Finite Group Databasebeta

← #7720530

Subgroups — #7720530

Order 512.

5011 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51091C214yesmaximal, complemented
2#51088C214yesmaximal, complemented
3#51041C214yesmaximal, complemented
4#50878C214yesmaximal, complemented
5#45072C214yesmaximal, complemented
6#45019C214yesmaximal, complemented
7#44965C214yesmaximal, complemented
8#44901C214yesmaximal, complemented
9#39736C212yesmaximal, complemented
10#39147C212yesmaximal, complemented
11#38254C214yesmaximal, complemented
12#37786C214yesmaximal, complemented
13#37432C212yesmaximal, complemented
14#37321C212yesmaximal, complemented
15#36302C212yesmaximal, complemented
16#36117C212yesmaximal, complemented
17#35343C212yesmaximal, complemented
18#35296C212yesmaximal, complemented
19#35285C211yesmaximal, characteristic, complemented
20#35272C211yesmaximal, characteristic
21#35202C211yesmaximal, characteristic, complemented
22#34627C211yesmaximal, characteristic, complemented
23#34373C211yesmaximal, characteristic, complemented
24#34364C211yesmaximal, characteristic, complemented
25#34121C211yesmaximal, characteristic, complemented
26C2×#535C2212yes—
27C2×#533C2211yescharacteristic
28C22×#127C2211yescharacteristic
29C2×#529C2214yescomplemented
30C2×C4×#41C2211yescharacteristic
31#2864C2212yescomplemented
32#2861C2214yescomplemented
33#2859C2212yescomplemented
34#2858C2212yes—
35#2858C2212yes—
36#2856C2212yes—
37#2856C2212yes—
38#2854C2214yescomplemented
39#2797C2218yescomplemented
40#2796C2218yescomplemented
41#2796C2218yescomplemented
42#2786C2218yescomplemented
43#2786C2218yescomplemented
44#2761C2218yescomplemented
45#2757C2218yescomplemented
46#2752C2218yescomplemented
47#2740C2218yescomplemented
48#2735C2218yes—
49#2735C2218yes—
50#2715C2218yescomplemented
51#2715C2218yescomplemented
52#2710C2218yescomplemented
53#2709C2218yescomplemented
54#2705C2218yescomplemented
55#2701C2218yescomplemented
56#2697C2218yes—
57#2691C2218yescomplemented
58#2685C2218yes—
59#2667C2214yes—
60#2644C2214yescomplemented
61#2641C2214yes—
62#2638C2212yes—
63#2638C2212yes—
64#2634C2212yescomplemented
65#2633C2212yescomplemented
66#2628C2211yescharacteristic, complemented
67#2628C2211yescharacteristic, complemented
68#2625C2212yes—
69#2621C2211yescharacteristic, complemented
70#2621C2211yescharacteristic, complemented
71#2620C2214yescomplemented
72#2619C2212yes—
73#2619C2212yes—
74#2616C2212yes—
75#2606C2214yescomplemented
76#2602C2218yescomplemented
77#2602C2218yescomplemented
78#2601C2218yescomplemented
79#2601C2218yescomplemented
80#2601C2218yescomplemented
81#2595C2218yescomplemented
82#2566C2214yescomplemented
83#2566C2214yescomplemented
84#2557C2218yescomplemented
85#2552C2212yescomplemented
86#2552C2212yescomplemented
87#2548C2214yes—
88#2548C2212yes—
89#2548C2212yes—
90#2548C2212yes—
91#2548C2212yes—
92#2541C2212yes—
93#2541C2212yes—
94#2531C2218yescomplemented
95#2516C2218yescomplemented
96#2513C2214yescomplemented
97#2513C2214yescomplemented
98#2512C2214yescomplemented
99#2512C2214yescomplemented
100#2512C2214yescomplemented
101#2501C2214yescomplemented
102#2500C2214yescomplemented
103#2490C2214yescomplemented
