Finite Group Databasebeta

← #7711353

Subgroups — #7711353

Order 512.

5498 conjugacy classes of subgroups.

The subgroup lattice has 1225 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59863C211yesmaximal, characteristic, complemented
3#59823C211yesmaximal, characteristic, complemented
4#59815C211yesmaximal, characteristic, complemented
5#59304C212yesmaximal, complemented
6#59125C212yesmaximal, complemented
7#46340C214yesmaximal, complemented
8#46090C214yesmaximal, complemented
9#40214C214yesmaximal, complemented
10#40188C214yesmaximal, complemented
11#39201C212yesmaximal, complemented
12#39192C212yesmaximal, complemented
13#38965C212yesmaximal, complemented
14#38952C212yesmaximal, complemented
15#38042C214yesmaximal, complemented
16#38025C214yesmaximal, complemented
17#37627C212yesmaximal, complemented
18#37251C214yesmaximal, complemented
19#36631C211yesmaximal, characteristic, complemented
20#36631C211yesmaximal, characteristic, complemented
21#36596C212yesmaximal, complemented
22#36576C212yesmaximal, complemented
23#36551C212yesmaximal, complemented
24#36544C212yesmaximal, complemented
25#35082C214yesmaximal, complemented
26#34480C212yesmaximal, complemented
27C2×C4×C4⋊Q8C211yesmaximal, characteristic, complemented
28C2×#554C2212yes—
29C2×#553C2214yes—
30C2×#550C2212yes—
31C2×#548C2214yes—
32C2×#547C2212yes—
33C22×C4⋊Q8C2211yescharacteristic
34C2×#529C2212yes—
35C2×#529C2212yes—
36C22×C4×Q8C2212yes—
37#2861C2212yes—
38#2861C2212yes—
39#2860C2212yes—
40#2860C2212yes—
41#2860C2212yes—
42#2860C2212yes—
43#2859C2211yescharacteristic
44#2859C2211yescharacteristic
45#2858C2211yescharacteristic
46#2858C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic
49#2856C2214yes—
50#2856C2211yescharacteristic
51#2856C2211yescharacteristic
52#2854C2212yes—
53#2854C2212yes—
54#2854C2212yes—
55#2854C2212yes—
56#2851C2214yes—
57#2850C2212yes—
58#2850C2212yes—
59#2837C2218yes—
60#2808C2214yes—
61#2806C2214yes—
62#2772C2218yes—
63#2768C2218yes—
64#2732C2214yes—
65#2727C2218yes—
66#2725C2218yes—
67#2718C2218yes—
68#2715C2218yes—
69#2712C2218yes—
70#2710C2218yes—
71#2704C2218yes—
72#2702C2218yes—
73#2695C2218yes—
74#2682C2214yes—
75#2674C2218yes—
76#2672C2218yes—
77#2672C2218yes—
78#2651C2218yes—
79#2651C2218yes—
80#2629C2214yes—
81#2625C2214yes—
82#2624C2214yes—
83#2620C2214yes—
84#2592C2214yes—
85#2589C2218yes—
86#2584C2214yes—
87#2584C2214yes—
88#2582C2214yes—
89#2580C2214yes—
90#2567C2212yes—
91#2563C2212yes—
92#2554C2218yes—
93#2552C2212yes—
94#2552C2212yes—
95#2552C2212yes—
96#2548C2214yes—
97#2548C2212yes—
98#2547C2212yes—
99#2543C2218yes—
100#2542C2212yes—
101#2541C2212yes—
102#2538C2214yes—
103#2538C2212yes—
104#2538C2212yes—
105#2538C2214yes—
106#2537C2212yes—
107#2513C2214yes—
108#2513C2214yes—
109#2512C2214yes—
