Finite Group Databasebeta

← #7658696

Subgroups — #7658696

Order 512.

6318 conjugacy classes of subgroups.

The subgroup lattice has 1204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3523C211yesmaximal, characteristic, complemented
2C2×#3507C211yesmaximal, characteristic, complemented
3#42884C212yesmaximal, complemented
4#42877C212yesmaximal, complemented
5#42812C212yesmaximal, complemented
6#42791C212yesmaximal, complemented
7#42787C214yesmaximal, complemented
8#42389C214yesmaximal, complemented
9#42312C214yesmaximal, complemented
10#42175C214yesmaximal, complemented
11#42171C214yesmaximal, complemented
12#41377C218yesmaximal, complemented
13#37635C211yesmaximal, characteristic, complemented
14#37619C211yesmaximal, characteristic, complemented
15#37560C212yesmaximal, complemented
16#37559C211yesmaximal, characteristic
17#37552C212yesmaximal, complemented
18#37552C212yesmaximal, complemented
19#36699C211yesmaximal, characteristic, complemented
20#36699C212yesmaximal, complemented
21#36048C212yesmaximal, complemented
22#36041C212yesmaximal, complemented
23#35938C212yesmaximal, complemented
24#35802C214yesmaximal, complemented
25#35749C212yesmaximal, complemented
26#34192C211yesmaximal, characteristic, complemented
27#3523—216no—
28#3507—216no—
29C2×#559C2211yescharacteristic
30C2×#559C2211yescharacteristic
31C2×#557C2211yescharacteristic
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#557C2212yes—
36C2×#556C2212yes—
37C2×#556C2212yes—
38C2×#556C2212yes—
39C2×#556C2212yes—
40C2×#556C2211yescharacteristic
41C2×#554C2212yes—
42C2×#552C2214yes—
43C2×#552C2214yes—
44C2×#552C2212yes—
45C2×D4×Q8C2212yes—
46C2×D4×Q8C2211yescharacteristic
47C2×#541C2212yes—
48C2×#541C2214yes—
49C2×#539C2214yes—
50C2×#536C2212yes—
51C2×#533C2211yescharacteristic
52C2×#533C2211yescharacteristic
53C2×#533C2212yes—
54C2×#532C2211yescharacteristic
55C2×#529C2212yes—
56C2×#529C2212yes—
57C2×#529C2211yescharacteristic
58C2×#529C2212yes—
59C2×#520C2212yes—
60C2×#519C2212yes—
61C22×C4×Q8C2211yescharacteristic
62#2822C2214yes—
63#2822C2212yes—
64#2821C2214yes—
65#2821C2212yes—
66#2821C2214yes—
67#2821C2212yes—
68#2820C2214yes—
69#2820C2212yes—
70#2817C2212yes—
71#2817C2212yes—
72#2817C2211yescharacteristic
73#2817C2211yescharacteristic
74#2816C2211yescharacteristic
75#2816C2211yescharacteristic
76#2816C2212yes—
77#2816C2212yes—
78#2816C2212yes—
79#2815C2212yes—
80#2814C2218yes—
81#2814C2214yes—
82#2732C2218yes—
83#2729C2218yes—
84#2729C2218yes—
85#2728C2218yes—
86#2726C2218yes—
87#2725C2218yes—
88#2723C2218yes—
89#2721C2218yes—
90#2707C2218yes—
91#2705C2218yes—
92#2692C2218yes—
93#2690C2218yes—
94#2664C2214yes—
95#2664C2214yes—
96#2663C2218yes—
97#2662C2214yes—
98#2662C2214yes—
99#2661C2214yes—
100#2660C2212yes—
101#2658C2212yes—
