Finite Group Databasebeta

← #7661704

Subgroups — #7661704

Order 512.

4219 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#52251C213yesmaximal, complemented
2#42780C213yesmaximal, complemented
3#42755C213yesmaximal, complemented
4#42748C213yesmaximal, complemented
5#42723C213yesmaximal, complemented
6#42704C213yesmaximal, complemented
7#42687C213yesmaximal, complemented
8#40130C213yesmaximal, complemented
9#40075C213yesmaximal, complemented
10#40075C213yesmaximal, complemented
11#39928C213yesmaximal, complemented
12#39217C213yesmaximal, complemented
13#39157C213yesmaximal, complemented
14#37353C213yesmaximal, complemented
15#37337C213yesmaximal, complemented
16#37291C213yesmaximal, complemented
17#36585C211yesmaximal, characteristic
18#36584C211yesmaximal, characteristic, complemented
19#36458C211yesmaximal, characteristic
20#36447C211yesmaximal, characteristic, complemented
21#36445C211yesmaximal, characteristic
22#36431C211yesmaximal, characteristic
23#35971C211yesmaximal, characteristic, complemented
24#35957C211yesmaximal, characteristic, complemented
25#35898C211yesmaximal, characteristic
26#35898C211yesmaximal, characteristic
27#35868C211yesmaximal, characteristic, complemented
28#35868C211yesmaximal, characteristic, complemented
29#34336C211yesmaximal, characteristic, complemented
30#34336C211yesmaximal, characteristic, complemented
31#34197C211yesmaximal, characteristic
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35#2860C2213yes—
36#2860C2213yes—
37#2859C2213yes—
38#2859C2213yes—
39#2857C2213yes—
40#2851C2213yes—
41#2836C2216yes—
42#2831C2216yes—
43#2798C2216yes—
44#2783C2216yes—
45#2776C2213yes—
46#2769C2211yescharacteristic
47#2766C2213yes—
48#2766C2216yes—
49#2762C2213yes—
50#2762C2213yes—
51#2762C2216yes—
52#2758C2213yes—
53#2755C2213yes—
54#2754C2216yes—
55#2747C2213yes—
56#2744C2216yes—
57#2744C2213yes—
58#2744C2216yes—
59#2739C2213yes—
60#2739C2216yes—
61#2725C2216yes—
62#2725C2216yes—
63#2725C2216yes—
64#2722C2213yes—
65#2721C2216yes—
66#2721C2216yes—
67#2719C2213yes—
68#2719C2216yes—
69#2704C2213yes—
70#2704C2216yes—
71#2698C2213yes—
72#2698C2216yes—
73#2690C2213yes—
74#2690C2216yes—
75#2689C2213yes—
76#2689C2216yes—
77#2689C2216yes—
78#2664C2216yes—
79#2660C2213yes—
80#2654C2216yes—
81#2654C2216yes—
82#2652C2216yes—
83#2650C2216yes—
84#2647C2213yes—
85#2647C2213yes—
86#2647C2213yes—
87#2645C2216yes—
88#2644C2213yes—
89#2644C2213yes—
90#2584C2213yes—
91#2580C2213yes—
92#2571C2213yes—
93#2571C2213yes—
94#2571C2213yes—
95#2571C2213yes—
96#2570C2213yes—
97#2570C2213yes—
98#2570C2213yes—
99#2567C2213yes—
100#2566C2213yes—
101#2552C2213yes—
102#2552C2213yes—
103#2552C2213yes—
104#2552C2213yes—
105#2552C2213yes—
106#2550C2213yes—
107#2550C2213yes—
108#2542C2213yes—
109#2538C2213yes—
110#2528C2216yes—
111#2528C2216yes—
112#2519C2216yes—
113#2519C2216yes—
114#2513C2213yes—
115#2513C2213yes—
116#2513C2213yes—
117#2513C2213yes—
118#2513C2213yes—
119#2513C2213yes—
120#2512C2213yes—
121#2512C2213yes—
122#2512C2213yes—
123#2512C2213yes—
124#2512C2213yes—
125#2512C2213yes—
