Finite Group Databasebeta

← #7657324

Subgroups — #7657324

Order 512.

6820 conjugacy classes of subgroups.

The subgroup lattice has 1284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3522C211yesmaximal, characteristic, complemented
2C2×Q8×#41C211yesmaximal, characteristic, complemented
3#42806C214yesmaximal, complemented
4#42789C212yesmaximal, complemented
5#42788C212yesmaximal, complemented
6#42154C214yesmaximal, complemented
7#41957C214yesmaximal, complemented
8#40599C218yesmaximal, complemented
9#39725C212yesmaximal, complemented
10#39718C214yesmaximal, complemented
11#39597C212yesmaximal, complemented
12#39590C214yesmaximal, complemented
13#37640C211yesmaximal, characteristic, complemented
14#37622C211yesmaximal, characteristic, complemented
15#37619C212yesmaximal, complemented
16#37551C212yesmaximal, complemented
17#36580C212yesmaximal, complemented
18#36544C212yesmaximal, complemented
19#35712C212yesmaximal, complemented
20#35701C212yesmaximal, complemented
21#35697C214yesmaximal, complemented
22#35342C212yesmaximal, complemented
23#35292C211yesmaximal, characteristic, complemented
24#34614C211yesmaximal, characteristic, complemented
25#34609C212yesmaximal, complemented
26#34187C211yesmaximal, characteristic, complemented
27#3522—216no—
28C2×#559C2212yes—
29C2×#559C2211yescharacteristic
30Q8×#41—216no—
31C2×Q82C2211yescharacteristic
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2212yes—
35C2×#554C2212yes—
36C2×#554C2211yescharacteristic
37C2×#554C2212yes—
38C2×#554C2211yescharacteristic
39C2×#554C2214yes—
40C2×#554C2212yes—
41C2×#550C2211yescharacteristic
42C2×D4×Q8C2211yescharacteristic
43C2×D4×Q8C2212yes—
44C2×#548C2212yes—
45C2×#547C2212yes—
46C2×#547C2214yes—
47C2×#542C2212yes—
48C2×#542C2214yes—
49C2×#533C2211yescharacteristic
50C2×#533C2214yes—
51C2×#533C2212yes—
52C2×#533C2212yes—
53C2×#532C2211yescharacteristic
54C2×#532C2212yes—
55C2×#529C2212yes—
56C2×#529C2211yescharacteristic
57C2×#520C2212yes—
58C2×C4×#41C2212yes—
59C2×C4×#41C2211yescharacteristic
60C22×C4×Q8C2212yes—
61C22×C4×Q8C2211yescharacteristic
62#2857C2212yes—
63#2856C2212yes—
64#2851C2214yes—
65#2850C2214yes—
66#2821C2214yes—
67#2821C2214yes—
68#2820C2214yes—
69#2816C2218yes—
70#2814C2214yes—
71#2732C2218yes—
72#2731C2218yes—
73#2730C2218yes—
74#2729C2218yes—
75#2713C2218yes—
76#2711C2218yes—
77#2696C2218yes—
78#2692C2218yes—
79#2677C2218yes—
80#2677C2218yes—
81#2676C2218yes—
82#2674C2218yes—
83#2664C2214yes—
84#2663C2218yes—
85#2658C2214yes—
86#2640C2214yes—
87#2638C2218yes—
88#2637C2212yes—
89#2636C2212yes—
90#2635C2218yes—
91#2633C2214yes—
92#2633C2214yes—
93#2632C2214yes—
94#2631C2214yes—
95#2630C2214yes—
96#2629C2212yes—
97#2628C2212yes—
98#2628C2214yes—
99#2625C2212yes—
100#2625C2211yescharacteristic
101#2624C2212yes—
102#2624C2212yes—
103#2624C2212yes—
104#2624C2211yescharacteristic
105#2624C2212yes—
106#2621C2212yes—
