Finite Group Databasebeta

← #7657045

Subgroups — #7657045

Order 512.

4291 conjugacy classes of subgroups.

The subgroup lattice has 1207 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42704C213yesmaximal, complemented
2#42670C213yesmaximal, complemented
3#42626C213yesmaximal, complemented
4#42623C213yesmaximal, complemented
5#42587C213yesmaximal, complemented
6#42582C213yesmaximal, complemented
7#42509C213yesmaximal, complemented
8#42461C213yesmaximal, complemented
9#40213C213yesmaximal, complemented
10#40202C213yesmaximal, complemented
11#39780C213yesmaximal, complemented
12#39661C213yesmaximal, complemented
13#37628C213yesmaximal, complemented
14#37597C213yesmaximal, complemented
15#36585C211yesmaximal, characteristic
16Q8×#125C211yesmaximal, characteristic, complemented
17#36475C211yesmaximal, characteristic, complemented
18#36458C211yesmaximal, characteristic
19#35971C211yesmaximal, characteristic, complemented
20#35971C211yesmaximal, characteristic, complemented
21#35937C211yesmaximal, characteristic, complemented
22#35898C211yesmaximal, characteristic
23#35898C211yesmaximal, characteristic
24#35868C211yesmaximal, characteristic, complemented
25#35816C211yesmaximal, characteristic
26#35748C211yesmaximal, characteristic
27#35116C213yesmaximal, complemented
28#34604C213yesmaximal, complemented
29#34336C211yesmaximal, characteristic, complemented
30#34263C211yesmaximal, characteristic
31C4×Q82C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#520C2211yescharacteristic
35#2864C2213yes—
36#2860C2213yes—
37#2860C2213yes—
38#2859C2213yes—
39#2836C2216yes—
40#2836C2216yes—
41#2833C2216yes—
42#2831C2216yes—
43#2802C2216yes—
44#2798C2216yes—
45#2789C2216yes—
46#2772C2216yes—
47#2766C2216yes—
48#2739C2216yes—
49#2725C2216yes—
50#2722C2216yes—
51#2716C2216yes—
52#2713C2216yes—
53#2704C2216yes—
54#2704C2216yes—
55#2698C2216yes—
56#2698C2216yes—
57#2690C2216yes—
58#2689C2216yes—
59#2666C2213yes—
60#2666C2213yes—
61#2664C2216yes—
62#2664C2213yes—
63#2664C2213yes—
64#2660C2213yes—
65#2655C2213yes—
66#2655C2213yes—
67#2655C2213yes—
68#2655C2213yes—
69#2655C2216yes—
70#2654C2213yes—
71#2654C2213yes—
72#2654C2216yes—
73#2650C2213yes—
74#2650C2213yes—
75#2647C2213yes—
76#2647C2213yes—
77#2647C2213yes—
78#2644C2213yes—
79#2644C2213yes—
80#2637C2213yes—
81#2637C2213yes—
82#2634C2211yescharacteristic
83#2634C2213yes—
84#2629C2213yes—
85#2628C2213yes—
86#2625C2216yes—
87#2621C2216yes—
88#2584C2213yes—
89#2580C2213yes—
90#2571C2213yes—
91#2571C2213yes—
92#2570C2213yes—
93#2570C2213yes—
94#2570C2213yes—
95#2570C2213yes—
96#2570C2213yes—
97#2566C2213yes—
98#2552C2213yes—
99#2552C2213yes—
100#2552C2213yes—
101#2551C2213yes—
102#2551C2213yes—
103#2550C2213yes—
104#2550C2213yes—
105#2546C2213yes—
106#2542C2213yes—
107#2538C2213yes—
108#2519C2216yes—
109#2513C2213yes—
