Finite Group Databasebeta

← #7986721

Subgroups — #7986721

Order 512.

4955 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59863C211yesmaximal, characteristic, complemented
2#59821C212yesmaximal, complemented
3#59640C212yesmaximal
4#59036C212yesmaximal, complemented
5#51167C218yesmaximal, complemented
6#46109C214yesmaximal, complemented
7#45291C214yesmaximal, complemented
8#44979C214yesmaximal, complemented
9#42714C214yesmaximal, complemented
10#42699C214yesmaximal, complemented
11#40203C214yesmaximal, complemented
12#39761C212yesmaximal, complemented
13#39200C212yesmaximal, complemented
14#39167C212yesmaximal, complemented
15#38911C212yesmaximal, complemented
16#36598C211yesmaximal, characteristic, complemented
17#36563C212yesmaximal, complemented
18Q8×#127C211yesmaximal, characteristic, complemented
19#36473C212yesmaximal, complemented
20#36134C211yesmaximal, characteristic, complemented
21#35201C212yesmaximal, complemented
22#35186C212yesmaximal, complemented
23#34950C211yesmaximal, characteristic, complemented
24#34934C211yesmaximal, characteristic
25#34487C212yesmaximal, complemented
26C4×#556C211yesmaximal, characteristic, complemented
27C2×#556C2211yescharacteristic
28C2×#556C2214yes—
29C2×D4×Q8C2212yes—
30C2×D4×Q8C2212yes—
31C2×D4×Q8C2212yes—
32C2×#533C2212yes—
33C2×#529C2212yes—
34#2868C2211yescharacteristic
35#2868C2212yes—
36#2862C2212yes—
37#2861C2214yes—
38#2860C2214yes—
39#2859C2214yes—
40#2857C2212yes—
41#2837C2218yes—
42#2808C2214yes—
43#2803C2218yes—
44#2793C2218yes—
45#2777C2218yes—
46#2777C2218yes—
47#2773C2218yes—
48#2754C2218yes—
49#2727C2218yes—
50#2723C2218yes—
51#2723C2218yes—
52#2716C2218yes—
53#2702C2218yes—
54#2700C2218yes—
55#2692C2218yes—
56#2689C2218yes—
57#2689C2218yes—
58#2687C2218yes—
59#2663C2218yes—
60#2651C2218yes—
61#2651C2218yes—
62#2640C2214yes—
63#2625C2214yes—
64#2604C2218yes—
65#2604C2218yes—
66#2592C2214yes—
67#2592C2214yes—
68#2586C2214yes—
69#2582C2214yes—
70#2582C2212yes—
71#2582C2211yescharacteristic
72#2571C2212yes—
73#2570C2214yes—
74#2568C2212yes—
75#2567C2211yescharacteristic
76#2567C2211yescharacteristic
77#2567C2214yes—
78#2563C2212yes—
79#2554C2214yes—
80#2552C2212yes—
81#2552C2211yescharacteristic
82#2551C2211yescharacteristic
83#2550C2214yes—
84#2550C2214yes—
85#2548C2211yescharacteristic
86#2548C2212yes—
87#2548C2214yes—
88#2547C2212yes—
89#2544C2214yes—
90#2542C2214yes—
91#2542C2212yes—
92#2542C2212yes—
93#2542C2212yes—
94#2542C2214yes—
95#2542C2212yes—
96#2542C2214yes—
97#2541C2211yescharacteristic
98#2538C2212yes—
99#2538C2211yescharacteristic
100#2538C2214yes—
101#2521C2218yes—
102#2513C2214yes—
103#2512C2214yes—
104#2512C2214yes—
105#2512C2212yes—
106#2511C2214yes—
107#2511C2214yes—
108#2507C2212yes—
109#2507C2212yes—
110#2507C2218yes—
111#2500C2214yes—
112#2499C2214yes—
113#2496C2214yes—
114#2492C2214yes—
115#2492C2214yes—
116#2491C2214yes—
117#2490C2212yes—
118#2485C2214yes—
119#2468C2218yes—
120#2465C2218yes—
121#2465C2218yes—
122#2459C2218yes—
123#2454C2214yes—
124#2451C2212yes—
125#2451C2212yes—
126#2451C2218yes—
127#2448C2218yes—
128#2448C2214yes—
129#2447C2214yes—
130#2446C2214yes—
131#2445C2212yes—
132#2441C2214yes—
