Finite Group Databasebeta

← #7656029

Subgroups — #7656029

Order 512.

6636 conjugacy classes of subgroups.

The subgroup lattice has 1260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3523C211yesmaximal, characteristic, complemented
2C2×#3522C211yesmaximal, characteristic, complemented
3#42880C212yesmaximal, complemented
4#42875C212yesmaximal, complemented
5#42793C212yesmaximal, complemented
6#42788C212yesmaximal, complemented
7#42389C214yesmaximal, complemented
8#42388C214yesmaximal, complemented
9#42154C214yesmaximal, complemented
10#42153C214yesmaximal, complemented
11#39166C214yesmaximal, complemented
12#38087C218yesmaximal, complemented
13#37557C212yesmaximal, complemented
14#37556C212yesmaximal, complemented
15#37555C211yesmaximal, characteristic, complemented
16#37554C211yesmaximal, characteristic, complemented
17#36424C214yesmaximal, complemented
18#36041C212yesmaximal, complemented
19#36019C212yesmaximal, complemented
20#35738C212yesmaximal, complemented
21#35712C212yesmaximal, complemented
22#35180C211yesmaximal, characteristic, complemented
23#35119C212yesmaximal, complemented
24#34637C212yesmaximal, complemented
25#34594C211yesmaximal, characteristic, complemented
26C2×#2356C211yesmaximal, characteristic, complemented
27#3523—216no—
28#3522—216no—
29C2×#559C2212yes—
30C2×#559C2211yescharacteristic
31C2×Q82C2211yescharacteristic
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2212yes—
35C2×#556C2212yes—
36C2×#556C2211yescharacteristic
37C2×#554C2212yes—
38C2×#554C2211yescharacteristic
39C2×#552C2212yes—
40C2×#552C2214yes—
41C2×#550C2211yescharacteristic
42C2×D4×Q8C2211yescharacteristic
43C2×D4×Q8C2212yes—
44C2×#548C2212yes—
45C2×#547C2212yes—
46C2×#547C2214yes—
47C2×#542C2212yes—
48C2×#542C2214yes—
49C2×#541C2212yes—
50C2×#541C2214yes—
51C2×#533C2212yes—
52C2×#533C2211yescharacteristic
53C2×#532C2212yes—
54C2×#532C2211yescharacteristic
55C2×#529C2211yescharacteristic
56C2×#529C2211yescharacteristic
57C2×#529C2212yes—
58C2×#529C2212yes—
59C2×#520C2212yes—
60C2×#519C2212yes—
61C22×C4×Q8C2211yescharacteristic
62#2854C2218yes—
63#2850C2214yes—
64#2822C2212yes—
65#2821C2214yes—
66#2821C2214yes—
67#2821C2214yes—
68#2820C2212yes—
69#2820C2212yes—
70#2819C2212yes—
71#2818C2214yes—
72#2731C2218yes—
73#2730C2218yes—
74#2729C2218yes—
75#2728C2218yes—
76#2716C2218yes—
77#2714C2218yes—
78#2713C2218yes—
79#2711C2218yes—
80#2696C2218yes—
81#2694C2218yes—
82#2692C2218yes—
83#2690C2218yes—
84#2664C2212yes—
85#2664C2212yes—
86#2662C2212yes—
87#2662C2212yes—
88#2659C2211yescharacteristic
89#2659C2212yes—
90#2656C2211yescharacteristic
91#2656C2212yes—
92#2642C2214yes—
93#2641C2214yes—
94#2640C2214yes—
95#2640C2214yes—
96#2639C2211yescharacteristic
97#2639C2211yescharacteristic
98#2639C2212yes—
99#2639C2212yes—
100#2639C2212yes—
101#2639C2218yes—
102#2639C2212yes—
103#2637C2214yes—
