Finite Group Databasebeta

← #7986690

Subgroups — #7986690

Order 512.

5191 conjugacy classes of subgroups.

The subgroup lattice has 1151 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59870C211yesmaximal, characteristic, complemented
2#59863C212yesmaximal, complemented
3#59465C212yesmaximal, complemented
4#59064C212yesmaximal, complemented
5#49241C218yesmaximal, complemented
6#45594C214yesmaximal, complemented
7#45007C214yesmaximal, complemented
8#44995C214yesmaximal, complemented
9#42612C214yesmaximal, complemented
10#42519C214yesmaximal, complemented
11#39857C214yesmaximal, complemented
12#39726C212yesmaximal, complemented
13#38987C212yesmaximal, complemented
14#38985C212yesmaximal, complemented
15#38952C212yesmaximal, complemented
16#36595C211yesmaximal, characteristic, complemented
17#36595C211yesmaximal, characteristic, complemented
18#36128C211yesmaximal, characteristic
19#36117C212yesmaximal, complemented
20#36115C212yesmaximal, complemented
21#35197C212yesmaximal, complemented
22#35180C212yesmaximal, complemented
23#34951C211yesmaximal, characteristic, complemented
24#34929C211yesmaximal, characteristic, complemented
25#34494C212yesmaximal, complemented
26C4×#554C211yesmaximal, characteristic, complemented
27C2×#559C2212yes—
28C2×#559C2212yes—
29C2×#554C2211yescharacteristic
30C2×#550C2212yes—
31C2×#533C2212yes—
32C2×#532C2212yes—
33C2×#529C2214yes—
34#2867C2211yescharacteristic
35#2858C2212yes—
36#2858C2212yes—
37#2856C2212yes—
38#2854C2214yes—
39#2850C2214yes—
40#2850C2214yes—
41#2824C2218yes—
42#2808C2218yes—
43#2805C2214yes—
44#2786C2218yes—
45#2784C2218yes—
46#2779C2218yes—
47#2743C2218yes—
48#2740C2218yes—
49#2715C2218yes—
50#2708C2218yes—
51#2707C2218yes—
52#2700C2218yes—
53#2696C2218yes—
54#2695C2218yes—
55#2693C2218yes—
56#2681C2218yes—
57#2672C2218yes—
58#2672C2218yes—
59#2648C2218yes—
60#2644C2214yes—
61#2639C2218yes—
62#2630C2218yes—
63#2620C2214yes—
64#2592C2214yes—
65#2592C2214yes—
66#2592C2214yes—
67#2585C2214yes—
68#2582C2211yescharacteristic
69#2581C2214yes—
70#2571C2212yes—
71#2568C2211yescharacteristic
72#2568C2212yes—
73#2567C2212yes—
74#2564C2218yes—
75#2563C2214yes—
76#2563C2214yes—
77#2562C2218yes—
78#2556C2214yes—
79#2552C2211yescharacteristic
80#2551C2211yescharacteristic
81#2548C2212yes—
82#2548C2212yes—
83#2548C2212yes—
84#2548C2212yes—
85#2548C2212yes—
86#2548C2212yes—
87#2548C2212yes—
88#2547C2214yes—
89#2547C2214yes—
90#2546C2211yescharacteristic
91#2546C2211yescharacteristic
92#2545C2214yes—
93#2544C2214yes—
94#2544C2214yes—
95#2542C2211yescharacteristic
96#2541C2212yes—
97#2541C2212yes—
98#2538C2214yes—
99#2538C2211yescharacteristic
100#2513C2214yes—
101#2513C2214yes—
102#2512C2214yes—
103#2512C2214yes—
104#2511C2214yes—
105#2511C2212yes—
106#2509C2212yes—
107#2509C2214yes—
108#2506C2212yes—
109#2501C2214yes—
110#2498C2218yes—
111#2492C2212yes—
112#2485C2218yes—
113#2479C2218yes—
114#2471C2218yes—
115#2467C2218yes—
116#2457C2218yes—
117#2454C2214yes—
118#2454C2214yes—
119#2454C2214yes—
120#2453C2212yes—
121#2452C2214yes—
122#2452C2214yes—
123#2452C2212yes—
124#2448C2214yes—
125#2447C2214yes—
126#2447C2214yes—
127#2446C2212yes—
