Finite Group Databasebeta

← #7987198

Subgroups — #7987198

Order 512.

6337 conjugacy classes of subgroups.

The subgroup lattice has 1153 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3555C212yesmaximal, complemented
2#59828C211yesmaximal, characteristic, complemented
3#59428C212yesmaximal, complemented
4#59312C212yesmaximal, complemented
5#59067C212yesmaximal, complemented
6#51330C218yesmaximal, complemented
7#45993C214yesmaximal, complemented
8#45238C214yesmaximal, complemented
9#45077C214yesmaximal, complemented
10#42918C214yesmaximal, complemented
11#42879C214yesmaximal, complemented
12#39597C212yesmaximal, complemented
13#39407C214yesmaximal, complemented
14#39377C212yesmaximal
15#39353C212yesmaximal, complemented
16#38921C212yesmaximal, complemented
17#36593C212yesmaximal, complemented
18Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
19#36473C212yesmaximal, complemented
20#36180C211yesmaximal, characteristic, complemented
21#36134C211yesmaximal, characteristic, complemented
22#35275C212yesmaximal, complemented
23#35209C212yesmaximal, complemented
24#34932C211yesmaximal, characteristic
25#34929C211yesmaximal, characteristic, complemented
26C4×#556C211yesmaximal, characteristic, complemented
27#3555—232no—
28C2×#563C2218yes—
29C2×Q82C2212yes—
30C2×#557C2214yes—
31C2×#557C2212yes—
32C2×#556C2214yes—
33C2×#556C2214yes—
34C2×#556C2211yescharacteristic
35C2×#554C2212yes—
36C2×#552C2214yes—
37C2×#544C2214yes—
38C2×#542C2214yes—
39C2×#541C2214yes—
40C2×#541C2218yes—
41C2×#541C2214yes—
42C2×#533C2212yes—
43C2×#533C2212yes—
44C2×#529C2212yes—
45#2868C2211yescharacteristic
46#2868C2214yes—
47#2868C2212yes—
48#2860C2214yes—
49#2859C2214yes—
50#2857C2212yes—
51#2857C2212yes—
52#2821C2218yes—
53#2726C2214yes—
54#2722C2218yes—
55#2721C2218yes—
56#2721C2218yes—
57#2720C2218yes—
58#2719C2218yes—
59#2719C2218yes—
60#2718C2218yes—
61#2718C2218yes—
62#2713C2218yes—
63#2698C2218yes—
64#2689C2218yes—
65#2689C2218yes—
66#2680C2218yes—
67#2677C2218yes—
68#2674C2218yes—
69#2674C2218yes—
70#2664C2218yes—
71#2660C2218yes—
72#2634C2218yes—
73#2628C2214yes—
74#2625C2214yes—
75#2604C2218yes—
76#2582C2212yes—
77#2581C2214yes—
78#2567C2212yes—
79#2567C2214yes—
80#2567C2212yes—
81#2556C2214yes—
82#2553C2214yes—
83#2552C2214yes—
84#2552C2212yes—
85#2552C2212yes—
86#2552C2212yes—
87#2552C2211yescharacteristic
88#2552C2218yes—
89#2552C2214yes—
90#2552C2212yes—
91#2552C2214yes—
92#2552C2214yes—
93#2551C2211yescharacteristic
94#2551C2212yes—
95#2551C2214yes—
96#2551C2212yes—
97#2551C2214yes—
98#2551C2214yes—
99#2547C2211yescharacteristic
100#2546C2214yes—
101#2546C2212yes—
102#2546C2211yescharacteristic
103#2546C2218yes—
104#2542C2212yes—
105#2542C2211yescharacteristic
106#2542C2211yescharacteristic
107#2538C2212yes—
108#2538C2211yescharacteristic
109#2537C2211yescharacteristic
110#2521C2218yes—
111#2519C2218yes—
112#2512C2214yes—
113#2506C2212yes—
114#2506C2214yes—
115#2506C2214yes—
116#2502C2214yes—
117#2501C2214yes—
118#2496C2214yes—
119#2496C2214yes—
120#2496C2212yes—
121#2496C2214yes—
122#2492C2212yes—
