Finite Group Databasebeta

← #7712568

Subgroups — #7712568

Order 512.

5656 conjugacy classes of subgroups.

The subgroup lattice has 1248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59272C214yesmaximal, complemented
2#59094C214yesmaximal, complemented
3#46016C212yesmaximal, complemented
4#46015C212yesmaximal, complemented
5#46014C212yesmaximal, complemented
6#46013C212yesmaximal, complemented
7#39790C214yesmaximal, complemented
8#39789C214yesmaximal, complemented
9#39765C212yesmaximal, complemented
10#39511C212yesmaximal, complemented
11#39503C212yesmaximal, complemented
12#39495C212yesmaximal, complemented
13#39486C212yesmaximal, complemented
14#39381C212yesmaximal, complemented
15#37696C214yesmaximal, complemented
16#37546C212yesmaximal, complemented
17#37329C214yesmaximal, complemented
18#36645C211yesmaximal, characteristic, complemented
19C2×#2858C211yesmaximal, characteristic, complemented
20#36609C212yesmaximal, complemented
21#36150C212yesmaximal, complemented
22#36129C212yesmaximal, complemented
23#36121C212yesmaximal, complemented
24#35298C212yesmaximal, complemented
25#35277C212yesmaximal, complemented
26#34377C212yesmaximal, complemented
27C4×#529C211yesmaximal, characteristic, complemented
28C2×#546C2214yes—
29C2×#542C2214yescomplemented
30C2×#533C2212yes—
31C2×#533C2212yescomplemented
32C2×#532C2212yes—
33C22×C4⋊Q8C2211yescharacteristic
34C22×#127C2211yescharacteristic
35C2×#529C2211yescharacteristic
36C22×#124C2212yes—
37C22×#124C2212yes—
38#2868C2211yescharacteristic, complemented
39#2868C2211yescharacteristic, complemented
40#2862C2212yescomplemented
41#2862C2212yescomplemented
42#2859C2212yescomplemented
43#2859C2212yescomplemented
44#2858C2212yes—
45#2858C2212yes—
46#2858C2212yes—
47#2858C2212yes—
48#2858C2212yes—
49#2858C2212yes—
50#2858C2212yes—
51#2858C2212yes—
52#2858C2212yes—
53#2857C2212yes—
54#2857C2212yes—
55#2857C2212yes—
56#2857C2212yes—
57#2857C2212yescomplemented
58#2856C2212yes—
59#2820C2214yescomplemented
60#2819C2214yescomplemented
61#2808C2214yescomplemented
62#2808C2214yescomplemented
63#2804C2214yescomplemented
64#2803C2218yescomplemented
65#2800C2218yescomplemented
66#2780C2218yescomplemented
67#2761C2218yescomplemented
68#2753C2218yescomplemented
69#2733C2214yescomplemented
70#2732C2214yescomplemented
71#2727C2214yescomplemented
72#2724C2214yescomplemented
73#2715C2218yescomplemented
74#2712C2218yescomplemented
75#2711C2218yescomplemented
76#2710C2218yescomplemented
77#2707C2218yescomplemented
78#2701C2218yescomplemented
79#2700C2218yescomplemented
80#2682C2214yescomplemented
81#2662C2218yescomplemented
82#2640C2214yescomplemented
83#2626C2214yes—
84#2620C2214yescomplemented
85#2620C2214yescomplemented
86#2620C2214yescomplemented
87#2617C2214yes—
88#2597C2218yescomplemented
89#2592C2214yescomplemented
90#2592C2214yescomplemented
91#2580C2214yescomplemented
92#2566C2214yescomplemented
93#2566C2214yescomplemented
94#2554C2218yescomplemented
95#2550C2214yescomplemented
96#2545C2214yescomplemented
97#2545C2214yescomplemented
98#2544C2214yes—
99#2540C2214yescomplemented
100#2513C2214yescomplemented
101#2513C2214yescomplemented
102#2512C2214yescomplemented
103#2512C2214yescomplemented
104#2500C2214yescomplemented
105#2500C2214yescomplemented
106#2492C2214yescomplemented
107#2491C2214yescomplemented
108#2491C2214yescomplemented
109#2490C2214yescomplemented
110#2480C2218yes—
111#2472C2218yes—