110#2509C2214yes—
111#2507C2214yes—
112#2507C2214yes—
113#2501C2214yes—
114#2497C2214yes—
115#2496C2214yes—
116#2491C2214yes—
117#2490C2214yes—
118#2487C2214yes—
119#2485C2214yes—
120#2465C2218yes—
121#2454C2214yes—
122#2454C2214yes—
123#2454C2214yes—
124#2450C2218yes—
125#2449C2218yes—
126#2445C2214yes—
127#2445C2214yes—
128#2445C2214yes—
129#2443C2218yes—
130#2443C2218yes—
131#2441C2214yes—
132#2440C2214yes—
133#2432C2214yes—
134#2429C2214yes—
135#2426C2214yes—
136#2426C2218yes—
137#2425C2218yes—
138#2425C2218yes—
139#2423C2214yes—
140#2422C2214yes—
141#2417C2214yes—
142#2416C2218yes—
143#2416C2214yes—
144#2416C2214yes—
145#2416C2214yes—
146#2409C2214yes—
147#2407C2214yes—
148#2376C2218yes—
149#2369C2212yes—
150#2366C2212yes—
151#2365C2212yes—
152#2363C2214yes—
153#2360C2214yes—
154#2355C2212yes—
155#2354C2212yes—
156#2354C2212yes—
157Q8×C4⋊C4C2212yes—
158D4×C4⋊C4C2212yes—
159D4×C4⋊C4C2214yes—
160D4×C4⋊C4C2214yes—
161D4×C4⋊C4C2212yes—
162#2345C2214yes—
163#2341C2214yes—
164#2335C2218yes—
165#2335C2218yes—
166#2324C2214yes—
167#2323C2214yes—
168#2316C2214yes—
169#2311C2214yes—
170C4×C4⋊Q8C2212yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2211yescharacteristic
173C4×C4⋊Q8C2211yescharacteristic
174C4×C4⋊Q8C2212yes—
175C4×C4⋊Q8C2212yes—
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2211yescharacteristic
178C4×C4⋊Q8C2211yescharacteristic
179C4×C4⋊Q8C2211yescharacteristic
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2212yes—
182C4×#127C2211yescharacteristic
183C4×#127C2211yescharacteristic
184C4×#124C2212yes—
185C4×#124C2212yes—
186C4×#121C2214yes—
187C4×#121C2214yes—
188C4×#121C2212yes—
189C4×#121C2212yes—
190C4×#121C2212yes—
191C4×#121C2212yes—
192C2×#391C2212yes—
193#2293C2212yes—
194#2293C2212yes—
195#2293C2212yes—
196#2293C2212yes—
197C2×#389C2212yes—
198C2×#389C2212yes—
199C2×#384C2211yescharacteristic
200C2×C4×C4⋊C4C2212yes—
201C2×C4×C4⋊C4C2212yes—
202C2×C43C2211yescharacteristic
203C22×#41C2314yes—
204C23×Q8C2312yes—
205#554—48no—
206#553—416no—
207#550—48no—
208#548—416no—
209#547—216no—
210C2×C4⋊Q8—28no—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#127C2314yes—
221#529—48no—
222#529—48no—
223C2×#126C2314yes—
224C2×#126C2314yes—
225C2×#126C2318yes—
226C2×#125C2314yes—
227C2×#125C2314yes—
228C2×#125C2312yes—
229C2×#125C2312yes—
230C2×#124C2314yes—
231C2×#124C2312yes—
232C2×#124C2312yes—
233C2×#124C2312yes—
234C2×#124C2312yes—
235C2×#124C2318yes—
236C2×#123C2318yes—
237C2×#123C2318yes—
238C2×#123C2314yes—
239C2×#123C2314yes—
240C2×#123C2318yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2312yes—
244C2×C22⋊Q8C2314yes—
245C2×C22⋊Q8C2314yes—
246C2×C22⋊Q8C2318yes—
247C2×C22⋊Q8C2318yes—
248C2×#121C2314yes—
249C2×#121C2312yes—
250C2×#121C2312yes—
251C2×#121C2312yes—
252C2×#121C2312yes—
