Finite Group Databasebeta

← #7658631

Subgroups — #7658631

Order 512.

6686 conjugacy classes of subgroups.

The subgroup lattice has 1248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3522C211yesmaximal, characteristic, complemented
2C2×#3507C211yesmaximal, characteristic, complemented
3#42889C212yesmaximal, complemented
4#42881C212yesmaximal, complemented
5#42809C212yesmaximal, complemented
6#42797C214yesmaximal, complemented
7#42795C212yesmaximal, complemented
8#42153C214yesmaximal, complemented
9#41991C214yesmaximal, complemented
10#41987C214yesmaximal, complemented
11#41957C214yesmaximal, complemented
12#40497C218yesmaximal, complemented
13#37619C211yesmaximal, characteristic, complemented
14#37618C211yesmaximal, characteristic, complemented
15#37559C212yesmaximal, complemented
16#37559C211yesmaximal, characteristic, complemented
17#37552C212yesmaximal, complemented
18#37552C212yesmaximal, complemented
19#36699C211yesmaximal, characteristic, complemented
20#36687C212yesmaximal, complemented
21#35956C212yesmaximal, complemented
22#35909C212yesmaximal, complemented
23#35844C212yesmaximal, complemented
24#35715C214yesmaximal, complemented
25#35712C212yesmaximal, complemented
26#34192C211yesmaximal, characteristic, complemented
27#3522—216no—
28#3507—216no—
29C2×#559C2212yes—
30C2×#559C2211yescharacteristic
31C2×#559C2211yescharacteristic
32C2×#559C2211yescharacteristic
33C2×Q82C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#557C2211yescharacteristic
36C2×#556C2212yes—
37C2×#556C2212yes—
38C2×#556C2212yes—
39C2×#554C2212yes—
40C2×#554C2212yes—
41C2×#554C2211yescharacteristic
42C2×#552C2214yes—
43C2×#550C2211yescharacteristic
44C2×#548C2212yes—
45C2×#547C2214yes—
46C2×#547C2212yes—
47C2×#542C2212yes—
48C2×#542C2214yes—
49C2×#539C2214yes—
50C2×#536C2212yes—
51C2×#533C2211yescharacteristic
52C2×#532C2211yescharacteristic
53C2×#532C2212yes—
54C2×#532C2211yescharacteristic
55C2×#529C2212yes—
56C2×#529C2212yes—
57C2×#529C2211yescharacteristic
58C2×#529C2212yes—
59C2×#520C2212yes—
60C2×#520C2212yes—
61C22×C4×Q8C2211yescharacteristic
62#2822C2212yes—
63#2821C2214yes—
64#2821C2212yes—
65#2821C2212yes—
66#2820C2212yes—
67#2820C2214yes—
68#2819C2214yes—
69#2818C2214yes—
70#2817C2211yescharacteristic
71#2817C2211yescharacteristic
72#2816C2211yescharacteristic
73#2816C2212yes—
74#2816C2211yescharacteristic
75#2816C2212yes—
76#2816C2212yes—
77#2815C2212yes—
78#2815C2212yes—
79#2815C2212yes—
80#2814C2214yes—
81#2813C2218yes—
82#2732C2218yes—
83#2730C2218yes—
84#2730C2218yes—
85#2728C2218yes—
86#2716C2218yes—
87#2714C2218yes—
88#2707C2218yes—
89#2704C2218yes—
90#2682C2218yes—
91#2681C2218yes—
92#2677C2218yes—
93#2676C2218yes—
94#2664C2214yes—
95#2664C2214yes—
96#2662C2214yes—
97#2662C2214yes—
98#2661C2218yes—
