Finite Group Databasebeta

← #7661809

Subgroups — #7661809

Order 512.

4225 conjugacy classes of subgroups.

The subgroup lattice has 1198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52283C213yesmaximal, complemented
2#42723C213yesmaximal, complemented
3#42657C213yesmaximal, complemented
4#42623C213yesmaximal, complemented
5#42610C213yesmaximal, complemented
6#42569C213yesmaximal, complemented
7#42461C213yesmaximal, complemented
8#40213C213yesmaximal, complemented
9#40178C213yesmaximal, complemented
10#40059C213yesmaximal, complemented
11#40027C213yesmaximal, complemented
12#39250C213yesmaximal, complemented
13#39192C213yesmaximal, complemented
14#37367C213yesmaximal, complemented
15#37367C213yesmaximal, complemented
16#37328C213yesmaximal, complemented
17#36585C211yesmaximal, characteristic
18#36584C211yesmaximal, characteristic, complemented
19#36475C211yesmaximal, characteristic, complemented
20#36475C211yesmaximal, characteristic, complemented
21#36466C211yesmaximal, characteristic, complemented
22#36458C211yesmaximal, characteristic
23#36059C211yesmaximal, characteristic
24#35971C211yesmaximal, characteristic, complemented
25#35898C211yesmaximal, characteristic
26#35868C211yesmaximal, characteristic, complemented
27#35816C211yesmaximal, characteristic
28#35816C211yesmaximal, characteristic
29#34337C211yesmaximal, characteristic, complemented
30#34336C211yesmaximal, characteristic, complemented
31#34263C211yesmaximal, characteristic
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#520C2211yescharacteristic
35#2864C2213yes—
36#2864C2213yes—
37#2860C2213yes—
38#2860C2213yes—
39#2859C2213yes—
40#2859C2213yes—
41#2836C2216yes—
42#2833C2216yes—
43#2802C2213yes—
44#2802C2216yes—
45#2798C2213yes—
46#2794C2213yes—
47#2789C2213yes—
48#2783C2213yes—
49#2783C2216yes—
50#2783C2216yes—
51#2776C2213yes—
52#2776C2216yes—
53#2772C2216yes—
54#2772C2216yes—
55#2772C2213yes—
56#2772C2216yes—
57#2766C2211yescharacteristic
58#2766C2216yes—
59#2758C2213yes—
60#2754C2213yes—
61#2747C2216yes—
62#2747C2216yes—
63#2739C2216yes—
64#2739C2216yes—
65#2725C2216yes—
66#2725C2213yes—
67#2725C2216yes—
68#2725C2213yes—
69#2725C2216yes—
70#2721C2213yes—
71#2719C2213yes—
72#2716C2213yes—
73#2713C2213yes—
74#2698C2216yes—
75#2698C2216yes—
76#2690C2216yes—
77#2690C2216yes—
78#2655C2216yes—
79#2654C2216yes—
80#2652C2216yes—
81#2650C2216yes—
82#2647C2213yes—
83#2647C2213yes—
84#2644C2213yes—
85#2644C2213yes—
86#2634C2216yes—
87#2629C2213yes—
88#2629C2213yes—
89#2625C2216yes—
90#2584C2213yes—
91#2584C2213yes—
92#2571C2213yes—
93#2571C2213yes—
94#2571C2213yes—
95#2570C2213yes—
96#2570C2213yes—
97#2570C2213yes—
98#2570C2213yes—
99#2570C2213yes—
100#2570C2213yes—
101#2566C2213yes—
102#2566C2213yes—
103#2552C2213yes—
104#2552C2213yes—
105#2551C2213yes—
106#2550C2213yes—
107#2550C2213yes—
108#2538C2213yes—
109#2538C2213yes—
110#2524C2216yes—
111#2513C2213yes—
112#2513C2213yes—
