Finite Group Databasebeta

← #7686617

Subgroups — #7686617

Order 512.

4952 conjugacy classes of subgroups.

The subgroup lattice has 1271 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59749C213yesmaximal, complemented
2#59502C213yesmaximal, complemented
3#59332C213yesmaximal, complemented
4#59291C213yesmaximal, complemented
5#59290C213yesmaximal, complemented
6#45407C213yesmaximal, complemented
7#45350C213yesmaximal, complemented
8#45346C213yesmaximal, complemented
9#45210C213yesmaximal, complemented
10#38273C213yesmaximal, complemented
11#38225C213yesmaximal, complemented
12#38068C213yesmaximal, complemented
13#37884C213yesmaximal, complemented
14#36578C211yesmaximal, characteristic
15Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
16#36483C211yesmaximal, characteristic
17#36458C211yesmaximal, characteristic, complemented
18#36447C211yesmaximal, characteristic, complemented
19#36265C213yesmaximal, complemented
20#36186C213yesmaximal, complemented
21#35898C211yesmaximal, characteristic, complemented
22#35868C211yesmaximal, characteristic, complemented
23#35868C211yesmaximal, characteristic, complemented
24#35748C211yesmaximal, characteristic, complemented
25#34808C213yesmaximal, complemented
26#34335C211yesmaximal, characteristic, complemented
27#34294C211yesmaximal, characteristic
28#34263C211yesmaximal, characteristic, complemented
29#34196C211yesmaximal, characteristic, complemented
30Q8×#117C211yesmaximal, characteristic, complemented
31C2×#2351C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#552C2216yes—
34C2×#548C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C22×C4×Q8C2211yescharacteristic
37C22×C4×Q8C2211yescharacteristic
38C22×C4×Q8C2211yescharacteristic
39#2860C2213yes—
40#2859C2213yes—
41#2857C2213yes—
42#2854C2213yes—
43#2854C2213yes—
44#2775C2216yes—
45#2774C2216yes—
46#2773C2216yes—
47#2773C2216yes—
48#2772C2216yes—
49#2770C2216yes—
50#2768C2216yes—
51#2767C2216yes—
52#2762C2216yes—
53#2754C2216yes—
54#2754C2216yes—
55#2719C2216yes—
56#2698C2216yes—
57#2698C2216yes—
58#2647C2213yes—
59#2647C2213yes—
60#2644C2213yes—
61#2628C2213yes—
62#2611C2216yes—
63#2604C2216yes—
64#2590C2216yes—
65#2582C2213yes—
66#2580C2213yes—
67#2575C2216yes—
68#2571C2213yes—
69#2570C2213yes—
70#2570C2213yes—
71#2567C2213yes—
72#2556C2216yes—
73#2556C2216yes—
74#2552C2213yes—
75#2552C2213yes—
76#2552C2213yes—
77#2542C2213yes—
78#2533C2213yes—
79#2532C2213yes—
80#2529C2213yes—
81#2528C2213yes—
82#2525C2213yes—
83#2524C2213yes—
84#2520C2213yes—
85#2519C2216yes—
86#2519C2216yes—
87#2519C2213yes—
88#2519C2216yes—
89#2517C2216yes—
90#2513C2213yes—
91#2513C2213yes—
92#2512C2213yes—
93#2512C2213yes—
94#2512C2213yes—
95#2512C2213yes—
96#2509C2213yes—
97#2509C2213yes—
98#2508C2213yes—
99#2508C2213yes—
100#2507C2213yes—
101#2507C2213yes—
102#2506C2213yes—
103#2506C2213yes—
104#2506C2213yes—
105#2506C2213yes—
106#2506C2213yes—
107#2506C2213yes—
108#2504C2213yes—
109#2501C2213yes—
110#2498C2213yes—
111#2498C2216yes—
