Finite Group Databasebeta

← #7658958

Subgroups — #7658958

Order 512.

6336 conjugacy classes of subgroups.

The subgroup lattice has 1235 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3518C211yesmaximal, characteristic, complemented
2C2×#3515C211yesmaximal, characteristic, complemented
3#42926C214yesmaximal, complemented
4#42793C212yesmaximal, complemented
5#42792C212yesmaximal, complemented
6#42648C212yesmaximal, complemented
7#42647C212yesmaximal, complemented
8#42386C214yesmaximal, complemented
9#42310C214yesmaximal, complemented
10#42179C218yesmaximal, complemented
11#41385C214yesmaximal, complemented
12#41384C214yesmaximal, complemented
13#37641C211yesmaximal, characteristic, complemented
14#37607C212yesmaximal, complemented
15#37555C211yesmaximal, characteristic, complemented
16#37555C211yesmaximal, characteristic, complemented
17#37541C212yesmaximal, complemented
18#37540C212yesmaximal, complemented
19#36699C212yesmaximal, complemented
20#36684C211yesmaximal, characteristic, complemented
21#36011C212yesmaximal, complemented
22#35846C212yesmaximal, complemented
23#35834C214yesmaximal, complemented
24#35749C212yesmaximal, complemented
25#35738C212yesmaximal, complemented
26#34189C211yesmaximal, characteristic, complemented
27#3518—216no—
28#3515—216no—
29C2×Q82C2211yescharacteristic
30C2×#557C2211yescharacteristic
31C2×#556C2211yescharacteristic
32C2×#556C2212yes—
33C2×#556C2214yes—
34C2×#556C2212yes—
35C2×#555C2212yes—
36C2×#555C2211yescharacteristic
37C2×#554C2211yescharacteristic
38C2×#554C2211yescharacteristic
39C2×#553C2212yes—
40C2×#552C2212yes—
41C2×#552C2214yes—
42C2×#552C2212yes—
43C2×D4×Q8C2211yescharacteristic
44C2×#548C2212yes—
45C2×#547C2211yescharacteristic
46C2×#547C2212yes—
47C2×#542C2214yes—
48C2×#542C2212yes—
49C2×#541C2212yes—
50C2×#539C2214yes—
51C2×#533C2211yescharacteristic
52C2×#533C2211yescharacteristic
53C2×#533C2212yes—
54C2×#529C2211yescharacteristic
55C2×#529C2212yes—
56C2×#529C2211yescharacteristic
57C2×#529C2212yes—
58C22×#125C2212yes—
59C2×#520C2212yes—
60C2×#519C2212yes—
61C2×C4×#41C2211yescharacteristic
62#2823C2214yes—
63#2822C2212yes—
64#2822C2212yes—
65#2822C2211yescharacteristic
66#2822C2212yes—
67#2822C2212yes—
68#2821C2214yes—
69#2821C2214yes—
70#2820C2211yescharacteristic
71#2820C2211yescharacteristic
72#2820C2212yes—
73#2820C2212yes—
74#2819C2211yescharacteristic
75#2817C2214yes—
76#2816C2214yes—
77#2814C2212yes—
78#2814C2212yes—
79#2814C2218yes—
80#2813C2212yes—
81#2813C2212yes—
82#2723C2218yes—
83#2720C2218yes—
84#2718C2218yes—
85#2717C2218yes—
86#2716C2218yes—
87#2713C2218yes—
88#2710C2218yes—
89#2708C2218yes—
90#2700C2218yes—
91#2698C2218yes—
92#2688C2218yes—
93#2686C2218yes—
94#2664C2218yes—
95#2663C2214yes—
