Finite Group Databasebeta

← #7712010

Subgroups — #7712010

Order 512.

5432 conjugacy classes of subgroups.

The subgroup lattice has 1285 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59305C212yesmaximal, complemented
2#59303C212yesmaximal, complemented
3#59134C212yesmaximal, complemented
4#59125C212yesmaximal, complemented
5#46020C214yesmaximal, complemented
6#46019C214yesmaximal, complemented
7#39732C214yesmaximal, complemented
8#39721C214yesmaximal, complemented
9#39633C212yesmaximal, complemented
10#39513C212yesmaximal, complemented
11#39505C212yesmaximal, complemented
12#39505C212yesmaximal, complemented
13#39497C212yesmaximal, complemented
14#39488C212yesmaximal, complemented
15#37892C214yesmaximal, complemented
16#37620C212yesmaximal, complemented
17#37327C214yesmaximal, complemented
18C2×#2868C211yesmaximal, characteristic, complemented
19#36631C211yesmaximal, characteristic, complemented
20#36598C211yesmaximal, characteristic, complemented
21#36594C211yesmaximal, characteristic, complemented
22#36134C211yesmaximal, characteristic, complemented
23#36129C212yesmaximal, complemented
24#36127C211yesmaximal, characteristic, complemented
25#36122C212yesmaximal, complemented
26#35298C212yesmaximal, complemented
27#35284C212yesmaximal, complemented
28#34384C212yesmaximal, complemented
29C4×#529C211yesmaximal, characteristic, complemented
30C2×#556C2212yes—
31C2×#548C2214yes—
32C2×#547C2212yes—
33C2×#533C2212yes—
34C2×#532C2212yes—
35C22×C4⋊Q8C2212yes—
36C22×C4⋊Q8C2212yes—
37C22×C4⋊Q8C2212yes—
38C2×#529C2212yes—
39C2×#529C2211yescharacteristic
40#2868C2211yescharacteristic
41#2868C2211yescharacteristic
42#2868C2212yes—
43#2868C2212yes—
44#2868C2212yes—
45#2868C2212yes—
46#2868C2212yes—
47#2868C2212yes—
48#2868C2212yes—
49#2862C2212yes—
50#2861C2212yes—
51#2860C2212yes—
52#2860C2212yes—
53#2859C2211yescharacteristic
54#2858C2211yescharacteristic
55#2858C2212yes—
56#2857C2211yescharacteristic
57#2857C2212yes—
58#2857C2212yes—
59#2856C2211yescharacteristic
60#2854C2212yes—
61#2854C2212yes—
62#2850C2212yes—
63#2823C2218yes—
64#2795C2218yes—
65#2795C2218yes—
66#2795C2218yes—
67#2793C2218yes—
68#2793C2218yes—
69#2790C2218yes—
70#2790C2218yes—
71#2790C2218yes—
72#2731C2218yes—
73#2731C2218yes—
74#2729C2218yes—
75#2729C2218yes—
76#2718C2218yes—
77#2718C2218yes—
78#2716C2218yes—
79#2674C2218yes—
80#2647C2214yes—
81#2629C2214yes—
82#2629C2214yes—
83#2620C2214yes—
84#2620C2214yes—
85#2620C2214yes—
86#2618C2218yes—
87#2591C2218yes—
88#2582C2212yes—
89#2579C2218yes—
90#2571C2212yes—
91#2570C2214yes—
92#2568C2212yes—
93#2566C2214yes—
94#2566C2214yes—
95#2552C2212yes—
96#2550C2214yes—
97#2547C2212yes—
98#2547C2212yes—
99#2545C2214yes—
100#2545C2214yes—
101#2545C2214yes—
102#2545C2214yes—
103#2542C2212yes—
104#2538C2212yes—
105#2538C2212yes—
106#2538C2212yes—
107#2537C2212yes—
108#2537C2212yes—
109#2512C2214yes—
110#2512C2214yes—
111#2511C2214yes—
112#2507C2214yes—
113#2507C2214yes—
114#2502C2214yes—
115#2500C2214yes—
116#2500C2214yes—
117#2500C2214yes—
118#2497C2214yes—
119#2497C2214yes—
120#2497C2214yes—
121#2497C2214yes—
122#2492C2214yes—