128#2445C2214yes—
129#2445C2214yes—
130#2445C2214yes—
131#2445C2214yes—
132#2445C2214yes—
133#2445C2214yes—
134#2432C2214yes—
135#2431C2214yes—
136#2429C2212yes—
137#2428C2214yes—
138#2428C2214yes—
139#2427C2214yes—
140#2427C2214yes—
141#2426C2214yes—
142#2425C2218yes—
143#2420C2214yes—
144#2419C2218yes—
145#2402C2214yes—
146#2396C2214yes—
147#2377C2218yes—
148#2370C2212yes—
149#2369C2211yescharacteristic
150#2368C2214yes—
151#2366C2212yes—
152#2366C2214yes—
153#2366C2212yes—
154#2366C2212yes—
155#2366C2212yes—
156#2366C2212yes—
157#2366C2212yes—
158#2365C2212yes—
159#2361C2214yes—
160#2360C2212yes—
161#2355C2211yescharacteristic
162#2355C2212yes—
163#2354C2214yes—
164#2354C2214yes—
165Q8×C4⋊C4C2212yes—
166#2349C2214yes—
167#2349C2214yes—
168#2349C2212yes—
169D4×C4⋊C4C2211yescharacteristic
170#2345C2212yes—
171#2339C2214yes—
172#2328C2214yes—
173#2325C2218yes—
174#2324C2214yes—
175#2319C2214yes—
176#2319C2214yes—
177#2311C2214yes—
178#2311C2214yes—
179C4×C4⋊Q8C2211yescharacteristic
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2212yes—
182C4×C4⋊Q8C2211yescharacteristic
183C4×C4⋊Q8C2211yescharacteristic
184C4×#127C2212yes—
185C4×#127C2212yes—
186C4×#125C2212yes—
187C4×#125C2212yes—
188C4×C22⋊Q8C2212yes—
189C4×C22⋊Q8C2214yes—
190C4×C22⋊Q8C2212yes—
191#2295C2212yes—
192#2295C2212yes—
193#2293C2212yes—
194C42×Q8C2211yescharacteristic
195C42×Q8C2211yescharacteristic
196C42×D4C2212yes—
197C42×D4C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2314yes—
200#559—48no—
201#559—48no—
202#554—28no—
203#550—216no—
204#533—48no—
205#532—48no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×#127C2312yes—
214C2×#127C2312yes—
215C2×#127C2314yes—
216C2×#127C2312yes—
217C2×#127C2312yes—
218C2×#127C2312yes—
219C2×#127C2312yes—
220C2×#127C2312yes—
221#529—416no—
222C2×#126C2318yes—
223C2×#125C2312yes—
224C2×#125C2312yes—
225C2×#125C2314yes—
226C2×#124C2314yes—
227C2×#124C2314yes—
228C2×#124C2314yes—
229C2×#124C2314yes—
230C2×#124C2314yes—
231C2×#124C2314yes—
232C2×#124C2314yes—
233C2×#123C2318yes—
234C2×#123C2318yes—
235C2×#123C2318yes—
236C2×#123C2318yes—
237C2×C22⋊Q8C2312yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2312yes—
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2318yes—
244C2×#121C2314yes—
245C2×#121C2318yes—
246C2×#121C2314yes—
247C2×#121C2314yes—
248C2×#121C2314yes—
249C2×#121C2314yes—
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2314yes—
259C2×C4×Q8C2314yes—
260C2×C4×Q8C2311yescharacteristic
261C2×C4×D4C2314yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2312yes—
264C2×C4×D4C2311yescharacteristic
265C2×C4×D4C2314yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2318yes—
274C2×C4×D4C2312yes—
275C2×C4×D4C2311yescharacteristic
276C2×C4×D4C2314yes—
277C2×C4×D4C2311yescharacteristic
278C2×#117C2314yes—
279C2×#117C2318yes—
280C22×C4⋊C4C2312yes—
281C22×C4⋊C4C2312yes—
282C22×C42C2312yes—
283C22×C42C2314yes—
284#400C2314yes—
285#400C2318yes—
286#400C2318yes—
287#400C2314yes—
288#400C2318yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#399C2318yes—
293#399C2314yes—
294#399C2318yes—
295#398C2314yes—
296#398C2314yes—
297#398C2314yes—
298#398C2314yes—