102#2642C2212yes—
103#2640C2212yes—
104#2637C2214yes—
105#2637C2214yes—
106#2636C2214yes—
107#2636C2214yes—
108#2634C2214yes—
109#2634C2214yes—
110#2633C2214yes—
111#2633C2212yes—
112#2632C2214yes—
113#2631C2212yes—
114#2630C2218yes—
115#2630C2218yes—
116#2628C2214yes—
117#2628C2214yes—
118#2625C2214yes—
119#2624C2214yes—
120#2621C2212yes—
121#2619C2212yes—
122#2611C2214yes—
123#2611C2214yes—
124#2610C2214yes—
125#2610C2214yes—
126#2604C2214yes—
127#2604C2214yes—
128#2603C2214yes—
129#2602C2218yes—
130#2602C2218yes—
131#2599C2214yes—
132#2599C2214yes—
133#2598C2214yes—
134#2598C2214yes—
135#2592C2212yes—
136#2584C2214yes—
137#2581C2212yes—
138#2581C2212yes—
139#2580C2214yes—
140#2568C2212yes—
141#2567C2212yes—
142#2562C2214yes—
143#2560C2218yes—
144#2556C2218yes—
145#2548C2212yes—
146#2546C2214yes—
147#2546C2212yes—
148#2545C2214yes—
149#2540C2212yes—
150#2519C2218yes—
151#2512C2218yes—
152#2499C2214yes—
153#2485C2218yes—
154#2481C2218yes—
155#2479C2218yes—
156#2475C2218yes—
157#2475C2218yes—
158#2473C2218yes—
159#2471C2218yes—
160#2462C2218yes—
161#2458C2218yes—
162#2454C2214yes—
163#2453C2214yes—
164#2448C2214yes—
165#2446C2214yes—
166#2436C2214yes—
167#2434C2214yes—
168#2432C2214yes—
169#2429C2214yes—
170#2429C2214yes—
171#2427C2214yes—
172#2426C2214yes—
173#2407C2214yes—
174#2399C2214yes—
175#2399C2212yes—
176#2398C2212yes—
177#2398C2214yes—
178#2396C2212yes—
179#2396C2214yes—
180#2396C2212yes—
181#2396C2214yes—
182#2395C2214yes—
183#2395C2218yes—
184#2367C2214yes—
185#2365C2214yes—
186#2363C2214yes—
187#2362C2214yes—
188#2356C2214yes—
189#2356C2212yes—
190#2351C2212yes—
191#2345C2214yes—
192#2345C2212yes—
193Q8×C22⋊C4C2212yes—
194#2320C2212yes—
195#2320C2214yes—
196#2283C2211yescharacteristic
197#2283C2212yes—
198#2283C2211yescharacteristic
199#2283C2212yes—
200#2276C2212yes—
201C22×#41C2312yes—
202C23×Q8C2312yes—
203C23×Q8C2311yescharacteristic
204#559—28no—
205#559—28no—
206#557—28no—
207#557—28no—
208#557—28no—
209#557—216no—
210#557—28no—
211#556—216no—
212#556—216no—
213#556—216no—
214#556—216no—
215#556—28no—
216#554—216no—
217#552—232no—
218#552—216no—
219#552—232no—
220D4×Q8—216no—
221D4×Q8—28no—
222#541—232no—
223#541—216no—
224#539—232no—
225#536—216no—
226#533—28no—
227#533—216no—
228#533—28no—
229#532—28no—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2311yescharacteristic
236C2×C4⋊Q8C2311yescharacteristic
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2312yes—
239C2×C4⋊Q8C2314yes—
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2314yes—
242C2×#127C2311yescharacteristic
243#529—216no—
244#529—216no—
245#529—216no—
246#529—28no—
247C2×#126C2314yes—
248C2×#126C2312yes—
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#126C2314yes—
252C2×#126C2314yes—
253C2×#126C2314yes—
