Finite Group Databasebeta

← #7656436

Subgroups — #7656436

Order 512.

4231 conjugacy classes of subgroups.

The subgroup lattice has 1199 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42780C213yesmaximal, complemented
2#42773C213yesmaximal, complemented
3#42748C213yesmaximal, complemented
4#42738C213yesmaximal, complemented
5#42638C213yesmaximal, complemented
6#42626C213yesmaximal, complemented
7#42582C213yesmaximal, complemented
8#42569C213yesmaximal, complemented
9#40027C213yesmaximal, complemented
10#39997C213yesmaximal, complemented
11#39927C213yesmaximal, complemented
12#39901C213yesmaximal, complemented
13#37571C213yesmaximal, complemented
14#37571C213yesmaximal, complemented
15#36475C211yesmaximal, characteristic, complemented
16#36466C211yesmaximal, characteristic, complemented
17#36431C211yesmaximal, characteristic
18#36431C211yesmaximal, characteristic
19#36059C211yesmaximal, characteristic
20#35971C211yesmaximal, characteristic, complemented
21#35898C211yesmaximal, characteristic
22#35898C211yesmaximal, characteristic
23#35898C211yesmaximal, characteristic
24#35868C211yesmaximal, characteristic, complemented
25#35868C211yesmaximal, characteristic, complemented
26#35868C211yesmaximal, characteristic, complemented
27#35142C213yesmaximal, complemented
28#34629C213yesmaximal, complemented
29#34336C211yesmaximal, characteristic, complemented
30#34336C211yesmaximal, characteristic, complemented
31#34129C211yesmaximal, characteristic
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35#2864C2213yes—
36#2859C2213yes—
37#2851C2213yes—
38#2851C2213yes—
39#2836C2216yes—
40#2836C2216yes—
41#2831C2216yes—
42#2831C2216yes—
43#2798C2216yes—
44#2783C2216yes—
45#2772C2216yes—
46#2766C2216yes—
47#2762C2216yes—
48#2755C2216yes—
49#2754C2216yes—
50#2747C2216yes—
51#2725C2216yes—
52#2725C2216yes—
53#2722C2216yes—
54#2721C2216yes—
55#2719C2216yes—
56#2716C2216yes—
57#2704C2216yes—
58#2690C2216yes—
59#2664C2216yes—
60#2664C2216yes—
61#2655C2211yescharacteristic
62#2655C2213yes—
63#2655C2213yes—
64#2655C2213yes—
65#2652C2213yes—
66#2652C2213yes—
67#2652C2213yes—
68#2652C2213yes—
69#2652C2216yes—
70#2650C2216yes—
71#2650C2216yes—
72#2647C2213yes—
73#2647C2213yes—
74#2647C2213yes—
75#2647C2213yes—
76#2647C2213yes—
77#2645C2213yes—
78#2645C2213yes—
79#2644C2213yes—
80#2644C2213yes—
81#2644C2213yes—
82#2644C2213yes—
83#2642C2213yes—
84#2629C2213yes—
85#2625C2213yes—
86#2625C2213yes—
87#2621C2213yes—
88#2584C2213yes—
89#2584C2213yes—
90#2580C2213yes—
91#2580C2213yes—
92#2571C2213yes—
93#2570C2213yes—
94#2570C2213yes—
95#2570C2213yes—
96#2570C2213yes—
97#2570C2213yes—
98#2570C2213yes—
99#2566C2213yes—
100#2566C2213yes—
101#2552C2213yes—
102#2552C2213yes—
103#2552C2213yes—
104#2552C2213yes—
105#2551C2213yes—
106#2550C2213yes—
107#2550C2213yes—
108#2533C2216yes—
109#2528C2216yes—
110#2513C2213yes—
111#2513C2213yes—
112#2513C2213yes—
113#2513C2213yes—
114#2513C2213yes—
115#2513C2213yes—
116#2512C2213yes—
117#2512C2213yes—
118#2512C2213yes—
119#2512C2213yes—
120#2512C2213yes—
121#2512C2213yes—
122#2509C2213yes—
123#2509C2213yes—
124#2509C2213yes—
125#2509C2213yes—
126#2509C2213yes—
127#2508C2213yes—
128#2508C2213yes—
129#2508C2213yes—
130#2507C2213yes—
131#2507C2213yes—
