Finite Group Databasebeta

← #7674339

Subgroups — #7674339

Order 512.

4517 conjugacy classes of subgroups.

The subgroup lattice has 1286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45407C212yesmaximal, complemented
2#45403C212yesmaximal, complemented
3#45346C212yesmaximal, complemented
4#45296C212yesmaximal
5#45277C211yesmaximal, characteristic, complemented
6#45266C211yesmaximal, characteristic, complemented
7#45242C212yesmaximal, complemented
8#44982C211yesmaximal, characteristic, complemented
9#44965C211yesmaximal, characteristic, complemented
10#44911C212yesmaximal, complemented
11#40474C214yesmaximal, complemented
12#40467C214yesmaximal, complemented
13#40093C214yesmaximal, complemented
14#40089C214yesmaximal, complemented
15#38803C214yesmaximal, complemented
16#38797C214yesmaximal, complemented
17#38622C214yesmaximal, complemented
18#38615C214yesmaximal, complemented
19#35587C212yesmaximal, complemented
20#35586C212yesmaximal, complemented
21#35186C212yesmaximal, complemented
22#35175C212yesmaximal, complemented
23#34644C211yesmaximal, characteristic, complemented
24#34336C212yesmaximal, complemented
25#34324C212yesmaximal, complemented
26C4×#541C211yesmaximal, characteristic, complemented
27C4×#540C211yesmaximal, characteristic
28C2×#557C2212yes—
29C2×#556C2212yes—
30C2×#541C2211yescharacteristic
31C2×#540C2211yescharacteristic
32#2861C2214yes—
33#2860C2214yes—
34#2855C2214yes—
35#2851C2214yes—
36#2802C2214yes—
37#2798C2214yes—
38#2788C2214yes—
39#2786C2214yes—
40#2775C2214yes—
41#2772C2214yes—
42#2772C2214yes—
43#2768C2214yes—
44#2768C2214yes—
45#2767C2214yes—
46#2754C2214yes—
47#2754C2214yes—
48#2738C2214yes—
49#2727C2214yes—
50#2727C2214yes—
51#2726C2214yes—
52#2726C2214yes—
53#2725C2214yes—
54#2723C2214yes—
55#2723C2214yes—
56#2723C2214yes—
57#2721C2214yes—
58#2720C2214yes—
59#2719C2214yes—
60#2715C2214yes—
61#2715C2214yes—
62#2713C2214yes—
63#2711C2214yes—
64#2711C2214yes—
65#2707C2214yes—
66#2698C2214yes—
67#2674C2214yes—
68#2667C2212yes—
69#2667C2212yes—
70#2667C2214yes—
71#2666C2212yes—
72#2666C2212yes—
73#2666C2212yes—
74#2666C2212yes—
75#2665C2212yes—
76#2665C2212yes—
77#2665C2214yes—
78#2651C2214yes—
79#2651C2214yes—
80#2601C2214yes—
81#2601C2214yes—
82#2596C2214yes—
83#2592C2214yes—
84#2590C2214yes—
85#2589C2214yes—
86#2587C2214yes—
87#2584C2214yes—
88#2584C2212yes—
89#2582C2212yes—
90#2580C2212yes—
91#2577C2214yes—
92#2575C2214yes—
93#2575C2214yes—
94#2574C2214yes—
95#2574C2214yes—
96#2573C2214yes—
97#2566C2212yes—
98#2558C2214yes—
99#2556C2214yes—
100#2552C2212yes—
101#2550C2212yes—
102#2548C2212yes—
103#2548C2212yes—
104#2532C2214yes—
105#2531C2214yes—
106#2529C2214yes—
107#2526C2214yes—
108#2525C2214yes—
109#2525C2214yes—
110#2521C2214yes—
111#2520C2214yes—
112#2519C2214yes—
113#2519C2214yes—
114#2519C2214yes—
115#2519C2214yes—
116#2519C2214yes—
117#2519C2214yes—
118#2516C2214yes—
119#2515C2214yes—
120#2513C2212yes—
121#2512C2212yes—
122#2512C2212yes—
123#2512C2212yes—
124#2512C2214yes—
125#2508C2212yes—
126#2507C2212yes—
127#2506C2212yes—
128#2506C2212yes—
129#2497C2212yes—
130#2496C2212yes—
131#2496C2214yes—
132#2491C2212yes—
133#2491C2214yes—
134#2490C2212yes—