112#2497C2213yes—
113#2497C2213yes—
114#2496C2213yes—
115#2496C2213yes—
116#2495C2213yes—
117#2494C2213yes—
118#2493C2213yes—
119#2489C2216yes—
120#2488C2216yes—
121#2488C2213yes—
122#2487C2213yes—
123#2486C2213yes—
124#2484C2213yes—
125#2481C2213yes—
126#2478C2216yes—
127#2473C2213yes—
128#2462C2216yes—
129#2452C2213yes—
130#2452C2213yes—
131#2451C2213yes—
132#2451C2213yes—
133#2448C2213yes—
134#2448C2213yes—
135#2448C2213yes—
136#2448C2213yes—
137#2440C2213yes—
138#2440C2213yes—
139#2440C2213yes—
140#2440C2213yes—
141#2438C2216yes—
142#2438C2211yescharacteristic
143#2423C2213yes—
144#2423C2213yes—
145#2421C2213yes—
146#2421C2213yes—
147#2419C2216yes—
148#2417C2216yes—
149#2413C2213yes—
150#2402C2213yes—
151#2402C2213yes—
152#2401C2213yes—
153#2396C2213yes—
154#2369C2213yes—
155#2367C2213yes—
156#2365C2213yes—
157#2365C2213yes—
158#2362C2216yes—
159#2361C2213yes—
160#2360C2213yes—
161#2359C2216yes—
162#2357C2213yes—
163#2355C2213yes—
164#2355C2213yes—
165#2355C2213yes—
166#2355C2213yes—
167#2355C2213yes—
168#2354C2213yes—
169#2351C2211yescharacteristic
170#2351C2211yescharacteristic
171#2351C2211yescharacteristic
172#2351C2211yescharacteristic
173#2351C2211yescharacteristic
174#2351C2213yes—
175#2351C2213yes—
176#2351C2211yescharacteristic
177#2351C2213yes—
178#2351C2213yes—
179Q8×C4⋊C4C2211yescharacteristic
180Q8×C4⋊C4C2211yescharacteristic
181Q8×C4⋊C4C2211yescharacteristic
182Q8×C4⋊C4C2211yescharacteristic
183Q8×C4⋊C4C2211yescharacteristic
184Q8×C4⋊C4C2211yescharacteristic
185Q8×C4⋊C4C2211yescharacteristic
186Q8×C4⋊C4C2211yescharacteristic
187Q8×C4⋊C4C2211yescharacteristic
188Q8×C4⋊C4C2211yescharacteristic
189D4×C4⋊C4C2213yes—
190#2345C2213yes—
191#2345C2213yes—
192#2345C2213yes—
193#2344C2213yes—
194#2344C2213yes—
195#2344C2213yes—
196#2341C2211yescharacteristic
197#2341C2211yescharacteristic
198#2341C2211yescharacteristic
199#2341C2211yescharacteristic
200#2341C2211yescharacteristic
201Q8×C22⋊C4C2211yescharacteristic
202Q8×C22⋊C4C2211yescharacteristic
203Q8×C22⋊C4C2211yescharacteristic
204#2331C2213yes—
205#2331C2213yes—
206#2326C2213yes—
207#2323C2213yes—
208#2320C2213yes—
209#2320C2213yes—
210#2319C2213yes—
211#2314C2213yes—
212C4×C4⋊Q8C2213yes—
213C4×#125C2213yes—
214C4×#126C2213yes—
215C4×C22⋊Q8C2213yes—
216C4×#123C2213yes—
217C4×#123C2213yes—
218C4×#121C2213yes—
219#2298C2213yes—
220#2295C2213yes—
221#2295C2213yes—
222#2295C2213yes—
223#2293C2213yes—
224C2×#389C2213yes—
225C2×#389C2213yes—
226#2290C2213yes—
227#2285C2213yes—
228#2285C2213yes—
229#2283C2213yes—
230C2×#382C2213yes—
231#2276C2211yescharacteristic
232#2276C2211yescharacteristic
233#2276C2211yescharacteristic
234C42×Q8C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C4×#117C2213yes—
237C2×C4×C4⋊C4C2213yes—
238C22×#41C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240Q82—28no—
241#552—424no—
242#548—28no—
243C2×C4⋊Q8C2313yes—
244C2×C4⋊Q8C2313yes—
245C2×C4⋊Q8C2313yes—
246C2×#126C2313yes—
247C2×#126C2316yes—
248C2×#126C2316yes—