110#2513C2213yes—
111#2513C2213yes—
112#2513C2213yes—
113#2513C2213yes—
114#2513C2213yes—
115#2512C2213yes—
116#2512C2213yes—
117#2512C2213yes—
118#2512C2213yes—
119#2512C2213yes—
120#2512C2213yes—
121#2509C2213yes—
122#2509C2213yes—
123#2509C2213yes—
124#2509C2213yes—
125#2508C2213yes—
126#2508C2213yes—
127#2508C2213yes—
128#2508C2213yes—
129#2508C2213yes—
130#2507C2213yes—
131#2507C2213yes—
132#2507C2213yes—
133#2507C2213yes—
134#2507C2213yes—
135#2507C2213yes—
136#2507C2213yes—
137#2507C2213yes—
138#2506C2213yes—
139#2506C2213yes—
140#2506C2213yes—
141#2497C2213yes—
142#2497C2213yes—
143#2497C2213yes—
144#2496C2213yes—
145#2496C2213yes—
146#2496C2213yes—
147#2495C2213yes—
148#2494C2213yes—
149#2494C2213yes—
150#2494C2213yes—
151#2494C2213yes—
152#2494C2213yes—
153#2478C2216yes—
154#2475C2216yes—
155#2469C2216yes—
156#2469C2216yes—
157#2462C2216yes—
158#2454C2213yes—
159#2452C2213yes—
160#2452C2213yes—
161#2452C2213yes—
162#2442C2213yes—
163#2440C2213yes—
164#2440C2213yes—
165#2440C2213yes—
166#2429C2216yes—
167#2421C2216yes—
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#2357C2213yes—
183#2355C2213yes—
184#2354C2213yes—
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#2345C2213yes—
207#2344C2213yes—
208#2341C2211yescharacteristic
209#2341C2211yescharacteristic
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212#2341C2211yescharacteristic
213#2341C2211yescharacteristic
214#2334C2216yes—
215#2334C2216yes—
216#2331C2213yes—
217#2330C2213yes—
218#2319C2213yes—
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#2293C2213yes—
231#2276C2211yescharacteristic
232#2276C2211yescharacteristic
233#2276C2211yescharacteristic
234C42×Q8C2211yescharacteristic
235C42×Q8C2213yes—
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
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×#126C2316yes—
249C2×#126C2316yes—
250C2×#126C2316yes—
251C2×#125C2311yescharacteristic
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2316yes—
256C2×#125C2316yes—
257C2×C22⋊Q8C2316yes—
258C2×C22⋊Q8C2316yes—
259C2×C22⋊Q8C2316yes—
260#520—28no—
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×Q8C2311yescharacteristic
277C2×C4×Q8C2313yes—
278C2×C4×Q8C2316yes—
279C2×C4×Q8C2311yescharacteristic
280C2×C4×D4C2313yes—
281C2×C4×D4C2313yes—
282C2×#117C2313yes—
283C2×#117C2316yes—
284C22×C4⋊C4C2313yes—
285#401C2313yes—
286#401C2316yes—
287#401C2313yes—
288#400C2313yes—
289#400C2316yes—
290#400C2316yes—
291#400C2316yes—
292#400C2316yes—
293#400C2313yes—
294#400C2313yes—
295#400C2313yes—
296#400C2313yes—
297#400C2313yes—
298#400C2316yes—
299#400C2316yes—
300#400C2316yes—
301#400C2316yes—
302#400C2313yes—
303#400C2313yes—
304#400C2311yescharacteristic
305#400C2311yescharacteristic
306#400C2311yescharacteristic
307#400C2313yes—
308#400C2311yescharacteristic
309#400C2313yes—
