Finite Group Databasebeta

← #7718440

Subgroups — #7718440

Order 512.

6452 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3552C211yesmaximal, characteristic
2C22×#557C211yesmaximal, characteristic, complemented
3#52065C218yesmaximal, complemented
4#52058C214yesmaximal, complemented
5#52055C214yesmaximal, complemented
6#45394C212yesmaximal, complemented
7#45336C212yesmaximal, complemented
8#45335C212yesmaximal, complemented
9#45334C212yesmaximal, complemented
10#45324C214yesmaximal, complemented
11#45323C214yesmaximal, complemented
12#39721C212yesmaximal, complemented
13#39717C214yesmaximal, complemented
14#39593C212yesmaximal, complemented
15#39589C214yesmaximal, complemented
16#37120C214yesmaximal, complemented
17#36578C212yesmaximal, complemented
18Q8×#123C212yesmaximal, complemented
19#35246C211yesmaximal, characteristic, complemented
20#35245C211yesmaximal, characteristic, complemented
21#35111C211yesmaximal, characteristic, complemented
22#35092C214yesmaximal, complemented
23#34602C211yesmaximal, characteristic, complemented
24#34371C211yesmaximal, characteristic, complemented
25#3552—216no—
26C2×#563C2214yes—
27C2×#557—216no—
28C2×#557C2214yes—
29C2×#557C2211yescharacteristic
30C2×#557C2212yes—
31C2×#557C2212yes—
32C2×#557C2214yes—
33C2×#557C2214yes—
34C2×#556C2211yescharacteristic
35C2×#554C2212yes—
36C2×#553C2212yes—
37C2×D4×Q8C2211yescharacteristic
38C2×D4×Q8C2212yes—
39C2×#548C2212yes—
40C2×#547C2211yescharacteristic
41C2×#544C2212yes—
42C2×#542C2212yes—
43C2×#541C2212yes—
44C2×#539C2214yes—
45C2×#536C2212yes—
46C22×C4⋊Q8C2212yes—
47C22×C4⋊Q8C2211yescharacteristic
48C2×#529C2211yescharacteristic
49C2×#529C2211yescharacteristic
50C22×#125C2212yes—
51C22×#125C2214yes—
52C22×C4×Q8C2212yes—
53C22×C4×Q8C2211yescharacteristic
54C22×C4×Q8C2211yescharacteristic
55C22×C4×Q8C2212yes—
56#2855C2214yes—
57#2855C2212yes—
58#2854C2214yes—
59#2854C2212yes—
60#2853C2214yes—
61#2853C2214yes—
62#2734C2218yes—
63#2731C2218yes—
64#2729C2218yes—
65#2729C2218yes—
66#2726C2218yes—
67#2725C2218yes—
68#2721C2218yes—
69#2721C2218yes—
70#2720C2218yes—
71#2719C2218yes—
72#2719C2218yes—
73#2719C2218yes—
74#2713C2218yes—
75#2711C2218yes—
76#2707C2218yes—
77#2704C2218yes—
78#2694C2218yes—
79#2694C2218yes—
80#2690C2218yes—
81#2690C2218yes—
82#2637C2214yes—
83#2637C2214yes—
84#2634C2212yes—
85#2634C2212yes—
86#2632C2212yes—
87#2632C2212yes—
88#2627C2214yes—
89#2627C2212yes—
90#2623C2212yes—
91#2623C2212yes—
92#2618C2214yes—
93#2618C2212yes—
94#2614C2212yes—
95#2614C2212yes—
96#2604C2214yes—
97#2604C2214yes—
98#2599C2214yes—
99#2599C2214yes—
100#2592C2212yes—
101#2591C2214yes—
102#2591C2212yes—
103#2584C2212yes—
104#2583C2214yes—
105#2583C2212yes—
106#2581C2212yes—
107#2581C2212yes—
108#2580C2212yes—
109#2579C2214yes—
110#2579C2214yes—
111#2579C2214yes—
112#2565C2212yes—
113#2558C2218yes—
114#2556C2218yes—
115#2546C2214yes—
116#2545C2212yes—
117#2545C2214yes—
