Finite Group Databasebeta

← #7688355

Subgroups — #7688355

Order 512.

5271 conjugacy classes of subgroups.

The subgroup lattice has 1149 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59905C214yesmaximal, complemented
2#59875C211yesmaximal, characteristic, complemented
3#59863C212yesmaximal, complemented
4#59702C214yesmaximal, complemented
5#59647C212yesmaximal, complemented
6#59064C212yesmaximal, complemented
7#44970C214yesmaximal, complemented
8#44191C218yesmaximal, complemented
9#40032C214yesmaximal, complemented
10#39771C212yesmaximal, complemented
11#39248C214yesmaximal, complemented
12#39171C212yesmaximal, complemented
13#36595C211yesmaximal, characteristic, complemented
14#36595C211yesmaximal, characteristic, complemented
15#36591C212yesmaximal, complemented
16#36580C212yesmaximal, complemented
17#36419C212yesmaximal, complemented
18#36302C212yesmaximal, complemented
19#36128C211yesmaximal, characteristic
20#35970C214yesmaximal, complemented
21#34955C212yesmaximal, complemented
22#34951C211yesmaximal, characteristic, complemented
23#34331C212yesmaximal, complemented
24#34330C212yesmaximal, complemented
25C4×#556C211yesmaximal, characteristic, complemented
26C4×D4×Q8C211yesmaximal, characteristic, complemented
27C2×#559C2212yes—
28C2×#559C2212yes—
29C2×#556C2211yescharacteristic
30C2×#550C2212yes—
31C2×D4×Q8C2211yescharacteristic
32C2×#532C2212yes—
33C22×C4×Q8C2212yes—
34#2867C2211yescharacteristic
35#2861C2214yes—
36#2858C2212yes—
37#2858C2212yes—
38#2856C2212yes—
39#2850C2214yes—
40#2810C2214yes—
41#2808C2218yes—
42#2797C2218yes—
43#2796C2218yes—
44#2778C2218yes—
45#2778C2218yes—
46#2756C2218yes—
47#2751C2218yes—
48#2708C2218yes—
49#2696C2218yes—
50#2696C2218yes—
51#2653C2218yes—
52#2640C2214yes—
53#2600C2218yes—
54#2598C2218yes—
55#2595C2218yes—
56#2592C2214yes—
57#2592C2214yes—
58#2592C2214yes—
59#2591C2218yes—
60#2585C2214yes—
61#2582C2211yescharacteristic
62#2580C2214yes—
63#2578C2218yes—
64#2572C2218yes—
65#2568C2212yes—
66#2568C2212yes—
67#2568C2211yescharacteristic
68#2568C2212yes—
69#2563C2214yes—
70#2559C2218yes—
71#2559C2218yes—
72#2552C2211yescharacteristic
73#2548C2212yes—
74#2548C2212yes—
75#2548C2212yes—
76#2548C2212yes—
77#2548C2212yes—
78#2548C2212yes—
79#2548C2212yes—
80#2547C2214yes—
81#2546C2211yescharacteristic
82#2544C2214yes—
83#2544C2214yes—
84#2544C2214yes—
85#2544C2214yes—
86#2541C2212yes—
87#2541C2212yes—
88#2531C2218yes—
89#2516C2218yes—
90#2514C2214yes—
91#2514C2214yes—
92#2514C2214yes—
93#2513C2214yes—
94#2513C2214yes—
95#2513C2214yes—
96#2511C2212yes—
97#2510C2218yes—
98#2509C2212yes—
99#2504C2214yes—
100#2500C2214yes—
101#2490C2214yes—
102#2485C2218yes—
103#2476C2218yes—
104#2458C2218yes—
105#2453C2212yes—
106#2448C2214yes—
107#2448C2214yes—
108#2447C2214yes—
109#2447C2214yes—
110#2447C2214yes—
111#2446C2212yes—
112#2445C2214yes—
113#2445C2214yes—
114#2445C2214yes—
115#2445C2214yes—
116#2443C2218yes—
117#2436C2214yes—
118#2436C2214yes—
119#2432C2214yes—
120#2431C2214yes—
121#2428C2214yes—
122#2428C2214yes—
123#2427C2214yes—
124#2427C2214yes—
125#2420C2214yes—
126#2419C2218yes—
127#2402C2214yes—
128#2398C2218yes—
129#2373C2214yes—
130#2367C2214yes—
131#2367C2214yes—
132#2367C2214yes—
