Finite Group Databasebeta

← #7647855

Subgroups — #7647855

Order 512.

5744 conjugacy classes of subgroups.

The subgroup lattice has 1101 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41058C218yesmaximal, complemented
2#41021C218yesmaximal, complemented
3#39434C214yesmaximal, complemented
4#39270C214yesmaximal, complemented
5#37786C214yesmaximal, complemented
6#37775C214yesmaximal, complemented
7#37625C212yesmaximal, complemented
8#37621C211yesmaximal, characteristic, complemented
9#37614C211yesmaximal, characteristic, complemented
10#37331C214yesmaximal, complemented
11#37321C212yesmaximal, complemented
12#37319C212yesmaximal, complemented
13#35538C214yesmaximal, complemented
14#35296C212yesmaximal, complemented
15#35278C212yesmaximal, complemented
16#35274C211yesmaximal, characteristic, complemented
17#35202C211yesmaximal, characteristic, complemented
18#35171C212yesmaximal, complemented
19#35171C212yesmaximal, complemented
20#34934C212yesmaximal, complemented
21#34210C211yesmaximal, characteristic, complemented
22#34151C211yesmaximal, characteristic, complemented
23#34086C211yesmaximal, characteristic, complemented
24C2×#540C2214yescomplemented
25C2×#540C2214yescomplemented
26C2×#535C2214yes—
27C2×#532C2211yescharacteristic
28C22×#127C2211yescharacteristic
29C2×#529C2211yescharacteristic
30C2×#529C2214yescomplemented
31C2×#518C2212yes—
32#2867C2212yes—
33#2864C2212yescomplemented
34#2859C2212yescomplemented
35#2858C2212yes—
36#2856C2214yescomplemented
37#2856C2214yescomplemented
38#2854C2214yescomplemented
39#2854C2214yescomplemented
40#2829C2218yescomplemented
41#2818C2214yes—
42#2813C2214yes—
43#2803C2218yescomplemented
44#2797C2218yescomplemented
45#2796C2218yescomplemented
46#2715C2218yescomplemented
47#2714C2218yescomplemented
48#2710C2218yescomplemented
49#2709C2218yescomplemented
50#2709C2218yescomplemented
51#2705C2218yescomplemented
52#2697C2218yes—
53#2685C2218yes—
54#2682C2218yescomplemented
55#2678C2218yes—
56#2673C2218yescomplemented
57#2673C2218yescomplemented
58#2668C2218yes—
59#2667C2214yes—
60#2662C2214yescomplemented
61#2661C2218yescomplemented
62#2661C2218yescomplemented
63#2657C2214yes—
64#2657C2212yes—
65#2644C2214yescomplemented
66#2641C2212yes—
67#2641C2214yescomplemented
68#2630C2218yescomplemented
69#2628C2212yescomplemented
70#2624C2214yescomplemented
71#2620C2214yescomplemented
72#2619C2212yes—
73#2619C2212yes—
74#2619C2212yescomplemented
75#2616C2212yes—
76#2615C2212yes—
77#2613C2214yes—
78#2606C2214yescomplemented
79#2602C2218yescomplemented
80#2595C2218yescomplemented
81#2562C2212yescomplemented
82#2557C2218yescomplemented
83#2554C2218yescomplemented
84#2552C2212yescomplemented
85#2552C2212yescomplemented
86#2548C2212yes—
87#2541C2212yes—
88#2541C2212yes—
89#2541C2212yes—
90#2541C2214yes—
91#2540C2212yescomplemented
92#2539C2218yes—
93#2538C2212yescomplemented
94#2537C2212yescomplemented
95#2512C2214yescomplemented