123#2492C2214yes—
124#2491C2214yes—
125#2489C2214yes—
126#2489C2212yes—
127#2486C2214yes—
128#2478C2218yes—
129#2478C2218yes—
130#2462C2218yes—
131#2453C2214yes—
132#2453C2214yes—
133#2452C2212yes—
134#2447C2214yes—
135#2446C2214yes—
136#2446C2214yes—
137#2446C2214yes—
138#2441C2214yes—
139#2441C2214yes—
140#2440C2218yes—
141#2440C2214yes—
142#2440C2214yes—
143#2440C2214yes—
144#2440C2214yes—
145#2429C2214yes—
146#2429C2214yes—
147#2429C2212yes—
148#2427C2212yes—
149#2423C2214yes—
150#2423C2214yes—
151#2423C2214yes—
152#2422C2214yes—
153#2422C2212yes—
154#2415C2214yes—
155#2413C2218yes—
156#2396C2214yes—
157#2395C2214yes—
158#2373C2214yes—
159#2367C2212yes—
160#2365C2212yes—
161#2365C2211yescharacteristic
162#2365C2212yes—
163#2362C2212yes—
164#2362C2214yes—
165#2356C2212yes—
166#2355C2211yescharacteristic
167#2354C2211yescharacteristic
168#2354C2212yes—
169Q8×C4⋊C4C2214yes—
170Q8×C4⋊C4C2212yes—
171Q8×C4⋊C4C2212yes—
172Q8×C4⋊C4C2212yes—
173Q8×C4⋊C4C2212yes—
174D4×C4⋊C4C2212yes—
175D4×C4⋊C4C2212yes—
176#2347C2212yes—
177#2344C2214yes—
178#2323C2214yes—
179#2317C2214yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2212yes—
182C4×C4⋊Q8C2211yescharacteristic
183C4×C4⋊Q8C2211yescharacteristic
184C4×C4⋊Q8C2211yescharacteristic
185C4×C4⋊Q8C2214yes—
186C4×#126C2214yes—
187C4×#124C2212yes—
188C4×C22⋊Q8C2212yes—
189C4×C22⋊Q8C2212yes—
190C4×C22⋊Q8C2212yes—
191C4×#121C2212yes—
192#2293C2212yes—
193#2285C2212yes—
194C2×#384C2212yes—
195C42×Q8C2211yescharacteristic
196C42×Q8C2212yes—
197C42×D4C2211yescharacteristic
198C42×D4C2211yescharacteristic
199C4×#117C2212yes—
200#563—264no—
201Q82—216no—
202#557—216no—
203#557—232no—
204#556—232no—
205#556—232no—
206#556D4116yescomplemented
207#554—216no—
208#552—232no—
209#544—232no—
210#542—232no—
211#541—264no—
212#541—232no—
213#541—232no—
214#533—216no—
215#533—216no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2318yes—
219C2×C4⋊Q8C2312yes—
220C2×C4⋊Q8C2314yes—
221C2×C4⋊Q8C2312yes—
222C2×C4⋊Q8C2312yes—
223C2×C4⋊Q8C2318yes—
224C2×C4⋊Q8C2314yes—
225C2×C4⋊Q8C2314yes—
226C2×C4⋊Q8C2312yes—
227C2×C4⋊Q8C2314yes—
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2314yes—
230C2×C4⋊Q8C2318yes—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2311yescharacteristic
233#529—216no—
234C2×#126C2318yes—
235C2×#126C2314yes—
236C2×#126C2318yes—
237C2×#126C2318yes—
238C2×#126C2318yes—
239C2×#126C2318yes—
240C2×#126C2314yes—
241C2×#125C2318yes—
242C2×#125C2312yes—
243C2×#125C2314yes—
244C2×#125C2314yes—
245C2×#125C2318yes—
246C2×#125C2318yes—
247C2×#125C2314yes—
248C2×#125C2318yes—
249C2×#125C2318yes—
250C2×#125C2314yes—
251C2×#124C2312yes—
252C2×#124C2318yes—
253C2×#124C2312yes—
254C2×#123C2318yes—
255C2×#123C2314yes—
256C2×#123C2318yes—
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2318yes—
262C2×C22⋊Q8C2318yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2318yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2312yes—
271C2×#121C2312yes—
272C2×#121C2312yes—
273C2×C4×Q8C2314yes—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2314yes—