107#2620C2214yes—
108#2620C2212yes—
109#2619C2214yes—
110#2616C2214yes—
111#2616C2211yescharacteristic
112#2615C2212yes—
113#2615C2211yescharacteristic
114#2611C2214yes—
115#2611C2214yes—
116#2604C2214yes—
117#2603C2214yes—
118#2602C2218yes—
119#2600C2218yes—
120#2599C2214yes—
121#2598C2214yes—
122#2592C2212yes—
123#2592C2214yes—
124#2592C2212yes—
125#2584C2212yes—
126#2584C2214yes—
127#2582C2212yes—
128#2581C2214yes—
129#2580C2212yes—
130#2580C2214yes—
131#2580C2214yes—
132#2580C2214yes—
133#2567C2212yes—
134#2558C2218yes—
135#2556C2218yes—
136#2551C2214yes—
137#2548C2212yes—
138#2548C2214yes—
139#2547C2212yes—
140#2546C2214yes—
141#2542C2212yes—
142#2540C2214yes—
143#2540C2212yes—
144#2538C2214yes—
145#2538C2212yes—
146#2535C2212yes—
147#2492C2214yes—
148#2491C2214yes—
149#2473C2218yes—
150#2465C2218yes—
151#2463C2218yes—
152#2461C2218yes—
153#2460C2218yes—
154#2458C2218yes—
155#2452C2218yes—
156#2449C2218yes—
157#2449C2218yes—
158#2448C2214yes—
159#2446C2214yes—
160#2443C2218yes—
161#2436C2214yes—
162#2432C2214yes—
163#2432C2218yes—
164#2423C2214yes—
165#2423C2214yes—
166#2415C2214yes—
167#2414C2214yes—
168#2409C2214yes—
169#2407C2214yes—
170#2407C2214yes—
171#2398C2214yes—
172#2397C2214yes—
173#2396C2212yes—
174#2392C2212yes—
175#2392C2214yes—
176#2388C2218yes—
177#2367C2214yes—
178#2361C2214yes—
179#2360C2214yes—
180#2356C2212yes—
181#2356C2212yes—
182#2356C2214yes—
183#2355C2214yes—
184#2355C2212yes—
185#2355C2212yes—
186D4×C4⋊C4C2214yes—
187#2324C2214yes—
188#2324C2214yes—
189#2323C2214yes—
190#2313C2214yes—
191#2310C2212yes—
192C4×C22⋊Q8C2212yes—
193C4×#121C2214yes—
194C4×#121C2212yes—
195C4×#121C2214yes—
196#2285C2211yescharacteristic
197#2285C2211yescharacteristic
198#2283C2212yes—
199#2283C2212yes—
200#2274C2212yes—
201C22×#41C2311yescharacteristic
202C22×#41C2312yes—
203C22×#41C2312yes—
204C22×#41C2314yes—
205C23×Q8C2312yes—
206C23×Q8C2311yescharacteristic
207#559—28no—
208#559—216no—
209Q82—28no—
210Q82—28no—
211#557—28no—
212#557—216no—
213#554—28no—
214#554—216no—
215#554—28no—
216#554—216no—
217#554—216no—
218#554—232no—
219#550—28no—
220D4×Q8—216no—
221D4×Q8—28no—
222#548—216no—
223#547—216no—
224#547—232no—
225#542—216no—
226#542—232no—
227#533—216no—
228#533—232no—
229#533—28no—
230#533—216no—
231#532—28no—
232#532—216no—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2311yescharacteristic
236C2×C4⋊Q8C2311yescharacteristic
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2314yes—
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2314yes—
242C2×C4⋊Q8C2312yes—
243C2×C4⋊Q8C2314yes—
244C2×C4⋊Q8C2312yes—
245C2×C4⋊Q8C2318yes—
246C2×#127C2311yescharacteristic
247C2×#127C2312yes—
248#529—216no—
249#529—28no—
250C2×#126C2314yes—
251C2×#126C2312yes—
252C2×#125C2312yes—
253C2×#125C2312yes—
254C2×#125C2311yescharacteristic
255C2×#125C2312yes—
256C2×#125C2312yes—
257C2×#125C2314yes—
258C2×#125C2314yes—