104#2636C2214yes—
105#2634C2214yes—
106#2634C2214yes—
107#2633C2214yes—
108#2633C2214yes—
109#2632C2214yes—
110#2632C2214yes—
111#2631C2214yes—
112#2631C2214yes—
113#2628C2212yes—
114#2628C2212yes—
115#2621C2212yes—
116#2619C2212yes—
117#2618C2214yes—
118#2611C2214yes—
119#2611C2214yes—
120#2610C2214yes—
121#2610C2214yes—
122#2604C2214yes—
123#2604C2214yes—
124#2603C2214yes—
125#2603C2214yes—
126#2599C2214yes—
127#2599C2214yes—
128#2598C2214yes—
129#2598C2214yes—
130#2592C2214yes—
131#2581C2212yes—
132#2580C2212yes—
133#2568C2212yes—
134#2564C2218yes—
135#2563C2212yes—
136#2562C2214yes—
137#2560C2218yes—
138#2558C2218yes—
139#2556C2218yes—
140#2554C2218yes—
141#2550C2214yes—
142#2548C2212yes—
143#2547C2212yes—
144#2543C2218yes—
145#2540C2214yes—
146#2536C2212yes—
147#2535C2212yes—
148#2498C2218yes—
149#2498C2214yes—
150#2492C2214yes—
151#2490C2214yes—
152#2481C2218yes—
153#2477C2218yes—
154#2473C2218yes—
155#2471C2218yes—
156#2467C2218yes—
157#2465C2218yes—
158#2460C2218yes—
159#2458C2218yes—
160#2448C2214yes—
161#2446C2214yes—
162#2436C2214yes—
163#2432C2214yes—
164#2430C2218yes—
165#2430C2214yes—
166#2421C2214yes—
167#2421C2214yes—
168#2417C2214yes—
169#2416C2214yes—
170#2409C2214yes—
171#2407C2214yes—
172#2398C2214yes—
173#2398C2214yes—
174#2398C2214yes—
175#2398C2214yes—
176#2396C2212yes—
177#2396C2212yes—
178#2392C2212yes—
179#2392C2212yes—
180#2367C2214yes—
181#2363C2214yes—
182#2360C2214yes—
183#2356C2212yes—
184#2356C2212yes—
185#2356C2212yes—
186#2356C2214yes—
187#2356C2212yes—
188#2356C2214yes—
189#2352C2214yes—
190#2325C2218yes—
191#2311C2214yes—
192C4×#121C2214yes—
193#2297C2218yes—
194C2×#391C2212yes—
195C2×#387C2214yes—
196C2×#383C2212yes—
197C2×#382C2211yescharacteristic
198C2×C4×C4⋊C4C2211yescharacteristic
199C2×C4×C4⋊C4C2212yes—
200C2×#376C2212yes—
201C22×#41C2312yes—
202C22×#41C2312yes—
203C22×#41C2314yes—
204C23×Q8C2312yes—
205C23×Q8C2311yescharacteristic
206#559—28no—
207#559—216no—
208Q82—28no—
209#557—28no—
210#557—28no—
211#557—216no—
212#556—28no—
213#556—216no—
214#554—28no—
215#554—216no—
216#552—216no—
217#552—232no—
218#550—28no—
219D4×Q8—216no—
220D4×Q8—28no—
221#548—216no—
222#547—216no—
223#547—232no—
224#542—216no—
225#542—232no—
226#541—216no—
227#541—232no—
228#533—216no—
229#533—28no—
230#532—216no—
231#532—28no—
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2311yescharacteristic
237C2×C4⋊Q8C2311yescharacteristic
238C2×C4⋊Q8C2312yes—
239C2×C4⋊Q8C2314yes—
240C2×C4⋊Q8C2314yes—
241C2×C4⋊Q8C2312yes—
242C2×#127C2312yes—
243C2×#127C2311yescharacteristic
244#529—28no—
245#529—216no—
246#529—28no—
247#529—216no—
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#126C2312yes—
252C2×#126C2312yes—
253C2×#126C2314yes—
254C2×#126C2314yes—
255C2×#125C2312yes—
256C2×#125C2311yescharacteristic
257C2×#125C2311yescharacteristic
258C2×#125C2312yes—
259C2×#125C2312yes—