249C2×#125C2313yes—
250C2×#125C2316yes—
251C2×#125C2316yes—
252C2×#125C2316yes—
253C2×#124C2313yes—
254C2×#123C2313yes—
255C2×#123C2313yes—
256C2×#123C2316yes—
257C2×C22⋊Q8C2313yes—
258C2×C22⋊Q8C2311yescharacteristic
259C2×C22⋊Q8C2316yes—
260C2×C22⋊Q8C2316yes—
261C2×C22⋊Q8C2316yes—
262C2×#121C2313yes—
263#520—28no—
264C2×C4×Q8—28no—
265C2×C4×Q8—28no—
266C2×C4×Q8—28no—
267C2×C4×Q8C2313yes—
268C2×C4×Q8C2313yes—
269C2×C4×Q8C2313yes—
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2313yes—
283C2×C4×Q8C2313yes—
284C2×C4×Q8C2313yes—
285C2×C4×Q8C2313yes—
286C2×C4×Q8C2316yes—
287C2×C4×Q8C2311yescharacteristic
288C2×C4×D4C2313yes—
289C2×C4×D4C2313yes—
290C2×C4×D4C2313yes—
291C2×C4×D4C2316yes—
292C2×#117C2313yes—
293C2×#117C2311yescharacteristic
294C2×#117C2313yes—
295C2×#117C2316yes—
296C2×#117C2316yes—
297C22×C4⋊C4C2313yes—
298C22×C4⋊C4C2313yes—
299C22×C4⋊C4C2313yes—
300C22×C4⋊C4C2313yes—
301C22×C4⋊C4C2313yes—
302C22×C4⋊C4C2313yes—
303C22×C42C2313yes—
304C22×C42C2313yes—
305C22×C42C2313yes—
306#401C2313yes—
307#400C2313yes—
308#400C2313yes—
309#400C2316yes—
310#400C2316yes—
311#400C2316yes—
312#400C2316yes—
313#400C2316yes—
314#400C2313yes—
315#400C2313yes—
316#400C2313yes—
317#400C2311yescharacteristic
318#400C2313yes—
319#400C2313yes—
320#400C2313yes—
321#400C2313yes—
322#400C2313yes—
323#400C2313yes—
324#400C2316yes—
325#399C2316yes—
326#399C2316yes—
327#399C2316yes—
328#399C2313yes—
329#399C2316yes—
330#398C2316yes—
331#398C2316yes—
332#398C2316yes—
333#398C2316yes—
334#398C2313yes—
335#398C2316yes—
336#398C2316yes—
337#398C2316yes—
338#398C2313yes—
339#398C2311yescharacteristic
340#398C2311yescharacteristic
341#398C2313yes—
342#398C2313yes—
343#398C2313yes—
344#398C2313yes—
345#398C2313yes—
346#398C2313yes—
347#398C2316yes—
348#398C2316yes—
349#397C2316yes—
350#397C2316yes—
351#397C2313yes—
352#397C2316yes—
353#397C2313yes—
354#397C2313yes—
355#397C2316yes—
356#397C2316yes—
357#397C2316yes—
358#397C2316yes—
359#396C2316yes—
360#396C2313yes—
361#396C2313yes—
362#396C2313yes—
363#396C2316yes—
364#395C2316yes—
365#395C2316yes—
366#395C2316yes—
367#395C2311yescharacteristic
368#393C2313yes—
369#393C2316yes—
370#391C2316yes—
371#391C2313yes—
372#391C2313yes—
373#391C2313yes—
374#391C2313yes—
375#391C2313yes—
376#391C2313yes—
377#391C2313yes—
378#391C2316yes—
379#391C2316yes—
380#391C2316yes—
381#391C2313yes—
382#391C2311yescharacteristic
383#390C2313yes—
384#390C2313yes—
385#390C2313yes—
386#390C2313yes—
387#390C2313yes—
388#390C2313yes—
389#390C2313yes—
390#390C2313yes—
391#390C2313yes—
392#390C2313yes—
393#389C2311yescharacteristic
394#389C2313yes—
395#389C2313yes—
396#389C2313yes—
397#389C2313yes—
398#389C2313yes—
399#389C2316yes—
400#389C2313yes—
401#389C2313yes—
402#389C2313yes—
403#389C2313yes—
404#389C2313yes—
405#389C2316yes—
406#389C2313yes—
407#389C2313yes—
408#389C2313yes—
409#389C2313yes—
410#389C2316yes—
411#389C2313yes—
412#389C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2316yes—
418#389C2316yes—