99#2661C2214yes—
100#2658C2212yes—
101#2657C2212yes—
102#2640C2212yes—
103#2640C2212yes—
104#2637C2214yes—
105#2637C2214yes—
106#2636C2214yes—
107#2636C2214yes—
108#2633C2214yes—
109#2633C2212yes—
110#2633C2214yes—
111#2631C2212yes—
112#2631C2214yes—
113#2631C2214yes—
114#2630C2218yes—
115#2630C2218yes—
116#2624C2214yes—
117#2621C2214yes—
118#2621C2212yes—
119#2619C2214yes—
120#2619C2212yes—
121#2615C2214yes—
122#2611C2214yes—
123#2611C2214yes—
124#2610C2214yes—
125#2610C2214yes—
126#2603C2214yes—
127#2603C2214yes—
128#2603C2214yes—
129#2602C2218yes—
130#2602C2218yes—
131#2599C2214yes—
132#2599C2214yes—
133#2598C2214yes—
134#2598C2214yes—
135#2592C2214yes—
136#2592C2212yes—
137#2580C2212yes—
138#2580C2212yes—
139#2560C2218yes—
140#2554C2218yes—
141#2548C2214yes—
142#2548C2212yes—
143#2547C2212yes—
144#2546C2212yes—
145#2545C2214yes—
146#2541C2212yes—
147#2540C2212yes—
148#2540C2214yes—
149#2535C2214yes—
150#2477C2218yes—
151#2473C2218yes—
152#2471C2218yes—
153#2461C2218yes—
154#2460C2218yes—
155#2456C2218yes—
156#2452C2218yes—
157#2452C2214yes—
158#2451C2214yes—
159#2449C2218yes—
160#2448C2214yes—
161#2446C2214yes—
162#2443C2218yes—
163#2443C2218yes—
164#2432C2214yes—
165#2432C2214yes—
166#2431C2214yes—
167#2431C2214yes—
168#2429C2214yes—
169#2428C2214yes—
170#2426C2214yes—
171#2426C2214yes—
172#2407C2214yes—
173#2407C2218yes—
174#2399C2212yes—
175#2398C2212yes—
176#2398C2214yes—
177#2397C2214yes—
178#2396C2212yes—
179#2396C2212yes—
180#2395C2214yes—
181#2392C2214yes—
182#2392C2214yes—
183#2388C2218yes—
184#2367C2214yes—
185#2366C2214yes—
186#2361C2214yes—
187#2360C2214yes—
188#2356C2212yes—
189#2356C2214yes—
190#2351C2212yes—
191#2345C2214yes—
192#2345C2212yes—
193Q8×C22⋊C4C2212yes—
194#2320C2214yes—
195#2320C2212yes—
196#2283C2212yes—
197#2283C2211yescharacteristic
198#2283C2212yes—
199#2283C2211yescharacteristic
200#2276C2212yes—
201C22×#41C2312yes—
202C22×#41C2312yes—
203C22×#41C2312yes—
204C22×#41C2314yes—
205C23×Q8C2311yescharacteristic
206#559—28no—
207#559—28no—
208#559—216no—
209#559—28no—
210Q82—28no—
211#557—28no—
212#557—28no—
213#556—216no—
214#556—216no—
215#556—216no—
216#554—216no—
217#554—216no—
218#554—28no—
219#552—232no—
220#550—28no—
221#548—216no—
222#547—216no—
223#547—232no—
224#542—232no—
225#542—216no—
226#539—232no—
227#536—216no—
228#533—28no—
229#532—28no—
230#532—216no—
231#532—28no—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2311yescharacteristic
236C2×C4⋊Q8C2311yescharacteristic
237C2×C4⋊Q8C2314yes—
238C2×C4⋊Q8C2312yes—
239C2×C4⋊Q8C2312yes—
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2314yes—
242C2×#127C2312yes—
243C2×#127C2311yescharacteristic
244C2×#127C2311yescharacteristic
245C2×#127C2314yes—
246#529—216no—
247#529—216no—
248#529—216no—
249#529—28no—
250C2×#126C2314yes—
