Finite Group Databasebeta

← #7712489

Subgroups — #7712489

Order 512.

6520 conjugacy classes of subgroups.

The subgroup lattice has 1162 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3557C212yesmaximal, complemented
2#59838C218yesmaximal, complemented
3#46312C214yesmaximal, complemented
4#46281C214yesmaximal, complemented
5#39741C212yesmaximal, complemented
6#39740C211yesmaximal, characteristic, complemented
7#39739C211yesmaximal, characteristic, complemented
8#39613C212yesmaximal, complemented
9#39612C211yesmaximal, characteristic, complemented
10#39611C211yesmaximal, characteristic, complemented
11#39455C214yesmaximal, complemented
12#39453C214yesmaximal, complemented
13#39393C218yesmaximal, complemented
14#37542C212yesmaximal, complemented
15#37389C212yesmaximal, complemented
16#37301C212yesmaximal, complemented
17#36631C211yesmaximal, characteristic, complemented
18#36631C211yesmaximal, characteristic, complemented
19#36538C212yesmaximal, complemented
20#36534C212yesmaximal, complemented
21#36508C212yesmaximal, complemented
22#36496C212yesmaximal, complemented
23#35318C212yesmaximal, complemented
24#35276C212yesmaximal, complemented
25C4×#533C211yesmaximal, characteristic, complemented
26#3557—232no—
27C2×#563C2214yes—
28C2×#563C2214yes—
29C2×#559C2212yes—
30C2×#559C2212yes—
31C2×#557C2212yes—
32C2×#557C2212yes—
33C2×#556C2212yes—
34C2×#556C2212yes—
35C2×#554C2212yes—
36C2×#554C2212yes—
37C2×#552C2214yes—
38C2×#552C2214yes—
39C2×#542C2212yes—
40C2×#542C2214yes—
41C2×#542C2212yes—
42C2×#542C2214yes—
43C2×#541C2212yes—
44C2×#540C2212yes—
45C2×#539C2214yes—
46C2×#539C2214yes—
47C2×#533C2211yescharacteristic
48C2×#529C2212yes—
49C2×#529C2212yes—
50#2862C2212yes—
51#2861C2212yes—
52#2861C2212yes—
53#2861C2212yes—
54#2861C2212yes—
55#2860C2214yes—
56#2860C2214yes—
57#2859C2211yescharacteristic
58#2859C2211yescharacteristic
59#2858C2211yescharacteristic
60#2858C2211yescharacteristic
61#2858C2212yes—
62#2857C2211yescharacteristic
63#2857C2211yescharacteristic
64#2856C2211yescharacteristic
65#2856C2211yescharacteristic
66#2854C2214yes—
67#2854C2214yes—
68#2850C2212yes—
69#2850C2212yes—
70#2823C2218yes—
71#2734C2214yes—
72#2733C2214yes—
73#2732C2214yes—
74#2732C2214yes—
75#2730C2218yes—
76#2729C2218yes—
77#2727C2214yes—
78#2726C2214yes—
79#2725C2218yes—
80#2715C2218yes—
81#2705C2218yes—
82#2705C2218yes—
83#2704C2218yes—
84#2704C2218yes—
85#2695C2218yes—
86#2683C2214yes—
87#2682C2214yes—
88#2681C2218yes—
89#2676C2218yes—
90#2671C2218yes—
91#2660C2212yes—
92#2660C2212yes—
93#2658C2212yes—
94#2657C2212yes—
95#2630C2218yes—
96#2630C2218yes—
97#2621C2212yes—
98#2620C2212yes—
99#2620C2212yes—
100#2619C2212yes—
101#2609C2218yes—
102#2568C2212yes—
103#2567C2212yes—
104#2566C2212yes—
105#2566C2212yes—
106#2566C2212yes—
107#2566C2212yes—
108#2565C2212yes—
109#2565C2212yes—
110#2565C2212yes—
111#2565C2212yes—
112#2563C2212yes—
113#2560C2218yes—
114#2560C2218yes—
115#2558C2218yes—
116#2558C2218yes—
117#2556C2218yes—