299#398C2314yes—
300#398C2314yes—
301#397C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2318yes—
308#397C2318yes—
309#396C2318yes—
310#396C2318yes—
311#396C2314yes—
312#396C2318yes—
313#396C2318yes—
314#396C2314yes—
315#396C2318yes—
316#395C2314yes—
317#395C2318yes—
318#394C2318yes—
319#394C2318yes—
320#394C2318yes—
321#394C2318yes—
322#394C2318yes—
323#394C2318yes—
324#394C2318yes—
325#394C2318yes—
326#394C2318yes—
327#394C2318yes—
328#394C2318yes—
329#393C2318yes—
330#393C2318yes—
331#393C2318yes—
332#393C2314yes—
333#392C2318yes—
334#392C2318yes—
335#391C2312yes—
336#391C2312yes—
337#391C2312yes—
338#391C2312yes—
339#391C2312yes—
340#391C2314yes—
341#391C2312yes—
342#391C2314yes—
343#391C2314yes—
344#391C2314yes—
345#391C2312yes—
346#391C2312yes—
347#391C2312yes—
348#391C2312yes—
349#391C2314yes—
350#391C2312yes—
351#390C2314yes—
352#390C2314yes—
353#390C2314yes—
354#390C2314yes—
355#390C2314yes—
356#390C2314yes—
357#390C2314yes—
358#390C2314yes—
359#390C2314yes—
360#390C2314yes—
361#390C2314yes—
362#390C2314yes—
363#390C2314yes—
364#390C2314yes—
365#390C2318yes—
366#390C2312yes—
367#390C2314yes—
368#390C2314yes—
369#390C2314yes—
370#390C2314yes—
371#390C2314yes—
372#390C2314yes—
373#390C2314yes—
374#390C2314yes—
375#390C2314yes—
376#390C2312yes—
377#389C2312yes—
378#389C2312yes—
379#389C2312yes—
380#389C2312yes—
381#389C2312yes—
382#389C2312yes—
383#389C2312yes—
384#389C2314yes—
385#389C2314yes—
386#389C2312yes—
387#389C2312yes—
388#389C2312yes—
389#389C2314yes—
390#389C2312yes—
391#389C2312yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2312yes—
396#389C2312yes—
397#389C2312yes—
398#389C2312yes—
399#389C2312yes—
400#389C2312yes—
401#389C2318yes—
402#389C2314yes—
403#389C2312yes—
404#389C2312yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2314yes—
413#388C2318yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2314yes—
418#387C2314yes—
419#387C2314yes—
420#387C2314yes—
421#387C2314yes—
422#387C2314yes—
423#387C2318yes—
424#387C2318yes—
425#387C2314yes—
426#387C2314yes—
427#387C2314yes—
428#387C2314yes—
429#387C2314yes—
430#387C2318yes—
431#387C2314yes—
432#387C2314yes—
433#386C2318yes—
434#386C2318yes—
435#386C2318yes—
436#386C2318yes—
437#386C2318yes—
438#386C2318yes—
439#386C2318yes—
440#386C2318yes—
441#386C2318yes—
442#386C2318yes—
443#386C2318yes—
444#386C2318yes—
445#386C2318yes—
446#386C2318yes—
447#385C2318yes—
448#385C2318yes—
449#385C2314yes—
450#385C2314yes—
451#385C2318yes—
452#385C2314yes—
453#385C2318yes—
454#385C2318yes—
455#385C2314yes—
456#384C2311yescharacteristic
457#384C2311yescharacteristic
458#384C2311yescharacteristic
459#384C2312yes—
460#384C2312yes—
461#384C2314yes—
462#382C2312yes—
463#382C2312yes—
464#382C2314yes—
465#382C2314yes—
466#381C2318yes—
467#381C2318yes—
468#380C2318yes—
469#380C2318yes—
470#380C2318yes—
471#380C2318yes—
472#380C2318yes—
473#380C2318yes—
474#380C2318yes—
475#380C2312yes—
476#380C2312yes—
477#380C2314yes—
478#380C2318yes—
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2311yescharacteristic
508C4×C4⋊C4C2311yescharacteristic
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2311yescharacteristic
