Finite Group Databasebeta

← #7677556

Subgroups — #7677556

Order 512.

6902 conjugacy classes of subgroups.

The subgroup lattice has 1227 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3507C212yesmaximal, complemented
2#59828C212yesmaximal, complemented
3#59821C212yesmaximal, complemented
4#59641C212yesmaximal, complemented
5#59428C212yesmaximal, complemented
6#59314C212yesmaximal, complemented
7#59312C212yesmaximal, complemented
8#59258C212yesmaximal, complemented
9#59244C212yesmaximal, complemented
10#45394C214yesmaximal, complemented
11#45261C214yesmaximal, complemented
12#44964C214yesmaximal, complemented
13#44921C214yesmaximal, complemented
14#39348C214yesmaximal, complemented
15#37790C218yesmaximal, complemented
16#36118C214yesmaximal, complemented
17#35519C212yesmaximal, complemented
18#35517C212yesmaximal, complemented
19#35182C212yesmaximal, complemented
20#35178C211yesmaximal, characteristic, complemented
21#34938C211yesmaximal, characteristic, complemented
22#34937C211yesmaximal, characteristic
23#34207C211yesmaximal, characteristic, complemented
24#34183C211yesmaximal, characteristic, complemented
25C2×Q8×C4⋊C4C211yesmaximal, characteristic, complemented
26C4×#536C211yesmaximal, characteristic, complemented
27#3507—232no—
28C2×#559C2214yes—
29C2×#557C2214yes—
30C2×#556C2214yes—
31C2×#556C2214yes—
32C2×#556C2214yes—
33C2×#554C2214yes—
34C2×#552C2214yes—
35C2×#552C2214yes—
36C2×#539C2218yes—
37C2×#536C2212yes—
38C2×#536C2211yescharacteristic
39C2×#533C2212yes—
40C2×#532C2212yes—
41C2×#532C2211yescharacteristic
42C2×#529C2218yes—
43C2×#520C2212yes—
44C2×#520C2212yes—
45C2×C4×#41C2211yescharacteristic
46C22×C4×Q8C2211yescharacteristic
47C22×C4×Q8C2212yes—
48#2854C2214yes—
49#2853C2218yes—
50#2727C2218yes—
51#2726C2218yes—
52#2721C2218yes—
53#2721C2218yes—
54#2720C2218yes—
55#2720C2218yes—
56#2718C2218yes—
57#2715C2218yes—
58#2710C2218yes—
59#2695C2218yes—
60#2689C2218yes—
61#2680C2218yes—
62#2623C2218yes—
63#2618C2214yes—
64#2582C2214yes—
65#2581C2214yes—
66#2580C2214yes—
67#2552C2211yescharacteristic
68#2552C2211yescharacteristic
69#2552C2214yes—
70#2551C2211yescharacteristic
71#2551C2211yescharacteristic
72#2550C2212yes—
73#2550C2212yes—
74#2549C2214yes—
75#2548C2212yes—
76#2548C2211yescharacteristic
77#2547C2211yescharacteristic
78#2546C2212yes—
79#2546C2211yescharacteristic
80#2545C2212yes—
81#2545C2214yes—
82#2544C2212yes—
83#2543C2214yes—
84#2542C2214yes—
85#2541C2211yescharacteristic
86#2538C2212yes—
87#2538C2212yes—
88#2538C2214yes—
89#2536C2214yes—
90#2512C2214yes—
91#2512C2214yes—
92#2506C2214yes—
93#2506C2214yes—
94#2501C2214yes—
95#2496C2214yes—
96#2496C2214yes—
97#2491C2214yes—
98#2487C2214yes—
99#2486C2214yes—
100#2485C2214yes—
101#2485C2214yes—
102#2478C2218yes—
103#2475C2218yes—
104#2475C2218yes—
105#2474C2218yes—
106#2469C2218yes—
107#2469C2218yes—
108#2468C2218yes—
109#2455C2218yes—
110#2453C2218yes—
111#2450C2218yes—
112#2449C2218yes—