260C2×#125C2314yes—
261C2×#125C2314yes—
262C2×#125C2314yes—
263C2×#125C2314yes—
264C2×#125C2312yes—
265C2×#125C2314yes—
266C2×#124C2311yescharacteristic
267C2×#124C2312yes—
268C2×#124C2311yescharacteristic
269C2×#124C2312yes—
270C2×#124C2312yes—
271C2×#124C2314yes—
272C2×#124C2312yes—
273C2×#124C2314yes—
274C2×#124C2314yes—
275C2×#123C2314yes—
276C2×#123C2314yes—
277C2×#123C2312yes—
278C2×#123C2312yes—
279C2×#123C2314yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2311yescharacteristic
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2311yescharacteristic
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×#121C2312yes—
298C2×#121C2311yescharacteristic
299C2×#121C2312yes—
300C2×#121C2314yes—
301C2×#121C2311yescharacteristic
302C2×#121C2314yes—
303C2×#121C2312yes—
304C2×#121C2318yes—
305C2×#121C2314yes—
306C2×#121C2314yes—
307#520—216no—
308#519—216no—
309C2×C4×Q8D4116yescomplemented
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2314yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2314yes—
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2311yescharacteristic
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2314yes—
339C2×C4×D4C2311yescharacteristic
340C2×C4×D4C2311yescharacteristic
341C2×C4×D4C2314yes—
342C2×C4×D4C2312yes—
343C2×C4×D4C2312yes—
344C2×C4×D4C2314yes—
345C2×#117C2312yes—
346C2×#117C2314yes—
347C2×#117C2314yes—
348C2×#117C2312yes—
349C2×#117C2312yes—
350C2×#117C2312yes—
351C2×#117C2314yes—
352C2×#117C2314yes—
353C22×C4⋊C4C2312yes—
354C22×C4⋊C4C2314yes—
355C22×C4⋊C4C2312yes—
356C22×C4⋊C4C2312yes—
357C22×C4⋊C4C2311yescharacteristic
358C22×C4⋊C4C2312yes—
359C22×C42C2312yes—
360C22×C42C2314yes—
361C22×C42C2312yes—
362C22×C42C2311yescharacteristic
363#400C2314yes—
364#400C2314yes—
365#400C2318yes—
366#400C2314yes—
367#400C2318yes—
368#400C2314yes—
369#400C2312yes—
370#400C2314yes—
371#400C2312yes—
372#400C2318yes—
373#400C2318yes—
374#399C2318yes—
375#399C2314yes—
376#399C2314yes—
377#399C2312yes—
378#399C2314yes—
379#399C2318yes—
380#399C2312yes—
381#398C2318yes—
382#398C2312yes—
383#398C2314yes—
384#398C2318yes—
385#398C2318yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2312yes—
391#397C2318yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2318yes—
396#397C2314yes—
397#397C2312yes—
398#397C2314yes—
399#397C2312yes—
400#397C2318yes—
401#397C2318yes—
402#396C2318yes—
403#396C2318yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#395C2318yes—
409#395C2314yes—
410#395C2314yes—
411#395C2312yes—
412#395C2314yes—
413#395C2318yes—
414#395C2312yes—
415#394C2318yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2318yes—
420#394C2318yes—
421#394C2314yes—
422#394C2312yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2312yes—
427#394C2318yes—
428#394C2318yes—
429#393C2318yes—
430#393C2314yes—
431#393C2314yes—
432#393C2314yes—
