Finite Group Databasebeta

← #7688350

Subgroups — #7688350

Order 512.

7065 conjugacy classes of subgroups.

The subgroup lattice has 1225 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3515C212yesmaximal, complemented
2#59842C214yesmaximal, complemented
3#59815C212yesmaximal, complemented
4#59815C211yesmaximal, characteristic, complemented
5#59680C212yesmaximal, complemented
6#59139C214yesmaximal, complemented
7#59034C212yesmaximal, complemented
8#45243C214yesmaximal, complemented
9#44248C218yesmaximal, complemented
10#39883C214yesmaximal, complemented
11#39397C214yesmaximal, complemented
12#39379C212yesmaximal, complemented
13#39126C212yesmaximal, complemented
14#36559C211yesmaximal, characteristic, complemented
15#36559C211yesmaximal, characteristic, complemented
16#36492C212yesmaximal, complemented
17#36270C212yesmaximal, complemented
18#36270C212yesmaximal, complemented
19#36134C211yesmaximal, characteristic, complemented
20D4×#125C212yesmaximal, complemented
21#35772C214yesmaximal, complemented
22#34934C212yesmaximal, complemented
23#34934C211yesmaximal, characteristic, complemented
24#34313C212yesmaximal, complemented
25C4×#557C211yesmaximal, characteristic, complemented
26C4×#550C211yesmaximal, characteristic, complemented
27#3515—232no—
28C2×#557C2211yescharacteristic
29C2×#554C2212yes—
30C2×#554C2212yes—
31C2×#553C2214yes—
32C2×#552C2214yes—
33C2×#552C2214yes—
34C2×#552C2218yes—
35C2×#550C2212yes—
36C2×#550C2211yescharacteristic
37C2×#547C2212yes—
38C2×#547C2214yes—
39C2×#541C2214yes—
40C2×#539C2218yes—
41C2×#533C2212yes—
42C2×#529C2214yes—
43C2×#529C2212yes—
44C22×#125C2214yes—
45C2×#520C2214yes—
46C2×C4×#41C2212yes—
47#2868C2211yescharacteristic
48#2860C2214yes—
49#2859C2212yes—
50#2859C2212yes—
51#2857C2212yes—
52#2851C2214yes—
53#2725C2218yes—
54#2725C2218yes—
55#2714C2218yes—
56#2711C2218yes—
57#2707C2218yes—
58#2705C2218yes—
59#2702C2218yes—
60#2696C2218yes—
61#2682C2218yes—
62#2682C2214yes—
63#2681C2218yes—
64#2636C2218yes—
65#2629C2214yes—
66#2609C2218yes—
67#2601C2218yes—
68#2601C2218yes—
69#2566C2214yes—
70#2566C2214yes—
71#2563C2212yes—
72#2563C2212yes—
73#2562C2214yes—
74#2562C2214yes—
75#2558C2218yes—
76#2558C2218yes—
77#2554C2218yes—
78#2554C2214yes—
79#2552C2211yescharacteristic
80#2552C2212yes—
81#2548C2211yescharacteristic
82#2542C2212yes—
83#2541C2211yescharacteristic
84#2541C2212yes—
85#2541C2214yes—
86#2538C2212yes—
87#2538C2211yescharacteristic
88#2538C2212yes—
89#2538C2212yes—
90#2538C2212yes—
91#2538C2212yes—
92#2538C2212yes—
93#2537C2212yes—
94#2537C2214yes—
95#2536C2214yes—
96#2536C2214yes—
97#2535C2214yes—
98#2512C2214yes—
99#2512C2212yes—
100#2512C2214yes—
101#2506C2214yes—
102#2506C2214yes—
103#2506C2214yes—
104#2490C2212yes—
105#2490C2214yes—
106#2481C2218yes—
107#2477C2218yes—
108#2473C2218yes—
109#2473C2218yes—
110#2463C2218yes—
111#2460C2218yes—
112#2458C2218yes—
113#2456C2218yes—