112#2458C2218yescomplemented
113#2454C2214yescomplemented
114#2452C2214yescomplemented
115#2452C2214yescomplemented
116#2451C2214yescomplemented
117#2448C2214yescomplemented
118#2448C2214yescomplemented
119#2448C2214yescomplemented
120#2447C2214yescomplemented
121#2447C2214yescomplemented
122#2446C2214yescomplemented
123#2445C2214yes—
124#2445C2214yes—
125#2442C2214yes—
126#2439C2214yescomplemented
127#2437C2218yes—
128#2435C2214yes—
129#2432C2214yescomplemented
130#2432C2214yescomplemented
131#2431C2214yes—
132#2429C2214yescomplemented
133#2428C2214yes—
134#2428C2214yes—
135#2427C2214yescomplemented
136#2426C2214yescomplemented
137#2426C2214yescomplemented
138#2426C2218yescomplemented
139#2422C2214yescomplemented
140#2422C2214yescomplemented
141#2417C2214yes—
142#2414C2214yescomplemented
143#2412C2218yes—
144#2411C2218yes—
145#2409C2214yes—
146#2408C2214yes—
147#2408C2214yes—
148#2407C2214yescomplemented
149#2379C2214yescomplemented
150#2379C2214yescomplemented
151#2367C2214yescomplemented
152#2367C2214yescomplemented
153#2367C2214yescomplemented
154#2363C2214yescomplemented
155#2360C2214yes—
156#2357C2214yescomplemented
157#2352C2214yes—
158#2342C2218yes—
159#2341C2214yescomplemented
160Q8×C22⋊C4C2214yes—
161D4×C22⋊C4C2214yes—
162D4×C22⋊C4C2214yes—
163#2337C2218yescomplemented
164#2326C2214yescomplemented
165#2326C2214yescomplemented
166#2326C2214yescomplemented
167#2315C2214yes—
168#2312C2214yes—
169C4×C4⋊Q8C2212yescomplemented
170C4×C4⋊Q8C2212yescomplemented
171C4×C4⋊Q8C2212yescomplemented
172C4×C4⋊Q8C2212yescomplemented
173C4×C4⋊Q8C2212yescomplemented
174C4×#127C2212yes—
175C4×#125C2211yescharacteristic, complemented
176C4×#125C2211yescharacteristic, complemented
177C4×#126C2212yescomplemented
178C4×#126C2212yescomplemented
179C4×#124C2211yescharacteristic, complemented
180C4×#124C2211yescharacteristic, complemented
181C4×C22⋊Q8C2211yescharacteristic
182C4×C22⋊Q8C2211yescharacteristic
183C4×#123C2212yes—
184C4×#123C2212yes—
185C4×#121C2211yescharacteristic
186C4×#121C2211yescharacteristic
187#2298C2212yescomplemented
188#2295C2211yescharacteristic, complemented
189#2293C2211yescharacteristic, complemented
190C2×#390C2212yes—
191C2×#390C2212yes—
192C2×#390C2212yes—
193C2×#390C2212yes—
194#2290C2212yes—
195#2285C2212yes—
196#2285C2212yes—
197#2283C2211yescharacteristic
198C42×Q8C2211yescharacteristic, complemented
199C42×D4C2212yes—
200C42×D4C2211yescharacteristic, complemented
201C4×#117C2212yescomplemented
202C2×C43C2211yescharacteristic
203C22×#41C2314yes—
204C23×Q8C2312yes—
205C23×D4C2312yes—
206C23×D4C2312yes—
207C23×D4C2312yes—
208#546—416no—
209#542—416no—
210#533—48no—
211#533—48no—
212#532—48no—
213C2×C4⋊Q8—44no—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C2312yes—
217C2×C4⋊Q8C2312yes—
218C2×C4⋊Q8C2312yes—
219C2×C4⋊Q8C2312yes—
220C2×C4⋊Q8C2312yes—
221C2×C4⋊Q8C2312yes—
222C2×C4⋊Q8C2312yes—
223C2×C4⋊Q8C2312yes—
224C2×#127—44no—
225C2×#127C2312yes—
226C2×#127C2312yes—
227C2×#127C2312yes—
228C2×#127C2312yes—
229#529—28no—
230C2×#126C2312yes—
231C2×#126C2318yes—
232C2×#125C2311yescharacteristic
233C2×#125C2314yes—
234C2×#125C2314yes—
235C2×#124—216no—
236C2×#124—48no—
237C2×#124C2311yescharacteristic
238C2×#124C2314yes—
239C2×#124C2314yes—
240C2×#124C2314yes—
241C2×#124C2314yes—
242C2×#124C2314yes—
243C2×#124C2314yes—
244C2×#124C2314yes—
245C2×#124C2314yes—
246C2×#124C2314yes—
247C2×#124C2314yes—
248C2×#124C2314yes—