277C2×C4×Q8C2318yes—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2314yes—
282C2×C4×Q8C2314yes—
283C2×C4×Q8C2314yes—
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2314yes—
286C2×C4×Q8C2314yes—
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2312yes—
289C2×C4×D4C2311yescharacteristic
290C2×C4×D4C2314yes—
291C2×C4×D4C2311yescharacteristic
292C2×C4×D4C2311yescharacteristic
293C2×C4×D4C2314yes—
294C2×C4×D4C2311yescharacteristic
295C2×C4×D4C2311yescharacteristic
296C2×C4×D4C2311yescharacteristic
297C2×#117C2312yes—
298C2×#117C2314yes—
299C2×#117C2314yes—
300C2×#117C2318yes—
301C2×#117C2314yes—
302C2×#117C2312yes—
303C22×C4⋊C4C2314yes—
304C22×C4⋊C4C2314yes—
305C22×C4⋊C4C2314yes—
306C22×C42C2312yes—
307C22×C42C2312yes—
308#400C2318yes—
309#400C2318yes—
310#400C2318yes—
311#400C2318yes—
312#400C2318yes—
313#400C2314yes—
314#400C2314yes—
315#399C2318yes—
316#399C2318yes—
317#399C2314yes—
318#399C2318yes—
319#399C2314yes—
320#398C2318yes—
321#398C2318yes—
322#398C2318yes—
323#398C2318yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2318yes—
328#398C2318yes—
329#398C2318yes—
330#398C2318yes—
331#398C2318yes—
332#398C2318yes—
333#398C2318yes—
334#398C2318yes—
335#398C2318yes—
336#397C2314yes—
337#397C2318yes—
338#397C2318yes—
339#397C2318yes—
340#397C2314yes—
341#397C2314yes—
342#397C2318yes—
343#396C2314yes—
344#396C2314yes—
345#396C2318yes—
346#396C2318yes—
347#395C2318yes—
348#395C2318yes—
349#395C2318yes—
350#395C2318yes—
351#395C2318yes—
352#395C2318yes—
353#395C2314yes—
354#394C2314yes—
355#394C2314yes—
356#394C2318yes—
357#393C2314yes—
358#393C2318yes—
359#391C2312yes—
360#391C2314yes—
361#391C2312yes—
362#391C2312yes—
363#391C2314yes—
364#391C2318yes—
365#391C2314yes—
366#391C2314yes—
367#391C2312yes—
368#391C2314yes—
369#391C2314yes—
370#391C2312yes—
371#391C2312yes—
372#391C2312yes—
373#390C2312yes—
374#390C2312yes—
375#390C2314yes—
376#390C2312yes—
377#390C2312yes—
378#389C2312yes—
379#389C2312yes—
380#389C2314yes—
381#389C2312yes—
382#389C2314yes—
383#389C2318yes—
384#389C2312yes—
385#389C2314yes—
386#389C2312yes—
387#389C2314yes—
388#389C2312yes—
389#389C2312yes—
390#389C2312yes—
391#389C2312yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2318yes—
397#389C2318yes—
398#389C2312yes—
399#389C2314yes—
400#389C2314yes—
401#389C2318yes—
402#389C2314yes—
403#389C2314yes—
404#389C2314yes—
405#389C2314yes—
406#389C2312yes—
407#389C2312yes—
408#389C2314yes—
409#389C2318yes—
410#389C2314yes—
411#389C2312yes—
412#389C2318yes—
413#389C2318yes—
414#389C2318yes—
415#389C2318yes—
416#389C2312yes—
417#388C2314yes—
418#388C2314yes—
419#388C2314yes—
420#388C2318yes—
421#388C2318yes—
422#388C2314yes—
423#388C2314yes—
424#388C2318yes—
425#388C2318yes—
426#388C2318yes—
427#388C2318yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#387C2314yes—
432#387C2314yes—
433#387C2314yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2318yes—
440#387C2314yes—
441#387C2318yes—
442#387C2318yes—
443#387C2318yes—
444#387C2314yes—
445#387C2314yes—
446#386C2314yes—
447#385C2318yes—