104#2490C2214yescomplemented
105#2490C2214yescomplemented
106#2482C2218yes—
107#2480C2218yes—
108#2479C2218yescomplemented
109#2476C2218yescomplemented
110#2474C2218yescomplemented
111#2474C2218yescomplemented
112#2471C2218yescomplemented
113#2454C2214yescomplemented
114#2448C2214yescomplemented
115#2447C2214yescomplemented
116#2445C2218yescomplemented
117#2441C2214yes—
118#2441C2214yes—
119#2435C2214yes—
120#2435C2214yes—
121#2427C2214yescomplemented
122#2426C2214yescomplemented
123#2425C2218yescomplemented
124#2422C2214yescomplemented
125#2422C2214yescomplemented
126#2420C2214yescomplemented
127#2418C2218yes—
128#2411C2218yes—
129#2408C2212yes—
130#2408C2212yes—
131#2408C2212yes—
132#2408C2212yes—
133#2399C2212yescomplemented
134#2398C2212yescomplemented
135#2395C2212yes—
136#2395C2212yes—
137#2380C2214yes—
138#2378C2214yes—
139#2366C2212yes—
140#2366C2212yes—
141#2363C2214yescomplemented
142#2362C2214yes—
143#2361C2214yescomplemented
144#2357C2212yes—
145#2356C2212yescomplemented
146#2355C2214yescomplemented
147#2355C2212yescomplemented
148#2355C2212yescomplemented
149#2354C2212yes—
150#2354C2214yescomplemented
151#2354C2214yescomplemented
152#2353C2212yes—
153#2353C2212yescomplemented
154#2352C2212yes—
155#2352C2212yescomplemented
156Q8×C4⋊C4C2212yescomplemented
157D4×C22⋊C4C2214yes—
158D4×C22⋊C4C2214yes—
159#2336C2214yescomplemented
160#2331C2212yescomplemented
161#2330C2214yescomplemented
162#2328C2212yes—
163#2328C2214yes—
164#2328C2212yes—
165#2327C2212yescomplemented
166#2326C2214yescomplemented
167#2324C2214yescomplemented
168#2314C2214yes—
169#2309C2214yes—
170#2309C2212yes—
171#2308C2214yes—
172C4×C22⋊Q8C2212yescomplemented
173C4×C22⋊Q8C2212yescomplemented
174#2298C2212yes—
175#2298C2212yescomplemented
176#2297C2212yes—
177#2293C2214yescomplemented
178#2285C2211yescharacteristic
179#2285C2211yescharacteristic, complemented
180#2283C2211yescharacteristic
181#2283C2211yescharacteristic
182#2283C2211yescharacteristic, complemented
183C4×#117C2211yescharacteristic
184C4×#117C2212yescomplemented
185C4×#117C2211yescharacteristic, complemented
186C2×C4×C4⋊C4C2211yescharacteristic, complemented
187C22×#41C2311yescharacteristic
188C23×D4C2312yes—
189C23×D4C2312yes—
190C23×D4C2312yes—
191#535—48no—
192#533—28no—
193C2×C4⋊Q8C2311yescharacteristic
194C2×C4⋊Q8C2311yescharacteristic
195C2×#127—28no—
196C2×#127C2312yes—
197C2×#127C2312yes—
198C2×#127C2312yes—
199C2×#127C2312yes—
200C2×#127C2314yes—
201#529—416no—
202C2×#126C2318yes—
203C2×#126C2318yes—
204C2×#125C2312yes—
205C2×#125C2314yes—
206C2×#125C2314yes—
207C2×#124C2314yes—
208C2×#124C2314yes—
209C2×#124C2314yes—
210C2×#124C2318yes—
211C2×#123C2318yes—
212C2×#123C2318yes—
213C2×#123C2318yes—
214C2×C22⋊Q8C2312yes—
215C2×C22⋊Q8C2312yes—
216C2×C22⋊Q8C2312yes—
217C2×C22⋊Q8C2312yes—
218C2×#121C2314yes—
219C2×#121C2314yes—
220C2×#121C2314yes—
221C2×#121C2314yes—
222C2×#121C2314yes—
223C2×#121C2314yes—
224C2×#120C2314yes—
225C2×#120C2314yes—
226C4×#41—28no—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2314yes—
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2314yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2314yes—
242C2×C4×D4C2318yes—