123#2492C2214yes—
124#2491C2214yes—
125#2491C2214yes—
126#2491C2214yes—
127#2481C2218yes—
128#2452C2214yes—
129#2452C2214yes—
130#2451C2214yes—
131#2446C2214yes—
132#2446C2214yes—
133#2446C2214yes—
134#2446C2214yes—
135#2443C2218yes—
136#2442C2214yes—
137#2441C2214yes—
138#2440C2214yes—
139#2439C2214yes—
140#2439C2214yes—
141#2436C2214yes—
142#2432C2214yes—
143#2432C2214yes—
144#2432C2214yes—
145#2432C2214yes—
146#2429C2214yes—
147#2429C2214yes—
148#2429C2214yes—
149#2429C2214yes—
150#2423C2214yes—
151#2422C2214yes—
152#2422C2214yes—
153#2417C2214yes—
154#2417C2214yes—
155#2416C2214yes—
156#2416C2214yes—
157#2416C2214yes—
158#2409C2214yes—
159#2383C2218yes—
160#2365C2212yes—
161#2365C2212yes—
162#2361C2214yes—
163#2361C2214yes—
164#2360C2214yes—
165#2355C2212yes—
166#2355C2212yes—
167#2354C2212yes—
168#2354C2212yes—
169#2354C2212yes—
170#2352C2214yes—
171#2352C2214yes—
172Q8×C4⋊C4C2212yes—
173D4×C4⋊C4C2212yes—
174D4×C4⋊C4C2212yes—
175D4×C4⋊C4C2214yes—
176Q8×C22⋊C4C2214yes—
177#2330C2214yes—
178#2326C2214yes—
179#2326C2214yes—
180#2322C2218yes—
181#2317C2214yes—
182#2314C2214yes—
183#2314C2214yes—
184C4×C4⋊Q8C2211yescharacteristic
185C4×C4⋊Q8C2212yes—
186C4×C4⋊Q8C2212yes—
187C4×#127C2211yescharacteristic
188C4×#125C2211yescharacteristic
189C4×#125C2211yescharacteristic
190C4×#126C2212yes—
191C4×#126C2212yes—
192C4×#124C2212yes—
193C4×#124C2211yescharacteristic
194C4×#124C2211yescharacteristic
195C4×C22⋊Q8C2211yescharacteristic
196C4×C22⋊Q8C2211yescharacteristic
197C4×#123C2212yes—
198C4×#123C2212yes—
199C4×#121C2212yes—
200C4×#121C2212yes—
201C4×#121C2211yescharacteristic
202C4×#121C2211yescharacteristic
203#2298C2212yes—
204#2295C2211yescharacteristic
205#2293C2212yes—
206#2293C2212yes—
207#2293C2211yescharacteristic
208#2290C2212yes—
209C2×#384C2212yes—
210C2×#384C2212yes—
211C2×#384C2212yes—
212C2×#384C2212yes—
213#2283C2211yescharacteristic
214C42×Q8C2211yescharacteristic
215C42×D4C2212yes—
216C42×D4C2211yescharacteristic
217C4×#117C2212yes—
218C2×C43C2211yescharacteristic
219C22×#41C2314yes—
220C23×Q8C2314yes—
221#556—48no—
222#548—416no—
223#547—48no—
224#533—48no—
225#532—48no—
226C2×C4⋊Q8—48no—
227C2×C4⋊Q8—48no—
228C2×C4⋊Q8—48no—
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2314yes—
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2314yes—
237C2×C4⋊Q8C2314yes—
238C2×C4⋊Q8C2314yes—
239C2×C4⋊Q8C2312yes—
240C2×C4⋊Q8C2314yes—
241C2×C4⋊Q8C2314yes—
242C2×C4⋊Q8C2314yes—
243C2×C4⋊Q8C2314yes—
244C2×C4⋊Q8C2314yes—
245C2×#127C2311yescharacteristic
246#529—216no—
247#529—28no—
248C2×#126C2312yes—
249C2×#126C2314yes—
250C2×#126C2318yes—
251C2×#125C2311yescharacteristic
252C2×#125C2312yes—
253C2×#125C2314yes—
254C2×#124C2312yes—
255C2×#124C2312yes—
256C2×#124C2311yescharacteristic
257C2×#124C2314yes—
258C2×#124C2314yes—
259C2×#124C2318yes—
260C2×#124C2314yes—
261C2×#123C2314yes—
262C2×#123C2312yes—
263C2×#123C2318yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2311yescharacteristic
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2318yes—
272C2×#121C2312yes—
273C2×#121C2312yes—
274C2×#121C2312yes—
275C2×#121C2311yescharacteristic
