Finite Group Databasebeta

← #7661989

Subgroups — #7661989

Order 512.

4235 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52251C213yesmaximal, complemented
2#42764C213yesmaximal, complemented
3#42687C213yesmaximal, complemented
4#42597C213yesmaximal, complemented
5#42582C213yesmaximal, complemented
6#42582C213yesmaximal, complemented
7#42530C213yesmaximal, complemented
8#40227C213yesmaximal, complemented
9#40167C213yesmaximal, complemented
10#40059C213yesmaximal, complemented
11#39901C213yesmaximal, complemented
12#39734C213yesmaximal, complemented
13#39225C213yesmaximal, complemented
14#37367C213yesmaximal, complemented
15#37358C213yesmaximal, complemented
16#37291C213yesmaximal, complemented
17#36585C211yesmaximal, characteristic
18#36475C211yesmaximal, characteristic, complemented
19#36475C211yesmaximal, characteristic, complemented
20#36458C211yesmaximal, characteristic
21#36456C211yesmaximal, characteristic
22#36431C211yesmaximal, characteristic
23#36059C211yesmaximal, characteristic
24#35971C211yesmaximal, characteristic, complemented
25#35971C211yesmaximal, characteristic, complemented
26#35937C211yesmaximal, characteristic, complemented
27#35898C211yesmaximal, characteristic
28#35868C211yesmaximal, characteristic, complemented
29#34336C211yesmaximal, characteristic, complemented
30#34335C211yesmaximal, characteristic, complemented
31#34193C211yesmaximal, characteristic
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35#2864C2213yes—
36#2864C2213yes—
37#2860C2213yes—
38#2860C2213yes—
39#2857C2213yes—
40#2851C2213yes—
41#2831C2216yes—
42#2831C2216yes—
43#2798C2216yes—
44#2783C2216yes—
45#2776C2213yes—
46#2772C2216yes—
47#2772C2216yes—
48#2769C2213yes—
49#2766C2213yes—
50#2766C2216yes—
51#2762C2211yescharacteristic
52#2762C2213yes—
53#2762C2216yes—
54#2758C2216yes—
55#2758C2213yes—
56#2755C2213yes—
57#2754C2216yes—
58#2747C2213yes—
59#2747C2216yes—
60#2747C2216yes—
61#2744C2213yes—
62#2744C2216yes—
63#2739C2213yes—
64#2739C2216yes—
65#2725C2216yes—
66#2722C2213yes—
67#2722C2216yes—
68#2719C2213yes—
69#2716C2216yes—
70#2716C2216yes—
71#2704C2213yes—
72#2704C2216yes—
73#2698C2213yes—
74#2690C2213yes—
75#2690C2216yes—
76#2690C2216yes—
77#2689C2213yes—
78#2660C2213yes—
79#2655C2216yes—
80#2654C2216yes—
81#2650C2216yes—
82#2650C2216yes—
83#2647C2213yes—
84#2647C2213yes—
85#2647C2213yes—
86#2644C2213yes—
87#2644C2213yes—
88#2637C2216yes—
89#2621C2216yes—
90#2584C2213yes—
91#2580C2213yes—
92#2571C2213yes—
93#2571C2213yes—
94#2570C2213yes—
95#2570C2213yes—
96#2570C2213yes—
97#2570C2213yes—
98#2570C2213yes—
99#2570C2213yes—
100#2570C2213yes—
101#2566C2213yes—
102#2563C2213yes—
103#2552C2213yes—
104#2551C2213yes—
105#2551C2213yes—
106#2550C2213yes—
107#2550C2213yes—
108#2546C2213yes—
109#2538C2213yes—
110#2519C2216yes—
111#2514C2216yes—
112#2513C2213yes—
113#2513C2213yes—
114#2513C2213yes—
115#2513C2213yes—
116#2513C2213yes—
117#2513C2213yes—
118#2513C2213yes—
119#2513C2213yes—
120#2512C2213yes—
121#2512C2213yes—
122#2512C2213yes—
123#2512C2213yes—
124#2509C2213yes—
125#2509C2213yes—
126#2509C2213yes—
127#2509C2213yes—
128#2509C2213yes—