249C2×#124C2318yes—
250C2×#123C2312yes—
251C2×#123C2318yes—
252C2×#123C2318yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2311yescharacteristic
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2318yes—
260C2×#121C2311yescharacteristic
261C2×#121C2314yes—
262C2×#121C2314yes—
263C2×#121C2314yes—
264C2×#121C2314yes—
265C2×#121C2314yes—
266C2×#121C2318yes—
267C2×#120C2318yes—
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2314yes—
270C2×C4×Q8C2314yes—
271C2×C4×Q8C2314yes—
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2314yes—
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2314yes—
276C2×C4×D4C2312yes—
277C2×C4×D4C2312yes—
278C2×C4×D4C2311yescharacteristic
279C2×C4×D4C2312yes—
280C2×C4×D4C2314yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2314yes—
283C2×C4×D4C2314yes—
284C2×C4×D4C2314yes—
285C2×C4×D4C2311yescharacteristic
286C2×C4×D4C2311yescharacteristic
287C2×#117C2312yes—
288C2×#117C2312yes—
289C2×#117C2314yes—
290C2×#117C2314yes—
291C22×C4⋊C4C2312yes—
292C22×C4⋊C4C2312yes—
293C22×C22⋊C4C2314yes—
294C22×C22⋊C4C2314yes—
295C22×C22⋊C4C2318yes—
296C22×C22⋊C4C2314yes—
297C22×C22⋊C4C2314yes—
298C22×C42C2312yes—
299C22×C42C2311yescharacteristic
300C22×C42C2311yescharacteristic
301C22×C42C2311yescharacteristic
302C22×C42C2311yescharacteristic
303C22×C42C2311yescharacteristic
304C22×C42C2311yescharacteristic
305C22×C42C2311yescharacteristic
306#400C2318yes—
307#399C2318yes—
308#399C2318yes—
309#398C2318yes—
310#398C2318yes—
311#397C2318yes—
312#397C2318yes—
313#397C2318yes—
314#397C2318yes—
315#397C2318yes—
316#397C2318yes—
317#397C2318yes—
318#396C2318yes—
319#396C2318yes—
320#396C2318yes—
321#396C2318yes—
322#396C2318yes—
323#396C2318yes—
324#396C2318yes—
325#396C2318yes—
326#395C2318yes—
327#394C2318yes—
328#394C2318yes—
329#394C2318yes—
330#394C2318yes—
331#394C2318yes—
332#394C2318yes—
333#394C2318yes—
334#394C2318yes—
335#394C2318yes—
336#394C2318yes—
337#394C2318yes—
338#394C2318yes—
339#393C2318yes—
340#393C2318yes—
341#393C2318yes—
342#393C2318yes—
343#392C2318yes—
344#392C2318yes—
345#392C2318yes—
346#391C2314yes—
347#391C2314yes—
348#391C2314yes—
349#391C2314yes—
350#391C2314yes—
351#391C2314yes—
352#391C2314yes—
353#391C2314yes—
354#391C2314yes—
355#391C2318yes—
356#391C2318yes—
357#391C2314yes—
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#390C2314yes—
361#390C2314yes—
362#390C2314yes—
363#390C2314yes—
364#390C2314yes—
365#390C2314yes—
366#390C2314yes—
367#390C2314yes—
368#390C2314yes—
369#390C2314yes—
370#390C2314yes—
371#390C2314yes—
372#390C2314yes—
373#390C2314yes—
374#390C2314yes—
375#390C2318yes—
376#390C2318yes—
377#390C2314yes—
378#390C2314yes—
379#390C2314yes—
380#390C2314yes—
381#390C2314yes—
382#390C2314yes—
383#390C2314yes—
384#390C2314yes—
385#390C2314yes—
386#390C2314yes—
387#390C2314yes—
388#390C2318yes—
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2314yes—
405#389C2314yes—
406#389C2314yes—
407#389C2318yes—
408#388C2312yes—
409#388C2312yes—
410#388C2312yes—
411#388C2312yes—
412#388C2312yes—
413#388C2312yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2318yes—
422#388C2318yes—
423#388C2318yes—
424#388C2318yes—
425#388C2318yes—
426#388C2318yes—
427#388C2318yes—
428#388C2318yes—
429#388C2318yes—
430#388C2312yes—
431#388C2312yes—
432#387C2312yes—
433#387C2312yes—
434#387C2312yes—
435#387C2312yes—
436#387C2312yes—
437#387C2312yes—
438#387C2312yes—
439#387C2312yes—