259C2×#125C2314yes—
260C2×#124C2312yes—
261C2×#124C2312yes—
262C2×#124C2311yescharacteristic
263C2×#124C2314yes—
264C2×#124C2312yes—
265C2×#124C2314yes—
266C2×#124C2314yes—
267C2×#124C2318yes—
268C2×#123C2314yes—
269C2×#123C2312yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2311yescharacteristic
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2318yes—
294C2×#121C2314yes—
295C2×#121C2314yes—
296C2×#121C2312yes—
297C2×#121C2312yes—
298C2×#121C2311yescharacteristic
299C2×#121C2312yes—
300C2×#121C2314yes—
301C2×#121C2312yes—
302C2×#121C2314yes—
303C2×#121C2314yes—
304#520—216no—
305C4×#41—216no—
306C4×#41—28no—
307C2×C4×Q8—216no—
308C2×C4×Q8D4116yescomplemented
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2314yes—
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2314yes—
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2314yes—
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2314yes—
336C2×C4×D4C2314yes—
337C2×C4×D4C2314yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2312yes—
341C2×C4×D4C2314yes—
342C2×C4×D4C2311yescharacteristic
343C2×C4×D4C2312yes—
344C2×C4×D4C2311yescharacteristic
345C2×C4×D4C2312yes—
346C2×C4×D4C2314yes—
347C2×C4×D4C2311yescharacteristic
348C2×C4×D4C2314yes—
349C2×C4×D4C2318yes—
350C2×C4×D4C2318yes—
351C2×#117C2314yes—
352C2×#117C2312yes—
353C2×#117C2314yes—
354C2×#117C2312yes—
355C2×#117C2312yes—
356C2×#117C2311yescharacteristic
357C2×#117C2312yes—
358C2×#117C2312yes—
359C22×C4⋊C4C2312yes—
360C22×C4⋊C4C2312yes—
361C22×C4⋊C4C2314yes—
362C22×C4⋊C4C2314yes—
363C22×C4⋊C4C2312yes—
364C22×C4⋊C4C2311yescharacteristic
365C22×C42C2314yes—
366C22×C42C2312yes—
367C22×C42C2312yes—
368C22×C42C2311yescharacteristic
369#400C2312yes—
370#400C2318yes—
371#400C2314yes—
372#400C2318yes—
373#399C2318yes—
374#399C2318yes—
375#399C2314yes—
376#399C2314yes—
377#399C2314yes—
378#399C2318yes—
379#399C2314yes—
380#399C2312yes—
381#399C2318yes—
382#398C2318yes—
383#398C2318yes—
384#398C2312yes—
385#398C2318yes—
386#398C2314yes—
387#398C2318yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2318yes—
395#397C2314yes—
396#397C2318yes—
397#397C2314yes—
398#397C2312yes—
399#397C2314yes—
400#396C2318yes—
401#396C2318yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2318yes—
407#395C2318yes—
408#395C2318yes—
409#395C2318yes—
410#395C2314yes—
411#395C2312yes—
412#395C2318yes—
413#394C2314yes—
414#394C2318yes—
415#394C2318yes—
416#394C2318yes—
417#394C2318yes—
418#394C2318yes—
419#394C2318yes—
420#394C2312yes—
421#394C2314yes—
422#394C2318yes—
423#394C2318yes—
424#394C2318yes—
425#394C2314yes—
426#394C2314yes—
427#393C2318yes—
428#393C2318yes—
429#393C2318yes—
430#393C2318yes—
431#393C2314yes—
432#393C2314yes—
433#393C2312yes—
434#393C2318yes—
435#392C2314yes—
436#392C2318yes—
437#392C2314yes—
438#392C2312yes—
439#392C2318yes—
440#392C2318yes—
441#391C2314yes—
442#391C2314yes—