129#2508C2213yes—
130#2508C2213yes—
131#2508C2213yes—
132#2508C2213yes—
133#2508C2213yes—
134#2508C2213yes—
135#2507C2213yes—
136#2507C2213yes—
137#2507C2213yes—
138#2507C2213yes—
139#2507C2213yes—
140#2506C2213yes—
141#2506C2213yes—
142#2506C2213yes—
143#2506C2213yes—
144#2497C2213yes—
145#2497C2213yes—
146#2496C2213yes—
147#2496C2213yes—
148#2495C2213yes—
149#2495C2213yes—
150#2495C2213yes—
151#2495C2213yes—
152#2494C2213yes—
153#2494C2213yes—
154#2494C2213yes—
155#2494C2213yes—
156#2478C2216yes—
157#2478C2216yes—
158#2469C2216yes—
159#2454C2213yes—
160#2452C2213yes—
161#2452C2213yes—
162#2452C2213yes—
163#2446C2216yes—
164#2441C2213yes—
165#2439C2213yes—
166#2439C2213yes—
167#2439C2213yes—
168#2402C2213yes—
169#2402C2213yes—
170#2402C2213yes—
171#2401C2213yes—
172#2401C2213yes—
173#2399C2213yes—
174#2370C2213yes—
175#2370C2213yes—
176#2369C2213yes—
177#2369C2213yes—
178#2365C2213yes—
179#2365C2213yes—
180#2355C2213yes—
181#2355C2213yes—
182#2354C2213yes—
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
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#2347C2213yes—
205#2347C2213yes—
206#2341C2211yescharacteristic
207#2341C2211yescharacteristic
208#2341C2211yescharacteristic
209#2341C2211yescharacteristic
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212#2336C2216yes—
213#2331C2213yes—
214#2331C2213yes—
215#2331C2213yes—
216#2330C2213yes—
217#2323C2216yes—
218#2319C2213yes—
219#2319C2213yes—
220C4×C4⋊Q8C2213yes—
221C4×#125C2213yes—
222C4×#125C2213yes—
223C4×#125C2213yes—
224C4×#126C2213yes—
225C4×#126C2213yes—
226C4×C22⋊Q8C2213yes—
227C4×C22⋊Q8C2213yes—
228#2295C2213yes—
229#2295C2213yes—
230#2285C2213yes—
231#2283C2213yes—
232#2276C2211yescharacteristic
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235#2276C2211yescharacteristic
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×#125C2313yes—
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2316yes—
255C2×C22⋊Q8C2316yes—
256C2×C22⋊Q8C2313yes—
257C2×C22⋊Q8C2313yes—
258C4×#41—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×C42C2313yes—
281#401C2316yes—
282#401C2311yescharacteristic
283#401C2313yes—
284#400C2313yes—
285#400C2316yes—
286#400C2316yes—
287#400C2316yes—
288#400C2316yes—
289#400C2316yes—
290#400C2316yes—
291#400C2313yes—
292#400C2313yes—
293#400C2313yes—
294#400C2313yes—
295#400C2316yes—
296#400C2316yes—
297#400C2316yes—
298#400C2313yes—
299#400C2313yes—
300#400C2313yes—
301#400C2313yes—
302#400C2316yes—
303#400C2311yescharacteristic
304#400C2313yes—
305#400C2313yes—
306#400C2313yes—
307#400C2311yescharacteristic
308#400C2311yescharacteristic
309#400C2313yes—
310#400C2313yes—
311#400C2313yes—
312#399C2316yes—
313#398C2313yes—
314#398C2313yes—
315#398C2316yes—
316#398C2316yes—
317#398C2316yes—
318#398C2316yes—
319#398C2316yes—
320#398C2313yes—
321#398C2316yes—
322#398C2316yes—
323#398C2316yes—
324#398C2313yes—
325#398C2313yes—
326#398C2313yes—
327#398C2313yes—
328#398C2316yes—
329#398C2313yes—
330#398C2313yes—
331#398C2313yes—
332#398C2313yes—
333#398C2311yescharacteristic
334#398C2313yes—
335#398C2313yes—
336#398C2313yes—
337#398C2313yes—
338#397C2313yes—
339#397C2316yes—