126#2509C2213yes—
127#2509C2213yes—
128#2509C2213yes—
129#2509C2213yes—
130#2509C2213yes—
131#2509C2213yes—
132#2509C2213yes—
133#2508C2213yes—
134#2508C2213yes—
135#2508C2213yes—
136#2508C2213yes—
137#2507C2213yes—
138#2507C2213yes—
139#2507C2213yes—
140#2506C2213yes—
141#2506C2213yes—
142#2506C2213yes—
143#2506C2213yes—
144#2506C2213yes—
145#2506C2213yes—
146#2497C2213yes—
147#2497C2213yes—
148#2497C2213yes—
149#2496C2213yes—
150#2496C2213yes—
151#2496C2213yes—
152#2496C2216yes—
153#2495C2213yes—
154#2494C2213yes—
155#2494C2213yes—
156#2494C2213yes—
157#2494C2213yes—
158#2494C2213yes—
159#2489C2216yes—
160#2454C2213yes—
161#2454C2213yes—
162#2454C2213yes—
163#2452C2213yes—
164#2441C2213yes—
165#2441C2213yes—
166#2441C2213yes—
167#2439C2213yes—
168#2402C2213yes—
169#2402C2213yes—
170#2402C2213yes—
171#2401C2213yes—
172#2401C2213yes—
173#2399C2213yes—
174#2370C2213yes—
175#2370C2213yes—
176#2370C2213yes—
177#2370C2213yes—
178#2369C2213yes—
179#2369C2213yes—
180#2357C2213yes—
181#2357C2213yes—
182#2355C2213yes—
183#2355C2213yes—
184#2351C2211yescharacteristic
185#2351C2211yescharacteristic
186#2351C2211yescharacteristic
187#2351C2211yescharacteristic
188#2351C2211yescharacteristic
189#2351C2211yescharacteristic
190#2351C2211yescharacteristic
191#2351C2211yescharacteristic
192#2351C2211yescharacteristic
193#2351C2211yescharacteristic
194Q8×C4⋊C4C2211yescharacteristic
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#2346C2213yes—
205#2346C2213yes—
206#2341C2211yescharacteristic
207#2341C2211yescharacteristic
208#2341C2211yescharacteristic
209#2341C2211yescharacteristic
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212#2334C2216yes—
213#2331C2213yes—
214#2331C2213yes—
215#2330C2213yes—
216#2330C2213yes—
217#2330C2216yes—
218#2319C2213yes—
219#2319C2213yes—
220C4×#125C2213yes—
221C4×#125C2213yes—
222C4×#125C2213yes—
223C4×#125C2213yes—
224C4×#126C2213yes—
225C4×#126C2213yes—
226C4×C22⋊Q8C2213yes—
227C4×C22⋊Q8C2213yes—
228#2295C2213yes—
229#2295C2213yes—
230#2283C2213yes—
231#2283C2213yes—
232#2276C2211yescharacteristic
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239#557—28no—
240#557—28no—
241C2×C4⋊Q8C2313yes—
242C2×C4⋊Q8C2313yes—
243C2×#126C2313yes—
244C2×#126C2313yes—
245C2×#126C2316yes—
246C2×#126C2316yes—
247C2×#126C2316yes—
248C2×#125C2313yes—
249C2×#125C2313yes—
250C2×#125C2313yes—
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2316yes—
255C2×#125C2316yes—
256C2×#125C2316yes—
257C2×C22⋊Q8C2313yes—
258C2×C22⋊Q8C2313yes—
259C2×C22⋊Q8C2316yes—
260C4×#41—28no—
261C2×C4×Q8C2313yes—
262C2×C4×Q8C2313yes—
263C2×C4×Q8C2311yescharacteristic
264C2×C4×Q8C2311yescharacteristic
265C2×C4×Q8C2311yescharacteristic
266C2×C4×Q8C2311yescharacteristic
267C2×C4×Q8C2311yescharacteristic
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
277C2×C4×D4C2313yes—
278C2×C4×D4C2313yes—
279C2×#117C2313yes—
280C22×C42C2313yes—
281#401C2313yes—
282#401C2316yes—
283#401C2313yes—
284#400C2313yes—
285#400C2313yes—
286#400C2316yes—
287#400C2313yes—
288#400C2316yes—
289#400C2316yes—
290#400C2316yes—