276C2×#121C2318yes—
277C2×#121C2314yes—
278C2×#121C2314yes—
279C2×#121C2314yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2314yes—
285C2×C4×Q8C2314yes—
286C2×C4×Q8C2314yes—
287C2×C4×Q8C2314yes—
288C2×C4×D4C2312yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2311yescharacteristic
294C2×C4×D4C2312yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2311yescharacteristic
297C2×C4×D4C2311yescharacteristic
298C2×C4×D4C2314yes—
299C2×C4×D4C2318yes—
300C2×C4×D4C2314yes—
301C2×#117C2312yes—
302C2×#117C2314yes—
303C2×#117C2312yes—
304C2×#117C2314yes—
305C2×#117C2314yes—
306C22×C4⋊C4C2314yes—
307C22×C4⋊C4C2314yes—
308C22×C4⋊C4C2314yes—
309C22×C4⋊C4C2314yes—
310C22×C4⋊C4C2314yes—
311C22×C4⋊C4C2314yes—
312C22×C4⋊C4C2314yes—
313C22×C42C2311yescharacteristic
314C22×C42C2311yescharacteristic
315C22×C42C2311yescharacteristic
316C22×C42C2311yescharacteristic
317C22×C42C2312yes—
318C22×C42C2311yescharacteristic
319C22×C42C2311yescharacteristic
320C22×C42C2311yescharacteristic
321#400C2318yes—
322#400C2318yes—
323#400C2318yes—
324#400C2318yes—
325#400C2318yes—
326#399C2318yes—
327#398C2318yes—
328#398C2318yes—
329#398C2318yes—
330#398C2318yes—
331#398C2318yes—
332#398C2318yes—
333#398C2318yes—
334#398C2318yes—
335#397C2318yes—
336#397C2318yes—
337#396C2318yes—
338#396C2318yes—
339#396C2318yes—
340#396C2318yes—
341#396C2318yes—
342#396C2318yes—
343#396C2318yes—
344#396C2318yes—
345#396C2318yes—
346#396C2318yes—
347#396C2318yes—
348#396C2318yes—
349#395C2318yes—
350#394C2318yes—
351#394C2318yes—
352#394C2318yes—
353#394C2318yes—
354#394C2318yes—
355#394C2318yes—
356#394C2318yes—
357#394C2318yes—
358#393C2318yes—
359#393C2318yes—
360#393C2318yes—
361#391C2314yes—
362#391C2312yes—
363#391C2314yes—
364#391C2314yes—
365#391C2314yes—
366#391C2314yes—
367#391C2314yes—
368#391C2314yes—
369#391C2318yes—
370#391C2318yes—
371#391C2312yes—
372#391C2314yes—
373#391C2314yes—
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#390C2312yes—
377#390C2312yes—
378#390C2312yes—
379#390C2312yes—
380#390C2312yes—
381#390C2314yes—
382#390C2314yes—
383#390C2314yes—
384#390C2314yes—
385#390C2312yes—
386#390C2312yes—
387#390C2312yes—
388#390C2312yes—
389#390C2312yes—
390#390C2314yes—
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2312yes—
398#389C2314yes—
399#389C2314yes—
400#389C2312yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2318yes—
405#389C2318yes—
406#389C2318yes—
407#389C2314yes—
408#389C2314yes—
409#389C2318yes—
410#389C2312yes—
411#389C2312yes—
412#389C2314yes—
413#389C2312yes—
414#389C2312yes—
415#389C2314yes—
416#389C2312yes—
417#389C2312yes—
418#389C2314yes—
419#388C2312yes—
420#388C2312yes—
421#388C2312yes—
422#388C2312yes—
423#388C2312yes—
424#388C2312yes—
425#388C2318yes—
426#388C2318yes—
427#388C2318yes—
428#388C2318yes—
429#388C2318yes—
430#388C2318yes—
431#388C2318yes—
432#388C2318yes—
433#388C2318yes—
434#388C2318yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2318yes—
444#388C2318yes—
445#388C2312yes—
446#388C2312yes—
447#387C2312yes—
448#387C2312yes—
449#387C2312yes—
450#387C2312yes—
451#387C2312yes—
452#387C2312yes—