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2312yes—
520#376C2314yes—
521C2×#95C2318yes—
522C2×#95C2314yes—
523C43C2312yes—
524C43C2312yes—
525C43C2311yescharacteristic
526C2×#41—216no—
527C2×#41—48no—
528C2×#41—48no—
529C22×Q8C2411yescharacteristic
530C22×Q8C2411yescharacteristic
531C22×Q8C2412yes—
532C22×Q8C2412yes—
533C22×Q8C2412yes—
534C22×Q8C2414yes—
535C22×D4C2414yes—
536C22×D4C2414yes—
537C22×D4C2414yes—
538C22×D4C2411yescharacteristic
539C22×D4C2418yes—
540C22×D4C2414yes—
541C22×D4C2414yes—
542C22×D4C2414yes—
543C22×D4C2418yes—
544C22×D4C2414yes—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2414yes—
548C23×C4C2418yes—
549C23×C4C2418yes—
550C23×C4C2412yes—
551C23×C4C2414yes—
552C23×C4C2418yes—
553C4⋊Q8—24no—
554C4⋊Q8—24no—
555C4⋊Q8—24no—
556C4⋊Q8—44no—
557C4⋊Q8—44no—
558C4⋊Q8—44no—
559C4⋊Q8—44no—
560#127—216no—
561#127—28no—
562#127—28no—
563#127—28no—
564#127—44no—
565#127—44no—
566#127—44no—
567#127—82no—
568#126—416no—
569#125—28no—
570#125—28no—
571#125—48no—
572#124—48no—
573#124—48no—
574#124—48no—
575#124—48no—
576#124—48no—
577#124—48no—
578#124—84no—
579#123—416no—
580#123—416no—
581#123—416no—
582#123—88no—
583C22⋊Q8—28no—
584C22⋊Q8—28no—
585C22⋊Q8—216no—
586C22⋊Q8—48no—
587C22⋊Q8—44no—
588C22⋊Q8—44no—
589C22⋊Q8—88no—
590#121—216no—
591#121—232no—
592#121—48no—
593#121—48no—
594#121—48no—
595#121—84no—
596C4×Q8—24no—
597C4×Q8—28no—
598C4×Q8—24no—
599C4×Q8—24no—
600C4×Q8—28no—
601C4×Q8—24no—
602C4×Q8—24no—
603C4×Q8—48no—
604C4×Q8—44no—
605C4×Q8—42no—
606C4×Q8—48no—
607C4×D4—28no—
608C4×D4—216no—
609C4×D4—216no—
610C4×D4—24no—
611C4×D4—44no—
612C4×D4—48no—
613C4×D4—48no—
614C4×D4—48no—
615C4×D4—42no—
616C4×D4—48no—
617C4×D4—48no—
618C4×D4—48no—
619C4×D4—48no—
620C4×D4—48no—
621C4×D4—416no—
622C4×D4—84no—
623C4×D4#4118yes—
624#117—48no—
625#117—416no—
626C2×C4⋊C4—28no—
627C2×C4⋊C4—44no—
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2412yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2412yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2418yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2412yes—
708C2×C42—28no—
709C2×C42—48no—
710C2×C42C2412yes—
711C2×C42C2414yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2412yes—
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2414yes—
720C2×C42C2412yes—
721C2×C42C2414yes—
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2412yes—
725C2×C42C2411yescharacteristic
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2414yes—
729C2×C42C2418yes—
730C2×C42C2412yes—
731C2×C42C2412yes—
732C2×C42C2412yes—
733C2×C42C2414yes—
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738#95C2414yes—
739#95C2412yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2418yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2412yes—
753#95C2412yes—
754#95C2414yes—
755#95C2412yes—
756#95C2414yes—
757#95C2412yes—
758#95C2412yes—
759#95C2412yes—
760#95C2412yes—
761#95C2412yes—
762#95C2418yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2418yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2418yes—
777#95C2418yes—
778C24C2518yes—
779C24C2512yes—
780#41—832no—
781C2×Q8—22no—
782C2×Q8—24no—