96#2490C2214yescomplemented
97#2490C2214yescomplemented
98#2490C2214yescomplemented
99#2474C2218yescomplemented
100#2471C2218yescomplemented
101#2464C2218yescomplemented
102#2464C2218yescomplemented
103#2456C2218yescomplemented
104#2455C2218yescomplemented
105#2454C2214yescomplemented
106#2445C2218yescomplemented
107#2445C2218yescomplemented
108#2445C2214yescomplemented
109#2445C2214yescomplemented
110#2441C2214yes—
111#2441C2214yes—
112#2435C2212yes—
113#2433C2212yes—
114#2433C2214yes—
115#2433C2214yes—
116#2428C2218yescomplemented
117#2428C2214yescomplemented
118#2428C2214yescomplemented
119#2428C2218yescomplemented
120#2428C2214yescomplemented
121#2428C2214yescomplemented
122#2427C2214yescomplemented
123#2426C2214yescomplemented
124#2424C2218yes—
125#2422C2214yescomplemented
126#2422C2214yescomplemented
127#2422C2214yescomplemented
128#2418C2218yes—
129#2414C2214yes—
130#2414C2218yescomplemented
131#2411C2218yes—
132#2408C2214yes—
133#2392C2218yescomplemented
134#2374C2214yes—
135#2373C2214yescomplemented
136#2370C2212yescomplemented
137#2367C2212yescomplemented
138#2366C2214yes—
139#2366C2214yes—
140#2363C2212yes—
141#2362C2212yes—
142D4×C22⋊C4C2214yes—
143D4×C22⋊C4C2214yes—
144#2337C2214yescomplemented
145#2333C2214yes—
146#2331C2211yescharacteristic, complemented
147#2331C2211yescharacteristic, complemented
148#2330C2214yescomplemented
149#2328C2212yes—
150#2328C2212yes—
151#2328C2211yescharacteristic, complemented
152#2328C2211yescharacteristic, complemented
153#2324C2212yes—
154#2324C2212yes—
155#2324C2214yescomplemented
156#2324C2214yescomplemented
157#2309C2212yes—
158C4×#127C2212yes—
159C4×#127C2212yes—
160C4×#127C2214yescomplemented
161C4×#121C2214yescomplemented
162#2298C2212yescomplemented
163#2297C2214yes—
164#2295C2211yescharacteristic, complemented
165#2293C2212yes—
166#2293C2212yescomplemented
167#2293C2211yescharacteristic, complemented
168#2293C2214yescomplemented
169#2290C2212yes—
170#2290C2214yescomplemented
171#2285C2211yescharacteristic
172#2283C2211yescharacteristic
173C42×Q8C2211yescharacteristic, complemented
174C42×D4C2212yescomplemented
175C42×D4C2211yescharacteristic, complemented
176C4×#117C2211yescharacteristic
177C4×#117C2211yescharacteristic
178C4×#117C2212yescomplemented
179C22×#41C2312yes—
180C23×D4C2312yes—
181C23×D4C2312yes—
182C23×D4C2312yes—
183#540—416no—
184#540—416no—
185#535—416no—
186#532—28no—
187C2×C4⋊Q8C2311yescharacteristic
188C2×#127—28no—
189C2×#127C2312yes—
190C2×#127C2312yes—
191C2×#127C2312yes—
192C2×#127C2311yescharacteristic
193C2×#127C2312yes—
194C2×#127C2314yes—
195C2×#127C2314yes—
196C2×#127C2314yes—
197C2×#127C2318yes—
198C2×#127C2318yes—
199#529—28no—
200#529—416no—
201C2×#126C2312yes—
202C2×#126C2318yes—
203C2×#125C2311yescharacteristic
204C2×#125C2314yes—
205C2×#125C2314yes—
206C2×#124C2312yes—
207C2×#124C2311yescharacteristic
208C2×#124C2318yes—
209C2×#124C2314yes—
210C2×#123C2312yes—
211C2×#123C2318yes—