118#2536C2212yes—
119#2519C2218yes—
120#2506C2218yes—
121#2504C2214yes—
122#2504C2211yescharacteristic
123#2502C2214yes—
124#2502C2211yescharacteristic
125#2487C2214yes—
126#2487C2214yes—
127#2487C2212yes—
128#2475C2218yes—
129#2473C2218yes—
130#2469C2218yes—
131#2469C2218yes—
132#2465C2218yes—
133#2465C2218yes—
134#2462C2218yes—
135#2462C2218yes—
136#2462C2218yes—
137#2460C2218yes—
138#2458C2218yes—
139#2458C2218yes—
140#2448C2214yes—
141#2448C2218yes—
142#2446C2214yes—
143#2446C2214yes—
144#2446C2214yes—
145#2446C2218yes—
146#2436C2211yescharacteristic
147#2434C2214yes—
148#2434C2211yescharacteristic
149#2432C2214yes—
150#2429C2214yes—
151#2429C2214yes—
152#2423C2214yes—
153#2423C2218yes—
154#2421C2214yes—
155#2421C2218yes—
156#2409C2212yes—
157#2399C2212yes—
158#2398C2212yes—
159#2396C2214yes—
160#2381C2214yes—
161#2365C2214yes—
162#2351C2214yes—
163Q8×C4⋊C4C2214yes—
164#2345C2214yes—
165#2341C2214yes—
166Q8×C22⋊C4C2214yes—
167Q8×C22⋊C4C2212yes—
168Q8×C22⋊C4C2212yes—
169#2331C2214yes—
170#2327C2212yes—
171#2327C2212yes—
172#2327C2212yes—
173#2326C2212yes—
174#2323C2214yes—
175#2322C2214yes—
176#2322C2214yes—
177#2322C2214yes—
178#2313C2214yes—
179C4×#123C2214yes—
180C4×#123C2214yes—
181C4×#123C2212yes—
182C4×#123C2212yes—
183#2283C2211yescharacteristic
184#2283C2211yescharacteristic
185C22×#41C2312yes—
186C23×Q8C2311yescharacteristic
187C23×Q8C2312yes—
188C23×Q8C2311yescharacteristic
189C23×Q8C2312yes—
190#563—232no—
191#557—232no—
192#557—232no—
193#557—216no—
194#557—216no—
195#557—232no—
196#557—28no—
197#556—28no—
198#554—216no—
199#553—216no—
200D4×Q8—216no—
201D4×Q8—28no—
202#548—216no—
203#547—28no—
204#544—216no—
205#542—216no—
206#541—216no—
207#539—232no—
208#536—216no—
209C2×C4⋊Q8—216no—
210C2×C4⋊Q8D4116yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2318yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2312yes—
217C2×C4⋊Q8C2312yes—
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2312yes—
221C2×C4⋊Q8C2312yes—
222C2×C4⋊Q8C2312yes—
223#529—28no—
224#529—28no—
225C2×#126C2312yes—
226C2×#126C2312yes—
227C2×#126C2314yes—
228C2×#126C2314yes—
229C2×#126C2314yes—
230C2×#125—232no—
231C2×#125—216no—
232C2×#125C2311yescharacteristic
233C2×#125C2311yescharacteristic
234C2×#125C2314yes—
235C2×#125C2318yes—
236C2×#125C2314yes—
237C2×#125C2318yes—
238C2×#125C2318yes—
239C2×#125C2318yes—
240C2×#125C2318yes—
241C2×#125C2314yes—
242C2×#125C2314yes—
243C2×#125C2314yes—
244C2×#125C2312yes—
245C2×#124C2311yescharacteristic
246C2×#124C2311yescharacteristic
247C2×#124C2312yes—
248C2×#124C2314yes—
249C2×#124C2312yes—
250C2×#123C2312yes—
251C2×#123C2314yes—
252C2×#123C2312yes—
253C2×#123C2312yes—
254C2×#123C2312yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×#123C2314yes—
258C2×C22⋊Q8C2311yescharacteristic
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2311yescharacteristic
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2314yes—