118#2555C2218yes—
119#2554C2218yes—
120#2553C2218yes—
121#2548C2212yes—
122#2547C2212yes—
123#2546C2212yes—
124#2545C2212yes—
125#2545C2212yes—
126#2545C2218yes—
127#2545C2212yes—
128#2545C2212yes—
129#2544C2212yes—
130#2544C2212yes—
131#2544C2212yes—
132#2544C2212yes—
133#2542C2212yes—
134#2541C2212yes—
135#2536C2218yes—
136#2521C2218yes—
137#2519C2218yes—
138#2519C2218yes—
139#2519C2218yes—
140#2479C2218yes—
141#2473C2218yes—
142#2471C2218yes—
143#2467C2218yes—
144#2465C2218yes—
145#2464C2218yes—
146#2462C2218yes—
147#2461C2218yes—
148#2461C2218yes—
149#2461C2218yes—
150#2456C2218yes—
151#2449C2218yes—
152#2429C2218yes—
153#2426C2218yes—
154#2367C2218yes—
155#2362C2218yes—
156#2361C2218yes—
157#2352C2218yes—
158#2328C2212yes—
159#2327C2212yes—
160#2326C2212yes—
161#2326C2212yes—
162C4×C4⋊Q8C2211yescharacteristic
163C4×C4⋊Q8C2211yescharacteristic
164C4×C4⋊Q8C2212yes—
165C4×C4⋊Q8C2212yes—
166C4×C4⋊Q8C2212yes—
167C4×#127C2211yescharacteristic
168C4×#127C2211yescharacteristic
169C4×#127C2212yes—
170C4×#125C2214yes—
171C4×#124C2212yes—
172C4×#124C2212yes—
173C4×#124C2212yes—
174C4×#124C2212yes—
175C4×C22⋊Q8C2212yes—
176C4×C22⋊Q8C2212yes—
177C4×C22⋊Q8C2214yes—
178C4×#121C2214yes—
179C4×#121C2214yes—
180#2296C2212yes—
181#2295C2211yescharacteristic
182#2295C2211yescharacteristic
183#2295C2212yes—
184#2293C2214yes—
185#2293C2214yes—
186#2285C2211yescharacteristic
187C42×Q8C2212yes—
188C42×Q8C2211yescharacteristic
189C42×Q8C2211yescharacteristic
190C4×#117C2212yes—
191C2×C43C2211yescharacteristic
192#563—232no—
193#563—232no—
194#559—216no—
195#559—216no—
196#557—216no—
197#557—216no—
198#556—216no—
199#556—216no—
200#554—216no—
201#554—216no—
202#552—232no—
203#552—232no—
204#542—232no—
205#542—232no—
206#542—216no—
207#542—216no—
208#541—216no—
209#540—216no—
210#539—232no—
211#539—232no—
212#533D4116yescomplemented
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C2312yes—
217C2×C4⋊Q8C2314yes—
218C2×C4⋊Q8C2314yes—
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2312yes—
221C2×C4⋊Q8C2311yescharacteristic
222C2×C4⋊Q8C2311yescharacteristic
223C2×#127C2311yescharacteristic
224C2×#127C2312yes—
225C2×#127C2311yescharacteristic
226C2×#127C2312yes—
227#529—216no—
228#529—216no—
229C2×#126C2314yes—
230C2×#126C2314yes—
231C2×#126C2314yes—
232C2×#126C2314yes—
233C2×#126C2314yes—
234C2×#126C2314yes—
235C2×#126C2314yes—
236C2×#126C2314yes—
237C2×#126C2314yes—
238C2×#126C2314yes—
239C2×#125C2312yes—
240C2×#125C2312yes—
241C2×#125C2312yes—
242C2×#125C2312yes—
243C2×#125C2314yes—
244C2×#125C2314yes—
245C2×#125C2314yes—
246C2×#125C2314yes—
247C2×#125C2314yes—
248C2×#125C2314yes—
249C2×#125C2312yes—
250C2×#124C2312yes—
251C2×#124C2312yes—
252C2×#124C2312yes—
253C2×#124C2312yes—
254C2×#124C2312yes—
255C2×#124C2314yes—
256C2×#124C2314yes—
257C2×#124C2314yes—
258C2×#124C2314yes—
259C2×#124C2312yes—
260C2×#124C2318yes—
261C2×#124C2312yes—
262C2×#124C2312yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×#123C2314yes—