212C2×#123C2318yes—
213C2×#123C2318yes—
214C2×#123C2318yes—
215C2×#123C2318yes—
216C2×#123C2318yes—
217C2×C22⋊Q8C2311yescharacteristic
218C2×C22⋊Q8C2314yes—
219C2×#121C2312yes—
220C2×#121C2314yes—
221C2×#121C2312yes—
222C2×#121C2311yescharacteristic
223C2×#121C2314yes—
224C2×#121C2314yes—
225C2×#121C2314yes—
226C2×#121C2314yes—
227C2×#121C2314yes—
228C2×#121C2314yes—
229C2×#121C2314yes—
230C2×#121C2318yes—
231C2×#121C2318yes—
232C2×#121C2318yes—
233C2×#121C2318yes—
234C2×#121C2318yes—
235C2×#121C2318yes—
236C2×#120C2318yes—
237C2×#120C2318yes—
238C2×#120C2318yes—
239#518—48no—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×D4C2314yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2312yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2314yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2318yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2318yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2318yes—
258C2×#117C2311yescharacteristic
259C2×#117C2312yes—
260C2×#117C2312yes—
261C2×#117C2312yes—
262C2×#117C2311yescharacteristic
263C2×#117C2312yes—
264C2×#117C2314yes—
265C2×#117C2318yes—
266C22×C22⋊C4C2318yes—
267C22×C42C2312yes—
268C22×C42C2314yes—
269C22×C42C2311yescharacteristic
270#400C2314yes—
271#399C2318yes—
272#399C2314yes—
273#399C2318yes—
274#398C2318yes—
275#398C2318yes—
276#397C2318yes—
277#397C2318yes—
278#397C2318yes—
279#397C2318yes—
280#397C2318yes—
281#397C2318yes—
282#396C2318yes—
283#396C2318yes—
284#396C2318yes—
285#396C2318yes—
286#396C2318yes—
287#395C2314yes—
288#394C2314yes—
289#394C2318yes—
290#394C2318yes—
291#394C2314yes—
292#394C2314yes—
293#394C2318yes—
294#394C2318yes—
295#394C2318yes—
296#394C2318yes—
297#394C2314yes—
298#394C2314yes—
299#394C2314yes—
300#394C2318yes—
301#394C2318yes—
302#394C2318yes—
303#394C2318yes—
304#394C2318yes—
305#394C2318yes—
306#394C2318yes—
307#394C2318yes—
308#394C2318yes—
309#394C2318yes—
310#393C2314yes—
311#392C2318yes—
312#392C2314yes—
313#392C2314yes—
314#392C2318yes—
315#392C2318yes—
316#392C2318yes—
317#392C2314yes—
318#392C2314yes—
319#392C2314yes—
320#392C2318yes—
321#392C2314yes—
322#392C2318yes—
323#392C2318yes—
324#392C2318yes—
325#392C2318yes—
326#391C2314yes—
327#391C2314yes—
328#391C2312yes—
329#390C2314yes—
330#390C2314yes—
331#390C2314yes—
332#390C2314yes—
333#390C2314yes—
334#390C2314yes—
335#390C2318yes—
336#390C2314yes—
337#390C2314yes—
338#390C2318yes—
339#390C2318yes—
340#390C2312yes—
341#390C2312yes—
342#390C2314yes—
343#390C2314yes—
344#390C2314yes—
345#390C2318yes—
346#390C2318yes—
347#390C2314yes—
348#390C2318yes—
349#390C2314yes—
350#390C2312yes—
351#390C2318yes—
352#390C2318yes—
353#390C2314yes—
354#390C2314yes—
355#390C2314yes—
356#390C2318yes—
357#389C2312yes—
358#389C2312yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2318yes—
363#389C2318yes—
364#389C2312yes—
365#389C2314yes—
366#389C2314yes—
367#389C2318yes—
368#389C2312yes—
369#389C2314yes—