310#400C2313yes—
311#400C2313yes—
312#400C2313yes—
313#400C2313yes—
314#400C2313yes—
315#400C2313yes—
316#399C2316yes—
317#399C2313yes—
318#399C2313yes—
319#398C2313yes—
320#398C2313yes—
321#398C2316yes—
322#398C2316yes—
323#398C2316yes—
324#398C2316yes—
325#398C2316yes—
326#398C2316yes—
327#398C2316yes—
328#398C2316yes—
329#398C2313yes—
330#398C2316yes—
331#398C2316yes—
332#398C2316yes—
333#398C2316yes—
334#398C2313yes—
335#398C2313yes—
336#398C2311yescharacteristic
337#398C2311yescharacteristic
338#398C2313yes—
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#397C2316yes—
352#397C2316yes—
353#397C2316yes—
354#397C2316yes—
355#397C2316yes—
356#397C2316yes—
357#397C2316yes—
358#397C2316yes—
359#397C2316yes—
360#397C2313yes—
361#397C2313yes—
362#397C2313yes—
363#397C2313yes—
364#397C2313yes—
365#397C2313yes—
366#396C2313yes—
367#396C2316yes—
368#396C2316yes—
369#396C2316yes—
370#396C2313yes—
371#396C2316yes—
372#396C2316yes—
373#396C2313yes—
374#396C2313yes—
375#396C2313yes—
376#396C2313yes—
377#395C2316yes—
378#395C2316yes—
379#395C2316yes—
380#395C2313yes—
381#395C2311yescharacteristic
382#395C2311yescharacteristic
383#395C2313yes—
384#395C2313yes—
385#395C2313yes—
386#393C2316yes—
387#393C2313yes—
388#393C2313yes—
389#391C2316yes—
390#391C2316yes—
391#391C2316yes—
392#391C2313yes—
393#391C2316yes—
394#391C2313yes—
395#391C2316yes—
396#390C2313yes—
397#390C2313yes—
398#390C2313yes—
399#390C2313yes—
400#390C2313yes—
401#390C2313yes—
402#390C2313yes—
403#390C2313yes—
404#390C2313yes—
405#390C2313yes—
406#390C2313yes—
407#390C2313yes—
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#389C2316yes—
421#389C2316yes—
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#389C2313yes—
436#389C2316yes—
437#389C2316yes—
438#389C2313yes—
439#389C2313yes—
440#389C2316yes—
441#389C2316yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2316yes—
447#389C2313yes—
448#389C2313yes—
449#389C2316yes—
450#389C2316yes—
451#389C2313yes—
452#389C2313yes—
453#389C2316yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2313yes—
463#389C2313yes—
464#389C2313yes—
465#388C2313yes—
466#388C2313yes—
467#388C2313yes—
468#388C2313yes—
469#388C2313yes—
470#388C2313yes—
471#388C2316yes—
472#388C2316yes—
473#388C2313yes—
474#388C2313yes—
475#388C2316yes—
476#388C2316yes—
477#388C2316yes—
478#388C2316yes—
479#388C2316yes—
480#388C2316yes—
481#388C2316yes—
482#388C2316yes—
483#388C2313yes—
484#388C2313yes—
485#388C2316yes—
486#387C2311yescharacteristic
487#387C2313yes—
488#387C2313yes—
489#387C2313yes—
490#387C2313yes—
491#387C2313yes—
492#387C2311yescharacteristic
493#387C2313yes—
494#387C2313yes—
495#387C2313yes—
496#387C2316yes—
497#387C2313yes—
498#387C2313yes—
499#387C2313yes—
500#387C2313yes—
501#387C2313yes—
502#387C2313yes—
503#387C2316yes—
504#387C2316yes—
505#387C2316yes—