114#2452C2214yes—
115#2452C2214yes—
116#2452C2214yes—
117#2452C2214yes—
118#2445C2214yes—
119#2445C2214yes—
120#2445C2212yes—
121#2445C2214yes—
122#2445C2214yes—
123#2443C2218yes—
124#2442C2214yes—
125#2442C2214yes—
126#2441C2214yes—
127#2429C2214yes—
128#2426C2212yes—
129#2426C2214yes—
130#2423C2214yes—
131#2421C2214yes—
132#2421C2214yes—
133#2416C2214yes—
134#2416C2214yes—
135#2416C2218yes—
136#2414C2214yes—
137#2407C2214yes—
138#2407C2214yes—
139#2407C2214yes—
140#2392C2214yes—
141#2392C2218yes—
142#2370C2212yes—
143#2370C2214yes—
144#2366C2211yescharacteristic
145#2366C2214yes—
146#2366C2212yes—
147#2365C2212yes—
148#2365C2211yescharacteristic
149#2365C2212yes—
150#2363C2212yes—
151#2363C2214yes—
152#2361C2218yes—
153#2361C2214yes—
154#2355C2211yescharacteristic
155#2355C2212yes—
156#2354C2212yes—
157#2354C2211yescharacteristic
158#2354C2212yes—
159#2352C2214yes—
160#2352C2214yes—
161#2351C2212yes—
162Q8×C4⋊C4C2212yes—
163Q8×C4⋊C4C2211yescharacteristic
164Q8×C4⋊C4C2211yescharacteristic
165D4×C4⋊C4C2212yes—
166D4×C4⋊C4C2214yes—
167D4×C4⋊C4C2212yes—
168D4×C4⋊C4C2212yes—
169D4×C4⋊C4C2212yes—
170D4×C4⋊C4C2214yes—
171D4×C4⋊C4C2212yes—
172#2341C2214yes—
173#2341C2212yes—
174#2324C2214yes—
175#2324C2218yes—
176C4×C4⋊Q8C2211yescharacteristic
177C4×C4⋊Q8C2212yes—
178C4×#127C2214yes—
179C4×#127C2212yes—
180C4×#127C2212yes—
181C4×#127C2212yes—
182C4×#127C2211yescharacteristic
183C4×#127C2212yes—
184C4×#127C2211yescharacteristic
185C4×#125C2212yes—
186C4×#125C2214yes—
187C4×#121C2214yes—
188C4×#121C2214yes—
189C4×#121C2212yes—
190C4×#121C2212yes—
191#2293C2212yes—
192#2293C2214yes—
193#2293C2214yes—
194C42×Q8C2212yes—
195C42×Q8C2211yescharacteristic
196C42×Q8C2212yes—
197C42×Q8C2211yescharacteristic
198C42×D4C2212yes—
199C42×D4C2211yescharacteristic
200C22×#41C2312yes—
201C22×#41C2314yes—
202#557D4116yescomplemented
203#554—216no—
204#554—216no—
205#553—232no—
206#552—264no—
207#552—232no—
208#552—232no—
209#550—216no—
210#550—28no—
211#547—216no—
212#547—232no—
213#541—232no—
214#539—264no—
215#533—216no—
216C2×C4⋊Q8C2312yes—
217C2×C4⋊Q8C2312yes—
218C2×C4⋊Q8C2312yes—
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2312yes—
221C2×#127C2311yescharacteristic
222C2×#127C2314yes—
223C2×#127C2312yes—
224C2×#127C2312yes—
225C2×#127C2311yescharacteristic
226#529—232no—
227#529—216no—
228C2×#126C2318yes—
229C2×#126C2318yes—
230C2×#126C2314yes—
231C2×#126C2318yes—
232C2×#125—232no—
233C2×#125C2314yes—
234C2×#125C2314yes—
235C2×#125C2312yes—
236C2×#125C2314yes—
237C2×#125C2318yes—
238C2×#125C2318yes—
239C2×#125C2318yes—
240C2×#125C2312yes—
241C2×#125C2314yes—
242C2×#124C2312yes—
243C2×#123C2314yes—
244C2×#123C2318yes—
245C2×#123C2318yes—
246C2×#123C2318yes—
247C2×#123C2318yes—
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2314yes—
250C2×C22⋊Q8C2314yes—
251C2×C22⋊Q8C2312yes—
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2318yes—
255C2×C22⋊Q8C2318yes—