370#388C2318yes—
371#388C2314yes—
372#388C2314yes—
373#388C2314yes—
374#388C2318yes—
375#388C2318yes—
376#388C2314yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2314yes—
381#388C2314yes—
382#388C2314yes—
383#388C2314yes—
384#388C2314yes—
385#388C2314yes—
386#388C2318yes—
387#388C2318yes—
388#387C2314yes—
389#387C2318yes—
390#387C2318yes—
391#387C2314yes—
392#387C2314yes—
393#387C2318yes—
394#387C2314yes—
395#387C2314yes—
396#387C2314yes—
397#386C2314yes—
398#386C2314yes—
399#386C2318yes—
400#386C2318yes—
401#386C2318yes—
402#386C2318yes—
403#386C2318yes—
404#386C2318yes—
405#386C2314yes—
406#386C2314yes—
407#386C2314yes—
408#386C2314yes—
409#386C2318yes—
410#386C2318yes—
411#386C2314yes—
412#386C2318yes—
413#386C2318yes—
414#385C2314yes—
415#385C2314yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#385C2314yes—
420#384C2312yes—
421#384C2314yes—
422#384C2314yes—
423#383C2312yes—
424#382C2312yes—
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#381C2312yes—
428#380C2314yes—
429#380C2314yes—
430#380C2312yes—
431#380C2314yes—
432#380C2312yes—
433#380C2312yes—
434#380C2318yes—
435#379C2318yes—
436#379C2318yes—
437C4×C4⋊C4C2312yes—
438C4×C4⋊C4C2312yes—
439C4×C4⋊C4C2312yes—
440C4×C4⋊C4C2312yes—
441C4×C4⋊C4C2312yes—
442C4×C4⋊C4C2312yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2312yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2312yes—
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2312yes—
454C4×C22⋊C4C2312yes—
455C4×C22⋊C4C2314yes—
456C4×C22⋊C4C2314yes—
457C4×C22⋊C4C2312yes—
458C4×C22⋊C4C2318yes—
459C4×C22⋊C4C2314yes—
460C4×C22⋊C4C2314yes—
461C4×C22⋊C4C2314yes—
462C4×C22⋊C4C2312yes—
463C4×C22⋊C4C2312yes—
464C4×C22⋊C4C2314yes—
465C4×C22⋊C4C2314yes—
466C4×C22⋊C4C2312yes—
467C4×C22⋊C4C2312yes—
468C4×C22⋊C4C2312yes—
469#376C2311yescharacteristic
470#376C2311yescharacteristic
471#376C2312yes—
472#376C2312yes—
473#376C2312yes—
474C43C2311yescharacteristic
475C43C2311yescharacteristic
476C43C2312yes—
477C43C2312yes—
478C25C2414yes—
479C2×#41—28no—
480C2×#41—48no—
481C22×Q8C2411yescharacteristic
482C22×Q8C2412yes—
483C22×D4—28no—
484C22×D4—28no—
485C22×D4—28no—
486C22×D4—44no—
487C22×D4—44no—
488C22×D4—48no—
489C22×D4—84no—
490C22×D4C2411yescharacteristic
491C22×D4C2412yes—
492C22×D4C2414yes—
493C22×D4C2414yes—
494C22×D4C2414yes—
495C22×D4C2414yes—
496C22×D4C2412yes—
497C22×D4C2418yes—
498C22×D4C2418yes—
499C22×D4C2412yes—
500C22×D4C2414yes—
501C22×D4C2414yes—
502C22×D4C2412yes—
503C22×D4C2414yes—
504C22×D4C2418yes—
505C22×D4C2418yes—
506C22×D4C2418yes—
507C22×D4C2418yes—
508C22×D4C2418yes—
509C23×C4C2412yes—
510C23×C4C2414yes—
511C23×C4C2411yescharacteristic
512C23×C4C2411yescharacteristic
513C23×C4C2418yes—
514C23×C4C2414yes—
515C23×C4C2414yes—
516C23×C4C2418yes—
517C23×C4C2414yes—
518C23×C4C2411yescharacteristic
519C4⋊Q8—24no—
520#127—28no—
521#127—28no—
522#127—28no—
523#127—28no—
524#127—24no—
525#127—48no—
526#127—416no—
527#127—48no—