135#2489C2214yes—
136#2479C2214yes—
137#2479C2214yes—
138#2479C2214yes—
139#2478C2214yes—
140#2475C2214yes—
141#2474C2214yes—
142#2469C2214yes—
143#2468C2214yes—
144#2468C2214yes—
145#2468C2214yes—
146#2468C2214yes—
147#2462C2214yes—
148#2462C2214yes—
149#2458C2214yes—
150#2454C2214yes—
151#2454C2212yes—
152#2454C2214yes—
153#2453C2212yes—
154#2452C2212yes—
155#2451C2212yes—
156#2451C2214yes—
157#2448C2212yes—
158#2448C2212yes—
159#2448C2212yes—
160#2448C2212yes—
161#2447C2214yes—
162#2447C2214yes—
163#2426C2212yes—
164#2426C2212yes—
165#2426C2214yes—
166#2423C2212yes—
167#2421C2212yes—
168#2402C2211yescharacteristic
169#2402C2211yescharacteristic
170#2399C2211yescharacteristic
171#2399C2211yescharacteristic
172#2396C2212yes—
173#2396C2212yes—
174#2373C2214yes—
175#2373C2214yes—
176#2370C2212yes—
177#2370C2214yes—
178#2370C2214yes—
179#2370C2212yes—
180#2369C2212yes—
181#2369C2214yes—
182#2367C2212yes—
183#2367C2212yes—
184#2365C2212yes—
185#2362C2214yes—
186#2355C2212yes—
187#2355C2212yes—
188#2355C2212yes—
189#2355C2214yes—
190#2354C2212yes—
191#2351C2212yes—
192#2351C2212yes—
193Q8×C4⋊C4C2212yes—
194Q8×C4⋊C4C2212yes—
195#2346C2214yes—
196#2336C2214yes—
197#2335C2214yes—
198#2334C2214yes—
199#2334C2214yes—
200#2334C2214yes—
201#2333C2214yes—
202#2331C2212yes—
203#2331C2214yes—
204#2330C2212yes—
205#2330C2214yes—
206#2330C2211yescharacteristic
207#2330C2211yescharacteristic
208#2328C2211yescharacteristic
209#2327C2211yescharacteristic
210#2326C2212yes—
211#2326C2212yes—
212#2324C2212yes—
213#2323C2212yes—
214#2320C2212yes—
215#2319C2212yes—
216#2319C2212yes—
217#2319C2212yes—
218#2314C2211yescharacteristic
219#2314C2211yescharacteristic
220C4×C4⋊Q8C2211yescharacteristic
221C4×#127C2211yescharacteristic
222C4×#125C2214yes—
223C4×#125C2214yes—
224C4×#125C2211yescharacteristic
225C4×#125C2211yescharacteristic
226C4×#126C2214yes—
227C4×C22⋊Q8C2212yes—
228C4×C22⋊Q8C2214yes—
229C4×#123C2214yes—
230C4×#121C2212yes—
231C4×#121C2214yes—
232#2296C2214yes—
233#2295C2212yes—
234#2295C2212yes—
235#2295C2214yes—
236#2283C2211yescharacteristic
237#2283C2211yescharacteristic
238#2276C2212yes—
239#2276C2212yes—
240C42×Q8C2212yes—
241C42×D4C2212yes—
242C4×#117C2211yescharacteristic
243#557—216no—
244#556—216no—
245#541—28no—
246#540—28no—
247C2×C4⋊Q8C2314yes—
248C2×C4⋊Q8C2312yes—
249C2×C4⋊Q8C2311yescharacteristic
250C2×#127C2311yescharacteristic
251C2×#126C2314yes—
252C2×#126C2314yes—
253C2×#126C2314yes—
254C2×#126C2314yes—
255C2×#126C2314yes—
256C2×#126C2314yes—
257C2×#126C2314yes—
258C2×#125C2311yescharacteristic
259C2×#125C2314yes—
260C2×#125C2314yes—
261C2×#125C2312yes—
262C2×#125C2314yes—
263C2×#125C2314yes—
264C2×#125C2314yes—
265C2×#125C2314yes—
266C2×#125C2311yescharacteristic
267C2×#124C2312yes—
268C2×#124C2312yes—
269C2×#124C2314yes—
270C2×#124C2314yes—
271C2×#123C2314yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×#121C2312yes—
276C2×#121C2314yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2314yes—
287C2×C4×Q8C2314yes—
288C2×C4×D4C2312yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2314yes—
293C2×#117C2311yescharacteristic
294C2×#117C2311yescharacteristic
295C2×#117C2314yes—
296C2×#117C2314yes—