96#2661C2214yes—
97#2660C2214yes—
98#2659C2212yes—
99#2659C2212yes—
100#2642C2214yes—
101#2639C2212yes—
102#2639C2212yes—
103#2638C2214yes—
104#2637C2214yes—
105#2637C2214yes—
106#2635C2214yes—
107#2634C2214yes—
108#2634C2214yes—
109#2634C2214yes—
110#2633C2214yes—
111#2630C2218yes—
112#2628C2212yes—
113#2628C2212yes—
114#2627C2218yes—
115#2625C2214yes—
116#2625C2214yes—
117#2623C2214yes—
118#2623C2214yes—
119#2621C2212yes—
120#2621C2214yes—
121#2621C2212yes—
122#2611C2214yes—
123#2611C2214yes—
124#2604C2214yes—
125#2603C2214yes—
126#2601C2218yes—
127#2599C2214yes—
128#2598C2214yes—
129#2591C2214yes—
130#2583C2214yes—
131#2582C2214yes—
132#2581C2212yes—
133#2581C2212yes—
134#2579C2218yes—
135#2568C2212yes—
136#2568C2212yes—
137#2565C2218yes—
138#2557C2218yes—
139#2553C2218yes—
140#2550C2214yes—
141#2546C2212yes—
142#2546C2212yes—
143#2542C2214yes—
144#2536C2212yes—
145#2536C2212yes—
146#2521C2218yes—
147#2503C2214yes—
148#2502C2214yes—
149#2498C2214yes—
150#2498C2214yes—
151#2496C2218yes—
152#2492C2214yes—
153#2489C2214yes—
154#2484C2214yes—
155#2484C2214yes—
156#2478C2218yes—
157#2477C2218yes—
158#2475C2218yes—
159#2474C2218yes—
160#2466C2218yes—
161#2465C2218yes—
162#2462C2218yes—
163#2459C2218yes—
164#2447C2214yes—
165#2446C2214yes—
166#2434C2214yes—
167#2432C2214yes—
168#2421C2214yes—
169#2420C2214yes—
170#2417C2214yes—
171#2417C2214yes—
172#2409C2214yes—
173#2407C2214yes—
174#2399C2214yes—
175#2398C2214yes—
176#2396C2212yes—
177#2396C2212yes—
178#2396C2218yes—
179#2395C2214yes—
180#2395C2214yes—
181#2392C2212yes—
182#2392C2212yes—
183#2392C2214yes—
184#2365C2214yes—
185#2362C2214yes—
186#2360C2214yes—
187#2357C2212yes—
188#2357C2212yes—
189#2356C2212yes—
190#2356C2212yes—
191#2353C2214yes—
192#2353C2214yes—
193#2352C2214yes—
194#2314C2214yes—
195#2311C2212yes—
196#2285C2211yescharacteristic
197#2283C2212yes—
198#2283C2212yes—
199C2×#382C2211yescharacteristic
200#2274C2212yes—
201C22×#41C2312yes—
202C22×#41C2311yescharacteristic
203C23×Q8C2312yes—
204Q82—28no—
205#557—28no—
206#556—28no—
207#556—216no—
208#556—232no—
209#556—216no—
210#555—28no—
211#555—216no—
212#554—28no—
213#554—28no—
214#553—216no—
215#552—216no—
216#552—232no—
217#552—216no—
218D4×Q8—28no—
219#548—216no—
220#547—216no—
221#547—28no—
222#542—216no—
223#542—232no—
224#541—216no—
225#539—232no—
226#533—28no—
227#533—216no—
228#533—28no—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2314yes—
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2314yes—
239#529—216no—
240#529—28no—
241#529—216no—
242#529—28no—
243C2×#126C2314yes—
244C2×#126C2312yes—
245C2×#126C2312yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#126C2314yes—
252C2×#125—216no—
253C2×#125C2311yescharacteristic