256C2×C22⋊Q8C2314yes—
257C2×#121C2314yes—
258C2×#121C2318yes—
259C2×#121C2312yes—
260C2×#121C2314yes—
261C2×#121C2314yes—
262C2×#121C2312yes—
263C2×#121C2318yes—
264C2×#121C2312yes—
265C2×#121C2314yes—
266C2×#121C2318yes—
267#520—232no—
268C4×#41—216no—
269C2×C4×Q8C2312yes—
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2312yes—
272C2×C4×Q8C2314yes—
273C2×C4×Q8C2314yes—
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2312yes—
283C2×C4×D4C2312yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2311yescharacteristic
286C2×C4×D4C2311yescharacteristic
287C2×C4×D4C2314yes—
288C2×C4×D4C2314yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2314yes—
293C2×C4×D4C2318yes—
294C2×C4×D4C2314yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2318yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2314yes—
305C2×C4×D4C2314yes—
306C2×C4×D4C2311yescharacteristic
307C2×C4×D4C2314yes—
308C2×C4×D4C2314yes—
309C2×C4×D4C2318yes—
310C2×#117C2318yes—
311C2×#117C2314yes—
312C2×#117C2318yes—
313C2×#117C2312yes—
314C2×#117C2314yes—
315C2×#117C2314yes—
316C22×C4⋊C4C2314yes—
317C22×C4⋊C4C2314yes—
318C22×C4⋊C4C2314yes—
319C22×C4⋊C4C2318yes—
320C22×C4⋊C4C2318yes—
321C22×C42C2314yes—
322C22×C42C2312yes—
323#400C2318yes—
324#400C2318yes—
325#400C2318yes—
326#399C2318yes—
327#398C2318yes—
328#398C2318yes—
329#398C2318yes—
330#398C2318yes—
331#398C2314yes—
332#397C2318yes—
333#397C2314yes—
334#397C2318yes—
335#396C2318yes—
336#396C2318yes—
337#396C2318yes—
338#396C2318yes—
339#396C2314yes—
340#396C2318yes—
341#396C2318yes—
342#396C2314yes—
343#396C2318yes—
344#396C2318yes—
345#394C2318yes—
346#394C2318yes—
347#394C2318yes—
348#394C2318yes—
349#394C2318yes—
350#394C2314yes—
351#394C2318yes—
352#394C2314yes—
353#394C2318yes—
354#394C2314yes—
355#394C2318yes—
356#393C2318yes—
357#393C2318yes—
358#392C2318yes—
359#392C2318yes—
360#392C2314yes—
361#392C2318yes—
362#391C2312yes—
363#391C2312yes—
364#391C2312yes—
365#391C2314yes—
366#390C2314yes—
367#390C2312yes—
368#390C2314yes—
369#390C2314yes—
370#390C2312yes—
371#390C2312yes—
372#390C2318yes—
373#390C2314yes—
374#390C2318yes—
375#390C2314yes—
376#390C2314yes—
377#390C2314yes—
378#390C2312yes—
379#390C2312yes—
380#390C2312yes—
381#390C2312yes—
382#390C2312yes—
383#390C2314yes—
384#390C2312yes—
385#390C2312yes—
386#390C2312yes—
387#390C2314yes—
388#390C2314yes—
389#390C2312yes—
390#390C2318yes—
391#390C2314yes—
392#390C2314yes—
393#390C2312yes—
394#390C2314yes—
395#390C2312yes—
396#389C2312yes—
397#389C2314yes—
398#389C2312yes—
399#389C2314yes—
400#389C2312yes—
401#389C2314yes—
402#389C2314yes—
403#389C2312yes—
404#389C2314yes—
405#389C2318yes—
406#389C2312yes—
407#389C2314yes—
408#389C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2312yes—
417#389C2314yes—
418#389C2314yes—
419#389C2312yes—
420#389C2314yes—
421#389C2312yes—
422#388C2318yes—
423#388C2318yes—
424#388C2318yes—
425#388C2318yes—