270C2×#121C2311yescharacteristic
271C2×#121C2314yes—
272C2×#121C2311yescharacteristic
273C2×#121C2312yes—
274C2×C4×Q8—216no—
275C2×C4×Q8—216no—
276C2×C4×Q8—28no—
277C2×C4×Q8—28no—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2314yes—
285C2×C4×Q8C2314yes—
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2318yes—
293C2×C4×Q8C2314yes—
294C2×C4×Q8C2318yes—
295C2×C4×Q8C2314yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2314yes—
298C2×C4×Q8C2314yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2311yescharacteristic
303C2×C4×D4C2311yescharacteristic
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×#117C2312yes—
307C2×#117C2312yes—
308C2×#117C2312yes—
309C22×C4⋊C4C2312yes—
310C22×C4⋊C4C2314yes—
311C22×C4⋊C4C2312yes—
312C22×C4⋊C4C2314yes—
313C22×C4⋊C4C2311yescharacteristic
314C22×C4⋊C4C2311yescharacteristic
315C22×C4⋊C4C2314yes—
316C22×C4⋊C4C2312yes—
317C22×C4⋊C4C2312yes—
318C22×C4⋊C4C2312yes—
319C22×C42C2312yes—
320C22×C42C2314yes—
321C22×C42C2312yes—
322C22×C42C2311yescharacteristic
323#400C2314yes—
324#400C2314yes—
325#400C2318yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2318yes—
330#400C2318yes—
331#400C2318yes—
332#399C2314yes—
333#399C2314yes—
334#399C2314yes—
335#399C2318yes—
336#399C2318yes—
337#398C2318yes—
338#398C2318yes—
339#398C2318yes—
340#398C2314yes—
341#398C2318yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2318yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2318yes—
350#398C2318yes—
351#398C2318yes—
352#398C2318yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2318yes—
357#397C2318yes—
358#396C2318yes—
359#396C2318yes—
360#396C2318yes—
361#396C2314yes—
362#396C2314yes—
363#396C2318yes—
364#396C2318yes—
365#395C2314yes—
366#395C2314yes—
367#395C2318yes—
368#395C2314yes—
369#395C2314yes—
370#395C2314yes—
371#395C2314yes—
372#395C2314yes—
373#395C2314yes—
374#395C2318yes—
375#394C2314yes—
376#394C2318yes—
377#394C2314yes—
378#394C2318yes—
379#393C2314yes—
380#393C2314yes—
381#393C2314yes—
382#393C2314yes—
383#393C2314yes—
384#393C2314yes—
385#391C2312yes—
386#391C2312yes—
387#391C2314yes—
388#391C2314yes—
389#391C2312yes—
390#391C2314yes—
391#391C2314yes—
392#391C2318yes—
393#391C2318yes—
394#391C2318yes—
395#391C2318yes—
396#390C2314yes—
397#390C2312yes—
398#390C2318yes—
399#390C2318yes—
400#389C2318yes—
401#389C2318yes—
402#389C2318yes—
403#389C2314yes—
404#389C2318yes—
405#389C2314yes—
406#389C2314yes—
407#389C2318yes—
408#389C2318yes—
409#389C2318yes—
410#389C2318yes—
411#389C2318yes—
412#389C2318yes—
413#389C2318yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2318yes—
422#388C2318yes—
423#388C2318yes—
424#388C2318yes—
425#388C2318yes—
426#388C2318yes—
427#388C2314yes—
428#388C2314yes—
429#388C2318yes—
430#388C2318yes—
431#387C2318yes—
432#387C2318yes—
433#387C2318yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2318yes—
440#387C2318yes—
441#387C2318yes—
442#387C2318yes—