133#2367C2212yes—
134#2366C2212yes—
135#2366C2212yes—
136#2366C2214yes—
137#2366C2212yes—
138#2366C2212yes—
139#2366C2212yes—
140#2366C2212yes—
141#2365C2211yescharacteristic
142#2365C2212yes—
143#2365C2211yescharacteristic
144#2364C2218yes—
145#2363C2214yes—
146#2362C2212yes—
147#2361C2214yes—
148#2360C2212yes—
149#2360C2214yes—
150#2359C2218yes—
151#2357C2214yes—
152#2356C2212yes—
153#2355C2212yes—
154#2355C2212yes—
155#2355C2211yescharacteristic
156#2355C2212yes—
157#2354C2214yes—
158#2354C2211yescharacteristic
159#2354C2214yes—
160Q8×C4⋊C4C2211yescharacteristic
161#2349C2214yes—
162D4×C4⋊C4C2212yes—
163D4×C4⋊C4C2211yescharacteristic
164#2347C2212yes—
165Q8×C22⋊C4C2212yes—
166#2339C2214yes—
167#2335C2218yes—
168#2333C2218yes—
169#2328C2214yes—
170#2326C2214yes—
171C4×C4⋊Q8C2211yescharacteristic
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2211yescharacteristic
175C4×C4⋊Q8C2211yescharacteristic
176C4×#127C2212yes—
177C4×#127C2212yes—
178C4×#125C2212yes—
179C4×#126C2214yes—
180C4×#124C2212yes—
181C4×#124C2214yes—
182C4×#124C2214yes—
183C4×C22⋊Q8C2214yes—
184C4×C22⋊Q8C2212yes—
185C4×C22⋊Q8C2212yes—
186C4×#121C2214yes—
187#2297C2214yes—
188#2297C2214yes—
189#2295C2212yes—
190#2295C2212yes—
191#2293C2214yes—
192#2275C2214yes—
193C42×Q8C2212yes—
194C42×Q8C2211yescharacteristic
195C42×Q8C2211yescharacteristic
196C42×D4C2212yes—
197C42×D4C2211yescharacteristic
198C4×#117C2212yes—
199C22×#41C2314yes—
200C23×Q8C2312yes—
201#559—216no—
202#559—48no—
203#556—28no—
204#550—216no—
205D4×Q8—28no—
206#532—48no—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2312yes—
212C2×#127C2312yes—
213C2×#127C2312yes—
214C2×#127C2314yes—
215C2×#127C2312yes—
216C2×#127C2312yes—
217C2×#127C2312yes—
218C2×#127C2312yes—
219C2×#127C2312yes—
220C2×#126C2314yes—
221C2×#125C2312yes—
222C2×#124C2314yes—
223C2×#124C2314yes—
224C2×#124C2312yes—
225C2×#124C2314yes—
226C2×#124C2314yes—
227C2×#124C2314yes—
228C2×#124C2314yes—
229C2×#124C2314yes—
230C2×#123C2318yes—
231C2×#123C2318yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2314yes—
235C2×#121C2318yes—
236C2×#121C2314yes—
237C2×#121C2314yes—
238C2×#121C2314yes—
239C2×#121C2314yes—
240C2×#121C2314yes—
241C2×C4×Q8—48no—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2314yes—
254C2×C4×Q8C2312yes—
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×D4C2314yes—
258C2×C4×D4C2312yes—
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2314yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2312yes—
267C2×C4×D4C2311yescharacteristic
268C2×C4×D4C2314yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2318yes—
273C2×C4×D4C2311yescharacteristic
274C2×#117C2312yes—
275C2×#117C2312yes—
276C2×#117C2318yes—
277C22×C4⋊C4C2314yes—
278C22×C4⋊C4C2312yes—
279C22×C42C2312yes—
280C22×C42C2314yes—
281#401C2318yes—
282#400C2314yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#399C2318yes—
290#398C2314yes—
291#398C2314yes—
292#398C2314yes—
293#398C2314yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2318yes—
303#394C2318yes—
304#394C2318yes—
305#394C2318yes—
306#394C2318yes—
307#394C2318yes—
308#394C2318yes—
309#394C2318yes—
310#394C2318yes—
311#394C2318yes—
312#394C2318yes—
313#394C2318yes—