291#400C2316yes—
292#400C2316yes—
293#400C2316yes—
294#400C2316yes—
295#400C2313yes—
296#400C2313yes—
297#400C2316yes—
298#400C2316yes—
299#400C2313yes—
300#400C2313yes—
301#400C2316yes—
302#400C2313yes—
303#400C2313yes—
304#400C2311yescharacteristic
305#400C2311yescharacteristic
306#400C2313yes—
307#400C2313yes—
308#400C2313yes—
309#400C2311yescharacteristic
310#400C2313yes—
311#400C2313yes—
312#400C2313yes—
313#399C2316yes—
314#399C2316yes—
315#399C2316yes—
316#398C2313yes—
317#398C2316yes—
318#398C2316yes—
319#398C2313yes—
320#398C2316yes—
321#398C2316yes—
322#398C2316yes—
323#398C2313yes—
324#398C2313yes—
325#398C2316yes—
326#398C2316yes—
327#398C2313yes—
328#398C2313yes—
329#398C2313yes—
330#398C2316yes—
331#398C2311yescharacteristic
332#398C2313yes—
333#398C2311yescharacteristic
334#398C2311yescharacteristic
335#398C2313yes—
336#398C2313yes—
337#398C2313yes—
338#398C2313yes—
339#398C2313yes—
340#398C2316yes—
341#397C2313yes—
342#397C2316yes—
343#397C2316yes—
344#397C2316yes—
345#397C2316yes—
346#397C2316yes—
347#397C2313yes—
348#397C2313yes—
349#397C2316yes—
350#397C2316yes—
351#397C2313yes—
352#397C2316yes—
353#397C2316yes—
354#397C2313yes—
355#397C2313yes—
356#396C2316yes—
357#396C2316yes—
358#396C2316yes—
359#396C2316yes—
360#396C2313yes—
361#396C2316yes—
362#396C2316yes—
363#396C2316yes—
364#396C2313yes—
365#395C2313yes—
366#395C2316yes—
367#395C2313yes—
368#395C2313yes—
369#395C2313yes—
370#393C2316yes—
371#391C2316yes—
372#391C2316yes—
373#391C2313yes—
374#391C2313yes—
375#391C2316yes—
376#391C2313yes—
377#391C2313yes—
378#391C2313yes—
379#391C2313yes—
380#390C2313yes—
381#390C2313yes—
382#390C2313yes—
383#390C2313yes—
384#390C2313yes—
385#390C2313yes—
386#390C2313yes—
387#390C2313yes—
388#390C2313yes—
389#390C2313yes—
390#390C2313yes—
391#390C2313yes—
392#389C2311yescharacteristic
393#389C2313yes—
394#389C2313yes—
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#389C2316yes—
413#389C2313yes—
414#389C2316yes—
415#389C2313yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2313yes—
422#389C2316yes—
423#389C2316yes—
424#389C2313yes—
425#389C2313yes—
426#389C2316yes—
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2316yes—
431#389C2313yes—
432#389C2316yes—
433#389C2313yes—
434#389C2313yes—
435#389C2316yes—
436#389C2316yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2316yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2316yes—
452#389C2311yescharacteristic
453#388C2313yes—
454#388C2313yes—
455#388C2313yes—
456#388C2313yes—
457#388C2313yes—
458#388C2313yes—
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#388C2316yes—
472#387C2311yescharacteristic
473#387C2313yes—
474#387C2313yes—
475#387C2313yes—
476#387C2313yes—
477#387C2313yes—
478#387C2313yes—
479#387C2313yes—
480#387C2316yes—
481#387C2316yes—
482#387C2313yes—
483#387C2313yes—
484#387C2313yes—
485#387C2313yes—
486#387C2313yes—
487#387C2313yes—
488#387C2313yes—
489#387C2313yes—
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#387C2316yes—
504#387C2313yes—
505#387C2313yes—
506#387C2313yes—