443#387C2318yes—
444#387C2318yes—
445#387C2318yes—
446#387C2318yes—
447#387C2318yes—
448#387C2318yes—
449#387C2318yes—
450#387C2314yes—
451#387C2314yes—
452#387C2318yes—
453#387C2318yes—
454#386C2314yes—
455#386C2314yes—
456#386C2314yes—
457#386C2312yes—
458#386C2314yes—
459#386C2312yes—
460#386C2314yes—
461#385C2314yes—
462#385C2314yes—
463#385C2314yes—
464#385C2318yes—
465#385C2318yes—
466#385C2318yes—
467#385C2312yes—
468#385C2318yes—
469#385C2314yes—
470#385C2318yes—
471#385C2318yes—
472#385C2312yes—
473#385C2314yes—
474#384C2312yes—
475#384C2318yes—
476#383C2312yes—
477#383C2312yes—
478#382C2312yes—
479#382C2312yes—
480#382C2312yes—
481#382C2318yes—
482#381C2312yes—
483#381C2312yes—
484#381C2312yes—
485#381C2314yes—
486#381C2312yes—
487#380C2314yes—
488#380C2314yes—
489#380C2314yes—
490#380C2312yes—
491#380C2312yes—
492#380C2318yes—
493#380C2318yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2318yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2318yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2318yes—
501C4×C22⋊C4C2314yes—
502C4×C22⋊C4C2314yes—
503C4×C22⋊C4C2312yes—
504C4×C22⋊C4C2311yescharacteristic
505C4×C22⋊C4C2311yescharacteristic
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2318yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2318yes—
510#376C2312yes—
511#376C2312yes—
512C2×#41—28no—
513C2×#41—48no—
514C22×Q8—28no—
515C22×Q8—24no—
516C22×Q8—24no—
517C22×Q8—28no—
518C22×Q8—48no—
519C22×Q8—44no—
520C22×Q8—48no—
521C22×Q8C2×D4116yes—
522C22×Q8C2412yes—
523C22×Q8C2412yes—
524C22×Q8C2412yes—
525C22×Q8C2411yescharacteristic
526C22×Q8C2412yes—
527C22×Q8C2412yes—
528C22×Q8C2411yescharacteristic
529C22×Q8C2412yes—
530C22×Q8C2414yes—
531C22×Q8C2414yes—
532C22×D4C2412yes—
533C22×D4C2412yes—
534C22×D4C2411yescharacteristic
535C22×D4C2411yescharacteristic
536C22×D4C2414yes—
537C23×C4C2412yes—
538C23×C4C2411yescharacteristic
539C23×C4C2411yescharacteristic
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C23×C4C2414yes—
546C23×C4C2414yes—
547C23×C4C2411yescharacteristic
548C23×C4C2414yes—
549C4⋊Q8—216no—
550C4⋊Q8—216no—
551C4⋊Q8—232no—
552C4⋊Q8—28no—
553C4⋊Q8—216no—
554C4⋊Q8—28no—
555C4⋊Q8—44no—
556C4⋊Q8C2×D4116yes—
557C4⋊Q8C2×D4116yes—
558C4⋊Q8C2×D418yes—
559C4⋊Q8C2×D418yes—
560C4⋊Q8C2×D4116yes—
561#126—216no—
562#126—216no—
563#126—216no—
564#126—28no—
565#126—28no—
566#125—232no—
567#125—232no—
568#125—232no—
569#125—232no—
570#125—216no—
571#125—232no—
572#125—216no—
573#125—216no—
574#125—216no—
575#125—216no—
576#125—28no—
577#125—24no—
578#125—24no—
579#124—28no—
580#124—216no—
581#124—24no—
582#124—24no—
583#124—44no—
584#123—28no—
585#123—28no—
586#123—28no—
587#123—216no—
588#123—28no—
589#123—216no—
590#123—216no—
591#123—216no—
592C22⋊Q8—28no—
593C22⋊Q8—28no—
594C22⋊Q8—216no—
595C22⋊Q8—216no—
596C22⋊Q8—24no—
597C22⋊Q8—24no—
598C22⋊Q8—216no—
599C22⋊Q8—216no—
600C22⋊Q8—216no—
601C22⋊Q8—216no—
602C22⋊Q8—28no—