254C2×#125C2312yes—
255C2×#125C2311yescharacteristic
256C2×#125C2312yes—
257C2×#125C2314yes—
258C2×#125C2312yes—
259C2×#125C2312yes—
260C2×#125C2314yes—
261C2×#125C2314yes—
262C2×#125C2314yes—
263C2×#125C2312yes—
264C2×#124C2311yescharacteristic
265C2×#124C2311yescharacteristic
266C2×#124C2314yes—
267C2×#124C2312yes—
268C2×#124C2314yes—
269C2×#124C2314yes—
270C2×#124C2314yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×#123C2312yes—
274C2×#123C2312yes—
275C2×#123C2314yes—
276C2×#123C2314yes—
277C2×#123C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2311yescharacteristic
287C2×C22⋊Q8C2311yescharacteristic
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×#121C2312yes—
297C2×#121C2312yes—
298C2×#121C2311yescharacteristic
299C2×#121C2311yescharacteristic
300C2×#121C2312yes—
301C2×#121C2314yes—
302C2×#121C2314yes—
303#520—216no—
304#519—216no—
305C4×#41D4116yescomplemented
306C2×C4×Q8C2314yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2314yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2314yes—
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2311yescharacteristic
322C2×C4×D4C2314yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2311yescharacteristic
329C2×C4×D4C2311yescharacteristic
330C2×C4×D4C2312yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2311yescharacteristic
336C2×C4×D4C2311yescharacteristic
337C2×#117C2314yes—
338C2×#117C2314yes—
339C2×#117C2312yes—
340C2×#117C2312yes—
341C2×#117C2312yes—
342C2×#117C2312yes—
343C2×#117C2312yes—
344C2×#117C2312yes—
345C2×#117C2312yes—
346C2×#117C2314yes—
347C2×#117C2314yes—
348C2×#117C2312yes—
349C2×#117C2312yes—
350C2×#117C2311yescharacteristic
351C22×C4⋊C4C2314yes—
352C22×C4⋊C4C2314yes—
353C22×C4⋊C4C2312yes—
354C22×C4⋊C4C2312yes—
355C22×C4⋊C4C2312yes—
356C22×C4⋊C4C2312yes—
357C22×C42C2312yes—
358C22×C42C2311yescharacteristic
359#400C2318yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2312yes—
369#400C2312yes—
370#400C2318yes—
371#400C2318yes—
372#400C2318yes—
373#399C2318yes—
374#399C2312yes—
375#399C2314yes—
376#399C2314yes—
377#399C2312yes—
378#399C2318yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2318yes—
383#398C2318yes—
384#398C2318yes—
385#398C2314yes—
386#398C2314yes—
387#398C2318yes—
388#398C2318yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2312yes—
394#398C2312yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2318yes—
400#397C2318yes—
401#397C2318yes—
402#397C2312yes—
403#397C2314yes—
404#397C2314yes—
405#397C2312yes—
406#397C2318yes—
407#397C2318yes—
408#397C2318yes—
409#397C2314yes—
410#397C2314yes—
411#397C2318yes—
412#397C2318yes—
413#397C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2318yes—
417#396C2318yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#395C2312yes—
