Finite Group Databasebeta

← #7987068

Subgroups — #7987068

Order 512.

4935 conjugacy classes of subgroups.

The subgroup lattice has 1137 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59312C212yesmaximal, complemented
3#59304C212yesmaximal, complemented
4#59213C212yesmaximal, complemented
5#49135C218yesmaximal, complemented
6#46174C214yesmaximal, complemented
7#45071C214yesmaximal, complemented
8#44917C214yesmaximal, complemented
9#42946C214yesmaximal, complemented
10#42775C214yesmaximal, complemented
11#39952C214yesmaximal, complemented
12#39479C212yesmaximal, complemented
13#39157C212yesmaximal, complemented
14#39146C212yesmaximal, complemented
15#38922C212yesmaximal, complemented
16#36301C212yesmaximal, complemented
17#36272C212yesmaximal, complemented
18#36194C211yesmaximal, characteristic, complemented
19#36180C211yesmaximal, characteristic, complemented
20#36180C211yesmaximal, characteristic, complemented
21#35286C212yesmaximal, complemented
22#35202C212yesmaximal, complemented
23#34943C211yesmaximal, characteristic, complemented
24#34932C211yesmaximal, characteristic, complemented
25#34384C212yesmaximal, complemented
26C4×#555C211yesmaximal, characteristic, complemented
27C2×#555C2211yescharacteristic
28C2×#554C2212yes—
29C2×#554C2212yes—
30C2×#553C2214yes—
31C2×#552C2214yes—
32C2×#529C2212yes—
33#2868C2211yescharacteristic
34#2864C2214yes—
35#2859C2214yes—
36#2859C2214yes—
37#2857C2212yes—
38#2857C2212yes—
39#2857C2212yes—
40#2838C2218yes—
41#2806C2214yes—
42#2774C2218yes—
43#2770C2218yes—
44#2762C2218yes—
45#2754C2218yes—
46#2746C2218yes—
47#2723C2218yes—
48#2721C2218yes—
49#2718C2218yes—
50#2715C2218yes—
51#2708C2218yes—
52#2702C2218yes—
53#2698C2218yes—
54#2690C2218yes—
55#2689C2218yes—
56#2681C2218yes—
57#2672C2218yes—
58#2667C2218yes—
59#2663C2218yes—
60#2647C2218yes—
61#2645C2214yes—
62#2624C2214yes—
63#2611C2218yes—
64#2606C2218yes—
65#2584C2214yes—
66#2582C2214yes—
67#2572C2214yes—
68#2571C2212yes—
69#2571C2211yescharacteristic
70#2571C2214yes—
71#2567C2212yes—
72#2567C2212yes—
73#2567C2212yes—
74#2563C2211yescharacteristic
75#2563C2212yes—
76#2563C2211yescharacteristic
77#2562C2214yes—
78#2553C2214yes—
79#2553C2218yes—
80#2552C2212yes—
81#2552C2212yes—
82#2552C2212yes—
83#2552C2212yes—
84#2552C2212yes—
85#2552C2211yescharacteristic
86#2552C2214yes—
87#2552C2212yes—
88#2547C2211yescharacteristic
89#2542C2211yescharacteristic
90#2538C2212yes—
91#2537C2214yes—
92#2537C2211yescharacteristic
93#2537C2211yescharacteristic
94#2527C2218yes—
95#2512C2214yes—
96#2509C2214yes—
97#2507C2214yes—
98#2502C2214yes—
99#2502C2214yes—
100#2501C2214yes—
101#2497C2214yes—
102#2496C2214yes—
103#2496C2214yes—
104#2496C2212yes—
105#2496C2214yes—
106#2495C2212yes—
107#2495C2212yes—
108#2494C2214yes—
109#2494C2214yes—
110#2492C2214yes—
111#2489C2214yes—
112#2489C2212yes—
113#2487C2214yes—
114#2486C2214yes—
115#2485C2214yes—
116#2485C2214yes—
117#2477C2218yes—
118#2468C2218yes—
119#2443C2218yes—
120#2442C2218yes—
121#2442C2214yes—