132#2507C2213yes—
133#2507C2213yes—
134#2507C2213yes—
135#2506C2213yes—
136#2506C2213yes—
137#2506C2213yes—
138#2506C2213yes—
139#2506C2213yes—
140#2506C2213yes—
141#2506C2213yes—
142#2497C2213yes—
143#2497C2213yes—
144#2497C2213yes—
145#2496C2213yes—
146#2496C2213yes—
147#2496C2213yes—
148#2495C2213yes—
149#2495C2213yes—
150#2495C2213yes—
151#2494C2213yes—
152#2494C2213yes—
153#2494C2213yes—
154#2478C2216yes—
155#2478C2216yes—
156#2478C2216yes—
157#2475C2216yes—
158#2475C2216yes—
159#2475C2216yes—
160#2454C2213yes—
161#2454C2213yes—
162#2452C2213yes—
163#2452C2213yes—
164#2441C2213yes—
165#2441C2213yes—
166#2439C2213yes—
167#2439C2213yes—
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#2355C2213yes—
183#2355C2213yes—
184#2354C2213yes—
185#2354C2213yes—
186#2351C2211yescharacteristic
187#2351C2211yescharacteristic
188#2351C2211yescharacteristic
189#2351C2211yescharacteristic
190#2351C2211yescharacteristic
191#2351C2211yescharacteristic
192#2351C2211yescharacteristic
193#2351C2211yescharacteristic
194#2351C2211yescharacteristic
195#2351C2211yescharacteristic
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#2346C2213yes—
207#2346C2213yes—
208#2341C2211yescharacteristic
209#2341C2211yescharacteristic
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212#2341C2211yescharacteristic
213#2341C2211yescharacteristic
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#2293C2213yes—
229#2293C2213yes—
230#2285C2213yes—
231#2276C2211yescharacteristic
232#2276C2211yescharacteristic
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C4×#117C2213yes—
238C22×#41C2311yescharacteristic
239#557—28no—
240#557—28no—
241C2×C4⋊Q8C2313yes—
242C2×C4⋊Q8C2313yes—
243C2×C4⋊Q8C2313yes—
244C2×#126C2316yes—
245C2×#126C2316yes—
246C2×#126C2316yes—
247C2×#125C2313yes—
248C2×#125C2313yes—
249C2×#125C2313yes—
250C2×#125C2313yes—
251C2×#125C2313yes—
252C2×#125C2316yes—
253C2×#125C2316yes—
254C2×#125C2316yes—
255C2×C22⋊Q8C2313yes—
256C2×C22⋊Q8C2313yes—
257C4×#41—28no—
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×Q8C2311yescharacteristic
274C2×C4×D4C2313yes—
275C2×C4×D4C2313yes—
276C2×#117C2313yes—
277C2×#117C2313yes—
278C2×#117C2313yes—
279C2×#117C2316yes—
280C22×C42C2313yes—
281#401C2311yescharacteristic
282#401C2313yes—
283#401C2313yes—
284#401C2313yes—
285#400C2313yes—
286#400C2313yes—
287#400C2313yes—
288#400C2316yes—
289#400C2316yes—
290#400C2316yes—
291#400C2313yes—
292#400C2313yes—
293#400C2313yes—
294#400C2316yes—
295#400C2316yes—
296#400C2316yes—
297#400C2313yes—
298#400C2316yes—
299#400C2311yescharacteristic
300#400C2313yes—
301#400C2313yes—
302#400C2311yescharacteristic
303#400C2313yes—
304#400C2313yes—
305#400C2313yes—
306#400C2313yes—
307#400C2313yes—
308#400C2311yescharacteristic
309#400C2313yes—
310#400C2313yes—
311#400C2313yes—
312#400C2313yes—
313#400C2313yes—
314#400C2313yes—
315#400C2313yes—
316#400C2311yescharacteristic
317#400C2313yes—
318#400C2313yes—
319#400C2313yes—
320#399C2316yes—
321#399C2316yes—
322#398C2313yes—
323#398C2316yes—
324#398C2316yes—
325#398C2316yes—
326#398C2316yes—
327#398C2316yes—
328#398C2316yes—
329#398C2313yes—
330#398C2316yes—
331#398C2316yes—
332#398C2316yes—
333#398C2316yes—
334#398C2316yes—
335#398C2311yescharacteristic