603C22⋊Q8—48no—
604#121—24no—
605#121—24no—
606#121—216no—
607#121—28no—
608C4×Q8—216no—
609C4×Q8—216no—
610C4×Q8—232no—
611C4×Q8—28no—
612C4×Q8—28no—
613C4×Q8—216no—
614C4×Q8—232no—
615C4×Q8—216no—
616C4×Q8—28no—
617C4×Q8—28no—
618C4×Q8—28no—
619C4×Q8—28no—
620C4×Q8—28no—
621C4×Q8—28no—
622C4×Q8—28no—
623C4×Q8—28no—
624C4×Q8—28no—
625C4×Q8—24no—
626C4×Q8—24no—
627C4×Q8—48no—
628C4×Q8—48no—
629C4×D4—28no—
630C4×D4—28no—
631C4×D4—216no—
632C4×D4—216no—
633C4×D4—28no—
634C4×D4—24no—
635C4×D4—24no—
636#117—28no—
637#117—28no—
638#117—28no—
639C2×C4⋊C4—24no—
640C2×C4⋊C4—28no—
641C2×C4⋊C4—216no—
642C2×C4⋊C4—28no—
643C2×C4⋊C4—24no—
644C2×C4⋊C4—216no—
645C2×C4⋊C4—216no—
646C2×C4⋊C4—28no—
647C2×C4⋊C4C2×D4116yes—
648C2×C4⋊C4C2×D4116yes—
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2412yes—
681C2×C4⋊C4C2412yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2418yes—
685C2×C4⋊C4C2418yes—
686C2×C4⋊C4C2418yes—
687C2×C4⋊C4C2418yes—
688C2×C4⋊C4C2418yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2418yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2418yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2418yes—
695C2×C4⋊C4C2412yes—
696C2×C4⋊C4C2412yes—
697C2×C4⋊C4C2412yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2412yes—
700C2×C4⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2412yes—
703C2×C22⋊C4C2412yes—
704C2×C22⋊C4C2412yes—
705C2×C22⋊C4C2412yes—
706C2×C22⋊C4C2412yes—
707C2×C22⋊C4C2412yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2412yes—
711C2×C22⋊C4C2412yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2412yes—
714C2×C22⋊C4C2412yes—
715C2×C22⋊C4C2412yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2412yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2418yes—
721C2×C22⋊C4C2418yes—
722C2×C22⋊C4C2418yes—
723C2×C22⋊C4C2418yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2418yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2418yes—
728C2×C42—216no—
729C2×C42—28no—
730C2×C42—28no—
731C2×C42C2×D418yes—
732C2×C42C2412yes—
733C2×C42C2412yes—
734C2×C42C2414yes—
735C2×C42C2414yes—
736C2×C42C2418yes—
737C2×C42C2418yes—
738C2×C42C2414yes—
739C2×C42C2414yes—
740C2×C42C2414yes—
741C2×C42C2414yes—
742C2×C42C2412yes—
743C2×C42C2412yes—
744C2×C42C2418yes—
745C2×C42C2418yes—
746C2×C42C2414yes—
747C2×C42C2411yescharacteristic
748C2×C42C2411yescharacteristic
749C2×C42C2411yescharacteristic
750C2×C42C2411yescharacteristic
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2418yes—
757#95C2414yes—
758#95C2418yes—
759#95C2414yes—
760#95C2418yes—
761#95C2414yes—
762#95C2412yes—
763#95C2412yes—
764#95C2414yes—
765#95C2418yes—
766#95C2418yes—
767#95C2414yes—
768#95C2418yes—
769#95C2418yes—
770#95C2414yes—
771#95C2414yes—
772#95C2418yes—
773#95C2414yes—
774#95C2418yes—
775#95C2414yes—
776#95C2418yes—
777#95C2414yes—
778#95C2418yes—
779#95C2418yes—
780#95C2418yes—
781#95C2418yes—
782#95C2418yes—
783#95C2418yes—