423#395C2314yes—
424#395C2318yes—
425#395C2314yes—
426#395C2312yes—
427#395C2318yes—
428#395C2318yes—
429#395C2318yes—
430#395C2314yes—
431#395C2314yes—
432#394C2312yes—
433#394C2314yes—
434#394C2318yes—
435#394C2318yes—
436#394C2314yes—
437#394C2312yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2318yes—
442#394C2318yes—
443#394C2314yes—
444#394C2314yes—
445#393C2318yes—
446#393C2312yes—
447#393C2312yes—
448#393C2318yes—
449#393C2314yes—
450#393C2314yes—
451#392C2312yes—
452#392C2312yes—
453#392C2318yes—
454#392C2314yes—
455#391C2318yes—
456#391C2318yes—
457#391C2314yes—
458#391C2318yes—
459#391C2318yes—
460#391C2314yes—
461#391C2314yes—
462#391C2314yes—
463#391C2314yes—
464#390C2314yes—
465#390C2318yes—
466#389C2314yes—
467#389C2314yes—
468#389C2318yes—
469#389C2318yes—
470#389C2318yes—
471#389C2318yes—
472#389C2318yes—
473#388C2318yes—
474#388C2318yes—
475#388C2318yes—
476#388C2318yes—
477#388C2318yes—
478#388C2318yes—
479#388C2318yes—
480#388C2318yes—
481#388C2318yes—
482#388C2318yes—
483#387C2318yes—
484#387C2318yes—
485#387C2318yes—
486#387C2318yes—
487#387C2318yes—
488#387C2318yes—
489#387C2318yes—
490#387C2318yes—
491#387C2318yes—
492#387C2318yes—
493#387C2318yes—
494#387C2318yes—
495#386C2318yes—
496#386C2318yes—
497#386C2318yes—
498#386C2318yes—
499#386C2318yes—
500#386C2318yes—
501#386C2318yes—
502#385C2318yes—
503#385C2318yes—
504#385C2318yes—
505#385C2318yes—
506#385C2318yes—
507#385C2318yes—
508#385C2318yes—
509#385C2318yes—
510#384C2318yes—
511#384C2312yes—
512#383C2314yes—
513#383C2314yes—
514#382C2311yescharacteristic
515#382C2312yes—
516#382C2311yescharacteristic
517#382C2318yes—
518#382C2314yes—
519#382C2312yes—
520#382C2312yes—
521#382C2312yes—
522#381C2314yes—
523#381C2314yes—
524#381C2318yes—
525#381C2318yes—
526#380C2314yes—
527#380C2314yes—
528#380C2314yes—
529#380C2314yes—
530#380C2312yes—
531#380C2312yes—
532#380C2318yes—
533#380C2318yes—
534C4×C4⋊C4C2314yes—
535C4×C4⋊C4C2312yes—
536C4×C4⋊C4C2312yes—
537C4×C4⋊C4C2314yes—
538C4×C4⋊C4C2314yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2318yes—
541C4×C4⋊C4C2314yes—
542C4×C4⋊C4C2318yes—
543C4×C22⋊C4C2314yes—
544C4×C22⋊C4C2318yes—
545C4×C22⋊C4C2318yes—
546C4×C22⋊C4C2314yes—
547C4×C22⋊C4C2314yes—
548C4×C22⋊C4C2318yes—
549C4×C22⋊C4C2314yes—
550#376C2314yes—
551#376C2314yes—
552C2×#95C2312yes—
553C2×#95C2312yes—
554C2×#41—28no—
555C2×#41—42no—
556C2×#41—42no—
557C2×#41—44no—
558C2×#41—44no—
559C2×#41C2×D418yes—
560C22×Q8—28no—
561C22×Q8—44no—
562C22×Q8—44no—
563C22×Q8C2412yes—
564C22×Q8C2412yes—
565C22×Q8C2411yescharacteristic
566C22×Q8C2411yescharacteristic
567C22×Q8C2411yescharacteristic
568C22×Q8C2414yes—
569C22×Q8C2412yes—
570C22×Q8C2414yes—