113#2449C2218yes—
114#2448C2214yes—
115#2448C2214yes—
116#2448C2214yes—
117#2447C2214yes—
118#2446C2214yes—
119#2446C2214yes—
120#2446C2214yes—
121#2445C2214yes—
122#2444C2218yes—
123#2443C2218yes—
124#2442C2214yes—
125#2441C2214yes—
126#2440C2212yes—
127#2440C2214yes—
128#2440C2214yes—
129#2440C2212yes—
130#2439C2214yes—
131#2423C2214yes—
132#2423C2214yes—
133#2422C2214yes—
134#2421C2214yes—
135#2421C2214yes—
136#2416C2212yes—
137#2416C2212yes—
138#2415C2218yes—
139#2413C2218yes—
140#2399C2214yes—
141#2392C2214yes—
142#2365C2214yes—
143#2361C2214yes—
144#2361C2214yes—
145#2361C2214yes—
146#2354C2214yes—
147#2354C2212yes—
148#2354C2212yes—
149Q8×C4⋊C4C2212yes—
150Q8×C4⋊C4C2214yes—
151Q8×C4⋊C4C2212yes—
152Q8×C4⋊C4C2214yes—
153Q8×C4⋊C4C2212yes—
154Q8×C4⋊C4C2212yes—
155Q8×C4⋊C4C2212yes—
156Q8×C4⋊C4C2212yes—
157D4×C4⋊C4C2214yes—
158D4×C4⋊C4C2212yes—
159D4×C4⋊C4C2212yes—
160D4×C4⋊C4C2212yes—
161D4×C4⋊C4C2214yes—
162D4×C4⋊C4C2212yes—
163#2344C2214yes—
164#2327C2212yes—
165#2326C2212yes—
166#2326C2214yes—
167#2323C2212yes—
168#2323C2212yes—
169#2322C2214yes—
170#2317C2211yescharacteristic
171#2317C2212yes—
172#2317C2214yes—
173#2311C2211yescharacteristic
174#2311C2212yes—
175#2311C2212yes—
176#2310C2211yescharacteristic
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2212yes—
181C4×#127C2212yes—
182C4×#124C2212yes—
183C4×C22⋊Q8C2212yes—
184C4×C22⋊Q8C2212yes—
185C4×#123C2214yes—
186C4×#121C2212yes—
187C4×#121C2212yes—
188#2297C2212yes—
189#2296C2212yes—
190C2×#389C2214yes—
191C2×#389C2212yes—
192#2285C2211yescharacteristic
193#2285C2212yes—
194C2×#384C2211yescharacteristic
195C2×#384C2212yes—
196C2×#384C2212yes—
197C4×#117C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199C2×C4×C4⋊C4C2211yescharacteristic
200C22×#41C2312yes—
201C22×#41C2311yescharacteristic
202C23×Q8C2311yescharacteristic
203#559—232no—
204#557—232no—
205#556—232no—
206#556—232no—
207#556—232no—
208#554—232no—
209#552—232no—
210#552—232no—
211#539—264no—
212#536—216no—
213#536D4116yescomplemented
214#533—216no—
215#532—216no—
216#532—28no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2312yes—
219C2×C4⋊Q8C2312yes—
220C2×C4⋊Q8C2312yes—
221C2×C4⋊Q8C2312yes—
222C2×C4⋊Q8C2314yes—
223C2×C4⋊Q8C2312yes—
224C2×C4⋊Q8C2312yes—
225C2×#127C2311yescharacteristic
226C2×#127C2312yes—
227#529—264no—
228C2×#126C2318yes—
229C2×#126C2318yes—
230C2×#126C2318yes—
231C2×#126C2318yes—
232C2×#125C2318yes—
233C2×#125C2312yes—
234C2×#125C2312yes—
235C2×#125C2318yes—
236C2×#125C2318yes—
237C2×#124C2312yes—
238C2×#124C2318yes—
239C2×#124C2312yes—
240C2×#124C2312yes—
241C2×#124C2314yes—
242C2×#124C2312yes—
243C2×#123C2318yes—
244C2×#123C2318yes—
245C2×#123C2318yes—
246C2×#123C2318yes—
247C2×#123C2314yes—
248C2×C22⋊Q8C2318yes—
249C2×C22⋊Q8C2314yes—
250C2×C22⋊Q8C2314yes—
251C2×C22⋊Q8C2314yes—
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2318yes—
254C2×C22⋊Q8C2318yes—
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2312yes—