506#387C2316yes—
507#387C2316yes—
508#387C2316yes—
509#387C2316yes—
510#387C2316yes—
511#387C2313yes—
512#387C2313yes—
513#387C2313yes—
514#387C2316yes—
515#387C2316yes—
516#387C2316yes—
517#387C2313yes—
518#387C2316yes—
519#387C2311yescharacteristic
520#387C2311yescharacteristic
521#387C2316yes—
522#387C2316yes—
523#385C2316yes—
524#385C2316yes—
525#385C2316yes—
526#385C2316yes—
527#384C2313yes—
528#384C2313yes—
529#384C2313yes—
530#384C2313yes—
531#384C2313yes—
532#384C2313yes—
533#384C2313yes—
534#384C2313yes—
535#384C2313yes—
536#384C2313yes—
537#384C2313yes—
538#383C2311yescharacteristic
539#383C2313yes—
540#382C2313yes—
541#382C2313yes—
542#382C2313yes—
543#382C2313yes—
544#382C2313yes—
545#382C2313yes—
546#382C2313yes—
547#382C2313yes—
548#382C2313yes—
549#382C2313yes—
550#382C2316yes—
551#382C2313yes—
552#382C2316yes—
553#381C2316yes—
554#380C2313yes—
555#380C2313yes—
556#380C2316yes—
557#380C2313yes—
558#380C2313yes—
559#380C2313yes—
560#380C2313yes—
561#380C2316yes—
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⋊C4C2313yes—
575C4×C4⋊C4C2316yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2316yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊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×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⋊C4C2316yes—
614C4×C22⋊C4C2313yes—
615#376C2313yes—
616#376C2313yes—
617#376C2313yes—
618C43C2313yes—
619C43C2313yes—
620C43C2313yes—
621C2×#41—24no—
622C2×#41—24no—
623C2×#41—24no—
624C22×Q8C2411yescharacteristic
625C22×Q8C2413yes—
626C22×Q8C2416yes—
627C22×Q8C2411yescharacteristic
628C22×D4C2413yes—
629C23×C4C2413yes—
630C23×C4C2416yes—
631C4⋊Q8—212no—
632C4⋊Q8—212no—
633C4⋊Q8—212no—
634C4⋊Q8—212no—
635C4⋊Q8—86no—
636#126—212no—
637#126—46no—
638#126—412no—
639#126—86no—
640#126—86no—
641#125—212no—
642#125—212no—
643#125—24no—
644#125—46no—
645#125—86no—
646#125—86no—
647C22⋊Q8—86no—
648C22⋊Q8—86no—
649C22⋊Q8—86no—
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—24no—
663C4×Q8—212no—
664C4×Q8—212no—
665C4×Q8—24no—
666C4×Q8—46no—
667C4×Q8—86no—
668C4×Q8#4118yes—
669C4×D4—212no—
670C4×D4—212no—
671#117—212no—
672#117—86no—
673C2×C4⋊C4—212no—
674C2×C4⋊C4C2413yes—
675C2×C4⋊C4C2413yes—
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
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⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2413yes—
694C2×C4⋊C4C2413yes—
695C2×C4⋊C4C2413yes—
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2416yes—
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2416yes—
714C2×C4⋊C4C2416yes—
715C2×C4⋊C4C2416yes—
716C2×C4⋊C4C2416yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2416yes—
725C2×C4⋊C4C2416yes—
726C2×C4⋊C4C2416yes—