433#393C2314yes—
434#393C2318yes—
435#393C2312yes—
436#393C2314yes—
437#393C2312yes—
438#393C2318yes—
439#393C2318yes—
440#392C2312yes—
441#392C2314yes—
442#392C2318yes—
443#392C2318yes—
444#392C2314yes—
445#392C2314yes—
446#392C2312yes—
447#391C2318yes—
448#391C2318yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#391C2314yes—
453#391C2318yes—
454#391C2318yes—
455#390C2318yes—
456#390C2314yes—
457#390C2318yes—
458#390C2314yes—
459#390C2318yes—
460#390C2318yes—
461#390C2318yes—
462#390C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2318yes—
466#389C2318yes—
467#389C2314yes—
468#388C2314yes—
469#388C2318yes—
470#388C2318yes—
471#388C2318yes—
472#388C2318yes—
473#388C2318yes—
474#388C2318yes—
475#388C2318yes—
476#388C2318yes—
477#388C2318yes—
478#388C2318yes—
479#388C2318yes—
480#388C2318yes—
481#388C2318yes—
482#388C2314yes—
483#387C2318yes—
484#387C2318yes—
485#387C2318yes—
486#387C2318yes—
487#387C2318yes—
488#387C2318yes—
489#387C2318yes—
490#387C2318yes—
491#387C2318yes—
492#387C2318yes—
493#387C2318yes—
494#386C2318yes—
495#386C2318yes—
496#386C2318yes—
497#386C2318yes—
498#386C2314yes—
499#386C2318yes—
500#386C2318yes—
501#386C2318yes—
502#386C2318yes—
503#386C2318yes—
504#386C2314yes—
505#386C2318yes—
506#386C2318yes—
507#385C2318yes—
508#385C2318yes—
509#385C2318yes—
510#385C2318yes—
511#385C2318yes—
512#385C2318yes—
513#385C2318yes—
514#383C2314yes—
515#383C2314yes—
516#383C2314yes—
517#383C2314yes—
518#382C2314yes—
519#382C2312yes—
520#382C2312yes—
521#382C2312yes—
522#382C2312yes—
523#380C2318yes—
524#380C2318yes—
525#380C2314yes—
526#380C2318yes—
527#380C2314yes—
528#380C2314yes—
529C4×C4⋊C4C2318yes—
530C4×C4⋊C4C2312yes—
531C4×C4⋊C4C2312yes—
532C4×C4⋊C4C2312yes—
533C4×C4⋊C4C2312yes—
534C4×C4⋊C4C2314yes—
535C4×C4⋊C4C2314yes—
536C4×C4⋊C4C2314yes—
537C4×C22⋊C4C2318yes—
538C4×C22⋊C4C2318yes—
539C4×C22⋊C4C2314yes—
540C4×C22⋊C4C2318yes—
541C4×C22⋊C4C2314yes—
542C4×C22⋊C4C2318yes—
543#376C2314yes—
544#376C2314yes—
545#376C2314yes—
546#376C2314yes—
547C2×#95C2314yes—
548C2×#95C2314yes—
549C2×#95C2311yescharacteristic
550C2×#95C2312yes—
551C2×#95C2311yescharacteristic
552C2×#95C2314yes—
553C2×#95C2312yes—
554C2×#41—28no—
555C2×#41—28no—
556C2×#41—216no—
557C2×#41—416no—
558C2×#41—48no—
559C2×#41—44no—
560C2×#41—44no—
561C22×Q8—28no—
562C22×Q8—42no—
563C22×Q8—42no—
564C22×Q8—44no—
565C22×Q8—44no—
566C22×Q8C2×D418yes—
567C22×Q8C2412yes—
568C22×Q8C2411yescharacteristic
569C22×Q8C2411yescharacteristic
570C22×Q8C2411yescharacteristic
571C22×Q8C2411yescharacteristic
572C22×Q8C2412yes—
573C22×Q8C2414yes—
574C22×Q8C2414yes—
575C22×Q8C2412yes—
576C22×Q8C2412yes—
577C22×D4C2412yes—
578C22×D4C2412yes—
579C22×D4C2414yes—
580C22×D4C2412yes—
581C22×D4C2411yescharacteristic
582C22×D4C2412yes—
583C22×D4C2411yescharacteristic
584C22×D4C2414yes—
585C22×D4C2412yes—
586C22×D4C2414yes—
587C22×D4C2414yes—