340#397C2316yes—
341#397C2316yes—
342#397C2316yes—
343#397C2316yes—
344#397C2316yes—
345#397C2316yes—
346#397C2313yes—
347#397C2313yes—
348#397C2316yes—
349#397C2316yes—
350#397C2316yes—
351#397C2313yes—
352#397C2313yes—
353#397C2313yes—
354#396C2316yes—
355#396C2316yes—
356#396C2313yes—
357#396C2316yes—
358#396C2316yes—
359#396C2313yes—
360#396C2316yes—
361#396C2316yes—
362#395C2313yes—
363#395C2316yes—
364#395C2313yes—
365#395C2316yes—
366#395C2313yes—
367#395C2311yescharacteristic
368#393C2316yes—
369#393C2316yes—
370#393C2316yes—
371#391C2316yes—
372#391C2316yes—
373#391C2316yes—
374#391C2316yes—
375#391C2313yes—
376#391C2316yes—
377#391C2316yes—
378#391C2313yes—
379#391C2313yes—
380#391C2313yes—
381#391C2311yescharacteristic
382#391C2311yescharacteristic
383#390C2313yes—
384#390C2313yes—
385#390C2313yes—
386#390C2313yes—
387#390C2313yes—
388#390C2313yes—
389#390C2313yes—
390#390C2313yes—
391#390C2313yes—
392#390C2313yes—
393#390C2313yes—
394#390C2313yes—
395#389C2313yes—
396#389C2313yes—
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#389C2316yes—
417#389C2316yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2313yes—
422#389C2316yes—
423#389C2313yes—
424#389C2313yes—
425#389C2316yes—
426#389C2313yes—
427#389C2313yes—
428#389C2313yes—
429#389C2316yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2316yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
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#388C2313yes—
452#388C2313yes—
453#388C2313yes—
454#388C2313yes—
455#388C2313yes—
456#388C2313yes—
457#388C2316yes—
458#388C2316yes—
459#388C2316yes—
460#388C2316yes—
461#388C2316yes—
462#388C2316yes—
463#388C2316yes—
464#388C2316yes—
465#388C2316yes—
466#388C2316yes—
467#388C2316yes—
468#388C2316yes—
469#388C2316yes—
470#388C2316yes—
471#387C2311yescharacteristic
472#387C2313yes—
473#387C2313yes—
474#387C2313yes—
475#387C2313yes—
476#387C2313yes—
477#387C2311yescharacteristic
478#387C2311yescharacteristic
479#387C2313yes—
480#387C2313yes—
481#387C2313yes—
482#387C2313yes—
483#387C2313yes—
484#387C2316yes—
485#387C2313yes—
486#387C2313yes—
487#387C2316yes—
488#387C2316yes—
489#387C2316yes—
490#387C2316yes—
491#387C2316yes—
492#387C2316yes—
493#387C2316yes—
494#387C2316yes—
495#387C2316yes—
496#387C2316yes—
497#387C2316yes—
498#387C2313yes—
499#387C2313yes—
500#387C2316yes—
501#387C2313yes—
502#387C2316yes—
503#387C2316yes—
504#387C2316yes—
505#387C2313yes—
506#387C2316yes—
507#387C2316yes—
508#387C2316yes—
509#387C2313yes—
510#387C2313yes—
511#387C2313yes—
512#387C2313yes—
513#387C2313yes—
514#387C2311yescharacteristic
515#387C2311yescharacteristic
516#385C2313yes—
517#385C2316yes—
518#385C2313yes—
519#385C2316yes—
520#385C2313yes—
521#385C2313yes—
522#384C2313yes—
523#384C2313yes—
524#384C2313yes—
525#384C2313yes—
526#384C2313yes—
527#384C2313yes—
528#384C2313yes—
529#384C2313yes—
530#383C2311yescharacteristic
531#383C2313yes—
532#383C2316yes—
533#383C2313yes—
534#383C2313yes—
535#382C2313yes—
536#382C2313yes—
537#382C2313yes—
538#382C2313yes—
539#382C2313yes—
540#382C2313yes—
541#382C2313yes—
542#382C2313yes—
543#382C2313yes—