336#398C2313yes—
337#398C2313yes—
338#398C2311yescharacteristic
339#398C2313yes—
340#398C2313yes—
341#398C2313yes—
342#398C2311yescharacteristic
343#398C2313yes—
344#398C2313yes—
345#398C2313yes—
346#398C2313yes—
347#398C2313yes—
348#398C2313yes—
349#397C2313yes—
350#397C2313yes—
351#397C2316yes—
352#397C2316yes—
353#397C2316yes—
354#397C2316yes—
355#397C2313yes—
356#397C2316yes—
357#397C2316yes—
358#397C2316yes—
359#397C2316yes—
360#397C2316yes—
361#397C2313yes—
362#397C2313yes—
363#397C2313yes—
364#397C2313yes—
365#397C2313yes—
366#397C2313yes—
367#397C2313yes—
368#397C2313yes—
369#397C2313yes—
370#396C2316yes—
371#396C2316yes—
372#396C2316yes—
373#396C2316yes—
374#396C2316yes—
375#396C2316yes—
376#396C2313yes—
377#396C2316yes—
378#396C2313yes—
379#396C2313yes—
380#396C2313yes—
381#395C2316yes—
382#395C2316yes—
383#393C2316yes—
384#393C2316yes—
385#391C2313yes—
386#391C2313yes—
387#391C2313yes—
388#391C2313yes—
389#391C2313yes—
390#391C2313yes—
391#391C2316yes—
392#391C2316yes—
393#391C2313yes—
394#391C2313yes—
395#390C2313yes—
396#390C2313yes—
397#390C2313yes—
398#390C2313yes—
399#390C2313yes—
400#390C2313yes—
401#390C2313yes—
402#390C2313yes—
403#390C2313yes—
404#390C2313yes—
405#390C2313yes—
406#390C2313yes—
407#389C2313yes—
408#389C2313yes—
409#389C2313yes—
410#389C2313yes—
411#389C2313yes—
412#389C2313yes—
413#389C2311yescharacteristic
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#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2316yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2316yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2316yes—
450#389C2316yes—
451#389C2313yes—
452#389C2313yes—
453#389C2316yes—
454#389C2316yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2316yes—
460#389C2316yes—
461#389C2313yes—
462#389C2313yes—
463#389C2313yes—
464#389C2313yes—
465#389C2313yes—
466#389C2313yes—
467#389C2316yes—
468#388C2316yes—
469#388C2316yes—
470#388C2316yes—
471#388C2316yes—
472#388C2316yes—
473#388C2316yes—
474#388C2316yes—
475#388C2316yes—
476#388C2316yes—
477#388C2316yes—
478#388C2316yes—
479#388C2316yes—
480#388C2316yes—
481#387C2311yescharacteristic
482#387C2313yes—
483#387C2313yes—
484#387C2313yes—
485#387C2313yes—
486#387C2316yes—
487#387C2316yes—
488#387C2313yes—
489#387C2316yes—
490#387C2316yes—
491#387C2316yes—
492#387C2316yes—
493#387C2316yes—
494#387C2316yes—
495#387C2316yes—
496#387C2316yes—
497#387C2316yes—
498#387C2316yes—
499#387C2316yes—
500#387C2316yes—
501#387C2316yes—
502#387C2313yes—
503#387C2313yes—
504#387C2316yes—
505#387C2316yes—
506#387C2316yes—
507#387C2316yes—
508#387C2316yes—
509#387C2316yes—
510#387C2316yes—
511#387C2313yes—
512#387C2313yes—
513#387C2313yes—
514#387C2313yes—
515#387C2311yescharacteristic
516#387C2311yescharacteristic
517#387C2311yescharacteristic
518#387C2311yescharacteristic
519#385C2313yes—
520#385C2313yes—
521#385C2316yes—
522#385C2316yes—
523#385C2313yes—
524#385C2313yes—
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#383C2316yes—
539#382C2313yes—
540#382C2313yes—
541#382C2313yes—
542#382C2313yes—
543#382C2313yes—
544#382C2313yes—
545#382C2313yes—
546#382C2313yes—
547#382C2313yes—
548#382C2313yes—
549#382C2316yes—
550#382C2313yes—
551#382C2316yes—