419#389C2313yes—
420#389C2313yes—
421#389C2313yes—
422#389C2313yes—
423#389C2313yes—
424#389C2313yes—
425#389C2313yes—
426#389C2313yes—
427#389C2316yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2316yes—
433#389C2313yes—
434#389C2313yes—
435#389C2316yes—
436#389C2313yes—
437#389C2313yes—
438#389C2316yes—
439#388C2313yes—
440#388C2313yes—
441#388C2313yes—
442#388C2316yes—
443#388C2316yes—
444#388C2313yes—
445#388C2316yes—
446#388C2316yes—
447#388C2316yes—
448#388C2313yes—
449#388C2316yes—
450#388C2316yes—
451#388C2316yes—
452#388C2316yes—
453#388C2313yes—
454#388C2316yes—
455#388C2316yes—
456#388C2316yes—
457#388C2313yes—
458#388C2313yes—
459#388C2313yes—
460#388C2313yes—
461#388C2313yes—
462#388C2313yes—
463#388C2313yes—
464#387C2311yescharacteristic
465#387C2313yes—
466#387C2313yes—
467#387C2313yes—
468#387C2313yes—
469#387C2313yes—
470#387C2313yes—
471#387C2313yes—
472#387C2316yes—
473#387C2316yes—
474#387C2316yes—
475#387C2316yes—
476#387C2316yes—
477#387C2313yes—
478#387C2316yes—
479#387C2316yes—
480#387C2316yes—
481#387C2316yes—
482#387C2316yes—
483#387C2313yes—
484#387C2313yes—
485#387C2313yes—
486#387C2316yes—
487#387C2316yes—
488#387C2313yes—
489#387C2316yes—
490#387C2313yes—
491#387C2313yes—
492#387C2316yes—
493#387C2316yes—
494#387C2316yes—
495#387C2313yes—
496#387C2313yes—
497#387C2313yes—
498#387C2313yes—
499#387C2313yes—
500#387C2313yes—
501#387C2311yescharacteristic
502#387C2313yes—
503#386C2313yes—
504#386C2316yes—
505#386C2313yes—
506#386C2313yes—
507#386C2313yes—
508#385C2316yes—
509#385C2316yes—
510#385C2316yes—
511#385C2316yes—
512#385C2313yes—
513#385C2313yes—
514#385C2313yes—
515#385C2313yes—
516#385C2311yescharacteristic
517#385C2311yescharacteristic
518#384C2313yes—
519#384C2313yes—
520#384C2313yes—
521#384C2313yes—
522#384C2313yes—
523#384C2313yes—
524#384C2313yes—
525#384C2313yes—
526#384C2313yes—
527#384C2313yes—
528#383C2313yes—
529#383C2313yes—
530#383C2313yes—
531#382C2313yes—
532#382C2313yes—
533#382C2313yes—
534#382C2313yes—
535#382C2313yes—
536#382C2313yes—
537#382C2313yes—
538#382C2316yes—
539#382C2316yes—
540#382C2316yes—
541#382C2316yes—
542#382C2313yes—
543#382C2316yes—
544#382C2313yes—
545#381C2316yes—
546#381C2313yes—
547#381C2313yes—
548#381C2313yes—
549#381C2311yescharacteristic
550#380C2313yes—
551#380C2313yes—
552#380C2316yes—
553#380C2313yes—
554#380C2313yes—
555#380C2313yes—
556#380C2313yes—
557#380C2313yes—
558#380C2313yes—
559#380C2316yes—
560#380C2313yes—
561#380C2313yes—
562#380C2311yescharacteristic
563C4×C4⋊C4C2313yes—
564C4×C4⋊C4C2313yes—
565C4×C4⋊C4C2313yes—
566C4×C4⋊C4C2313yes—
567C4×C4⋊C4C2313yes—
568C4×C4⋊C4C2313yes—
569C4×C4⋊C4C2313yes—
570C4×C4⋊C4C2313yes—
571C4×C4⋊C4C2316yes—
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⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2316yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊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×C22⋊C4C2313yes—
604C4×C22⋊C4C2313yes—
605C4×C22⋊C4C2313yes—