243C2×#117C2312yes—
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2312yes—
248C2×#117C2312yes—
249C2×#117C2312yes—
250C2×#117C2318yes—
251C2×#117C2312yes—
252C2×#117C2318yes—
253C22×C4⋊C4C2312yes—
254C22×C22⋊C4C2318yes—
255C22×C42C2312yes—
256C22×C42C2311yescharacteristic
257C22×C42C2311yescharacteristic
258C22×C42C2311yescharacteristic
259#400C2312yes—
260#400C2314yes—
261#400C2312yes—
262#399C2312yes—
263#399C2312yes—
264#399C2318yes—
265#399C2318yes—
266#399C2318yes—
267#398C2312yes—
268#398C2312yes—
269#398C2314yes—
270#398C2318yes—
271#398C2318yes—
272#398C2312yes—
273#398C2312yes—
274#397C2318yes—
275#397C2318yes—
276#397C2312yes—
277#397C2312yes—
278#397C2312yes—
279#397C2312yes—
280#397C2314yes—
281#397C2314yes—
282#397C2318yes—
283#397C2318yes—
284#397C2318yes—
285#397C2318yes—
286#397C2318yes—
287#397C2318yes—
288#397C2318yes—
289#397C2318yes—
290#396C2318yes—
291#396C2318yes—
292#396C2318yes—
293#396C2318yes—
294#396C2318yes—
295#396C2318yes—
296#396C2318yes—
297#395C2314yes—
298#395C2312yes—
299#395C2312yes—
300#394C2314yes—
301#394C2314yes—
302#394C2318yes—
303#394C2318yes—
304#394C2318yes—
305#394C2314yes—
306#394C2314yes—
307#394C2314yes—
308#394C2314yes—
309#394C2314yes—
310#394C2318yes—
311#394C2318yes—
312#394C2318yes—
313#394C2318yes—
314#394C2318yes—
315#394C2318yes—
316#394C2318yes—
317#393C2312yes—
318#393C2312yes—
319#392C2314yes—
320#392C2314yes—
321#392C2314yes—
322#392C2314yes—
323#391C2312yes—
324#391C2314yes—
325#391C2318yes—
326#391C2314yes—
327#391C2312yes—
328#390C2314yes—
329#390C2314yes—
330#390C2314yes—
331#390C2318yes—
332#390C2314yes—
333#390C2314yes—
334#390C2318yes—
335#390C2314yes—
336#390C2314yes—
337#390C2314yes—
338#390C2314yes—
339#390C2314yes—
340#390C2314yes—
341#390C2318yes—
342#390C2314yes—
343#390C2314yes—
344#390C2314yes—
345#390C2314yes—
346#390C2314yes—
347#390C2314yes—
348#390C2314yes—
349#390C2318yes—
350#390C2314yes—
351#390C2318yes—
352#390C2318yes—
353#389C2314yes—
354#389C2318yes—
355#389C2318yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2318yes—
360#389C2314yes—
361#389C2318yes—
362#389C2312yes—
363#389C2312yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2314yes—
378#388C2314yes—
379#388C2314yes—
380#388C2314yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2314yes—
395#387C2314yes—
396#387C2314yes—
397#387C2314yes—
398#387C2314yes—
399#387C2314yes—
400#386C2318yes—
401#386C2318yes—
402#386C2318yes—
403#386C2318yes—
404#386C2318yes—
405#386C2318yes—
406#386C2318yes—
407#386C2318yes—
408#386C2318yes—
409#386C2318yes—
410#386C2314yes—
411#386C2314yes—
412#386C2318yes—
413#385C2318yes—
414#385C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#385C2314yes—
420#385C2314yes—
421#384C2312yes—
422#384C2314yes—
423#384C2314yes—
424#384C2314yes—
425#384C2312yes—
426#383C2312yes—
427#383C2312yes—
428#383C2312yes—
429#382C2312yes—
430#382C2314yes—
431#382C2312yes—
432#382C2311yescharacteristic
433#382C2312yes—
434#382C2311yescharacteristic
435#382C2312yes—
436#381C2312yes—
437#381C2312yes—
438#381C2312yes—
439#381C2318yes—
440#380C2312yes—
441#380C2312yes—
442#380C2312yes—
443#380C2312yes—
444#380C2312yes—
445#380C2312yes—