443#391C2318yes—
444#391C2314yes—
445#391C2314yes—
446#391C2312yes—
447#391C2314yes—
448#391C2314yes—
449#391C2318yes—
450#390C2314yes—
451#390C2314yes—
452#390C2318yes—
453#390C2318yes—
454#390C2312yes—
455#390C2314yes—
456#390C2314yes—
457#390C2314yes—
458#390C2314yes—
459#390C2314yes—
460#390C2318yes—
461#389C2314yes—
462#389C2314yes—
463#389C2318yes—
464#389C2314yes—
465#389C2314yes—
466#389C2312yes—
467#389C2312yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2318yes—
472#389C2318yes—
473#389C2318yes—
474#388C2318yes—
475#388C2318yes—
476#388C2318yes—
477#388C2318yes—
478#388C2318yes—
479#388C2318yes—
480#388C2318yes—
481#388C2318yes—
482#388C2318yes—
483#388C2314yes—
484#388C2318yes—
485#388C2318yes—
486#387C2318yes—
487#387C2318yes—
488#387C2318yes—
489#387C2318yes—
490#387C2318yes—
491#387C2318yes—
492#387C2318yes—
493#387C2318yes—
494#387C2318yes—
495#387C2314yes—
496#386C2318yes—
497#386C2318yes—
498#386C2318yes—
499#386C2318yes—
500#386C2314yes—
501#386C2318yes—
502#386C2318yes—
503#385C2318yes—
504#385C2318yes—
505#385C2318yes—
506#385C2318yes—
507#385C2318yes—
508#385C2318yes—
509#385C2318yes—
510#385C2318yes—
511#385C2318yes—
512#385C2318yes—
513#385C2314yes—
514#384C2314yes—
515#384C2312yes—
516#384C2312yes—
517#383C2314yes—
518#383C2314yes—
519#382C2312yes—
520#382C2314yes—
521#382C2314yes—
522#382C2312yes—
523#381C2314yes—
524#381C2314yes—
525#380C2312yes—
526#380C2312yes—
527#380C2314yes—
528#380C2312yes—
529#380C2314yes—
530#380C2314yes—
531#380C2312yes—
532#380C2311yescharacteristic
533#380C2312yes—
534#380C2311yescharacteristic
535#380C2318yes—
536C4×C4⋊C4C2312yes—
537C4×C4⋊C4C2314yes—
538C4×C4⋊C4C2312yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2312yes—
541C4×C4⋊C4C2314yes—
542C4×C4⋊C4C2318yes—
543C4×C4⋊C4C2314yes—
544C4×C4⋊C4C2312yes—
545C4×C4⋊C4C2314yes—
546C4×C22⋊C4C2314yes—
547C4×C22⋊C4C2314yes—
548C4×C22⋊C4C2318yes—
549C4×C22⋊C4C2314yes—
550C4×C22⋊C4C2314yes—
551C4×C22⋊C4C2318yes—
552#376C2314yes—
553#376C2314yes—
554C2×#41—28no—
555C2×#41—24no—
556C2×#41—28no—
557C2×#41—216no—
558C2×#41—28no—
559C2×#41—44no—
560C2×#41—44no—
561C2×#41—88no—
562C2×#41—84no—
563C22×Q8—28no—
564C22×Q8—42no—
565C22×Q8—42no—
566C22×Q8—44no—
567C22×Q8—44no—
568C22×Q8C2×D418yes—
569C22×Q8C2411yescharacteristic
570C22×Q8C2411yescharacteristic
571C22×Q8C2412yes—
572C22×Q8C2411yescharacteristic
573C22×Q8C2411yescharacteristic
574C22×Q8C2414yes—
575C22×Q8C2412yes—
576C22×Q8C2414yes—
577C22×Q8C2412yes—
578C22×Q8C2414yes—
579C22×Q8C2412yes—
580C22×D4C2411yescharacteristic
581C22×D4C2412yes—
582C22×D4C2412yes—
583C22×D4C2411yescharacteristic
584C22×D4C2412yes—
585C22×D4C2414yes—
586C22×D4C2414yes—
587C22×D4C2414yes—
588C22×D4C2412yes—
589C22×D4C2418yes—
590C22×D4C2412yes—
591C22×D4C2414yes—
592C23×C4C2412yes—
593C23×C4C2412yes—
594C23×C4C2411yescharacteristic
595C23×C4C2411yescharacteristic
596C23×C4C2412yes—