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×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2416yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2416yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C22⋊C4C2413yes—
749C2×C22⋊C4C2413yes—
750C2×C22⋊C4C2413yes—
751C2×C22⋊C4C2413yes—
752C2×C22⋊C4C2413yes—
753C2×C22⋊C4C2413yes—
754C2×C22⋊C4C2413yes—
755C2×C22⋊C4C2416yes—
756C2×C22⋊C4C2413yes—
757C2×C22⋊C4C2413yes—
758C2×C22⋊C4C2413yes—
759C2×C22⋊C4C2416yes—
760C2×C22⋊C4C2416yes—
761C2×C22⋊C4C2416yes—
762C2×C22⋊C4C2413yes—
763C2×C22⋊C4C2413yes—
764C2×C22⋊C4C2413yes—
765C2×C22⋊C4C2416yes—
766C2×C22⋊C4C2413yes—
767C2×C22⋊C4C2416yes—
768C2×C42C2413yes—
769C2×C42C2413yes—
770C2×C42C2413yes—
771C2×C42C2413yes—
772C2×C42C2413yes—
773C2×C42C2413yes—
774C2×C42C2413yes—
775C2×C42C2411yescharacteristic
776C2×C42C2411yescharacteristic
777C2×C42C2413yes—
778C2×C42C2413yes—
779C2×C42C2413yes—
780C2×C42C2413yes—
781C2×C42C2413yes—
782C2×C42C2413yes—
783C2×C42C2413yes—
784C2×C42C2413yes—
785C2×C42C2416yes—
786C2×C42C2413yes—
787C2×C42C2413yes—
788C2×C42C2413yes—
789C2×C42C2413yes—
790C2×C42C2413yes—
791C2×C42C2413yes—
792C2×C42C2416yes—
793C2×C42C2413yes—
794C2×C42C2416yes—
795C2×C42C2413yes—
796C2×C42C2411yescharacteristic
797#95C2411yescharacteristic
798#95C2411yescharacteristic
799#95C2411yescharacteristic
800#95C2413yes—
801#95C2413yes—
802#95C2413yes—
803#95C2413yes—
804#95C2413yes—
805#95C2413yes—
806#95C2413yes—
807#95C2413yes—
808#95C2413yes—
809#95C2411yescharacteristic
810#95C2411yescharacteristic
811#95C2411yescharacteristic
812#95C2411yescharacteristic
813#95C2411yescharacteristic
814#95C2411yescharacteristic
815#95C2413yes—
816#95C2413yes—
817#95C2413yes—
818#95C2413yes—
819#95C2413yes—
820#95C2413yes—
821#95C2413yes—
822#95C2416yes—
823#95C2416yes—
824#95C2411yescharacteristic
825#95C2413yes—
826#95C2413yes—
827#95C2413yes—
828#95C2411yescharacteristic
829#95C2411yescharacteristic
830#95C2411yescharacteristic
831#95C2413yes—
832#95C2413yes—
833#95C2411yescharacteristic
834#95C2411yescharacteristic
835#95C2411yescharacteristic
836#95C2411yescharacteristic
837#95C2411yescharacteristic
838#95C2413yes—
839#95C2416yes—
840#95C2416yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2416yes—
856#95C2413yes—
857#95C2416yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2413yes—
865#95C2413yes—
866#95C2413yes—
867#95C2416yes—
868#95C2416yes—
869#95C2416yes—
870#95C2416yes—
871#95C2416yes—
872#95C2416yes—
873C24C2513yes—
874#41—416no—
875C2×Q8—22no—
876C2×Q8—26no—
877C2×Q8—212no—
878C2×Q8—22no—
879C2×Q8—22no—
880C2×Q8—46no—
881C2×Q8—43no—
882C2×Q8—46no—
883C2×Q8—43no—
884C2×Q8C2×#4114yes—
885C2×Q82−1+414yes—
886C2×Q82−1+414yes—
887C2×D4—26no—
888C2×D4—26no—
889C2×D4—26no—
890C22×C4—26no—
891C22×C4—26no—
892C22×C4—26no—
893C22×C4—212no—
894C22×C4—46no—
895C22×C4—46no—
896C22×C4C2511yescharacteristic
897C22×C4C2511yescharacteristic
898C22×C4C2511yescharacteristic