606C4×C22⋊C4C2316yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2316yes—
615#376C2313yes—
616#376C2313yes—
617#376C2313yes—
618#376C2313yes—
619#376C2313yes—
620C2×#95C2316yes—
621C2×#95C2311yescharacteristic
622C2×#95C2313yes—
623C43C2313yes—
624C43C2313yes—
625C2×#41—24no—
626C2×#41—24no—
627C2×#41—24no—
628C22×Q8—24no—
629C22×Q8—24no—
630C22×Q8#4118yes—
631C22×Q8C2411yescharacteristic
632C22×Q8C2413yes—
633C22×Q8C2416yes—
634C22×Q8C2411yescharacteristic
635C22×D4C2413yes—
636C22×D4C2413yes—
637C23×C4C2413yes—
638C23×C4C2413yes—
639C23×C4C2413yes—
640C23×C4C2411yescharacteristic
641C23×C4C2411yescharacteristic
642C23×C4C2413yes—
643C23×C4C2411yescharacteristic
644C23×C4C2413yes—
645C23×C4C2416yes—
646C4⋊Q8—212no—
647C4⋊Q8—212no—
648C4⋊Q8—212no—
649#126—412no—
650#126—46no—
651#126—412no—
652#125—412no—
653#125—46no—
654#125—412no—
655#125—412no—
656#124—212no—
657#123—212no—
658#123—212no—
659#123—412no—
660C22⋊Q8—212no—
661C22⋊Q8—24no—
662C22⋊Q8—412no—
663C22⋊Q8—412no—
664C22⋊Q8—412no—
665#121—212no—
666C4×Q8—212no—
667C4×Q8—212no—
668C4×Q8—212no—
669C4×Q8—212no—
670C4×Q8—24no—
671C4×Q8—24no—
672C4×Q8—24no—
673C4×Q8—24no—
674C4×Q8—24no—
675C4×Q8—24no—
676C4×Q8—24no—
677C4×Q8—24no—
678C4×Q8—24no—
679C4×Q8—24no—
680C4×Q8—24no—
681C4×Q8—24no—
682C4×Q8—212no—
683C4×Q8—212no—
684C4×Q8—212no—
685C4×Q8—412no—
686C4×Q8#4118yes—
687C4×D4—212no—
688C4×D4—212no—
689C4×D4—212no—
690C4×D4—412no—
691#117—212no—
692#117—24no—
693#117—212no—
694#117—412no—
695#117—412no—
696C2×C4⋊C4—212no—
697C2×C4⋊C4—212no—
698C2×C4⋊C4—212no—
699C2×C4⋊C4—212no—
700C2×C4⋊C4—212no—
701C2×C4⋊C4—46no—
702C2×C4⋊C4C2413yes—
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⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2411yescharacteristic
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2416yes—
746C2×C4⋊C4C2416yes—
747C2×C4⋊C4C2416yes—
748C2×C4⋊C4C2416yes—
749C2×C4⋊C4C2416yes—
750C2×C4⋊C4C2416yes—
751C2×C4⋊C4C2416yes—
752C2×C4⋊C4C2416yes—
753C2×C4⋊C4C2416yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2411yescharacteristic
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2411yescharacteristic
761C2×C4⋊C4C2411yescharacteristic
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2416yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C22⋊C4C2413yes—
767C2×C22⋊C4C2413yes—
768C2×C22⋊C4C2413yes—
769C2×C22⋊C4C2413yes—
770C2×C22⋊C4C2413yes—
771C2×C22⋊C4C2413yes—
772C2×C22⋊C4C2411yescharacteristic
773C2×C22⋊C4C2411yescharacteristic
774C2×C22⋊C4C2413yes—
775C2×C22⋊C4C2416yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2411yescharacteristic
779C2×C22⋊C4C2413yes—
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2416yes—
782C2×C22⋊C4C2416yes—
783C2×C22⋊C4C2416yes—
784C2×C22⋊C4C2416yes—
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2416yes—
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2411yescharacteristic
792C2×C42—212no—
793C2×C42—212no—
794C2×C42—212no—
795C2×C42C2413yes—
796C2×C42C2413yes—
797C2×C42C2413yes—