528#127—48no—
529#127—88no—
530#126—28no—
531#126—416no—
532#125—216no—
533#125—24no—
534#125—48no—
535#124—24no—
536#124—28no—
537#124—416no—
538#124—48no—
539#123—28no—
540#123—416no—
541#123—416no—
542#123—416no—
543#123—416no—
544#123—416no—
545#123—88no—
546C22⋊Q8—24no—
547C22⋊Q8—48no—
548#121—24no—
549#121—28no—
550#121—28no—
551#121—216no—
552#121—216no—
553#121—416no—
554#121—416no—
555#121—416no—
556#121—48no—
557#121—48no—
558#121—48no—
559#121—416no—
560#121—48no—
561#121—48no—
562#121—48no—
563#121—88no—
564#121—88no—
565#120—416no—
566#120—416no—
567#120—88no—
568C4×Q8—28no—
569C4×Q8—24no—
570C4×D4—28no—
571C4×D4—28no—
572C4×D4—24no—
573C4×D4—28no—
574C4×D4—28no—
575C4×D4—216no—
576C4×D4—28no—
577C4×D4—44no—
578C4×D4—48no—
579C4×D4—48no—
580C4×D4—416no—
581C4×D4—48no—
582C4×D4—416no—
583C4×D4—88no—
584C4×D4—84no—
585C4×D4—84no—
586#117—28no—
587#117—28no—
588#117—24no—
589#117—28no—
590#117—42no—
591#117—48no—
592#117—416no—
593#117—44no—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2418yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2412yes—
623C2×C22⋊C4—416no—
624C2×C22⋊C4C2412yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2412yes—
630C2×C22⋊C4C2412yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2412yes—
636C2×C22⋊C4C2412yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2412yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2414yes—
665C2×C42—48no—
666C2×C42—44no—
667C2×C42#4118yes—
668C2×C42C2412yes—
669C2×C42C2414yes—
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2412yes—
673C2×C42C2414yes—
674C2×C42C2414yes—
675C2×C42C2412yes—
676C2×C42C2411yescharacteristic
677C2×C42C2412yes—
678C2×C42C2412yes—
679C2×C42C2414yes—
680C2×C42C2414yes—
681C2×C42C2412yes—
682C2×C42C2414yes—
683C2×C42C2412yes—
684C2×C42C2414yes—
685C2×C42C2414yes—
686C2×C42C2414yes—
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692#95C2412yes—
693#95C2412yes—
694#95C2412yes—
695#95C2414yes—
696#95C2414yes—
697#95C2412yes—
698#95C2412yes—
699#95C2414yes—
700#95C2412yes—
701#95C2414yes—
702#95C2412yes—
703#95C2412yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2418yes—
710#95C2412yes—
711#95C2412yes—
712#95C2418yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2418yes—
720#95C2418yes—
721C24—28no—
722C24—44no—
723C24—44no—
724C24—48no—
725C24—48no—
726C24C2518yes—
727C24C2512yes—
728C24C2514yes—
729C24C2511yescharacteristic
730#41—816no—
731C2×Q8—22no—
732C2×Q8—24no—
733C2×Q8—24no—
734C2×Q8—44no—
735C2×D4—24no—
736C2×D4—28no—
737C2×D4—22no—
738C2×D4—24no—
739C2×D4—28no—
740C2×D4—28no—
741C2×D4—28no—
742C2×D4—28no—
743C2×D4—24no—
744C2×D4—24no—
745C2×D4—28no—
746C2×D4—28no—
747C2×D4—28no—
748C2×D4—24no—
749C2×D4—24no—
750C2×D4—28no—
751C2×D4—28no—
752C2×D4—216no—
753C2×D4—216no—
754C2×D4—24no—
755C2×D4—28no—
756C2×D4—44no—
757C2×D4—44no—
758C2×D4—44no—
759C2×D4—44no—
760C2×D4—432no—
761C2×D4—48no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—48no—