440#387C2318yes—
441#387C2318yes—
442#386C2318yes—
443#386C2318yes—
444#386C2318yes—
445#386C2318yes—
446#386C2318yes—
447#386C2318yes—
448#386C2312yes—
449#386C2312yes—
450#385C2318yes—
451#385C2318yes—
452#385C2318yes—
453#385C2318yes—
454#385C2318yes—
455#385C2318yes—
456#385C2318yes—
457#385C2318yes—
458#385C2318yes—
459#385C2318yes—
460#385C2312yes—
461#385C2312yes—
462#384C2312yes—
463#384C2312yes—
464#384C2312yes—
465#384C2312yes—
466#384C2312yes—
467#384C2312yes—
468#384C2312yes—
469#384C2312yes—
470#383C2312yes—
471#382C2311yescharacteristic
472#382C2311yescharacteristic
473#382C2314yes—
474#382C2314yes—
475#382C2314yes—
476#382C2314yes—
477#381C2312yes—
478#381C2318yes—
479#380C2311yescharacteristic
480#380C2314yes—
481#380C2311yescharacteristic
482#380C2318yes—
483#380C2314yes—
484#380C2314yes—
485#380C2314yes—
486#380C2318yes—
487#380C2314yes—
488#380C2314yes—
489#379C2318yes—
490#379C2318yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2314yes—
508C4×C4⋊C4C2314yes—
509C4×C4⋊C4C2311yescharacteristic
510C4×C4⋊C4C2311yescharacteristic
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2312yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2318yes—
520C4×C22⋊C4C2318yes—
521C4×C22⋊C4C2318yes—
522C4×C22⋊C4C2312yes—
523C4×C22⋊C4C2312yes—
524C4×C22⋊C4C2312yes—
525C4×C22⋊C4C2312yes—
526C4×C22⋊C4C2312yes—
527C4×C22⋊C4C2312yes—
528C4×C22⋊C4C2312yes—
529#376C2312yes—
530#376C2312yes—
531C43C2311yescharacteristic
532C43C2311yescharacteristic
533C43C2311yescharacteristic
534C43C2311yescharacteristic
535C43C2312yes—
536C43C2311yescharacteristic
537C43C2311yescharacteristic
538C43C2311yescharacteristic
539C43C2311yescharacteristic
540C25C2414yes—
541C2×#41—48no—
542C2×#41—48no—
543C2×#41—48no—
544C22×Q8—28no—
545C22×Q8—44no—
546C22×Q8—44no—
547C22×Q8C2414yes—
548C22×Q8C2414yes—
549C22×Q8C2411yescharacteristic
550C22×Q8C2414yes—
551C22×Q8C2414yes—
552C22×D4—28no—
553C22×D4—28no—
554C22×D4—28no—
555C22×D4—44no—
556C22×D4—44no—
557C22×D4—44no—
558C22×D4—44no—
559C22×D4—44no—
560C22×D4—44no—
561C22×D4C2412yes—
562C22×D4C2414yes—
563C22×D4C2414yes—
564C22×D4C2414yes—
565C22×D4C2411yescharacteristic
566C22×D4C2414yes—
567C22×D4C2414yes—
568C22×D4C2414yes—
569C22×D4C2418yes—
570C22×D4C2418yes—
571C23×C4C2412yes—
572C23×C4C2412yes—
573C23×C4C2412yes—
574C23×C4C2411yescharacteristic
575C23×C4C2411yescharacteristic
576C23×C4C2411yescharacteristic
577C23×C4C2411yescharacteristic
578C23×C4C2411yescharacteristic
579C23×C4C2411yescharacteristic
580C23×C4C2414yes—
581C23×C4C2418yes—
582C23×C4C2418yes—
583C23×C4C2411yescharacteristic
584C4⋊Q8—28no—
585C4⋊Q8—28no—
586C4⋊Q8—28no—
587C4⋊Q8—44no—
588C4⋊Q8—44no—
589C4⋊Q8—44no—
590C4⋊Q8—44no—
591C4⋊Q8—44no—
592C4⋊Q8—44no—
593C4⋊Q8—44no—
594#127—28no—
595#127—44no—
596#127—44no—
597#127—44no—
598#126—28no—
599#126—416no—
600#125—24no—
601#125—48no—
602#125—48no—
603#124—216no—
604#124—216no—
605#124—216no—
606#124—216no—
607#124—24no—
608#124—216no—
609#124—48no—
610#124—48no—
611#124—48no—
612#124—48no—
613#124—48no—
614#124—48no—
615#124—416no—
616#123—28no—
617#123—416no—
618#123—416no—
619C22⋊Q8—24no—
620C22⋊Q8—216no—
621C22⋊Q8—48no—
622C22⋊Q8—416no—
623C22⋊Q8—48no—
624C22⋊Q8—48no—
625C22⋊Q8—48no—
626#121—24no—
627#121—416no—
628#121—48no—
629#121—48no—
630#121—48no—
631#121—48no—
632#121—48no—
633#120—416no—
634C4×Q8—24no—
635C4×Q8—42no—
636C4×Q8—42no—
637C4×Q8—48no—
638C4×Q8—48no—