113#2513C2213yes—
114#2513C2213yes—
115#2513C2213yes—
116#2513C2213yes—
117#2513C2213yes—
118#2513C2213yes—
119#2512C2213yes—
120#2512C2213yes—
121#2512C2213yes—
122#2512C2213yes—
123#2509C2213yes—
124#2509C2213yes—
125#2509C2213yes—
126#2509C2213yes—
127#2509C2213yes—
128#2509C2213yes—
129#2509C2213yes—
130#2509C2213yes—
131#2508C2213yes—
132#2508C2213yes—
133#2508C2213yes—
134#2508C2213yes—
135#2507C2213yes—
136#2507C2213yes—
137#2507C2213yes—
138#2507C2213yes—
139#2506C2213yes—
140#2506C2213yes—
141#2506C2213yes—
142#2506C2213yes—
143#2497C2213yes—
144#2497C2213yes—
145#2496C2216yes—
146#2496C2213yes—
147#2496C2213yes—
148#2495C2213yes—
149#2495C2213yes—
150#2495C2213yes—
151#2495C2213yes—
152#2494C2213yes—
153#2494C2213yes—
154#2494C2213yes—
155#2494C2213yes—
156#2478C2216yes—
157#2475C2216yes—
158#2469C2216yes—
159#2454C2213yes—
160#2454C2213yes—
161#2452C2213yes—
162#2452C2213yes—
163#2442C2213yes—
164#2442C2213yes—
165#2440C2213yes—
166#2440C2213yes—
167#2429C2216yes—
168#2402C2213yes—
169#2402C2213yes—
170#2401C2213yes—
171#2401C2213yes—
172#2396C2213yes—
173#2396C2213yes—
174#2370C2213yes—
175#2370C2213yes—
176#2370C2213yes—
177#2370C2213yes—
178#2369C2213yes—
179#2365C2213yes—
180#2357C2213yes—
181#2355C2213yes—
182#2354C2213yes—
183#2351C2211yescharacteristic
184#2351C2211yescharacteristic
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
204#2345C2213yes—
205#2344C2213yes—
206#2341C2211yescharacteristic
207#2341C2211yescharacteristic
208#2341C2211yescharacteristic
209#2341C2211yescharacteristic
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212#2334C2216yes—
213#2331C2213yes—
214#2330C2213yes—
215#2330C2213yes—
216#2330C2213yes—
217#2323C2216yes—
218#2319C2213yes—
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#2293C2213yes—
232#2276C2211yescharacteristic
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239#557—28no—
240#557—28no—
241C2×C4⋊Q8C2313yes—
242C2×C4⋊Q8C2313yes—
243C2×C4⋊Q8C2313yes—
244C2×#126C2313yes—
245C2×#126C2313yes—
246C2×#126C2316yes—
247C2×#126C2316yes—
248C2×#125C2313yes—
249C2×#125C2313yes—
250C2×#125C2313yes—
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2316yes—
256C2×C22⋊Q8C2316yes—
257C2×C22⋊Q8C2316yes—
258#520—28no—
259C2×C4×Q8C2313yes—
260C2×C4×Q8C2313yes—
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×Q8C2311yescharacteristic
274C2×C4×Q8C2316yes—
275C2×C4×Q8C2311yescharacteristic
276C2×C4×D4C2313yes—
277C2×C4×D4C2313yes—
278C2×#117C2313yes—
279C2×#117C2316yes—
280C22×C4⋊C4C2313yes—
281#401C2313yes—
282#401C2316yes—
283#401C2311yescharacteristic
284#400C2313yes—
285#400C2316yes—
286#400C2316yes—
287#400C2316yes—
288#400C2316yes—
289#400C2316yes—
290#400C2313yes—
291#400C2316yes—
292#400C2316yes—
293#400C2316yes—
294#400C2316yes—
295#400C2313yes—
296#400C2316yes—
297#400C2316yes—
298#400C2313yes—
299#400C2313yes—
300#400C2316yes—
301#400C2313yes—
302#400C2313yes—