254C2×#126C2314yes—
255C2×#126C2314yes—
256C2×#125C2314yes—
257C2×#125C2312yes—
258C2×#125C2311yescharacteristic
259C2×#125C2312yes—
260C2×#125C2312yes—
261C2×#125C2312yes—
262C2×#125C2312yes—
263C2×#125C2314yes—
264C2×#125C2314yes—
265C2×#125C2314yes—
266C2×#125C2314yes—
267C2×#125C2312yes—
268C2×#125C2314yes—
269C2×#125C2314yes—
270C2×#124C2311yescharacteristic
271C2×#124C2312yes—
272C2×#124C2312yes—
273C2×#124C2312yes—
274C2×#124C2312yes—
275C2×#124C2312yes—
276C2×#124C2312yes—
277C2×#124C2314yes—
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×#123C2314yes—
281C2×#123C2312yes—
282C2×#123C2314yes—
283C2×#123C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2311yescharacteristic
287C2×C22⋊Q8C2311yescharacteristic
288C2×C22⋊Q8C2311yescharacteristic
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×#121C2312yes—
301C2×#121C2311yescharacteristic
302C2×#121C2312yes—
303C2×#121C2314yes—
304#520—216no—
305#519—216no—
306C2×C4×Q8D4116yescomplemented
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2314yes—
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2314yes—
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2314yes—
325C2×C4×Q8C2311yescharacteristic
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2311yescharacteristic
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2311yescharacteristic
331C2×C4×D4C2312yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2314yes—
336C2×C4×D4C2314yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2314yes—
340C2×C4×D4C2312yes—
341C2×C4×D4C2311yescharacteristic
342C2×C4×D4C2312yes—
343C2×#117C2314yes—
344C2×#117C2314yes—
345C2×#117C2314yes—
346C2×#117C2312yes—
347C2×#117C2312yes—
348C2×#117C2312yes—
349C2×#117C2312yes—
350C2×#117C2314yes—
351C2×#117C2314yes—
352C2×#117C2314yes—
353C22×C4⋊C4C2314yes—
354C22×C4⋊C4C2311yescharacteristic
355C22×C4⋊C4C2312yes—
356C22×C42C2312yes—
357C22×C42C2311yescharacteristic
358#400C2312yes—
359#400C2314yes—
360#400C2312yes—
361#400C2312yes—
362#400C2314yes—
363#400C2314yes—
364#400C2312yes—
365#400C2314yes—
366#400C2318yes—
367#400C2314yes—
368#400C2318yes—
369#400C2318yes—
370#399C2314yes—
371#399C2312yes—
372#399C2314yes—
373#399C2312yes—
374#399C2314yes—
375#399C2318yes—
376#399C2314yes—
377#399C2318yes—
378#399C2318yes—
379#398C2318yes—
380#398C2314yes—
381#398C2312yes—
382#398C2312yes—
383#398C2314yes—
384#398C2314yes—
385#398C2318yes—
386#398C2314yes—
387#398C2318yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2318yes—
392#398C2314yes—
393#398C2318yes—
394#398C2318yes—
395#398C2318yes—
396#397C2318yes—
397#397C2318yes—
398#397C2318yes—
399#397C2314yes—
400#397C2314yes—
401#397C2318yes—
402#397C2314yes—
403#397C2318yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#396C2318yes—
409#396C2314yes—