257C2×#121C2312yes—
258C2×#121C2312yes—
259C2×#121C2312yes—
260C2×#121C2314yes—
261C2×#121C2314yes—
262C2×#121C2312yes—
263#520—216no—
264#520—216no—
265C4×#41—28no—
266C2×C4×Q8—216no—
267C2×C4×Q8—28no—
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2314yes—
270C2×C4×Q8C2314yes—
271C2×C4×Q8C2314yes—
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2312yes—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2314yes—
277C2×C4×Q8C2314yes—
278C2×C4×Q8C2314yes—
279C2×C4×Q8C2314yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2314yes—
282C2×C4×Q8C2318yes—
283C2×C4×D4C2314yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2311yescharacteristic
286C2×C4×D4C2312yes—
287C2×C4×D4C2311yescharacteristic
288C2×C4×D4C2318yes—
289C2×C4×D4C2314yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2312yes—
292C2×C4×D4C2318yes—
293C2×C4×D4C2318yes—
294C2×C4×D4C2314yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2314yes—
297C2×C4×D4C2314yes—
298C2×#117C2311yescharacteristic
299C2×#117C2311yescharacteristic
300C2×#117C2312yes—
301C2×#117C2312yes—
302C2×#117C2314yes—
303C2×#117C2318yes—
304C2×#117C2314yes—
305C2×#117C2318yes—
306C2×#117C2311yescharacteristic
307C22×C4⋊C4C2311yescharacteristic
308C22×C4⋊C4C2312yes—
309C22×C4⋊C4C2314yes—
310C22×C4⋊C4C2312yes—
311C22×C4⋊C4C2314yes—
312C22×C4⋊C4C2314yes—
313C22×C4⋊C4C2311yescharacteristic
314C22×C4⋊C4C2314yes—
315C22×C4⋊C4C2312yes—
316C22×C4⋊C4C2311yescharacteristic
317C22×C4⋊C4C2312yes—
318C22×C4⋊C4C2314yes—
319C22×C4⋊C4C2314yes—
320C22×C42C2314yes—
321C22×C42C2312yes—
322C22×C42C2312yes—
323C22×C42C2312yes—
324C22×C42C2311yescharacteristic
325#400C2318yes—
326#400C2318yes—
327#400C2318yes—
328#400C2318yes—
329#399C2318yes—
330#399C2318yes—
331#399C2318yes—
332#399C2318yes—
333#398C2318yes—
334#398C2318yes—
335#398C2318yes—
336#398C2318yes—
337#398C2318yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2318yes—
344#397C2318yes—
345#397C2318yes—
346#397C2314yes—
347#397C2318yes—
348#397C2318yes—
349#397C2318yes—
350#396C2318yes—
351#396C2318yes—
352#396C2314yes—
353#396C2314yes—
354#396C2318yes—
355#396C2318yes—
356#395C2318yes—
357#395C2314yes—
358#395C2314yes—
359#395C2314yes—
360#395C2314yes—
361#394C2318yes—
362#394C2314yes—
363#394C2314yes—
364#394C2314yes—
365#394C2318yes—
366#394C2318yes—
367#393C2318yes—
368#392C2314yes—
369#391C2312yes—
370#391C2314yes—
371#391C2312yes—
372#391C2314yes—
373#391C2314yes—
374#391C2312yes—
375#391C2312yes—
376#391C2312yes—
377#391C2314yes—
378#391C2312yes—
379#391C2312yes—
380#391C2318yes—
381#390C2314yes—
382#390C2314yes—
383#390C2314yes—
384#390C2314yes—
385#390C2312yes—
386#390C2312yes—
387#390C2314yes—
388#390C2314yes—
389#390C2312yes—
390#390C2312yes—
391#390C2312yes—
392#389C2314yes—
393#389C2314yes—
394#389C2312yes—
395#389C2314yes—
396#389C2314yes—
397#389C2312yes—
398#389C2312yes—
399#389C2312yes—
400#389C2314yes—
401#389C2314yes—
402#389C2312yes—