571C22×Q8C2412yes—
572C22×D4C2411yescharacteristic
573C22×D4C2411yescharacteristic
574C22×D4C2411yescharacteristic
575C22×D4C2414yes—
576C22×D4C2412yes—
577C22×D4C2414yes—
578C22×D4C2412yes—
579C22×D4C2414yes—
580C22×D4C2412yes—
581C23×C4C2412yes—
582C23×C4C2412yes—
583C23×C4C2411yescharacteristic
584C23×C4C2414yes—
585C23×C4C2414yes—
586C23×C4C2414yes—
587C23×C4C2414yes—
588C23×C4C2414yes—
589C23×C4C2412yes—
590C23×C4C2412yes—
591C23×C4C2412yes—
592C23×C4C2411yescharacteristic
593C23×C4C2411yescharacteristic
594C4⋊Q8—28no—
595C4⋊Q8—28no—
596C4⋊Q8—216no—
597C4⋊Q8—24no—
598C4⋊Q8—24no—
599C4⋊Q8—28no—
600C4⋊Q8—24no—
601C4⋊Q8—24no—
602C4⋊Q8—28no—
603C4⋊Q8—48no—
604#126—216no—
605#126—216no—
606#126—216no—
607#126—216no—
608#126—216no—
609#126—216no—
610#126—28no—
611#126—216no—
612#126—28no—
613#125—216no—
614#125—216no—
615#125—28no—
616#125—24no—
617#125—28no—
618#125—216no—
619#125—216no—
620#125—28no—
621#125—28no—
622#125—24no—
623#125—28no—
624#124—28no—
625#124—216no—
626#124—216no—
627#124—216no—
628#124—216no—
629#124—24no—
630#124—24no—
631#123—216no—
632#123—28no—
633#123—216no—
634#123—28no—
635#123—216no—
636#123—216no—
637#123—216no—
638C22⋊Q8—28no—
639C22⋊Q8—24no—
640C22⋊Q8—28no—
641C22⋊Q8—28no—
642C22⋊Q8—24no—
643C22⋊Q8—28no—
644C22⋊Q8—216no—
645C22⋊Q8—28no—
646C22⋊Q8—28no—
647C22⋊Q8—28no—
648C22⋊Q8—216no—
649C22⋊Q8—216no—
650C22⋊Q8—28no—
651C22⋊Q8—28no—
652C22⋊Q8—216no—
653C22⋊Q8—216no—
654C22⋊Q8—48no—
655C22⋊Q8—48no—
656#121—216no—
657#121—28no—
658#121—216no—
659#121—28no—
660#121—24no—
661#121—28no—
662#121—24no—
663C4×Q8—28no—
664C4×Q8—28no—
665C4×Q8—216no—
666C4×Q8—28no—
667C4×Q8—216no—
668C4×Q8—28no—
669C4×Q8—28no—
670C4×Q8—28no—
671C4×Q8—24no—
672C4×Q8—24no—
673C4×Q8—28no—
674C4×Q8—28no—
675C4×Q8—216no—
676C4×Q8—28no—
677C4×Q8C2×D418yes—
678C4×Q8C2×D418yes—
679C4×D4—28no—
680C4×D4—216no—
681C4×D4—28no—
682C4×D4—28no—
683C4×D4—216no—
684C4×D4—216no—
685C4×D4—24no—
686C4×D4—24no—
687C4×D4—28no—
688C4×D4—28no—
689C4×D4—48no—
690C4×D4C2×D418yes—
691C4×D4C2×D4116yes—
692C4×D4C2×D418yes—
693C4×D4C2×D4116yes—
694#117—28no—
695#117—28no—
696#117—28no—
697#117—28no—
698#117—28no—
699#117—216no—
700#117—216no—
701#117—216no—
702#117—28no—
703#117—28no—
704#117—216no—
705#117—44no—
706#117C2×D418yes—
707#117C2×D4116yes—
708C2×C4⋊C4—216no—
709C2×C4⋊C4—28no—
710C2×C4⋊C4—216no—
711C2×C4⋊C4—28no—
712C2×C4⋊C4—28no—
713C2×C4⋊C4—44no—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2418yes—
756C2×C4⋊C4C2418yes—
757C2×C4⋊C4C2418yes—
758C2×C4⋊C4C2418yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2418yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2418yes—
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2412yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2412yes—