446#380C2312yes—
447#380C2318yes—
448#380C2318yes—
449#380C2312yes—
450#380C2312yes—
451#379C2318yes—
452#379C2314yes—
453#379C2314yes—
454#379C2318yes—
455#379C2318yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2318yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2311yescharacteristic
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2311yescharacteristic
477C4×C22⋊C4C2312yes—
478C4×C22⋊C4C2312yes—
479C4×C22⋊C4C2318yes—
480C4×C22⋊C4C2314yes—
481C4×C22⋊C4C2314yes—
482C4×C22⋊C4C2312yes—
483C4×C22⋊C4C2312yes—
484C4×C22⋊C4C2314yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2312yes—
487C4×C22⋊C4C2312yes—
488C4×C22⋊C4C2312yes—
489#376C2312yes—
490#376C2312yes—
491#376C2312yes—
492#376C2312yes—
493#376C2312yes—
494C2×#95C2312yes—
495C43C2312yes—
496C43C2312yes—
497C25C2414yes—
498C2×#41—24no—
499C2×#41—24no—
500C2×#41—42no—
501C22×Q8C2412yes—
502C22×Q8C2411yescharacteristic
503C22×Q8C2412yes—
504C22×D4—28no—
505C22×D4—28no—
506C22×D4—28no—
507C22×D4—44no—
508C22×D4—48no—
509C22×D4—44no—
510C22×D4—84no—
511C22×D4C2414yes—
512C22×D4C2414yes—
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C22×D4C2411yescharacteristic
516C22×D4C2418yes—
517C22×D4C2414yes—
518C22×D4C2414yes—
519C22×D4C2414yes—
520C22×D4C2414yes—
521C22×D4C2418yes—
522C23×C4C2411yescharacteristic
523C23×C4C2411yescharacteristic
524C23×C4C2411yescharacteristic
525C23×C4C2411yescharacteristic
526C23×C4C2411yescharacteristic
527C23×C4C2411yescharacteristic
528C23×C4C2414yes—
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C23×C4C2418yes—
532C23×C4C2418yes—
533C23×C4C2411yescharacteristic
534C4⋊Q8—24no—
535C4⋊Q8—24no—
536#127—28no—
537#127—28no—
538#127—28no—
539#127—28no—
540#127—48no—
541#126—416no—
542#126—88no—
543#125—28no—
544#125—48no—
545#125—48no—
546#124—48no—
547#124—48no—
548#124—48no—
549#124—88no—
550#123—416no—
551#123—88no—
552#123—88no—
553C22⋊Q8—28no—
554C22⋊Q8—28no—
555C22⋊Q8—28no—
556C22⋊Q8—44no—
557#121—216no—
558#121—48no—
559#121—48no—
560#121—48no—
561#121—84no—
562#121—84no—
563#120—48no—
564#120—48no—
565C4×Q8—24no—
566C4×Q8—24no—
567C4×Q8—28no—
568C4×Q8—28no—
569C4×Q8—48no—
570C4×D4—24no—
571C4×D4—24no—
572C4×D4—24no—
573C4×D4—24no—
574C4×D4—24no—
575C4×D4—24no—
576C4×D4—48no—
577C4×D4—48no—
578C4×D4—48no—
579C4×D4—48no—
580C4×D4—416no—
581#117—24no—
582#117—28no—
583#117—24no—
584#117—24no—
585#117—44no—
586#117—416no—
587#117—44no—
588#117—44no—
589#117—44no—
590#117—88no—
591C2×C4⋊C4—44no—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2418yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C22⋊C4—88no—
629C2×C22⋊C4C2411yescharacteristic
630C2×C22⋊C4C2411yescharacteristic
631C2×C22⋊C4C2411yescharacteristic
632C2×C22⋊C4C2411yescharacteristic
633C2×C22⋊C4C2411yescharacteristic
634C2×C22⋊C4C2411yescharacteristic
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2418yes—
667C2×C42—28no—
668C2×C42—24no—
669C2×C42—24no—
670C2×C42#4118yes—
671C2×C42C2414yes—
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2412yes—
675C2×C42C2414yes—
676C2×C42C2412yes—
677C2×C42C2412yes—
678C2×C42C2414yes—
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2412yes—
684C2×C42C2414yes—