403#389C2312yes—
404#389C2314yes—
405#389C2314yes—
406#389C2318yes—
407#389C2318yes—
408#389C2314yes—
409#389C2314yes—
410#389C2318yes—
411#389C2314yes—
412#389C2314yes—
413#389C2318yes—
414#389C2318yes—
415#389C2314yes—
416#389C2314yes—
417#389C2318yes—
418#389C2318yes—
419#389C2312yes—
420#389C2312yes—
421#389C2312yes—
422#389C2312yes—
423#389C2312yes—
424#389C2312yes—
425#388C2314yes—
426#388C2314yes—
427#388C2314yes—
428#388C2314yes—
429#388C2318yes—
430#388C2318yes—
431#388C2318yes—
432#388C2318yes—
433#388C2318yes—
434#388C2318yes—
435#388C2318yes—
436#388C2318yes—
437#388C2318yes—
438#388C2318yes—
439#388C2314yes—
440#388C2314yes—
441#387C2314yes—
442#387C2314yes—
443#387C2314yes—
444#387C2314yes—
445#387C2318yes—
446#387C2318yes—
447#387C2318yes—
448#387C2318yes—
449#387C2318yes—
450#387C2318yes—
451#387C2318yes—
452#387C2318yes—
453#386C2314yes—
454#386C2318yes—
455#386C2318yes—
456#386C2314yes—
457#386C2318yes—
458#386C2314yes—
459#386C2314yes—
460#386C2314yes—
461#385C2314yes—
462#385C2318yes—
463#385C2318yes—
464#385C2318yes—
465#385C2314yes—
466#385C2314yes—
467#385C2318yes—
468#385C2318yes—
469#385C2318yes—
470#385C2318yes—
471#385C2314yes—
472#385C2314yes—
473#385C2318yes—
474#384C2312yes—
475#384C2312yes—
476#384C2312yes—
477#384C2312yes—
478#384C2312yes—
479#384C2314yes—
480#384C2312yes—
481#384C2312yes—
482#384C2314yes—
483#384C2314yes—
484#384C2314yes—
485#384C2318yes—
486#384C2314yes—
487#384C2311yescharacteristic
488#384C2311yescharacteristic
489#382C2314yes—
490#382C2312yes—
491#382C2312yes—
492#381C2314yes—
493#381C2318yes—
494#380C2312yes—
495#380C2312yes—
496#380C2314yes—
497#380C2314yes—
498#380C2314yes—
499#380C2314yes—
500#380C2312yes—
501#380C2312yes—
502#380C2312yes—
503#380C2314yes—
504#380C2314yes—
505#380C2318yes—
506#380C2312yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2311yescharacteristic
509C4×C4⋊C4C2311yescharacteristic
510C4×C4⋊C4C2314yes—
511C4×C4⋊C4C2314yes—
512C4×C4⋊C4C2314yes—
513C4×C4⋊C4C2314yes—
514C4×C4⋊C4C2314yes—
515C4×C4⋊C4C2314yes—
516C4×C4⋊C4C2311yescharacteristic
517C4×C4⋊C4C2311yescharacteristic
518C4×C4⋊C4C2314yes—
519C4×C4⋊C4C2311yescharacteristic
520C4×C4⋊C4C2314yes—
521C4×C4⋊C4C2312yes—
522C4×C4⋊C4C2314yes—
523C4×C4⋊C4C2314yes—
524C4×C4⋊C4C2312yes—
525C4×C4⋊C4C2312yes—
526C4×C4⋊C4C2318yes—
527C4×C4⋊C4C2311yescharacteristic
528C4×C4⋊C4C2311yescharacteristic
529C4×C4⋊C4C2311yescharacteristic
530C4×C22⋊C4C2312yes—
531C4×C22⋊C4C2314yes—
532C4×C22⋊C4C2312yes—
533C4×C22⋊C4C2314yes—
534C4×C22⋊C4C2314yes—
535C4×C22⋊C4C2314yes—
536#376C2312yes—
537C2×#95C2314yes—
538C2×#95C2312yes—
539C43C2312yes—
540C2×#41—28no—
541C2×#41—24no—
542C2×#41—28no—
543C2×#41—24no—
544C2×#41—28no—
545C2×#41C2×D418yes—
546C22×Q8—24no—
547C22×Q8—24no—
548C22×Q8C2×D418yes—
549C22×Q8C2412yes—
550C22×Q8C2414yes—
551C22×Q8C2412yes—
552C22×Q8C2412yes—
553C22×Q8C2411yescharacteristic
554C22×Q8C2414yes—
555C22×D4C2412yes—