426#388C2314yes—
427#388C2318yes—
428#388C2314yes—
429#388C2318yes—
430#388C2318yes—
431#388C2314yes—
432#388C2318yes—
433#388C2314yes—
434#388C2314yes—
435#388C2318yes—
436#388C2314yes—
437#388C2318yes—
438#387C2314yes—
439#387C2314yes—
440#387C2314yes—
441#387C2314yes—
442#387C2314yes—
443#387C2314yes—
444#387C2318yes—
445#387C2318yes—
446#387C2318yes—
447#387C2318yes—
448#386C2314yes—
449#386C2318yes—
450#386C2318yes—
451#386C2318yes—
452#386C2318yes—
453#386C2318yes—
454#386C2314yes—
455#386C2314yes—
456#386C2318yes—
457#386C2314yes—
458#385C2318yes—
459#385C2318yes—
460#385C2318yes—
461#385C2318yes—
462#385C2318yes—
463#385C2318yes—
464#385C2318yes—
465#385C2318yes—
466#385C2318yes—
467#384C2311yescharacteristic
468#384C2311yescharacteristic
469#384C2312yes—
470#384C2312yes—
471#384C2312yes—
472#384C2314yes—
473#384C2312yes—
474#384C2311yescharacteristic
475#384C2312yes—
476#384C2312yes—
477#384C2312yes—
478#382C2312yes—
479#382C2314yes—
480#382C2314yes—
481#382C2314yes—
482#380C2312yes—
483#380C2312yes—
484#380C2314yes—
485#380C2314yes—
486#380C2314yes—
487#380C2314yes—
488#380C2314yes—
489#380C2314yes—
490#380C2314yes—
491#380C2314yes—
492#380C2318yes—
493#380C2314yes—
494#380C2318yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2314yes—
510C4×C4⋊C4C2314yes—
511C4×C4⋊C4C2311yescharacteristic
512C4×C4⋊C4C2311yescharacteristic
513C4×C4⋊C4C2311yescharacteristic
514C4×C4⋊C4C2311yescharacteristic
515C4×C4⋊C4C2314yes—
516C4×C4⋊C4C2312yes—
517C4×C4⋊C4C2312yes—
518C4×C4⋊C4C2312yes—
519C4×C4⋊C4C2311yescharacteristic
520C4×C4⋊C4C2312yes—
521C4×C4⋊C4C2314yes—
522C4×C4⋊C4C2312yes—
523C4×C4⋊C4C2314yes—
524C4×C4⋊C4C2312yes—
525C4×C4⋊C4C2311yescharacteristic
526C4×C22⋊C4C2318yes—
527C4×C22⋊C4C2314yes—
528C4×C22⋊C4C2312yes—
529C4×C22⋊C4C2314yes—
530C4×C22⋊C4C2318yes—
531C4×C22⋊C4C2314yes—
532C4×C22⋊C4C2312yes—
533C4×C22⋊C4C2312yes—
534C4×C22⋊C4C2314yes—
535C43C2312yes—
536C43C2314yes—
537C43C2312yes—
538C43C2311yescharacteristic
539C2×#41—28no—
540C2×#41—216no—
541C2×#41—28no—
542C2×#41—216no—
543C2×#41—44no—
544C2×#41—48no—
545C22×Q8C2411yescharacteristic
546C22×Q8C2411yescharacteristic
547C22×Q8C2412yes—
548C22×Q8C2414yes—
549C22×D4C2412yes—
550C22×D4C2411yescharacteristic
551C22×D4C2412yes—
552C22×D4C2414yes—
553C22×D4C2418yes—
554C22×D4C2412yes—
555C22×D4C2412yes—
556C22×D4C2412yes—
557C22×D4C2414yes—
558C22×D4C2414yes—
559C22×D4C2418yes—
560C22×D4C2414yes—
561C22×D4C2412yes—
562C23×C4C2414yes—
563C23×C4C2414yes—
564C23×C4C2412yes—
565C23×C4C2412yes—
566C23×C4C2418yes—
567C23×C4C2414yes—
568C23×C4C2418yes—
569C23×C4C2414yes—
570C23×C4C2418yes—
571C23×C4C2412yes—
572C4⋊Q8—28no—
573C4⋊Q8—44no—
574C4⋊Q8—82no—
575C4⋊Q8C2×D418yes—
576C4⋊Q8C2×D4116yes—
577#127—216no—
578#127—28no—
579#127—24no—
580#127—44no—
581#127#4118yes—
582#126—232no—
583#126—216no—
584#126—232no—
585#126—232no—
586#125—28no—
587#125—216no—
588#125—232no—
589#125—232no—