122#2442C2214yes—
123#2441C2214yes—
124#2441C2214yes—
125#2441C2214yes—
126#2441C2214yes—
127#2440C2214yes—
128#2440C2214yes—
129#2440C2214yes—
130#2440C2214yes—
131#2439C2214yes—
132#2427C2214yes—
133#2427C2212yes—
134#2423C2214yes—
135#2422C2212yes—
136#2422C2214yes—
137#2420C2212yes—
138#2420C2214yes—
139#2420C2212yes—
140#2416C2214yes—
141#2415C2214yes—
142#2415C2218yes—
143#2413C2218yes—
144#2398C2214yes—
145#2395C2214yes—
146#2383C2218yes—
147#2372C2214yes—
148#2369C2212yes—
149#2369C2212yes—
150#2369C2211yescharacteristic
151#2365C2212yes—
152#2363C2212yes—
153#2363C2212yes—
154#2361C2214yes—
155#2360C2214yes—
156#2355C2212yes—
157#2354C2212yes—
158#2354C2211yescharacteristic
159#2354C2211yescharacteristic
160#2352C2214yes—
161Q8×C4⋊C4C2212yes—
162D4×C4⋊C4C2212yes—
163D4×C4⋊C4C2212yes—
164D4×C4⋊C4C2212yes—
165D4×C4⋊C4C2214yes—
166D4×C4⋊C4C2212yes—
167#2346C2212yes—
168#2346C2212yes—
169#2344C2214yes—
170#2330C2214yes—
171#2330C2214yes—
172#2326C2214yes—
173#2322C2218yes—
174#2317C2214yes—
175#2316C2214yes—
176#2314C2214yes—
177C4×C4⋊Q8C2211yescharacteristic
178C4×C4⋊Q8C2211yescharacteristic
179C4×C4⋊Q8C2211yescharacteristic
180C4×#124C2214yes—
181C4×C22⋊Q8C2212yes—
182C4×#121C2212yes—
183C4×#121C2212yes—
184C4×#121C2212yes—
185C4×#121C2212yes—
186C4×#121C2212yes—
187#2293C2214yes—
188#2285C2212yes—
189#2285C2212yes—
190C2×#384C2212yes—
191C2×#384C2212yes—
192#2283C2212yes—
193#2283C2212yes—
194C42×D4C2211yescharacteristic
195C42×D4C2211yescharacteristic
196C42×D4C2211yescharacteristic
197C4×#117C2212yes—
198C4×#117C2212yes—
199#555—28no—
200#554—48no—
201#554—48no—
202#553—416no—
203#552—416no—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210#529—216no—
211C2×#126C2314yes—
212C2×#126C2318yes—
213C2×#126C2318yes—
214C2×#125C2312yes—
215C2×#125C2314yes—
216C2×#125C2314yes—
217C2×#125C2314yes—
218C2×#125C2318yes—
219C2×#124C2312yes—
220C2×#124C2314yes—
221C2×#123C2314yes—
222C2×#123C2318yes—
223C2×#123C2318yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2318yes—
230C2×C22⋊Q8C2318yes—
231C2×#121C2312yes—
232C2×#121C2312yes—
233C2×#121C2312yes—
234C2×#121C2312yes—
235C2×#121C2312yes—
236C2×#121C2312yes—
237C2×#121C2318yes—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2314yes—
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2314yes—
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2314yes—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2314yes—
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2318yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2311yescharacteristic
257C2×#117C2314yes—
258C2×#117C2312yes—
259C2×#117C2312yes—
260C2×#117C2312yes—
261C2×#117C2312yes—
262C2×#117C2318yes—
263C2×#117C2314yes—
264C22×C4⋊C4C2314yes—
265C22×C4⋊C4C2314yes—
266C22×C4⋊C4C2314yes—
267C22×C4⋊C4C2314yes—
268C22×C4⋊C4C2314yes—
269C22×C4⋊C4C2314yes—
270C22×C42C2312yes—
271C22×C42C2312yes—
272C22×C42C2312yes—
273#401C2318yes—
274#400C2318yes—
275#400C2314yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2314yes—
