4C2511yescharacteristic
916C22×C4C2511yescharacteristic
917C22×C4C2513yes—
918C4⋊C4—26no—
919C4⋊C4—26no—
920C4⋊C4—26no—
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—212no—
932C4⋊C4—22no—
933C4⋊C4—22no—
934C4⋊C4—22no—
935C4⋊C4—26no—
936C4⋊C4—26no—
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—26no—
946C4⋊C4—26no—
947C4⋊C4—26no—
948C4⋊C4—26no—
949C4⋊C4—22no—
950C4⋊C4—22no—
951C4⋊C4—22no—
952C4⋊C4—26no—
953C4⋊C4—26no—
954C4⋊C4—22no—
955C4⋊C4—26no—
956C4⋊C4—41no—
957C4⋊C4—41no—
958C4⋊C4—43no—
959C4⋊C4—41no—
960C4⋊C4—41no—
961C4⋊C4—46no—
962C4⋊C4—43no—
963C4⋊C4—43no—
964C4⋊C4—43no—
965C4⋊C4—43no—
966C4⋊C4—43no—
967C4⋊C4—46no—
968C4⋊C4—46no—
969C4⋊C4—46no—
970C4⋊C4—43no—
971C4⋊C4—43no—
972C4⋊C4—43no—
973C4⋊C4—43no—
974C4⋊C4—46no—
975C4⋊C4—46no—
976C4⋊C4—46no—
977C4⋊C4—43no—
978C4⋊C4—43no—
979C4⋊C4—46no—
980C4⋊C4—43no—
981C4⋊C4—43no—
982C4⋊C4—43no—
983C4⋊C4—43no—
984C4⋊C4—46no—
985C4⋊C4—46no—
986C4⋊C4—43no—
987C4⋊C4—43no—
988C4⋊C4—46no—
989C4⋊C4—43no—
990C4⋊C4—43no—
991C4⋊C4C2×#41112yes—
992C22⋊C4—26no—
993C22⋊C4—22no—
994C22⋊C4—22no—
995C22⋊C4—22no—
996C22⋊C4—22no—
997C22⋊C4—22no—
998C22⋊C4—41no—
999C22⋊C4—41no—
1000C22⋊C4—43no—
1001C22⋊C4—43no—
1002C22⋊C4—43no—
1003C22⋊C4—43no—
1004C22⋊C4—43no—
1005C22⋊C4—43no—
1006C42—26no—
1007C42—212no—
1008C42—26no—
1009C42—26no—
1010C42—26no—
1011C42—26no—
1012C42—26no—
1013C42—26no—
1014C42—22no—
1015C42—22no—
1016C42—26no—
1017C42—26no—
1018C42—26no—
1019C42—26no—
1020C42—26no—
1021C42—26no—
1022C42—26no—
1023C42—43no—
1024C42—43no—
1025C42—43no—
1026C42—43no—
1027C42—43no—
1028C42—43no—
1029C42—43no—
1030C42—43no—
1031C42—46no—
1032C42—46no—
1033C42—46no—
1034C42C2×#41112yes—
1035C422−1+414yes—
1036C23—21no—
1037C23—21no—
1038C23—21no—
1039C23—21no—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23C2611yescharacteristic
1044Q8—28no—
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—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—23no—
1059C2×C4—21no—
1060C2×C4—23no—
1061C2×C4—23no—
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—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—23no—
1077C2×C4—23no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—23no—
1081C2×C4—23no—
1082C2×C4—23no—
1083C2×C4—23no—
1084C2×C4—23no—
1085C2×C4—23no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—23no—
1090C2×C4—23no—
1091C2×C4—23no—
1092C2×C4—23no—
1093C2×C4—23no—
1094C2×C4—23no—
1095C2×C4—23no—
1096C2×C4—23no—
1097C2×C4—23no—
1098C2×C4—23no—
1099C2×C4—23no—
1100C2×C4—23no—
1101C2×C4—21no—
1102C2×C4—23no—
1103C2×C4—23no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—23no—
1107C2×C4—23no—
1108C2×C4—23no—
1109C2×C4—23no—
1110C2×C4—23no—
1111C2×C4—23no—
1112C2×C4—23no—
1113C2×C4—23no—
1114C2×C4—23no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—23no—
1121C2×C4—23no—
1122C2×C4—23no—
1123C2×C4—21no—
1124C2×C4—23no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—23no—
1130C2×C4—412no—
1131C2×C4C22×#4116yes—
1132C2×C4C22×#4112yes—
1133C2×C4C22×#4116yes—
1134C2×C4C2×2−1+412yes—
1135C2×C4C2×2−1+412yes—
1136C2×C4C2×2−1+412yes—
1137C2×C4C2×2−1+416yes—
1138C2×C4C2×2−1+416yes—
1139C2×C4#58512yes—
1140C22—41no—
1141C22—41no—
1142C22—41no—
1143C22—41no—
1144C22—41no—
1145C22—41no—
1146C22—41no—
1147C22C23×#4111yescharacteristic
1148C22C22×2−1+411yescharacteristic
1149C22C22×2−1+411yescharacteristic
1150C22C22×2−1+411yescharacteristic
1151C22C2×#58511yescharacteristic
1152C22H(7,𝔽2)11yescharacteristic
1153C222−1+611yescharacteristic
1154C4—22no—
1155C4—22no—
1156C4—22no—
1157C4—26no—
1158C4—22no—
1159C4—22no—
1160C4—43no—
1161C4—41no—
1162C4—43no—
1163C4—41no—
1164C4—43no—
1165C4—43no—
1166C4—43no—
1167C4—41no—
1168C4—43no—
1169C4—41no—
1170C4—43no—
1171C4—43no—
1172C4—41no—
1173C4—41no—
1174C4—41no—
1175C4—43no—
1176C4—43no—
1177C4—43no—
1178C4—43no—
1179C4—41no—
1180C4—41no—
1181C4—43no—
1182C4—43no—
1183C4C2×#541112yes—
1184C2—81no—
1185C2C22×#54111yescharacteristic
1186C2#6278811yescharacteristic
1187C2#6285711yescharacteristic
1188C2#6294311yescharacteristic
1189C2#6294711yescharacteristic
1190C2#6295211yescharacteristic
1191C2#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
4. #42733C2semidirect
5. #42703C2semidirect
7. #42511C2semidirect
10. #40189C2semidirect
12. #39653C2semidirect
13. #37630C2semidirect
15. #36584C2semidirect
17. #36475C2semidirect
19. #35937C2semidirect
22. #35868C2semidirect
23. #35868C2semidirect
24. #35868C2semidirect
27. #35115C2semidirect
29. #34336C2semidirect
31. C4×Q82C2semidirect

Maximal subgroups

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

subgroupindex
#427822
#427802
#427382
#427332
#427032
#426672
#425112
#424552
#402272
#401892
#397882
#396532
#376302
#375972
#365842
Q8×#1262
#364752
#364482
#359372
#359202
#358832
#358682
#357862
#357112
#351152
#346042
#343362
#342622
C4×Q822