590#125—232no—
591#125—216no—
592#125—216no—
593#125C2×D4116yes—
594#125C2×D4132yes—
595#124—28no—
596#123—216no—
597#123—232no—
598#123—232no—
599#123—232no—
600#123—232no—
601C22⋊Q8—28no—
602C22⋊Q8—216no—
603C22⋊Q8—216no—
604C22⋊Q8—216no—
605C22⋊Q8—216no—
606C22⋊Q8—216no—
607C22⋊Q8—232no—
608C22⋊Q8—232no—
609C22⋊Q8—84no—
610#121—216no—
611#121—28no—
612#121—232no—
613#121—216no—
614#121—216no—
615#121—28no—
616#121—232no—
617#121—44no—
618#121—48no—
619#121—88no—
620C4×Q8—28no—
621C4×Q8—216no—
622C4×Q8—216no—
623C4×Q8—28no—
624C4×Q8—24no—
625C4×Q8—24no—
626C4×Q8—44no—
627C4×Q8—42no—
628C4×Q8—44no—
629C4×Q8—42no—
630C4×Q8C2×D418yes—
631C4×Q8C2×D4116yes—
632C4×Q8C2×D4116yes—
633C4×Q8C2×D418yes—
634C4×D4—216no—
635C4×D4—28no—
636C4×D4—28no—
637C4×D4—216no—
638C4×D4—232no—
639C4×D4—28no—
640C4×D4—216no—
641C4×D4—232no—
642C4×D4—216no—
643C4×D4—216no—
644C4×D4—28no—
645C4×D4—216no—
646C4×D4—28no—
647C4×D4—24no—
648C4×D4—28no—
649C4×D4—24no—
650C4×D4—44no—
651C4×D4—48no—
652C4×D4—48no—
653C4×D4—42no—
654C4×D4—44no—
655C4×D4—48no—
656C4×D4—44no—
657C4×D4—48no—
658C4×D4—88no—
659C4×D4—84no—
660C4×D4—84no—
661#117—28no—
662#117—216no—
663#117—216no—
664#117—216no—
665#117—232no—
666#117—232no—
667C2×C4⋊C4—232no—
668C2×C4⋊C4—216no—
669C2×C4⋊C4—216no—
670C2×C4⋊C4—232no—
671C2×C4⋊C4—216no—
672C2×C4⋊C4C2418yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2418yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2418yes—
680C2×C4⋊C4C2418yes—
681C2×C4⋊C4C2418yes—
682C2×C4⋊C4C2418yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2412yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2418yes—
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2412yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2412yes—
693C2×C4⋊C4C2411yescharacteristic
694C2×C4⋊C4C2411yescharacteristic
695C2×C4⋊C4C2412yes—
696C2×C4⋊C4C2412yes—
697C2×C4⋊C4C2411yescharacteristic
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2412yes—
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2412yes—
702C2×C4⋊C4C2418yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2412yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2418yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2418yes—
733C2×C22⋊C4C2418yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2412yes—
736C2×C22⋊C4C2418yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2418yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2412yes—
743C2×C22⋊C4C2418yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2418yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C2414yes—
749C2×C22⋊C4C2412yes—
750C2×C22⋊C4C2418yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2418yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2418yes—
757C2×C22⋊C4C2418yes—
758C2×C22⋊C4C2414yes—
759C2×C42—216no—
760C2×C42—28no—
761C2×C42C2414yes—
762C2×C42C2412yes—
763C2×C42C2418yes—
764C2×C42C2412yes—
765C2×C42C2412yes—