267C2×#123C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2318yes—
286C2×C22⋊Q8C2311yescharacteristic
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2311yescharacteristic
289C2×#121C2312yes—
290C2×#121C2312yes—
291C2×#121C2314yes—
292C2×#121C2314yes—
293C2×#121C2314yes—
294C2×#121C2314yes—
295C2×#121C2318yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2314yes—
303C2×C4×Q8C2314yes—
304C2×C4×Q8C2314yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2311yescharacteristic
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2312yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2314yes—
318C2×C4×D4C2314yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2318yes—
321C2×C4×D4C2314yes—
322C2×C4×D4C2314yes—
323C2×#117C2314yes—
324C2×#117C2314yes—
325C2×#117C2314yes—
326C2×#117C2314yes—
327C2×#117C2312yes—
328C2×#117C2312yes—
329C22×C4⋊C4C2314yes—
330C22×C4⋊C4C2314yes—
331C22×C42C2311yescharacteristic
332C22×C42C2311yescharacteristic
333C22×C42C2312yes—
334C22×C42C2312yes—
335C22×C42C2311yescharacteristic
336#400C2318yes—
337#399C2318yes—
338#399C2318yes—
339#399C2318yes—
340#398C2318yes—
341#398C2318yes—
342#398C2318yes—
343#398C2318yes—
344#398C2318yes—
345#398C2318yes—
346#398C2318yes—
347#398C2318yes—
348#397C2318yes—
349#397C2318yes—
350#396C2318yes—
351#396C2318yes—
352#396C2318yes—
353#396C2318yes—
354#396C2318yes—
355#396C2318yes—
356#396C2318yes—
357#396C2318yes—
358#396C2318yes—
359#396C2318yes—
360#395C2318yes—
361#395C2318yes—
362#395C2318yes—
363#394C2318yes—
364#394C2318yes—
365#394C2318yes—
366#394C2318yes—
367#394C2318yes—
368#394C2318yes—
369#394C2318yes—
370#394C2318yes—
371#393C2318yes—
372#392C2318yes—
373#392C2318yes—
374#392C2318yes—
375#392C2318yes—
376#391C2318yes—
377#391C2312yes—
378#391C2312yes—
379#391C2312yes—
380#391C2314yes—
381#391C2312yes—
382#391C2312yes—
383#391C2312yes—
384#391C2312yes—
385#391C2312yes—
386#391C2312yes—
387#391C2312yes—
388#391C2318yes—
389#390C2318yes—
390#390C2312yes—
391#390C2312yes—
392#390C2314yes—
393#390C2314yes—
394#390C2312yes—
395#390C2312yes—
396#390C2312yes—
397#390C2312yes—
398#390C2312yes—
399#390C2312yes—
400#390C2314yes—
401#390C2314yes—
402#390C2314yes—
403#390C2314yes—
404#390C2314yes—
405#390C2314yes—
406#390C2318yes—
407#390C2318yes—
408#389C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2312yes—
413#389C2312yes—
414#389C2318yes—
415#389C2314yes—
416#389C2318yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2318yes—
424#388C2318yes—
425#388C2318yes—
426#388C2318yes—
427#388C2318yes—
428#388C2318yes—
429#388C2318yes—
430#388C2318yes—
431#388C2318yes—
432#388C2318yes—
433#388C2318yes—
434#388C2318yes—
435#388C2318yes—
436#388C2318yes—
437#388C2318yes—
438#388C2318yes—
439#388C2318yes—
440#388C2318yes—
441#388C2318yes—
442#388C2318yes—
443#388C2318yes—
444#387C2318yes—
445#387C2318yes—
446#387C2314yes—
447#387C2314yes—
448#387C2314yes—
449#387C2314yes—
450#387C2318yes—
451#387C2318yes—
452#387C2318yes—
453#387C2318yes—
