Finite Group Databasebeta

← #7661734

Subgroups — #7661734

Order 512.

4229 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#52283C213yesmaximal, complemented
2#42753C213yesmaximal, complemented
3#42670C213yesmaximal, complemented
4#42623C213yesmaximal, complemented
5#42569C213yesmaximal, complemented
6#42538C213yesmaximal, complemented
7#42469C213yesmaximal, complemented
8#40202C213yesmaximal, complemented
9#40167C213yesmaximal, complemented
10#40051C213yesmaximal, complemented
11#39997C213yesmaximal, complemented
12#39217C213yesmaximal, complemented
13#39203C213yesmaximal, complemented
14#37433C213yesmaximal, complemented
15#37358C213yesmaximal, complemented
16#37337C213yesmaximal, complemented
17#36585C211yesmaximal, characteristic
18#36585C211yesmaximal, characteristic
19#36475C211yesmaximal, characteristic, complemented
20#36475C211yesmaximal, characteristic, complemented
21#36474C211yesmaximal, characteristic, complemented
22#36447C211yesmaximal, characteristic, complemented
23#36040C211yesmaximal, characteristic
24#35971C211yesmaximal, characteristic, complemented
25#35971C211yesmaximal, characteristic, complemented
26#35898C211yesmaximal, characteristic
27#35898C211yesmaximal, characteristic
28#35748C211yesmaximal, characteristic
29#34336C211yesmaximal, characteristic, complemented
30#34335C211yesmaximal, characteristic, complemented
31#34263C211yesmaximal, characteristic
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#520C2211yescharacteristic
35#2864C2213yes—
36#2864C2213yes—
37#2862C2213yes—
38#2860C2213yes—
39#2860C2213yes—
40#2859C2213yes—
41#2836C2216yes—
42#2833C2216yes—
43#2802C2213yes—
44#2798C2216yes—
45#2798C2216yes—
46#2798C2213yes—
47#2794C2213yes—
48#2789C2216yes—
49#2789C2213yes—
50#2789C2216yes—
51#2789C2216yes—
52#2783C2213yes—
53#2776C2213yes—
54#2772C2213yes—
55#2766C2213yes—
56#2758C2211yescharacteristic
57#2754C2213yes—
58#2754C2216yes—
59#2754C2216yes—
60#2754C2216yes—
61#2754C2216yes—
62#2747C2216yes—
63#2744C2216yes—
64#2739C2216yes—
65#2725C2213yes—
66#2725C2213yes—
67#2722C2216yes—
68#2721C2213yes—
69#2721C2216yes—
70#2719C2213yes—
71#2716C2213yes—
72#2716C2216yes—
73#2713C2213yes—
74#2704C2216yes—
75#2698C2216yes—
76#2690C2216yes—
77#2689C2216yes—
78#2655C2216yes—
79#2655C2216yes—
80#2652C2216yes—
81#2650C2216yes—
82#2647C2213yes—
83#2647C2213yes—
84#2644C2213yes—
85#2644C2213yes—
86#2637C2216yes—
87#2628C2213yes—
88#2628C2213yes—
89#2625C2216yes—
90#2580C2213yes—
91#2580C2213yes—
92#2571C2213yes—
93#2571C2213yes—
94#2571C2213yes—
95#2570C2213yes—
96#2570C2213yes—
97#2570C2213yes—
98#2570C2213yes—
99#2570C2213yes—
100#2570C2213yes—
101#2567C2213yes—
102#2563C2213yes—
103#2552C2213yes—
104#2550C2213yes—
105#2550C2213yes—
106#2550C2213yes—
107#2550C2213yes—
108#2546C2213yes—
109#2542C2213yes—
110#2519C2216yes—
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#2508C2213yes—
128#2508C2213yes—
129#2508C2213yes—
130#2508C2213yes—
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#2496C2213yes—
146#2496C2213yes—
147#2494C2213yes—
148#2494C2213yes—
149#2494C2213yes—
150#2494C2213yes—
151#2494C2213yes—
152#2494C2213yes—
153#2494C2213yes—
154#2494C2213yes—
155#2489C2216yes—
156#2478C2216yes—
157#2475C2216yes—
158#2462C2216yes—
159#2454C2213yes—
160#2454C2213yes—
161#2452C2213yes—
162#2452C2213yes—
163#2442C2213yes—
164#2442C2213yes—
165#2440C2213yes—
166#2440C2213yes—
167#2421C2216yes—
168#2402C2213yes—
169#2402C2213yes—
170#2401C2213yes—