453#387C2312yes—
454#387C2312yes—
455#387C2318yes—
456#387C2318yes—
457#387C2318yes—
458#387C2318yes—
459#387C2318yes—
460#387C2318yes—
461#387C2318yes—
462#387C2318yes—
463#387C2318yes—
464#387C2318yes—
465#386C2318yes—
466#386C2314yes—
467#386C2318yes—
468#386C2312yes—
469#386C2318yes—
470#386C2314yes—
471#386C2312yes—
472#385C2318yes—
473#385C2318yes—
474#385C2318yes—
475#385C2318yes—
476#385C2318yes—
477#385C2318yes—
478#385C2318yes—
479#385C2312yes—
480#385C2318yes—
481#385C2318yes—
482#385C2312yes—
483#384C2311yescharacteristic
484#384C2311yescharacteristic
485#384C2314yes—
486#384C2314yes—
487#384C2314yes—
488#384C2314yes—
489#384C2314yes—
490#384C2312yes—
491#384C2312yes—
492#384C2314yes—
493#384C2314yes—
494#384C2312yes—
495#384C2312yes—
496#384C2312yes—
497#384C2312yes—
498#384C2312yes—
499#384C2312yes—
500#384C2314yes—
501#384C2314yes—
502#384C2314yes—
503#384C2314yes—
504#384C2314yes—
505#384C2314yes—
506#383C2312yes—
507#382C2311yescharacteristic
508#382C2311yescharacteristic
509#382C2314yes—
510#382C2314yes—
511#382C2314yes—
512#382C2312yes—
513#381C2312yes—
514#380C2314yes—
515#380C2314yes—
516#380C2314yes—
517#380C2314yes—
518#380C2318yes—
519#380C2312yes—
520#380C2312yes—
521#380C2314yes—
522#380C2314yes—
523#380C2311yescharacteristic
524#380C2314yes—
525#380C2311yescharacteristic
526#380C2314yes—
527C4×C4⋊C4C2312yes—
528C4×C4⋊C4C2312yes—
529C4×C4⋊C4C2312yes—
530C4×C4⋊C4C2312yes—
531C4×C4⋊C4C2312yes—
532C4×C4⋊C4C2312yes—
533C4×C4⋊C4C2312yes—
534C4×C4⋊C4C2311yescharacteristic
535C4×C4⋊C4C2311yescharacteristic
536C4×C4⋊C4C2311yescharacteristic
537C4×C4⋊C4C2311yescharacteristic
538C4×C4⋊C4C2312yes—
539C4×C4⋊C4C2312yes—
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2314yes—
542C4×C4⋊C4C2314yes—
543C4×C4⋊C4C2312yes—
544C4×C4⋊C4C2314yes—
545C4×C4⋊C4C2314yes—
546C4×C4⋊C4C2314yes—
547C4×C4⋊C4C2311yescharacteristic
548C4×C4⋊C4C2311yescharacteristic
549C4×C4⋊C4C2312yes—
550C4×C4⋊C4C2312yes—
551C4×C22⋊C4C2312yes—
552C4×C22⋊C4C2312yes—
553C4×C22⋊C4C2312yes—
554C4×C22⋊C4C2312yes—
555C4×C22⋊C4C2312yes—
556C4×C22⋊C4C2312yes—
557C4×C22⋊C4C2318yes—
558C4×C22⋊C4C2312yes—
559C4×C22⋊C4C2312yes—
560C4×C22⋊C4C2312yes—
561C4×C22⋊C4C2312yes—
562C4×C22⋊C4C2312yes—
563C4×C22⋊C4C2314yes—
564C4×C22⋊C4C2312yes—
565C4×C22⋊C4C2312yes—
566C4×C22⋊C4C2314yes—
567#376C2312yes—
568#376C2312yes—
569C43C2311yescharacteristic
570C43C2311yescharacteristic
571C43C2311yescharacteristic
572C43C2311yescharacteristic
573C43C2311yescharacteristic
574C43C2312yes—
575C43C2311yescharacteristic
576C43C2311yescharacteristic
577C43C2311yescharacteristic
578C2×#41—48no—
579C2×#41—48no—
580C2×#41—48no—
581C22×Q8—216no—
582C22×Q8—48no—
583C22×Q8—48no—
584C22×Q8C2411yescharacteristic
585C22×Q8C2412yes—
586C22×Q8C2414yes—
587C22×Q8C2414yes—
588C22×Q8C2418yes—
589C22×D4C2412yes—
590C22×D4C2414yes—
591C22×D4C2411yescharacteristic
592C22×D4C2412yes—
593C22×D4C2412yes—
594C22×D4C2412yes—
595C22×D4C2418yes—
596C23×C4C2411yescharacteristic
597C23×C4C2411yescharacteristic
598C23×C4C2414yes—
599C23×C4C2412yes—
600C23×C4C2412yes—
601C23×C4C2412yes—
602C23×C4C2411yescharacteristic