280#400C2318yes—
281#400C2318yes—
282#400C2314yes—
283#399C2318yes—
284#399C2314yes—
285#399C2318yes—
286#399C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2314yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#397C2314yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2314yes—
302#397C2314yes—
303#397C2314yes—
304#397C2314yes—
305#397C2318yes—
306#397C2318yes—
307#396C2318yes—
308#396C2318yes—
309#396C2318yes—
310#395C2318yes—
311#395C2318yes—
312#395C2318yes—
313#394C2318yes—
314#394C2314yes—
315#394C2318yes—
316#394C2314yes—
317#394C2314yes—
318#394C2314yes—
319#394C2318yes—
320#394C2318yes—
321#393C2314yes—
322#393C2314yes—
323#393C2318yes—
324#391C2312yes—
325#391C2312yes—
326#391C2312yes—
327#391C2314yes—
328#391C2314yes—
329#391C2314yes—
330#391C2314yes—
331#391C2318yes—
332#391C2314yes—
333#391C2318yes—
334#391C2312yes—
335#390C2314yes—
336#390C2312yes—
337#390C2312yes—
338#390C2312yes—
339#390C2312yes—
340#390C2314yes—
341#390C2312yes—
342#389C2312yes—
343#389C2312yes—
344#389C2312yes—
345#389C2312yes—
346#389C2312yes—
347#389C2312yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2312yes—
355#389C2314yes—
356#389C2314yes—
357#389C2318yes—
358#389C2314yes—
359#389C2312yes—
360#389C2318yes—
361#389C2318yes—
362#389C2318yes—
363#389C2318yes—
364#389C2318yes—
365#389C2318yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2312yes—
370#389C2314yes—
371#389C2318yes—
372#389C2318yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2312yes—
377#389C2312yes—
378#389C2318yes—
379#389C2312yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2314yes—
384#388C2314yes—
385#388C2314yes—
386#388C2318yes—
387#388C2314yes—
388#388C2314yes—
389#388C2314yes—
390#388C2314yes—
391#388C2314yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2314yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2314yes—
407#387C2318yes—
408#386C2314yes—
409#386C2314yes—
410#386C2318yes—
411#386C2314yes—
412#386C2314yes—
413#386C2318yes—
414#386C2314yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2318yes—
422#385C2318yes—
423#385C2314yes—
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2314yes—
428#384C2314yes—
429#384C2314yes—
430#384C2314yes—
431#384C2312yes—
432#384C2314yes—
433#384C2314yes—
434#384C2314yes—
435#384C2312yes—
436#384C2312yes—
437#384C2314yes—
438#384C2312yes—
439#384C2312yes—
440#384C2312yes—
441#383C2314yes—
442#383C2314yes—
443#382C2312yes—
444#382C2314yes—
445#382C2312yes—
446#382C2312yes—
447#382C2312yes—
448#382C2314yes—
449#382C2318yes—
450#382C2314yes—
451#382C2314yes—
452#381C2314yes—
453#381C2314yes—
454#381C2318yes—
455#380C2312yes—
456#380C2312yes—
457#380C2314yes—
458#380C2314yes—
459#380C2312yes—
460#380C2314yes—
461#380C2312yes—
462#380C2314yes—
463#380C2312yes—
464#380C2312yes—
465#380C2314yes—
466#380C2318yes—
467#380C2318yes—
468#380C2314yes—
469#380C2314yes—
470#380C2312yes—
471#380C2312yes—
472#380C2314yes—
473#380C2314yes—
474#380C2312yes—
475#380C2312yes—