314#393C2318yes—
315#393C2318yes—
316#393C2318yes—
317#393C2318yes—
318#392C2318yes—
319#392C2318yes—
320#391C2312yes—
321#391C2312yes—
322#391C2314yes—
323#391C2312yes—
324#391C2312yes—
325#391C2312yes—
326#391C2314yes—
327#391C2314yes—
328#391C2314yes—
329#391C2314yes—
330#391C2312yes—
331#391C2314yes—
332#391C2314yes—
333#391C2312yes—
334#391C2314yes—
335#391C2312yes—
336#391C2312yes—
337#391C2312yes—
338#391C2312yes—
339#391C2312yes—
340#390C2314yes—
341#390C2314yes—
342#390C2314yes—
343#390C2314yes—
344#390C2314yes—
345#390C2314yes—
346#390C2314yes—
347#390C2314yes—
348#390C2314yes—
349#390C2314yes—
350#390C2314yes—
351#390C2312yes—
352#390C2314yes—
353#390C2318yes—
354#390C2314yes—
355#390C2314yes—
356#390C2314yes—
357#390C2314yes—
358#390C2314yes—
359#390C2314yes—
360#390C2314yes—
361#390C2314yes—
362#390C2314yes—
363#390C2314yes—
364#390C2314yes—
365#389C2312yes—
366#389C2312yes—
367#389C2312yes—
368#389C2314yes—
369#389C2314yes—
370#389C2312yes—
371#389C2312yes—
372#389C2312yes—
373#389C2312yes—
374#389C2312yes—
375#389C2314yes—
376#389C2312yes—
377#389C2312yes—
378#389C2312yes—
379#389C2312yes—
380#389C2314yes—
381#389C2312yes—
382#389C2312yes—
383#389C2312yes—
384#389C2312yes—
385#388C2314yes—
386#388C2314yes—
387#388C2314yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2314yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2314yes—
406#387C2314yes—
407#387C2314yes—
408#387C2314yes—
409#387C2314yes—
410#387C2314yes—
411#387C2314yes—
412#387C2314yes—
413#387C2314yes—
414#387C2314yes—
415#387C2314yes—
416#387C2318yes—
417#387C2318yes—
418#387C2314yes—
419#387C2318yes—
420#387C2314yes—
421#387C2314yes—
422#386C2318yes—
423#386C2318yes—
424#386C2318yes—
425#386C2318yes—
426#386C2318yes—
427#386C2318yes—
428#386C2318yes—
429#386C2318yes—
430#386C2318yes—
431#386C2318yes—
432#386C2318yes—
433#386C2318yes—
434#386C2318yes—
435#386C2318yes—
436#386C2318yes—
437#386C2318yes—
438#385C2318yes—
439#385C2318yes—
440#385C2318yes—
441#385C2318yes—
442#385C2318yes—
443#385C2314yes—
444#385C2314yes—
445#385C2314yes—
446#385C2314yes—
447#384C2311yescharacteristic
448#384C2311yescharacteristic
449#384C2312yes—
450#384C2311yescharacteristic
451#384C2312yes—
452#383C2314yes—
453#383C2318yes—
454#382C2312yes—
455#382C2312yes—
456#382C2314yes—
457#382C2314yes—
458#382C2314yes—
459#381C2318yes—
460#381C2318yes—
461#380C2318yes—
462#380C2318yes—
463#380C2318yes—
464#380C2312yes—
465#380C2312yes—
466#380C2314yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2311yescharacteristic
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2312yes—
504C4×C22⋊C4C2312yes—
505C4×C22⋊C4C2314yes—
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2318yes—
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2318yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2318yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2318yes—
519#376C2314yes—
520#376C2314yes—
521C2×#95C2318yes—
522C43C2314yes—
523C43C2312yes—
524C43C2312yes—
525C43C2311yescharacteristic
526C2×#41—216no—
527C2×#41—48no—
528C2×#41—48no—
529C22×Q8—28no—
530C22×Q8—44no—
531C22×Q8—44no—
532C22×Q8C2411yescharacteristic
533C22×Q8C2412yes—
534C22×Q8C2412yes—
535C22×Q8C2412yes—