603C23×C4C2411yescharacteristic
604C23×C4C2411yescharacteristic
605C23×C4C2411yescharacteristic
606C23×C4C2411yescharacteristic
607C23×C4C2418yes—
608C23×C4C2418yes—
609C4⋊Q8—28no—
610C4⋊Q8—28no—
611C4⋊Q8—28no—
612C4⋊Q8—28no—
613C4⋊Q8—24no—
614C4⋊Q8—48no—
615C4⋊Q8—48no—
616C4⋊Q8—48no—
617C4⋊Q8—48no—
618C4⋊Q8—48no—
619C4⋊Q8—48no—
620C4⋊Q8—44no—
621C4⋊Q8—48no—
622C4⋊Q8—44no—
623C4⋊Q8—48no—
624C4⋊Q8—48no—
625#127—24no—
626#126—28no—
627#126—216no—
628#126—416no—
629#125—24no—
630#125—28no—
631#125—48no—
632#124—24no—
633#124—28no—
634#124—28no—
635#124—48no—
636#124—48no—
637#124—48no—
638#124—416no—
639#123—216no—
640#123—28no—
641#123—416no—
642C22⋊Q8—24no—
643C22⋊Q8—28no—
644C22⋊Q8—416no—
645C22⋊Q8—48no—
646C22⋊Q8—48no—
647C22⋊Q8—48no—
648C22⋊Q8—48no—
649C22⋊Q8—48no—
650#121—24no—
651#121—28no—
652#121—28no—
653#121—28no—
654#121—48no—
655#121—48no—
656#121—48no—
657#121—416no—
658C4×Q8—28no—
659C4×Q8—24no—
660C4×Q8—24no—
661C4×Q8—24no—
662C4×Q8—48no—
663C4×Q8—48no—
664C4×Q8—48no—
665C4×Q8—48no—
666C4×D4—216no—
667C4×D4—28no—
668C4×D4—28no—
669C4×D4—28no—
670C4×D4—28no—
671C4×D4—24no—
672C4×D4—24no—
673C4×D4—28no—
674C4×D4—28no—
675C4×D4—24no—
676C4×D4—48no—
677C4×D4—48no—
678C4×D4—416no—
679#117—216no—
680#117—28no—
681#117—28no—
682#117—48no—
683#117—48no—
684C2×C4⋊C4—48no—
685C2×C4⋊C4—48no—
686C2×C4⋊C4—48no—
687C2×C4⋊C4—48no—
688C2×C4⋊C4—48no—
689C2×C4⋊C4—48no—
690C2×C4⋊C4—48no—
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2412yes—
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2412yes—
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2418yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2418yes—
731C2×C4⋊C4C2418yes—
732C2×C4⋊C4C2418yes—
733C2×C4⋊C4C2418yes—
734C2×C4⋊C4C2418yes—
735C2×C4⋊C4C2418yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2418yes—
739C2×C4⋊C4C2418yes—
740C2×C4⋊C4C2418yes—
741C2×C4⋊C4C2418yes—
742C2×C4⋊C4C2418yes—
743C2×C22⋊C4C2412yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2412yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2412yes—
748C2×C22⋊C4C2412yes—
749C2×C22⋊C4C2412yes—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2412yes—
752C2×C22⋊C4C2412yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2412yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2412yes—
757C2×C22⋊C4C2412yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2412yes—
760C2×C22⋊C4C2412yes—
761C2×C22⋊C4C2412yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2418yes—
768C2×C22⋊C4C2418yes—
769C2×C22⋊C4C2418yes—
770C2×C22⋊C4C2418yes—
771C2×C22⋊C4C2418yes—
772C2×C22⋊C4C2418yes—
773C2×C22⋊C4C2418yes—
774C2×C22⋊C4C2418yes—
775C2×C22⋊C4C2418yes—
776C2×C42—24no—
777C2×C42—24no—
778C2×C42—24no—
779C2×C42—24no—
780C2×C42—28no—
781C2×C42—24no—
782C2×C42—24no—
783C2×C42#4118yescomplemented
784C2×C42C2412yes—
785C2×C42C2414yes—
786C2×C42C2412yes—
787C2×C42C2412yes—
788C2×C42C2412yes—
789C2×C42C2412yes—
790C2×C42C2412yes—
791C2×C42C2412yes—
792C2×C42C2412yes—
793C2×C42C2412yes—
794C2×C42C2411yescharacteristic
795C2×C42C2411yescharacteristic
796C2×C42C2411yescharacteristic
797C2×C42C2411yescharacteristic