552#380C2313yes—
553#380C2313yes—
554#380C2313yes—
555#380C2313yes—
556#380C2313yes—
557#380C2313yes—
558#380C2316yes—
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⋊C4C2316yes—
571C4×C4⋊C4C2316yes—
572C4×C4⋊C4C2313yes—
573C4×C4⋊C4C2316yes—
574C4×C4⋊C4C2316yes—
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×C4⋊C4C2311yescharacteristic
605C4×C22⋊C4C2313yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613#376C2313yes—
614#376C2313yes—
615#376C2313yes—
616#376C2313yes—
617#376C2313yes—
618#376C2313yes—
619C43C2313yes—
620C43C2313yes—
621C2×#41—24no—
622C2×#41—24no—
623C2×#41—24no—
624C22×Q8C2413yes—
625C22×Q8C2413yes—
626C22×Q8C2411yescharacteristic
627C22×D4C2413yes—
628C23×C4C2413yes—
629C23×C4C2413yes—
630C23×C4C2413yes—
631C4⋊Q8—212no—
632C4⋊Q8—212no—
633C4⋊Q8—46no—
634#126—412no—
635#126—86no—
636#126—86no—
637#125—212no—
638#125—212no—
639#125—212no—
640#125—212no—
641#125—46no—
642#125—412no—
643#125—86no—
644#125—86no—
645C22⋊Q8—46no—
646C22⋊Q8—46no—
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#4118yes—
663C4×D4—212no—
664C4×D4—212no—
665#117—212no—
666#117—46no—
667#117—46no—
668#117—86no—
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2413yes—
672C2×C4⋊C4C2413yes—
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
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⋊C4C2413yes—
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2416yes—
697C2×C4⋊C4C2416yes—
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2416yes—
702C2×C4⋊C4C2416yes—
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2416yes—
713C2×C4⋊C4C2416yes—
714C2×C4⋊C4C2416yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2416yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2416yes—
721C2×C4⋊C4C2416yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2416yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2411yescharacteristic
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2413yes—
741C2×C22⋊C4C2416yes—
742C2×C22⋊C4C2413yes—
743C2×C22⋊C4C2416yes—
744C2×C22⋊C4C2416yes—
745C2×C22⋊C4C2413yes—
746C2×C22⋊C4C2413yes—
747C2×C22⋊C4C2413yes—
748C2×C22⋊C4C2413yes—
749C2×C22⋊C4C2413yes—
750C2×C22⋊C4C2413yes—
751C2×C22⋊C4C2413yes—
752C2×C22⋊C4C2413yes—
753C2×C22⋊C4C2413yes—
754C2×C22⋊C4C2416yes—
755C2×C22⋊C4C2416yes—
756C2×C22⋊C4C2416yes—
757C2×C22⋊C4C2413yes—
758C2×C22⋊C4C2413yes—
759C2×C22⋊C4C2416yes—
760C2×C42—212no—
761C2×C42C2413yes—
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×C42C2413yes—
776C2×C42C2411yescharacteristic
777C2×C42C2413yes—
778C2×C42C2413yes—
779C2×C42C2413yes—
780C2×C42C2413yes—
781C2×C42C2413yes—
782C2×C42C2416yes—
783C2×C42C2416yes—
784C2×C42C2416yes—
785C2×C42C2416yes—
786C2×C42C2411yescharacteristic
787C2×C42C2411yescharacteristic
788C2×C42C2413yes—
789#95C2411yescharacteristic
790#95C2411yescharacteristic
791#95C2411yescharacteristic
792#95C2411yescharacteristic
793#95C2411yescharacteristic
794#95C2411yescharacteristic
795#95C2413yes—
796#95C2413yes—
797#95C2413yes—
798#95C2413yes—
799#95C2413yes—
800#95C2413yes—
801#95C2413yes—
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#95C2411yescharacteristic
815#95C2411yescharacteristic
816#95C2411yescharacteristic
817#95C2413yes—
818#95C2413yes—