171#2401C2213yes—
172#2396C2213yes—
173#2396C2213yes—
174#2370C2213yes—
175#2370C2213yes—
176#2369C2213yes—
177#2369C2213yes—
178#2365C2213yes—
179#2365C2213yes—
180#2357C2213yes—
181#2355C2213yes—
182#2355C2213yes—
183#2354C2213yes—
184#2351C2211yescharacteristic
185#2351C2211yescharacteristic
186#2351C2211yescharacteristic
187#2351C2211yescharacteristic
188#2351C2211yescharacteristic
189#2351C2211yescharacteristic
190#2351C2211yescharacteristic
191#2351C2211yescharacteristic
192#2351C2211yescharacteristic
193#2351C2211yescharacteristic
194#2351C2211yescharacteristic
195#2351C2211yescharacteristic
196#2351C2211yescharacteristic
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#2331C2213yes—
215#2331C2213yes—
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
239Q82—28no—
240#557—28no—
241C2×C4⋊Q8C2313yes—
242C2×C4⋊Q8C2313yes—
243C2×C4⋊Q8C2313yes—
244C2×C4⋊Q8C2313yes—
245C2×C4⋊Q8C2313yes—
246C2×#126C2313yes—
247C2×#126C2313yes—
248C2×#126C2316yes—
249C2×#126C2316yes—
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#401C2316yes—
282#401C2316yes—
283#401C2313yes—
284#401C2313yes—
285#400C2316yes—
286#400C2316yes—
287#400C2316yes—
288#400C2316yes—
289#400C2316yes—
290#400C2316yes—
291#400C2313yes—
292#400C2313yes—
293#400C2316yes—
294#400C2316yes—
295#400C2313yes—
296#400C2313yes—
297#400C2313yes—
298#400C2316yes—
299#400C2316yes—
300#400C2316yes—
301#400C2311yescharacteristic
302#400C2313yes—
303#400C2313yes—
304#400C2313yes—
305#400C2311yescharacteristic
306#400C2311yescharacteristic
307#400C2311yescharacteristic
308#400C2311yescharacteristic
309#400C2313yes—
310#400C2313yes—
311#400C2313yes—
312#399C2313yes—
313#399C2316yes—
314#399C2316yes—
315#399C2313yes—
316#398C2313yes—
317#398C2313yes—
318#398C2316yes—
319#398C2316yes—
320#398C2316yes—
321#398C2316yes—
322#398C2313yes—
323#398C2316yes—
324#398C2313yes—
325#398C2316yes—
326#398C2316yes—
327#398C2313yes—
328#398C2313yes—
329#398C2313yes—
330#398C2316yes—
331#398C2313yes—
332#398C2313yes—
333#398C2313yes—
334#398C2316yes—
335#398C2316yes—
336#398C2313yes—
337#398C2313yes—
338#397C2316yes—
339#397C2316yes—
340#397C2316yes—
341#397C2313yes—
342#397C2316yes—
343#397C2316yes—
344#397C2316yes—
345#397C2313yes—
346#397C2313yes—
347#397C2316yes—
348#397C2316yes—
349#397C2316yes—
350#397C2313yes—
351#397C2316yes—
352#397C2313yes—
353#397C2313yes—
354#396C2313yes—
355#396C2316yes—
356#396C2313yes—
357#396C2316yes—
358#396C2313yes—
359#396C2313yes—
360#396C2313yes—
361#396C2313yes—
362#395C2316yes—
363#395C2316yes—
364#395C2316yes—
365#395C2313yes—
366#395C2311yescharacteristic
367#393C2313yes—
368#393C2316yes—
369#393C2313yes—
370#393C2316yes—
371#391C2311yescharacteristic
372#391C2316yes—
373#391C2313yes—
374#391C2316yes—
375#391C2316yes—
376#391C2316yes—
377#391C2313yes—
378#391C2316yes—
379#391C2316yes—
380#391C2316yes—
381#391C2313yes—
382#391C2313yes—
383#391C2311yescharacteristic
384#390C2313yes—
385#390C2313yes—
386#390C2313yes—
387#390C2313yes—
388#390C2313yes—
389#390C2313yes—
390#390C2313yes—
391#390C2313yes—
392#390C2313yes—
393#390C2313yes—
394#390C2313yes—
395#390C2313yes—
396#389C2311yescharacteristic
397#389C2313yes—
398#389C2313yes—
399#389C2313yes—
400#389C2313yes—
401#389C2313yes—
402#389C2313yes—
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#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2313yes—
422#389C2313yes—
423#389C2313yes—
424#389C2313yes—
425#389C2316yes—
426#389C2316yes—
427#389C2313yes—