771C2×C22⋊C4C2412yes—
772C2×C22⋊C4C2412yes—
773C2×C22⋊C4C2412yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2412yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2412yes—
784C2×C22⋊C4C2412yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2418yes—
793C2×C22⋊C4C2418yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2418yes—
796C2×C22⋊C4C2418yes—
797C2×C22⋊C4C2418yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2418yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2412yes—
805C2×C42C2×D4116yes—
806C2×C42C2×D418yes—
807C2×C42C2414yes—
808C2×C42C2414yes—
809C2×C42C2414yes—
810C2×C42C2414yes—
811C2×C42C2414yes—
812C2×C42C2412yes—
813C2×C42C2412yes—
814C2×C42C2414yes—
815C2×C42C2414yes—
816C2×C42C2418yes—
817C2×C42C2418yes—
818C2×C42C2412yes—
819C2×C42C2412yes—
820C2×C42C2411yescharacteristic
821C2×C42C2411yescharacteristic
822C2×C42C2411yescharacteristic
823C2×C42C2412yes—
824C2×C42C2411yescharacteristic
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2412yes—
830#95C2412yes—
831#95C2418yes—
832#95C2418yes—
833#95C2412yes—
834#95C2412yes—
835#95C2418yes—
836#95C2418yes—
837#95C2414yes—
838#95C2418yes—
839#95C2414yes—
840#95C2418yes—
841#95C2418yes—
842#95C2414yes—
843#95C2414yes—
844#95C2418yes—
845#95C2418yes—
846#95C2414yes—
847#95C2418yes—
848#95C2418yes—
849#95C2414yes—
850#95C2418yes—
851#95C2418yes—
852#95C2418yes—
853#95C2418yes—
854#95C2418yes—
855#95C2418yes—
856#95C2418yes—
857C24C2512yes—
858C24C2512yes—
859C24C2511yescharacteristic
860C24C2512yes—
861#41—416no—
862#41—432no—
863C2×Q8—22no—
864C2×Q8—22no—
865C2×Q8—28no—
866C2×Q8—24no—
867C2×Q8—24no—
868C2×Q8—24no—
869C2×Q8—24no—
870C2×Q8—28no—
871C2×Q8—22no—
872C2×Q8—22no—
873C2×Q8—24no—
874C2×Q8—24no—
875C2×Q8—24no—
876C2×Q8—24no—
877C2×Q8—44no—
878C2×Q8—44no—
879C2×Q8—42no—
880C2×Q8—42no—
881C2×Q8—48no—
882C2×Q8—44no—
883C2×Q8—44no—
884C2×Q8—432no—
885C2×Q8C22×D414yes—
886C2×D4—28no—
887C2×D4—24no—
888C2×D4—24no—
889C2×D4—28no—
890C2×D4—22no—
891C2×D4—22no—
892C2×D4—22no—
893C2×D4—22no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—48no—
905C2×D4—44no—
906C2×D4C22×D414yes—
907C2×D4C22×D418yes—
908C22×C4—22no—
909C22×C4—22no—
910C22×C4—28no—
911C22×C4—28no—
912C22×C4—24no—
913C22×C4—28no—
914C22×C4—24no—
915C22×C4—24no—
916C22×C4—24no—
917C22×C4—24no—
918C22×C4—24no—
919C22×C4—28no—
920C22×C4—44no—
921C22×C4—44no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—44no—
925C22×C4—44no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—44no—
929C22×C4—44no—
930C22×C4—48no—
931C22×C4—48no—
932C22×C4—44no—
933C22×C4—44no—
934C22×C4—44no—
935C22×C4C22×D414yes—
936C22×C4C22×D418yes—
937C22×C4C22×D418yes—
938C22×C4C22×D418yes—
939C22×C4C22×D414yes—