544#382C2313yes—
545#382C2313yes—
546#382C2313yes—
547#382C2313yes—
548#382C2313yes—
549#382C2316yes—
550#382C2316yes—
551#382C2311yescharacteristic
552#382C2313yes—
553#381C2313yes—
554#381C2313yes—
555#380C2313yes—
556#380C2316yes—
557#380C2316yes—
558#380C2313yes—
559#380C2313yes—
560#380C2313yes—
561#380C2313yes—
562#380C2313yes—
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⋊C4C2316yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2316yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2316yes—
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⋊C4C2316yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615#376C2313yes—
616#376C2313yes—
617#376C2313yes—
618#376C2313yes—
619C43C2313yes—
620C43C2313yes—
621C2×#41—24no—
622C2×#41—24no—
623C2×#41—24no—
624C22×Q8C2411yescharacteristic
625C22×Q8C2413yes—
626C22×Q8C2416yes—
627C22×Q8C2411yescharacteristic
628C22×D4C2413yes—
629C23×C4C2413yes—
630C23×C4C2413yes—
631C23×C4C2413yes—
632C4⋊Q8—212no—
633C4⋊Q8—212no—
634C4⋊Q8—212no—
635C4⋊Q8—212no—
636C4⋊Q8—86no—
637#126—46no—
638#126—46no—
639#126—86no—
640#126—86no—
641#125—212no—
642#125—212no—
643#125—46no—
644#125—46no—
645#125—412no—
646C22⋊Q8—46no—
647C22⋊Q8—46no—
648C22⋊Q8—412no—
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—24no—
662C4×Q8—212no—
663C4×Q8—212no—
664C4×Q8—86no—
665C4×Q8#4118yes—
666C4×D4—212no—
667C4×D4—212no—
668#117—212no—
669#117—86no—
670C2×C4⋊C4C2413yes—
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2413yes—
673C2×C4⋊C4C2413yes—
674C2×C4⋊C4C2413yes—
675C2×C4⋊C4C2413yes—
676C2×C4⋊C4C2413yes—
677C2×C4⋊C4C2413yes—
678C2×C4⋊C4C2413yes—
679C2×C4⋊C4C2413yes—
680C2×C4⋊C4C2413yes—
681C2×C4⋊C4C2413yes—
682C2×C4⋊C4C2413yes—
683C2×C4⋊C4C2413yes—
684C2×C4⋊C4C2413yes—
685C2×C4⋊C4C2413yes—
686C2×C4⋊C4C2413yes—
687C2×C4⋊C4C2413yes—
688C2×C4⋊C4C2413yes—
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2413yes—
691C2×C4⋊C4C2413yes—
692C2×C4⋊C4C2413yes—
693C2×C4⋊C4C2413yes—
694C2×C4⋊C4C2411yescharacteristic
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2416yes—
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2413yes—
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2416yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2416yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2416yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2416yes—
717C2×C4⋊C4C2416yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2416yes—
722C2×C4⋊C4C2416yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2411yescharacteristic
731C2×C4⋊C4C2411yescharacteristic
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2416yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C22⋊C4C2416yes—
740C2×C22⋊C4C2413yes—
741C2×C22⋊C4C2416yes—
742C2×C22⋊C4C2416yes—
743C2×C22⋊C4C2413yes—
744C2×C22⋊C4C2413yes—
745C2×C22⋊C4C2413yes—
746C2×C22⋊C4C2416yes—
747C2×C22⋊C4C2416yes—
748C2×C22⋊C4C2413yes—
749C2×C22⋊C4C2413yes—
750C2×C22⋊C4C2416yes—
751C2×C22⋊C4C2413yes—
752C2×C22⋊C4C2413yes—
753C2×C22⋊C4C2413yes—
754C2×C22⋊C4C2413yes—
755C2×C22⋊C4C2413yes—
756C2×C22⋊C4C2413yes—
757C2×C22⋊C4C2416yes—
758C2×C42—212no—
759C2×C42C2413yes—