428#389C2316yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2316yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#388C2313yes—
455#388C2313yes—
456#388C2313yes—
457#388C2313yes—
458#388C2313yes—
459#388C2313yes—
460#388C2316yes—
461#388C2316yes—
462#388C2313yes—
463#388C2316yes—
464#388C2316yes—
465#388C2316yes—
466#388C2316yes—
467#388C2316yes—
468#388C2316yes—
469#388C2316yes—
470#388C2316yes—
471#388C2316yes—
472#388C2313yes—
473#388C2313yes—
474#388C2316yes—
475#388C2313yes—
476#387C2313yes—
477#387C2313yes—
478#387C2313yes—
479#387C2313yes—
480#387C2313yes—
481#387C2313yes—
482#387C2311yescharacteristic
483#387C2311yescharacteristic
484#387C2313yes—
485#387C2313yes—
486#387C2313yes—
487#387C2313yes—
488#387C2313yes—
489#387C2316yes—
490#387C2313yes—
491#387C2313yes—
492#387C2313yes—
493#387C2313yes—
494#387C2313yes—
495#387C2313yes—
496#387C2313yes—
497#387C2316yes—
498#387C2316yes—
499#387C2316yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2316yes—
504#387C2316yes—
505#387C2316yes—
506#387C2313yes—
507#387C2313yes—
508#387C2316yes—
509#387C2316yes—
510#387C2316yes—
511#387C2316yes—
512#387C2313yes—
513#387C2313yes—
514#387C2316yes—
515#387C2316yes—
516#387C2313yes—
517#387C2313yes—
518#387C2313yes—
519#387C2313yes—
520#387C2316yes—
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#383C2311yescharacteristic
537#383C2311yescharacteristic
538#382C2313yes—
539#382C2313yes—
540#382C2313yes—
541#382C2313yes—
542#382C2313yes—
543#382C2313yes—
544#382C2313yes—
545#382C2313yes—
546#382C2313yes—
547#382C2313yes—
548#382C2313yes—
549#382C2313yes—
550#382C2313yes—
551#382C2313yes—
552#382C2316yes—
553#382C2313yes—
554#382C2313yes—
555#382C2316yes—
556#382C2316yes—
557#381C2316yes—
558#380C2316yes—
559#380C2316yes—
560#380C2313yes—
561#380C2313yes—
562#380C2316yes—
563#380C2313yes—
564#380C2313yes—
565#380C2313yes—
566#380C2313yes—
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⋊C4C2313yes—
581C4×C4⋊C4C2316yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2316yes—
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×Q8C2411yescharacteristic
625C22×Q8C2416yes—
626C22×Q8C2413yes—
627C22×Q8C2411yescharacteristic
628C22×D4C2413yes—
629C23×C4C2413yes—
630C23×C4C2416yes—
631C4⋊Q8—212no—
632C4⋊Q8—212no—
633C4⋊Q8—212no—
634C4⋊Q8—212no—
635C4⋊Q8—46no—
636#126—46no—
637#126—46no—
638#126—412no—
639#126—86no—
640#125—212no—
641#125—212no—
642#125—46no—
643#125—46no—
644#125—46no—
645#125—86no—
646C22⋊Q8—412no—
647C22⋊Q8—86no—
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—24no—
661C4×Q8—212no—
662C4×Q8—212no—
663C4×Q8—86no—
664C4×Q8#4118yes—
665C4×D4—212no—
666C4×D4—212no—
667#117—212no—
668#117—86no—
669C2×C4⋊C4—212no—
670C2×C4⋊C4C2413yes—
671C2×C4⋊C4C2413yes—
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⋊C4C2413yes—
692C2×C4⋊C4C2413yes—
693C2×C4⋊C4C2411yescharacteristic
694C2×C4⋊C4C2411yescharacteristic
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2416yes—
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2416yes—
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2416yes—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2416yes—
709C2×C4⋊C4C2416yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2416yes—
713C2×C4⋊C4C2413yes—
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⋊C4C2413yes—
728C2×C4⋊C4C2416yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2411yescharacteristic