639C4×Q8—48no—
640C4×Q8—48no—
641C4×Q8—48no—
642C4×D4—28no—
643C4×D4—28no—
644C4×D4—28no—
645C4×D4—24no—
646C4×D4—48no—
647C4×D4—48no—
648C4×D4—48no—
649C4×D4—48no—
650C4×D4—48no—
651C4×D4—42no—
652C4×D4—42no—
653#117—28no—
654#117—28no—
655#117—48no—
656#117—48no—
657C2×C4⋊C4—44no—
658C2×C4⋊C4—44no—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2418yes—
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2418yes—
685C2×C4⋊C4C2418yes—
686C2×C4⋊C4C2418yes—
687C2×C4⋊C4C2418yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2412yes—
692C2×C4⋊C4C2412yes—
693C2×C4⋊C4C2418yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C22⋊C4—216no—
698C2×C22⋊C4—216no—
699C2×C22⋊C4—48no—
700C2×C22⋊C4—48no—
701C2×C22⋊C4—416no—
702C2×C22⋊C4C2412yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2418yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2418yes—
708C2×C22⋊C4C2418yes—
709C2×C22⋊C4C2418yes—
710C2×C22⋊C4C2412yes—
711C2×C22⋊C4C2412yes—
712C2×C22⋊C4C2412yes—
713C2×C22⋊C4C2412yes—
714C2×C22⋊C4C2412yes—
715C2×C22⋊C4C2412yes—
716C2×C22⋊C4C2412yes—
717C2×C22⋊C4C2412yes—
718C2×C22⋊C4C2412yes—
719C2×C22⋊C4C2412yes—
720C2×C22⋊C4C2418yes—
721C2×C22⋊C4C2418yes—
722C2×C22⋊C4C2418yes—
723C2×C22⋊C4C2418yes—
724C2×C22⋊C4C2418yes—
725C2×C22⋊C4C2418yes—
726C2×C22⋊C4C2418yes—
727C2×C22⋊C4C2418yes—
728C2×C22⋊C4C2418yes—
729C2×C22⋊C4C2412yes—
730C2×C22⋊C4C2412yes—
731C2×C22⋊C4C2418yes—
732C2×C22⋊C4C2418yes—
733C2×C22⋊C4C2418yes—
734C2×C22⋊C4C2418yes—
735C2×C22⋊C4C2418yes—
736C2×C22⋊C4C2418yes—
737C2×C22⋊C4C2418yes—
738C2×C42—24no—
739C2×C42—24no—
740C2×C42—24no—
741C2×C42—24no—
742C2×C42—28no—
743C2×C42—42no—
744C2×C42—42no—
745C2×C42#4118yescomplemented
746C2×C42C2412yes—
747C2×C42C2412yes—
748C2×C42C2412yes—
749C2×C42C2412yes—
750C2×C42C2412yes—
751C2×C42C2412yes—
752C2×C42C2411yescharacteristic
753C2×C42C2411yescharacteristic
754C2×C42C2412yes—
755C2×C42C2411yescharacteristic
756C2×C42C2411yescharacteristic
757C2×C42C2412yes—
758C2×C42C2412yes—
759C2×C42C2411yescharacteristic
760C2×C42C2411yescharacteristic
761C2×C42C2411yescharacteristic
762C2×C42C2411yescharacteristic
763C2×C42C2411yescharacteristic
764C2×C42C2411yescharacteristic
765C2×C42C2411yescharacteristic
766C2×C42C2411yescharacteristic
767C2×C42C2411yescharacteristic
768C2×C42C2411yescharacteristic
769C2×C42C2411yescharacteristic
770C2×C42C2411yescharacteristic
771C2×C42C2411yescharacteristic
772C2×C42C2411yescharacteristic
773C2×C42C2418yes—
774C2×C42C2418yes—
775C2×C42C2418yes—
776C2×C42C2411yescharacteristic
777C2×C42C2411yescharacteristic
778C2×C42C2411yescharacteristic
779C2×C42C2411yescharacteristic
780C2×C42C2411yescharacteristic
781C2×C42C2411yescharacteristic
782C2×C42C2411yescharacteristic
783C2×C42C2411yescharacteristic
784C2×C42C2411yescharacteristic
785C2×C42C2411yescharacteristic
786#95C2412yes—
787#95C2412yes—
788#95C2412yes—
789#95C2412yes—
790#95C2412yes—
791#95C2412yes—
792#95C2412yes—
793#95C2412yes—
794#95C2412yes—
795#95C2412yes—
796#95C2412yes—
797#95C2412yes—
798#95C2412yes—
799#95C2412yes—
800#95C2412yes—
801#95C2412yes—
802#95C2412yes—
803#95C2412yes—
804#95C2418yes—
805#95C2418yes—
806#95C2418yes—
807#95C2418yes—
808#95C2412yes—
809#95C2412yes—
810#95C2418yes—
811#95C2418yes—
812#95C2418yes—
813#95C2418yes—
814#95C2418yes—
815#95C2418yes—
816#95C2418yes—
817#95C2418yes—
818C24—28no—
819C24—28no—
820C24—28no—
821C24—44no—
822C24—44no—
823C24—44no—
824C24—44no—