303#400C2313yes—
304#400C2313yes—
305#400C2311yescharacteristic
306#400C2313yes—
307#400C2313yes—
308#400C2311yescharacteristic
309#400C2313yes—
310#400C2313yes—
311#400C2313yes—
312#399C2313yes—
313#399C2313yes—
314#398C2313yes—
315#398C2316yes—
316#398C2316yes—
317#398C2316yes—
318#398C2316yes—
319#398C2316yes—
320#398C2316yes—
321#398C2316yes—
322#398C2313yes—
323#398C2316yes—
324#398C2316yes—
325#398C2313yes—
326#398C2313yes—
327#398C2313yes—
328#398C2316yes—
329#398C2313yes—
330#398C2316yes—
331#398C2311yescharacteristic
332#398C2311yescharacteristic
333#398C2313yes—
334#398C2311yescharacteristic
335#398C2313yes—
336#398C2313yes—
337#397C2316yes—
338#397C2316yes—
339#397C2316yes—
340#397C2313yes—
341#397C2316yes—
342#397C2316yes—
343#397C2313yes—
344#397C2316yes—
345#397C2316yes—
346#397C2316yes—
347#397C2316yes—
348#397C2313yes—
349#397C2316yes—
350#397C2313yes—
351#397C2313yes—
352#397C2313yes—
353#396C2313yes—
354#396C2313yes—
355#396C2316yes—
356#396C2316yes—
357#396C2316yes—
358#396C2316yes—
359#396C2316yes—
360#396C2313yes—
361#396C2313yes—
362#396C2313yes—
363#396C2316yes—
364#396C2313yes—
365#395C2313yes—
366#395C2316yes—
367#395C2316yes—
368#395C2313yes—
369#393C2313yes—
370#393C2313yes—
371#391C2313yes—
372#391C2313yes—
373#391C2313yes—
374#391C2316yes—
375#391C2313yes—
376#391C2313yes—
377#391C2313yes—
378#390C2313yes—
379#390C2313yes—
380#390C2313yes—
381#390C2313yes—
382#390C2313yes—
383#390C2313yes—
384#390C2313yes—
385#390C2313yes—
386#390C2313yes—
387#390C2313yes—
388#390C2313yes—
389#390C2313yes—
390#389C2313yes—
391#389C2313yes—
392#389C2313yes—
393#389C2313yes—
394#389C2313yes—
395#389C2313yes—
396#389C2313yes—
397#389C2313yes—
398#389C2311yescharacteristic
399#389C2313yes—
400#389C2313yes—
401#389C2313yes—
402#389C2316yes—
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#389C2313yes—
416#389C2316yes—
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2313yes—
422#389C2313yes—
423#389C2316yes—
424#389C2316yes—
425#389C2316yes—
426#389C2313yes—
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2316yes—
436#389C2313yes—
437#389C2316yes—
438#389C2313yes—
439#389C2313yes—
440#389C2316yes—
441#389C2316yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2316yes—
447#389C2316yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2311yescharacteristic
455#388C2313yes—
456#388C2313yes—
457#388C2313yes—
458#388C2313yes—
459#388C2313yes—
460#388C2313yes—
461#388C2316yes—
462#388C2316yes—
463#388C2313yes—
464#388C2316yes—
465#388C2316yes—
466#388C2316yes—
467#388C2316yes—
468#388C2316yes—
469#388C2316yes—
470#388C2316yes—
471#388C2316yes—
472#388C2313yes—
473#388C2313yes—
474#388C2316yes—
475#388C2316yes—
476#388C2313yes—
477#387C2311yescharacteristic
478#387C2313yes—
479#387C2313yes—
480#387C2313yes—
481#387C2313yes—
482#387C2313yes—
483#387C2311yescharacteristic
484#387C2311yescharacteristic
485#387C2313yes—
486#387C2313yes—