536C22×Q8C2411yescharacteristic
537C22×Q8C2414yes—
538C22×D4C2414yes—
539C22×D4C2414yes—
540C22×D4C2414yes—
541C22×D4C2411yescharacteristic
542C22×D4C2418yes—
543C22×D4C2414yes—
544C22×D4C2414yes—
545C22×D4C2414yes—
546C22×D4C2418yes—
547C22×D4C2414yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2412yes—
551C23×C4C2414yes—
552C23×C4C2418yes—
553C23×C4C2418yes—
554C23×C4C2414yes—
555C23×C4C2418yes—
556C4⋊Q8—28no—
557C4⋊Q8—24no—
558C4⋊Q8—24no—
559C4⋊Q8—24no—
560C4⋊Q8—44no—
561#127—216no—
562#127—28no—
563#127—28no—
564#127—28no—
565#127—44no—
566#127—44no—
567#127—44no—
568#127—82no—
569#126—216no—
570#125—44no—
571#124—216no—
572#124—28no—
573#124—216no—
574#124—48no—
575#124—48no—
576#124—48no—
577#124—48no—
578#124—48no—
579#123—232no—
580#123—416no—
581C22⋊Q8—28no—
582C22⋊Q8—28no—
583C22⋊Q8—216no—
584#121—216no—
585#121—232no—
586#121—48no—
587#121—48no—
588#121—48no—
589#121—84no—
590C4×Q8—28no—
591C4×Q8—28no—
592C4×Q8—24no—
593C4×Q8—28no—
594C4×Q8—24no—
595C4×Q8—28no—
596C4×Q8—24no—
597C4×Q8—48no—
598C4×Q8—48no—
599C4×Q8—44no—
600C4×Q8—44no—
601C4×Q8—44no—
602C4×Q8—42no—
603C4×Q8—42no—
604C4×Q8#4118yescomplemented
605C4×D4—216no—
606C4×D4—216no—
607C4×D4—28no—
608C4×D4—24no—
609C4×D4—216no—
610C4×D4—48no—
611C4×D4—48no—
612C4×D4—44no—
613C4×D4—42no—
614C4×D4—48no—
615C4×D4—48no—
616C4×D4—48no—
617C4×D4—48no—
618C4×D4—88no—
619C4×D4—84no—
620C4×D4—84no—
621C4×D4#4118yes—
622#117—28no—
623#117—44no—
624#117—88no—
625C2×C4⋊C4—44no—
626C2×C4⋊C4—48no—
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2412yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2412yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2412yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2412yes—
701C2×C42—28no—
702C2×C42—48no—
703C2×C42C2414yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2412yes—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2414yes—
710C2×C42C2414yes—
711C2×C42C2414yes—
712C2×C42C2412yes—
713C2×C42C2411yescharacteristic
714C2×C42C2412yes—
715C2×C42C2412yes—
716C2×C42C2412yes—
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2412yes—
720C2×C42C2414yes—
721C2×C42C2418yes—
722C2×C42C2414yes—
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2414yes—
726C2×C42C2414yes—
727C2×C42C2412yes—
728C2×C42C2414yes—
729C2×C42C2412yes—
730C2×C42C2411yescharacteristic
731C2×C42C2412yes—
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2418yes—
739#95C2412yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2412yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2412yes—
751#95C2414yes—
752#95C2414yes—
753#95C2412yes—
754#95C2414yes—
755#95C2418yes—
756#95C2414yes—
757#95C2418yes—
758#95C2418yes—
759#95C2414yes—
760#95C2412yes—
761#95C2412yes—
762#95C2412yes—
763#95C2412yes—
764#95C2412yes—
765#95C2414yes—
766#95C2418yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2418yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2418yes—
777C24C2518yes—
778C24C2512yes—
779#41—832no—
780C2×Q8—22no—
781C2×Q8—24no—
782C2×Q8—24no—
783C2×Q8—24no—
784C2×Q8—28no—
785C2×Q8—24no—
786C2×Q8—22no—
787C2×Q8—24no—
788C2×Q8—22no—
789C2×Q8—24no—
790C2×Q8—22no—
791C2×Q8—24no—
792C2×Q8—22no—
793C2×Q8—24no—
794C2×Q8—24no—
795C2×Q8—44no—