253C2×#121C2312yes—
254C2×#121C2312yes—
255C2×#121C2318yes—
256C2×#121C2318yes—
257C2×#121C2314yes—
258C2×#121C2314yes—
259C2×#121C2318yes—
260C2×C4×Q8—48no—
261C2×C4×Q8C2312yes—
262C2×C4×Q8C2312yes—
263C2×C4×Q8C2314yes—
264C2×C4×Q8C2312yes—
265C2×C4×Q8C2312yes—
266C2×C4×Q8C2314yes—
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2314yes—
270C2×C4×D4C2312yes—
271C2×C4×D4C2312yes—
272C2×C4×D4C2312yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2312yes—
277C2×C4×D4C2312yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2318yes—
281C2×C4×D4C2318yes—
282C2×C4×D4C2314yes—
283C2×#117C2314yes—
284C2×#117C2314yes—
285C2×#117C2314yes—
286C22×C4⋊C4C2314yes—
287C22×C4⋊C4C2312yes—
288C22×C4⋊C4C2312yes—
289C22×C4⋊C4C2312yes—
290C22×C4⋊C4C2314yes—
291C22×C4⋊C4C2312yes—
292C22×C4⋊C4C2314yes—
293C22×C4⋊C4C2312yes—
294C22×C42C2311yescharacteristic
295C22×C42C2311yescharacteristic
296C22×C42C2311yescharacteristic
297C22×C42C2311yescharacteristic
298C22×C42C2311yescharacteristic
299C22×C42C2311yescharacteristic
300C22×C42C2311yescharacteristic
301C22×C42C2314yes—
302#400C2318yes—
303#400C2318yes—
304#399C2318yes—
305#399C2318yes—
306#399C2318yes—
307#399C2318yes—
308#398C2318yes—
309#398C2318yes—
310#398C2318yes—
311#398C2318yes—
312#398C2318yes—
313#398C2318yes—
314#398C2318yes—
315#397C2318yes—
316#397C2318yes—
317#397C2318yes—
318#397C2318yes—
319#397C2318yes—
320#396C2318yes—
321#396C2318yes—
322#396C2318yes—
323#396C2318yes—
324#396C2318yes—
325#396C2318yes—
326#396C2318yes—
327#396C2318yes—
328#395C2318yes—
329#395C2318yes—
330#394C2318yes—
331#394C2318yes—
332#394C2318yes—
333#394C2318yes—
334#394C2318yes—
335#394C2318yes—
336#394C2318yes—
337#394C2318yes—
338#394C2318yes—
339#393C2318yes—
340#393C2318yes—
341#392C2318yes—
342#391C2312yes—
343#391C2312yes—
344#391C2312yes—
345#391C2312yes—
346#391C2314yes—
347#391C2314yes—
348#391C2312yes—
349#391C2312yes—
350#391C2314yes—
351#391C2318yes—
352#391C2312yes—
353#391C2314yes—
354#391C2312yes—
355#390C2312yes—
356#390C2312yes—
357#390C2312yes—
358#390C2312yes—
359#390C2312yes—
360#390C2312yes—
361#390C2314yes—
362#390C2312yes—
363#390C2314yes—
364#390C2312yes—
365#390C2318yes—
366#390C2312yes—
367#390C2314yes—
368#390C2318yes—
369#390C2318yes—
370#390C2312yes—
371#390C2312yes—
372#390C2312yes—
373#390C2312yes—
374#390C2312yes—
375#390C2312yes—
376#390C2312yes—
377#390C2312yes—
378#390C2314yes—
379#390C2314yes—
380#390C2312yes—
381#390C2312yes—
382#390C2312yes—
383#390C2314yes—
384#389C2312yes—
385#389C2312yes—
386#389C2312yes—
387#389C2312yes—
388#389C2312yes—
389#389C2314yes—
390#389C2314yes—
391#389C2312yes—
392#389C2314yes—
393#389C2314yes—
394#389C2312yes—
395#389C2312yes—
396#389C2312yes—
397#389C2312yes—
398#389C2312yes—
399#389C2312yes—
400#389C2314yes—