588C22×D4C2418yes—
589C23×C4C2412yes—
590C23×C4C2412yes—
591C23×C4C2411yescharacteristic
592C23×C4C2411yescharacteristic
593C23×C4C2412yes—
594C23×C4C2414yes—
595C23×C4C2414yes—
596C23×C4C2414yes—
597C23×C4C2414yes—
598C23×C4C2414yes—
599C23×C4C2412yes—
600C23×C4C2412yes—
601C23×C4C2414yes—
602C23×C4C2412yes—
603C23×C4C2411yescharacteristic
604C4⋊Q8—28no—
605C4⋊Q8—216no—
606C4⋊Q8—28no—
607C4⋊Q8—216no—
608C4⋊Q8—24no—
609C4⋊Q8—28no—
610C4⋊Q8—24no—
611C4⋊Q8—28no—
612C4⋊Q8—24no—
613C4⋊Q8—28no—
614#127—24no—
615#127—28no—
616#126—216no—
617#126—216no—
618#126—216no—
619#126—28no—
620#126—216no—
621#126—216no—
622#126—28no—
623#125—216no—
624#125—216no—
625#125—216no—
626#125—28no—
627#125—216no—
628#125—28no—
629#125—24no—
630#125—28no—
631#125—24no—
632#125—28no—
633#125—216no—
634#124—28no—
635#124—216no—
636#124—28no—
637#124—24no—
638#124—28no—
639#124—24no—
640#124—216no—
641#124—28no—
642#124—48no—
643#123—216no—
644#123—28no—
645#123—216no—
646#123—28no—
647#123—216no—
648#123—216no—
649#123—216no—
650C22⋊Q8—28no—
651C22⋊Q8—216no—
652C22⋊Q8—28no—
653C22⋊Q8—216no—
654C22⋊Q8—24no—
655C22⋊Q8—24no—
656C22⋊Q8—28no—
657C22⋊Q8—28no—
658C22⋊Q8—216no—
659C22⋊Q8—28no—
660C22⋊Q8—216no—
661C22⋊Q8—216no—
662C22⋊Q8—216no—
663C22⋊Q8—216no—
664C22⋊Q8—48no—
665#121—24no—
666#121—24no—
667#121—28no—
668#121—28no—
669#121—216no—
670#121—28no—
671#121—216no—
672#121—48no—
673#121—416no—
674#121—48no—
675C4×Q8—28no—
676C4×Q8—28no—
677C4×Q8—28no—
678C4×Q8—216no—
679C4×Q8—216no—
680C4×Q8—28no—
681C4×Q8—24no—
682C4×Q8—28no—
683C4×Q8—24no—
684C4×Q8—28no—
685C4×Q8—28no—
686C4×Q8—28no—
687C4×Q8—28no—
688C4×Q8C2×D418yes—
689C4×Q8C2×D418yes—
690C4×Q8C2×D418yes—
691C4×Q8C2×D4116yes—
692C4×Q8C2×D418yes—
693C4×Q8C2×D4116yes—
694C4×D4—28no—
695C4×D4—216no—
696C4×D4—28no—
697C4×D4—216no—
698C4×D4—28no—
699C4×D4—216no—
700C4×D4—28no—
701C4×D4—216no—
702C4×D4—24no—
703C4×D4—28no—
704C4×D4—24no—
705C4×D4—28no—
706C4×D4—28no—
707C4×D4—28no—
708C4×D4—28no—
709C4×D4—48no—
710#117—28no—
711#117—216no—
712#117—28no—
713#117—216no—
714#117—216no—
715#117—28no—
716#117—28no—
717#117—216no—
718C2×C4⋊C4—28no—
719C2×C4⋊C4—216no—
720C2×C4⋊C4—44no—
721C2×C4⋊C4—44no—
722C2×C4⋊C4C2×D418yes—
723C2×C4⋊C4C2×D4116yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2411yescharacteristic
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2418yes—
763C2×C4⋊C4C2418yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2418yes—
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2411yescharacteristic
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C22⋊C4C2412yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2412yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2412yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2412yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2412yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2412yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2418yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2418yes—