825C24C2518yes—
826C24C2512yes—
827C24C2511yescharacteristic
828#41—832no—
829C2×Q8—22no—
830C2×Q8—28no—
831C2×Q8—28no—
832C2×Q8—28no—
833C2×Q8—28no—
834C2×Q8—28no—
835C2×Q8—28no—
836C2×Q8—28no—
837C2×Q8—28no—
838C2×Q8—41no—
839C2×Q8—41no—
840C2×Q8—44no—
841C2×Q8—44no—
842C2×Q8—44no—
843C2×Q8—44no—
844C2×Q8—816no—
845C2×D4—24no—
846C2×D4—24no—
847C2×D4—24no—
848C2×D4—22no—
849C2×D4—28no—
850C2×D4—28no—
851C2×D4—28no—
852C2×D4—28no—
853C2×D4—28no—
854C2×D4—28no—
855C2×D4—28no—
856C2×D4—28no—
857C2×D4—28no—
858C2×D4—28no—
859C2×D4—28no—
860C2×D4—28no—
861C2×D4—41no—
862C2×D4—41no—
863C2×D4—48no—
864C2×D4—48no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—48no—
872C2×D4—48no—
873C2×D4—48no—
874C2×D4—48no—
875C2×D4—816no—
876C2×D4—816no—
877C2×D4—816no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—28no—
889C22×C4—24no—
890C22×C4—22no—
891C22×C4—22no—
892C22×C4—24no—
893C22×C4—24no—
894C22×C4—24no—
895C22×C4—24no—
896C22×C4—24no—
897C22×C4—24no—
898C22×C4—24no—
899C22×C4—24no—
900C22×C4—41no—
901C22×C4—41no—
902C22×C4—41no—
903C22×C4—41no—
904C22×C4—44no—
905C22×C4—48no—
906C22×C4—44no—
907C22×C4—48no—
908C22×C4—48no—
909C22×C4—48no—
910C22×C4—48no—
911C22×C4—48no—
912C22×C4C2×#4114yes—
913C22×C4C2×#4114yes—
914C22×C4C2×#4114yes—
915C22×C4H(5,𝔽2)14yes—
916C22×C42−1+414yes—
917C22×C4C2512yes—
918C22×C4C2511yescharacteristic
919C22×C4C2512yes—
920C22×C4C2512yes—
921C22×C4C2512yes—
922C22×C4C2512yes—
923C22×C4C2512yes—
924C22×C4C2518yes—
925C22×C4C2518yes—
926C22×C4C2518yes—
927C22×C4C2511yescharacteristic
928C22×C4C2512yes—
929C22×C4C2511yescharacteristic
930C22×C4C2511yescharacteristic
931C22×C4C2511yescharacteristic
932C22×C4C2511yescharacteristic
933C22×C4C2511yescharacteristic
934C22×C4C2511yescharacteristic
935C22×C4C2511yescharacteristic
936C22×C4C2511yescharacteristic
937C22×C4C2511yescharacteristic
938C22×C4C2511yescharacteristic
939C22×C4C2511yescharacteristic
940C22×C4C2511yescharacteristic
941C4⋊C4—24no—
942C4⋊C4—24no—
943C4⋊C4—22no—
944C4⋊C4—24no—
945C4⋊C4—22no—
946C4⋊C4—24no—
947C4⋊C4—28no—
948C4⋊C4—28no—
949C4⋊C4—24no—
950C4⋊C4—24no—
951C4⋊C4—28no—
952C4⋊C4—24no—
953C4⋊C4—28no—
954C4⋊C4—28no—
955C4⋊C4—28no—
956C4⋊C4—216no—
957C4⋊C4—28no—
958C4⋊C4—24no—
959C4⋊C4—28no—
960C4⋊C4—44no—
961C4⋊C4—44no—
962C4⋊C4—44no—
963C4⋊C4—44no—
964C4⋊C4—41no—
965C4⋊C4—41no—
966C4⋊C4—41no—
967C4⋊C4—41no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—48no—
971C4⋊C4—48no—
972C4⋊C4—48no—
973C4⋊C4—48no—
974C4⋊C4—44no—
975C4⋊C4—48no—
976C4⋊C4—44no—
977C4⋊C4—44no—
978C4⋊C4—44no—
979C22⋊C4—24no—
980C22⋊C4—24no—
981C22⋊C4—216no—
982C22⋊C4—24no—
983C22⋊C4—216no—
984C22⋊C4—216no—
985C22⋊C4—216no—
986C22⋊C4—216no—
987C22⋊C4—24no—
988C22⋊C4—24no—
989C22⋊C4—24no—
990C22⋊C4—24no—
991C22⋊C4—216no—
992C22⋊C4—216no—
993C22⋊C4—24no—
994C22⋊C4—24no—
995C22⋊C4—24no—
996C22⋊C4—24no—
997C22⋊C4—48no—
998C22⋊C4—48no—
999C22⋊C4—48no—
1000C22⋊C4—48no—
1001C22⋊C4—48no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—48no—
1005C22⋊C4—48no—
1006C22⋊C4—48no—
1007C22⋊C4—48no—
1008C22⋊C4—48no—
1009C22⋊C4—48no—
1010C22⋊C4—48no—
1011C22⋊C4—48no—
1012C22⋊C4—48no—
1013C22⋊C4—48no—
1014C22⋊C4—48no—
1015C42—24no—
1016C42—24no—
1017C42—24no—
1018C42—22no—
1019C42—22no—
1020C42—24no—
1021C42—22no—
1022C42—22no—
1023C42—22no—
1024C42—22no—
1025C42—22no—
1026C42—22no—
1027C42—22no—
1028C42—22no—
1029C42—24no—
1030C42—24no—
1031C42—22no—
1032C42—22no—
1033C42—22no—