133#2439C2214yes—
134#2429C2214yes—
135#2426C2212yes—
136#2423C2214yes—
137#2423C2214yes—
138#2420C2214yes—
139#2415C2214yes—
140#2415C2214yes—
141#2415C2214yes—
142#2415C2214yes—
143#2409C2214yes—
144#2409C2214yes—
145#2399C2214yes—
146#2392C2214yes—
147#2378C2218yes—
148#2373C2214yes—
149#2369C2214yes—
150#2367C2212yes—
151#2365C2211yescharacteristic
152#2365C2212yes—
153#2365C2212yes—
154#2363C2214yes—
155#2362C2212yes—
156#2362C2214yes—
157#2357C2214yes—
158#2356C2212yes—
159#2355C2212yes—
160#2355C2212yes—
161#2355C2211yescharacteristic
162#2355C2212yes—
163#2354C2212yes—
164#2354C2211yescharacteristic
165#2354C2212yes—
166#2354C2212yes—
167Q8×C4⋊C4C2212yes—
168Q8×C4⋊C4C2214yes—
169#2347C2212yes—
170Q8×C22⋊C4C2214yes—
171#2332C2218yes—
172#2331C2214yes—
173#2326C2214yes—
174#2323C2214yes—
175#2323C2214yes—
176#2319C2214yes—
177#2310C2214yes—
178C4×C4⋊Q8C2214yes—
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2211yescharacteristic
182C4×C4⋊Q8C2212yes—
183C4×C4⋊Q8C2212yes—
184C4×#127C2212yes—
185C4×#127C2212yes—
186C4×#127C2211yescharacteristic
187C4×#126C2214yes—
188C4×#124C2212yes—
189C4×C22⋊Q8C2212yes—
190C4×#121C2212yes—
191#2295C2212yes—
192#2295C2212yes—
193#2293C2212yes—
194C42×Q8C2212yes—
195C42×Q8C2211yescharacteristic
196C42×Q8C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C4×#117C2212yes—
199C23×Q8C2314yes—
200#556—28no—
201#556—416no—
202D4×Q8—216no—
203D4×Q8—48no—
204D4×Q8—48no—
205#533—48no—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2314yes—
216C2×#127C2311yescharacteristic
217C2×#127C2312yes—
218#529—48no—
219C2×#126C2314yes—
220C2×#126C2314yes—
221C2×#126C2318yes—
222C2×#126C2318yes—
223C2×#125C2312yes—
224C2×#125C2314yes—
225C2×#124C2312yes—
226C2×#124C2314yes—
227C2×#124C2312yes—
228C2×#124C2318yes—
229C2×#123C2314yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2318yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2312yes—
239C2×C22⋊Q8C2318yes—
240C2×C22⋊Q8C2318yes—
241C2×#121C2312yes—
242C2×#121C2312yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2314yes—
253C2×C4×Q8C2318yes—
254C2×C4×Q8C2314yes—
255C2×C4×Q8C2312yes—
256C2×C4×Q8C2314yes—
257C2×C4×Q8C2311yescharacteristic
258C2×C4×D4C2312yes—
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2312yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2314yes—
264C2×C4×D4C2312yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2311yescharacteristic
269C2×#117C2312yes—
270C2×#117C2312yes—
271C2×#117C2314yes—
272C2×#117C2314yes—
273C2×#117C2314yes—
274C22×C42C2312yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#399C2318yes—
280#399C2318yes—
281#399C2318yes—
282#399C2318yes—
283#399C2318yes—
284#398C2318yes—
285#398C2314yes—
286#398C2318yes—
287#398C2314yes—
288#398C2318yes—
289#398C2314yes—
290#398C2314yes—
291#398C2318yes—
292#398C2314yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2314yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#396C2318yes—
303#396C2318yes—
304#396C2314yes—
305#396C2314yes—
306#396C2318yes—
307#395C2314yes—
308#395C2314yes—
309#395C2318yes—
310#395C2318yes—
311#395C2314yes—
312#395C2314yes—
313#394C2314yes—
314#394C2318yes—
315#394C2318yes—