454#386C2318yes—
455#386C2318yes—
456#386C2318yes—
457#386C2318yes—
458#386C2318yes—
459#386C2318yes—
460#386C2318yes—
461#386C2318yes—
462#385C2318yes—
463#385C2318yes—
464#385C2318yes—
465#385C2318yes—
466#385C2318yes—
467#385C2318yes—
468#385C2314yes—
469#385C2314yes—
470#384C2312yes—
471#384C2311yescharacteristic
472#384C2311yescharacteristic
473#384C2312yes—
474#384C2311yescharacteristic
475#384C2312yes—
476#384C2311yescharacteristic
477#382C2312yes—
478#382C2312yes—
479#382C2312yes—
480#382C2312yes—
481#382C2312yes—
482#382C2318yes—
483#380C2318yes—
484#380C2314yes—
485#380C2314yes—
486#380C2318yes—
487#380C2312yes—
488#380C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2318yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2312yes—
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2318yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2318yes—
513C4×C22⋊C4C2314yes—
514#376C2312yes—
515#376C2312yes—
516C43C2312yes—
517C43C2311yescharacteristic
518C43C2311yescharacteristic
519C43C2312yes—
520C43C2312yes—
521C43C2312yes—
522C43C2311yescharacteristic
523C43C2311yescharacteristic
524C22×Q8C2412yes—
525C22×Q8C2412yes—
526C22×Q8C2414yes—
527C22×Q8C2414yes—
528C22×Q8C2411yescharacteristic
529C22×Q8C2412yes—
530C22×Q8C2411yescharacteristic
531C22×D4C2412yes—
532C22×D4C2412yes—
533C22×D4C2414yes—
534C22×D4C2414yes—
535C22×D4C2414yes—
536C22×D4C2414yes—
537C22×D4C2414yes—
538C22×D4C2414yes—
539C22×D4C2418yes—
540C23×C4C2412yes—
541C23×C4C2411yescharacteristic
542C23×C4C2414yes—
543C23×C4C2414yes—
544C23×C4C2414yes—
545C23×C4C2414yes—
546C23×C4C2414yes—
547C23×C4C2414yes—
548C23×C4C2412yes—
549C23×C4C2411yescharacteristic
550C23×C4C2411yescharacteristic
551C4⋊Q8—216no—
552C4⋊Q8—216no—
553C4⋊Q8—28no—
554C4⋊Q8—28no—
555C4⋊Q8—28no—
556C4⋊Q8—24no—
557C4⋊Q8—42no—
558C4⋊Q8—44no—
559C4⋊Q8C2×D418yes—
560C4⋊Q8C2×D418yes—
561#127—28no—
562#127—24no—
563#127—42no—
564#127—44no—
565#126—216no—
566#126—216no—
567#126—216no—
568#126—216no—
569#126—216no—
570#126—216no—
571#126—216no—
572#126—216no—
573#126—216no—
574#126—216no—
575#125—216no—
576#125—216no—
577#125—216no—
578#125—216no—
579#125—216no—
580#125—216no—
581#125—28no—
582#125—28no—
583#125—28no—
584#125—28no—
585#125C2×D4116yes—
586#124—216no—
587#124—216no—
588#124—216no—
589#124—216no—
590#124—28no—
591#124—28no—
592#124—28no—
593#124—28no—
594#124—28no—
595#124—416no—
596#124—44no—
597#124—44no—
598#124—44no—
599#123—216no—
600#123—216no—
601#123—216no—
602#123—216no—
603#123—216no—
604#123—216no—
605#123—216no—
606#123—216no—
607#123—216no—
608#123—216no—
609C22⋊Q8—216no—
610C22⋊Q8—216no—
611C22⋊Q8—216no—
612C22⋊Q8—216no—
613C22⋊Q8—28no—
614C22⋊Q8—28no—
615C22⋊Q8—216no—
616C22⋊Q8—216no—
617C22⋊Q8—216no—
618C22⋊Q8—216no—
619C22⋊Q8—216no—
620C22⋊Q8—216no—
621C22⋊Q8—416no—
622C22⋊Q8C2×D418yes—
623C22⋊Q8C2×D4116yes—
624C22⋊Q8C2×D418yes—
625#121—28no—
626#121—28no—
627#121—216no—
628#121—216no—
629#121—48no—
630#121—416no—
631#121—48no—
632C4×Q8—216no—