476#380C2312yes—
477#380C2312yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2311yescharacteristic
503C4×C22⋊C4C2312yes—
504C4×C22⋊C4C2312yes—
505C4×C22⋊C4C2318yes—
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2314yes—
520#376C2314yes—
521#376C2314yes—
522#376C2314yes—
523C43C2311yescharacteristic
524C43C2314yes—
525C22×Q8C2412yes—
526C22×Q8C2412yes—
527C22×Q8C2412yes—
528C22×Q8C2414yes—
529C22×D4C2411yescharacteristic
530C22×D4C2414yes—
531C22×D4C2411yescharacteristic
532C22×D4C2411yescharacteristic
533C22×D4C2414yes—
534C22×D4C2414yes—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2418yes—
544C23×C4C2412yes—
545C23×C4C2418yes—
546C4⋊Q8—24no—
547C4⋊Q8—24no—
548C4⋊Q8—24no—
549C4⋊Q8—44no—
550C4⋊Q8—44no—
551C4⋊Q8—44no—
552#126—216no—
553#126—416no—
554#126—416no—
555#125—28no—
556#125—216no—
557#125—416no—
558#125—48no—
559#125—48no—
560#124—28no—
561#124—216no—
562#123—216no—
563#123—416no—
564#123—416no—
565C22⋊Q8—28no—
566C22⋊Q8—28no—
567C22⋊Q8—48no—
568C22⋊Q8—416no—
569C22⋊Q8—416no—
570C22⋊Q8—48no—
571C22⋊Q8—48no—
572#121—28no—
573#121—28no—
574#121—28no—
575#121—28no—
576#121—28no—
577#121—416no—
578#121—44no—
579C4×Q8—28no—
580C4×Q8—44no—
581C4×Q8—44no—
582C4×Q8—48no—
583C4×D4—216no—
584C4×D4—24no—
585C4×D4—216no—
586C4×D4—24no—
587C4×D4—24no—
588C4×D4—24no—
589C4×D4—24no—
590C4×D4—24no—
591C4×D4—24no—
592C4×D4—42no—
593C4×D4—48no—
594C4×D4—48no—
595C4×D4—48no—
596C4×D4—416no—
597C4×D4#4118yes—
598#117—216no—
599#117—28no—
600#117—28no—
601#117—28no—
602#117—416no—
603#117—44no—
604#117—48no—
605C2×C4⋊C4—48no—
606C2×C4⋊C4—48no—
607C2×C4⋊C4—48no—
608C2×C4⋊C4—48no—
609C2×C4⋊C4—48no—
610C2×C4⋊C4—48no—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2418yes—
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2418yes—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2412yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2412yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2412yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2412yes—
695C2×C42—28no—
696C2×C42—28no—
697C2×C42—28no—
698C2×C42C2414yes—
699C2×C42C2414yes—
700C2×C42C2412yes—
701C2×C42C2414yes—
702C2×C42C2414yes—
703C2×C42C2414yes—
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2418yes—
716C2×C42C2418yes—
717C2×C42C2414yes—
718C2×C42C2411yescharacteristic
719C2×C42C2414yes—
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723#95C2412yes—
724#95C2412yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2412yes—
736#95C2412yes—
737#95C2412yes—
738#95C2412yes—
739#95C2412yes—
740#95C2412yes—
741#95C2412yes—
742#95C2414yes—
743#95C2418yes—
744#95C2414yes—
745#95C2414yes—
746#95C2418yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2418yes—
751#95C2414yes—
752#95C2418yes—
753#95C2414yes—
754#95C2414yes—
755#95C2418yes—
756#95C2414yes—
757#95C2414yes—
758#95C2418yes—
759#95C2418yes—
760#95C2414yes—
761#95C2418yes—
762#95C2418yes—
763#95C2418yes—
764#95C2418yes—
765C24C2512yes—
766C24C2512yes—
767C24C2512yes—
768C2×Q8—24no—