410#396C2318yes—
411#396C2314yes—
412#396C2318yes—
413#396C2318yes—
414#396C2318yes—
415#396C2318yes—
416#395C2312yes—
417#395C2312yes—
418#395C2314yes—
419#395C2312yes—
420#395C2314yes—
421#395C2312yes—
422#395C2314yes—
423#395C2314yes—
424#395C2318yes—
425#395C2314yes—
426#395C2318yes—
427#394C2318yes—
428#394C2314yes—
429#394C2314yes—
430#394C2312yes—
431#394C2312yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2318yes—
436#394C2318yes—
437#394C2318yes—
438#394C2314yes—
439#394C2318yes—
440#393C2314yes—
441#393C2314yes—
442#393C2314yes—
443#393C2312yes—
444#393C2312yes—
445#393C2314yes—
446#393C2318yes—
447#393C2318yes—
448#392C2314yes—
449#392C2314yes—
450#392C2318yes—
451#392C2314yes—
452#391C2314yes—
453#391C2314yes—
454#391C2314yes—
455#391C2314yes—
456#391C2314yes—
457#391C2318yes—
458#391C2314yes—
459#391C2314yes—
460#390C2318yes—
461#390C2318yes—
462#390C2314yes—
463#390C2318yes—
464#390C2318yes—
465#390C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2318yes—
470#389C2318yes—
471#389C2318yes—
472#389C2318yes—
473#389C2318yes—
474#389C2318yes—
475#389C2318yes—
476#389C2318yes—
477#388C2318yes—
478#388C2318yes—
479#388C2318yes—
480#388C2318yes—
481#388C2318yes—
482#388C2318yes—
483#388C2318yes—
484#388C2318yes—
485#388C2318yes—
486#388C2318yes—
487#388C2318yes—
488#388C2318yes—
489#388C2318yes—
490#387C2318yes—
491#387C2318yes—
492#387C2318yes—
493#387C2318yes—
494#387C2318yes—
495#387C2318yes—
496#387C2318yes—
497#387C2318yes—
498#387C2318yes—
499#387C2318yes—
500#387C2318yes—
501#386C2318yes—
502#386C2318yes—
503#386C2318yes—
504#386C2318yes—
505#386C2318yes—
506#385C2318yes—
507#385C2318yes—
508#385C2318yes—
509#385C2318yes—
510#385C2318yes—
511#385C2318yes—
512#385C2318yes—
513#384C2314yes—
514#383C2314yes—
515#383C2312yes—
516#383C2312yes—
517#383C2314yes—
518#382C2312yes—
519#382C2314yes—
520#382C2314yes—
521#382C2314yes—
522#382C2312yes—
523#381C2311yescharacteristic
524#381C2311yescharacteristic
525#381C2312yes—
526#380C2318yes—
527#380C2318yes—
528#380C2312yes—
529#380C2314yes—
530#380C2312yes—
531#380C2314yes—
532C4×C4⋊C4C2318yes—
533C4×C4⋊C4C2314yes—
534C4×C4⋊C4C2312yes—
535C4×C4⋊C4C2314yes—
536C4×C4⋊C4C2314yes—
537C4×C4⋊C4C2312yes—
538C4×C4⋊C4C2318yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2318yes—
541C4×C4⋊C4C2314yes—
542C4×C22⋊C4C2318yes—
543C4×C22⋊C4C2314yes—
544C4×C22⋊C4C2312yes—
545C4×C22⋊C4C2314yes—
546C4×C22⋊C4C2312yes—
547C4×C22⋊C4C2314yes—
548C4×C22⋊C4C2314yes—
549C4×C22⋊C4C2318yes—
550#376C2314yes—
551#376C2312yes—
552#376C2312yes—
553#376C2314yes—
554C2×#41—28no—
555C2×#41—48no—
556C22×Q8—28no—
557C22×Q8—44no—
558C22×Q8—44no—
559C22×Q8—44no—
560C22×Q8C2×D418yes—
561C22×Q8C2412yes—
562C22×Q8C2412yes—
563C22×Q8C2411yescharacteristic
564C22×Q8C2411yescharacteristic