784C24C2512yes—
785C24C2512yes—
786C24C2511yescharacteristic
787#41—816no—
788C2×Q8—232no—
789C2×Q8—24no—
790C2×Q8—24no—
791C2×Q8—22no—
792C2×Q8—24no—
793C2×Q8—24no—
794C2×Q8—22no—
795C2×Q8—28no—
796C2×Q8—28no—
797C2×Q8—28no—
798C2×Q8—28no—
799C2×Q8—28no—
800C2×Q8—24no—
801C2×Q8—24no—
802C2×Q8—24no—
803C2×Q8—48no—
804C2×Q8—44no—
805C2×Q8—42no—
806C2×Q8—48no—
807C2×Q8—432no—
808C2×Q8—416no—
809C2×Q8—816no—
810C2×Q8C22×D418yes—
811C2×Q8C22×D418yes—
812C2×Q8C22×D4116yes—
813C2×D4—24no—
814C2×D4—24no—
815C2×D4—28no—
816C2×D4—24no—
817C2×D4—24no—
818C2×D4—22no—
819C2×D4—22no—
820C2×D4—28no—
821C2×D4—24no—
822C2×D4—42no—
823C2×D4—48no—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—28no—
834C22×C4—28no—
835C22×C4—28no—
836C22×C4—42no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—48no—
841C22×C4—44no—
842C22×C4—48no—
843C22×C4—48no—
844C22×C4C22×D414yes—
845C22×C4C22×D414yes—
846C22×C4C22×D4116yes—
847C22×C4C22×D414yes—
848C22×C42−1+418yes—
849C22×C4C2514yes—
850C22×C4C2514yes—
851C22×C4C2518yes—
852C22×C4C2512yes—
853C22×C4C2512yes—
854C22×C4C2512yes—
855C22×C4C2512yes—
856C22×C4C2514yes—
857C22×C4C2512yes—
858C22×C4C2512yes—
859C22×C4C2514yes—
860C22×C4C2514yes—
861C22×C4C2511yescharacteristic
862C22×C4C2511yescharacteristic
863C22×C4C2511yescharacteristic
864C22×C4C2511yescharacteristic
865C22×C4C2514yes—
866C22×C4C2514yes—
867C22×C4C2511yescharacteristic
868C22×C4C2514yes—
869C22×C4C2511yescharacteristic
870C4⋊C4—22no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—28no—
874C4⋊C4—28no—
875C4⋊C4—216no—
876C4⋊C4—216no—
877C4⋊C4—28no—
878C4⋊C4—28no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—216no—
882C4⋊C4—216no—
883C4⋊C4—28no—
884C4⋊C4—216no—
885C4⋊C4—216no—
886C4⋊C4—22no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—24no—
891C4⋊C4—22no—
892C4⋊C4—28no—
893C4⋊C4—24no—
894C4⋊C4—28no—
895C4⋊C4—24no—
896C4⋊C4—22no—
897C4⋊C4—28no—
898C4⋊C4—28no—
899C4⋊C4—28no—
900C4⋊C4—24no—
901C4⋊C4—24no—
902C4⋊C4—28no—
903C4⋊C4—28no—
904C4⋊C4—216no—
905C4⋊C4—28no—
906C4⋊C4—44no—
907C4⋊C4—48no—
908C4⋊C4—48no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—48no—
912C4⋊C4—48no—
913C4⋊C4—48no—
914C4⋊C4—48no—
915C4⋊C4—48no—
916C4⋊C4C22×D418yes—
917C4⋊C4C22×D418yes—
918C4⋊C4C22×D418yes—
919C4⋊C4C22×D4116yes—
920C4⋊C4C22×D418yes—
921C4⋊C4C22×D4116yes—
922C22⋊C4—24no—
923C22⋊C4—24no—
924C22⋊C4—24no—
925C22⋊C4—28no—
926C22⋊C4—24no—
927C22⋊C4—28no—
928C22⋊C4—24no—
929C22⋊C4—24no—
930C22⋊C4—24no—
931C22⋊C4—24no—
932C22⋊C4—28no—
933C22⋊C4—28no—
934C22⋊C4—24no—
935C22⋊C4—24no—
936C22⋊C4—28no—
937C22⋊C4—24no—
938C22⋊C4—24no—
939C22⋊C4—28no—
940C22⋊C4—28no—
941C22⋊C4—216no—
942C22⋊C4—48no—
943C22⋊C4—48no—
944C22⋊C4—48no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—48no—
948C22⋊C4—48no—
949C42—216no—
950C42—216no—
951C42—28no—
952C42—28no—
953C42—28no—
954C42—28no—
955C42—24no—
956C42—24no—
957C42—28no—
958C42—28no—
959C42—24no—
960C42—24no—
961C42—44no—