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2416yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C22⋊C4C2413yes—
741C2×C22⋊C4C2413yes—
742C2×C22⋊C4C2413yes—
743C2×C22⋊C4C2413yes—
744C2×C22⋊C4C2413yes—
745C2×C22⋊C4C2416yes—
746C2×C22⋊C4C2413yes—
747C2×C22⋊C4C2416yes—
748C2×C22⋊C4C2416yes—
749C2×C22⋊C4C2413yes—
750C2×C22⋊C4C2413yes—
751C2×C22⋊C4C2413yes—
752C2×C22⋊C4C2416yes—
753C2×C22⋊C4C2413yes—
754C2×C22⋊C4C2413yes—
755C2×C22⋊C4C2416yes—
756C2×C22⋊C4C2413yes—
757C2×C22⋊C4C2413yes—
758C2×C22⋊C4C2413yes—
759C2×C22⋊C4C2416yes—
760C2×C42C2413yes—
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×C42C2411yescharacteristic
774C2×C42C2411yescharacteristic
775C2×C42C2413yes—
776C2×C42C2416yes—
777C2×C42C2413yes—
778C2×C42C2416yes—
779C2×C42C2413yes—
780C2×C42C2413yes—
781C2×C42C2413yes—
782C2×C42C2413yes—
783C2×C42C2416yes—
784C2×C42C2413yes—
785C2×C42C2411yescharacteristic
786C2×C42C2413yes—
787C2×C42C2413yes—
788C2×C42C2413yes—
789#95C2411yescharacteristic
790#95C2411yescharacteristic
791#95C2411yescharacteristic
792#95C2413yes—
793#95C2413yes—
794#95C2413yes—
795#95C2413yes—
796#95C2413yes—
797#95C2413yes—
798#95C2413yes—
799#95C2413yes—
800#95C2413yes—
801#95C2411yescharacteristic
802#95C2411yescharacteristic
803#95C2411yescharacteristic
804#95C2411yescharacteristic
805#95C2411yescharacteristic
806#95C2411yescharacteristic
807#95C2413yes—
808#95C2413yes—
809#95C2413yes—
810#95C2413yes—
811#95C2413yes—
812#95C2413yes—
813#95C2413yes—
814#95C2416yes—
815#95C2416yes—
816#95C2411yescharacteristic
817#95C2411yescharacteristic
818#95C2413yes—
819#95C2411yescharacteristic
820#95C2411yescharacteristic
821#95C2411yescharacteristic
822#95C2411yescharacteristic
823#95C2411yescharacteristic
824#95C2411yescharacteristic
825#95C2411yescharacteristic
826#95C2411yescharacteristic
827#95C2411yescharacteristic
828#95C2413yes—
829#95C2416yes—
830#95C2416yes—
831#95C2411yescharacteristic
832#95C2411yescharacteristic
833#95C2413yes—
834#95C2413yes—
835#95C2413yes—
836#95C2413yes—
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2416yes—
845#95C2413yes—
846#95C2413yes—
847#95C2416yes—
848#95C2413yes—
849#95C2413yes—
850#95C2416yes—
851#95C2416yes—
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—22no—
872C2×Q8—26no—
873C2×Q8—212no—
874C2×Q8—22no—
875C2×Q8—41no—
876C2×Q8—46no—
877C2×Q8—46no—
878C2×Q8—43no—
879C2×Q8—43no—
880C2×Q8C2×#4114yes—
881C2×Q82−1+414yes—
882C2×Q82−1+414yes—
883C2×D4—26no—
884C2×D4—26no—
885C2×D4—26no—
886C22×C4—26no—
887C22×C4—26no—
888C22×C4—26no—
889C22×C4—212no—
890C22×C4—46no—
891C22×C4—46no—
892C22×C4C2511yescharacteristic
893C22×C4C2511yescharacteristic
894C22×C4C2511yescharacteristic
895C22×C4C2511yescharacteristic
896C22×C4C2513yes—
897C22×C4C2511yescharacteristic
898C22×C4C2511yescharacteristic
899C22×C4C2513yes—
900C22×C4C2511yescharacteristic
901C22×C4C2513yes—
902C22×C4C2513yes—
903C22×C4C2513yes—
904C22×C4C2511yescharacteristic
905C22×C4C2513yes—
906C22×C4C2513yes—
907C22×C4C2511yescharacteristic
908C22×C4C2513yes—
909C22×C4C2511yescharacteristic
910C22×C4C2513yes—
911C22×C4C2513yes—
912C22×C4C2513yes—
913C22×C4C2513yes—
914C22×C4C2513yes—
915C22×C4C2511yescharacteristic
916C22×C4C2511yescharacteristic
917C22×C4C2511yescharacteristic
918C22×C4C2513yes—
919C22×C4C2511yescharacteristic
920C22×C4C2511yescharacteristic
921C22×C4C2513yes—
922C4⋊C4—26no—
923C4⋊C4—26no—
924C4⋊C4—22no—
925C4⋊C4—22no—
926C4⋊C4—26no—
927C4⋊C4—26no—
928C4⋊C4—26no—
929C4⋊C4—26no—
930C4⋊C4—26no—
931C4⋊C4—26no—
932C4⋊C4—26no—
933C4⋊C4—26no—