487#387C2313yes—
488#387C2313yes—
489#387C2313yes—
490#387C2316yes—
491#387C2313yes—
492#387C2313yes—
493#387C2313yes—
494#387C2313yes—
495#387C2313yes—
496#387C2313yes—
497#387C2313yes—
498#387C2316yes—
499#387C2316yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2316yes—
504#387C2316yes—
505#387C2316yes—
506#387C2316yes—
507#387C2316yes—
508#387C2313yes—
509#387C2313yes—
510#387C2316yes—
511#387C2316yes—
512#387C2313yes—
513#387C2313yes—
514#387C2316yes—
515#387C2316yes—
516#387C2316yes—
517#387C2313yes—
518#387C2313yes—
519#387C2313yes—
520#387C2313yes—
521#387C2316yes—
522#387C2311yescharacteristic
523#387C2311yescharacteristic
524#385C2316yes—
525#385C2316yes—
526#385C2316yes—
527#385C2316yes—
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#383C2316yes—
541#382C2311yescharacteristic
542#382C2313yes—
543#382C2313yes—
544#382C2313yes—
545#382C2313yes—
546#382C2313yes—
547#382C2313yes—
548#382C2313yes—
549#382C2313yes—
550#382C2313yes—
551#382C2313yes—
552#382C2313yes—
553#382C2313yes—
554#382C2316yes—
555#382C2316yes—
556#382C2313yes—
557#381C2316yes—
558#380C2313yes—
559#380C2313yes—
560#380C2316yes—
561#380C2316yes—
562#380C2313yes—
563#380C2313yes—
564#380C2313yes—
565#380C2313yes—
566#380C2316yes—
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⋊C4C2313yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2316yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2316yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2316yes—
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×Q8C2413yes—
625C22×Q8C2413yes—
626C22×Q8C2411yescharacteristic
627C22×D4C2413yes—
628C23×C4C2413yes—
629C23×C4C2416yes—
630C4⋊Q8—212no—
631C4⋊Q8—212no—
632C4⋊Q8—46no—
633#126—46no—
634#126—46no—
635#126—412no—
636#126—86no—
637#125—212no—
638#125—212no—
639#125—212no—
640#125—212no—
641#125—46no—
642#125—46no—
643#125—46no—
644#125—86no—
645C22⋊Q8—412no—
646C22⋊Q8—86no—
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—24no—
659C4×Q8—24no—
660C4×Q8—212no—
661C4×Q8—212no—
662C4×Q8—86no—
663C4×Q8#4118yes—
664C4×D4—212no—
665C4×D4—212no—
666#117—212no—
667#117—86no—
668C2×C4⋊C4—212no—
669C2×C4⋊C4C2413yes—
670C2×C4⋊C4C2413yes—
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2413yes—
675C2×C4⋊C4C2413yes—
676C2×C4⋊C4C2413yes—
677C2×C4⋊C4C2413yes—
678C2×C4⋊C4C2413yes—
679C2×C4⋊C4C2413yes—
680C2×C4⋊C4C2413yes—
681C2×C4⋊C4C2413yes—
682C2×C4⋊C4C2413yes—
683C2×C4⋊C4C2413yes—
684C2×C4⋊C4C2413yes—
685C2×C4⋊C4C2413yes—
686C2×C4⋊C4C2413yes—
687C2×C4⋊C4C2413yes—
688C2×C4⋊C4C2413yes—
689C2×C4⋊C4C2413yes—
690C2×C4⋊C4C2413yes—
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2413yes—
694C2×C4⋊C4C2416yes—
695C2×C4⋊C4C2416yes—
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2416yes—
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2416yes—
705C2×C4⋊C4C2416yes—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2416yes—
708C2×C4⋊C4C2416yes—