685C2×C42C2418yes—
686C2×C42C2414yes—
687C2×C42C2418yes—
688C2×C42C2414yes—
689C2×C42C2414yes—
690C2×C42C2414yes—
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695#95C2412yes—
696#95C2414yes—
697#95C2412yes—
698#95C2414yes—
699#95C2412yes—
700#95C2412yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2412yes—
708#95C2412yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2412yes—
714#95C2412yes—
715#95C2414yes—
716#95C2414yes—
717#95C2418yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726#95C2414yes—
727#95C2418yes—
728#95C2414yes—
729#95C2414yes—
730#95C2418yes—
731C24—28no—
732C24—48no—
733C24—44no—
734C24—48no—
735C24—44no—
736C24C2518yes—
737C24C2511yescharacteristic
738C24C2511yescharacteristic
739C24C2511yescharacteristic
740#41—416no—
741C2×Q8—22no—
742C2×Q8—24no—
743C2×Q8—24no—
744C2×Q8—24no—
745C2×Q8—22no—
746C2×Q8—24no—
747C2×Q8—41no—
748C2×Q8—44no—
749C2×D4—22no—
750C2×D4—22no—
751C2×D4—22no—
752C2×D4—22no—
753C2×D4—216no—
754C2×D4—22no—
755C2×D4—28no—
756C2×D4—28no—
757C2×D4—28no—
758C2×D4—28no—
759C2×D4—28no—
760C2×D4—28no—
761C2×D4—28no—
762C2×D4—22no—
763C2×D4—28no—
764C2×D4—28no—
765C2×D4—28no—
766C2×D4—41no—
767C2×D4—41no—
768C2×D4—41no—
769C2×D4—48no—
770C2×D4—48no—
771C2×D4—44no—
772C2×D4—44no—
773C2×D4—44no—
774C2×D4—48no—
775C2×D4—48no—
776C2×D4—44no—
777C2×D4—48no—
778C2×D4—48no—
779C2×D4—48no—
780C2×D4—816no—
781C2×D4—816no—
782C2×D4—816no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—24no—
787C22×C4—22no—
788C22×C4—28no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—42no—
799C22×C4—48no—
800C22×C4—48no—
801C22×C4—44no—
802C22×C4—48no—
803C22×C4—48no—
804C22×C4—48no—
805C22×C4—48no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—44no—
809C22×C4C2×#4114yes—
810C22×C4C2×#4114yes—
811C22×C4C2×#4114yes—
812C22×C4H(5,𝔽2)14yes—
813C22×C4C2511yescharacteristic
814C22×C4C2514yes—
815C22×C4C2511yescharacteristic
816C22×C4C2511yescharacteristic
817C22×C4C2514yes—
818C22×C4C2514yes—
819C22×C4C2511yescharacteristic
820C22×C4C2514yes—
821C22×C4C2514yes—
822C22×C4C2514yes—
823C22×C4C2518yes—
824C22×C4C2511yescharacteristic
825C22×C4C2514yes—
826C22×C4C2514yes—
827C22×C4C2511yescharacteristic
828C22×C4C2511yescharacteristic
829C22×C4C2511yescharacteristic
830C22×C4C2511yescharacteristic
831C22×C4C2511yescharacteristic
832C22×C4C2511yescharacteristic
833C22×C4C2511yescharacteristic
834C4⋊C4—22no—
835C4⋊C4—22no—
836C4⋊C4—22no—
837C4⋊C4—22no—
838C4⋊C4—22no—
839C4⋊C4—22no—
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—28no—
843C4⋊C4—28no—
844C4⋊C4—24no—
845C4⋊C4—24no—
846C4⋊C4—28no—
847C4⋊C4—28no—
848C4⋊C4—24no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—28no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4—48no—
858C4⋊C4—44no—
859C4⋊C4—48no—
860C4⋊C4—48no—
861C4⋊C4—48no—
862C4⋊C4—44no—
863C4⋊C4—44no—
864C4⋊C4—48no—
865C4⋊C4—48no—
866C4⋊C4—48no—
867C4⋊C4—48no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C22⋊C4—22no—
871C22⋊C4—22no—
872C22⋊C4—28no—
873C22⋊C4—28no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—216no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C22⋊C4—48no—
882C22⋊C4—48no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C22⋊C4—44no—