401#389C2314yes—
402#389C2312yes—
403#389C2318yes—
404#389C2318yes—
405#389C2314yes—
406#389C2314yes—
407#389C2312yes—
408#389C2312yes—
409#389C2318yes—
410#389C2314yes—
411#389C2312yes—
412#389C2314yes—
413#389C2318yes—
414#389C2318yes—
415#389C2314yes—
416#389C2318yes—
417#389C2312yes—
418#389C2312yes—
419#389C2312yes—
420#389C2312yes—
421#389C2312yes—
422#389C2312yes—
423#389C2312yes—
424#389C2312yes—
425#389C2314yes—
426#388C2318yes—
427#388C2318yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2318yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2318yes—
437#388C2318yes—
438#388C2318yes—
439#388C2318yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2318yes—
450#387C2318yes—
451#387C2318yes—
452#387C2318yes—
453#387C2318yes—
454#387C2318yes—
455#387C2318yes—
456#386C2318yes—
457#386C2318yes—
458#386C2318yes—
459#386C2314yes—
460#386C2314yes—
461#386C2314yes—
462#386C2314yes—
463#386C2318yes—
464#386C2318yes—
465#386C2318yes—
466#385C2318yes—
467#385C2318yes—
468#385C2318yes—
469#385C2318yes—
470#385C2318yes—
471#385C2318yes—
472#385C2318yes—
473#385C2318yes—
474#384C2311yescharacteristic
475#384C2311yescharacteristic
476#384C2311yescharacteristic
477#384C2312yes—
478#384C2312yes—
479#384C2312yes—
480#384C2311yescharacteristic
481#384C2311yescharacteristic
482#384C2311yescharacteristic
483#384C2314yes—
484#384C2314yes—
485#384C2314yes—
486#382C2314yes—
487#382C2312yes—
488#382C2312yes—
489#380C2314yes—
490#380C2314yes—
491#380C2318yes—
492#380C2318yes—
493#380C2318yes—
494#380C2314yes—
495#380C2318yes—
496#380C2312yes—
497#380C2312yes—
498#380C2312yes—
499#380C2312yes—
500#380C2314yes—
501#380C2314yes—
502#380C2314yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2314yes—
512C4×C4⋊C4C2314yes—
513C4×C4⋊C4C2312yes—
514C4×C4⋊C4C2312yes—
515C4×C4⋊C4C2312yes—
516C4×C4⋊C4C2312yes—
517C4×C4⋊C4C2312yes—
518C4×C4⋊C4C2312yes—
519C4×C4⋊C4C2314yes—
520C4×C4⋊C4C2314yes—
521C4×C4⋊C4C2314yes—
522C4×C4⋊C4C2314yes—
523C4×C22⋊C4C2318yes—
524C4×C22⋊C4C2318yes—
525C4×C22⋊C4C2314yes—
526C4×C22⋊C4C2314yes—
527C4×C22⋊C4C2314yes—
528C4×C22⋊C4C2314yes—
529C2×#95C2314yes—
530C2×#95C2314yes—
531C43C2311yescharacteristic
532C43C2311yescharacteristic
533C43C2311yescharacteristic
534C43C2311yescharacteristic
535C43C2311yescharacteristic
536C43C2311yescharacteristic
537C43C2311yescharacteristic
538C43C2311yescharacteristic
539C2×#41—216no—
540C2×#41—48no—
541C2×#41—48no—
542C22×Q8—28no—
543C22×Q8—28no—
544C22×Q8—44no—
545C22×Q8C2412yes—
546C22×Q8C2414yes—
547C22×Q8C2412yes—
548C22×Q8C2412yes—
549C22×Q8C2412yes—
550C22×D4C2414yes—
551C22×D4C2414yes—
552C22×D4C2412yes—
553C22×D4C2412yes—
554C22×D4C2412yes—
555C22×D4C2412yes—
556C22×D4C2412yes—
557C22×D4C2412yes—
558C22×D4C2418yes—
559C22×D4C2418yes—
560C23×C4C2411yescharacteristic