251C2×#126C2314yes—
252C2×#126C2312yes—
253C2×#126C2314yes—
254C2×#126C2314yes—
255C2×#126C2314yes—
256C2×#125C2312yes—
257C2×#125C2312yes—
258C2×#125C2311yescharacteristic
259C2×#125C2312yes—
260C2×#125C2312yes—
261C2×#125C2314yes—
262C2×#125C2314yes—
263C2×#124C2312yes—
264C2×#124C2314yes—
265C2×#124C2311yescharacteristic
266C2×#124C2312yes—
267C2×#124C2312yes—
268C2×#124C2312yes—
269C2×#124C2312yes—
270C2×#124C2312yes—
271C2×#124C2312yes—
272C2×#124C2314yes—
273C2×#124C2312yes—
274C2×#124C2314yes—
275C2×#124C2314yes—
276C2×#123C2314yes—
277C2×#123C2314yes—
278C2×#123C2314yes—
279C2×#123C2312yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×#123C2314yes—
284C2×#123C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2311yescharacteristic
287C2×C22⋊Q8C2311yescharacteristic
288C2×C22⋊Q8C2311yescharacteristic
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2318yes—
300C2×#121C2311yescharacteristic
301C2×#121C2312yes—
302C2×#121C2312yes—
303C2×#121C2312yes—
304C2×#121C2312yes—
305C2×#121C2314yes—
306C2×#121C2314yes—
307C2×#121C2312yes—
308C2×#121C2314yes—
309C2×#121C2318yes—
310C2×#121C2318yes—
311#520—216no—
312#520—216no—
313C2×C4×Q8D4116yescomplemented
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2311yescharacteristic
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2312yes—
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×D4C2314yes—
335C2×C4×D4C2314yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2312yes—
341C2×C4×D4C2314yes—
342C2×C4×D4C2314yes—
343C2×C4×D4C2312yes—
344C2×C4×D4C2312yes—
345C2×C4×D4C2312yes—
346C2×C4×D4C2312yes—
347C2×C4×D4C2311yescharacteristic
348C2×C4×D4C2312yes—
349C2×C4×D4C2314yes—
350C2×C4×D4C2318yes—
351C2×C4×D4C2318yes—
352C2×#117C2314yes—
353C2×#117C2314yes—
354C2×#117C2314yes—
355C2×#117C2312yes—
356C2×#117C2312yes—
357C2×#117C2314yes—
358C22×C4⋊C4C2312yes—
359C22×C4⋊C4C2314yes—
360C22×C4⋊C4C2314yes—
361C22×C4⋊C4C2311yescharacteristic
362C22×C4⋊C4C2312yes—
363C22×C42C2312yes—
364C22×C42C2311yescharacteristic
365#400C2312yes—
366#400C2312yes—
367#400C2312yes—
368#400C2312yes—
369#400C2314yes—
370#400C2318yes—
371#399C2312yes—
372#399C2314yes—
373#399C2312yes—
374#399C2314yes—
375#399C2314yes—
376#399C2314yes—
377#399C2318yes—
378#399C2318yes—
379#398C2318yes—
380#398C2312yes—
381#398C2314yes—
382#398C2312yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2318yes—
390#398C2314yes—
391#398C2318yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2318yes—
403#397C2314yes—
404#397C2318yes—
405#396C2318yes—
406#396C2318yes—
407#396C2314yes—
408#396C2314yes—
409#396C2318yes—
410#396C2318yes—
411#396C2318yes—
412#396C2318yes—
413#395C2312yes—
414#395C2312yes—
415#395C2312yes—
416#395C2312yes—
417#395C2318yes—
418#395C2314yes—
419#394C2318yes—
420#394C2312yes—