709C2×C4⋊C4C2416yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2416yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2416yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2411yescharacteristic
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2416yes—
741C2×C4⋊C4C2413yes—
742C2×C22⋊C4C2413yes—
743C2×C22⋊C4C2413yes—
744C2×C22⋊C4C2413yes—
745C2×C22⋊C4C2413yes—
746C2×C22⋊C4C2413yes—
747C2×C22⋊C4C2416yes—
748C2×C22⋊C4C2413yes—
749C2×C22⋊C4C2416yes—
750C2×C22⋊C4C2416yes—
751C2×C22⋊C4C2413yes—
752C2×C22⋊C4C2413yes—
753C2×C22⋊C4C2413yes—
754C2×C22⋊C4C2413yes—
755C2×C22⋊C4C2413yes—
756C2×C22⋊C4C2416yes—
757C2×C22⋊C4C2416yes—
758C2×C22⋊C4C2413yes—
759C2×C22⋊C4C2416yes—
760C2×C22⋊C4C2413yes—
761C2×C22⋊C4C2413yes—
762C2×C42C2413yes—
763C2×C42C2413yes—
764C2×C42C2413yes—
765C2×C42C2413yes—
766C2×C42C2413yes—
767C2×C42C2413yes—
768C2×C42C2413yes—
769C2×C42C2413yes—
770C2×C42C2413yes—
771C2×C42C2413yes—
772C2×C42C2413yes—
773C2×C42C2413yes—
774C2×C42C2413yes—
775C2×C42C2411yescharacteristic
776C2×C42C2411yescharacteristic
777C2×C42C2413yes—
778C2×C42C2416yes—
779C2×C42C2413yes—
780C2×C42C2416yes—
781C2×C42C2413yes—
782C2×C42C2413yes—
783C2×C42C2413yes—
784C2×C42C2413yes—
785C2×C42C2416yes—
786C2×C42C2413yes—
787C2×C42C2411yescharacteristic
788C2×C42C2413yes—
789C2×C42C2413yes—
790C2×C42C2413yes—
791#95C2411yescharacteristic
792#95C2411yescharacteristic
793#95C2411yescharacteristic
794#95C2413yes—
795#95C2413yes—
796#95C2413yes—
797#95C2413yes—
798#95C2413yes—
799#95C2413yes—
800#95C2413yes—
801#95C2413yes—
802#95C2413yes—
803#95C2411yescharacteristic
804#95C2411yescharacteristic
805#95C2411yescharacteristic
806#95C2411yescharacteristic
807#95C2411yescharacteristic
808#95C2411yescharacteristic
809#95C2413yes—
810#95C2413yes—
811#95C2413yes—
812#95C2413yes—
813#95C2413yes—
814#95C2413yes—
815#95C2413yes—
816#95C2416yes—
817#95C2416yes—
818#95C2411yescharacteristic
819#95C2411yescharacteristic
820#95C2413yes—
821#95C2413yes—
822#95C2411yescharacteristic
823#95C2411yescharacteristic
824#95C2411yescharacteristic
825#95C2411yescharacteristic
826#95C2411yescharacteristic
827#95C2411yescharacteristic
828#95C2413yes—
829#95C2413yes—
830#95C2411yescharacteristic
831#95C2411yescharacteristic
832#95C2416yes—
833#95C2416yes—
834#95C2411yescharacteristic
835#95C2413yes—
836#95C2413yes—
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2416yes—
849#95C2413yes—
850#95C2416yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2416yes—
862#95C2416yes—
863#95C2416yes—
864#95C2416yes—
865#95C2416yes—
866#95C2416yes—
867#95C2416yes—
868#95C2416yes—
869C24C2513yes—
870#41—416no—
871C2×Q8—26no—
872C2×Q8—26no—
873C2×Q8—26no—
874C2×Q8—43no—
875C2×Q8—43no—
876C2×Q8—43no—
877C2×Q8C2×#4114yes—
878C2×Q82−1+414yes—
879C2×Q82−1+414yes—
880C2×D4—26no—
881C2×D4—26no—
882C2×D4—26no—
883C22×C4—26no—
884C22×C4—26no—
885C22×C4—26no—
886C22×C4—212no—
887C22×C4—46no—
888C22×C4—46no—