766C2×C42C2412yes—
767C2×C42C2412yes—
768C2×C42C2411yescharacteristic
769C2×C42C2411yescharacteristic
770C2×C42C2412yes—
771C2×C42C2414yes—
772C2×C42C2414yes—
773C2×C42C2412yes—
774C2×C42C2411yescharacteristic
775C2×C42C2412yes—
776C2×C42C2412yes—
777C2×C42C2414yes—
778C2×C42C2412yes—
779C2×C42C2412yes—
780C2×C42C2414yes—
781C2×C42C2412yes—
782C2×C42C2414yes—
783C2×C42C2412yes—
784C2×C42C2411yescharacteristic
785C2×C42C2414yes—
786C2×C42C2412yes—
787C2×C42C2412yes—
788C2×C42C2411yescharacteristic
789C2×C42C2411yescharacteristic
790C2×C42C2411yescharacteristic
791#95C2412yes—
792#95C2414yes—
793#95C2412yes—
794#95C2414yes—
795#95C2412yes—
796#95C2414yes—
797#95C2418yes—
798#95C2414yes—
799#95C2418yes—
800#95C2418yes—
801#95C2412yes—
802#95C2412yes—
803#95C2414yes—
804#95C2412yes—
805#95C2412yes—
806#95C2414yes—
807#95C2414yes—
808#95C2412yes—
809#95C2414yes—
810#95C2412yes—
811#95C2414yes—
812#95C2418yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2418yes—
817#95C2418yes—
818#95C2418yes—
819C24C2512yes—
820C24C2514yes—
821C24C2514yes—
822#41—432no—
823#41—464no—
824C2×Q8—28no—
825C2×Q8—22no—
826C2×Q8—24no—
827C2×Q8—22no—
828C2×Q8—22no—
829C2×Q8—24no—
830C2×Q8—22no—
831C2×Q8—44no—
832C2×Q8—44no—
833C2×Q8C22×D414yes—
834C2×Q8C22×D418yes—
835C2×Q8C22×D414yes—
836C2×D4—216no—
837C2×D4—28no—
838C2×D4—28no—
839C2×D4—216no—
840C2×D4—24no—
841C2×D4—24no—
842C2×D4—28no—
843C2×D4—216no—
844C2×D4—28no—
845C2×D4—22no—
846C2×D4—24no—
847C2×D4—24no—
848C2×D4—22no—
849C2×D4—24no—
850C2×D4—24no—
851C2×D4—24no—
852C2×D4—24no—
853C2×D4—24no—
854C2×D4—24no—
855C2×D4—22no—
856C2×D4—24no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—44no—
862C2×D4—48no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—48no—
866C2×D4—48no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4C2×#4118yes—
873C2×D4C2×#4118yes—
874C2×D4C2×#4118yes—
875C22×C4—216no—
876C22×C4—28no—
877C22×C4—28no—
878C22×C4—28no—
879C22×C4—24no—
880C22×C4—24no—
881C22×C4—216no—
882C22×C4—28no—
883C22×C4—28no—
884C22×C4—24no—
885C22×C4—28no—
886C22×C4—24no—
887C22×C4—28no—
888C22×C4—24no—
889C22×C4—28no—
890C22×C4—24no—
891C22×C4—28no—
892C22×C4—24no—
893C22×C4—216no—
894C22×C4—216no—
895C22×C4—48no—
896C22×C4—44no—
897C22×C4—44no—
898C22×C4—48no—
899C22×C4—48no—
900C22×C4—42no—
901C22×C4—48no—
902C22×C4—44no—
903C22×C4—48no—
904C22×C4—42no—
905C22×C4C2512yes—
906C22×C4C2512yes—
907C22×C4C2512yes—
908C22×C4C2514yes—
909C22×C4C2512yes—
910C22×C4C2511yescharacteristic
911C22×C4C2512yes—
912C22×C4C2512yes—
913C22×C4C2514yes—
914C22×C4C2514yes—
915C22×C4C2512yes—
916C22×C4C2518yes—
917C22×C4C2512yes—
918C22×C4C2511yescharacteristic
919C22×C4C2514yes—
920C22×C4C2512yes—
921C22×C4C2512yes—
922C22×C4C2512yes—
923C22×C4C2511yescharacteristic
924C22×C4C2511yescharacteristic
925C22×C4C2511yescharacteristic
926C22×C4C2511yescharacteristic
927C22×C4C2511yescharacteristic
928C4⋊C4—216no—