421#394C2314yes—
422#394C2312yes—
423#394C2314yes—
424#394C2314yes—
425#394C2318yes—
426#394C2318yes—
427#394C2318yes—
428#394C2314yes—
429#394C2314yes—
430#394C2318yes—
431#394C2318yes—
432#394C2318yes—
433#394C2318yes—
434#394C2314yes—
435#394C2318yes—
436#394C2318yes—
437#393C2318yes—
438#393C2312yes—
439#393C2314yes—
440#393C2312yes—
441#393C2314yes—
442#393C2314yes—
443#393C2318yes—
444#393C2314yes—
445#392C2318yes—
446#392C2314yes—
447#392C2314yes—
448#392C2318yes—
449#392C2314yes—
450#392C2314yes—
451#392C2314yes—
452#392C2318yes—
453#392C2318yes—
454#392C2314yes—
455#392C2318yes—
456#392C2314yes—
457#392C2318yes—
458#392C2318yes—
459#391C2314yes—
460#391C2314yes—
461#391C2318yes—
462#391C2314yes—
463#391C2318yes—
464#391C2314yes—
465#390C2318yes—
466#390C2314yes—
467#390C2314yes—
468#390C2314yes—
469#390C2318yes—
470#390C2318yes—
471#390C2318yes—
472#390C2318yes—
473#390C2318yes—
474#390C2314yes—
475#390C2314yes—
476#389C2318yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2318yes—
481#389C2318yes—
482#388C2318yes—
483#388C2318yes—
484#388C2318yes—
485#388C2318yes—
486#388C2318yes—
487#388C2318yes—
488#388C2318yes—
489#388C2318yes—
490#388C2318yes—
491#388C2318yes—
492#388C2318yes—
493#387C2318yes—
494#387C2318yes—
495#387C2318yes—
496#387C2318yes—
497#387C2318yes—
498#387C2318yes—
499#387C2318yes—
500#386C2318yes—
501#386C2318yes—
502#386C2318yes—
503#386C2318yes—
504#386C2318yes—
505#386C2318yes—
506#386C2318yes—
507#386C2318yes—
508#386C2318yes—
509#385C2318yes—
510#385C2318yes—
511#385C2318yes—
512#385C2318yes—
513#385C2318yes—
514#385C2318yes—
515#385C2318yes—
516#385C2318yes—
517#385C2318yes—
518#383C2314yes—
519#383C2312yes—
520#383C2312yes—
521#383C2314yes—
522#382C2314yes—
523#382C2312yes—
524#382C2314yes—
525#382C2312yes—
526#381C2312yes—
527#381C2311yescharacteristic
528#381C2311yescharacteristic
529#380C2312yes—
530#380C2314yes—
531#380C2312yes—
532#380C2314yes—
533#380C2318yes—
534C4×C4⋊C4C2318yes—
535C4×C4⋊C4C2312yes—
536C4×C4⋊C4C2314yes—
537C4×C4⋊C4C2314yes—
538C4×C4⋊C4C2314yes—
539C4×C4⋊C4C2312yes—
540C4×C4⋊C4C2314yes—
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—28no—
556C2×#41—216no—
557C2×#41—28no—
558C2×#41—48no—
559C2×#41—44no—
560C2×#41—44no—
561C2×#41—88no—
562C2×#41—84no—
563C22×Q8—44no—
564C22×Q8C2×D418yes—
565C22×Q8C2412yes—
566C22×Q8C2411yescharacteristic
567C22×Q8C2411yescharacteristic
568C22×Q8C2411yescharacteristic
569C22×Q8C2411yescharacteristic
570C22×Q8C2411yescharacteristic
571C22×Q8C2412yes—
572C22×Q8C2414yes—
573C22×Q8C2412yes—
574C22×Q8C2412yes—
575C22×D4C2412yes—
576C22×D4C2412yes—
577C22×D4C2412yes—
578C22×D4C2412yes—
579C22×D4C2411yescharacteristic
580C22×D4C2414yes—
581C22×D4C2414yes—
582C22×D4C2412yes—
583C22×D4C2414yes—
584C22×D4C2412yes—
585C22×D4C2414yes—