889C22×C4C2511yescharacteristic
890C22×C4C2511yescharacteristic
891C22×C4C2511yescharacteristic
892C22×C4C2511yescharacteristic
893C22×C4C2513yes—
894C22×C4C2511yescharacteristic
895C22×C4C2511yescharacteristic
896C22×C4C2513yes—
897C22×C4C2511yescharacteristic
898C22×C4C2513yes—
899C22×C4C2513yes—
900C22×C4C2513yes—
901C22×C4C2511yescharacteristic
902C22×C4C2511yescharacteristic
903C22×C4C2511yescharacteristic
904C22×C4C2513yes—
905C22×C4C2511yescharacteristic
906C22×C4C2511yescharacteristic
907C22×C4C2513yes—
908C22×C4C2513yes—
909C22×C4C2513yes—
910C22×C4C2513yes—
911C22×C4C2513yes—
912C22×C4C2513yes—
913C22×C4C2513yes—
914C22×C4C2513yes—
915C22×C4C2511yescharacteristic
916C22×C4C2511yescharacteristic
917C22×C4C2511yescharacteristic
918C22×C4C2513yes—
919C4⋊C4—26no—
920C4⋊C4—26no—
921C4⋊C4—22no—
922C4⋊C4—22no—
923C4⋊C4—22no—
924C4⋊C4—26no—
925C4⋊C4—26no—
926C4⋊C4—26no—
927C4⋊C4—26no—
928C4⋊C4—26no—
929C4⋊C4—26no—
930C4⋊C4—26no—
931C4⋊C4—26no—
932C4⋊C4—212no—
933C4⋊C4—212no—
934C4⋊C4—26no—
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—22no—
944C4⋊C4—22no—
945C4⋊C4—26no—
946C4⋊C4—26no—
947C4⋊C4—26no—
948C4⋊C4—26no—
949C4⋊C4—22no—
950C4⋊C4—22no—
951C4⋊C4—41no—
952C4⋊C4—41no—
953C4⋊C4—41no—
954C4⋊C4—43no—
955C4⋊C4—43no—
956C4⋊C4—43no—
957C4⋊C4—43no—
958C4⋊C4—46no—
959C4⋊C4—41no—
960C4⋊C4—41no—
961C4⋊C4—43no—
962C4⋊C4—46no—
963C4⋊C4—43no—
964C4⋊C4—46no—
965C4⋊C4—46no—
966C4⋊C4—46no—
967C4⋊C4—46no—
968C4⋊C4—43no—
969C4⋊C4—46no—
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—43no—
982C4⋊C4—43no—
983C4⋊C4—46no—
984C4⋊C4—43no—
985C4⋊C4—43no—
986C4⋊C4—46no—
987C4⋊C4—43no—
988C4⋊C4—43no—
989C4⋊C4—43no—
990C4⋊C4—43no—
991C4⋊C4C2×#41112yes—
992C22⋊C4—26no—
993C22⋊C4—26no—
994C22⋊C4—26no—
995C22⋊C4—26no—
996C22⋊C4—43no—
997C22⋊C4—46no—
998C22⋊C4—43no—
999C22⋊C4—43no—
1000C22⋊C4—43no—
1001C22⋊C4—46no—
1002C22⋊C4—46no—
1003C22⋊C4—43no—
1004C22⋊C4—46no—
1005C22⋊C4—43no—
1006C22⋊C4—43no—
1007C22⋊C4—43no—
1008C22⋊C4—46no—
1009C22⋊C4—46no—
1010C22⋊C4—43no—
1011C22⋊C4—43no—
1012C42—26no—
1013C42—26no—
1014C42—26no—
1015C42—26no—
1016C42—26no—
1017C42—26no—
1018C42—26no—
1019C42—26no—
1020C42—26no—
1021C42—26no—
1022C42—26no—
1023C42—26no—
1024C42—26no—
1025C42—22no—
1026C42—22no—
1027C42—43no—
1028C42—43no—
1029C42—41no—
1030C42—43no—
1031C42—46no—
1032C42—43no—
1033C42—46no—
1034C42—43no—
1035C42—43no—
1036C42—43no—
1037C42—46no—
1038C42—43no—
1039C42—43no—
1040C42C2×#41112yes—
1041C23—23no—
1042C23—23no—
1043C23—23no—
1044C23—23no—
1045C23—23no—
1046C23—23no—
1047C23—23no—
1048C23C2611yescharacteristic
1049Q8—412no—
1050Q8—86no—
1051Q8#541116yes—
1052D4—412no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—23no—
1058C2×C4—21no—
1059C2×C4—23no—
1060C2×C4—21no—
1061C2×C4—21no—
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—21no—
1077C2×C4—21no—
1078C2×C4—23no—
1079C2×C4—23no—
1080C2×C4—23no—
1081C2×C4—23no—
1082C2×C4—23no—
1083C2×C4—23no—