597C23×C4C2414yes—
598C23×C4C2412yes—
599C23×C4C2414yes—
600C23×C4C2414yes—
601C23×C4C2414yes—
602C23×C4C2414yes—
603C23×C4C2414yes—
604C23×C4C2412yes—
605C23×C4C2411yescharacteristic
606C23×C4C2412yes—
607C4⋊Q8—28no—
608C4⋊Q8—216no—
609C4⋊Q8—28no—
610C4⋊Q8—216no—
611C4⋊Q8—216no—
612C4⋊Q8—28no—
613C4⋊Q8—24no—
614C4⋊Q8—28no—
615C4⋊Q8—24no—
616C4⋊Q8—28no—
617C4⋊Q8—24no—
618C4⋊Q8—28no—
619C4⋊Q8—88no—
620#127—24no—
621#127—28no—
622#126—28no—
623#126—216no—
624#125—216no—
625#125—216no—
626#125—216no—
627#125—28no—
628#125—24no—
629#125—28no—
630#125—28no—
631#125—28no—
632#124—28no—
633#124—216no—
634#124—28no—
635#124—24no—
636#124—28no—
637#124—216no—
638#124—48no—
639#124—88no—
640#123—216no—
641#123—28no—
642#123—216no—
643#123—216no—
644#123—216no—
645C22⋊Q8—28no—
646C22⋊Q8—216no—
647C22⋊Q8—28no—
648C22⋊Q8—216no—
649C22⋊Q8—24no—
650C22⋊Q8—28no—
651C22⋊Q8—216no—
652C22⋊Q8—28no—
653C22⋊Q8—216no—
654C22⋊Q8—28no—
655C22⋊Q8—28no—
656C22⋊Q8—216no—
657C22⋊Q8—216no—
658C22⋊Q8—216no—
659C22⋊Q8—216no—
660C22⋊Q8—216no—
661C22⋊Q8—216no—
662C22⋊Q8—216no—
663C22⋊Q8—48no—
664C22⋊Q8—84no—
665C22⋊Q8—88no—
666#121—28no—
667#121—24no—
668#121—28no—
669#121—216no—
670#121—28no—
671#121—216no—
672#121—216no—
673#121—28no—
674#121—48no—
675#121—84no—
676C4×Q8—28no—
677C4×Q8—28no—
678C4×Q8—28no—
679C4×Q8—216no—
680C4×Q8—216no—
681C4×Q8—28no—
682C4×Q8—28no—
683C4×Q8—24no—
684C4×Q8—24no—
685C4×Q8—28no—
686C4×Q8—24no—
687C4×Q8—28no—
688C4×Q8—28no—
689C4×Q8—216no—
690C4×Q8C2×D418yes—
691C4×Q8C2×D418yes—
692C4×Q8C2×D418yes—
693C4×Q8C2×D4116yes—
694C4×Q8C2×D418yes—
695C4×Q8C2×D4116yes—
696C4×D4—28no—
697C4×D4—216no—
698C4×D4—216no—
699C4×D4—28no—
700C4×D4—28no—
701C4×D4—216no—
702C4×D4—28no—
703C4×D4—216no—
704C4×D4—24no—
705C4×D4—28no—
706C4×D4—28no—
707C4×D4—24no—
708C4×D4—216no—
709C4×D4—28no—
710C4×D4—24no—
711C4×D4—28no—
712C4×D4—28no—
713C4×D4—28no—
714C4×D4—28no—
715C4×D4—48no—
716C4×D4—88no—
717C4×D4—88no—
718#117—28no—
719#117—24no—
720#117—28no—
721#117—216no—
722#117—216no—
723#117—28no—
724#117—44no—
725#117—44no—
726C2×C4⋊C4—28no—
727C2×C4⋊C4—216no—
728C2×C4⋊C4—28no—
729C2×C4⋊C4—216no—
730C2×C4⋊C4C2×D418yes—
731C2×C4⋊C4C2×D4116yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2411yescharacteristic
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2411yescharacteristic
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2418yes—
769C2×C4⋊C4C2418yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2418yes—
774C2×C4⋊C4C2418yes—
775C2×C4⋊C4C2418yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2411yescharacteristic
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2412yes—
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2412yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2412yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2412yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2418yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2418yes—