586C22×D4C2412yes—
587C22×D4C2418yes—
588C22×D4C2418yes—
589C22×D4C2418yes—
590C23×C4C2412yes—
591C23×C4C2411yescharacteristic
592C23×C4C2414yes—
593C23×C4C2414yes—
594C23×C4C2414yes—
595C23×C4C2414yes—
596C23×C4C2414yes—
597C23×C4C2414yes—
598C23×C4C2414yes—
599C23×C4C2412yes—
600C23×C4C2411yescharacteristic
601C23×C4C2412yes—
602C23×C4C2411yescharacteristic
603C4⋊Q8—28no—
604C4⋊Q8—28no—
605C4⋊Q8—28no—
606C4⋊Q8—216no—
607C4⋊Q8—28no—
608C4⋊Q8—24no—
609C4⋊Q8—24no—
610C4⋊Q8—24no—
611C4⋊Q8—24no—
612C4⋊Q8—84no—
613#127—28no—
614#127—24no—
615#127—24no—
616#127—48no—
617#126—216no—
618#126—216no—
619#126—28no—
620#126—216no—
621#126—216no—
622#126—216no—
623#125—216no—
624#125—216no—
625#125—28no—
626#125—24no—
627#125—28no—
628#125—28no—
629#125—28no—
630#124—28no—
631#124—28no—
632#124—28no—
633#124—216no—
634#124—28no—
635#124—28no—
636#124—28no—
637#124—24no—
638#124—28no—
639#124—216no—
640#124—28no—
641#124—48no—
642#124—84no—
643#123—216no—
644#123—216no—
645#123—216no—
646#123—28no—
647#123—216no—
648#123—216no—
649#123—216no—
650#123—216no—
651#123—216no—
652C22⋊Q8—216no—
653C22⋊Q8—216no—
654C22⋊Q8—28no—
655C22⋊Q8—216no—
656C22⋊Q8—24no—
657C22⋊Q8—24no—
658C22⋊Q8—24no—
659C22⋊Q8—28no—
660C22⋊Q8—216no—
661C22⋊Q8—216no—
662C22⋊Q8—216no—
663C22⋊Q8—216no—
664C22⋊Q8—216no—
665C22⋊Q8—48no—
666C22⋊Q8—88no—
667#121—28no—
668#121—24no—
669#121—28no—
670#121—28no—
671#121—28no—
672#121—216no—
673#121—28no—
674#121—216no—
675#121—48no—
676#121—88no—
677#121—88no—
678C4×Q8—28no—
679C4×Q8—28no—
680C4×Q8—28no—
681C4×Q8—28no—
682C4×Q8—28no—
683C4×Q8—28no—
684C4×Q8—24no—
685C4×Q8—28no—
686C4×Q8—24no—
687C4×Q8—24no—
688C4×Q8—48no—
689C4×Q8C2×D418yes—
690C4×Q8C2×D4116yes—
691C4×Q8C2×D418yes—
692C4×Q8C2×D418yes—
693C4×Q8C2×D4116yes—
694C4×Q8C2×D418yes—
695C4×D4—216no—
696C4×D4—216no—
697C4×D4—28no—
698C4×D4—216no—
699C4×D4—28no—
700C4×D4—216no—
701C4×D4—28no—
702C4×D4—28no—
703C4×D4—216no—
704C4×D4—28no—
705C4×D4—28no—
706C4×D4—24no—
707C4×D4—28no—
708C4×D4—28no—
709C4×D4—28no—
710C4×D4—28no—
711C4×D4—28no—
712C4×D4—28no—
713C4×D4—28no—
714C4×D4—88no—
715C4×D4—88no—
716#117—28no—
717#117—216no—
718#117—216no—
719#117—28no—
720#117—216no—
721#117—216no—
722C2×C4⋊C4—28no—
723C2×C4⋊C4—216no—
724C2×C4⋊C4—216no—
725C2×C4⋊C4C2×D418yes—
726C2×C4⋊C4C2×D4116yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2418yes—
759C2×C4⋊C4C2418yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2418yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2418yes—
764C2×C4⋊C4C2418yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2412yes—
777C2×C22⋊C4C2412yes—
778C2×C22⋊C4C2412yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2412yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2418yes—
798C2×C22⋊C4C2418yes—