929C4⋊C4—28no—
930C4⋊C4—24no—
931C4⋊C4—28no—
932C4⋊C4—28no—
933C4⋊C4—216no—
934C4⋊C4—28no—
935C4⋊C4—216no—
936C4⋊C4—216no—
937C4⋊C4—216no—
938C4⋊C4—216no—
939C4⋊C4—28no—
940C4⋊C4—24no—
941C4⋊C4—28no—
942C4⋊C4—216no—
943C4⋊C4—22no—
944C4⋊C4—24no—
945C4⋊C4—28no—
946C4⋊C4—24no—
947C4⋊C4—24no—
948C4⋊C4—22no—
949C4⋊C4—22no—
950C4⋊C4—24no—
951C4⋊C4—24no—
952C4⋊C4—22no—
953C4⋊C4—22no—
954C4⋊C4—28no—
955C4⋊C4—22no—
956C4⋊C4—22no—
957C4⋊C4—24no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—44no—
961C4⋊C4—44no—
962C4⋊C4—48no—
963C4⋊C4—44no—
964C4⋊C4—44no—
965C4⋊C4—42no—
966C4⋊C4—44no—
967C4⋊C4—42no—
968C4⋊C4—44no—
969C4⋊C4—44no—
970C4⋊C4—42no—
971C4⋊C4—44no—
972C4⋊C4C22×D414yes—
973C4⋊C4C22×D414yes—
974C4⋊C4C22×D418yes—
975C4⋊C4C22×D4116yes—
976C4⋊C4C22×D4116yes—
977C4⋊C4C22×D418yes—
978C4⋊C4C22×D418yes—
979C4⋊C4C22×D418yes—
980C4⋊C4C22×D4116yes—
981C22⋊C4—28no—
982C22⋊C4—216no—
983C22⋊C4—28no—
984C22⋊C4—28no—
985C22⋊C4—28no—
986C22⋊C4—28no—
987C22⋊C4—216no—
988C22⋊C4—28no—
989C22⋊C4—28no—
990C22⋊C4—216no—
991C22⋊C4—216no—
992C22⋊C4—216no—
993C22⋊C4—28no—
994C22⋊C4—28no—
995C22⋊C4—24no—
996C22⋊C4—28no—
997C22⋊C4—28no—
998C22⋊C4—24no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—48no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C22⋊C4—48no—
1008C22⋊C4—42no—
1009C22⋊C4—48no—
1010C22⋊C4—44no—
1011C22⋊C4—48no—
1012C22⋊C4—48no—
1013C22⋊C4—44no—
1014C22⋊C4—48no—
1015C42—24no—
1016C42—28no—
1017C42—24no—
1018C42—24no—
1019C42—28no—
1020C42—216no—
1021C42—28no—
1022C42—24no—
1023C42—24no—
1024C42—24no—
1025C42—22no—
1026C42—22no—
1027C42—24no—
1028C42—24no—
1029C42—24no—
1030C42—22no—
1031C42—42no—
1032C42—42no—
1033C42—44no—
1034C42—42no—
1035C42—42no—
1036C42—44no—
1037C42—44no—
1038C42—41no—
1039C42C22×D418yes—
1040C42C22×D414yes—
1041C42C22×D4116yes—
1042C42C22×D418yes—
1043C42C2×#4114yes—
1044C422−1+414yes—
1045C23—24no—
1046C23—24no—
1047C23—24no—
1048C23—24no—
1049C23—24no—
1050C23—24no—
1051C23—24no—
1052C23—22no—
1053C23—24no—
1054C23—22no—
1055C23—22no—
1056C23—24no—
1057C23—24no—
1058C23—22no—
1059C23—22no—
1060C23—24no—
1061C23—24no—
1062C23—22no—
1063C23—22no—
1064C23—24no—
1065C23C22×#4118yes—
1066C23C2611yescharacteristic
1067Q8—28no—
1068Q8—216no—
1069Q8—28no—
1070Q8—88no—
1071D4—216no—
1072D4—216no—
1073D4—48no—
1074D4—416no—
1075D4—432no—
1076D4—48no—
1077D4—48no—
1078D4—44no—
1079D4—48no—
1080D4—88no—
1081D4—88no—
1082D4—816no—
1083D4—88no—
1084C2×C4—24no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—21no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—24no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—21no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—28no—
1105C2×C4—24no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—22no—
1109C2×C4—24no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—24no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—22no—