633C4×Q8—216no—
634C4×Q8—28no—
635C4×Q8—28no—
636C4×Q8—28no—
637C4×Q8—28no—
638C4×Q8—28no—
639C4×Q8—28no—
640C4×Q8—44no—
641C4×Q8—44no—
642C4×Q8—48no—
643C4×Q8C2×D418yes—
644C4×Q8C2×D4116yes—
645C4×Q8C2×D418yes—
646C4×D4—216no—
647C4×D4—216no—
648C4×D4—216no—
649C4×D4—216no—
650C4×D4—28no—
651C4×D4—28no—
652C4×D4—28no—
653C4×D4—28no—
654C4×D4—28no—
655C4×D4—28no—
656C4×D4—48no—
657C4×D4—48no—
658C4×D4—416no—
659#117—216no—
660#117—216no—
661#117—216no—
662#117—216no—
663#117—44no—
664#117C2×D4116yes—
665C2×C4⋊C4—216no—
666C2×C4⋊C4—216no—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2412yes—
680C2×C4⋊C4C2412yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2418yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2418yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2418yes—
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2411yescharacteristic
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2418yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2418yes—
727C2×C22⋊C4C2418yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2414yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2418yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2418yes—
741C2×C22⋊C4C2418yes—
742C2×C22⋊C4C2418yes—
743C2×C22⋊C4C2418yes—
744C2×C22⋊C4C2418yes—
745C2×C22⋊C4C2418yes—
746C2×C22⋊C4C2418yes—
747C2×C22⋊C4C2418yes—
748C2×C22⋊C4C2412yes—
749C2×C22⋊C4C2412yes—
750C2×C42—24no—
751C2×C42—44no—
752C2×C42—44no—
753C2×C42—42no—
754C2×C42C2×D418yes—
755C2×C42C2414yes—
756C2×C42C2414yes—
757C2×C42C2414yes—
758C2×C42C2414yes—
759C2×C42C2412yes—
760C2×C42C2412yes—
761C2×C42C2414yes—
762C2×C42C2412yes—
763C2×C42C2412yes—
764C2×C42C2414yes—
765C2×C42C2414yes—
766C2×C42C2412yes—
767C2×C42C2412yes—
768C2×C42C2414yes—
769C2×C42C2411yescharacteristic
770C2×C42C2411yescharacteristic
771C2×C42C2411yescharacteristic
772C2×C42C2412yes—
773C2×C42C2414yes—
774C2×C42C2414yes—
775C2×C42C2412yes—
776C2×C42C2412yes—
777C2×C42C2412yes—
778C2×C42C2412yes—
779C2×C42C2412yes—
780C2×C42C2411yescharacteristic
781C2×C42C2412yes—
782C2×C42C2412yes—
783C2×C42C2411yescharacteristic
784C2×C42C2411yescharacteristic
785C2×C42C2411yescharacteristic
786C2×C42C2411yescharacteristic
787#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
791#95C2418yes—
792#95C2418yes—
793#95C2418yes—
794#95C2418yes—
795#95C2418yes—
796#95C2418yes—
797#95C2418yes—
798#95C2412yes—
799#95C2414yes—
800#95C2412yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2418yes—
806#95C2418yes—
807#95C2418yes—
808#95C2418yes—
809#95C2418yes—
810C24C2514yes—
811C24C2514yes—
812C24C2511yescharacteristic
813C2×Q8—24no—
814C2×Q8—24no—
815C2×Q8—28no—
816C2×Q8—28no—
817C2×Q8—24no—
818C2×Q8—24no—
819C2×Q8—24no—
820C2×Q8—24no—
821C2×Q8—42no—
822C2×Q8—42no—
823C2×Q8—44no—
824C2×Q8—48no—
825C2×Q8—48no—
826C2×Q8C22×D414yes—
827C2×Q8C22×D418yes—
828C2×Q8C22×D414yes—
829C2×D4—28no—
830C2×D4—28no—
831C2×D4—24no—
832C2×D4—24no—
833C2×D4—28no—
834C2×D4—28no—
835C2×D4—24no—
836C2×D4—24no—