799C2×C22⋊C4C2418yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2418yes—
802C2×C22⋊C4C2418yes—
803C2×C22⋊C4C2418yes—
804C2×C22⋊C4C2418yes—
805C2×C22⋊C4C2418yes—
806C2×C22⋊C4C2418yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2412yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2418yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2418yes—
814C2×C22⋊C4C2418yes—
815C2×C42C2×D4116yes—
816C2×C42C2×D418yes—
817C2×C42C2414yes—
818C2×C42C2414yes—
819C2×C42C2412yes—
820C2×C42C2414yes—
821C2×C42C2412yes—
822C2×C42C2412yes—
823C2×C42C2414yes—
824C2×C42C2418yes—
825C2×C42C2418yes—
826C2×C42C2414yes—
827C2×C42C2412yes—
828C2×C42C2411yescharacteristic
829C2×C42C2412yes—
830C2×C42C2412yes—
831C2×C42C2411yescharacteristic
832C2×C42C2411yescharacteristic
833C2×C42C2411yescharacteristic
834C2×C42C2412yes—
835#95C2412yes—
836#95C2412yes—
837#95C2414yes—
838#95C2418yes—
839#95C2414yes—
840#95C2412yes—
841#95C2414yes—
842#95C2414yes—
843#95C2418yes—
844#95C2414yes—
845#95C2418yes—
846#95C2414yes—
847#95C2418yes—
848#95C2418yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2418yes—
854#95C2418yes—
855#95C2414yes—
856#95C2412yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2418yes—
861#95C2418yes—
862#95C2418yes—
863C24C2514yes—
864C24C2512yes—
865C24C2514yes—
866C24C2511yescharacteristic
867#41—432no—
868#41—432no—
869#41—832no—
870#41—816no—
871C2×Q8—22no—
872C2×Q8—22no—
873C2×Q8—22no—
874C2×Q8—24no—
875C2×Q8—24no—
876C2×Q8—28no—
877C2×Q8—24no—
878C2×Q8—24no—
879C2×Q8—24no—
880C2×Q8—28no—
881C2×Q8—44no—
882C2×Q8—42no—
883C2×Q8—42no—
884C2×Q8—42no—
885C2×Q8—48no—
886C2×Q8—42no—
887C2×Q8—42no—
888C2×Q8—44no—
889C2×Q8—416no—
890C2×Q8C22×D414yes—
891C2×Q8C22×D414yes—
892C2×Q8C22×D418yes—
893C2×D4—28no—
894C2×D4—24no—
895C2×D4—28no—
896C2×D4—24no—
897C2×D4—24no—
898C2×D4—22no—
899C2×D4—28no—
900C2×D4—24no—
901C2×D4—24no—
902C2×D4—24no—
903C2×D4—28no—
904C2×D4—24no—
905C2×D4—28no—
906C2×D4—24no—
907C2×D4—24no—
908C2×D4—42no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C2×D4—44no—
913C2×D4—48no—
914C2×D4—48no—
915C2×D4—44no—
916C2×D4—48no—
917C2×D4—48no—
918C2×D4—48no—
919C2×D4—44no—
920C2×D4—48no—
921C2×D4—44no—
922C2×D4—48no—
923C2×D4—48no—
924C2×D4—48no—
925C2×D4—48no—
926C2×D4—48no—
927C2×D4—48no—
928C22×C4—24no—
929C22×C4—28no—
930C22×C4—24no—
931C22×C4—28no—
932C22×C4—24no—
933C22×C4—24no—
934C22×C4—28no—
935C22×C4—28no—
936C22×C4—28no—
937C22×C4—28no—
938C22×C4—28no—
939C22×C4—42no—
940C22×C4—44no—
941C22×C4—48no—
942C22×C4—44no—
943C22×C4—44no—
944C22×C4—44no—
945C22×C4—42no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4—48no—
949C22×C4—48no—
950C22×C4—44no—
951C22×C4—48no—
952C22×C4—44no—
953C22×C4C22×D414yes—
954C22×C4C22×D414yes—
955C22×C4C22×D418yes—
956C22×C4C22×D414yes—
957C22×C4C22×D418yes—
958C22×C4C2514yes—