769C2×Q8—24no—
770C2×Q8—24no—
771C2×Q8—24no—
772C2×Q8—24no—
773C2×Q8—42no—
774C2×Q8—42no—
775C2×Q8—42no—
776C2×Q8—42no—
777C2×Q8—44no—
778C2×Q8—44no—
779C2×Q8—44no—
780C2×D4—28no—
781C2×D4—28no—
782C2×D4—28no—
783C2×D4—28no—
784C2×D4—22no—
785C2×D4—22no—
786C2×D4—22no—
787C2×D4—22no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—44no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—44no—
796C2×D4C2×#4114yes—
797C2×D4H(5,𝔽2)14yes—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—216no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—42no—
822C22×C4—42no—
823C22×C4—48no—
824C22×C4—48no—
825C22×C4—42no—
826C22×C4—42no—
827C22×C4—48no—
828C22×C4—48no—
829C22×C4—48no—
830C22×C4C2×#4118yes—
831C22×C4C2512yes—
832C22×C4C2512yes—
833C22×C4C2512yes—
834C22×C4C2512yes—
835C22×C4C2514yes—
836C22×C4C2512yes—
837C22×C4C2514yes—
838C22×C4C2514yes—
839C22×C4C2512yes—
840C22×C4C2511yescharacteristic
841C22×C4C2514yes—
842C22×C4C2512yes—
843C22×C4C2518yes—
844C22×C4C2514yes—
845C22×C4C2514yes—
846C22×C4C2512yes—
847C22×C4C2511yescharacteristic
848C22×C4C2512yes—
849C22×C4C2511yescharacteristic
850C22×C4C2511yescharacteristic
851C22×C4C2511yescharacteristic
852C22×C4C2511yescharacteristic
853C22×C4C2511yescharacteristic
854C4⋊C4—22no—
855C4⋊C4—24no—
856C4⋊C4—24no—
857C4⋊C4—28no—
858C4⋊C4—28no—
859C4⋊C4—28no—
860C4⋊C4—24no—
861C4⋊C4—28no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—28no—
865C4⋊C4—28no—
866C4⋊C4—216no—
867C4⋊C4—24no—
868C4⋊C4—216no—
869C4⋊C4—22no—
870C4⋊C4—28no—
871C4⋊C4—22no—
872C4⋊C4—22no—
873C4⋊C4—22no—
874C4⋊C4—22no—
875C4⋊C4—24no—
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—28no—
882C4⋊C4—22no—
883C4⋊C4—42no—
884C4⋊C4—42no—
885C4⋊C4—48no—
886C4⋊C4—48no—
887C4⋊C4—48no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—48no—
891C4⋊C4—48no—
892C4⋊C4—44no—
893C4⋊C4—42no—
894C4⋊C4—48no—
895C4⋊C4—48no—
896C4⋊C4—48no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—48no—
902C4⋊C4—48no—
903C4⋊C4—48no—
904C4⋊C4—44no—
905C4⋊C4C2×#4114yes—
906C4⋊C4H(5,𝔽2)14yes—
907C22⋊C4—28no—
908C22⋊C4—28no—
909C22⋊C4—28no—
910C22⋊C4—28no—
911C22⋊C4—216no—
912C22⋊C4—24no—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—24no—
918C22⋊C4—28no—
919C22⋊C4—28no—
920C22⋊C4—24no—
921C22⋊C4—24no—
922C22⋊C4—24no—
923C22⋊C4—24no—
924C22⋊C4—24no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—48no—
930C22⋊C4—42no—
931C22⋊C4—44no—
932C22⋊C4—48no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—48no—
937C22⋊C4C2×#4118yes—
938C42—24no—
939C42—24no—
940C42—24no—
941C42—28no—
942C42—28no—
943C42—28no—
944C42—28no—
945C42—22no—
946C42—22no—
947C42—28no—
948C42—24no—
949C42—24no—
950C42—24no—
951C42—24no—
952C42—24no—
953C42—24no—
954C42—22no—
955C42—44no—
956C42—41no—
957C42—44no—
958C42—48no—
959C42—48no—
960C42C2×#4114yes—
961C422−1+414yes—
962C422−1+414yes—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23C22×#4114yes—
983C23C2×H(5,𝔽2)14yes—
984C23C2611yescharacteristic
985Q8—48no—
986Q8—84no—
987Q8—84no—