798C2×C42C2411yescharacteristic
799C2×C42C2411yescharacteristic
800C2×C42C2411yescharacteristic
801C2×C42C2411yescharacteristic
802C2×C42C2411yescharacteristic
803C2×C42C2411yescharacteristic
804C2×C42C2411yescharacteristic
805C2×C42C2411yescharacteristic
806C2×C42C2411yescharacteristic
807C2×C42C2411yescharacteristic
808C2×C42C2411yescharacteristic
809C2×C42C2411yescharacteristic
810C2×C42C2411yescharacteristic
811C2×C42C2411yescharacteristic
812C2×C42C2411yescharacteristic
813C2×C42C2411yescharacteristic
814C2×C42C2418yes—
815C2×C42C2418yes—
816C2×C42C2418yes—
817C2×C42C2411yescharacteristic
818C2×C42C2411yescharacteristic
819C2×C42C2411yescharacteristic
820C2×C42C2411yescharacteristic
821C2×C42C2411yescharacteristic
822C2×C42C2411yescharacteristic
823C2×C42C2411yescharacteristic
824C2×C42C2411yescharacteristic
825#95C2412yes—
826#95C2412yes—
827#95C2412yes—
828#95C2412yes—
829#95C2412yes—
830#95C2412yes—
831#95C2412yes—
832#95C2412yes—
833#95C2412yes—
834#95C2412yes—
835#95C2412yes—
836#95C2412yes—
837#95C2412yes—
838#95C2412yes—
839#95C2412yes—
840#95C2412yes—
841#95C2412yes—
842#95C2418yes—
843#95C2414yes—
844#95C2414yes—
845#95C2418yes—
846#95C2414yes—
847#95C2414yes—
848#95C2412yes—
849#95C2412yes—
850#95C2412yes—
851#95C2418yes—
852#95C2418yes—
853#95C2418yes—
854#95C2418yes—
855#95C2418yes—
856#95C2418yes—
857#95C2414yes—
858#95C2414yes—
859#95C2418yes—
860#95C2418yes—
861#95C2418yes—
862#95C2418yes—
863C24C2514yes—
864C24C2512yes—
865C24C2511yescharacteristic
866#41—832no—
867C2×Q8—22no—
868C2×Q8—24no—
869C2×Q8—22no—
870C2×Q8—24no—
871C2×Q8—28no—
872C2×Q8—28no—
873C2×Q8—28no—
874C2×Q8—28no—
875C2×Q8—28no—
876C2×Q8—28no—
877C2×Q8—216no—
878C2×Q8—22no—
879C2×Q8—24no—
880C2×Q8—48no—
881C2×Q8—48no—
882C2×Q8—832no—
883C2×D4—24no—
884C2×D4—28no—
885C2×D4—24no—
886C2×D4—28no—
887C2×D4—24no—
888C2×D4—28no—
889C2×D4—22no—
890C2×D4—24no—
891C2×D4—22no—
892C2×D4—24no—
893C2×D4—24no—
894C2×D4—24no—
895C2×D4—24no—
896C2×D4—24no—
897C2×D4—22no—
898C2×D4—24no—
899C2×D4—24no—
900C2×D4—24no—
901C2×D4—48no—
902C2×D4—48no—
903C2×D4—48no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—22no—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—22no—
910C22×C4—22no—
911C22×C4—22no—
912C22×C4—22no—
913C22×C4—22no—
914C22×C4—22no—
915C22×C4—22no—
916C22×C4—22no—
917C22×C4—22no—
918C22×C4—22no—
919C22×C4—22no—
920C22×C4—216no—
921C22×C4—28no—
922C22×C4—24no—
923C22×C4—24no—
924C22×C4—24no—
925C22×C4—24no—
926C22×C4—28no—
927C22×C4—24no—
928C22×C4—24no—
929C22×C4—24no—
930C22×C4—28no—
931C22×C4—24no—
932C22×C4—24no—
933C22×C4—48no—
934C22×C4—48no—
935C22×C4—48no—
936C22×C4—48no—
937C22×C4—48no—
938C22×C4C2×#4114yes—
939C22×C4C2×#4114yes—
940C22×C4C2×#4114yes—
941C22×C4H(5,𝔽2)14yes—
942C22×C42−1+414yes—
943C22×C4C2512yes—
944C22×C4C2512yes—
945C22×C4C2512yes—
946C22×C4C2512yes—
947C22×C4C2514yes—
948C22×C4C2512yes—
949C22×C4C2514yes—
950C22×C4C2512yes—
951C22×C4C2514yes—
952C22×C4C2512yes—
953C22×C4C2518yes—
954C22×C4C2518yes—
955C22×C4C2511yescharacteristic
956C22×C4C2511yescharacteristic
957C22×C4C2511yescharacteristic
958C22×C4C2511yescharacteristic