448#385C2318yes—
449#385C2318yes—
450#385C2318yes—
451#385C2314yes—
452#385C2314yes—
453#385C2314yes—
454#384C2312yes—
455#384C2311yescharacteristic
456#384C2312yes—
457#384C2311yescharacteristic
458#384C2311yescharacteristic
459#384C2312yes—
460#384C2314yes—
461#384C2314yes—
462#384C2318yes—
463#384C2312yes—
464#384C2312yes—
465#384C2314yes—
466#384C2318yes—
467#384C2314yes—
468#384C2314yes—
469#384C2312yes—
470#384C2314yes—
471#384C2314yes—
472#384C2312yes—
473#384C2314yes—
474#383C2314yes—
475#382C2318yes—
476#382C2312yes—
477#382C2314yes—
478#381C2318yes—
479#380C2314yes—
480#380C2312yes—
481#380C2314yes—
482#380C2314yes—
483#380C2314yes—
484#380C2312yes—
485#380C2312yes—
486#380C2312yes—
487#380C2314yes—
488#380C2312yes—
489#380C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2318yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2311yescharacteristic
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2314yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2311yescharacteristic
514C4×C4⋊C4C2312yes—
515C4×C4⋊C4C2314yes—
516C4×C4⋊C4C2311yescharacteristic
517C4×C4⋊C4C2312yes—
518C4×C4⋊C4C2314yes—
519C4×C4⋊C4C2311yescharacteristic
520C4×C4⋊C4C2311yescharacteristic
521C4×C4⋊C4C2311yescharacteristic
522C4×C22⋊C4C2312yes—
523C4×C22⋊C4C2314yes—
524C4×C22⋊C4C2314yes—
525C4×C22⋊C4C2312yes—
526C4×C22⋊C4C2314yes—
527C4×C22⋊C4C2314yes—
528C4×C22⋊C4C2312yes—
529C4×C22⋊C4C2312yes—
530C4×C22⋊C4C2312yes—
531C4×C22⋊C4C2314yes—
532C4×C22⋊C4C2312yes—
533#376C2314yes—
534C43C2314yes—
535C43C2311yescharacteristic
536C43C2312yes—
537C22×Q8C2412yes—
538C22×Q8C2412yes—
539C22×Q8C2411yescharacteristic
540C22×Q8C2412yes—
541C22×Q8C2414yes—
542C22×Q8C2414yes—
543C22×Q8C2418yes—
544C22×D4C2411yescharacteristic
545C22×D4C2411yescharacteristic
546C22×D4C2414yes—
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2412yes—
551C23×C4C2412yes—
552C23×C4C2418yes—
553C23×C4C2412yes—
554C4⋊Q8—28no—
555C4⋊Q8—216no—
556C4⋊Q8—28no—
557C4⋊Q8—232no—
558C4⋊Q8—216no—
559C4⋊Q8—28no—
560C4⋊Q8—216no—
561C4⋊Q8—232no—
562C4⋊Q8—24no—
563C4⋊Q8—24no—
564C4⋊Q8—44no—
565C4⋊Q8—44no—
566C4⋊Q8—48no—
567C4⋊Q8—82no—
568C4⋊Q8—88no—
569C4⋊Q8—84no—
570C4⋊Q8C2×D418yes—
571#126—232no—
572#126—216no—
573#126—232no—
574#126—232no—
575#126—232no—
576#126—232no—
577#126C2×D4132yes—
578#125—28no—
579#125—216no—
580#125—216no—
581#125—232no—
582#125—232no—
583#125—216no—
584#125—232no—
585#125—232no—
586#125—216no—
587#125—232no—
588#124—28no—
589#124—232no—
590#124C2×D4116yes—
591#123—216no—
592#123—232no—
593#123—88no—
594C22⋊Q8—216no—
595C22⋊Q8—28no—
596C22⋊Q8—216no—
597C22⋊Q8—28no—
598C22⋊Q8—28no—
599C22⋊Q8—216no—
600C22⋊Q8—216no—
601C22⋊Q8—28no—
602C22⋊Q8—28no—
603C22⋊Q8—232no—
604C22⋊Q8—232no—
605C22⋊Q8—232no—
606C22⋊Q8—84no—
607C22⋊Q8C2×D4116yes—
608#121—28no—
609#121—44no—
610C4×Q8—216no—
611C4×Q8—216no—
612C4×Q8—216no—
613C4×Q8—216no—
614C4×Q8—216no—
615C4×Q8—24no—
616C4×Q8—28no—
617C4×Q8—28no—
618C4×Q8—28no—
619C4×Q8—216no—
620C4×Q8—232no—
621C4×Q8—216no—
622C4×Q8—24no—
623C4×Q8—28no—
624C4×Q8C2×D418yes—
625C4×Q8C2×D4116yes—