316#394C2314yes—
317#394C2314yes—
318#394C2318yes—
319#394C2318yes—
320#394C2318yes—
321#393C2318yes—
322#393C2318yes—
323#393C2318yes—
324#393C2318yes—
325#392C2314yes—
326#391C2314yes—
327#391C2318yes—
328#391C2312yes—
329#391C2314yes—
330#391C2314yes—
331#391C2312yes—
332#391C2312yes—
333#391C2312yes—
334#391C2318yes—
335#391C2314yes—
336#391C2318yes—
337#391C2314yes—
338#391C2314yes—
339#391C2312yes—
340#391C2312yes—
341#391C2314yes—
342#391C2314yes—
343#391C2314yes—
344#391C2312yes—
345#391C2318yes—
346#391C2318yes—
347#391C2312yes—
348#391C2314yes—
349#390C2312yes—
350#390C2312yes—
351#390C2314yes—
352#390C2314yes—
353#390C2312yes—
354#390C2314yes—
355#390C2314yes—
356#390C2312yes—
357#390C2314yes—
358#390C2312yes—
359#390C2314yes—
360#390C2312yes—
361#390C2314yes—
362#390C2312yes—
363#390C2312yes—
364#390C2314yes—
365#390C2312yes—
366#390C2314yes—
367#390C2318yes—
368#389C2312yes—
369#389C2312yes—
370#389C2318yes—
371#389C2312yes—
372#389C2312yes—
373#389C2314yes—
374#389C2314yes—
375#389C2312yes—
376#389C2312yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2312yes—
381#389C2312yes—
382#389C2312yes—
383#389C2312yes—
384#389C2318yes—
385#389C2312yes—
386#389C2314yes—
387#389C2314yes—
388#389C2318yes—
389#389C2318yes—
390#389C2312yes—
391#389C2312yes—
392#389C2314yes—
393#389C2312yes—
394#389C2318yes—
395#389C2312yes—
396#389C2318yes—
397#389C2318yes—
398#389C2318yes—
399#389C2312yes—
400#388C2314yes—
401#388C2314yes—
402#388C2314yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2314yes—
411#388C2318yes—
412#388C2318yes—
413#388C2318yes—
414#388C2318yes—
415#388C2318yes—
416#388C2314yes—
417#388C2314yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2314yes—
422#388C2314yes—
423#388C2318yes—
424#387C2314yes—
425#387C2314yes—
426#387C2314yes—
427#387C2318yes—
428#387C2318yes—
429#387C2318yes—
430#387C2318yes—
431#387C2314yes—
432#387C2314yes—
433#387C2314yes—
434#387C2314yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2314yes—
440#387C2318yes—
441#386C2318yes—
442#386C2318yes—
443#386C2314yes—
444#385C2318yes—
445#385C2318yes—
446#385C2314yes—
447#384C2312yes—
448#384C2312yes—
449#384C2311yescharacteristic
450#384C2311yescharacteristic
451#384C2312yes—
452#384C2312yes—
453#384C2311yescharacteristic
454#384C2314yes—
455#384C2314yes—
456#384C2312yes—
457#384C2312yes—
458#384C2314yes—
459#384C2312yes—
460#384C2314yes—
461#383C2314yes—
462#382C2314yes—
463#382C2314yes—
464#382C2314yes—
465#382C2314yes—
466#382C2312yes—
467#381C2318yes—
468#381C2318yes—
469#380C2314yes—
470#380C2314yes—
471#380C2318yes—
472#380C2314yes—
473#380C2314yes—
474#380C2312yes—
475#380C2314yes—
476#380C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2318yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2314yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2311yescharacteristic
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2318yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2312yes—
520#376C2314yes—
521#376C2314yes—
522C43C2314yes—
523C43C2312yes—
524C43C2311yescharacteristic
525C43C2312yes—
526C22×Q8—216no—
527C22×Q8—48no—
528C22×Q8—48no—
529C22×Q8C2411yescharacteristic