798C2×C42C2411yescharacteristic
799C2×C42C2411yescharacteristic
800C2×C42C2413yes—
801C2×C42C2413yes—
802C2×C42C2413yes—
803C2×C42C2413yes—
804C2×C42C2413yes—
805C2×C42C2413yes—
806C2×C42C2413yes—
807C2×C42C2413yes—
808C2×C42C2413yes—
809C2×C42C2413yes—
810C2×C42C2413yes—
811C2×C42C2413yes—
812C2×C42C2413yes—
813C2×C42C2413yes—
814C2×C42C2413yes—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2416yes—
818C2×C42C2416yes—
819C2×C42C2416yes—
820C2×C42C2413yes—
821C2×C42C2413yes—
822C2×C42C2413yes—
823C2×C42C2413yes—
824C2×C42C2413yes—
825#95C2416yes—
826#95C2411yescharacteristic
827#95C2411yescharacteristic
828#95C2411yescharacteristic
829#95C2411yescharacteristic
830#95C2413yes—
831#95C2413yes—
832#95C2413yes—
833#95C2413yes—
834#95C2416yes—
835#95C2416yes—
836#95C2416yes—
837#95C2411yescharacteristic
838#95C2411yescharacteristic
839#95C2411yescharacteristic
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2411yescharacteristic
858#95C2411yescharacteristic
859#95C2411yescharacteristic
860#95C2411yescharacteristic
861#95C2411yescharacteristic
862#95C2413yes—
863#95C2413yes—
864#95C2416yes—
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2416yes—
873#95C2416yes—
874#95C2411yescharacteristic
875#95C2411yescharacteristic
876#95C2416yes—
877#95C2416yes—
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2416yes—
891#95C2413yes—
892#95C2413yes—
893#95C2413yes—
894#95C2413yes—
895#95C2416yes—
896C24C2513yes—
897C24C2511yescharacteristic
898#41—416no—
899C2×Q8—232no—
900C2×Q8—26no—
901C2×Q8—22no—
902C2×Q8—212no—
903C2×Q8—26no—
904C2×Q8—22no—
905C2×Q8—41no—
906C2×Q8—46no—
907C2×Q8—46no—
908C2×Q8C2×#41112yes—
909C2×Q8C2×#4114yes—
910C2×Q8C2×#4114yes—
911C2×Q82−1+414yes—
912C2×D4—26no—
913C2×D4—26no—
914C2×D4—26no—
915C2×D4—26no—
916C2×D4—26no—
917C2×D4—26no—
918C22×C4—22no—
919C22×C4—22no—
920C22×C4—26no—
921C22×C4—26no—
922C22×C4—22no—
923C22×C4—26no—
924C22×C4—26no—
925C22×C4—26no—
926C22×C4—22no—
927C22×C4—26no—
928C22×C4—26no—
929C22×C4—22no—
930C22×C4—26no—
931C22×C4—26no—
932C22×C4—26no—
933C22×C4—26no—
934C22×C4—22no—
935C22×C4—212no—
936C22×C4—43no—
937C22×C4—41no—
938C22×C4—41no—
939C22×C4—43no—
940C22×C4—46no—
941C22×C4—46no—
942C22×C4—43no—
943C22×C4C2×#41112yes—
944C22×C4H(5,𝔽2)14yes—
945C22×C4C2511yescharacteristic
946C22×C4C2511yescharacteristic
947C22×C4C2511yescharacteristic
948C22×C4C2511yescharacteristic
949C22×C4C2511yescharacteristic
950C22×C4C2511yescharacteristic
951C22×C4C2511yescharacteristic
952C22×C4C2513yes—
953C22×C4C2513yes—
954C22×C4C2513yes—
955C22×C4C2513yes—
956C22×C4C2511yescharacteristic
957C22×C4C2513yes—
958C22×C4C2513yes—
959C22×C4C2513yes—
960C22×C4C2513yes—
961C22×C4C2513yes—
962C22×C4C2513yes—
963C22×C4C2513yes—
964C22×C4C2513yes—
965C22×C4C2511yescharacteristic
966C22×C4C2513yes—
967C22×C4C2513yes—
968C22×C4C2511yescharacteristic
969C22×C4C2511yescharacteristic
970C22×C4C2511yescharacteristic
971C22×C4C2511yescharacteristic
972C22×C4C2511yescharacteristic