1034C42—22no—
1035C42—24no—
1036C42—22no—
1037C42—22no—
1038C42—22no—
1039C42—22no—
1040C42—24no—
1041C42—24no—
1042C42—41no—
1043C42—41no—
1044C42—41no—
1045C42—41no—
1046C42—48no—
1047C42—48no—
1048C42—48no—
1049C42C2×#4114yes—
1050C42C2×#4114yes—
1051C42C2×#4114yes—
1052C42C2×#4114yes—
1053C42H(5,𝔽2)14yes—
1054C42H(5,𝔽2)14yes—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—22no—
1060C23—28no—
1061C23—22no—
1062C23—28no—
1063C23—22no—
1064C23—22no—
1065C23—28no—
1066C23—28no—
1067C23—22no—
1068C23—28no—
1069C23—28no—
1070C23—28no—
1071C23—22no—
1072C23—22no—
1073C23—416no—
1074C23—88no—
1075C23—88no—
1076C23—88no—
1077C23—88no—
1078C23—88no—
1079C23—88no—
1080C23C22×#4112yes—
1081C23C2×H(5,𝔽2)12yes—
1082C23C2×2−1+412yes—
1083C23C2611yescharacteristic
1084Q8—44no—
1085Q8—416no—
1086Q8—416no—
1087Q8—88no—
1088Q8—88no—
1089D4—44no—
1090D4—48no—
1091D4—416no—
1092D4—416no—
1093D4—416no—
1094D4—88no—
1095D4—88no—
1096D4—88no—
1097D4—816no—
1098D4—168no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—28no—
1118C2×C4—28no—
1119C2×C4—28no—
1120C2×C4—28no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—28no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—22no—
1129C2×C4—21no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—28no—
1136C2×C4—28no—
1137C2×C4—28no—
1138C2×C4—28no—
1139C2×C4—28no—
1140C2×C4—28no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—21no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—28no—
1155C2×C4—28no—
1156C2×C4—22no—
1157C2×C4—44no—
1158C2×C4—44no—
1159C2×C4—44no—
1160C2×C4—48no—
1161C2×C4—48no—
1162C2×C4—48no—
1163C2×C4—88no—
1164C2×C4—816no—
1165C2×C4—168no—
1166C2×C4C22×#4112yes—
1167C2×C4C22×#4112yes—
1168C2×C4C22×#4112yes—
1169C2×C4C22×#4112yes—
1170C2×C4C22×#4112yes—
1171C2×C4C22×#4112yes—
1172C2×C4C2×H(5,𝔽2)12yes—
1173C2×C4C2×H(5,𝔽2)12yes—
1174C2×C4C2×H(5,𝔽2)12yes—
1175C2×C4C2×H(5,𝔽2)12yes—
1176C2×C4C2×H(5,𝔽2)12yes—
1177C2×C4C2×H(5,𝔽2)12yes—
1178C2×C4C2×H(5,𝔽2)12yes—
1179C2×C4C2×H(5,𝔽2)12yes—
1180C2×C4C2×2−1+412yes—
1181C2×C4C2×2−1+412yes—
1182C2×C4#58512yes—
1183C2×C4#58512yes—
1184C22—22no—
1185C22—22no—
1186C22—22no—
1187C22—22no—
1188C22—22no—
1189C22—22no—
1190C22—42no—
1191C22—48no—
1192C22—42no—
1193C22—48no—
1194C22—42no—
1195C22—48no—
1196C22—42no—
1197C22—48no—
1198C22—42no—
1199C22—48no—
1200C22—48no—
1201C22—42no—
1202C22—42no—
1203C22—48no—
1204C22—1616no—
1205C22#351114yes—
1206C22C23×#4111yescharacteristic
1207C22C22×H(5,𝔽2)11yescharacteristic
1208C22C22×H(5,𝔽2)11yescharacteristic
1209C22C22×H(5,𝔽2)11yescharacteristic
1210C22C22×2−1+411yescharacteristic
1211C22C2×#58511yescharacteristic
1212C22C2×#58511yescharacteristic
1213C4—22no—
1214C4—22no—
1215C4—22no—
1216C4—22no—
1217C4—22no—
1218C4—22no—
1219C4—22no—
1220C4—22no—
1221C4—22no—
1222C4—42no—
1223C4—48no—
1224C4—42no—
1225C4—42no—
1226C4—48no—
1227C4—42no—
1228C4—42no—
1229C4—41no—
1230C4—42no—
1231C4—48no—
1232C4—42no—
1233C4—41no—
1234C4#350814yes—
1235C4#355814yes—
1236C4#356114yes—
1237C2—24no—
1238C2—82no—
1239C2—88no—
1240C2C2×#355811yescharacteristic
1241C2C2×#356111yescharacteristic
1242C2C2×#350811yescharacteristic
1243C2C2×#351111yescharacteristic
1244C2#6281511yescharacteristic
1245C2#6283411yescharacteristic
1246C2#6283511yescharacteristic
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. #59272C2semidirect
2. #59094C2semidirect
3. #46016C2semidirect
4. #46015C2semidirect
5. #46014C2semidirect