626C4×D4—216no—
627C4×D4—216no—
628C4×D4—24no—
629C4×D4—24no—
630C4×D4—24no—
631C4×D4—24no—
632C4×D4—42no—
633C4×D4C2×D418yes—
634#117—216no—
635#117—216no—
636#117—28no—
637#117—232no—
638#117—216no—
639#117C2×D4116yes—
640C2×C4⋊C4—216no—
641C2×C4⋊C4—48no—
642C2×C4⋊C4—84no—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2418yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2418yes—
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2412yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2412yes—
683C2×C4⋊C4C2412yes—
684C2×C4⋊C4C2412yes—
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2412yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2418yes—
689C2×C4⋊C4C2418yes—
690C2×C4⋊C4C2412yes—
691C2×C4⋊C4C2418yes—
692C2×C4⋊C4C2418yes—
693C2×C4⋊C4C2418yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2412yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2418yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2411yescharacteristic
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2412yes—
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2418yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2418yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2412yes—
718C2×C22⋊C4C2412yes—
719C2×C22⋊C4C2412yes—
720C2×C22⋊C4C2412yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2412yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2418yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2412yes—
731C2×C42—28no—
732C2×C42—28no—
733C2×C42C2418yes—
734C2×C42C2412yes—
735C2×C42C2414yes—
736C2×C42C2414yes—
737C2×C42C2418yes—
738C2×C42C2414yes—
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2412yes—
742C2×C42C2418yes—
743C2×C42C2412yes—
744C2×C42C2411yescharacteristic
745C2×C42C2414yes—
746C2×C42C2412yes—
747C2×C42C2412yes—
748C2×C42C2414yes—
749C2×C42C2412yes—
750C2×C42C2412yes—
751C2×C42C2412yes—
752C2×C42C2412yes—
753C2×C42C2412yes—
754C2×C42C2411yescharacteristic
755C2×C42C2414yes—
756C2×C42C2412yes—
757C2×C42C2412yes—
758C2×C42C2414yes—
759C2×C42C2411yescharacteristic
760C2×C42C2411yescharacteristic
761C2×C42C2411yescharacteristic
762#95C2412yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2412yes—
767#95C2412yes—
768#95C2412yes—
769#95C2412yes—
770#95C2412yes—
771#95C2412yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2412yes—
780#95C2412yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2418yes—
785#95C2414yes—
786#95C2414yes—
787#95C2418yes—
788#95C2418yes—
789#95C2418yes—
790#95C2414yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2418yes—
796#95C2418yes—
797#95C2418yes—
798#95C2418yes—
799#95C2418yes—
800C24C2512yes—
801C24C2512yes—
802C2×Q8—24no—
803C2×Q8—24no—
804C2×Q8—28no—
805C2×Q8—28no—
806C2×Q8—216no—
807C2×Q8—24no—
808C2×Q8—22no—
809C2×Q8—22no—
810C2×Q8—24no—
811C2×Q8—24no—
812C2×Q8—24no—
813C2×Q8—24no—
814C2×Q8—24no—
815C2×Q8—44no—
816C2×Q8—44no—
817C2×Q8—44no—
818C2×Q8—48no—
819C2×Q8—44no—
820C2×Q8—48no—
821C2×Q8C22×D414yes—
822C2×Q8C22×D418yes—
823C2×D4—28no—
824C2×D4—22no—
825C2×D4—22no—
826C2×D4—22no—
827C2×D4—22no—