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×C42C2416yes—
776C2×C42C2416yes—
777C2×C42C2413yes—
778C2×C42C2416yes—
779C2×C42C2413yes—
780C2×C42C2413yes—
781C2×C42C2416yes—
782C2×C42C2413yes—
783C2×C42C2413yes—
784C2×C42C2411yescharacteristic
785C2×C42C2413yes—
786C2×C42C2413yes—
787#95C2411yescharacteristic
788#95C2411yescharacteristic
789#95C2411yescharacteristic
790#95C2411yescharacteristic
791#95C2413yes—
792#95C2413yes—
793#95C2413yes—
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#95C2411yescharacteristic
816#95C2411yescharacteristic
817#95C2411yescharacteristic
818#95C2413yes—
819#95C2411yescharacteristic
820#95C2411yescharacteristic
821#95C2411yescharacteristic
822#95C2411yescharacteristic
823#95C2411yescharacteristic
824#95C2411yescharacteristic
825#95C2413yes—
826#95C2411yescharacteristic
827#95C2416yes—
828#95C2416yes—
829#95C2411yescharacteristic
830#95C2411yescharacteristic
831#95C2413yes—
832#95C2413yes—
833#95C2413yes—
834#95C2413yes—
835#95C2413yes—
836#95C2413yes—
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2416yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2416yes—
850#95C2413yes—
851#95C2416yes—
852#95C2416yes—
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—26no—
890C22×C4—26no—
891C22×C4—26no—
892C22×C4—43no—
893C22×C4—43no—
894C22×C4—43no—
895C22×C4C2511yescharacteristic
896C22×C4C2511yescharacteristic
897C22×C4C2511yescharacteristic
898C22×C4C2511yescharacteristic
899C22×C4C2513yes—
900C22×C4C2511yescharacteristic
901C22×C4C2511yescharacteristic
902C22×C4C2513yes—
903C22×C4C2511yescharacteristic
904C22×C4C2511yescharacteristic
905C22×C4C2513yes—
906C22×C4C2513yes—
907C22×C4C2513yes—
908C22×C4C2511yescharacteristic
909C22×C4C2511yescharacteristic
910C22×C4C2513yes—
911C22×C4C2511yescharacteristic
912C22×C4C2511yescharacteristic
913C22×C4C2513yes—
914C22×C4C2513yes—
915C22×C4C2513yes—
916C22×C4C2513yes—
917C22×C4C2513yes—
918C22×C4C2513yes—
919C22×C4C2513yes—
920C22×C4C2511yescharacteristic
921C22×C4C2513yes—
922C22×C4C2511yescharacteristic
923C22×C4C2511yescharacteristic
924C22×C4C2513yes—
925C4⋊C4—26no—
926C4⋊C4—22no—
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—26no—
936C4⋊C4—212no—
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—22no—
946C4⋊C4—26no—
947C4⋊C4—26no—
948C4⋊C4—26no—
949C4⋊C4—26no—
950C4⋊C4—22no—
951C4⋊C4—22no—
952C4⋊C4—26no—
953C4⋊C4—26no—
954C4⋊C4—22no—
955C4⋊C4—41no—
956C4⋊C4—41no—
957C4⋊C4—43no—
958C4⋊C4—43no—
959C4⋊C4—43no—
960C4⋊C4—46no—
961C4⋊C4—41no—
962C4⋊C4—41no—
963C4⋊C4—43no—
964C4⋊C4—43no—
965C4⋊C4—43no—
966C4⋊C4—43no—
967C4⋊C4—43no—
968C4⋊C4—43no—
969C4⋊C4—46no—
970C4⋊C4—46no—
971C4⋊C4—43no—
972C4⋊C4—43no—
973C4⋊C4—43no—
974C4⋊C4—46no—
975C4⋊C4—43no—
976C4⋊C4—43no—
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—43no—
989C4⋊C4—46no—
990C4⋊C4—46no—
991C4⋊C4—43no—
992C4⋊C4—43no—
993C4⋊C4C2×#41112yes—
994C22⋊C4—212no—
995C22⋊C4—26no—
996C22⋊C4—43no—
997C22⋊C4—46no—
998C22⋊C4—43no—
999C22⋊C4—46no—
1000C22⋊C4—46no—
1001C22⋊C4—43no—
1002C22⋊C4—46no—
1003C22⋊C4—43no—
1004C22⋊C4—43no—
1005C22⋊C4—46no—
1006C22⋊C4—43no—
1007C22⋊C4—43no—
1008C22⋊C4—43no—
1009C22⋊C4—43no—