973C22×C4C2513yes—
974C4⋊C4—26no—
975C4⋊C4—26no—
976C4⋊C4—212no—
977C4⋊C4—212no—
978C4⋊C4—212no—
979C4⋊C4—26no—
980C4⋊C4—26no—
981C4⋊C4—26no—
982C4⋊C4—26no—
983C4⋊C4—26no—
984C4⋊C4—22no—
985C4⋊C4—26no—
986C4⋊C4—26no—
987C4⋊C4—26no—
988C4⋊C4—26no—
989C4⋊C4—26no—
990C4⋊C4—26no—
991C4⋊C4—26no—
992C4⋊C4—26no—
993C4⋊C4—26no—
994C4⋊C4—26no—
995C4⋊C4—26no—
996C4⋊C4—26no—
997C4⋊C4—26no—
998C4⋊C4—26no—
999C4⋊C4—26no—
1000C4⋊C4—22no—
1001C4⋊C4—22no—
1002C4⋊C4—26no—
1003C4⋊C4—26no—
1004C4⋊C4—26no—
1005C4⋊C4—22no—
1006C4⋊C4—22no—
1007C4⋊C4—22no—
1008C4⋊C4—26no—
1009C4⋊C4—26no—
1010C4⋊C4—26no—
1011C4⋊C4—26no—
1012C4⋊C4—26no—
1013C4⋊C4—22no—
1014C4⋊C4—22no—
1015C4⋊C4—43no—
1016C4⋊C4—43no—
1017C4⋊C4—41no—
1018C4⋊C4—41no—
1019C4⋊C4—43no—
1020C4⋊C4—43no—
1021C4⋊C4—41no—
1022C4⋊C4—46no—
1023C4⋊C4—43no—
1024C4⋊C4—46no—
1025C4⋊C4—46no—
1026C4⋊C4—46no—
1027C4⋊C4—46no—
1028C4⋊C4—46no—
1029C4⋊C4—46no—
1030C4⋊C4—46no—
1031C4⋊C4—46no—
1032C4⋊C4—46no—
1033C4⋊C4—43no—
1034C4⋊C4—43no—
1035C4⋊C4—43no—
1036C4⋊C4—43no—
1037C4⋊C4C2×#41112yes—
1038C22⋊C4—22no—
1039C22⋊C4—26no—
1040C22⋊C4—26no—
1041C22⋊C4—26no—
1042C22⋊C4—22no—
1043C22⋊C4—22no—
1044C22⋊C4—26no—
1045C22⋊C4—26no—
1046C22⋊C4—26no—
1047C22⋊C4—212no—
1048C22⋊C4—26no—
1049C22⋊C4—26no—
1050C22⋊C4—26no—
1051C22⋊C4—26no—
1052C22⋊C4—26no—
1053C22⋊C4—46no—
1054C22⋊C4—43no—
1055C22⋊C4—43no—
1056C22⋊C4—43no—
1057C22⋊C4—46no—
1058C22⋊C4—46no—
1059C22⋊C4—46no—
1060C22⋊C4—46no—
1061C22⋊C4—43no—
1062C22⋊C4—43no—
1063C22⋊C42−1+414yes—
1064C42—26no—
1065C42—26no—
1066C42—26no—
1067C42—26no—
1068C42—26no—
1069C42—26no—
1070C42—26no—
1071C42—26no—
1072C42—26no—
1073C42—26no—
1074C42—26no—
1075C42—26no—
1076C42—26no—
1077C42—26no—
1078C42—26no—
1079C42—26no—
1080C42—26no—
1081C42—22no—
1082C42—22no—
1083C42—26no—
1084C42—26no—
1085C42—26no—
1086C42—43no—
1087C42—43no—
1088C42—46no—
1089C42—46no—
1090C42—46no—
1091C42—43no—
1092C42—43no—
1093C42C2×#41112yes—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—23no—
1099C23—23no—
1100C23—23no—
1101C23—23no—
1102C23—23no—
1103C23—23no—
1104C23—23no—
1105C23C22×#4112yes—
1106C23C2×H(5,𝔽2)12yes—
1107C23C2×2−1+412yes—
1108C23C2611yescharacteristic
1109Q8—224no—
1110Q8—44no—
1111Q8—812no—
1112Q8#552116yescomplemented
1113D4—412no—
1114D4—412no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—23no—
1120C2×C4—23no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—23no—
1126C2×C4—21no—
1127C2×C4—23no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—28no—
1132C2×C4—224no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—23no—
1139C2×C4—23no—
1140C2×C4—23no—
1141C2×C4—23no—
1142C2×C4—23no—
1143C2×C4—23no—
1144C2×C4—23no—
1145C2×C4—23no—
1146C2×C4—23no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—23no—
1150C2×C4—23no—
1151C2×C4—23no—
1152C2×C4—23no—
1153C2×C4—23no—
1154C2×C4—23no—
1155C2×C4—23no—
1156C2×C4—23no—
1157C2×C4—23no—
1158C2×C4—23no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—23no—
1164C2×C4—23no—
1165C2×C4—23no—
1166C2×C4—21no—