810C2×C22⋊C4C2418yes—
811C2×C22⋊C4C2418yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2418yes—
815C2×C22⋊C4C2418yes—
816C2×C22⋊C4C2418yes—
817C2×C22⋊C4C2418yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2418yes—
820C2×C22⋊C4C2418yes—
821C2×C42—216no—
822C2×C42—28no—
823C2×C42C2×D4116yes—
824C2×C42C2×D418yes—
825C2×C42C2414yes—
826C2×C42C2412yes—
827C2×C42C2412yes—
828C2×C42C2414yes—
829C2×C42C2414yes—
830C2×C42C2414yes—
831C2×C42C2412yes—
832C2×C42C2412yes—
833C2×C42C2414yes—
834C2×C42C2414yes—
835C2×C42C2418yes—
836C2×C42C2418yes—
837C2×C42C2412yes—
838C2×C42C2411yescharacteristic
839C2×C42C2411yescharacteristic
840C2×C42C2412yes—
841C2×C42C2412yes—
842C2×C42C2411yescharacteristic
843C2×C42C2411yescharacteristic
844C2×C42C2412yes—
845#95C2414yes—
846#95C2412yes—
847#95C2412yes—
848#95C2418yes—
849#95C2418yes—
850#95C2414yes—
851#95C2418yes—
852#95C2418yes—
853#95C2414yes—
854#95C2418yes—
855#95C2418yes—
856#95C2414yes—
857#95C2414yes—
858#95C2418yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2418yes—
863#95C2418yes—
864#95C2414yes—
865#95C2418yes—
866#95C2418yes—
867#95C2418yes—
868#95C2418yes—
869#95C2418yes—
870C24C2512yes—
871C24C2514yes—
872C24C2511yescharacteristic
873C24C2512yes—
874#41—232no—
875#41—432no—
876#41—832no—
877#41—816no—
878C2×Q8—22no—
879C2×Q8—22no—
880C2×Q8—28no—
881C2×Q8—24no—
882C2×Q8—24no—
883C2×Q8—28no—
884C2×Q8—24no—
885C2×Q8—28no—
886C2×Q8—24no—
887C2×Q8—24no—
888C2×Q8—22no—
889C2×Q8—22no—
890C2×Q8—22no—
891C2×Q8—22no—
892C2×Q8—24no—
893C2×Q8—24no—
894C2×Q8—42no—
895C2×Q8—42no—
896C2×Q8—44no—
897C2×Q8—44no—
898C2×Q8—44no—
899C2×Q8—44no—
900C2×Q8—44no—
901C2×Q8—44no—
902C2×Q8—48no—
903C2×Q8—416no—
904C2×Q8—432no—
905C2×Q8C22×D414yes—
906C2×Q8C22×D414yes—
907C2×Q8C22×D418yes—
908C2×D4—24no—
909C2×D4—24no—
910C2×D4—24no—
911C2×D4—24no—
912C2×D4—28no—
913C2×D4—28no—
914C2×D4—216no—
915C2×D4—22no—
916C2×D4—22no—
917C2×D4—24no—
918C2×D4—28no—
919C2×D4—24no—
920C2×D4—24no—
921C2×D4—28no—
922C2×D4—24no—
923C2×D4—24no—
924C2×D4—28no—
925C2×D4—24no—
926C2×D4—24no—
927C2×D4—44no—
928C2×D4—44no—
929C2×D4—44no—
930C2×D4—44no—
931C2×D4—44no—
932C2×D4—48no—
933C2×D4—48no—
934C2×D4—48no—
935C2×D4—44no—
936C2×D4—48no—
937C22×C4—24no—
938C22×C4—24no—
939C22×C4—24no—
940C22×C4—22no—
941C22×C4—22no—
942C22×C4—28no—
943C22×C4—24no—
944C22×C4—28no—
945C22×C4—24no—
946C22×C4—24no—
947C22×C4—24no—
948C22×C4—24no—
949C22×C4—24no—
950C22×C4—28no—
951C22×C4—24no—
952C22×C4—28no—
953C22×C4—28no—
954C22×C4—28no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—44no—
962C22×C4—42no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—48no—
966C22×C4—48no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—48no—
970C22×C4C22×D414yes—
971C22×C4C22×D414yes—
972C22×C4C22×D418yes—
973C22×C4C22×D414yes—
974C22×C4C22×D418yes—
975C22×C42−1+418yes—
976C22×C4C2514yes—