561C23×C4C2414yes—
562C23×C4C2414yes—
563C23×C4C2411yescharacteristic
564C23×C4C2411yescharacteristic
565C23×C4C2414yes—
566C23×C4C2411yescharacteristic
567C23×C4C2411yescharacteristic
568C23×C4C2411yescharacteristic
569C23×C4C2411yescharacteristic
570C23×C4C2414yes—
571C23×C4C2418yes—
572C23×C4C2418yes—
573C4⋊Q8—28no—
574C4⋊Q8—28no—
575C4⋊Q8—28no—
576C4⋊Q8—24no—
577C4⋊Q8—24no—
578C4⋊Q8—24no—
579C4⋊Q8#4118yes—
580#127—24no—
581#127—24no—
582#127—48no—
583#126—48no—
584#126—48no—
585#126—416no—
586#125—44no—
587#125—44no—
588#125—48no—
589#125—48no—
590#124—44no—
591#124—44no—
592#124—44no—
593#124—44no—
594#124—48no—
595#124—416no—
596#123—232no—
597#123—416no—
598#123—416no—
599#123—48no—
600#123—48no—
601C22⋊Q8—216no—
602C22⋊Q8—44no—
603C22⋊Q8—44no—
604C22⋊Q8—416no—
605C22⋊Q8—416no—
606C22⋊Q8—48no—
607C22⋊Q8—48no—
608#121—28no—
609#121—28no—
610#121—28no—
611#121—28no—
612#121—216no—
613#121—416no—
614#121—48no—
615#121—48no—
616#121—44no—
617#121—44no—
618#121—416no—
619#121—416no—
620C4×Q8—28no—
621C4×Q8—28no—
622C4×Q8—48no—
623C4×Q8—44no—
624C4×Q8—44no—
625C4×Q8—48no—
626C4×Q8—44no—
627C4×Q8—44no—
628C4×Q8—48no—
629C4×D4—216no—
630C4×D4—216no—
631C4×D4—28no—
632C4×D4—28no—
633C4×D4—28no—
634C4×D4—28no—
635C4×D4—48no—
636C4×D4—48no—
637C4×D4—48no—
638C4×D4—44no—
639C4×D4—44no—
640C4×D4—416no—
641C4×D4—416no—
642#117—48no—
643#117—48no—
644#117—48no—
645C2×C4⋊C4—28no—
646C2×C4⋊C4—28no—
647C2×C4⋊C4—28no—
648C2×C4⋊C4—216no—
649C2×C4⋊C4—44no—
650C2×C4⋊C4—44no—
651C2×C4⋊C4—48no—
652C2×C4⋊C4—48no—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2412yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2418yes—
684C2×C4⋊C4C2412yes—
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2418yes—
691C2×C4⋊C4C2412yes—
692C2×C4⋊C4C2412yes—
693C2×C4⋊C4C2418yes—
694C2×C4⋊C4C2418yes—
695C2×C4⋊C4C2412yes—
696C2×C4⋊C4C2412yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2418yes—
700C2×C4⋊C4C2418yes—
701C2×C4⋊C4C2418yes—
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2412yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2418yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2418yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2418yes—
725C2×C22⋊C4C2418yes—
726C2×C22⋊C4C2418yes—
727C2×C22⋊C4C2418yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2418yes—
731C2×C22⋊C4C2418yes—
732C2×C22⋊C4C2418yes—
733C2×C22⋊C4C2418yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2414yes—
736C2×C42—24no—
737C2×C42—24no—
738C2×C42—24no—
739C2×C42—24no—
740C2×C42—24no—
741C2×C42—24no—
742C2×C42—48no—
743C2×C42—42no—
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2414yes—
747C2×C42C2414yes—
748C2×C42C2411yescharacteristic
749C2×C42C2411yescharacteristic
750C2×C42C2414yes—
751C2×C42C2414yes—
752C2×C42C2411yescharacteristic