6. #46013C2semidirect
7. #39790C2semidirect
8. #39789C2semidirect
9. #39765C2semidirect
10. #39511C2semidirect
11. #39503C2semidirect
12. #39495C2semidirect
13. #39486C2semidirect
14. #39381C2semidirect
15. #37696C2semidirect
16. #37546C2semidirect
17. #37329C2semidirect
18. #36645C2semidirect
19. C2×#2858C2semidirect
20. #36609C2semidirect
21. #36150C2semidirect
22. #36129C2semidirect
23. #36121C2semidirect
24. #35298C2semidirect
25. #35277C2semidirect
26. #34377C2semidirect
27. C4×#529C2semidirect
29. C2×#542C22semidirect
31. C2×#533C22semidirect
38. #2868C22semidirect
39. #2868C22semidirect
40. #2862C22semidirect
41. #2862C22semidirect
42. #2859C22semidirect
43. #2859C22semidirect
57. #2857C22semidirect
59. #2820C22semidirect
60. #2819C22semidirect
61. #2808C22semidirect
62. #2808C22semidirect
63. #2804C22semidirect
64. #2803C22semidirect
65. #2800C22semidirect
66. #2780C22semidirect
67. #2761C22semidirect
68. #2753C22semidirect
69. #2733C22semidirect
70. #2732C22semidirect
71. #2727C22semidirect
72. #2724C22semidirect
73. #2715C22semidirect
74. #2712C22semidirect
75. #2711C22semidirect
76. #2710C22semidirect
77. #2707C22semidirect
78. #2701C22semidirect
79. #2700C22semidirect
80. #2682C22semidirect
81. #2662C22semidirect
82. #2640C22semidirect
84. #2620C22semidirect
85. #2620C22semidirect
86. #2620C22semidirect
88. #2597C22semidirect
89. #2592C22semidirect
90. #2592C22semidirect
91. #2580C22semidirect
92. #2566C22semidirect
93. #2566C22semidirect
94. #2554C22semidirect
95. #2550C22semidirect
96. #2545C22semidirect
97. #2545C22semidirect
99. #2540C22semidirect
100. #2513C22semidirect
101. #2513C22semidirect
102. #2512C22semidirect
103. #2512C22semidirect
104. #2500C22semidirect
105. #2500C22semidirect
106. #2492C22semidirect
107. #2491C22semidirect
108. #2491C22semidirect
109. #2490C22semidirect
112. #2458C22semidirect
113. #2454C22semidirect
114. #2452C22semidirect
115. #2452C22semidirect
116. #2451C22semidirect
117. #2448C22semidirect
118. #2448C22semidirect
119. #2448C22semidirect
120. #2447C22semidirect
121. #2447C22semidirect
122. #2446C22semidirect
126. #2439C22semidirect
129. #2432C22semidirect
130. #2432C22semidirect
132. #2429C22semidirect
135. #2427C22semidirect
136. #2426C22semidirect
137. #2426C22semidirect
138. #2426C22semidirect
139. #2422C22semidirect
140. #2422C22semidirect
142. #2414C22semidirect
148. #2407C22semidirect
149. #2379C22semidirect
150. #2379C22semidirect
151. #2367C22semidirect
152. #2367C22semidirect
153. #2367C22semidirect
154. #2363C22semidirect
156. #2357C22semidirect
159. #2341C22semidirect
163. #2337C22semidirect
164. #2326C22semidirect
165. #2326C22semidirect
166. #2326C22semidirect
169. C4×C4⋊Q8C22semidirect
170. C4×C4⋊Q8C22semidirect
171. C4×C4⋊Q8C22semidirect
172. C4×C4⋊Q8C22semidirect
173. C4×C4⋊Q8C22semidirect
175. C4×#125C22semidirect
176. C4×#125C22semidirect
177. C4×#126C22semidirect
178. C4×#126C22semidirect
179. C4×#124C22semidirect
180. C4×#124C22semidirect
187. #2298C22semidirect
188. #2295C22semidirect
189. #2293C22semidirect
198. C42×Q8C22semidirect
200. C42×D4C22semidirect
201. C4×#117C22semidirect
745. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
#592722
#590942
#460162
#460152
#460142
#460132
#397902
#397892
#397652
#395112
#395032
#394952
#394862
#393812
#376962
#375462
#373292
#366452
C2×#28582
#366092
#361502
#361292
#361212
#352982
#352772
#343772
C4×#5292