959C22×C4C2511yescharacteristic
960C22×C4C2511yescharacteristic
961C22×C4C2511yescharacteristic
962C22×C4C2511yescharacteristic
963C22×C4C2511yescharacteristic
964C22×C4C2511yescharacteristic
965C22×C4C2511yescharacteristic
966C22×C4C2511yescharacteristic
967C22×C4C2511yescharacteristic
968C22×C4C2511yescharacteristic
969C4⋊C4—24no—
970C4⋊C4—28no—
971C4⋊C4—24no—
972C4⋊C4—28no—
973C4⋊C4—22no—
974C4⋊C4—24no—
975C4⋊C4—24no—
976C4⋊C4—28no—
977C4⋊C4—22no—
978C4⋊C4—24no—
979C4⋊C4—24no—
980C4⋊C4—28no—
981C4⋊C4—22no—
982C4⋊C4—28no—
983C4⋊C4—28no—
984C4⋊C4—28no—
985C4⋊C4—28no—
986C4⋊C4—28no—
987C4⋊C4—28no—
988C4⋊C4—28no—
989C4⋊C4—28no—
990C4⋊C4—22no—
991C4⋊C4—24no—
992C4⋊C4—24no—
993C4⋊C4—24no—
994C4⋊C4—24no—
995C4⋊C4—24no—
996C4⋊C4—24no—
997C4⋊C4—24no—
998C4⋊C4—24no—
999C4⋊C4—24no—
1000C4⋊C4—22no—
1001C4⋊C4—24no—
1002C4⋊C4—22no—
1003C4⋊C4—24no—
1004C4⋊C4—24no—
1005C4⋊C4—48no—
1006C4⋊C4—48no—
1007C4⋊C4—48no—
1008C4⋊C4—48no—
1009C4⋊C4—48no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—48no—
1013C4⋊C4—48no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—48no—
1017C4⋊C4—48no—
1018C4⋊C4—48no—
1019C4⋊C4—48no—
1020C4⋊C4—48no—
1021C22⋊C4—28no—
1022C22⋊C4—24no—
1023C22⋊C4—24no—
1024C22⋊C4—24no—
1025C22⋊C4—24no—
1026C22⋊C4—28no—
1027C22⋊C4—24no—
1028C22⋊C4—28no—
1029C22⋊C4—24no—
1030C22⋊C4—28no—
1031C22⋊C4—24no—
1032C22⋊C4—28no—
1033C22⋊C4—24no—
1034C22⋊C4—28no—
1035C22⋊C4—24no—
1036C22⋊C4—28no—
1037C22⋊C4—24no—
1038C22⋊C4—24no—
1039C22⋊C4—24no—
1040C22⋊C4—24no—
1041C22⋊C4—28no—
1042C22⋊C4—28no—
1043C22⋊C4—28no—
1044C22⋊C4—28no—
1045C22⋊C4—48no—
1046C22⋊C4—48no—
1047C22⋊C4—48no—
1048C22⋊C4—48no—
1049C22⋊C4—48no—
1050C22⋊C4—48no—
1051C22⋊C4—48no—
1052C22⋊C4—48no—
1053C22⋊C4—48no—
1054C42—28no—
1055C42—24no—
1056C42—24no—
1057C42—24no—
1058C42—24no—
1059C42—22no—
1060C42—22no—
1061C42—22no—
1062C42—22no—
1063C42—22no—
1064C42—22no—
1065C42—22no—
1066C42—22no—
1067C42—22no—
1068C42—22no—
1069C42—24no—
1070C42—24no—
1071C42—22no—
1072C42—22no—
1073C42—22no—
1074C42—22no—
1075C42—22no—
1076C42—22no—
1077C42—22no—
1078C42—22no—
1079C42—22no—
1080C42—22no—
1081C42—24no—
1082C42—24no—
1083C42—24no—
1084C42—48no—
1085C42—48no—
1086C42—48no—
1087C42C2×#4114yes—
1088C42C2×#4114yes—
1089C42C2×#4114yes—
1090C42C2×#4114yes—
1091C42H(5,𝔽2)14yes—
1092C42H(5,𝔽2)14yes—
1093C422−1+414yes—
1094C422−1+414yes—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—24no—
1100C23—22no—
1101C23—24no—
1102C23—22no—
1103C23—22no—
1104C23—24no—
1105C23—22no—
1106C23—24no—
1107C23—22no—
1108C23—24no—
1109C23—22no—
1110C23—22no—
1111C23—24no—
1112C23—24no—
1113C23C22×#4112yes—
1114C23C2×H(5,𝔽2)12yes—
1115C23C2×2−1+412yes—
1116C23C2611yescharacteristic
1117Q8—44no—
1118Q8—48no—
1119Q8—416no—
1120Q8—416no—
1121Q8—816no—
1122D4—48no—
1123D4—416no—
1124D4—44no—
1125D4—48no—
1126D4—48no—
1127D4—48no—
1128D4—816no—
1129C2×C4—28no—
1130C2×C4—28no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—28no—
1152C2×C4—28no—
1153C2×C4—28no—
1154C2×C4—28no—
1155C2×C4—28no—
1156C2×C4—22no—
1157C2×C4—24no—
1158C2×C4—22no—
1159C2×C4—24no—
1160C2×C4—22no—
1161C2×C4—24no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—28no—