297C22×C42C2311yescharacteristic
298C22×C42C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2312yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2312yes—
308#400C2312yes—
309#400C2312yes—
310#400C2312yes—
311#400C2312yes—
312#399C2314yes—
313#399C2314yes—
314#399C2314yes—
315#399C2314yes—
316#399C2314yes—
317#399C2312yes—
318#399C2312yes—
319#399C2314yes—
320#399C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2312yes—
332#398C2312yes—
333#398C2314yes—
334#398C2312yes—
335#398C2312yes—
336#398C2312yes—
337#398C2312yes—
338#398C2312yes—
339#398C2312yes—
340#398C2312yes—
341#398C2312yes—
342#398C2312yes—
343#398C2312yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2312yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2312yes—
370#396C2312yes—
371#396C2312yes—
372#396C2314yes—
373#395C2314yes—
374#395C2314yes—
375#395C2312yes—
376#395C2312yes—
377#395C2312yes—
378#395C2312yes—
379#395C2312yes—
380#395C2312yes—
381#395C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#393C2314yes—
391#393C2314yes—
392#393C2314yes—
393#393C2312yes—
394#393C2312yes—
395#391C2312yes—
396#391C2312yes—
397#391C2314yes—
398#391C2312yes—
399#391C2312yes—
400#391C2312yes—
401#391C2314yes—
402#391C2314yes—
403#391C2312yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2312yes—
408#391C2314yes—
409#391C2312yes—
410#391C2314yes—
411#390C2312yes—
412#390C2314yes—
413#390C2312yes—
414#390C2312yes—
415#390C2312yes—
416#390C2312yes—
417#390C2312yes—
418#390C2314yes—
419#390C2312yes—
420#390C2312yes—
421#390C2314yes—
422#390C2314yes—
423#390C2314yes—
424#390C2314yes—
425#390C2314yes—
426#390C2314yes—
427#389C2312yes—
428#389C2312yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2312yes—
436#389C2312yes—
437#389C2312yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2312yes—
448#389C2314yes—
449#389C2312yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2312yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2312yes—
463#389C2314yes—
464#389C2314yes—
465#389C2312yes—
466#389C2314yes—
467#389C2312yes—
468#389C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2312yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2312yes—
543#387C2312yes—
544#387C2312yes—
545#387C2312yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2312yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2312yes—
555#387C2314yes—
556#387C2312yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#384C2311yescharacteristic
576#384C2311yescharacteristic
577#384C2312yes—
578#384C2312yes—
579#384C2312yes—
580#384C2314yes—
581#383C2314yes—
582#383C2311yescharacteristic
583#383C2311yescharacteristic
584#383C2311yescharacteristic
585#383C2311yescharacteristic
586#382C2311yescharacteristic
587#382C2311yescharacteristic
588#382C2314yes—
589#382C2314yes—
590#382C2312yes—
591#382C2312yes—
592#382C2314yes—
593#382C2314yes—
594#382C2314yes—
595#382C2314yes—
596#382C2312yes—
597#381C2314yes—
598#381C2314yes—
599#381C2314yes—
600#381C2311yescharacteristic
601#381C2311yescharacteristic
602#381C2311yescharacteristic
603#381C2311yescharacteristic
604#380C2312yes—
605#380C2312yes—
606#380C2314yes—
607#380C2314yes—
608#380C2314yes—
609#380C2314yes—