796C2×Q8—44no—
797C2×Q8—432no—
798C2×Q8C2×#4114yes—
799C2×D4—216no—
800C2×D4—216no—
801C2×D4—22no—
802C2×D4—28no—
803C2×D4—28no—
804C2×D4—28no—
805C2×D4—28no—
806C2×D4—28no—
807C2×D4—28no—
808C2×D4—28no—
809C2×D4—28no—
810C2×D4—28no—
811C2×D4—22no—
812C2×D4—28no—
813C2×D4—28no—
814C2×D4—28no—
815C2×D4—48no—
816C2×D4—44no—
817C2×D4—44no—
818C2×D4—48no—
819C2×D4—48no—
820C2×D4—44no—
821C2×D4—44no—
822C2×D4—44no—
823C2×D4—44no—
824C2×D4—48no—
825C2×D4—44no—
826C2×D4—44no—
827C2×D4—44no—
828C2×D4C2×#4114yes—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—28no—
832C22×C4—24no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—216no—
836C22×C4—216no—
837C22×C4—24no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—48no—
842C22×C4—48no—
843C22×C4—48no—
844C22×C4—42no—
845C22×C4—44no—
846C22×C4—44no—
847C22×C4—42no—
848C22×C4—48no—
849C22×C4—48no—
850C22×C4—48no—
851C22×C4—48no—
852C22×C4C2×#4118yes—
853C22×C4C2511yescharacteristic
854C22×C4C2514yes—
855C22×C4C2514yes—
856C22×C4C2514yes—
857C22×C4C2514yes—
858C22×C4C2512yes—
859C22×C4C2512yes—
860C22×C4C2514yes—
861C22×C4C2512yes—
862C22×C4C2514yes—
863C22×C4C2512yes—
864C22×C4C2512yes—
865C22×C4C2512yes—
866C22×C4C2512yes—
867C22×C4C2512yes—
868C22×C4C2512yes—
869C22×C4C2511yescharacteristic
870C22×C4C2511yescharacteristic
871C22×C4C2512yes—
872C22×C4C2512yes—
873C22×C4C2511yescharacteristic
874C22×C4C2511yescharacteristic
875C22×C4C2511yescharacteristic
876C22×C4C2511yescharacteristic
877C4⋊C4—22no—
878C4⋊C4—24no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—22no—
882C4⋊C4—24no—
883C4⋊C4—28no—
884C4⋊C4—28no—
885C4⋊C4—28no—
886C4⋊C4—24no—
887C4⋊C4—28no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—24no—
891C4⋊C4—22no—
892C4⋊C4—24no—
893C4⋊C4—28no—
894C4⋊C4—22no—
895C4⋊C4—24no—
896C4⋊C4—24no—
897C4⋊C4—24no—
898C4⋊C4—22no—
899C4⋊C4—24no—
900C4⋊C4—24no—
901C4⋊C4—22no—
902C4⋊C4—22no—
903C4⋊C4—24no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—42no—
910C4⋊C4—42no—
911C4⋊C4—44no—
912C4⋊C4—42no—
913C4⋊C4—44no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4C2×#4114yes—
921C4⋊C4C2×#4114yes—
922C4⋊C4C2×#4118yes—
923C22⋊C4—28no—
924C22⋊C4—28no—
925C22⋊C4—216no—
926C22⋊C4—28no—
927C22⋊C4—24no—
928C22⋊C4—216no—
929C22⋊C4—216no—
930C22⋊C4—216no—
931C22⋊C4—44no—
932C22⋊C4—48no—
933C22⋊C4—48no—
934C22⋊C4—48no—
935C22⋊C4—44no—
936C22⋊C4—48no—
937C22⋊C4—42no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—48no—
941C22⋊C4—48no—
942C22⋊C4—48no—
943C22⋊C4—44no—
944C22⋊C4—48no—
945C22⋊C4—48no—
946C22⋊C4—48no—
947C22⋊C4—48no—
948C22⋊C4—48no—
949C22⋊C4—48no—
950C22⋊C4C2×#4118yes—
951C42—28no—
952C42—28no—
953C42—28no—
954C42—24no—
955C42—24no—
956C42—24no—
957C42—24no—
958C42—24no—
959C42—28no—
960C42—24no—
961C42—24no—
962C42—24no—
963C42—24no—
964C42—22no—
965C42—22no—
966C42—22no—
967C42—24no—
968C42—44no—
969C42—44no—
970C42—44no—
971C42—44no—
972C42—48no—
973C42—42no—
974C42—42no—
975C42—42no—
976C42—42no—
977C42—44no—
978C42—41no—
979C42C2×#4118yes—
980C42C2×#4114yes—
981C42C2×#4114yes—
982C42H(5,𝔽2)14yes—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—28no—
990C23—28no—
991C23—28no—
992C23—28no—
993C23—28no—
994C23—28no—
995C23—28no—
996C23C22×#4114yes—