800C2×C22⋊C4C2418yes—
801C2×C22⋊C4C2418yes—
802C2×C22⋊C4C2418yes—
803C2×C22⋊C4C2418yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2418yes—
806C2×C22⋊C4C2418yes—
807C2×C22⋊C4C2418yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2418yes—
810C2×C42—44no—
811C2×C42—48no—
812C2×C42C2×D418yes—
813C2×C42C2×D4116yes—
814C2×C42C2414yes—
815C2×C42C2414yes—
816C2×C42C2414yes—
817C2×C42C2412yes—
818C2×C42C2414yes—
819C2×C42C2412yes—
820C2×C42C2414yes—
821C2×C42C2414yes—
822C2×C42C2418yes—
823C2×C42C2418yes—
824C2×C42C2414yes—
825C2×C42C2411yescharacteristic
826C2×C42C2412yes—
827C2×C42C2412yes—
828C2×C42C2411yescharacteristic
829C2×C42C2411yescharacteristic
830C2×C42C2412yes—
831C2×C42C2412yes—
832C2×C42C2411yescharacteristic
833#95C2412yes—
834#95C2412yes—
835#95C2414yes—
836#95C2414yes—
837#95C2418yes—
838#95C2418yes—
839#95C2412yes—
840#95C2412yes—
841#95C2418yes—
842#95C2418yes—
843#95C2414yes—
844#95C2414yes—
845#95C2418yes—
846#95C2418yes—
847#95C2414yes—
848#95C2414yes—
849#95C2418yes—
850#95C2414yes—
851#95C2418yes—
852#95C2418yes—
853#95C2414yes—
854#95C2414yes—
855#95C2418yes—
856#95C2418yes—
857#95C2418yes—
858#95C2414yes—
859#95C2418yes—
860#95C2418yes—
861#95C2418yes—
862#95C2418yes—
863C24C2512yes—
864C24C2512yes—
865C24C2514yes—
866C24C2511yescharacteristic
867#41—432no—
868#41—832no—
869#41—816no—
870C2×Q8—22no—
871C2×Q8—22no—
872C2×Q8—24no—
873C2×Q8—28no—
874C2×Q8—24no—
875C2×Q8—24no—
876C2×Q8—28no—
877C2×Q8—22no—
878C2×Q8—22no—
879C2×Q8—22no—
880C2×Q8—22no—
881C2×Q8—24no—
882C2×Q8—24no—
883C2×Q8—42no—
884C2×Q8—42no—
885C2×Q8—44no—
886C2×Q8—44no—
887C2×Q8—42no—
888C2×Q8—42no—
889C2×Q8—44no—
890C2×Q8—48no—
891C2×Q8—44no—
892C2×Q8—416no—
893C2×Q8—432no—
894C2×Q8C22×D414yes—
895C2×Q8C22×D414yes—
896C2×Q8C22×D418yes—
897C2×D4—24no—
898C2×D4—24no—
899C2×D4—28no—
900C2×D4—28no—
901C2×D4—28no—
902C2×D4—216no—
903C2×D4—22no—
904C2×D4—22no—
905C2×D4—24no—
906C2×D4—28no—
907C2×D4—24no—
908C2×D4—24no—
909C2×D4—28no—
910C2×D4—24no—
911C2×D4—24no—
912C2×D4—42no—
913C2×D4—44no—
914C2×D4—42no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—48no—
921C2×D4—44no—
922C2×D4—48no—
923C2×D4—48no—
924C2×D4—48no—
925C22×C4—28no—
926C22×C4—24no—
927C22×C4—22no—
928C22×C4—22no—
929C22×C4—24no—
930C22×C4—28no—
931C22×C4—24no—
932C22×C4—28no—
933C22×C4—24no—
934C22×C4—28no—
935C22×C4—24no—
936C22×C4—24no—
937C22×C4—24no—
938C22×C4—24no—
939C22×C4—24no—
940C22×C4—28no—
941C22×C4—28no—
942C22×C4—28no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—44no—
949C22×C4—44no—
950C22×C4—44no—
951C22×C4—44no—
952C22×C4—42no—
953C22×C4—44no—
954C22×C4—42no—
955C22×C4—44no—
956C22×C4—48no—
957C22×C4—48no—
958C22×C4—48no—
959C22×C4C22×D418yes—
960C22×C4C22×D414yes—