959C22×C4C2514yes—
960C22×C4C2518yes—
961C22×C4C2512yes—
962C22×C4C2512yes—
963C22×C4C2512yes—
964C22×C4C2514yes—
965C22×C4C2512yes—
966C22×C4C2514yes—
967C22×C4C2512yes—
968C22×C4C2512yes—
969C22×C4C2512yes—
970C22×C4C2511yescharacteristic
971C22×C4C2511yescharacteristic
972C22×C4C2512yes—
973C22×C4C2511yescharacteristic
974C22×C4C2512yes—
975C22×C4C2511yescharacteristic
976C22×C4C2512yes—
977C22×C4C2511yescharacteristic
978C22×C4C2512yes—
979C22×C4C2511yescharacteristic
980C4⋊C4—28no—
981C4⋊C4—24no—
982C4⋊C4—24no—
983C4⋊C4—28no—
984C4⋊C4—24no—
985C4⋊C4—28no—
986C4⋊C4—28no—
987C4⋊C4—24no—
988C4⋊C4—24no—
989C4⋊C4—24no—
990C4⋊C4—24no—
991C4⋊C4—28no—
992C4⋊C4—28no—
993C4⋊C4—22no—
994C4⋊C4—22no—
995C4⋊C4—24no—
996C4⋊C4—22no—
997C4⋊C4—22no—
998C4⋊C4—24no—
999C4⋊C4—24no—
1000C4⋊C4—28no—
1001C4⋊C4—24no—
1002C4⋊C4—24no—
1003C4⋊C4—24no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—24no—
1007C4⋊C4—28no—
1008C4⋊C4—24no—
1009C4⋊C4—28no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—48no—
1014C4⋊C4—48no—
1015C4⋊C4—44no—
1016C4⋊C4—48no—
1017C4⋊C4—48no—
1018C4⋊C4—44no—
1019C4⋊C4—48no—
1020C4⋊C4C22×D418yes—
1021C4⋊C4C22×D414yes—
1022C4⋊C4C22×D418yes—
1023C4⋊C4C22×D414yes—
1024C4⋊C4C22×D418yes—
1025C4⋊C4C22×D418yes—
1026C4⋊C4C22×D418yes—
1027C22⋊C4—24no—
1028C22⋊C4—24no—
1029C22⋊C4—24no—
1030C22⋊C4—28no—
1031C22⋊C4—28no—
1032C22⋊C4—24no—
1033C22⋊C4—28no—
1034C22⋊C4—24no—
1035C22⋊C4—28no—
1036C22⋊C4—28no—
1037C22⋊C4—28no—
1038C22⋊C4—28no—
1039C22⋊C4—28no—
1040C22⋊C4—24no—
1041C22⋊C4—28no—
1042C22⋊C4—28no—
1043C22⋊C4—28no—
1044C22⋊C4—28no—
1045C22⋊C4—28no—
1046C22⋊C4—28no—
1047C22⋊C4—28no—
1048C22⋊C4—24no—
1049C22⋊C4—44no—
1050C22⋊C4—48no—
1051C22⋊C4—48no—
1052C22⋊C4—48no—
1053C22⋊C4—44no—
1054C22⋊C4—44no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—44no—
1058C22⋊C4—48no—
1059C22⋊C4—48no—
1060C22⋊C4—48no—
1061C22⋊C4—48no—
1062C22⋊C4—44no—
1063C22⋊C4—48no—
1064C22⋊C4—48no—
1065C22⋊C4—48no—
1066C22⋊C4—48no—
1067C22⋊C4—48no—
1068C42—28no—
1069C42—28no—
1070C42—28no—
1071C42—24no—
1072C42—24no—
1073C42—24no—
1074C42—28no—
1075C42—48no—
1076C42—48no—
1077C42—44no—
1078C42C22×D418yes—
1079C42C22×D414yes—
1080C42C22×D418yes—
1081C42C22×D418yes—
1082C42C22×D414yes—
1083C42C22×D414yes—
1084C42C22×D414yes—
1085C42C22×D418yes—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—24no—
1090C23—24no—
1091C23—22no—
1092C23—22no—
1093C23—24no—
1094C23—28no—
1095C23—22no—
1096C23—24no—
1097C23—24no—
1098C23—24no—
1099C23—24no—
1100C23—28no—
1101C23—24no—
1102C23—28no—
1103C23—28no—
1104C23C23×D412yes—
1105C23C2611yescharacteristic
1106Q8—28no—
1107Q8—28no—
1108Q8—48no—
1109Q8—44no—
1110Q8—44no—
1111Q8—44no—
1112Q8—48no—
1113Q8—84no—
1114Q8—88no—
1115Q8—84no—
1116D4—44no—
1117D4—48no—
1118D4—48no—
1119D4—416no—
1120D4—416no—