556C22×D4C2414yes—
557C22×D4C2412yes—
558C22×D4C2414yes—
559C22×D4C2412yes—
560C22×D4C2411yescharacteristic
561C22×D4C2412yes—
562C22×D4C2414yes—
563C23×C4C2412yes—
564C23×C4C2414yes—
565C23×C4C2412yes—
566C23×C4C2412yes—
567C23×C4C2412yes—
568C23×C4C2411yescharacteristic
569C23×C4C2414yes—
570C23×C4C2412yes—
571C23×C4C2412yes—
572C23×C4C2418yes—
573C23×C4C2412yes—
574C23×C4C2418yes—
575C23×C4C2411yescharacteristic
576C23×C4C2411yescharacteristic
577C4⋊Q8—28no—
578C4⋊Q8—216no—
579C4⋊Q8—28no—
580C4⋊Q8—28no—
581C4⋊Q8—28no—
582C4⋊Q8—24no—
583C4⋊Q8—44no—
584C4⋊Q8C2×D4116yes—
585#127—28no—
586#127—24no—
587#126—232no—
588#126—232no—
589#126—232no—
590#126—232no—
591#125—232no—
592#125—28no—
593#125—28no—
594#125—232no—
595#125—232no—
596#124—28no—
597#124—216no—
598#124—28no—
599#124—232no—
600#124—28no—
601#124C2×D4116yes—
602#123—232no—
603#123—232no—
604#123—232no—
605#123—88no—
606#123C2×D4132yes—
607C22⋊Q8—216no—
608C22⋊Q8—216no—
609C22⋊Q8—232no—
610C22⋊Q8—216no—
611C22⋊Q8—216no—
612C22⋊Q8—232no—
613C22⋊Q8—88no—
614C22⋊Q8C2×D4116yes—
615C22⋊Q8C2×D4116yes—
616#121—216no—
617#121—216no—
618#121—28no—
619#121—28no—
620#121—28no—
621#121—44no—
622C4×Q8—216no—
623C4×Q8—216no—
624C4×Q8—216no—
625C4×Q8—216no—
626C4×Q8—216no—
627C4×Q8—232no—
628C4×Q8—216no—
629C4×Q8—216no—
630C4×Q8—216no—
631C4×Q8—28no—
632C4×Q8—28no—
633C4×Q8—28no—
634C4×Q8—28no—
635C4×Q8—24no—
636C4×Q8—24no—
637C4×D4—232no—
638C4×D4—216no—
639C4×D4—216no—
640C4×D4—216no—
641C4×D4—28no—
642C4×D4—28no—
643C4×D4—232no—
644C4×D4—232no—
645C4×D4—216no—
646C4×D4—24no—
647C4×D4—24no—
648C4×D4—28no—
649C4×D4—28no—
650C4×D4—48no—
651C4×D4—84no—
652#117—28no—
653#117—216no—
654#117—24no—
655#117—24no—
656#117—216no—
657#117—232no—
658#117—232no—
659#117—28no—
660#117C2×D418yes—
661C2×C4⋊C4—28no—
662C2×C4⋊C4—216no—
663C2×C4⋊C4—216no—
664C2×C4⋊C4—28no—
665C2×C4⋊C4—24no—
666C2×C4⋊C4—216no—
667C2×C4⋊C4—24no—
668C2×C4⋊C4—44no—
669C2×C4⋊C4—48no—
670C2×C4⋊C4—42no—
671C2×C4⋊C4—82no—
672C2×C4⋊C4—84no—
673C2×C4⋊C4—84no—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2418yes—
680C2×C4⋊C4C2418yes—
681C2×C4⋊C4C2418yes—
682C2×C4⋊C4C2418yes—
683C2×C4⋊C4C2412yes—
684C2×C4⋊C4C2412yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2412yes—
691C2×C4⋊C4C2412yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2411yescharacteristic
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2412yes—
697C2×C4⋊C4C2412yes—
698C2×C4⋊C4C2418yes—
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2418yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2418yes—
716C2×C4⋊C4C2418yes—
717C2×C4⋊C4C2418yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2418yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2411yescharacteristic
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2418yes—
736C2×C22⋊C4C2418yes—
737C2×C22⋊C4C2412yes—
738C2×C22⋊C4C2412yes—
739C2×C22⋊C4C2412yes—
740C2×C22⋊C4C2418yes—