530C22×Q8C2412yes—
531C22×Q8C2414yes—
532C22×Q8C2414yes—
533C22×Q8C2411yescharacteristic
534C22×Q8C2412yes—
535C22×Q8C2418yes—
536C22×D4C2412yes—
537C22×D4C2412yes—
538C22×D4C2411yescharacteristic
539C22×D4C2412yes—
540C22×D4C2414yes—
541C22×D4C2414yes—
542C23×C4C2412yes—
543C23×C4C2414yes—
544C23×C4C2412yes—
545C23×C4C2418yes—
546C23×C4C2412yes—
547C4⋊Q8—28no—
548C4⋊Q8—28no—
549C4⋊Q8—28no—
550C4⋊Q8—216no—
551C4⋊Q8—24no—
552C4⋊Q8—24no—
553C4⋊Q8—28no—
554C4⋊Q8—48no—
555C4⋊Q8—48no—
556C4⋊Q8—44no—
557#127—24no—
558#127—44no—
559#126—216no—
560#126—48no—
561#126—416no—
562#126—416no—
563#125—44no—
564#125—48no—
565#124—28no—
566#124—48no—
567#124—44no—
568#124—416no—
569#123—48no—
570C22⋊Q8—28no—
571C22⋊Q8—216no—
572C22⋊Q8—232no—
573C22⋊Q8—216no—
574C22⋊Q8—416no—
575C22⋊Q8—416no—
576C22⋊Q8—44no—
577C22⋊Q8—48no—
578C22⋊Q8—48no—
579C22⋊Q8—48no—
580C22⋊Q8—48no—
581#121—28no—
582#121—44no—
583C4×Q8—24no—
584C4×Q8—24no—
585C4×Q8—28no—
586C4×Q8—24no—
587C4×Q8—24no—
588C4×Q8—28no—
589C4×Q8—24no—
590C4×Q8—44no—
591C4×Q8—48no—
592C4×Q8—44no—
593C4×Q8—48no—
594C4×Q8—48no—
595C4×Q8—416no—
596C4×Q8—48no—
597C4×Q8#4118yes—
598C4×D4—28no—
599C4×D4—216no—
600C4×D4—24no—
601C4×D4—28no—
602C4×D4—24no—
603C4×D4—48no—
604C4×D4—42no—
605C4×D4—48no—
606C4×D4—48no—
607C4×D4—44no—
608C4×D4—48no—
609#117—28no—
610#117—28no—
611#117—48no—
612#117—48no—
613#117—48no—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2412yes—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2412yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2414yes—
697C2×C42—28no—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2414yes—
701C2×C42C2414yes—
702C2×C42C2412yes—
703C2×C42C2411yescharacteristic
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2411yescharacteristic
707C2×C42C2412yes—
708C2×C42C2414yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2414yes—
713C2×C42C2411yescharacteristic
714C2×C42C2412yes—
715C2×C42C2412yes—
716C2×C42C2412yes—
717C2×C42C2418yes—
718C2×C42C2418yes—
719C2×C42C2418yes—
720C2×C42C2414yes—
721C2×C42C2411yescharacteristic
722C2×C42C2414yes—
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2411yescharacteristic
726C2×C42C2412yes—
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729#95C2412yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2412yes—
739#95C2412yes—
740#95C2414yes—
741#95C2412yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2412yes—
748#95C2412yes—
749#95C2412yes—
750#95C2412yes—
751#95C2412yes—
752#95C2418yes—
753#95C2418yes—
754#95C2418yes—
755#95C2418yes—
756#95C2414yes—
757#95C2418yes—
758#95C2418yes—
759#95C2418yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2418yes—
766#95C2418yes—
767#95C2418yes—
768#95C2418yes—
769C24C2512yes—
770C24C2514yes—
771C2×Q8—24no—
772C2×Q8—28no—
773C2×Q8—216no—
774C2×Q8—22no—
775C2×Q8—22no—
776C2×Q8—22no—
777C2×Q8—24no—
778C2×Q8—28no—
779C2×Q8—28no—
780C2×Q8—28no—
781C2×Q8—24no—
782C2×Q8—22no—
783C2×Q8—22no—
784C2×Q8—28no—
785C2×Q8—24no—
786C2×Q8—44no—
787C2×Q8—42no—
788C2×Q8—42no—
789C2×Q8—48no—
790C2×Q8—48no—
791C2×Q8—832no—
792C2×Q8C2×#4114yes—
793C2×D4—24no—
794C2×D4—22no—
795C2×D4—24no—
796C2×D4—22no—
797C2×D4—24no—