1121D4—416no—
1122D4—48no—
1123D4—48no—
1124D4—48no—
1125D4—84no—
1126D4—88no—
1127D4—84no—
1128D4—816no—
1129D4—816no—
1130D4—168no—
1131C2×C4—24no—
1132C2×C4—22no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—24no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—28no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—24no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—28no—
1153C2×C4—22no—
1154C2×C4—28no—
1155C2×C4—22no—
1156C2×C4—28no—
1157C2×C4—24no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—24no—
1161C2×C4—22no—
1162C2×C4—28no—
1163C2×C4—24no—
1164C2×C4—22no—
1165C2×C4—28no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—44no—
1172C2×C4—48no—
1173C2×C4—48no—
1174C2×C4—44no—
1175C2×C4—416no—
1176C2×C4—416no—
1177C2×C4—48no—
1178C2×C4—88no—
1179C2×C4—88no—
1180C2×C4—88no—
1181C2×C4—88no—
1182C2×C4—88no—
1183C2×C4C23×D414yes—
1184C2×C4C23×D414yes—
1185C2×C4C23×D414yes—
1186C2×C4C23×D412yes—
1187C2×C4C23×D412yes—
1188C2×C4C23×D414yes—
1189C2×C4C23×D412yes—
1190C2×C4C23×D412yes—
1191C2×C4C23×D412yes—
1192C2×C4C23×D412yes—
1193C2×C4#58514yes—
1194C22—22no—
1195C22—22no—
1196C22—22no—
1197C22—44no—
1198C22—44no—
1199C22—48no—
1200C22—48no—
1201C22—48no—
1202C22—44no—
1203C22—48no—
1204C22—44no—
1205C22—42no—
1206C22—44no—
1207C22—42no—
1208C22—44no—
1209C22—44no—
1210C22—44no—
1211C22—44no—
1212C22—42no—
1213C22C24×D411yescharacteristic
1214C22C2×#58512yes—
1215C22H(7,𝔽2)12yes—
1216C222−1+612yes—
1217C4—22no—
1218C4—22no—
1219C4—24no—
1220C4—22no—
1221C4—24no—
1222C4—22no—
1223C4—22no—
1224C4—24no—
1225C4—24no—
1226C4—48no—
1227C4—44no—
1228C4—44no—
1229C4—42no—
1230C4—42no—
1231C4—42no—
1232C4—44no—
1233C4—42no—
1234C4—42no—
1235C4—42no—
1236C4—42no—
1237C4—44no—
1238C4#344914yes—
1239C2—42no—
1240C2—82no—
1241C2—84no—
1242C2—84no—
1243C2C2×#344911yescharacteristic
1244C2#6284811yescharacteristic
1245C2#6285211yescharacteristic
1246C2#6305614yes—
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×#3507C2semidirect
3. #42889C2semidirect
4. #42881C2semidirect
5. #42809C2semidirect
6. #42797C2semidirect
7. #42795C2semidirect
8. #42153C2semidirect
9. #41991C2semidirect
10. #41987C2semidirect
11. #41957C2semidirect
12. #40497C2semidirect
13. #37619C2semidirect
14. #37618C2semidirect
15. #37559C2semidirect
16. #37559C2semidirect
17. #37552C2semidirect
18. #37552C2semidirect
19. #36699C2semidirect
20. #36687C2semidirect
21. #35956C2semidirect
22. #35909C2semidirect
23. #35844C2semidirect
24. #35715C2semidirect
25. #35712C2semidirect
26. #34192C2semidirect
313. 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×#35072
#428892
#428812
#428092
#427972
#427952
#421532
#419912
#419872
#419572
#404972
#376192
#376182
#375592
#375522
#366992
#366872
#359562
#359092
#358442
#357152
#357122
#341922