753C2×C42C2411yescharacteristic
754C2×C42C2411yescharacteristic
755C2×C42C2411yescharacteristic
756C2×C42C2411yescharacteristic
757C2×C42C2411yescharacteristic
758C2×C42C2411yescharacteristic
759C2×C42C2411yescharacteristic
760C2×C42C2411yescharacteristic
761C2×C42C2411yescharacteristic
762C2×C42C2411yescharacteristic
763C2×C42C2411yescharacteristic
764C2×C42C2411yescharacteristic
765C2×C42C2411yescharacteristic
766C2×C42C2411yescharacteristic
767C2×C42C2411yescharacteristic
768C2×C42C2411yescharacteristic
769C2×C42C2411yescharacteristic
770C2×C42C2411yescharacteristic
771C2×C42C2418yes—
772C2×C42C2418yes—
773C2×C42C2414yes—
774C2×C42C2414yes—
775C2×C42C2411yescharacteristic
776C2×C42C2411yescharacteristic
777C2×C42C2411yescharacteristic
778C2×C42C2411yescharacteristic
779C2×C42C2411yescharacteristic
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2418yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2418yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2418yes—
799#95C2418yes—
800#95C2418yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2418yes—
806#95C2418yes—
807#95C2418yes—
808C24C2514yes—
809C24C2514yes—
810C24C2511yescharacteristic
811#41—832no—
812C2×Q8—28no—
813C2×Q8—24no—
814C2×Q8—24no—
815C2×Q8—24no—
816C2×Q8—24no—
817C2×Q8—28no—
818C2×Q8—24no—
819C2×Q8—24no—
820C2×Q8—24no—
821C2×Q8—44no—
822C2×Q8—42no—
823C2×Q8—42no—
824C2×Q8—42no—
825C2×Q8—42no—
826C2×Q8—432no—
827C2×Q8C2×#4118yes—
828C2×D4—28no—
829C2×D4—28no—
830C2×D4—28no—
831C2×D4—28no—
832C2×D4—28no—
833C2×D4—28no—
834C2×D4—24no—
835C2×D4—24no—
836C2×D4—216no—
837C2×D4—24no—
838C2×D4—24no—
839C2×D4—24no—
840C2×D4—24no—
841C2×D4—24no—
842C2×D4—24no—
843C2×D4—24no—
844C2×D4—24no—
845C2×D4—24no—
846C2×D4—24no—
847C2×D4—24no—
848C2×D4—24no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—48no—
852C2×D4—48no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—48no—
856C2×D4—48no—
857C2×D4—48no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—28no—
872C22×C4—22no—
873C22×C4—28no—
874C22×C4—28no—
875C22×C4—28no—
876C22×C4—28no—
877C22×C4—22no—
878C22×C4—28no—
879C22×C4—28no—
880C22×C4—28no—
881C22×C4—22no—
882C22×C4—28no—
883C22×C4—216no—
884C22×C4—44no—
885C22×C4—41no—
886C22×C4—41no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—48no—
890C22×C4—48no—
891C22×C4—48no—
892C22×C4—48no—
893C22×C4—48no—
894C22×C4H(5,𝔽2)14yes—
895C22×C4H(5,𝔽2)14yes—
896C22×C42−1+414yes—
897C22×C4C2511yescharacteristic
898C22×C4C2514yes—
899C22×C4C2514yes—
900C22×C4C2511yescharacteristic
901C22×C4C2511yescharacteristic
902C22×C4C2514yes—
903C22×C4C2514yes—
904C22×C4C2514yes—
905C22×C4C2514yes—
906C22×C4C2514yes—
907C22×C4C2514yes—
908C22×C4C2514yes—
909C22×C4C2511yescharacteristic
910C22×C4C2511yescharacteristic
911C22×C4C2514yes—