886C22⋊C4—44no—
887C22⋊C4—48no—
888C22⋊C4—48no—
889C22⋊C4—48no—
890C22⋊C4—48no—
891C22⋊C4—48no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C22⋊C4—48no—
897C22⋊C4—48no—
898C22⋊C4—48no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—48no—
904C22⋊C4—48no—
905C22⋊C4—48no—
906C22⋊C4—48no—
907C22⋊C4—48no—
908C42—22no—
909C42—22no—
910C42—22no—
911C42—22no—
912C42—22no—
913C42—22no—
914C42—28no—
915C42—28no—
916C42—24no—
917C42—24no—
918C42—24no—
919C42—24no—
920C42—28no—
921C42—44no—
922C42—44no—
923C42—48no—
924C42—44no—
925C42—44no—
926C42—48no—
927C42—44no—
928C42C2×#4114yes—
929C42C2×#4114yes—
930C42C2×#4114yes—
931C42C2×#4114yes—
932C23—21no—
933C23—21no—
934C23—21no—
935C23—22no—
936C23—22no—
937C23—21no—
938C23—22no—
939C23—22no—
940C23—21no—
941C23—28no—
942C23—28no—
943C23—21no—
944C23—21no—
945C23—28no—
946C23—22no—
947C23—28no—
948C23—28no—
949C23—28no—
950C23—22no—
951C23—28no—
952C23—416no—
953C23—88no—
954C23—88no—
955C23—168no—
956C23—168no—
957C23C22×#4112yes—
958C23C2×H(5,𝔽2)12yes—
959C23C2611yescharacteristic
960Q8—44no—
961Q8—48no—
962Q8—84no—
963D4—44no—
964D4—44no—
965D4—44no—
966D4—416no—
967D4—416no—
968D4—88no—
969D4—88no—
970D4—88no—
971D4—88no—
972D4—816no—
973D4—168no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—22no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—28no—
982C2×C4—28no—
983C2×C4—28no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—28no—
995C2×C4—24no—
996C2×C4—21no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—22no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—22no—
1007C2×C4—24no—
1008C2×C4—28no—
1009C2×C4—24no—
1010C2×C4—21no—
1011C2×C4—24no—
1012C2×C4—22no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—28no—
1017C2×C4—24no—
1018C2×C4—22no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—44no—
1023C2×C4—44no—
1024C2×C4—44no—
1025C2×C4—44no—
1026C2×C4—82no—
1027C2×C4—82no—
1028C2×C4—88no—
1029C2×C4—816no—
1030C2×C4—816no—
1031C2×C4C22×#4112yes—
1032C2×C4C22×#4112yes—
1033C2×C4C22×#4112yes—
1034C2×C4C22×#4112yes—
1035C2×C4C22×#4112yes—
1036C2×C4C22×#4112yes—
1037C2×C4C2×H(5,𝔽2)12yes—
1038C2×C4C2×H(5,𝔽2)12yes—
1039C2×C4#58512yes—
1040C2×C4#58514yes—
1041C22—22no—
1042C22—22no—
1043C22—22no—
1044C22—22no—
1045C22—24no—
1046C22—41no—
1047C22—41no—
1048C22—42no—
1049C22—42no—
1050C22—42no—
1051C22—41no—
1052C22—48no—
1053C22—41no—
1054C22—48no—
1055C22—41no—
1056C22—48no—
1057C22—48no—
1058C22—48no—
1059C22—42no—
1060C22—48no—
1061C22—42no—
1062C22—48no—
1063C22—1616no—
1064C22C23×#4111yescharacteristic
1065C22C22×H(5,𝔽2)11yescharacteristic
1066C22C2×#58511yescharacteristic
1067C22C2×#58512yes—
1068C22H(7,𝔽2)12yes—
1069C4—22no—
1070C4—22no—
1071C4—22no—
1072C4—22no—
1073C4—22no—
1074C4—41no—
1075C4—44no—
1076C4—41no—
1077C4—41no—
1078C4—41no—
1079C4—41no—
1080C4—44no—
1081C4—44no—
1082C4—44no—
1083C4—44no—
1084C4—48no—
1085C4—44no—
1086C4—44no—
1087C4—44no—
1088C4#349414yes—
1089C4#351014yes—
1090C2—42no—
1091C2—42no—
1092C2—81no—
1093C2—88no—
1094C2C2×#349411yescharacteristic
1095C2C2×#351011yescharacteristic
1096C2#6285511yescharacteristic
1097C2#6295512yes—