961C22×C4C22×D414yes—
962C22×C4C22×D414yes—
963C22×C4C22×D418yes—
964C22×C4C2514yes—
965C22×C4C2518yes—
966C22×C4C2514yes—
967C22×C4C2512yes—
968C22×C4C2514yes—
969C22×C4C2512yes—
970C22×C4C2512yes—
971C22×C4C2514yes—
972C22×C4C2512yes—
973C22×C4C2514yes—
974C22×C4C2512yes—
975C22×C4C2512yes—
976C22×C4C2511yescharacteristic
977C22×C4C2511yescharacteristic
978C22×C4C2512yes—
979C22×C4C2512yes—
980C22×C4C2512yes—
981C22×C4C2512yes—
982C22×C4C2511yescharacteristic
983C22×C4C2511yescharacteristic
984C22×C4C2511yescharacteristic
985C22×C4C2511yescharacteristic
986C4⋊C4—28no—
987C4⋊C4—24no—
988C4⋊C4—28no—
989C4⋊C4—24no—
990C4⋊C4—24no—
991C4⋊C4—28no—
992C4⋊C4—24no—
993C4⋊C4—28no—
994C4⋊C4—24no—
995C4⋊C4—28no—
996C4⋊C4—24no—
997C4⋊C4—24no—
998C4⋊C4—28no—
999C4⋊C4—24no—
1000C4⋊C4—28no—
1001C4⋊C4—22no—
1002C4⋊C4—24no—
1003C4⋊C4—22no—
1004C4⋊C4—24no—
1005C4⋊C4—22no—
1006C4⋊C4—28no—
1007C4⋊C4—24no—
1008C4⋊C4—28no—
1009C4⋊C4—24no—
1010C4⋊C4—22no—
1011C4⋊C4—28no—
1012C4⋊C4—28no—
1013C4⋊C4—28no—
1014C4⋊C4—24no—
1015C4⋊C4—28no—
1016C4⋊C4—24no—
1017C4⋊C4—28no—
1018C4⋊C4—28no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—44no—
1023C4⋊C4—48no—
1024C4⋊C4—44no—
1025C4⋊C4—48no—
1026C4⋊C4—44no—
1027C4⋊C4—48no—
1028C4⋊C4C22×D414yes—
1029C4⋊C4C22×D418yes—
1030C4⋊C4C22×D418yes—
1031C4⋊C4C22×D414yes—
1032C4⋊C4C22×D418yes—
1033C4⋊C4C22×D418yes—
1034C4⋊C4C22×D418yes—
1035C22⋊C4—28no—
1036C22⋊C4—24no—
1037C22⋊C4—24no—
1038C22⋊C4—24no—
1039C22⋊C4—28no—
1040C22⋊C4—24no—
1041C22⋊C4—28no—
1042C22⋊C4—24no—
1043C22⋊C4—28no—
1044C22⋊C4—24no—
1045C22⋊C4—24no—
1046C22⋊C4—28no—
1047C22⋊C4—28no—
1048C22⋊C4—28no—
1049C22⋊C4—28no—
1050C22⋊C4—24no—
1051C22⋊C4—28no—
1052C22⋊C4—28no—
1053C22⋊C4—24no—
1054C22⋊C4—28no—
1055C22⋊C4—24no—
1056C22⋊C4—44no—
1057C22⋊C4—48no—
1058C22⋊C4—44no—
1059C22⋊C4—48no—
1060C22⋊C4—48no—
1061C22⋊C4—48no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—48no—
1065C22⋊C4—48no—
1066C22⋊C4—48no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—48no—
1070C22⋊C4—48no—
1071C22⋊C4—48no—
1072C42—28no—
1073C42—28no—
1074C42—28no—
1075C42—28no—
1076C42—24no—
1077C42—28no—
1078C42—24no—
1079C42—28no—
1080C42—44no—
1081C42—48no—
1082C42—48no—
1083C42C22×D414yes—
1084C42C22×D418yes—
1085C42C22×D418yes—
1086C42C22×D414yes—
1087C42C22×D414yes—
1088C42C22×D418yes—
1089C42C22×D418yes—
1090C42C22×D414yes—
1091C23—21no—
1092C23—21no—
1093C23—22no—
1094C23—22no—
1095C23—24no—
1096C23—22no—
1097C23—22no—
1098C23—24no—
1099C23—24no—
1100C23—22no—
1101C23—22no—
1102C23—24no—
1103C23—24no—
1104C23—28no—
1105C23—22no—
1106C23—24no—
1107C23—28no—
1108C23—24no—
1109C23C23×D412yes—
1110C23#58514yes—
1111C23C2611yescharacteristic
1112Q8—28no—
1113Q8—28no—
1114Q8—48no—
1115Q8—44no—
1116Q8—44no—
1117Q8—48no—
1118Q8—416no—
1119Q8—48no—
1120Q8—88no—
1121Q8—84no—
1122D4—44no—
1123D4—48no—
1124D4—44no—
1125D4—416no—
1126D4—48no—