828C2×D4—22no—
829C2×D4—44no—
830C2×D4—44no—
831C2×D4C22×D414yes—
832C22×C4—24no—
833C22×C4—24no—
834C22×C4—216no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—24no—
841C22×C4—24no—
842C22×C4—24no—
843C22×C4—24no—
844C22×C4—24no—
845C22×C4—24no—
846C22×C4—24no—
847C22×C4—42no—
848C22×C4—48no—
849C22×C4—48no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4C22×D418yes—
853C22×C4C2512yes—
854C22×C4C2511yescharacteristic
855C22×C4C2514yes—
856C22×C4C2512yes—
857C22×C4C2512yes—
858C22×C4C2514yes—
859C22×C4C2514yes—
860C22×C4C2512yes—
861C22×C4C2514yes—
862C22×C4C2512yes—
863C22×C4C2518yes—
864C22×C4C2514yes—
865C22×C4C2514yes—
866C22×C4C2512yes—
867C22×C4C2512yes—
868C22×C4C2512yes—
869C22×C4C2511yescharacteristic
870C22×C4C2511yescharacteristic
871C22×C4C2512yes—
872C22×C4C2512yes—
873C22×C4C2511yescharacteristic
874C22×C4C2511yescharacteristic
875C22×C4C2511yescharacteristic
876C22×C4C2511yescharacteristic
877C4⋊C4—24no—
878C4⋊C4—28no—
879C4⋊C4—216no—
880C4⋊C4—28no—
881C4⋊C4—28no—
882C4⋊C4—28no—
883C4⋊C4—216no—
884C4⋊C4—28no—
885C4⋊C4—28no—
886C4⋊C4—28no—
887C4⋊C4—28no—
888C4⋊C4—24no—
889C4⋊C4—28no—
890C4⋊C4—28no—
891C4⋊C4—216no—
892C4⋊C4—216no—
893C4⋊C4—216no—
894C4⋊C4—216no—
895C4⋊C4—28no—
896C4⋊C4—216no—
897C4⋊C4—28no—
898C4⋊C4—216no—
899C4⋊C4—216no—
900C4⋊C4—24no—
901C4⋊C4—22no—
902C4⋊C4—22no—
903C4⋊C4—22no—
904C4⋊C4—24no—
905C4⋊C4—24no—
906C4⋊C4—28no—
907C4⋊C4—28no—
908C4⋊C4—22no—
909C4⋊C4—24no—
910C4⋊C4—28no—
911C4⋊C4—28no—
912C4⋊C4—24no—
913C4⋊C4—24no—
914C4⋊C4—24no—
915C4⋊C4—24no—
916C4⋊C4—24no—
917C4⋊C4—28no—
918C4⋊C4—22no—
919C4⋊C4—24no—
920C4⋊C4—48no—
921C4⋊C4—42no—
922C4⋊C4—48no—
923C4⋊C4—44no—
924C4⋊C4—42no—
925C4⋊C4—48no—
926C4⋊C4—48no—
927C4⋊C4—48no—
928C4⋊C4—44no—
929C4⋊C4—48no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—42no—
933C4⋊C4—44no—
934C4⋊C4C22×D418yes—
935C4⋊C4C22×D414yes—
936C4⋊C4C22×D414yes—
937C4⋊C4C22×D418yes—
938C4⋊C4C22×D418yes—
939C4⋊C4C22×D4116yes—
940C4⋊C42−1+414yes—
941C4⋊C42−1+414yes—
942C22⋊C4—28no—
943C22⋊C4—28no—
944C22⋊C4—28no—
945C22⋊C4—216no—
946C22⋊C4—28no—
947C22⋊C4—216no—
948C22⋊C4—28no—
949C22⋊C4—28no—
950C22⋊C4—28no—
951C22⋊C4—24no—
952C22⋊C4—24no—
953C22⋊C4—24no—
954C22⋊C4—24no—
955C22⋊C4—28no—
956C22⋊C4—28no—
957C22⋊C4—42no—
958C22⋊C4—44no—
959C22⋊C4—48no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4C22×D4116yes—
963C22⋊C4C22×D4116yes—
964C22⋊C4C22×D418yes—
965C42—24no—
966C42—24no—
967C42—24no—
968C42—216no—
969C42—28no—
970C42—28no—
971C42—216no—
972C42—216no—
973C42—24no—
974C42—24no—
975C42—24no—
976C42—28no—
977C42—22no—
978C42—24no—
979C42—28no—
980C42—24no—
981C42—22no—
982C42—28no—
983C42—24no—
984C42—22no—
985C42—24no—
986C42—42no—
987C42—41no—
988C42—44no—
989C42C22×D414yes—
990C42C22×D418yes—
991C42C22×D4116yes—
992C422−1+414yes—
993C422−1+414yes—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23C23×D414yes—
1008C23C2611yescharacteristic
1009Q8—28no—
1010Q8—216no—
1011Q8—48no—
1012Q8—48no—
1013Q8—88no—
1014Q8—88no—
1015Q8—816no—
1016D4—28no—
1017D4—44no—
1018D4—88no—
1019C2×C4—22no—