610#380C2314yes—
611#380C2312yes—
612#380C2312yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2312yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2312yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2312yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2314yes—
633C4×C4⋊C4C2314yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2311yescharacteristic
655C4×C4⋊C4C2311yescharacteristic
656C4×C4⋊C4C2311yescharacteristic
657C4×C4⋊C4C2311yescharacteristic
658C4×C22⋊C4C2312yes—
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2314yes—
663C4×C22⋊C4C2314yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2314yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2312yes—
668C4×C22⋊C4C2312yes—
669#376C2311yescharacteristic
670#376C2312yes—
671#376C2312yes—
672#376C2311yescharacteristic
673#376C2314yes—
674#376C2314yes—
675C43C2314yes—
676C43C2311yescharacteristic
677C43C2311yescharacteristic
678C22×Q8C2412yes—
679C22×Q8C2412yes—
680C22×Q8C2414yes—
681C22×Q8C2412yes—
682C22×D4C2412yes—
683C22×D4C2414yes—
684C22×D4C2414yes—
685C23×C4C2411yescharacteristic
686C23×C4C2414yes—
687C23×C4C2411yescharacteristic
688C23×C4C2414yes—
689C23×C4C2414yes—
690C23×C4C2411yescharacteristic
691C4⋊Q8—216no—
692C4⋊Q8—28no—
693C4⋊Q8#4118yes—
694#127—24no—
695#126—216no—
696#126—216no—
697#126—216no—
698#126—84no—
699#126—84no—
700#126—84no—
701#126—84no—
702#125—216no—
703#125—216no—
704#125—28no—
705#125—216no—
706#125—24no—
707#125—84no—
708#125—84no—
709#125—84no—
710#125#4118yes—
711#124—28no—
712#124—28no—
713#124—84no—
714#124—84no—
715#123—216no—
716C22⋊Q8—28no—
717C22⋊Q8—216no—
718C22⋊Q8—84no—
719#121—216no—
720#121—28no—
721C4×Q8—28no—
722C4×Q8—28no—
723C4×Q8—28no—
724C4×Q8—28no—
725C4×Q8—216no—
726C4×Q8—28no—
727C4×Q8—28no—
728C4×Q8—28no—
729C4×Q8—28no—
730C4×Q8—28no—
731C4×Q8—84no—
732C4×D4—28no—
733C4×D4—28no—
734C4×D4—28no—
735C4×D4—84no—
736C4×D4—84no—
737#117—216no—
738#117—24no—
739#117—24no—
740#117—84no—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2412yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2412yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C42—24no—
839C2×C42—84no—
840C2×C42C2411yescharacteristic
841C2×C42C2411yescharacteristic
842C2×C42C2414yes—
843C2×C42C2414yes—
844C2×C42C2412yes—
845C2×C42C2412yes—
846C2×C42C2414yes—
847C2×C42C2412yes—
848C2×C42C2414yes—
849C2×C42C2412yes—
850C2×C42C2414yes—
851C2×C42C2414yes—
852C2×C42C2414yes—
853C2×C42C2411yescharacteristic
854C2×C42C2411yescharacteristic
855C2×C42C2411yescharacteristic
856C2×C42C2414yes—
857C2×C42C2414yes—
858C2×C42C2412yes—
859C2×C42C2414yes—
860C2×C42C2414yes—
861C2×C42C2414yes—
862C2×C42C2414yes—
863C2×C42C2414yes—
864C2×C42C2414yes—
865C2×C42C2414yes—
866C2×C42C2412yes—
867C2×C42C2412yes—
868C2×C42C2412yes—
869C2×C42C2414yes—
870C2×C42C2411yescharacteristic
871C2×C42C2411yescharacteristic
872C2×C42C2411yescharacteristic
873#95C2412yes—
874#95C2412yes—
875#95C2414yes—
876#95C2412yes—
877#95C2412yes—
878#95C2412yes—
879#95C2412yes—
880#95C2412yes—
881#95C2412yes—
882#95C2412yes—
883#95C2414yes—
884#95C2414yes—
885#95C2412yes—
886#95C2412yes—
887#95C2412yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2412yes—