940C22×C4C22×D414yes—
941C22×C4C2514yes—
942C22×C4C2518yes—
943C22×C4C2514yes—
944C22×C4C2512yes—
945C22×C4C2514yes—
946C22×C4C2514yes—
947C22×C4C2512yes—
948C22×C4C2512yes—
949C22×C4C2512yes—
950C22×C4C2512yes—
951C22×C4C2514yes—
952C22×C4C2514yes—
953C22×C4C2512yes—
954C22×C4C2511yescharacteristic
955C22×C4C2511yescharacteristic
956C22×C4C2512yes—
957C22×C4C2512yes—
958C22×C4C2512yes—
959C22×C4C2511yescharacteristic
960C22×C4C2511yescharacteristic
961C22×C4C2511yescharacteristic
962C22×C4C2511yescharacteristic
963C4⋊C4—28no—
964C4⋊C4—24no—
965C4⋊C4—22no—
966C4⋊C4—24no—
967C4⋊C4—22no—
968C4⋊C4—24no—
969C4⋊C4—24no—
970C4⋊C4—28no—
971C4⋊C4—24no—
972C4⋊C4—28no—
973C4⋊C4—28no—
974C4⋊C4—28no—
975C4⋊C4—28no—
976C4⋊C4—28no—
977C4⋊C4—28no—
978C4⋊C4—24no—
979C4⋊C4—24no—
980C4⋊C4—22no—
981C4⋊C4—24no—
982C4⋊C4—22no—
983C4⋊C4—28no—
984C4⋊C4—24no—
985C4⋊C4—28no—
986C4⋊C4—24no—
987C4⋊C4—28no—
988C4⋊C4—24no—
989C4⋊C4—28no—
990C4⋊C4—28no—
991C4⋊C4—24no—
992C4⋊C4—24no—
993C4⋊C4—28no—
994C4⋊C4—24no—
995C4⋊C4—24no—
996C4⋊C4—28no—
997C4⋊C4—24no—
998C4⋊C4—28no—
999C4⋊C4—28no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—44no—
1003C4⋊C4—44no—
1004C4⋊C4—48no—
1005C4⋊C4—48no—
1006C4⋊C4—44no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—44no—
1010C4⋊C4—48no—
1011C4⋊C4—48no—
1012C4⋊C4—48no—
1013C4⋊C4—48no—
1014C4⋊C4C22×D414yes—
1015C4⋊C4C22×D418yes—
1016C4⋊C4C22×D414yes—
1017C4⋊C4C22×D418yes—
1018C22⋊C4—28no—
1019C22⋊C4—28no—
1020C22⋊C4—28no—
1021C22⋊C4—28no—
1022C22⋊C4—28no—
1023C22⋊C4—24no—
1024C22⋊C4—24no—
1025C22⋊C4—28no—
1026C22⋊C4—28no—
1027C22⋊C4—24no—
1028C22⋊C4—24no—
1029C22⋊C4—24no—
1030C22⋊C4—24no—
1031C22⋊C4—24no—
1032C22⋊C4—28no—
1033C22⋊C4—24no—
1034C22⋊C4—28no—
1035C22⋊C4—24no—
1036C22⋊C4—24no—
1037C22⋊C4—28no—
1038C22⋊C4—44no—
1039C22⋊C4—44no—
1040C22⋊C4—48no—
1041C22⋊C4—48no—
1042C22⋊C4—48no—
1043C22⋊C4—48no—
1044C22⋊C4—44no—
1045C22⋊C4—44no—
1046C22⋊C4—44no—
1047C22⋊C4—44no—
1048C22⋊C4—44no—
1049C22⋊C4—48no—
1050C22⋊C4—48no—
1051C22⋊C4C22×D418yes—
1052C22⋊C4C22×D418yes—
1053C22⋊C4C22×D418yes—
1054C42—28no—
1055C42—28no—
1056C42—28no—
1057C42—28no—
1058C42—28no—
1059C42—24no—
1060C42—28no—
1061C42—24no—
1062C42—28no—
1063C42—48no—
1064C42—48no—
1065C42C22×D414yes—
1066C42C22×D418yes—
1067C42C22×D418yes—
1068C42C22×D414yes—
1069C42C22×D414yes—
1070C42C22×D414yes—
1071C42C22×D418yes—
1072C23—21no—
1073C23—21no—
1074C23—22no—
1075C23—22no—
1076C23—24no—
1077C23—24no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—24no—
1087C23—24no—
1088C23—24no—
1089C23—24no—
1090C23C23×D412yes—
1091C23C23×D414yes—
1092C23C2611yescharacteristic
1093Q8—28no—
1094Q8—44no—
1095Q8—44no—
1096Q8—416no—
1097Q8—48no—
1098Q8—48no—
1099Q8—84no—
1100Q8—88no—
1101Q8—84no—
1102D4—28no—