1119C2×C4—21no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—24no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—24no—
1127C2×C4—22no—
1128C2×C4—28no—
1129C2×C4—22no—
1130C2×C4—24no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—24no—
1134C2×C4—28no—
1135C2×C4—22no—
1136C2×C4—416no—
1137C2×C4—432no—
1138C2×C4—48no—
1139C2×C4—416no—
1140C2×C4—416no—
1141C2×C4—48no—
1142C2×C4—88no—
1143C2×C4—816no—
1144C2×C4—816no—
1145C2×C4—84no—
1146C2×C4C23×D414yes—
1147C2×C4C23×D412yes—
1148C2×C4C23×D414yes—
1149C2×C4C23×D418yes—
1150C2×C4C23×D414yes—
1151C2×C4C23×D414yes—
1152C2×C4C23×D412yes—
1153C2×C4C23×D412yes—
1154C2×C4C22×#4112yes—
1155C2×C4C22×#4112yes—
1156C2×C4C22×#4112yes—
1157C2×C4C2×2−1+412yes—
1158C2×C4C2×2−1+412yes—
1159C2×C4C2×2−1+412yes—
1160C2×C4#58512yes—
1161C2×C4#58512yes—
1162C2×C4#58512yes—
1163C22—28no—
1164C22—28no—
1165C22—28no—
1166C22—44no—
1167C22—44no—
1168C22—44no—
1169C22—44no—
1170C22—44no—
1171C22—42no—
1172C22—44no—
1173C22—42no—
1174C22—42no—
1175C22—44no—
1176C22—42no—
1177C22—44no—
1178C22—42no—
1179C22—44no—
1180C22—44no—
1181C22—42no—
1182C22—44no—
1183C22—42no—
1184C22C24×D411yescharacteristic
1185C22C23×#4111yescharacteristic
1186C22C22×2−1+411yescharacteristic
1187C22C2×#58511yescharacteristic
1188C22C2×#58511yescharacteristic
1189C22C2×#58511yescharacteristic
1190C22H(7,𝔽2)11yescharacteristic
1191C4—22no—
1192C4—24no—
1193C4—24no—
1194C4—22no—
1195C4—24no—
1196C4—22no—
1197C4—24no—
1198C4—28no—
1199C4—42no—
1200C4—44no—
1201C4—42no—
1202C4—48no—
1203C4—42no—
1204C4—41no—
1205C4—42no—
1206C4—42no—
1207C4—44no—
1208C4—42no—
1209C4—42no—
1210C4—44no—
1211C4D4×#4114yes—
1212C4#349714yes—
1213C4#351514yescomplemented
1214C2—48no—
1215C2—84no—
1216C2—82no—
1217C2C2×D4×#4111yescharacteristic
1218C2C2×#351511yescharacteristic
1219C2C2×#349711yescharacteristic
1220C2#6292611yescharacteristic
1221C2#6299211yescharacteristic
1222C2#6300311yescharacteristic
1223C2#6303111yescharacteristic
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×#3515C2semidirect
2. #59842C2semidirect
3. #59815C2semidirect
4. #59815C2semidirect
5. #59680C2semidirect
6. #59139C2semidirect
7. #59034C2semidirect
8. #45243C2semidirect
9. #44248C2semidirect
10. #39883C2semidirect
11. #39397C2semidirect
12. #39379C2semidirect
13. #39126C2semidirect
14. #36559C2semidirect
15. #36559C2semidirect
16. #36492C2semidirect
17. #36270C2semidirect
18. #36270C2semidirect
19. #36134C2semidirect
20. D4×#125C2semidirect
21. #35772C2semidirect
22. #34934C2semidirect
23. #34934C2semidirect
24. #34313C2semidirect
25. C4×#557C2semidirect
26. C4×#550C2semidirect
202. #557D4semidirect
1213. C4#3515semidirect

Maximal subgroups

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

subgroupindex
C2×#35152
#598422
#598152
#596802
#591392
#590342
#452432
#442482
#398832
#393972
#393792
#391262
#365592
#364922
#362702
#361342
D4×#1252
#357722
#349342
#343132
C4×#5572
C4×#5502