962C42—48no—
963C42—48no—
964C42C22×D414yes—
965C42C22×D414yes—
966C42C22×D414yes—
967C42C22×D414yes—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23C23×D412yes—
980C23C2×2−1+414yes—
981C23C2611yescharacteristic
982Q8—216no—
983Q8—216no—
984Q8—216no—
985Q8—216no—
986Q8—416no—
987Q8—44no—
988Q8—48no—
989Q8—48no—
990Q8—44no—
991Q8—88no—
992D4—44no—
993D4—48no—
994D4—48no—
995D4—44no—
996D4—88no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—24no—
1001C2×C4—28no—
1002C2×C4—28no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—28no—
1007C2×C4—216no—
1008C2×C4—28no—
1009C2×C4—24no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—28no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—22no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—28no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—28no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—28no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—44no—
1040C2×C4—416no—
1041C2×C4—48no—
1042C2×C4—48no—
1043C2×C4—48no—
1044C2×C4—48no—
1045C2×C4—48no—
1046C2×C4—88no—
1047C2×C4—88no—
1048C2×C4C23×D412yes—
1049C2×C4C23×D412yes—
1050C2×C4C23×D412yes—
1051C2×C4C23×D418yes—
1052C2×C4C23×D418yes—
1053C2×C4C23×D412yes—
1054C2×C4C23×D412yes—
1055C2×C4C23×D412yes—
1056C2×C4C2×2−1+418yes—
1057C2×C4#58514yes—
1058C22—22no—
1059C22—22no—
1060C22—28no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—44no—
1068C22—44no—
1069C22—48no—
1070C22#348614yes—
1071C22C24×D411yescharacteristic
1072C22C22×2−1+412yes—
1073C22C2×#58512yes—
1074C222−1+612yes—
1075C4—22no—
1076C4—28no—
1077C4—28no—
1078C4—22no—
1079C4—22no—
1080C4—28no—
1081C4—22no—
1082C4—22no—
1083C4—42no—
1084C4—44no—
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—44no—
1089C4—42no—
1090C4—44no—
1091C4—42no—
1092C4—44no—
1093C4—44no—
1094C4—48no—
1095C4#348514yes—
1096C2—24no—
1097C2—82no—
1098C2—82no—
1099C2C2×#348511yescharacteristic
1100C2C2×#348611yescharacteristic
1101C2#6284811yescharacteristic
1102C2#6295614yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3552C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#557C2semidirect
3. #52065C2semidirect
4. #52058C2semidirect
5. #52055C2semidirect
6. #45394C2semidirect
7. #45336C2semidirect
8. #45335C2semidirect
9. #45334C2semidirect
10. #45324C2semidirect
11. #45323C2semidirect
12. #39721C2semidirect
13. #39717C2semidirect
14. #39593C2semidirect
15. #39589C2semidirect
16. #37120C2semidirect
17. #36578C2semidirect
18. Q8×#123C2semidirect
19. #35246C2semidirect
20. #35245C2semidirect
21. #35111C2semidirect
22. #35092C2semidirect
23. #34602C2semidirect
24. #34371C2semidirect

Maximal subgroups

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

subgroupindex
C2×#35522
C22×#5572
#520652
#520582
#520552
#453942
#453362
#453352
#453342
#453242
#453232
#397212
#397172
#395932
#395892
#371202
#365782
Q8×#1232
#352462
#352452
#351112
#350922
#346022
#343712