837C2×D4—28no—
838C2×D4—24no—
839C2×D4—24no—
840C2×D4—28no—
841C2×D4—44no—
842C2×D4—44no—
843C2×D4—48no—
844C2×D4—44no—
845C2×D4—48no—
846C2×D4—48no—
847C2×D4—48no—
848C2×D4—48no—
849C2×D4—48no—
850C2×D4—44no—
851C2×D4—48no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—24no—
857C22×C4—28no—
858C22×C4—28no—
859C22×C4—28no—
860C22×C4—28no—
861C22×C4—28no—
862C22×C4—28no—
863C22×C4—42no—
864C22×C4—42no—
865C22×C4—42no—
866C22×C4—42no—
867C22×C4—42no—
868C22×C4—48no—
869C22×C4—48no—
870C22×C4—48no—
871C22×C4—48no—
872C22×C4—48no—
873C22×C4—48no—
874C22×C4C22×D414yes—
875C22×C4C22×D414yes—
876C22×C4C22×D414yes—
877C22×C4C2514yes—
878C22×C4C2512yes—
879C22×C4C2514yes—
880C22×C4C2514yes—
881C22×C4C2514yes—
882C22×C4C2514yes—
883C22×C4C2514yes—
884C22×C4C2514yes—
885C22×C4C2514yes—
886C22×C4C2511yescharacteristic
887C22×C4C2511yescharacteristic
888C22×C4C2512yes—
889C22×C4C2512yes—
890C22×C4C2512yes—
891C22×C4C2512yes—
892C22×C4C2511yescharacteristic
893C22×C4C2511yescharacteristic
894C22×C4C2511yescharacteristic
895C22×C4C2512yes—
896C22×C4C2512yes—
897C22×C4C2512yes—
898C22×C4C2511yescharacteristic
899C4⋊C4—28no—
900C4⋊C4—28no—
901C4⋊C4—28no—
902C4⋊C4—28no—
903C4⋊C4—28no—
904C4⋊C4—28no—
905C4⋊C4—28no—
906C4⋊C4—28no—
907C4⋊C4—28no—
908C4⋊C4—28no—
909C4⋊C4—24no—
910C4⋊C4—24no—
911C4⋊C4—24no—
912C4⋊C4—24no—
913C4⋊C4—28no—
914C4⋊C4—28no—
915C4⋊C4—28no—
916C4⋊C4—28no—
917C4⋊C4—28no—
918C4⋊C4—28no—
919C4⋊C4—28no—
920C4⋊C4—28no—
921C4⋊C4—28no—
922C4⋊C4—28no—
923C4⋊C4—28no—
924C4⋊C4—28no—
925C4⋊C4—28no—
926C4⋊C4—28no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—44no—
930C4⋊C4—48no—
931C4⋊C4—42no—
932C4⋊C4—42no—
933C4⋊C4—44no—
934C4⋊C4—44no—
935C4⋊C4—44no—
936C4⋊C4—44no—
937C4⋊C4—48no—
938C4⋊C4—44no—
939C4⋊C4—48no—
940C4⋊C4C22×D418yes—
941C4⋊C4C22×D418yes—
942C4⋊C4C22×D418yes—
943C4⋊C4C22×D418yes—
944C4⋊C4C22×D418yes—
945C4⋊C4C22×D418yes—
946C4⋊C4C22×D414yes—
947C4⋊C4C22×D418yes—
948C4⋊C4C22×D414yes—
949C22⋊C4—28no—
950C22⋊C4—28no—
951C22⋊C4—28no—
952C22⋊C4—28no—
953C22⋊C4—28no—
954C22⋊C4—28no—
955C22⋊C4—28no—
956C22⋊C4—28no—
957C22⋊C4—28no—
958C22⋊C4—28no—
959C22⋊C4—28no—
960C22⋊C4—28no—
961C22⋊C4—28no—
962C22⋊C4—28no—
963C22⋊C4—28no—
964C22⋊C4—28no—
965C22⋊C4—28no—
966C22⋊C4—28no—
967C22⋊C4—216no—
968C22⋊C4—216no—
969C22⋊C4—216no—
970C22⋊C4—216no—
971C22⋊C4—44no—
972C22⋊C4—48no—
973C22⋊C4—48no—
974C22⋊C4—48no—
975C22⋊C4—48no—
976C22⋊C4—48no—
977C22⋊C4—48no—
978C22⋊C4—48no—
979C22⋊C4—48no—
980C22⋊C4C22×D418yes—
981C22⋊C4C22×D418yes—
982C42—28no—
983C42—28no—
984C42—28no—
985C42—28no—
986C42—28no—
987C42—28no—
988C42—24no—
989C42—22no—
990C42—24no—
991C42—24no—
992C42—24no—
993C42—24no—
994C42—22no—
995C42—22no—
996C42—24no—
997C42—24no—
998C42—28no—
999C42—28no—
1000C42—42no—
1001C42—42no—
1002C42—42no—
1003C42—42no—
1004C42—42no—
1005C42—44no—
1006C42—44no—
1007C42C22×D414yes—
1008C42C22×D414yes—
1009C42C22×D414yes—
1010C42C22×D414yes—
1011C42C22×D418yes—
1012C42C22×D418yes—
1013C422−1+414yes—
1014C23—21no—