934C4⋊C4—26no—
935C4⋊C4—212no—
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—22no—
947C4⋊C4—22no—
948C4⋊C4—22no—
949C4⋊C4—26no—
950C4⋊C4—26no—
951C4⋊C4—26no—
952C4⋊C4—26no—
953C4⋊C4—41no—
954C4⋊C4—41no—
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—43no—
965C4⋊C4—46no—
966C4⋊C4—46no—
967C4⋊C4—43no—
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—46no—
982C4⋊C4—43no—
983C4⋊C4—43no—
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—43no—
1009C22⋊C4—46no—
1010C22⋊C4—46no—
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—41no—
1029C42—43no—
1030C42—43no—
1031C42—46no—
1032C42—43no—
1033C42—46no—
1034C42—43no—
1035C42—43no—
1036C42—43no—
1037C42—43no—
1038C42—46no—
1039C42—43no—
1040C42C2×#41112yes—
1041C23—23no—
1042C23—23no—
1043C23—23no—
1044C23—23no—
1045C23—23no—
1046C23—23no—
1047C23—23no—
1048C23C2611yescharacteristic
1049Q8—44no—
1050Q8—86no—
1051Q8—812no—
1052Q8#541116yes—
1053D4—412no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—23no—
1059C2×C4—23no—
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—21no—
1079C2×C4—23no—
1080C2×C4—23no—
1081C2×C4—23no—
1082C2×C4—23no—
1083C2×C4—23no—
1084C2×C4—23no—
1085C2×C4—23no—
1086C2×C4—23no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—23no—
1094C2×C4—21no—
1095C2×C4—21no—
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—23no—
1105C2×C4—23no—
1106C2×C4—23no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—23no—
1111C2×C4—21no—
1112C2×C4—23no—
1113C2×C4—21no—
1114C2×C4—23no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—23no—
1118C2×C4—23no—
1119C2×C4—23no—
1120C2×C4—23no—
1121C2×C4—23no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—23no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—23no—
1128C2×C4—23no—
1129C2×C4—23no—
1130C2×C4—23no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—23no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—412no—
1138C2×C4—812no—
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—22no—
1162C4—26no—
1163C4—22no—
1164C4—41no—
1165C4—41no—
1166C4—43no—
1167C4—43no—
1168C4—41no—
1169C4—41no—
1170C4—43no—
1171C4—43no—
1172C4—43no—
1173C4—41no—
1174C4—43no—
1175C4—43no—
1176C4—41no—
1177C4—41no—
1178C4—43no—
1179C4—43no—
1180C4—41no—
1181C4—41no—
1182C4—43no—
1183C4—43no—
1184C4—43no—
1185C4—41no—
1186C4—41no—
1187C4—41no—
1188C4—43no—
1189C4C2×#541112yes—
1190C2—83no—
1191C2C22×#54111yescharacteristic
1192C2#6295211yescharacteristic
1193C2#6295311yescharacteristic
1194C2#6300511yescharacteristic
1195C2#6301011yescharacteristic
1196C2#6303311yescharacteristic
1197C2#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. #42753C2semidirect
3. #42670C2semidirect
4. #42623C2semidirect
5. #42569C2semidirect
6. #42538C2semidirect
7. #42469C2semidirect
8. #40202C2semidirect
9. #40167C2semidirect
10. #40051C2semidirect
11. #39997C2semidirect
12. #39217C2semidirect
13. #39203C2semidirect
14. #37433C2semidirect
15. #37358C2semidirect
16. #37337C2semidirect
19. #36475C2semidirect
20. #36475C2semidirect
21. #36474C2semidirect
22. #36447C2semidirect
24. #35971C2semidirect
25. #35971C2semidirect
29. #34336C2semidirect
30. #34335C2semidirect

Maximal subgroups

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

subgroupindex
#522832
#427532
#426702
#426232
#425692
#425382
#424692
#402022
#401672
#400512
#399972
#392172
#392032
#374332
#373582
#373372
#365852
#364752
#364742
#364472
#360402
#359712
#358982
#357482
#343362
#343352
#342632