819#95C2413yes—
820#95C2413yes—
821#95C2411yescharacteristic
822#95C2411yescharacteristic
823#95C2416yes—
824#95C2416yes—
825#95C2411yescharacteristic
826#95C2413yes—
827#95C2413yes—
828#95C2411yescharacteristic
829#95C2411yescharacteristic
830#95C2411yescharacteristic
831#95C2413yes—
832#95C2413yes—
833#95C2411yescharacteristic
834#95C2411yescharacteristic
835#95C2411yescharacteristic
836#95C2411yescharacteristic
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2416yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2416yes—
849#95C2416yes—
850#95C2416yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2416yes—
864#95C2416yes—
865#95C2416yes—
866#95C2416yes—
867#95C2416yes—
868#95C2416yes—
869C24C2513yes—
870#41—416no—
871C2×Q8—26no—
872C2×Q8—26no—
873C2×Q8—43no—
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—26no—
887C22×C4—26no—
888C22×C4—26no—
889C22×C4—43no—
890C22×C4—43no—
891C22×C4—43no—
892C22×C4C2511yescharacteristic
893C22×C4C2511yescharacteristic
894C22×C4C2511yescharacteristic
895C22×C4C2511yescharacteristic
896C22×C4C2511yescharacteristic
897C22×C4C2511yescharacteristic
898C22×C4C2513yes—
899C22×C4C2513yes—
900C22×C4C2511yescharacteristic
901C22×C4C2511yescharacteristic
902C22×C4C2513yes—
903C22×C4C2513yes—
904C22×C4C2511yescharacteristic
905C22×C4C2511yescharacteristic
906C22×C4C2513yes—
907C22×C4C2513yes—
908C22×C4C2513yes—
909C22×C4C2513yes—
910C22×C4C2513yes—
911C22×C4C2513yes—
912C22×C4C2513yes—
913C22×C4C2511yescharacteristic
914C22×C4C2511yescharacteristic
915C22×C4C2513yes—
916C22×C4C2513yes—
917C22×C4C2511yescharacteristic
918C22×C4C2513yes—
919C22×C4C2511yescharacteristic
920C22×C4C2511yescharacteristic
921C22×C4C2513yes—
922C4⋊C4—26no—
923C4⋊C4—22no—
924C4⋊C4—22no—
925C4⋊C4—26no—
926C4⋊C4—26no—
927C4⋊C4—26no—
928C4⋊C4—26no—
929C4⋊C4—26no—
930C4⋊C4—26no—
931C4⋊C4—26no—
932C4⋊C4—26no—
933C4⋊C4—212no—
934C4⋊C4—212no—
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—22no—
947C4⋊C4—22no—
948C4⋊C4—26no—
949C4⋊C4—26no—
950C4⋊C4—22no—
951C4⋊C4—26no—
952C4⋊C4—26no—
953C4⋊C4—22no—
954C4⋊C4—41no—
955C4⋊C4—43no—
956C4⋊C4—41no—
957C4⋊C4—41no—
958C4⋊C4—41no—
959C4⋊C4—43no—
960C4⋊C4—43no—
961C4⋊C4—43no—
962C4⋊C4—43no—
963C4⋊C4—43no—
964C4⋊C4—46no—
965C4⋊C4—43no—
966C4⋊C4—46no—
967C4⋊C4—46no—
968C4⋊C4—43no—
969C4⋊C4—43no—
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—43no—
980C4⋊C4—43no—
981C4⋊C4—46no—
982C4⋊C4—43no—
983C4⋊C4—43no—
984C4⋊C4—46no—
985C4⋊C4—46no—
986C4⋊C4—46no—
987C4⋊C4—43no—
988C4⋊C4—43no—
989C4⋊C4—43no—
990C4⋊C4—43no—
991C4⋊C4—43no—
992C4⋊C4—43no—
993C4⋊C4C2×#41112yes—
994C22⋊C4—212no—
995C22⋊C4—26no—
996C22⋊C4—43no—
997C22⋊C4—43no—
998C22⋊C4—46no—
999C22⋊C4—43no—
1000C22⋊C4—43no—
1001C22⋊C4—43no—
1002C22⋊C4—46no—
1003C22⋊C4—46no—
1004C22⋊C4—43no—
1005C22⋊C4—43no—
1006C22⋊C4—43no—
1007C22⋊C4—43no—
1008C22⋊C4—46no—
1009C22⋊C4—46no—
1010C22⋊C4—46no—
1011C22⋊C4—43no—
1012C22⋊C4—43no—
1013C42—22no—
1014C42—26no—
1015C42—26no—
1016C42—26no—
1017C42—26no—
1018C42—26no—
1019C42—26no—
1020C42—26no—
1021C42—26no—
1022C42—26no—
1023C42—26no—
1024C42—26no—
1025C42—26no—
1026C42—26no—
1027C42—26no—
1028C42—26no—
1029C42—41no—
1030C42—41no—
1031C42—43no—
1032C42—43no—
1033C42—43no—
1034C42—43no—
1035C42—43no—
1036C42—46no—