1173C2×C4—28no—
1174C2×C4—28no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—28no—
1178C2×C4—28no—
1179C2×C4—28no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—24no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—22no—
1192C2×C4—416no—
1193C2×C4—48no—
1194C2×C4—48no—
1195C2×C4—48no—
1196C2×C4—816no—
1197C2×C4—816no—
1198C2×C4C22×#4112yes—
1199C2×C4C22×#4112yes—
1200C2×C4C22×#4112yes—
1201C2×C4C22×#4112yes—
1202C2×C4C22×#4112yes—
1203C2×C4C22×#4112yes—
1204C2×C4C2×H(5,𝔽2)12yes—
1205C2×C4C2×H(5,𝔽2)12yes—
1206C2×C4C2×H(5,𝔽2)12yes—
1207C2×C4C2×H(5,𝔽2)12yes—
1208C2×C4C2×H(5,𝔽2)12yes—
1209C2×C4C2×H(5,𝔽2)12yes—
1210C2×C4C2×H(5,𝔽2)12yes—
1211C2×C4C2×H(5,𝔽2)12yes—
1212C2×C4C2×2−1+412yes—
1213C2×C4C2×2−1+412yes—
1214C2×C4C2×2−1+412yes—
1215C2×C4C2×2−1+412yes—
1216C2×C4C2×2−1+412yes—
1217C2×C4C2×2−1+412yes—
1218C2×C4C2×2−1+412yes—
1219C2×C4C2×2−1+412yes—
1220C22—22no—
1221C22—22no—
1222C22—22no—
1223C22—22no—
1224C22—22no—
1225C22—22no—
1226C22—42no—
1227C22—44no—
1228C22—42no—
1229C22—44no—
1230C22—44no—
1231C22—42no—
1232C22—42no—
1233C22—44no—
1234C22—42no—
1235C22—44no—
1236C22—44no—
1237C22—42no—
1238C22—42no—
1239C22—44no—
1240C22#351114yes—
1241C22C23×#4111yescharacteristic
1242C22C22×H(5,𝔽2)11yescharacteristic
1243C22C22×H(5,𝔽2)11yescharacteristic
1244C22C22×H(5,𝔽2)11yescharacteristic
1245C22C22×2−1+411yescharacteristic
1246C22C22×2−1+411yescharacteristic
1247C22C22×2−1+411yescharacteristic
1248C4—22no—
1249C4—22no—
1250C4—22no—
1251C4—22no—
1252C4—22no—
1253C4—22no—
1254C4—22no—
1255C4—22no—
1256C4—22no—
1257C4—22no—
1258C4—42no—
1259C4—48no—
1260C4—48no—
1261C4—42no—
1262C4—42no—
1263C4—44no—
1264C4—42no—
1265C4—44no—
1266C4—42no—
1267C4—44no—
1268C4—42no—
1269C4—42no—
1270C4#351114yes—
1271C4#351114yes—
1272C4#354314yes—
1273C4#355214yes—
1274C2—24no—
1275C2—82no—
1276C2—84no—
1277C2C2×#354311yescharacteristic
1278C2C2×#355211yescharacteristic
1279C2C2×#351111yescharacteristic
1280C2C2×#351111yescharacteristic
1281C2C2×#351111yescharacteristic
1282C2#6283311yescharacteristic
1283C2#6283311yescharacteristic
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. #59305C2semidirect
2. #59303C2semidirect
3. #59134C2semidirect
4. #59125C2semidirect
5. #46020C2semidirect
6. #46019C2semidirect
7. #39732C2semidirect
8. #39721C2semidirect
9. #39633C2semidirect
10. #39513C2semidirect
11. #39505C2semidirect
12. #39505C2semidirect
13. #39497C2semidirect
14. #39488C2semidirect
15. #37892C2semidirect
16. #37620C2semidirect
17. #37327C2semidirect
18. C2×#2868C2semidirect
19. #36631C2semidirect
20. #36598C2semidirect
21. #36594C2semidirect
22. #36134C2semidirect
23. #36129C2semidirect
24. #36127C2semidirect
25. #36122C2semidirect
26. #35298C2semidirect
27. #35284C2semidirect
28. #34384C2semidirect
29. C4×#529C2semidirect
783. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
#593052
#593032
#591342
#591252
#460202
#460192
#397322
#397212
#396332
#395132
#395052
#394972
#394882
#378922
#376202
#373272
C2×#28682
#366312
#365982
#365942
#361342
#361292
#361272
#361222
#352982
#352842
#343842
C4×#5292