766C2×D4—48no—
767C2×D4—44no—
768C2×D4—48no—
769C2×D4—48no—
770C2×D4—44no—
771C2×D4—48no—
772C2×D4—48no—
773C2×D4—48no—
774C2×D4—48no—
775C2×D4—48no—
776C2×D4—48no—
777C2×D4—48no—
778C2×D4—48no—
779C2×D4—48no—
780C2×D4—48no—
781C2×D4—48no—
782C2×D4—48no—
783C2×D4—48no—
784C2×D4—48no—
785C2×D4—48no—
786C2×D4—48no—
787C2×D4—816no—
788C2×D4—816no—
789C22×C4—22no—
790C22×C4—24no—
791C22×C4—22no—
792C22×C4—24no—
793C22×C4—28no—
794C22×C4—28no—
795C22×C4—24no—
796C22×C4—28no—
797C22×C4—24no—
798C22×C4—216no—
799C22×C4—28no—
800C22×C4—28no—
801C22×C4—42no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4—44no—
805C22×C4—48no—
806C22×C4—44no—
807C22×C4—44no—
808C22×C4—48no—
809C22×C4—44no—
810C22×C4—44no—
811C22×C4—48no—
812C22×C4—48no—
813C22×C4—48no—
814C22×C4C2×#4114yes—
815C22×C4C2×#4114yes—
816C22×C4C2×#4114yes—
817C22×C4C2514yes—
818C22×C4C2512yes—
819C22×C4C2512yes—
820C22×C4C2512yes—
821C22×C4C2512yes—
822C22×C4C2514yes—
823C22×C4C2512yes—
824C22×C4C2514yes—
825C22×C4C2514yes—
826C22×C4C2518yes—
827C22×C4C2512yes—
828C22×C4C2511yescharacteristic
829C22×C4C2511yescharacteristic
830C22×C4C2511yescharacteristic
831C22×C4C2511yescharacteristic
832C22×C4C2514yes—
833C22×C4C2512yes—
834C22×C4C2511yescharacteristic
835C22×C4C2511yescharacteristic
836C4⋊C4—24no—
837C4⋊C4—24no—
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—22no—
841C4⋊C4—24no—
842C4⋊C4—22no—
843C4⋊C4—24no—
844C4⋊C4—24no—
845C4⋊C4—24no—
846C4⋊C4—28no—
847C4⋊C4—28no—
848C4⋊C4—216no—
849C4⋊C4—24no—
850C4⋊C4—28no—
851C4⋊C4—216no—
852C4⋊C4—28no—
853C4⋊C4—24no—
854C4⋊C4—42no—
855C4⋊C4—48no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4—48no—
860C4⋊C4—48no—
861C4⋊C4—48no—
862C4⋊C4—48no—
863C4⋊C4—44no—
864C4⋊C4H(5,𝔽2)18yes—
865C22⋊C4—24no—
866C22⋊C4—24no—
867C22⋊C4—24no—
868C22⋊C4—28no—
869C22⋊C4—28no—
870C22⋊C4—24no—
871C22⋊C4—24no—
872C22⋊C4—24no—
873C22⋊C4—216no—
874C22⋊C4—28no—
875C22⋊C4—28no—
876C22⋊C4—216no—
877C22⋊C4—28no—
878C22⋊C4—28no—
879C22⋊C4—216no—
880C22⋊C4—44no—
881C22⋊C4—48no—
882C22⋊C4—42no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C22⋊C4—48no—
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—44no—
898C22⋊C4—48no—
899C22⋊C4—48no—
900C22⋊C4—48no—
901C22⋊C4—48no—
902C22⋊C4—48no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C42—24no—
907C42—24no—
908C42—28no—
909C42—22no—
910C42—28no—
911C42—24no—
912C42—24no—
913C42—28no—
914C42—22no—
915C42—24no—
916C42—22no—
917C42—44no—
918C42—44no—
919C42—44no—
920C42—44no—
921C42—44no—
922C42—42no—
923C42—42no—
924C42—44no—
925C42C2×#4114yes—
926C42C2×#4114yes—
927C42C2×#4114yes—
928C42C2×#4114yes—
929C42H(5,𝔽2)14yes—
930C23—21no—
931C23—22no—
932C23—21no—
933C23—22no—
934C23—22no—
935C23—24no—
936C23—28no—
937C23—22no—
938C23—28no—
939C23—28no—
940C23—24no—
941C23—24no—
942C23—28no—
943C23—24no—
944C23—24no—
945C23—24no—
946C23—28no—
947C23—22no—
948C23—24no—
949C23—28no—
950C23—28no—
951C23—24no—