507#387C2313yes—
508#387C2311yescharacteristic
509#387C2313yes—
510#387C2313yes—
511#387C2311yescharacteristic
512#387C2311yescharacteristic
513#385C2313yes—
514#385C2316yes—
515#385C2313yes—
516#385C2313yes—
517#385C2316yes—
518#385C2313yes—
519#384C2313yes—
520#384C2316yes—
521#384C2313yes—
522#384C2313yes—
523#384C2313yes—
524#384C2313yes—
525#384C2313yes—
526#384C2313yes—
527#384C2313yes—
528#384C2313yes—
529#384C2313yes—
530#383C2311yescharacteristic
531#383C2313yes—
532#383C2311yescharacteristic
533#383C2313yes—
534#382C2311yescharacteristic
535#382C2313yes—
536#382C2313yes—
537#382C2313yes—
538#382C2313yes—
539#382C2313yes—
540#382C2313yes—
541#382C2313yes—
542#382C2313yes—
543#382C2316yes—
544#382C2313yes—
545#382C2313yes—
546#382C2316yes—
547#382C2313yes—
548#382C2313yes—
549#382C2313yes—
550#382C2316yes—
551#381C2316yes—
552#381C2313yes—
553#381C2313yes—
554#380C2313yes—
555#380C2313yes—
556#380C2313yes—
557#380C2313yes—
558#380C2313yes—
559#380C2313yes—
560#380C2313yes—
561#380C2313yes—
562#380C2316yes—
563#380C2313yes—
564#380C2313yes—
565C4×C4⋊C4C2313yes—
566C4×C4⋊C4C2313yes—
567C4×C4⋊C4C2313yes—
568C4×C4⋊C4C2313yes—
569C4×C4⋊C4C2313yes—
570C4×C4⋊C4C2313yes—
571C4×C4⋊C4C2313yes—
572C4×C4⋊C4C2313yes—
573C4×C4⋊C4C2313yes—
574C4×C4⋊C4C2313yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2316yes—
577C4×C4⋊C4C2316yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2316yes—
582C4×C4⋊C4C2316yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2316yes—
613C4×C22⋊C4C2313yes—
614#376C2313yes—
615#376C2313yes—
616#376C2316yes—
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—
633#126—46no—
634#126—46no—
635#126—412no—
636#126—86no—
637#126—86no—
638#125—212no—
639#125—212no—
640#125—212no—
641#125—212no—
642#125—46no—
643#125—46no—
644#125—412no—
645#125—86no—
646#125—86no—
647C22⋊Q8—46no—
648C22⋊Q8—46no—
649C22⋊Q8—86no—
650C4×Q8—24no—
651C4×Q8—24no—
652C4×Q8—24no—
653C4×Q8—24no—
654C4×Q8—24no—
655C4×Q8—24no—
656C4×Q8—24no—
657C4×Q8—24no—
658C4×Q8—24no—
659C4×Q8—24no—
660C4×Q8—24no—
661C4×Q8—24no—
662C4×Q8—24no—
663C4×Q8—212no—
664C4×Q8—212no—
665C4×Q8#4118yes—
666C4×D4—212no—
667C4×D4—212no—
668#117—212no—
669C2×C4⋊C4C2413yes—
670C2×C4⋊C4C2411yescharacteristic
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⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2413yes—
691C2×C4⋊C4C2413yes—
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2413yes—
694C2×C4⋊C4C2413yes—
695C2×C4⋊C4C2416yes—
696C2×C4⋊C4C2416yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2413yes—
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⋊C4C2416yes—
711C2×C4⋊C4C2416yes—
712C2×C4⋊C4C2416yes—
713C2×C4⋊C4C2416yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2416yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2416yes—
723C2×C4⋊C4C2416yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2416yes—
731C2×C4⋊C4C2411yescharacteristic
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C22⋊C4C2416yes—
742C2×C22⋊C4C2413yes—
743C2×C22⋊C4C2413yes—
744C2×C22⋊C4C2416yes—
745C2×C22⋊C4C2416yes—