565C22×Q8C2411yescharacteristic
566C22×Q8C2411yescharacteristic
567C22×Q8C2412yes—
568C22×Q8C2411yescharacteristic
569C22×Q8C2414yes—
570C22×Q8C2412yes—
571C22×Q8C2412yes—
572C22×D4C2412yes—
573C22×D4C2412yes—
574C22×D4C2411yescharacteristic
575C22×D4C2412yes—
576C22×D4C2414yes—
577C22×D4C2412yes—
578C22×D4C2418yes—
579C23×C4C2412yes—
580C23×C4C2411yescharacteristic
581C23×C4C2414yes—
582C23×C4C2414yes—
583C23×C4C2414yes—
584C23×C4C2414yes—
585C23×C4C2412yes—
586C23×C4C2411yescharacteristic
587C23×C4C2412yes—
588C23×C4C2411yescharacteristic
589C4⋊Q8—28no—
590C4⋊Q8—28no—
591C4⋊Q8—28no—
592C4⋊Q8—216no—
593C4⋊Q8—24no—
594C4⋊Q8—28no—
595C4⋊Q8—24no—
596C4⋊Q8—24no—
597C4⋊Q8—24no—
598C4⋊Q8—28no—
599C4⋊Q8—24no—
600C4⋊Q8—48no—
601#127—24no—
602#126—216no—
603#126—216no—
604#126—216no—
605#126—216no—
606#126—216no—
607#126—28no—
608#126—216no—
609#126—216no—
610#126—216no—
611#125—216no—
612#125—216no—
613#125—216no—
614#125—216no—
615#125—216no—
616#125—28no—
617#125—216no—
618#125—28no—
619#125—28no—
620#125—28no—
621#125—24no—
622#125—28no—
623#125—216no—
624#125—28no—
625#124—28no—
626#124—28no—
627#124—28no—
628#124—24no—
629#124—28no—
630#124—28no—
631#124—28no—
632#124—48no—
633#123—216no—
634#123—216no—
635#123—216no—
636#123—28no—
637#123—216no—
638#123—216no—
639C22⋊Q8—216no—
640C22⋊Q8—216no—
641C22⋊Q8—28no—
642C22⋊Q8—216no—
643C22⋊Q8—24no—
644C22⋊Q8—24no—
645C22⋊Q8—28no—
646C22⋊Q8—24no—
647C22⋊Q8—28no—
648C22⋊Q8—28no—
649C22⋊Q8—216no—
650C22⋊Q8—216no—
651C22⋊Q8—216no—
652C22⋊Q8—28no—
653C22⋊Q8—216no—
654C22⋊Q8—48no—
655#121—24no—
656#121—28no—
657#121—28no—
658#121—48no—
659C4×Q8—28no—
660C4×Q8—28no—
661C4×Q8—216no—
662C4×Q8—28no—
663C4×Q8—28no—
664C4×Q8—216no—
665C4×Q8—28no—
666C4×Q8—28no—
667C4×Q8—28no—
668C4×Q8—28no—
669C4×Q8—24no—
670C4×Q8—28no—
671C4×Q8—28no—
672C4×Q8—28no—
673C4×Q8—28no—
674C4×Q8—24no—
675C4×Q8—24no—
676C4×Q8—48no—
677C4×Q8C2×D418yes—
678C4×Q8C2×D4116yes—
679C4×Q8C2×D418yes—
680C4×Q8C2×D418yes—
681C4×Q8C2×D4116yes—
682C4×Q8C2×D418yes—
683C4×D4—216no—
684C4×D4—216no—
685C4×D4—28no—
686C4×D4—216no—
687C4×D4—28no—
688C4×D4—28no—
689C4×D4—28no—
690C4×D4—24no—
691C4×D4—28no—
692C4×D4—28no—
693C4×D4—28no—
694C4×D4—28no—
695#117—28no—
696#117—216no—
697#117—28no—
698#117—28no—
699#117—216no—
700#117—216no—
701#117—216no—
702#117—28no—
703#117—216no—
704#117—216no—
705C2×C4⋊C4—216no—
706C2×C4⋊C4C2×D418yes—
707C2×C4⋊C4C2×D4116yes—
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2411yescharacteristic
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2418yes—
747C2×C4⋊C4C2418yes—
748C2×C4⋊C4C2418yes—
749C2×C4⋊C4C2418yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2418yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2418yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2418yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2411yescharacteristic