988Q8—164no—
989D4—28no—
990D4—28no—
991D4—416no—
992D4—44no—
993D4—88no—
994D4—88no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—21no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—216no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—22no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—28no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—28no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—21no—
1041C2×C4—22no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—24no—
1045C2×C4—28no—
1046C2×C4—22no—
1047C2×C4—24no—
1048C2×C4—22no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—48no—
1052C2×C4—48no—
1053C2×C4—48no—
1054C2×C4—48no—
1055C2×C4—48no—
1056C2×C4—48no—
1057C2×C4—48no—
1058C2×C4—84no—
1059C2×C4—816no—
1060C2×C4—168no—
1061C2×C4C22×#4112yes—
1062C2×C4C22×#4114yes—
1063C2×C4C22×#4112yes—
1064C2×C4C22×#4112yes—
1065C2×C4C2×H(5,𝔽2)14yes—
1066C2×C4C2×H(5,𝔽2)12yes—
1067C2×C4C2×H(5,𝔽2)12yes—
1068C2×C4C2×2−1+412yes—
1069C2×C4C2×2−1+412yes—
1070C2×C4C2×2−1+412yes—
1071C2×C4C2×2−1+412yes—
1072C2×C4C2×2−1+412yes—
1073C2×C4C2×2−1+412yes—
1074C2×C4#58512yes—
1075C22—24no—
1076C22—24no—
1077C22—24no—
1078C22—24no—
1079C22—24no—
1080C22—24no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22C23×#4111yescharacteristic
1097C22C22×H(5,𝔽2)11yescharacteristic
1098C22C22×H(5,𝔽2)11yescharacteristic
1099C22C22×2−1+411yescharacteristic
1100C22C22×2−1+411yescharacteristic
1101C22C2×#58511yescharacteristic
1102C222−1+611yescharacteristic
1103C4—22no—
1104C4—24no—
1105C4—22no—
1106C4—24no—
1107C4—22no—
1108C4—42no—
1109C4—44no—
1110C4—44no—
1111C4—42no—
1112C4—42no—
1113C4—44no—
1114C4—48no—
1115C4—44no—
1116C4—41no—
1117C4—42no—
1118C4—42no—
1119C4—42no—
1120C4—44no—
1121C4—44no—
1122C4—42no—
1123C4#351114yes—
1124C4#351514yes—
1125C4#354414yes—
1126C2—44no—
1127C2—44no—
1128C2—82no—
1129C2C2×#354411yescharacteristic
1130C2C2×#351511yescharacteristic
1131C2C2×#351111yescharacteristic
1132C2#6291511yescharacteristic
1133C2#6295911yescharacteristic
1134C2#6298511yescharacteristic
1135C2#6301411yescharacteristic
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. #59312C2semidirect
3. #59304C2semidirect
4. #59213C2semidirect
5. #49135C2semidirect
6. #46174C2semidirect
7. #45071C2semidirect
8. #44917C2semidirect
9. #42946C2semidirect
10. #42775C2semidirect
11. #39952C2semidirect
12. #39479C2semidirect
13. #39157C2semidirect
14. #39146C2semidirect
15. #38922C2semidirect
16. #36301C2semidirect
17. #36272C2semidirect
18. #36194C2semidirect
19. #36180C2semidirect
20. #36180C2semidirect
21. #35286C2semidirect
22. #35202C2semidirect
23. #34943C2semidirect
24. #34932C2semidirect
25. #34384C2semidirect
26. C4×#555C2semidirect

Maximal subgroups

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

subgroupindex
#598712
#593122
#593042
#592132
#491352
#461742
#450712
#449172
#429462
#427752
#399522
#394792
#391572
#391462
#389222
#363012
#362722
#361942
#361802
#352862
#352022
#349432
#349322
#343842
C4×#5552