893#95C2412yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2412yes—
899#95C2412yes—
900#95C2412yes—
901#95C2412yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2412yes—
908#95C2414yes—
909#95C2414yes—
910#95C2412yes—
911#95C2412yes—
912#95C2412yes—
913#95C2412yes—
914#95C2414yes—
915#95C2414yes—
916#95C2411yescharacteristic
917#95C2411yescharacteristic
918#95C2411yescharacteristic
919#95C2411yescharacteristic
920#95C2411yescharacteristic
921#95C2411yescharacteristic
922#95C2411yescharacteristic
923#95C2411yescharacteristic
924#95C2412yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2412yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2412yes—
936#95C2412yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2412yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945C24C2511yescharacteristic
946C24C2514yes—
947C2×Q8—24no—
948C2×Q8—24no—
949C2×Q8—24no—
950C2×Q8—28no—
951C2×Q8—24no—
952C2×Q8—42no—
953C2×Q8—42no—
954C2×Q8—44no—
955C2×Q8—42no—
956C2×Q8—42no—
957C2×Q8—44no—
958C2×Q8C2×#4118yes—
959C2×D4—24no—
960C2×D4—24no—
961C2×D4—28no—
962C2×D4—28no—
963C2×D4—24no—
964C2×D4—44no—
965C2×D4—44no—
966C2×D4—44no—
967C2×D4—44no—
968C22×C4—28no—
969C22×C4—22no—
970C22×C4—22no—
971C22×C4—22no—
972C22×C4—28no—
973C22×C4—22no—
974C22×C4—22no—
975C22×C4—28no—
976C22×C4—44no—
977C22×C4—44no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4—42no—
981C22×C4—44no—
982C22×C4—42no—
983C22×C4—44no—
984C22×C4C2511yescharacteristic
985C22×C4C2512yes—
986C22×C4C2511yescharacteristic
987C22×C4C2512yes—
988C22×C4C2514yes—
989C22×C4C2512yes—
990C22×C4C2512yes—
991C22×C4C2512yes—
992C22×C4C2514yes—
993C22×C4C2511yescharacteristic
994C22×C4C2514yes—
995C22×C4C2512yes—
996C22×C4C2514yes—
997C22×C4C2512yes—
998C22×C4C2512yes—
999C22×C4C2512yes—
1000C22×C4C2514yes—
1001C22×C4C2512yes—
1002C22×C4C2514yes—
1003C22×C4C2512yes—
1004C22×C4C2514yes—
1005C22×C4C2512yes—
1006C22×C4C2511yescharacteristic
1007C22×C4C2511yescharacteristic
1008C22×C4C2511yescharacteristic
1009C4⋊C4—24no—
1010C4⋊C4—24no—
1011C4⋊C4—24no—
1012C4⋊C4—24no—
1013C4⋊C4—24no—
1014C4⋊C4—24no—
1015C4⋊C4—28no—
1016C4⋊C4—28no—
1017C4⋊C4—28no—
1018C4⋊C4—24no—
1019C4⋊C4—28no—
1020C4⋊C4—24no—
1021C4⋊C4—28no—
1022C4⋊C4—28no—
1023C4⋊C4—28no—
1024C4⋊C4—24no—
1025C4⋊C4—24no—
1026C4⋊C4—24no—
1027C4⋊C4—28no—
1028C4⋊C4—28no—
1029C4⋊C4—28no—
1030C4⋊C4—28no—
1031C4⋊C4—24no—
1032C4⋊C4—28no—
1033C4⋊C4—24no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—42no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—42no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—44no—
1070C4⋊C4C2×#41116yes—
1071C4⋊C4C2×#4118yes—
1072C4⋊C4C2×#41116yes—
1073C22⋊C4—24no—
1074C22⋊C4—28no—
1075C22⋊C4—28no—
1076C22⋊C4—24no—
1077C22⋊C4—28no—
1078C22⋊C4—28no—
1079C22⋊C4—28no—
1080C22⋊C4—28no—
1081C22⋊C4—28no—
1082C22⋊C4—28no—
1083C22⋊C4—28no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—42no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—42no—
1106C42—22no—
1107C42—22no—
1108C42—28no—
1109C42—28no—
1110C42—24no—
1111C42—24no—
1112C42—28no—
1113C42—28no—
1114C42—24no—
1115C42—28no—
1116C42—24no—
1117C42—28no—
1118C42—22no—
1119C42—22no—
1120C42—22no—
1121C42—28no—