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2411yescharacteristic
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C22⋊C4C2412yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2412yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2412yes—
771C2×C22⋊C4C2412yes—
772C2×C22⋊C4C2412yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2418yes—
785C2×C22⋊C4C2418yes—
786C2×C22⋊C4C2418yes—
787C2×C22⋊C4C2418yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2418yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2418yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2418yes—
798C2×C22⋊C4C2418yes—
799C2×C42C2×D4116yes—
800C2×C42C2×D418yes—
801C2×C42C2414yes—
802C2×C42C2414yes—
803C2×C42C2414yes—
804C2×C42C2414yes—
805C2×C42C2414yes—
806C2×C42C2412yes—
807C2×C42C2412yes—
808C2×C42C2412yes—
809C2×C42C2414yes—
810C2×C42C2414yes—
811C2×C42C2418yes—
812C2×C42C2418yes—
813C2×C42C2414yes—
814C2×C42C2412yes—
815C2×C42C2412yes—
816C2×C42C2411yescharacteristic
817C2×C42C2412yes—
818C2×C42C2411yescharacteristic
819C2×C42C2411yescharacteristic
820C2×C42C2411yescharacteristic
821C2×C42C2412yes—
822#95C2412yes—
823#95C2414yes—
824#95C2412yes—
825#95C2418yes—
826#95C2414yes—
827#95C2414yes—
828#95C2412yes—
829#95C2414yes—
830#95C2418yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2418yes—
837#95C2418yes—
838#95C2414yes—
839#95C2418yes—
840#95C2418yes—
841#95C2414yes—
842#95C2412yes—
843#95C2414yes—
844#95C2418yes—
845#95C2418yes—
846#95C2418yes—
847#95C2414yes—
848#95C2414yes—
849#95C2418yes—
850#95C2418yes—
851#95C2418yes—
852#95C2418yes—
853#95C2418yes—
854C24C2512yes—
855C24C2514yes—
856C24C2511yescharacteristic
857#41—432no—
858C2×Q8—22no—
859C2×Q8—22no—
860C2×Q8—24no—
861C2×Q8—22no—
862C2×Q8—28no—
863C2×Q8—24no—
864C2×Q8—24no—
865C2×Q8—24no—
866C2×Q8—24no—
867C2×Q8—24no—
868C2×Q8—28no—
869C2×Q8—24no—
870C2×Q8—24no—
871C2×Q8—44no—
872C2×Q8—44no—
873C2×Q8—44no—
874C2×Q8—42no—
875C2×Q8—42no—
876C2×Q8—44no—
877C2×Q8—42no—
878C2×Q8—42no—
879C2×Q8—42no—
880C2×Q8—416no—
881C2×Q8—432no—
882C2×Q8C22×D414yes—
883C2×Q8C22×D414yes—
884C2×Q8C22×D418yes—
885C2×D4—24no—
886C2×D4—28no—
887C2×D4—22no—
888C2×D4—24no—
889C2×D4—24no—
890C2×D4—24no—
891C2×D4—28no—
892C2×D4—44no—
893C2×D4—42no—
894C2×D4—44no—
895C2×D4—48no—
896C2×D4—44no—
897C2×D4—48no—
898C2×D4—48no—
899C2×D4—48no—
900C22×C4—24no—
901C22×C4—28no—
902C22×C4—28no—
903C22×C4—24no—
904C22×C4—24no—
905C22×C4—24no—
906C22×C4—28no—
907C22×C4—28no—
908C22×C4—44no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—44no—
912C22×C4—44no—
913C22×C4—44no—
914C22×C4—48no—
915C22×C4—44no—
916C22×C4—44no—
917C22×C4—44no—
918C22×C4—44no—
919C22×C4C22×D414yes—
920C22×C4C22×D414yes—
921C22×C4C22×D418yes—