1015C23—21no—
1016C23—22no—
1017C23—22no—
1018C23—24no—
1019C23—24no—
1020C23—24no—
1021C23—24no—
1022C23—28no—
1023C23—28no—
1024C23—28no—
1025C23—24no—
1026C23—28no—
1027C23—24no—
1028C23C23×D412yes—
1029C23C2611yescharacteristic
1030Q8—44no—
1031Q8—48no—
1032Q8—44no—
1033Q8—48no—
1034Q8—48no—
1035Q8—88no—
1036Q8—88no—
1037D4—48no—
1038D4—48no—
1039D4—88no—
1040D4—88no—
1041D4—88no—
1042D4—88no—
1043D4—88no—
1044D4—88no—
1045D4—816no—
1046C2×C4—21no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—21no—
1059C2×C4—22no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—28no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—22no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—28no—
1081C2×C4—28no—
1082C2×C4—28no—
1083C2×C4—24no—
1084C2×C4—28no—
1085C2×C4—24no—
1086C2×C4—44no—
1087C2×C4—44no—
1088C2×C4—48no—
1089C2×C4—48no—
1090C2×C4—88no—
1091C2×C4—88no—
1092C2×C4—88no—
1093C2×C4—88no—
1094C2×C4—88no—
1095C2×C4—88no—
1096C2×C4C23×D412yes—
1097C2×C4C23×D412yes—
1098C2×C4C23×D414yes—
1099C2×C4C23×D414yes—
1100C2×C4C23×D414yes—
1101C2×C4C23×D412yes—
1102C2×C4C23×D412yes—
1103C2×C4C23×D412yes—
1104C2×C4C23×D414yes—
1105C2×C4C23×D412yes—
1106C2×C4C2×2−1+414yes—
1107C2×C4C2×2−1+412yes—
1108C2×C4#58514yes—
1109C2×C4#58514yes—
1110C2×C4#58512yes—
1111C22—22no—
1112C22—22no—
1113C22—22no—
1114C22—42no—
1115C22—42no—
1116C22—48no—
1117C22—48no—
1118C22—44no—
1119C22—44no—
1120C22—44no—
1121C22—44no—
1122C22—44no—
1123C22—44no—
1124C22—48no—
1125C22—48no—
1126C22C24×D411yescharacteristic
1127C22C22×2−1+411yescharacteristic
1128C22C2×#58511yescharacteristic
1129C22C2×#58512yes—
1130C22C2×#58512yes—
1131C4—24no—
1132C4—22no—
1133C4—22no—
1134C4—22no—
1135C4—22no—
1136C4—22no—
1137C4—24no—
1138C4—24no—
1139C4—24no—
1140C4—24no—
1141C4—24no—
1142C4—24no—
1143C4—44no—
1144C4—42no—
1145C4—44no—
1146C4—44no—
1147C4—44no—
1148C4—44no—
1149C4—44no—
1150C4—44no—
1151C4—44no—
1152C4#349714yes—
1153C2—42no—
1154C2—84no—
1155C2—84no—
1156C2#6274312yes—
1157C2C2×#349711yescharacteristic
1158C2#6281211yescharacteristic
1159C2#6281211yescharacteristic
1160C2#6283112yes—
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×#3557C2semidirect
2. #59838C2semidirect
3. #46312C2semidirect
4. #46281C2semidirect
5. #39741C2semidirect
6. #39740C2semidirect
7. #39739C2semidirect
8. #39613C2semidirect
9. #39612C2semidirect
10. #39611C2semidirect
11. #39455C2semidirect
12. #39453C2semidirect
13. #39393C2semidirect
14. #37542C2semidirect
15. #37389C2semidirect
16. #37301C2semidirect
17. #36631C2semidirect
18. #36631C2semidirect
19. #36538C2semidirect
20. #36534C2semidirect
21. #36508C2semidirect
22. #36496C2semidirect
23. #35318C2semidirect
24. #35276C2semidirect
25. C4×#533C2semidirect
212. #533D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35572
#598382
#463122
#462812
#397412
#397402
#397392
#396132
#396122
#396112
#394552
#394532
#393932
#375422
#373892
#373012
#366312
#365382
#365342
#365082
#364962
#353182
#352762
C4×#5332