798C2×D4—24no—
799C2×D4—24no—
800C2×D4—24no—
801C2×D4—28no—
802C2×D4—22no—
803C2×D4—24no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—44no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—44no—
810C2×D4—44no—
811C22×C4—24no—
812C22×C4—28no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—28no—
817C22×C4—28no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—216no—
821C22×C4—24no—
822C22×C4—48no—
823C22×C4—48no—
824C22×C4—42no—
825C22×C4—42no—
826C22×C4C2512yes—
827C22×C4C2514yes—
828C22×C4C2512yes—
829C22×C4C2514yes—
830C22×C4C2512yes—
831C22×C4C2514yes—
832C22×C4C2512yes—
833C22×C4C2512yes—
834C22×C4C2511yescharacteristic
835C22×C4C2514yes—
836C22×C4C2512yes—
837C22×C4C2514yes—
838C22×C4C2518yes—
839C22×C4C2512yes—
840C22×C4C2512yes—
841C22×C4C2511yescharacteristic
842C22×C4C2512yes—
843C22×C4C2511yescharacteristic
844C22×C4C2512yes—
845C22×C4C2512yes—
846C22×C4C2511yescharacteristic
847C22×C4C2511yescharacteristic
848C22×C4C2511yescharacteristic
849C22×C4C2511yescharacteristic
850C4⋊C4—24no—
851C4⋊C4—22no—
852C4⋊C4—24no—
853C4⋊C4—28no—
854C4⋊C4—28no—
855C4⋊C4—216no—
856C4⋊C4—28no—
857C4⋊C4—24no—
858C4⋊C4—24no—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—28no—
862C4⋊C4—24no—
863C4⋊C4—22no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—22no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—216no—
870C4⋊C4—28no—
871C4⋊C4—28no—
872C4⋊C4—22no—
873C4⋊C4—24no—
874C4⋊C4—22no—
875C4⋊C4—24no—
876C4⋊C4—28no—
877C4⋊C4—24no—
878C4⋊C4—28no—
879C4⋊C4—24no—
880C4⋊C4—22no—
881C4⋊C4—42no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4—42no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—42no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—48no—
897C4⋊C4—48no—
898C4⋊C4—48no—
899C4⋊C4—48no—
900C4⋊C4—44no—
901C4⋊C4—48no—
902C4⋊C4C2×#4114yes—
903C4⋊C4C2×#4118yes—
904C4⋊C4H(5,𝔽2)14yes—
905C4⋊C42−1+414yes—
906C22⋊C4—28no—
907C22⋊C4—216no—
908C22⋊C4—28no—
909C22⋊C4—24no—
910C22⋊C4—28no—
911C22⋊C4—28no—
912C22⋊C4—28no—
913C22⋊C4—216no—
914C22⋊C4—24no—
915C22⋊C4—28no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—48no—
919C22⋊C4—44no—
920C22⋊C4—48no—
921C22⋊C4—44no—
922C22⋊C4—48no—
923C22⋊C4—42no—
924C22⋊C4—44no—
925C22⋊C4—48no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—48no—
931C22⋊C4—48no—
932C22⋊C4—48no—
933C42—28no—
934C42—24no—
935C42—24no—
936C42—24no—
937C42—28no—
938C42—24no—
939C42—24no—
940C42—22no—
941C42—24no—
942C42—24no—
943C42—22no—
944C42—24no—
945C42—24no—
946C42—28no—
947C42—24no—
948C42—22no—
949C42—24no—
950C42—28no—
951C42—24no—
952C42—41no—
953C42—42no—
954C42—44no—
955C42—42no—
956C42—48no—
957C42—48no—
958C42—44no—
959C42—48no—
960C42C2×#4114yes—
961C42C2×#4118yes—
962C42H(5,𝔽2)14yes—
963C422−1+414yes—
964C23—22no—
965C23—24no—
966C23—22no—
967C23—24no—
968C23—24no—
969C23—22no—
970C23—22no—
971C23—24no—
972C23—22no—
973C23—24no—
974C23—24no—
975C23—22no—
976C23—24no—
977C23—22no—
978C23C2611yescharacteristic
979Q8—28no—
980Q8—416no—
981Q8—48no—
982Q8—416no—
983Q8—48no—
984Q8—44no—
985Q8—816no—
986D4—48no—
987D4—48no—
988D4—44no—
989D4—48no—
990D4—88no—
991D4—88no—