1037C42—46no—
1038C42—46no—
1039C42—46no—
1040C42C2×#41112yes—
1041C23—23no—
1042C23—23no—
1043C23—23no—
1044C23—23no—
1045C23—23no—
1046C23—23no—
1047C23—23no—
1048C23C2611yescharacteristic
1049Q8—86no—
1050Q8—86no—
1051Q8#541116yes—
1052D4—412no—
1053C2×C4—21no—
1054C2×C4—21no—
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—21no—
1065C2×C4—21no—
1066C2×C4—23no—
1067C2×C4—23no—
1068C2×C4—23no—
1069C2×C4—23no—
1070C2×C4—23no—
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—23no—
1089C2×C4—23no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—23no—
1094C2×C4—23no—
1095C2×C4—23no—
1096C2×C4—23no—
1097C2×C4—23no—
1098C2×C4—23no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—23no—
1104C2×C4—23no—
1105C2×C4—23no—
1106C2×C4—23no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—23no—
1112C2×C4—23no—
1113C2×C4—23no—
1114C2×C4—23no—
1115C2×C4—23no—
1116C2×C4—23no—
1117C2×C4—23no—
1118C2×C4—23no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—23no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—23no—
1130C2×C4—23no—
1131C2×C4—23no—
1132C2×C4—23no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—23no—
1136C2×C4—412no—
1137C2×C4—412no—
1138C2×C4—412no—
1139C2×C4C22×#4112yes—
1140C2×C4C22×#4116yes—
1141C2×C4C22×#4116yes—
1142C2×C4C2×2−1+416yes—
1143C2×C4C2×2−1+416yes—
1144C2×C4#58512yes—
1145C2×C4#58512yes—
1146C22—43no—
1147C22—43no—
1148C22—43no—
1149C22—43no—
1150C22—43no—
1151C22—43no—
1152C22—43no—
1153C22C23×#4111yescharacteristic
1154C22C22×2−1+411yescharacteristic
1155C22C22×2−1+411yescharacteristic
1156C22C2×#58511yescharacteristic
1157C22C2×#58511yescharacteristic
1158C22H(7,𝔽2)11yescharacteristic
1159C222−1+611yescharacteristic
1160C4—22no—
1161C4—26no—
1162C4—22no—
1163C4—22no—
1164C4—43no—
1165C4—43no—
1166C4—41no—
1167C4—41no—
1168C4—41no—
1169C4—41no—
1170C4—43no—
1171C4—43no—
1172C4—43no—
1173C4—41no—
1174C4—41no—
1175C4—41no—
1176C4—43no—
1177C4—41no—
1178C4—41no—
1179C4—43no—
1180C4—43no—
1181C4—43no—
1182C4—43no—
1183C4—43no—
1184C4—43no—
1185C4—41no—
1186C4—41no—
1187C4—41no—
1188C4—43no—
1189C4C2×#541112yes—
1190C2—83no—
1191C2C22×#54111yescharacteristic
1192C2#6281611yescharacteristic
1193C2#6285111yescharacteristic
1194C2#6294911yescharacteristic
1195C2#6295211yescharacteristic
1196C2#6295211yescharacteristic
1197C2#6295311yescharacteristic
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. #42780C2semidirect
2. #42773C2semidirect
3. #42748C2semidirect
4. #42738C2semidirect
5. #42638C2semidirect
6. #42626C2semidirect
7. #42582C2semidirect
8. #42569C2semidirect
9. #40027C2semidirect
10. #39997C2semidirect
11. #39927C2semidirect
12. #39901C2semidirect
13. #37571C2semidirect
14. #37571C2semidirect
15. #36475C2semidirect
16. #36466C2semidirect
20. #35971C2semidirect
24. #35868C2semidirect
25. #35868C2semidirect
26. #35868C2semidirect
27. #35142C2semidirect
28. #34629C2semidirect
29. #34336C2semidirect
30. #34336C2semidirect

Maximal subgroups

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

subgroupindex
#427802
#427732
#427482
#427382
#426382
#426262
#425822
#425692
#400272
#399972
#399272
#399012
#375712
#364752
#364662
#364312
#360592
#359712
#358982
#358682
#351422
#346292
#343362
#341292