1127D4—48no—
1128D4—416no—
1129D4—48no—
1130D4—88no—
1131D4—84no—
1132D4—88no—
1133D4—168no—
1134C2×C4—21no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—21no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—216no—
1147C2×C4—28no—
1148C2×C4—28no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—24no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—28no—
1162C2×C4—22no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—28no—
1166C2×C4—24no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—24no—
1170C2×C4—28no—
1171C2×C4—24no—
1172C2×C4—22no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—28no—
1176C2×C4—24no—
1177C2×C4—28no—
1178C2×C4—24no—
1179C2×C4—44no—
1180C2×C4—48no—
1181C2×C4—416no—
1182C2×C4—416no—
1183C2×C4—48no—
1184C2×C4—48no—
1185C2×C4—48no—
1186C2×C4—88no—
1187C2×C4—88no—
1188C2×C4—88no—
1189C2×C4—84no—
1190C2×C4—88no—
1191C2×C4C23×D414yes—
1192C2×C4C23×D412yes—
1193C2×C4C23×D414yes—
1194C2×C4C23×D414yes—
1195C2×C4C23×D412yes—
1196C2×C4C23×D412yes—
1197C2×C4C23×D412yes—
1198C2×C4C23×D412yes—
1199C2×C4C23×D414yes—
1200C2×C4C23×D412yes—
1201C2×C4#58512yes—
1202C2×C4#58512yes—
1203C22—22no—
1204C22—24no—
1205C22—22no—
1206C22—24no—
1207C22—42no—
1208C22—44no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—44no—
1213C22—44no—
1214C22—44no—
1215C22—48no—
1216C22—42no—
1217C22—44no—
1218C22—42no—
1219C22—44no—
1220C22—48no—
1221C22—44no—
1222C22#350014yes—
1223C22C24×D411yescharacteristic
1224C22C2×#58512yes—
1225C22C2×#58511yescharacteristic
1226C22C2×#58511yescharacteristic
1227C222−1+612yes—
1228C4—24no—
1229C4—22no—
1230C4—24no—
1231C4—22no—
1232C4—22no—
1233C4—22no—
1234C4—22no—
1235C4—24no—
1236C4—24no—
1237C4—44no—
1238C4—42no—
1239C4—42no—
1240C4—42no—
1241C4—42no—
1242C4—44no—
1243C4—44no—
1244C4—44no—
1245C4—42no—
1246C4—42no—
1247C4—44no—
1248C4—48no—
1249C4#344914yes—
1250C2—24no—
1251C2—82no—
1252C2—84no—
1253C2—82no—
1254C2C2×#344911yescharacteristic
1255C2C2×#350011yescharacteristic
1256C2#6284811yescharacteristic
1257C2#6290712yes—
1258C2#6296412yes—
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×#3523C2semidirect
2. C2×#3522C2semidirect
3. #42880C2semidirect
4. #42875C2semidirect
5. #42793C2semidirect
6. #42788C2semidirect
7. #42389C2semidirect
8. #42388C2semidirect
9. #42154C2semidirect
10. #42153C2semidirect
11. #39166C2semidirect
12. #38087C2semidirect
13. #37557C2semidirect
14. #37556C2semidirect
15. #37555C2semidirect
16. #37554C2semidirect
17. #36424C2semidirect
18. #36041C2semidirect
19. #36019C2semidirect
20. #35738C2semidirect
21. #35712C2semidirect
22. #35180C2semidirect
23. #35119C2semidirect
24. #34637C2semidirect
25. #34594C2semidirect
26. C2×#2356C2semidirect
309. 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×#35222
#428802
#428752
#427932
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C2×#23562