1020C2×C4—21no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—24no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—21no—
1029C2×C4—22no—
1030C2×C4—21no—
1031C2×C4—22no—
1032C2×C4—21no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—216no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—28no—
1045C2×C4—24no—
1046C2×C4—22no—
1047C2×C4—21no—
1048C2×C4—24no—
1049C2×C4—21no—
1050C2×C4—24no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—21no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—28no—
1068C2×C4—22no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—28no—
1072C2×C4—22no—
1073C2×C4—24no—
1074C2×C4—48no—
1075C2×C4—48no—
1076C2×C4—48no—
1077C2×C4—48no—
1078C2×C4—84no—
1079C2×C4—816no—
1080C2×C4C23×D418yes—
1081C2×C4C23×D414yes—
1082C2×C4C23×D412yes—
1083C2×C4C23×D414yes—
1084C2×C4C23×D414yes—
1085C2×C4C23×D412yes—
1086C2×C4C23×D412yes—
1087C2×C4C2×2−1+414yes—
1088C2×C4C2×2−1+412yes—
1089C2×C4C2×2−1+414yes—
1090C2×C4C2×2−1+412yes—
1091C2×C4C2×2−1+412yes—
1092C2×C4C2×2−1+412yes—
1093C2×C4C2×2−1+412yes—
1094C2×C4C2×2−1+412yes—
1095C2×C4C2×2−1+412yes—
1096C2×C4C2×2−1+412yes—
1097C2×C4#58512yes—
1098C22—24no—
1099C22—24no—
1100C22—24no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22C24×D411yescharacteristic
1113C22C22×2−1+411yescharacteristic
1114C22C22×2−1+411yescharacteristic
1115C22C22×2−1+411yescharacteristic
1116C22C22×2−1+411yescharacteristic
1117C22C2×#58511yescharacteristic
1118C22H(7,𝔽2)11yescharacteristic
1119C4—22no—
1120C4—24no—
1121C4—24no—
1122C4—24no—
1123C4—24no—
1124C4—28no—
1125C4—22no—
1126C4—22no—
1127C4—24no—
1128C4—44no—
1129C4—42no—
1130C4—48no—
1131C4—44no—
1132C4—42no—
1133C4—41no—
1134C4—42no—
1135C4—42no—
1136C4—44no—
1137C4—44no—
1138C4—44no—
1139C4—42no—
1140C4#349914yes—
1141C4#349914yes—
1142C4#355514yescomplemented
1143C2—44no—
1144C2—82no—
1145C2C2×#355511yescharacteristic
1146C2C2×#349911yescharacteristic
1147C2C2×#349911yescharacteristic
1148C2#6294311yescharacteristic
1149C2#6294511yescharacteristic
1150C2#6300311yescharacteristic
1151C2#6303211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2537C22
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×#3555C2semidirect
2. #59828C2semidirect
3. #59428C2semidirect
4. #59312C2semidirect
5. #59067C2semidirect
6. #51330C2semidirect
7. #45993C2semidirect
8. #45238C2semidirect
9. #45077C2semidirect
10. #42918C2semidirect
11. #42879C2semidirect
12. #39597C2semidirect
13. #39407C2semidirect
15. #39353C2semidirect
16. #38921C2semidirect
17. #36593C2semidirect
18. Q8×C4⋊Q8C2semidirect
19. #36473C2semidirect
20. #36180C2semidirect
21. #36134C2semidirect
22. #35275C2semidirect
23. #35209C2semidirect
25. #34929C2semidirect
26. C4×#556C2semidirect
206. #556D4semidirect
1142. C4#3555semidirect

Maximal subgroups

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

subgroupindex
C2×#35552
#598282
#594282
#593122
#590672
#513302
#459932
#452382
#450772
#429182
#428792
#395972
#394072
#393772
#393532
#389212
#365932
Q8×C4⋊Q82
#364732
#361802
#361342
#352752
#352092
#349322
#349292
C4×#5562