912C22×C4C2511yescharacteristic
913C22×C4C2511yescharacteristic
914C22×C4C2511yescharacteristic
915C22×C4C2511yescharacteristic
916C22×C4C2511yescharacteristic
917C22×C4C2511yescharacteristic
918C22×C4C2511yescharacteristic
919C22×C4C2511yescharacteristic
920C22×C4C2511yescharacteristic
921C4⋊C4—24no—
922C4⋊C4—216no—
923C4⋊C4—28no—
924C4⋊C4—28no—
925C4⋊C4—24no—
926C4⋊C4—24no—
927C4⋊C4—24no—
928C4⋊C4—24no—
929C4⋊C4—24no—
930C4⋊C4—28no—
931C4⋊C4—24no—
932C4⋊C4—24no—
933C4⋊C4—28no—
934C4⋊C4—24no—
935C4⋊C4—28no—
936C4⋊C4—24no—
937C4⋊C4—24no—
938C4⋊C4—28no—
939C4⋊C4—28no—
940C4⋊C4—24no—
941C4⋊C4—24no—
942C4⋊C4—24no—
943C4⋊C4—24no—
944C4⋊C4—24no—
945C4⋊C4—24no—
946C4⋊C4—24no—
947C4⋊C4—28no—
948C4⋊C4—42no—
949C4⋊C4—42no—
950C4⋊C4—44no—
951C4⋊C4—44no—
952C4⋊C4—44no—
953C4⋊C4—48no—
954C4⋊C4—44no—
955C4⋊C4—44no—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C4⋊C4—48no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—48no—
962C4⋊C4—48no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—44no—
966C4⋊C4—44no—
967C4⋊C4—48no—
968C4⋊C4—48no—
969C4⋊C4—48no—
970C4⋊C4C2×#4118yes—
971C4⋊C4C2×#4118yes—
972C22⋊C4—28no—
973C22⋊C4—28no—
974C22⋊C4—28no—
975C22⋊C4—28no—
976C22⋊C4—216no—
977C22⋊C4—28no—
978C22⋊C4—28no—
979C22⋊C4—28no—
980C22⋊C4—28no—
981C22⋊C4—28no—
982C22⋊C4—28no—
983C22⋊C4—28no—
984C22⋊C4—28no—
985C22⋊C4—28no—
986C22⋊C4—28no—
987C22⋊C4—48no—
988C22⋊C4—44no—
989C22⋊C4—44no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—48no—
993C22⋊C4—48no—
994C22⋊C4—48no—
995C22⋊C4—48no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—48no—
999C22⋊C4—48no—
1000C22⋊C4—48no—
1001C22⋊C4—48no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C42—22no—
1005C42—22no—
1006C42—22no—
1007C42—22no—
1008C42—22no—
1009C42—22no—
1010C42—22no—
1011C42—22no—
1012C42—22no—
1013C42—22no—
1014C42—22no—
1015C42—22no—
1016C42—22no—
1017C42—22no—
1018C42—28no—
1019C42—28no—
1020C42—28no—
1021C42—28no—
1022C42—22no—
1023C42—22no—
1024C42—22no—
1025C42—22no—
1026C42—22no—
1027C42—22no—
1028C42—22no—
1029C42—22no—
1030C42—22no—
1031C42—41no—
1032C42—41no—
1033C42—44no—
1034C42—44no—
1035C42—48no—
1036C42—48no—
1037C42C2×#4114yes—
1038C42H(5,𝔽2)14yes—
1039C422−1+414yes—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—24no—
1045C23—24no—
1046C23—24no—
1047C23—24no—
1048C23—24no—
1049C23—24no—
1050C23—24no—
1051C23—24no—
1052C23—24no—
1053C23—24no—
1054C23—24no—
1055C23—24no—
1056C23—24no—
1057C23—24no—
1058C23C2×H(5,𝔽2)12yes—
1059C23C2×H(5,𝔽2)12yes—
1060C23C2×2−1+412yes—
1061C23C2611yescharacteristic
1062Q8—216no—
1063Q8—416no—
1064Q8—48no—
1065Q8—84no—
1066Q8—84no—
1067D4—416no—
1068D4—416no—
1069D4—48no—
1070D4—48no—
1071D4—48no—
1072D4—48no—
1073D4—84no—
1074D4—84no—
1075D4—816no—
1076D4—168no—
1077C2×C4—28no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—28no—