977C22×C4C2518yes—
978C22×C4C2514yes—
979C22×C4C2512yes—
980C22×C4C2512yes—
981C22×C4C2514yes—
982C22×C4C2512yes—
983C22×C4C2514yes—
984C22×C4C2512yes—
985C22×C4C2512yes—
986C22×C4C2514yes—
987C22×C4C2511yescharacteristic
988C22×C4C2512yes—
989C22×C4C2512yes—
990C22×C4C2512yes—
991C22×C4C2512yes—
992C22×C4C2511yescharacteristic
993C22×C4C2511yescharacteristic
994C22×C4C2511yescharacteristic
995C22×C4C2512yes—
996C22×C4C2511yescharacteristic
997C22×C4C2511yescharacteristic
998C4⋊C4—28no—
999C4⋊C4—24no—
1000C4⋊C4—28no—
1001C4⋊C4—24no—
1002C4⋊C4—28no—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—24no—
1007C4⋊C4—24no—
1008C4⋊C4—28no—
1009C4⋊C4—24no—
1010C4⋊C4—24no—
1011C4⋊C4—28no—
1012C4⋊C4—24no—
1013C4⋊C4—22no—
1014C4⋊C4—24no—
1015C4⋊C4—22no—
1016C4⋊C4—22no—
1017C4⋊C4—24no—
1018C4⋊C4—22no—
1019C4⋊C4—28no—
1020C4⋊C4—24no—
1021C4⋊C4—28no—
1022C4⋊C4—28no—
1023C4⋊C4—28no—
1024C4⋊C4—24no—
1025C4⋊C4—28no—
1026C4⋊C4—24no—
1027C4⋊C4—28no—
1028C4⋊C4—24no—
1029C4⋊C4—28no—
1030C4⋊C4—24no—
1031C4⋊C4—28no—
1032C4⋊C4—28no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—48no—
1036C4⋊C4—48no—
1037C4⋊C4—44no—
1038C4⋊C4—48no—
1039C4⋊C4—44no—
1040C4⋊C4—48no—
1041C4⋊C4—48no—
1042C4⋊C4—44no—
1043C4⋊C4C22×D414yes—
1044C4⋊C4C22×D418yes—
1045C4⋊C4C22×D418yes—
1046C4⋊C4C22×D418yes—
1047C4⋊C4C22×D414yes—
1048C4⋊C4C22×D418yes—
1049C4⋊C4C22×D418yes—
1050C22⋊C4—28no—
1051C22⋊C4—24no—
1052C22⋊C4—24no—
1053C22⋊C4—28no—
1054C22⋊C4—28no—
1055C22⋊C4—24no—
1056C22⋊C4—28no—
1057C22⋊C4—24no—
1058C22⋊C4—24no—
1059C22⋊C4—28no—
1060C22⋊C4—28no—
1061C22⋊C4—24no—
1062C22⋊C4—24no—
1063C22⋊C4—28no—
1064C22⋊C4—28no—
1065C22⋊C4—28no—
1066C22⋊C4—28no—
1067C22⋊C4—28no—
1068C22⋊C4—24no—
1069C22⋊C4—28no—
1070C22⋊C4—216no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—48no—
1078C22⋊C4—48no—
1079C22⋊C4—48no—
1080C22⋊C4—48no—
1081C22⋊C4—48no—
1082C22⋊C4—48no—
1083C22⋊C4—48no—
1084C22⋊C4—48no—
1085C22⋊C4—48no—
1086C22⋊C4—44no—
1087C42—28no—
1088C42—24no—
1089C42—28no—
1090C42—24no—
1091C42—28no—
1092C42—24no—
1093C42—28no—
1094C42—24no—
1095C42—28no—
1096C42—44no—
1097C42—48no—
1098C42—48no—
1099C42C22×D418yes—
1100C42C22×D414yes—
1101C42C22×D418yes—
1102C42C22×D414yes—
1103C42C22×D414yes—
1104C42C22×D418yes—
1105C42C22×D414yes—
1106C42C22×D418yes—
1107C23—22no—
1108C23—22no—
1109C23—22no—
1110C23—21no—
1111C23—21no—
1112C23—22no—
1113C23—22no—
1114C23—22no—
1115C23—22no—
1116C23—22no—
1117C23—24no—
1118C23—22no—
1119C23—24no—
1120C23—28no—
1121C23—22no—
1122C23—24no—
1123C23—22no—
1124C23—24no—
1125C23—24no—
1126C23—28no—
1127C23C23×D412yes—
1128C23C2×2−1+414yes—
1129C23C2611yescharacteristic
1130Q8—28no—
1131Q8—28no—
1132Q8—28no—
1133Q8—48no—
1134Q8—416no—
1135Q8—48no—
1136Q8—44no—
1137Q8—84no—
1138Q8—88no—
1139Q8—84no—
1140Q8—88no—
1141D4—28no—
1142D4—216no—
1143D4—416no—
1144D4—416no—
1145D4—48no—
1146D4—416no—
1147D4—48no—
1148D4—44no—
1149D4—48no—