783C2×Q8—24no—
784C2×Q8—22no—
785C2×Q8—24no—
786C2×Q8—22no—
787C2×Q8—22no—
788C2×Q8—24no—
789C2×Q8—24no—
790C2×Q8—22no—
791C2×Q8—24no—
792C2×Q8—22no—
793C2×Q8—24no—
794C2×Q8—44no—
795C2×Q8—42no—
796C2×Q8—44no—
797C2×Q8—42no—
798C2×Q8—44no—
799C2×D4—216no—
800C2×D4—216no—
801C2×D4—28no—
802C2×D4—28no—
803C2×D4—28no—
804C2×D4—28no—
805C2×D4—28no—
806C2×D4—28no—
807C2×D4—28no—
808C2×D4—22no—
809C2×D4—28no—
810C2×D4—28no—
811C2×D4—28no—
812C2×D4—22no—
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—24no—
837C22×C4—216no—
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—42no—
847C22×C4—44no—
848C22×C4—48no—
849C22×C4—48no—
850C22×C4—48no—
851C22×C4—48no—
852C22×C4C2×#4118yes—
853C22×C4C2514yes—
854C22×C4C2511yescharacteristic
855C22×C4C2514yes—
856C22×C4C2512yes—
857C22×C4C2512yes—
858C22×C4C2512yes—
859C22×C4C2512yes—
860C22×C4C2514yes—
861C22×C4C2512yes—
862C22×C4C2512yes—
863C22×C4C2512yes—
864C22×C4C2512yes—
865C22×C4C2514yes—
866C22×C4C2512yes—
867C22×C4C2514yes—
868C22×C4C2514yes—
869C22×C4C2511yescharacteristic
870C22×C4C2512yes—
871C22×C4C2511yescharacteristic
872C22×C4C2512yes—
873C22×C4C2511yescharacteristic
874C22×C4C2511yescharacteristic
875C22×C4C2511yescharacteristic
876C22×C4C2511yescharacteristic
877C4⋊C4—22no—
878C4⋊C4—28no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—28no—
883C4⋊C4—24no—
884C4⋊C4—28no—
885C4⋊C4—28no—
886C4⋊C4—28no—
887C4⋊C4—22no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—24no—
891C4⋊C4—28no—
892C4⋊C4—24no—
893C4⋊C4—22no—
894C4⋊C4—28no—
895C4⋊C4—24no—
896C4⋊C4—24no—
897C4⋊C4—24no—
898C4⋊C4—22no—
899C4⋊C4—22no—
900C4⋊C4—24no—
901C4⋊C4—24no—
902C4⋊C4—24no—
903C4⋊C4—22no—
904C4⋊C4—24no—
905C4⋊C4—24no—
906C4⋊C4—24no—
907C4⋊C4—22no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—42no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—48no—
919C4⋊C4—42no—
920C4⋊C4—44no—
921C4⋊C4—44no—
922C4⋊C4—48no—
923C4⋊C4—44no—
924C4⋊C4—44no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4C2×#4114yes—
928C4⋊C4H(5,𝔽2)14yes—
929C22⋊C4—28no—
930C22⋊C4—216no—
931C22⋊C4—216no—
932C22⋊C4—28no—
933C22⋊C4—24no—
934C22⋊C4—48no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—48no—
941C22⋊C4—44no—
942C22⋊C4—42no—
943C22⋊C4—48no—
944C22⋊C4—48no—
945C22⋊C4—48no—
946C22⋊C4—48no—
947C22⋊C4—48no—
948C22⋊C4—48no—
949C22⋊C4—48no—
950C22⋊C4—48no—
951C22⋊C4—48no—
952C22⋊C4—48no—
953C22⋊C4—48no—
954C22⋊C4—44no—
955C22⋊C4—48no—
956C22⋊C4C2×#4118yes—
957C42—24no—
958C42—28no—
959C42—24no—
960C42—24no—
961C42—24no—
962C42—24no—
963C42—28no—
964C42—24no—
965C42—28no—
966C42—24no—
967C42—24no—
968C42—22no—
969C42—24no—
970C42—24no—
971C42—24no—
972C42—24no—
973C42—22no—
974C42—22no—
975C42—44no—
976C42—44no—
977C42—48no—
978C42—42no—
979C42—42no—
980C42—42no—
981C42—41no—
982C42C2×#4114yes—
983C42H(5,𝔽2)14yes—
984C422−1+414yes—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—28no—
992C23—28no—
993C23—28no—
994C23—28no—
995C23—28no—
996C23—28no—
997C23—28no—
998C23C22×#4114yes—
999C23C2611yescharacteristic
1000Q8—44no—
1001Q8—48no—
1002Q8—44no—
1003Q8—48no—
1004Q8—84no—
1005Q8—88no—
1006D4—28no—
1007D4—416no—
1008D4—416no—
1009D4—416no—