741C2×C22⋊C4C2412yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2418yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C2418yes—
749C2×C22⋊C4C2418yes—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2418yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2418yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2412yes—
759C2×C22⋊C4C2414yes—
760C2×C42—216no—
761C2×C42—28no—
762C2×C42—28no—
763C2×C42—28no—
764C2×C42#4118yes—
765C2×C42C2418yes—
766C2×C42C2418yes—
767C2×C42C2418yes—
768C2×C42C2412yes—
769C2×C42C2414yes—
770C2×C42C2412yes—
771C2×C42C2412yes—
772C2×C42C2412yes—
773C2×C42C2412yes—
774C2×C42C2418yes—
775C2×C42C2412yes—
776C2×C42C2412yes—
777C2×C42C2412yes—
778C2×C42C2412yes—
779C2×C42C2414yes—
780C2×C42C2414yes—
781C2×C42C2412yes—
782C2×C42C2412yes—
783C2×C42C2412yes—
784C2×C42C2412yes—
785C2×C42C2411yescharacteristic
786C2×C42C2411yescharacteristic
787C2×C42C2411yescharacteristic
788C2×C42C2411yescharacteristic
789#95C2418yes—
790#95C2418yes—
791#95C2412yes—
792#95C2412yes—
793#95C2412yes—
794#95C2412yes—
795#95C2412yes—
796#95C2412yes—
797#95C2412yes—
798#95C2412yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2418yes—
808#95C2418yes—
809#95C2418yes—
810#95C2414yes—
811#95C2414yes—
812#95C2418yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2418yes—
822#95C2418yes—
823C24C2514yes—
824C24C2512yes—
825C24C2511yescharacteristic
826#41—232no—
827#41—432no—
828C2×Q8—232no—
829C2×Q8—28no—
830C2×Q8—24no—
831C2×Q8—28no—
832C2×Q8—24no—
833C2×Q8—24no—
834C2×Q8—22no—
835C2×Q8—24no—
836C2×Q8—24no—
837C2×Q8—24no—
838C2×Q8—22no—
839C2×Q8—28no—
840C2×Q8—24no—
841C2×Q8—44no—
842C2×Q8—44no—
843C2×Q8—44no—
844C2×Q8C22×D418yes—
845C2×Q8C22×D418yes—
846C2×Q8C22×D414yes—
847C2×D4—24no—
848C2×D4—24no—
849C2×D4—28no—
850C2×D4—28no—
851C2×D4—28no—
852C2×D4—28no—
853C2×D4—28no—
854C2×D4—24no—
855C2×D4—22no—
856C2×D4—24no—
857C2×D4—24no—
858C2×D4—24no—
859C2×D4—22no—
860C2×D4—28no—
861C2×D4—24no—
862C2×D4—24no—
863C2×D4—24no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4C22×D418yes—
870C2×D4C22×D414yes—
871C22×C4—24no—
872C22×C4—24no—
873C22×C4—24no—
874C22×C4—22no—
875C22×C4—24no—
876C22×C4—22no—
877C22×C4—24no—
878C22×C4—24no—
879C22×C4—28no—
880C22×C4—24no—
881C22×C4—216no—
882C22×C4—28no—
883C22×C4—24no—
884C22×C4—24no—
885C22×C4—28no—
886C22×C4—24no—
887C22×C4—24no—
888C22×C4—28no—
889C22×C4—24no—
890C22×C4—216no—
891C22×C4—41no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—41no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—44no—
900C22×C4—48no—
901C22×C4—42no—
902C22×C4—44no—
903C22×C4—48no—
904C22×C4—48no—
905C22×C4—48no—
906C22×C4C22×D418yes—
907C22×C4C22×D418yes—
908C22×C4C22×D414yes—
909C22×C4C2×#4114yes—
910C22×C4C2×#4114yes—
911C22×C4C2×#4114yes—
912C22×C42−1+414yes—
913C22×C4C2512yes—
914C22×C4C2512yes—
915C22×C4C2512yes—
916C22×C4C2512yes—
917C22×C4C2514yes—
918C22×C4C2514yes—
919C22×C4C2512yes—
920C22×C4C2514yes—
921C22×C4C2518yes—
922C22×C4C2512yes—
923C22×C4C2512yes—