1167C2×C4—23no—
1168C2×C4—23no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—23no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—23no—
1175C2×C4—23no—
1176C2×C4—23no—
1177C2×C4—21no—
1178C2×C4—23no—
1179C2×C4—23no—
1180C2×C4—23no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—23no—
1185C2×C4—23no—
1186C2×C4—23no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—23no—
1191C2×C4—23no—
1192C2×C4—21no—
1193C2×C4—44no—
1194C2×C4—44no—
1195C2×C4—412no—
1196C2×C4—412no—
1197C2×C4—412no—
1198C2×C4—812no—
1199C2×C4—86no—
1200C2×C4C22×#4116yes—
1201C2×C4C22×#4112yes—
1202C2×C4C22×#4116yes—
1203C2×C4C22×#4116yes—
1204C2×C4C22×#4116yes—
1205C2×C4C2×H(5,𝔽2)12yes—
1206C2×C4C2×H(5,𝔽2)12yes—
1207C2×C4C2×2−1+412yes—
1208C2×C4C2×2−1+412yes—
1209C2×C4C2×2−1+416yes—
1210C2×C4#58512yes—
1211C22—22no—
1212C22—22no—
1213C22—22no—
1214C22—22no—
1215C22—22no—
1216C22—22no—
1217C22—43no—
1218C22—43no—
1219C22—43no—
1220C22—43no—
1221C22—43no—
1222C22—43no—
1223C22—43no—
1224C22#352214yes—
1225C22C23×#4111yescharacteristic
1226C22C23×#4111yescharacteristic
1227C22C22×H(5,𝔽2)11yescharacteristic
1228C22C22×2−1+411yescharacteristic
1229C22C22×2−1+411yescharacteristic
1230C22C2×#58511yescharacteristic
1231C222−1+611yescharacteristic
1232C4—22no—
1233C4—22no—
1234C4—22no—
1235C4—22no—
1236C4—22no—
1237C4—22no—
1238C4—26no—
1239C4—26no—
1240C4—41no—
1241C4—41no—
1242C4—41no—
1243C4—41no—
1244C4—41no—
1245C4—43no—
1246C4—43no—
1247C4—41no—
1248C4—41no—
1249C4—43no—
1250C4—43no—
1251C4—43no—
1252C4—43no—
1253C4—43no—
1254C4—43no—
1255C4—43no—
1256C4—43no—
1257C4—43no—
1258C4—43no—
1259C4—41no—
1260C4C2×#552112yes—
1261C2—24no—
1262C2—83no—
1263C2C22×#55211yescharacteristic
1264C2C2×#352211yescharacteristic
1265C2#6280011yescharacteristic
1266C2#6294611yescharacteristic
1267C2#6299811yescharacteristic
1268C2#6300511yescharacteristic
1269C2#6303211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#548C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #59749C2semidirect
2. #59502C2semidirect
3. #59332C2semidirect
4. #59291C2semidirect
5. #59290C2semidirect
6. #45407C2semidirect
7. #45350C2semidirect
8. #45346C2semidirect
9. #45210C2semidirect
10. #38273C2semidirect
11. #38225C2semidirect
12. #38068C2semidirect
13. #37884C2semidirect
15. Q8×C22⋊Q8C2semidirect
17. #36458C2semidirect
18. #36447C2semidirect
19. #36265C2semidirect
20. #36186C2semidirect
21. #35898C2semidirect
22. #35868C2semidirect
23. #35868C2semidirect
24. #35748C2semidirect
25. #34808C2semidirect
26. #34335C2semidirect
28. #34263C2semidirect
29. #34196C2semidirect
30. Q8×#117C2semidirect
31. C2×#2351C2semidirect
1112. Q8#552semidirect

Maximal subgroups

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

subgroupindex
#597492
#595022
#593322
#592912
#592902
#454072
#453502
#453462
#452102
#382732
#382252
#380682
#378842
#365782
Q8×C22⋊Q82
#364832
#364582
#364472
#362652
#361862
#358982
#358682
#357482
#348082
#343352
#342942
#342632
#341962
Q8×#1172
C2×#23512