997C23C2611yescharacteristic
998Q8—28no—
999Q8—416no—
1000Q8—48no—
1001Q8—48no—
1002Q8—44no—
1003Q8—48no—
1004D4—28no—
1005D4—416no—
1006D4—416no—
1007D4—416no—
1008D4—88no—
1009D4—88no—
1010D4—88no—
1011D4—816no—
1012D4—816no—
1013D4—164no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—22no—
1019C2×C4—21no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—22no—
1025C2×C4—21no—
1026C2×C4—216no—
1027C2×C4—22no—
1028C2×C4—24no—
1029C2×C4—22no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—22no—
1035C2×C4—24no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—24no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—21no—
1051C2×C4—22no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—22no—
1066C2×C4—24no—
1067C2×C4—22no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—416no—
1073C2×C4—48no—
1074C2×C4—816no—
1075C2×C4—84no—
1076C2×C4—816no—
1077C2×C4—88no—
1078C2×C4—168no—
1079C2×C4C22×#4114yes—
1080C2×C4C22×#4114yes—
1081C2×C4C22×#4114yes—
1082C2×C4C22×#4112yes—
1083C2×C4C22×#4112yes—
1084C2×C4C22×#4112yes—
1085C2×C4C22×#4112yes—
1086C2×C4C22×#4112yes—
1087C2×C4C22×#4112yes—
1088C2×C4C2×H(5,𝔽2)12yes—
1089C2×C4C2×H(5,𝔽2)12yes—
1090C2×C4C2×H(5,𝔽2)12yes—
1091C2×C4#58512yes—
1092C2×C4#58512yes—
1093C2×C4#58512yes—
1094C22—24no—
1095C22—24no—
1096C22—24no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—48no—
1102C22—48no—
1103C22—48no—
1104C22—48no—
1105C22—48no—
1106C22—48no—
1107C22—48no—
1108C22C23×#4111yescharacteristic
1109C22C23×#4111yescharacteristic
1110C22C22×H(5,𝔽2)11yescharacteristic
1111C22C2×#58511yescharacteristic
1112C22C2×#58511yescharacteristic
1113C22C2×#58511yescharacteristic
1114C22H(7,𝔽2)11yescharacteristic
1115C4—24no—
1116C4—22no—
1117C4—22no—
1118C4—24no—
1119C4—24no—
1120C4—22no—
1121C4—42no—
1122C4—44no—
1123C4—44no—
1124C4—42no—
1125C4—44no—
1126C4—44no—
1127C4—42no—
1128C4—42no—
1129C4—42no—
1130C4—41no—
1131C4—42no—
1132C4—42no—
1133C4—44no—
1134C4—42no—
1135C4—44no—
1136C4#348014yes—
1137C4#350614yes—
1138C4#351414yes—
1139C2—44no—
1140C2—88no—
1141C2C2×#348011yescharacteristic
1142C2C2×#350611yescharacteristic
1143C2C2×#351411yescharacteristic
1144C2#6295511yescharacteristic
1145C2#6301011yescharacteristic
1146C2#6301011yescharacteristic
1147C2#6303611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36128C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59905C2semidirect
2. #59875C2semidirect
3. #59863C2semidirect
4. #59702C2semidirect
5. #59647C2semidirect
6. #59064C2semidirect
7. #44970C2semidirect
8. #44191C2semidirect
9. #40032C2semidirect
10. #39771C2semidirect
11. #39248C2semidirect
12. #39171C2semidirect
13. #36595C2semidirect
14. #36595C2semidirect
15. #36591C2semidirect
16. #36580C2semidirect
17. #36419C2semidirect
18. #36302C2semidirect
20. #35970C2semidirect
21. #34955C2semidirect
22. #34951C2semidirect
23. #34331C2semidirect
24. #34330C2semidirect
25. C4×#556C2semidirect
26. C4×D4×Q8C2semidirect
604. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#599052
#598752
#598632
#597022
#596472
#590642
#449702
#441912
#400322
#397712
#392482
#391712
#365952
#365912
#365802
#364192
#363022
#361282
#359702
#349552
#349512
#343312
#343302
C4×#5562
C4×D4×Q82