899C22×C4C2511yescharacteristic
900C22×C4C2511yescharacteristic
901C22×C4C2513yes—
902C22×C4C2513yes—
903C22×C4C2511yescharacteristic
904C22×C4C2511yescharacteristic
905C22×C4C2513yes—
906C22×C4C2513yes—
907C22×C4C2513yes—
908C22×C4C2511yescharacteristic
909C22×C4C2511yescharacteristic
910C22×C4C2513yes—
911C22×C4C2513yes—
912C22×C4C2513yes—
913C22×C4C2513yes—
914C22×C4C2511yescharacteristic
915C22×C4C2513yes—
916C22×C4C2513yes—
917C22×C4C2513yes—
918C22×C4C2513yes—
919C22×C4C2511yescharacteristic
920C22×C4C2513yes—
921C22×C4C2511yescharacteristic
922C22×C4C2511yescharacteristic
923C22×C4C2511yescharacteristic
924C22×C4C2511yescharacteristic
925C22×C4C2513yes—
926C4⋊C4—26no—
927C4⋊C4—26no—
928C4⋊C4—22no—
929C4⋊C4—22no—
930C4⋊C4—26no—
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—212no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—22no—
943C4⋊C4—26no—
944C4⋊C4—26no—
945C4⋊C4—26no—
946C4⋊C4—26no—
947C4⋊C4—26no—
948C4⋊C4—26no—
949C4⋊C4—26no—
950C4⋊C4—26no—
951C4⋊C4—22no—
952C4⋊C4—22no—
953C4⋊C4—22no—
954C4⋊C4—22no—
955C4⋊C4—22no—
956C4⋊C4—22no—
957C4⋊C4—26no—
958C4⋊C4—26no—
959C4⋊C4—26no—
960C4⋊C4—26no—
961C4⋊C4—22no—
962C4⋊C4—26no—
963C4⋊C4—22no—
964C4⋊C4—43no—
965C4⋊C4—46no—
966C4⋊C4—43no—
967C4⋊C4—43no—
968C4⋊C4—46no—
969C4⋊C4—46no—
970C4⋊C4—46no—
971C4⋊C4—43no—
972C4⋊C4—43no—
973C4⋊C4—43no—
974C4⋊C4—43no—
975C4⋊C4—43no—
976C4⋊C4—46no—
977C4⋊C4—46no—
978C4⋊C4—46no—
979C4⋊C4—43no—
980C4⋊C4—43no—
981C4⋊C4—43no—
982C4⋊C4—43no—
983C4⋊C4—43no—
984C4⋊C4—43no—
985C4⋊C4—43no—
986C4⋊C4—43no—
987C4⋊C4—43no—
988C4⋊C4—46no—
989C4⋊C4—46no—
990C4⋊C4—43no—
991C4⋊C4—43no—
992C4⋊C4—46no—
993C4⋊C4—43no—
994C4⋊C4—43no—
995C4⋊C4—43no—
996C4⋊C4—46no—
997C4⋊C4—43no—
998C4⋊C4—43no—
999C4⋊C4C2×#41112yes—
1000C22⋊C4—26no—
1001C22⋊C4—26no—
1002C22⋊C4—26no—
1003C22⋊C4—26no—
1004C22⋊C4—26no—
1005C22⋊C4—26no—
1006C22⋊C4—43no—
1007C22⋊C4—46no—
1008C22⋊C4—43no—
1009C22⋊C4—43no—
1010C22⋊C4—43no—
1011C22⋊C4—46no—
1012C22⋊C4—46no—
1013C22⋊C4—46no—
1014C22⋊C4—43no—
1015C22⋊C4—43no—
1016C22⋊C4—46no—
1017C22⋊C4—46no—
1018C22⋊C4—43no—
1019C22⋊C4—43no—
1020C42—26no—
1021C42—26no—
1022C42—26no—
1023C42—26no—
1024C42—26no—
1025C42—26no—
1026C42—26no—
1027C42—22no—
1028C42—22no—
1029C42—26no—
1030C42—26no—
1031C42—26no—
1032C42—26no—
1033C42—26no—
1034C42—26no—
1035C42—26no—
1036C42—43no—
1037C42—46no—
1038C42—43no—
1039C42—43no—
1040C42—43no—
1041C42—43no—
1042C42—43no—
1043C42—43no—
1044C42—46no—
1045C42—46no—
1046C42—43no—
1047C42C2×#41112yes—
1048C422−1+414yes—
1049C23—23no—
1050C23—23no—
1051C23—23no—
1052C23—23no—
1053C23—23no—
1054C23—23no—
1055C23—23no—
1056C23C2611yescharacteristic
1057Q8—28no—
1058Q8—86no—
1059Q8—812no—
1060Q8#541116yes—
1061D4—412no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—23no—
1073C2×C4—23no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—23no—