1084C2×C4—23no—
1085C2×C4—23no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—23no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—23no—
1096C2×C4—23no—
1097C2×C4—23no—
1098C2×C4—23no—
1099C2×C4—23no—
1100C2×C4—23no—
1101C2×C4—23no—
1102C2×C4—23no—
1103C2×C4—23no—
1104C2×C4—21no—
1105C2×C4—23no—
1106C2×C4—23no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—23no—
1110C2×C4—21no—
1111C2×C4—23no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—23no—
1115C2×C4—23no—
1116C2×C4—23no—
1117C2×C4—23no—
1118C2×C4—23no—
1119C2×C4—23no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—23no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—23no—
1126C2×C4—23no—
1127C2×C4—23no—
1128C2×C4—23no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—23no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—412no—
1137C2×C4—812no—
1138C2×C4C22×#4112yes—
1139C2×C4C22×#4116yes—
1140C2×C4C22×#4116yes—
1141C2×C4C2×2−1+416yes—
1142C2×C4C2×2−1+416yes—
1143C2×C4#58512yes—
1144C2×C4#58512yes—
1145C22—43no—
1146C22—43no—
1147C22—43no—
1148C22—43no—
1149C22—43no—
1150C22—43no—
1151C22—43no—
1152C22C23×#4111yescharacteristic
1153C22C22×2−1+411yescharacteristic
1154C22C22×2−1+411yescharacteristic
1155C22C2×#58511yescharacteristic
1156C22C2×#58511yescharacteristic
1157C22H(7,𝔽2)11yescharacteristic
1158C222−1+611yescharacteristic
1159C4—22no—
1160C4—26no—
1161C4—22no—
1162C4—22no—
1163C4—41no—
1164C4—41no—
1165C4—41no—
1166C4—43no—
1167C4—43no—
1168C4—43no—
1169C4—43no—
1170C4—43no—
1171C4—41no—
1172C4—41no—
1173C4—43no—
1174C4—43no—
1175C4—41no—
1176C4—41no—
1177C4—43no—
1178C4—43no—
1179C4—41no—
1180C4—41no—
1181C4—43no—
1182C4—43no—
1183C4—43no—
1184C4—41no—
1185C4—41no—
1186C4—41no—
1187C4—43no—
1188C4C2×#541112yes—
1189C2—83no—
1190C2C22×#54111yescharacteristic
1191C2#6295211yescharacteristic
1192C2#6295311yescharacteristic
1193C2#6300711yescharacteristic
1194C2#6300811yescharacteristic
1195C2#6303311yescharacteristic
1196C2#6306111yescharacteristic
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. #52283C2semidirect
2. #42723C2semidirect
3. #42657C2semidirect
4. #42623C2semidirect
5. #42610C2semidirect
6. #42569C2semidirect
7. #42461C2semidirect
8. #40213C2semidirect
9. #40178C2semidirect
10. #40059C2semidirect
11. #40027C2semidirect
12. #39250C2semidirect
13. #39192C2semidirect
14. #37367C2semidirect
15. #37367C2semidirect
16. #37328C2semidirect
18. #36584C2semidirect
19. #36475C2semidirect
20. #36475C2semidirect
21. #36466C2semidirect
24. #35971C2semidirect
26. #35868C2semidirect
29. #34337C2semidirect
30. #34336C2semidirect

Maximal subgroups

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

subgroupindex
#522832
#427232
#426572
#426232
#426102
#425692
#424612
#402132
#401782
#400592
#400272
#392502
#391922
#373672
#373282
#365852
#365842
#364752
#364662
#364582
#360592
#359712
#358982
#358682
#358162
#343372
#343362
#342632