922C22×C4C22×D414yes—
923C22×C4C22×D418yes—
924C22×C4C2518yes—
925C22×C4C2514yes—
926C22×C4C2514yes—
927C22×C4C2512yes—
928C22×C4C2512yes—
929C22×C4C2512yes—
930C22×C4C2512yes—
931C22×C4C2512yes—
932C22×C4C2514yes—
933C22×C4C2512yes—
934C22×C4C2512yes—
935C22×C4C2514yes—
936C22×C4C2514yes—
937C22×C4C2511yescharacteristic
938C22×C4C2511yescharacteristic
939C22×C4C2512yes—
940C22×C4C2511yescharacteristic
941C22×C4C2512yes—
942C22×C4C2511yescharacteristic
943C22×C4C2511yescharacteristic
944C22×C4C2512yes—
945C22×C4C2512yes—
946C22×C4C2511yescharacteristic
947C4⋊C4—24no—
948C4⋊C4—28no—
949C4⋊C4—28no—
950C4⋊C4—24no—
951C4⋊C4—24no—
952C4⋊C4—24no—
953C4⋊C4—28no—
954C4⋊C4—24no—
955C4⋊C4—28no—
956C4⋊C4—24no—
957C4⋊C4—28no—
958C4⋊C4—24no—
959C4⋊C4—28no—
960C4⋊C4—28no—
961C4⋊C4—28no—
962C4⋊C4—24no—
963C4⋊C4—28no—
964C4⋊C4—24no—
965C4⋊C4—22no—
966C4⋊C4—22no—
967C4⋊C4—24no—
968C4⋊C4—24no—
969C4⋊C4—22no—
970C4⋊C4—24no—
971C4⋊C4—28no—
972C4⋊C4—24no—
973C4⋊C4—22no—
974C4⋊C4—28no—
975C4⋊C4—28no—
976C4⋊C4—28no—
977C4⋊C4—24no—
978C4⋊C4—24no—
979C4⋊C4—28no—
980C4⋊C4—28no—
981C4⋊C4—24no—
982C4⋊C4—28no—
983C4⋊C4—24no—
984C4⋊C4—28no—
985C4⋊C4—48no—
986C4⋊C4—44no—
987C4⋊C4—44no—
988C4⋊C4—44no—
989C4⋊C4—44no—
990C4⋊C4—48no—
991C4⋊C4—48no—
992C4⋊C4—44no—
993C4⋊C4—48no—
994C4⋊C4—48no—
995C4⋊C4—48no—
996C4⋊C4—48no—
997C4⋊C4C22×D418yes—
998C4⋊C4C22×D414yes—
999C4⋊C4C22×D418yes—
1000C4⋊C4C22×D414yes—
1001C4⋊C4C22×D418yes—
1002C4⋊C4C22×D418yes—
1003C4⋊C4C22×D418yes—
1004C22⋊C4—28no—
1005C22⋊C4—24no—
1006C22⋊C4—24no—
1007C22⋊C4—24no—
1008C22⋊C4—24no—
1009C22⋊C4—28no—
1010C22⋊C4—24no—
1011C22⋊C4—28no—
1012C22⋊C4—28no—
1013C22⋊C4—28no—
1014C22⋊C4—28no—
1015C22⋊C4—28no—
1016C22⋊C4—28no—
1017C22⋊C4—28no—
1018C22⋊C4—28no—
1019C22⋊C4—28no—
1020C22⋊C4—24no—
1021C22⋊C4—28no—
1022C22⋊C4—24no—
1023C22⋊C4—44no—
1024C22⋊C4—48no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—48no—
1028C22⋊C4—48no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—48no—
1033C22⋊C4—44no—
1034C22⋊C4—48no—
1035C22⋊C4—48no—
1036C22⋊C4—48no—
1037C22⋊C4—48no—
1038C42—28no—
1039C42—28no—
1040C42—28no—
1041C42—28no—
1042C42—28no—
1043C42—24no—
1044C42—24no—
1045C42—28no—
1046C42—24no—
1047C42—28no—
1048C42—48no—
1049C42—44no—
1050C42—48no—
1051C42C22×D418yes—
1052C42C22×D418yes—
1053C42C22×D414yes—
1054C42C22×D418yes—
1055C42C22×D414yes—
1056C42C22×D414yes—
1057C42C22×D414yes—
1058C42C22×D418yes—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—24no—
1064C23—22no—
1065C23—28no—
1066C23—22no—
1067C23—28no—
1068C23—24no—
1069C23—24no—
1070C23—24no—
1071C23—24no—
1072C23C23×D412yes—
1073C23C2611yescharacteristic
1074Q8—28no—
1075Q8—28no—
1076Q8—48no—
1077Q8—44no—
1078Q8—44no—
1079Q8—48no—
1080Q8—44no—
1081Q8—416no—
1082Q8—48no—
1083Q8—48no—
1084Q8—84no—
1085D4—48no—