1078C2×C4—23no—
1079C2×C4—23no—
1080C2×C4—23no—
1081C2×C4—23no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
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—23no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—23no—
1109C2×C4—23no—
1110C2×C4—23no—
1111C2×C4—23no—
1112C2×C4—23no—
1113C2×C4—23no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—23no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—23no—
1122C2×C4—23no—
1123C2×C4—23no—
1124C2×C4—23no—
1125C2×C4—23no—
1126C2×C4—23no—
1127C2×C4—23no—
1128C2×C4—23no—
1129C2×C4—23no—
1130C2×C4—23no—
1131C2×C4—23no—
1132C2×C4—23no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—23no—
1138C2×C4—23no—
1139C2×C4—21no—
1140C2×C4—23no—
1141C2×C4—23no—
1142C2×C4—21no—
1143C2×C4—412no—
1144C2×C4—812no—
1145C2×C4C22×#4112yes—
1146C2×C4C22×#4116yes—
1147C2×C4C22×#4116yes—
1148C2×C4C2×2−1+412yes—
1149C2×C4C2×2−1+412yes—
1150C2×C4C2×2−1+412yes—
1151C2×C4C2×2−1+416yes—
1152C2×C4C2×2−1+416yes—
1153C2×C4#58512yes—
1154C22—43no—
1155C22—43no—
1156C22—43no—
1157C22—43no—
1158C22—43no—
1159C22—43no—
1160C22—43no—
1161C22C23×#4111yescharacteristic
1162C22C22×2−1+411yescharacteristic
1163C22C22×2−1+411yescharacteristic
1164C22C22×2−1+411yescharacteristic
1165C22C2×#58511yescharacteristic
1166C22H(7,𝔽2)11yescharacteristic
1167C22H(7,𝔽2)11yescharacteristic
1168C4—22no—
1169C4—22no—
1170C4—22no—
1171C4—26no—
1172C4—22no—
1173C4—22no—
1174C4—41no—
1175C4—41no—
1176C4—43no—
1177C4—43no—
1178C4—43no—
1179C4—43no—
1180C4—43no—
1181C4—41no—
1182C4—41no—
1183C4—41no—
1184C4—41no—
1185C4—41no—
1186C4—41no—
1187C4—43no—
1188C4—43no—
1189C4—41no—
1190C4—41no—
1191C4—43no—
1192C4—43no—
1193C4—43no—
1194C4—43no—
1195C4—43no—
1196C4—43no—
1197C4C2×#541112yes—
1198C2—83no—
1199C2C22×#54111yescharacteristic
1200C2#6278811yescharacteristic
1201C2#6285811yescharacteristic
1202C2#6294311yescharacteristic
1203C2#6294311yescharacteristic
1204C2#6295211yescharacteristic
1205C2#6295211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42704C2semidirect
2. #42670C2semidirect
3. #42626C2semidirect
4. #42623C2semidirect
5. #42587C2semidirect
6. #42582C2semidirect
7. #42509C2semidirect
8. #42461C2semidirect
9. #40213C2semidirect
10. #40202C2semidirect
11. #39780C2semidirect
12. #39661C2semidirect
13. #37628C2semidirect
14. #37597C2semidirect
16. Q8×#125C2semidirect
17. #36475C2semidirect
19. #35971C2semidirect
20. #35971C2semidirect
21. #35937C2semidirect
24. #35868C2semidirect
27. #35116C2semidirect
28. #34604C2semidirect
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
#427042
#426702
#426262
#426232
#425872
#425822
#425092
#424612
#402132
#402022
#397802
#396612
#376282
#375972
#365852
Q8×#1252
#364752
#364582
#359712
#359372
#358982
#358682
#358162
#357482
#351162
#346042
#343362
#342632
C4×Q822