746C2×C22⋊C4C2413yes—
747C2×C22⋊C4C2413yes—
748C2×C22⋊C4C2416yes—
749C2×C22⋊C4C2413yes—
750C2×C22⋊C4C2413yes—
751C2×C22⋊C4C2413yes—
752C2×C22⋊C4C2413yes—
753C2×C22⋊C4C2416yes—
754C2×C22⋊C4C2413yes—
755C2×C22⋊C4C2413yes—
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×C42C2411yescharacteristic
776C2×C42C2411yescharacteristic
777C2×C42C2411yescharacteristic
778C2×C42C2413yes—
779C2×C42C2416yes—
780C2×C42C2413yes—
781C2×C42C2416yes—
782C2×C42C2413yes—
783C2×C42C2413yes—
784C2×C42C2416yes—
785C2×C42C2413yes—
786C2×C42C2413yes—
787C2×C42C2416yes—
788C2×C42C2413yes—
789#95C2411yescharacteristic
790#95C2411yescharacteristic
791#95C2411yescharacteristic
792#95C2411yescharacteristic
793#95C2413yes—
794#95C2413yes—
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#95C2416yes—
808#95C2416yes—
809#95C2411yescharacteristic
810#95C2411yescharacteristic
811#95C2411yescharacteristic
812#95C2411yescharacteristic
813#95C2411yescharacteristic
814#95C2411yescharacteristic
815#95C2413yes—
816#95C2413yes—
817#95C2413yes—
818#95C2413yes—
819#95C2413yes—
820#95C2413yes—
821#95C2411yescharacteristic
822#95C2411yescharacteristic
823#95C2411yescharacteristic
824#95C2413yes—
825#95C2413yes—
826#95C2411yescharacteristic
827#95C2411yescharacteristic
828#95C2411yescharacteristic
829#95C2411yescharacteristic
830#95C2411yescharacteristic
831#95C2413yes—
832#95C2411yescharacteristic
833#95C2413yes—
834#95C2416yes—
835#95C2416yes—
836#95C2411yescharacteristic
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2416yes—
847#95C2416yes—
848#95C2416yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2416yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2413yes—
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—43no—
889C22×C4—43no—
890C22×C4—43no—
891C22×C4—43no—
892C22×C4C2511yescharacteristic
893C22×C4C2511yescharacteristic
894C22×C4C2511yescharacteristic
895C22×C4C2513yes—
896C22×C4C2511yescharacteristic
897C22×C4C2511yescharacteristic
898C22×C4C2511yescharacteristic
899C22×C4C2513yes—
900C22×C4C2511yescharacteristic
901C22×C4C2511yescharacteristic
902C22×C4C2513yes—
903C22×C4C2513yes—
904C22×C4C2513yes—
905C22×C4C2513yes—
906C22×C4C2511yescharacteristic
907C22×C4C2511yescharacteristic
908C22×C4C2511yescharacteristic
909C22×C4C2513yes—
910C22×C4C2513yes—
911C22×C4C2513yes—
912C22×C4C2513yes—
913C22×C4C2513yes—
914C22×C4C2513yes—
915C22×C4C2511yescharacteristic
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—26no—
947C4⋊C4—22no—
948C4⋊C4—26no—
949C4⋊C4—26no—
950C4⋊C4—26no—
951C4⋊C4—26no—
952C4⋊C4—22no—
953C4⋊C4—41no—
954C4⋊C4—41no—
955C4⋊C4—43no—
956C4⋊C4—43no—
957C4⋊C4—43no—
958C4⋊C4—41no—
959C4⋊C4—41no—
960C4⋊C4—41no—
961C4⋊C4—41no—
962C4⋊C4—43no—
963C4⋊C4—43no—
964C4⋊C4—43no—
965C4⋊C4—46no—
966C4⋊C4—46no—
967C4⋊C4—43no—
968C4⋊C4—46no—
969C4⋊C4—43no—
970C4⋊C4—43no—
971C4⋊C4—43no—
972C4⋊C4—43no—
973C4⋊C4—43no—
974C4⋊C4—46no—
975C4⋊C4—46no—
976C4⋊C4—43no—
977C4⋊C4—43no—
978C4⋊C4—43no—
979C4⋊C4—43no—
980C4⋊C4—43no—
981C4⋊C4—46no—
982C4⋊C4—43no—
983C4⋊C4—46no—
984C4⋊C4—46no—
985C4⋊C4—46no—