924C22×C4C2514yes—
925C22×C4C2512yes—
926C22×C4C2514yes—
927C22×C4C2512yes—
928C22×C4C2512yes—
929C22×C4C2511yescharacteristic
930C22×C4C2511yescharacteristic
931C22×C4C2511yescharacteristic
932C22×C4C2512yes—
933C22×C4C2511yescharacteristic
934C22×C4C2511yescharacteristic
935C22×C4C2511yescharacteristic
936C4⋊C4—28no—
937C4⋊C4—24no—
938C4⋊C4—28no—
939C4⋊C4—216no—
940C4⋊C4—216no—
941C4⋊C4—216no—
942C4⋊C4—216no—
943C4⋊C4—24no—
944C4⋊C4—28no—
945C4⋊C4—28no—
946C4⋊C4—216no—
947C4⋊C4—28no—
948C4⋊C4—28no—
949C4⋊C4—28no—
950C4⋊C4—28no—
951C4⋊C4—28no—
952C4⋊C4—216no—
953C4⋊C4—28no—
954C4⋊C4—28no—
955C4⋊C4—28no—
956C4⋊C4—24no—
957C4⋊C4—24no—
958C4⋊C4—24no—
959C4⋊C4—24no—
960C4⋊C4—22no—
961C4⋊C4—22no—
962C4⋊C4—24no—
963C4⋊C4—24no—
964C4⋊C4—24no—
965C4⋊C4—22no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—28no—
969C4⋊C4—24no—
970C4⋊C4—28no—
971C4⋊C4—24no—
972C4⋊C4—22no—
973C4⋊C4—22no—
974C4⋊C4—42no—
975C4⋊C4—44no—
976C4⋊C4—48no—
977C4⋊C4—42no—
978C4⋊C4—44no—
979C4⋊C4—44no—
980C4⋊C4—48no—
981C4⋊C4—48no—
982C4⋊C4—48no—
983C4⋊C4—44no—
984C4⋊C4—42no—
985C4⋊C4—44no—
986C4⋊C4—44no—
987C4⋊C4—44no—
988C4⋊C4—44no—
989C4⋊C4C22×D414yes—
990C4⋊C4C22×D414yes—
991C4⋊C4C22×D4116yes—
992C4⋊C4C22×D4116yes—
993C4⋊C42−1+414yes—
994C22⋊C4—28no—
995C22⋊C4—28no—
996C22⋊C4—216no—
997C22⋊C4—28no—
998C22⋊C4—24no—
999C22⋊C4—24no—
1000C22⋊C4—28no—
1001C22⋊C4—216no—
1002C22⋊C4—216no—
1003C22⋊C4—28no—
1004C22⋊C4—216no—
1005C22⋊C4—24no—
1006C22⋊C4—24no—
1007C22⋊C4—28no—
1008C22⋊C4—28no—
1009C22⋊C4—28no—
1010C22⋊C4—44no—
1011C22⋊C4—48no—
1012C22⋊C4—44no—
1013C22⋊C4—48no—
1014C22⋊C4—48no—
1015C22⋊C4—44no—
1016C22⋊C4—44no—
1017C22⋊C4—48no—
1018C22⋊C4—44no—
1019C22⋊C4C22×D4116yes—
1020C22⋊C4C22×D418yes—
1021C22⋊C4C22×D4116yes—
1022C42—216no—
1023C42—24no—
1024C42—24no—
1025C42—216no—
1026C42—24no—
1027C42—24no—
1028C42—216no—
1029C42—216no—
1030C42—28no—
1031C42—24no—
1032C42—24no—
1033C42—24no—
1034C42—28no—
1035C42—28no—
1036C42—24no—
1037C42—24no—
1038C42—24no—
1039C42—42no—
1040C42—42no—
1041C42C22×D418yes—
1042C42C2×#4114yes—
1043C42C2×#4114yes—
1044C42C2×#4114yes—
1045C42C2×#4114yes—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—24no—
1057C23—24no—
1058C23—24no—
1059C23—24no—
1060C23—24no—
1061C23—24no—
1062C23—24no—
1063C23C23×D414yes—
1064C23C23×D412yes—
1065C23C22×#4112yes—
1066C23C2×2−1+412yes—
1067C23C2611yescharacteristic
1068Q8—216no—
1069Q8—216no—
1070Q8—28no—
1071Q8—416no—
1072Q8—48no—
1073Q8—88no—
1074D4—216no—
1075D4—28no—
1076D4—416no—
1077D4—48no—
1078D4—416no—
1079D4—48no—
1080D4—48no—
1081D4—88no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—22no—
1086C2×C4—21no—
1087C2×C4—22no—
1088C2×C4—24no—
1089C2×C4—22no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—22no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—22no—
1096C2×C4—21no—
1097C2×C4—22no—
1098C2×C4—216no—
1099C2×C4—216no—
1100C2×C4—28no—
1101C2×C4—22no—