1122C42—42no—
1123C42—44no—
1124C42—44no—
1125C42—44no—
1126C42—42no—
1127C42—42no—
1128C42—44no—
1129C42—44no—
1130C42—44no—
1131C42—42no—
1132C42—44no—
1133C42—44no—
1134C42—44no—
1135C42—44no—
1136C42C2×#4114yes—
1137C42C2×#4114yes—
1138C422−1+414yes—
1139C23—21no—
1140C23—24no—
1141C23—24no—
1142C23—21no—
1143C23—24no—
1144C23—21no—
1145C23—22no—
1146C23—24no—
1147C23—24no—
1148C23—24no—
1149C23—24no—
1150C23—22no—
1151C23C2611yescharacteristic
1152Q8—216no—
1153Q8—48no—
1154Q8—88no—
1155Q8—84no—
1156D4—48no—
1157D4—88no—
1158D4—88no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—24no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—24no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—24no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—24no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—22no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—24no—
1198C2×C4—22no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—24no—
1206C2×C4—22no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—24no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—416no—
1222C2×C4—44no—
1223C2×C4—88no—
1224C2×C4—82no—
1225C2×C4—88no—
1226C2×C4—82no—
1227C2×C4C22×#4118yes—
1228C2×C4C22×#4114yes—
1229C2×C4C22×#4118yes—
1230C2×C4C22×#4114yes—
1231C2×C4C22×#4112yes—
1232C2×C4C22×#4112yes—
1233C2×C4C2×2−1+412yes—
1234C2×C4C2×2−1+412yes—
1235C2×C4C2×2−1+412yes—
1236C22—44no—
1237C22—42no—
1238C22—44no—
1239C22—44no—
1240C22—44no—
1241C22—42no—
1242C22—44no—
1243C22—41no—
1244C22—41no—
1245C22—44no—
1246C22—41no—
1247C22—44no—
1248C22C23×#4111yescharacteristic
1249C22C23×#4111yescharacteristic
1250C22C22×2−1+411yescharacteristic
1251C22H(7,𝔽2)12yes—
1252C222−1+612yes—
1253C4—24no—
1254C4—28no—
1255C4—24no—
1256C4—22no—
1257C4—22no—
1258C4—28no—
1259C4—42no—
1260C4—42no—
1261C4—42no—
1262C4—44no—
1263C4—44no—
1264C4—42no—
1265C4—42no—
1266C4—42no—
1267C4—42no—
1268C4—42no—
1269C4—42no—
1270C4—44no—
1271C4—42no—
1272C4—44no—
1273C4—41no—
1274C4—44no—
1275C4—41no—
1276C4—41no—
1277C4#348214yes—
1278C2—84no—
1279C2—81no—
1280C2C2×#348211yescharacteristic
1281C2#6285112yes—
1282C2#6285712yes—
1283C2#6288111yescharacteristic
1284C2#6288911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#540C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45407C2semidirect
2. #45403C2semidirect
3. #45346C2semidirect
5. #45277C2semidirect
6. #45266C2semidirect
7. #45242C2semidirect
8. #44982C2semidirect
9. #44965C2semidirect
10. #44911C2semidirect
11. #40474C2semidirect
12. #40467C2semidirect
13. #40093C2semidirect
14. #40089C2semidirect
15. #38803C2semidirect
16. #38797C2semidirect
17. #38622C2semidirect
18. #38615C2semidirect
19. #35587C2semidirect
20. #35586C2semidirect
21. #35186C2semidirect
22. #35175C2semidirect
23. #34644C2semidirect
24. #34336C2semidirect
25. #34324C2semidirect
26. C4×#541C2semidirect

Maximal subgroups

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

subgroupindex
#454072
#454032
#453462
#452962
#452772
#452662
#452422
#449822
#449652
#449112
#404742
#404672
#400932
#400892
#388032
#387972
#386222
#386152
#355872
#355862
#351862
#351752
#346442
#343362
#343242
C4×#5412
C4×#5402