1095C2×C4—28no—
1096C2×C4—28no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—44no—
1137C2×C4—44no—
1138C2×C4—416no—
1139C2×C4—44no—
1140C2×C4—416no—
1141C2×C4—416no—
1142C2×C4—816no—
1143C2×C4—88no—
1144C2×C4—168no—
1145C2×C4C22×#4112yes—
1146C2×C4C22×#4118yes—
1147C2×C4C22×#4112yes—
1148C2×C4C22×#4112yes—
1149C2×C4C2×H(5,𝔽2)12yes—
1150C2×C4C2×H(5,𝔽2)12yes—
1151C2×C4C2×H(5,𝔽2)12yes—
1152C2×C4C2×H(5,𝔽2)12yes—
1153C2×C4C2×H(5,𝔽2)12yes—
1154C2×C4C2×H(5,𝔽2)12yes—
1155C2×C4C2×H(5,𝔽2)12yes—
1156C2×C4C2×2−1+412yes—
1157C2×C4C2×2−1+412yes—
1158C2×C4C2×2−1+412yes—
1159C2×C4C2×2−1+412yes—
1160C2×C4C2×2−1+412yes—
1161C2×C4#58512yes—
1162C22—22no—
1163C22—22no—
1164C22—22no—
1165C22—22no—
1166C22—22no—
1167C22—22no—
1168C22—44no—
1169C22—44no—
1170C22—44no—
1171C22—44no—
1172C22—44no—
1173C22—44no—
1174C22—44no—
1175C22—44no—
1176C22—44no—
1177C22—44no—
1178C22—44no—
1179C22—44no—
1180C22—44no—
1181C22—44no—
1182C22#354814yes—
1183C22C23×#4111yescharacteristic
1184C22C22×H(5,𝔽2)11yescharacteristic
1185C22C22×H(5,𝔽2)11yescharacteristic
1186C22C22×H(5,𝔽2)11yescharacteristic
1187C22C22×2−1+411yescharacteristic
1188C22C22×2−1+411yescharacteristic
1189C22C2×#58511yescharacteristic
1190C4—22no—
1191C4—22no—
1192C4—28no—
1193C4—22no—
1194C4—22no—
1195C4—22no—
1196C4—22no—
1197C4—22no—
1198C4—41no—
1199C4—41no—
1200C4—44no—
1201C4—44no—
1202C4—44no—
1203C4—44no—
1204C4—44no—
1205C4—41no—
1206C4—44no—
1207C4—44no—
1208C4—44no—
1209C4—41no—
1210C4—44no—
1211C4#351914yes—
1212C4#352214yes—
1213C4#355214yes—
1214C2—24no—
1215C2—84no—
1216C2—84no—
1217C2C2×#355211yescharacteristic
1218C2C2×#354811yescharacteristic
1219C2C2×#351911yescharacteristic
1220C2C2×#352211yescharacteristic
1221C2#6278811yescharacteristic
1222C2#6283411yescharacteristic
1223C2#6283511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59871C2semidirect
2. #59863C2semidirect
3. #59823C2semidirect
4. #59815C2semidirect
5. #59304C2semidirect
6. #59125C2semidirect
7. #46340C2semidirect
8. #46090C2semidirect
9. #40214C2semidirect
10. #40188C2semidirect
11. #39201C2semidirect
12. #39192C2semidirect
13. #38965C2semidirect
14. #38952C2semidirect
15. #38042C2semidirect
16. #38025C2semidirect
17. #37627C2semidirect
18. #37251C2semidirect
19. #36631C2semidirect
20. #36631C2semidirect
21. #36596C2semidirect
22. #36576C2semidirect
23. #36551C2semidirect
24. #36544C2semidirect
25. #35082C2semidirect
26. #34480C2semidirect
27. C2×C4×C4⋊Q8C2semidirect

Maximal subgroups

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

subgroupindex
#598712
#598632
#598232
#598152
#593042
#591252
#463402
#460902
#402142
#401882
#392012
#391922
#389652
#389522
#380422
#380252
#376272
#372512
#366312
#365962
#365762
#365512
#365442
#350822
#344802
C2×C4×C4⋊Q82