1086D4—44no—
1087D4—48no—
1088D4—416no—
1089D4—48no—
1090D4—84no—
1091D4—168no—
1092C2×C4—24no—
1093C2×C4—22no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—22no—
1097C2×C4—24no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—28no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—24no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—22no—
1109C2×C4—24no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—28no—
1115C2×C4—22no—
1116C2×C4—24no—
1117C2×C4—28no—
1118C2×C4—22no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—28no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—28no—
1125C2×C4—24no—
1126C2×C4—28no—
1127C2×C4—24no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—44no—
1136C2×C4—48no—
1137C2×C4—44no—
1138C2×C4—48no—
1139C2×C4—416no—
1140C2×C4—416no—
1141C2×C4—48no—
1142C2×C4—88no—
1143C2×C4—88no—
1144C2×C4C23×D414yes—
1145C2×C4C23×D412yes—
1146C2×C4C23×D414yes—
1147C2×C4C23×D414yes—
1148C2×C4C23×D412yes—
1149C2×C4C23×D412yes—
1150C2×C4C23×D414yes—
1151C2×C4C23×D412yes—
1152C2×C4C23×D412yes—
1153C2×C4C23×D412yes—
1154C2×C4#58514yes—
1155C22—22no—
1156C22—22no—
1157C22—22no—
1158C22—44no—
1159C22—44no—
1160C22—48no—
1161C22—44no—
1162C22—48no—
1163C22—42no—
1164C22—44no—
1165C22—44no—
1166C22—42no—
1167C22—42no—
1168C22—44no—
1169C22C24×D411yescharacteristic
1170C22C2×#58512yes—
1171C222−1+612yes—
1172C222−1+612yes—
1173C4—22no—
1174C4—22no—
1175C4—24no—
1176C4—24no—
1177C4—22no—
1178C4—22no—
1179C4—22no—
1180C4—24no—
1181C4—24no—
1182C4—44no—
1183C4—44no—
1184C4—48no—
1185C4—42no—
1186C4—42no—
1187C4—42no—
1188C4—44no—
1189C4—42no—
1190C4—42no—
1191C4—42no—
1192C4—44no—
1193C4—42no—
1194C4—44no—
1195C4#344914yes—
1196C2—42no—
1197C2—82no—
1198C2—84no—
1199C2C2×#344911yescharacteristic
1200C2#6284811yescharacteristic
1201C2#6285911yescharacteristic
1202C2#6306214yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37559C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3523C2semidirect
2. C2×#3507C2semidirect
3. #42884C2semidirect
4. #42877C2semidirect
5. #42812C2semidirect
6. #42791C2semidirect
7. #42787C2semidirect
8. #42389C2semidirect
9. #42312C2semidirect
10. #42175C2semidirect
11. #42171C2semidirect
12. #41377C2semidirect
13. #37635C2semidirect
14. #37619C2semidirect
15. #37560C2semidirect
17. #37552C2semidirect
18. #37552C2semidirect
19. #36699C2semidirect
20. #36699C2semidirect
21. #36048C2semidirect
22. #36041C2semidirect
23. #35938C2semidirect
24. #35802C2semidirect
25. #35749C2semidirect
26. #34192C2semidirect
306. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35232
C2×#35072
#428842
#428772
#428122
#427912
#427872
#423892
#423122
#421752
#421712
#413772
#376352
#376192
#375602
#375592
#375522
#366992
#360482
#360412
#359382
#358022
#357492
#341922