992C2×C4—21no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—21no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—21no—
1001C2×C4—22no—
1002C2×C4—21no—
1003C2×C4—22no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—22no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—28no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—24no—
1015C2×C4—22no—
1016C2×C4—21no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—28no—
1024C2×C4—28no—
1025C2×C4—24no—
1026C2×C4—21no—
1027C2×C4—24no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—24no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—24no—
1035C2×C4—21no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—22no—
1043C2×C4—24no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—24no—
1048C2×C4—48no—
1049C2×C4—416no—
1050C2×C4—48no—
1051C2×C4—84no—
1052C2×C4—816no—
1053C2×C4C22×#4114yes—
1054C2×C4C22×#4112yes—
1055C2×C4C22×#4114yes—
1056C2×C4C22×#4112yes—
1057C2×C4C22×#4112yes—
1058C2×C4C2×H(5,𝔽2)14yes—
1059C2×C4C2×H(5,𝔽2)12yes—
1060C2×C4C2×H(5,𝔽2)12yes—
1061C2×C4C2×H(5,𝔽2)12yes—
1062C2×C4C2×H(5,𝔽2)12yes—
1063C2×C4C2×2−1+414yes—
1064C2×C4C2×2−1+412yes—
1065C2×C4C2×2−1+412yes—
1066C2×C4C2×2−1+412yes—
1067C2×C4C2×2−1+412yes—
1068C2×C4#58512yes—
1069C22—42no—
1070C22—44no—
1071C22—42no—
1072C22—44no—
1073C22—42no—
1074C22—44no—
1075C22—42no—
1076C22—44no—
1077C22—44no—
1078C22—42no—
1079C22—44no—
1080C22—42no—
1081C22—42no—
1082C22—44no—
1083C22C23×#4111yescharacteristic
1084C22C22×H(5,𝔽2)11yescharacteristic
1085C22C22×H(5,𝔽2)11yescharacteristic
1086C22C22×2−1+411yescharacteristic
1087C22C22×2−1+411yescharacteristic
1088C22C2×#58511yescharacteristic
1089C222−1+611yescharacteristic
1090C4—22no—
1091C4—24no—
1092C4—24no—
1093C4—24no—
1094C4—24no—
1095C4—22no—
1096C4—22no—
1097C4—41no—
1098C4—44no—
1099C4—42no—
1100C4—42no—
1101C4—44no—
1102C4—42no—
1103C4—44no—
1104C4—48no—
1105C4—44no—
1106C4—42no—
1107C4—42no—
1108C4—42no—
1109C4—42no—
1110C4—44no—
1111C4#350814yes—
1112C4#351814yes—
1113C4#355014yes—
1114C2—82no—
1115C2—84no—
1116C2C2×#355011yescharacteristic
1117C2C2×#351811yescharacteristic
1118C2C2×#350811yescharacteristic
1119C2#6291311yescharacteristic
1120C2#6292511yescharacteristic
1121C2#6300111yescharacteristic
1122C2#6301311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2541C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59863C2semidirect
2. #59821C2semidirect
4. #59036C2semidirect
5. #51167C2semidirect
6. #46109C2semidirect
7. #45291C2semidirect
8. #44979C2semidirect
9. #42714C2semidirect
10. #42699C2semidirect
11. #40203C2semidirect
12. #39761C2semidirect
13. #39200C2semidirect
14. #39167C2semidirect
15. #38911C2semidirect
16. #36598C2semidirect
17. #36563C2semidirect
18. Q8×#127C2semidirect
19. #36473C2semidirect
20. #36134C2semidirect
21. #35201C2semidirect
22. #35186C2semidirect
23. #34950C2semidirect
25. #34487C2semidirect
26. C4×#556C2semidirect

Maximal subgroups

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

subgroupindex
#598632
#598212
#596402
#590362
#511672
#461092
#452912
#449792
#427142
#426992
#402032
#397612
#392002
#391672
#389112
#365982
#365632
Q8×#1272
#364732
#361342
#352012
#351862
#349502
#349342
#344872
C4×#5562