1010D4—88no—
1011D4—88no—
1012D4—88no—
1013D4—816no—
1014D4—816no—
1015D4—164no—
1016C2×C4—21no—
1017C2×C4—22no—
1018C2×C4—21no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—21no—
1022C2×C4—22no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—216no—
1027C2×C4—22no—
1028C2×C4—24no—
1029C2×C4—22no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—24no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—24no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—24no—
1041C2×C4—22no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—21no—
1046C2×C4—22no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—22no—
1066C2×C4—24no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—24no—
1072C2×C4—22no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—48no—
1076C2×C4—816no—
1077C2×C4—84no—
1078C2×C4—816no—
1079C2×C4—88no—
1080C2×C4—88no—
1081C2×C4—168no—
1082C2×C4C22×#4112yes—
1083C2×C4C22×#4114yes—
1084C2×C4C22×#4112yes—
1085C2×C4C22×#4112yes—
1086C2×C4C2×H(5,𝔽2)12yes—
1087C2×C4C2×H(5,𝔽2)14yes—
1088C2×C4C2×H(5,𝔽2)12yes—
1089C2×C4C2×H(5,𝔽2)12yes—
1090C2×C4C2×H(5,𝔽2)12yes—
1091C2×C4C2×2−1+412yes—
1092C2×C4C2×2−1+412yes—
1093C2×C4C2×2−1+412yes—
1094C2×C4#58512yes—
1095C2×C4#58512yes—
1096C22—24no—
1097C22—24no—
1098C22—24no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—48no—
1104C22—48no—
1105C22—48no—
1106C22—48no—
1107C22—48no—
1108C22—48no—
1109C22—48no—
1110C22C23×#4111yescharacteristic
1111C22C22×H(5,𝔽2)11yescharacteristic
1112C22C22×H(5,𝔽2)11yescharacteristic
1113C22C22×2−1+411yescharacteristic
1114C22C2×#58511yescharacteristic
1115C22C2×#58511yescharacteristic
1116C22H(7,𝔽2)11yescharacteristic
1117C4—22no—
1118C4—24no—
1119C4—24no—
1120C4—22no—
1121C4—22no—
1122C4—42no—
1123C4—44no—
1124C4—44no—
1125C4—42no—
1126C4—42no—
1127C4—44no—
1128C4—42no—
1129C4—44no—
1130C4—41no—
1131C4—44no—
1132C4—42no—
1133C4—42no—
1134C4—42no—
1135C4—44no—
1136C4—42no—
1137C4—42no—
1138C4#350714yes—
1139C4#351414yes—
1140C4#354814yes—
1141C2—44no—
1142C2—88no—
1143C2C2×#354811yescharacteristic
1144C2C2×#350711yescharacteristic
1145C2C2×#351411yescharacteristic
1146C2#6295511yescharacteristic
1147C2#6296211yescharacteristic
1148C2#6298611yescharacteristic
1149C2#6302111yescharacteristic
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. #59870C2semidirect
2. #59863C2semidirect
3. #59465C2semidirect
4. #59064C2semidirect
5. #49241C2semidirect
6. #45594C2semidirect
7. #45007C2semidirect
8. #44995C2semidirect
9. #42612C2semidirect
10. #42519C2semidirect
11. #39857C2semidirect
12. #39726C2semidirect
13. #38987C2semidirect
14. #38985C2semidirect
15. #38952C2semidirect
16. #36595C2semidirect
17. #36595C2semidirect
19. #36117C2semidirect
20. #36115C2semidirect
21. #35197C2semidirect
22. #35180C2semidirect
23. #34951C2semidirect
24. #34929C2semidirect
25. #34494C2semidirect
26. C4×#554C2semidirect

Maximal subgroups

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

subgroupindex
#598702
#598632
#594652
#590642
#492412
#455942
#450072
#449952
#426122
#425192
#398572
#397262
#389872
#389852
#389522
#365952
#361282
#361172
#361152
#351972
#351802
#349512
#349292
#344942
C4×#5542