1010C22⋊C4—43no—
1011C22⋊C4—46no—
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—22no—
1029C42—43no—
1030C42—41no—
1031C42—46no—
1032C42—46no—
1033C42—43no—
1034C42—46no—
1035C42—46no—
1036C42—43no—
1037C42—43no—
1038C42—43no—
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—23no—
1057C2×C4—21no—
1058C2×C4—23no—
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—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—23no—
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—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—23no—
1107C2×C4—23no—
1108C2×C4—23no—
1109C2×C4—23no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—23no—
1113C2×C4—23no—
1114C2×C4—21no—
1115C2×C4—23no—
1116C2×C4—21no—
1117C2×C4—23no—
1118C2×C4—23no—
1119C2×C4—23no—
1120C2×C4—23no—
1121C2×C4—23no—
1122C2×C4—23no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—23no—
1127C2×C4—23no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—23no—
1132C2×C4—23no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—23no—
1136C2×C4—21no—
1137C2×C4—412no—
1138C2×C4—412no—
1139C2×C4—86no—
1140C2×C4C22×#4112yes—
1141C2×C4C22×#4116yes—
1142C2×C4C22×#4116yes—
1143C2×C4C2×2−1+416yes—
1144C2×C4C2×2−1+416yes—
1145C2×C4#58512yes—
1146C2×C4#58512yes—
1147C22—43no—
1148C22—43no—
1149C22—43no—
1150C22—43no—
1151C22—43no—
1152C22—43no—
1153C22—43no—
1154C22C23×#4111yescharacteristic
1155C22C22×2−1+411yescharacteristic
1156C22C22×2−1+411yescharacteristic
1157C22C2×#58511yescharacteristic
1158C22C2×#58511yescharacteristic
1159C22H(7,𝔽2)11yescharacteristic
1160C222−1+611yescharacteristic
1161C4—22no—
1162C4—22no—
1163C4—22no—
1164C4—26no—
1165C4—41no—
1166C4—43no—
1167C4—43no—
1168C4—41no—
1169C4—43no—
1170C4—43no—
1171C4—43no—
1172C4—41no—
1173C4—41no—
1174C4—41no—
1175C4—43no—
1176C4—43no—
1177C4—41no—
1178C4—41no—
1179C4—43no—
1180C4—43no—
1181C4—41no—
1182C4—41no—
1183C4—43no—
1184C4—43no—
1185C4—43no—
1186C4—41no—
1187C4—41no—
1188C4—41no—
1189C4—43no—
1190C4C2×#541112yes—
1191C2—83no—
1192C2C22×#54111yescharacteristic
1193C2#6295211yescharacteristic
1194C2#6295311yescharacteristic
1195C2#6300511yescharacteristic
1196C2#6300811yescharacteristic
1197C2#6303411yescharacteristic
1198C2#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. #52251C2semidirect
2. #42764C2semidirect
3. #42687C2semidirect
4. #42597C2semidirect
5. #42582C2semidirect
6. #42582C2semidirect
7. #42530C2semidirect
8. #40227C2semidirect
9. #40167C2semidirect
10. #40059C2semidirect
11. #39901C2semidirect
12. #39734C2semidirect
13. #39225C2semidirect
14. #37367C2semidirect
15. #37358C2semidirect
16. #37291C2semidirect
18. #36475C2semidirect
19. #36475C2semidirect
24. #35971C2semidirect
25. #35971C2semidirect
26. #35937C2semidirect
28. #35868C2semidirect
29. #34336C2semidirect
30. #34335C2semidirect

Maximal subgroups

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

subgroupindex
#522512
#427642
#426872
#425972
#425822
#425302
#402272
#401672
#400592
#399012
#397342
#392252
#373672
#373582
#372912
#365852
#364752
#364582
#364562
#364312
#360592
#359712
#359372
#358982
#358682
#343362
#343352
#341932