1103D4—48no—
1104D4—44no—
1105D4—44no—
1106D4—416no—
1107D4—84no—
1108D4—88no—
1109D4—84no—
1110D4—88no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—28no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—24no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—28no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—28no—
1146C2×C4—28no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—28no—
1153C2×C4—28no—
1154C2×C4—24no—
1155C2×C4—48no—
1156C2×C4—48no—
1157C2×C4—44no—
1158C2×C4—44no—
1159C2×C4—48no—
1160C2×C4—416no—
1161C2×C4—416no—
1162C2×C4—48no—
1163C2×C4—48no—
1164C2×C4—88no—
1165C2×C4—88no—
1166C2×C4—164no—
1167C2×C4C23×D414yes—
1168C2×C4C23×D412yes—
1169C2×C4C23×D412yes—
1170C2×C4C23×D414yes—
1171C2×C4C23×D412yes—
1172C2×C4C23×D412yes—
1173C2×C4C23×D412yes—
1174C2×C4C23×D414yes—
1175C2×C4C23×D412yes—
1176C2×C4#58512yes—
1177C2×C4#58512yes—
1178C22—24no—
1179C22—24no—
1180C22—22no—
1181C22—22no—
1182C22—22no—
1183C22—24no—
1184C22—42no—
1185C22—44no—
1186C22—42no—
1187C22—44no—
1188C22—44no—
1189C22—44no—
1190C22—44no—
1191C22—44no—
1192C22—42no—
1193C22—42no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22C24×D411yescharacteristic
1199C22C2×#58511yescharacteristic
1200C22C2×#58511yescharacteristic
1201C222−1+612yes—
1202C222−1+612yes—
1203C4—22no—
1204C4—22no—
1205C4—24no—
1206C4—24no—
1207C4—22no—
1208C4—22no—
1209C4—22no—
1210C4—24no—
1211C4—44no—
1212C4—44no—
1213C4—48no—
1214C4—42no—
1215C4—44no—
1216C4—42no—
1217C4—44no—
1218C4—42no—
1219C4—42no—
1220C4—42no—
1221C4—44no—
1222C4—42no—
1223C4—44no—
1224C4#344914yes—
1225C2—44no—
1226C2—42no—
1227C2—82no—
1228C2—82no—
1229C2C2×#344911yescharacteristic
1230C2#6285911yescharacteristic
1231C2#6285911yescharacteristic
1232C2#6305312yes—
1233C2#6306212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
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×#3518C2semidirect
2. C2×#3515C2semidirect
3. #42926C2semidirect
4. #42793C2semidirect
5. #42792C2semidirect
6. #42648C2semidirect
7. #42647C2semidirect
8. #42386C2semidirect
9. #42310C2semidirect
10. #42179C2semidirect
11. #41385C2semidirect
12. #41384C2semidirect
13. #37641C2semidirect
14. #37607C2semidirect
15. #37555C2semidirect
16. #37555C2semidirect
17. #37541C2semidirect
18. #37540C2semidirect
19. #36699C2semidirect
20. #36684C2semidirect
21. #36011C2semidirect
22. #35846C2semidirect
23. #35834C2semidirect
24. #35749C2semidirect
25. #35738C2semidirect
26. #34189C2semidirect
305. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35182
C2×#35152
#429262
#427932
#427922
#426482
#426472
#423862
#423102
#421792
#413852
#413842
#376412
#376072
#375552
#375412
#375402
#366992
#366842
#360112
#358462
#358342
#357492
#357382
#341892