1102C2×C4—28no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—24no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—28no—
1123C2×C4—24no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—24no—
1127C2×C4—22no—
1128C2×C4—24no—
1129C2×C4—22no—
1130C2×C4—28no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—24no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—24no—
1137C2×C4—44no—
1138C2×C4—48no—
1139C2×C4—48no—
1140C2×C4—48no—
1141C2×C4—416no—
1142C2×C4—48no—
1143C2×C4—816no—
1144C2×C4—88no—
1145C2×C4—816no—
1146C2×C4—84no—
1147C2×C4#547116yes—
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×C4C22×#4112yes—
1158C2×C4C22×#4112yes—
1159C2×C4C22×#4112yes—
1160C2×C4C2×2−1+414yes—
1161C2×C4C2×2−1+412yes—
1162C2×C4C2×2−1+412yes—
1163C2×C4C2×2−1+412yes—
1164C2×C4#58512yes—
1165C22—22no—
1166C22—22no—
1167C22—22no—
1168C22—22no—
1169C22—22no—
1170C22—22no—
1171C22—24no—
1172C22—24no—
1173C22—24no—
1174C22—42no—
1175C22—42no—
1176C22—42no—
1177C22—42no—
1178C22—44no—
1179C22—44no—
1180C22—44no—
1181C22—44no—
1182C22—44no—
1183C22—44no—
1184C22—44no—
1185C22C2×#54714yes—
1186C22C24×D411yescharacteristic
1187C22C23×#4111yescharacteristic
1188C22C22×2−1+411yescharacteristic
1189C22C22×2−1+411yescharacteristic
1190C22C2×#58511yescharacteristic
1191C22H(7,𝔽2)11yescharacteristic
1192C222−1+611yescharacteristic
1193C4—24no—
1194C4—24no—
1195C4—24no—
1196C4—22no—
1197C4—22no—
1198C4—22no—
1199C4—24no—
1200C4—28no—
1201C4—42no—
1202C4—44no—
1203C4—48no—
1204C4—44no—
1205C4—42no—
1206C4—42no—
1207C4—42no—
1208C4—42no—
1209C4—44no—
1210C4—42no—
1211C4—44no—
1212C4—42no—
1213C4C2×#54714yes—
1214C4C2×#54714yes—
1215C4#350714yescomplemented
1216C2—24no—
1217C2—44no—
1218C2—84no—
1219C2C22×#54711yescharacteristic
1220C2C2×#350711yescharacteristic
1221C2#6284511yescharacteristic
1222C2#6294311yescharacteristic
1223C2#6295611yescharacteristic
1224C2D4×2−1+411yescharacteristic
1225C2#6300311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34937C2
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×#3507C2semidirect
2. #59828C2semidirect
3. #59821C2semidirect
4. #59641C2semidirect
5. #59428C2semidirect
6. #59314C2semidirect
7. #59312C2semidirect
8. #59258C2semidirect
9. #59244C2semidirect
10. #45394C2semidirect
11. #45261C2semidirect
12. #44964C2semidirect
13. #44921C2semidirect
14. #39348C2semidirect
15. #37790C2semidirect
16. #36118C2semidirect
17. #35519C2semidirect
18. #35517C2semidirect
19. #35182C2semidirect
20. #35178C2semidirect
21. #34938C2semidirect
23. #34207C2semidirect
24. #34183C2semidirect
25. C2×Q8×C4⋊C4C2semidirect
26. C4×#536C2semidirect
213. #536D4semidirect
1215. C4#3507semidirect

Maximal subgroups

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

subgroupindex
C2×#35072
#598282
#598212
#596412
#594282
#593142
#593122
#592582
#592442
#453942
#452612
#449642
#449212
#393482
#377902
#361182
#355192
#355172
#351822
#351782
#349382
#349372
#342072
#341832
C2×Q8×C4⋊C42
C4×#5362