1150D4—84no—
1151D4—88no—
1152D4—816no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—28no—
1167C2×C4—28no—
1168C2×C4—216no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—24no—
1172C2×C4—22no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—28no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—28no—
1184C2×C4—22no—
1185C2×C4—24no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—24no—
1189C2×C4—22no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—28no—
1193C2×C4—22no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—28no—
1198C2×C4—22no—
1199C2×C4—48no—
1200C2×C4—48no—
1201C2×C4—44no—
1202C2×C4—416no—
1203C2×C4—416no—
1204C2×C4—48no—
1205C2×C4—48no—
1206C2×C4—88no—
1207C2×C4—84no—
1208C2×C4—88no—
1209C2×C4—88no—
1210C2×C4—88no—
1211C2×C4C23×D414yes—
1212C2×C4C23×D414yes—
1213C2×C4C23×D414yes—
1214C2×C4C23×D412yes—
1215C2×C4C23×D412yes—
1216C2×C4C23×D412yes—
1217C2×C4C23×D412yes—
1218C2×C4C23×D414yes—
1219C2×C4C23×D412yes—
1220C2×C4C23×D412yes—
1221C2×C4C2×2−1+414yes—
1222C2×C4C2×2−1+414yes—
1223C2×C4#58512yes—
1224C2×C4#58512yes—
1225C22—22no—
1226C22—24no—
1227C22—22no—
1228C22—24no—
1229C22—22no—
1230C22—24no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—44no—
1239C22—42no—
1240C22—44no—
1241C22—44no—
1242C22—48no—
1243C22—44no—
1244C22—42no—
1245C22—48no—
1246C22—44no—
1247C22C24×D411yescharacteristic
1248C22C22×2−1+412yes—
1249C22C2×#58511yescharacteristic
1250C22C2×#58511yescharacteristic
1251C22H(7,𝔽2)12yes—
1252C4—22no—
1253C4—24no—
1254C4—24no—
1255C4—22no—
1256C4—22no—
1257C4—24no—
1258C4—22no—
1259C4—24no—
1260C4—24no—
1261C4—42no—
1262C4—42no—
1263C4—44no—
1264C4—42no—
1265C4—44no—
1266C4—44no—
1267C4—44no—
1268C4—42no—
1269C4—42no—
1270C4—44no—
1271C4—48no—
1272C4#344914yes—
1273C4#348614yes—
1274C2—42no—
1275C2—44no—
1276C2—82no—
1277C2—84no—
1278C2C2×#344911yescharacteristic
1279C2C2×#348611yescharacteristic
1280C2#6285211yescharacteristic
1281C2#6292612yes—
1282C2#6296212yes—
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×#3522C2semidirect
2. C2×Q8×#41C2semidirect
3. #42806C2semidirect
4. #42789C2semidirect
5. #42788C2semidirect
6. #42154C2semidirect
7. #41957C2semidirect
8. #40599C2semidirect
9. #39725C2semidirect
10. #39718C2semidirect
11. #39597C2semidirect
12. #39590C2semidirect
13. #37640C2semidirect
14. #37622C2semidirect
15. #37619C2semidirect
16. #37551C2semidirect
17. #36580C2semidirect
18. #36544C2semidirect
19. #35712C2semidirect
20. #35701C2semidirect
21. #35697C2semidirect
22. #35342C2semidirect
23. #35292C2semidirect
24. #34614C2semidirect
25. #34609C2semidirect
26. #34187C2semidirect
308. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35222
C2×Q8×#412
#428062
#427892
#427882
#421542
#419572
#405992
#397252
#397182
#395972
#395902
#376402
#376222
#376192
#375512
#365802
#365442
#357122
#357012
#356972
#353422
#352922
#346142
#346092
#341872