1098C2#6296912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35272C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #51091C2semidirect
2. #51088C2semidirect
3. #51041C2semidirect
4. #50878C2semidirect
5. #45072C2semidirect
6. #45019C2semidirect
7. #44965C2semidirect
8. #44901C2semidirect
9. #39736C2semidirect
10. #39147C2semidirect
11. #38254C2semidirect
12. #37786C2semidirect
13. #37432C2semidirect
14. #37321C2semidirect
15. #36302C2semidirect
16. #36117C2semidirect
17. #35343C2semidirect
18. #35296C2semidirect
19. #35285C2semidirect
21. #35202C2semidirect
22. #34627C2semidirect
23. #34373C2semidirect
24. #34364C2semidirect
25. #34121C2semidirect
29. C2×#529C22semidirect
31. #2864C22semidirect
32. #2861C22semidirect
33. #2859C22semidirect
38. #2854C22semidirect
39. #2797C22semidirect
40. #2796C22semidirect
41. #2796C22semidirect
42. #2786C22semidirect
43. #2786C22semidirect
44. #2761C22semidirect
45. #2757C22semidirect
46. #2752C22semidirect
47. #2740C22semidirect
50. #2715C22semidirect
51. #2715C22semidirect
52. #2710C22semidirect
53. #2709C22semidirect
54. #2705C22semidirect
55. #2701C22semidirect
57. #2691C22semidirect
60. #2644C22semidirect
64. #2634C22semidirect
65. #2633C22semidirect
66. #2628C22semidirect
67. #2628C22semidirect
69. #2621C22semidirect
70. #2621C22semidirect
71. #2620C22semidirect
75. #2606C22semidirect
76. #2602C22semidirect
77. #2602C22semidirect
78. #2601C22semidirect
79. #2601C22semidirect
80. #2601C22semidirect
81. #2595C22semidirect
82. #2566C22semidirect
83. #2566C22semidirect
84. #2557C22semidirect
85. #2552C22semidirect
86. #2552C22semidirect
94. #2531C22semidirect
95. #2516C22semidirect
96. #2513C22semidirect
97. #2513C22semidirect
98. #2512C22semidirect
99. #2512C22semidirect
100. #2512C22semidirect
101. #2501C22semidirect
102. #2500C22semidirect
103. #2490C22semidirect
104. #2490C22semidirect
105. #2490C22semidirect
108. #2479C22semidirect
109. #2476C22semidirect
110. #2474C22semidirect
111. #2474C22semidirect
112. #2471C22semidirect
113. #2454C22semidirect
114. #2448C22semidirect
115. #2447C22semidirect
116. #2445C22semidirect
121. #2427C22semidirect
122. #2426C22semidirect
123. #2425C22semidirect
124. #2422C22semidirect
125. #2422C22semidirect
126. #2420C22semidirect
133. #2399C22semidirect
134. #2398C22semidirect
141. #2363C22semidirect
143. #2361C22semidirect
145. #2356C22semidirect
146. #2355C22semidirect
147. #2355C22semidirect
148. #2355C22semidirect
150. #2354C22semidirect
151. #2354C22semidirect
153. #2353C22semidirect
155. #2352C22semidirect
156. Q8×C4⋊C4C22semidirect
159. #2336C22semidirect
160. #2331C22semidirect
161. #2330C22semidirect
165. #2327C22semidirect
166. #2326C22semidirect
167. #2324C22semidirect
172. C4×C22⋊Q8C22semidirect
173. C4×C22⋊Q8C22semidirect
175. #2298C22semidirect
177. #2293C22semidirect
179. #2285C22semidirect
182. #2283C22semidirect
184. C4×#117C22semidirect
185. C4×#117C22semidirect
186. C2×C4×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#510912
#510882
#510412
#508782
#450722
#450192
#449652
#449012
#397362
#391472
#382542
#377862
#374322
#373212
#363022
#361172
#353432
#352962
#352852
#352722
#352022
#346272
#343732
#343642
#341212