986C4⋊C4—43no—
987C4⋊C4—43no—
988C4⋊C4—46no—
989C4⋊C4—43no—
990C4⋊C4—43no—
991C4⋊C4—43no—
992C4⋊C4—43no—
993C4⋊C4C2×#41112yes—
994C22⋊C4—212no—
995C22⋊C4—26no—
996C22⋊C4—26no—
997C22⋊C4—43no—
998C22⋊C4—43no—
999C22⋊C4—46no—
1000C22⋊C4—43no—
1001C22⋊C4—43no—
1002C22⋊C4—46no—
1003C22⋊C4—46no—
1004C22⋊C4—43no—
1005C22⋊C4—43no—
1006C22⋊C4—43no—
1007C22⋊C4—46no—
1008C22⋊C4—46no—
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—22no—
1030C42—43no—
1031C42—46no—
1032C42—43no—
1033C42—43no—
1034C42—46no—
1035C42—43no—
1036C42—46no—
1037C42—43no—
1038C42—46no—
1039C42—43no—
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—21no—
1056C2×C4—23no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—23no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—23no—
1068C2×C4—23no—
1069C2×C4—23no—
1070C2×C4—23no—
1071C2×C4—23no—
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—21no—
1092C2×C4—21no—
1093C2×C4—23no—
1094C2×C4—23no—
1095C2×C4—23no—
1096C2×C4—23no—
1097C2×C4—23no—
1098C2×C4—23no—
1099C2×C4—23no—
1100C2×C4—23no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—23no—
1105C2×C4—23no—
1106C2×C4—23no—
1107C2×C4—23no—
1108C2×C4—21no—
1109C2×C4—23no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—23no—
1113C2×C4—21no—
1114C2×C4—23no—
1115C2×C4—23no—
1116C2×C4—23no—
1117C2×C4—23no—
1118C2×C4—23no—
1119C2×C4—21no—
1120C2×C4—23no—
1121C2×C4—23no—
1122C2×C4—21no—
1123C2×C4—23no—
1124C2×C4—23no—
1125C2×C4—23no—
1126C2×C4—21no—
1127C2×C4—23no—
1128C2×C4—23no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—412no—
1137C2×C4—86no—
1138C2×C4—86no—
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—41no—
1165C4—43no—
1166C4—43no—
1167C4—43no—
1168C4—43no—
1169C4—41no—
1170C4—41no—
1171C4—41no—
1172C4—43no—
1173C4—41no—
1174C4—41no—
1175C4—43no—
1176C4—43no—
1177C4—41no—
1178C4—41no—
1179C4—43no—
1180C4—43no—
1181C4—41no—
1182C4—41no—
1183C4—41no—
1184C4—43no—
1185C4—41no—
1186C4—43no—
1187C4—43no—
1188C4—43no—
1189C4C2×#541112yes—
1190C2—83no—
1191C2C22×#54111yescharacteristic
1192C2#6294911yescharacteristic
1193C2#6295211yescharacteristic
1194C2#6300611yescharacteristic
1195C2#6300911yescharacteristic
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. #52251C2semidirect
2. #42780C2semidirect
3. #42755C2semidirect
4. #42748C2semidirect
5. #42723C2semidirect
6. #42704C2semidirect
7. #42687C2semidirect
8. #40130C2semidirect
9. #40075C2semidirect
10. #40075C2semidirect
11. #39928C2semidirect
12. #39217C2semidirect
13. #39157C2semidirect
14. #37353C2semidirect
15. #37337C2semidirect
16. #37291C2semidirect
18. #36584C2semidirect
20. #36447C2semidirect
23. #35971C2semidirect
24. #35957C2semidirect
27. #35868C2semidirect
28. #35868C2semidirect
29. #34336C2semidirect
30. #34336C2semidirect

Maximal subgroups

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

subgroupindex
#522512
#427802
#427552
#427482
#427232
#427042
#426872
#401302
#400752
#399282
#392172
#391572
#373532
#373372
#372912
#365852
#365842
#364582
#364472
#364452
#364312
#359712
#359572
#358982
#358682
#343362
#341972