952C23—24no—
953C23—416no—
954C23—88no—
955C23—88no—
956C23—168no—
957C23—168no—
958C23C22×#4112yes—
959C23C2611yescharacteristic
960Q8—44no—
961Q8—84no—
962D4—416no—
963D4—416no—
964D4—48no—
965D4—416no—
966D4—44no—
967D4—416no—
968D4—84no—
969D4—816no—
970D4—816no—
971D4—88no—
972D4—88no—
973D4—84no—
974D4—84no—
975D4—88no—
976D4—168no—
977D4—168no—
978D4—168no—
979D4—168no—
980D4—168no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—21no—
984C2×C4—24no—
985C2×C4—21no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—24no—
989C2×C4—22no—
990C2×C4—28no—
991C2×C4—28no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—24no—
996C2×C4—22no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—22no—
1005C2×C4—24no—
1006C2×C4—28no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—22no—
1010C2×C4—28no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—28no—
1023C2×C4—44no—
1024C2×C4—48no—
1025C2×C4—416no—
1026C2×C4—816no—
1027C2×C4—88no—
1028C2×C4—88no—
1029C2×C4—88no—
1030C2×C4—168no—
1031C2×C4C22×#4112yes—
1032C2×C4C22×#4112yes—
1033C2×C4C22×#4112yes—
1034C2×C4C22×#4112yes—
1035C2×C4C22×#4112yes—
1036C2×C4C22×#4112yes—
1037C2×C4C2×H(5,𝔽2)18yes—
1038C2×C4C2×H(5,𝔽2)14yes—
1039C2×C4C2×H(5,𝔽2)12yes—
1040C2×C4C2×H(5,𝔽2)14yes—
1041C2×C4#58512yes—
1042C22—22no—
1043C22—22no—
1044C22—22no—
1045C22—42no—
1046C22—42no—
1047C22—44no—
1048C22—48no—
1049C22—42no—
1050C22—48no—
1051C22—44no—
1052C22—42no—
1053C22—44no—
1054C22—48no—
1055C22—48no—
1056C22—44no—
1057C22—44no—
1058C22—44no—
1059C22—44no—
1060C22—44no—
1061C22—48no—
1062C22—48no—
1063C22—42no—
1064C22—48no—
1065C22—44no—
1066C22—1616no—
1067C22C23×#4111yescharacteristic
1068C22C22×H(5,𝔽2)12yes—
1069C22C22×H(5,𝔽2)11yescharacteristic
1070C22C2×#58511yescharacteristic
1071C22H(7,𝔽2)12yes—
1072C4—22no—
1073C4—22no—
1074C4—22no—
1075C4—24no—
1076C4—28no—
1077C4—22no—
1078C4—44no—
1079C4—42no—
1080C4—42no—
1081C4—48no—
1082C4—44no—
1083C4—42no—
1084C4—44no—
1085C4—42no—
1086C4—42no—
1087C4—44no—
1088C4—42no—
1089C4#346014yes—
1090C4#350814yes—
1091C2—42no—
1092C2—84no—
1093C2—82no—
1094C2—88no—
1095C2C2×#346011yescharacteristic
1096C2C2×#350811yescharacteristic
1097C2#6285511yescharacteristic
1098C2#6291612yes—
1099C2#6292012yes—
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. #41058C2semidirect
2. #41021C2semidirect
3. #39434C2semidirect
4. #39270C2semidirect
5. #37786C2semidirect
6. #37775C2semidirect
7. #37625C2semidirect
8. #37621C2semidirect
9. #37614C2semidirect
10. #37331C2semidirect
11. #37321C2semidirect
12. #37319C2semidirect
13. #35538C2semidirect
14. #35296C2semidirect
15. #35278C2semidirect
16. #35274C2semidirect
17. #35202C2semidirect
18. #35171C2semidirect
19. #35171C2semidirect
20. #34934C2semidirect
21. #34210C2semidirect
22. #34151C2semidirect
23. #34086C2semidirect
24. C2×#540C22semidirect
25. C2×#540C22semidirect
30. C2×#529C22semidirect
33. #2864C22semidirect
34. #2859C22semidirect
36. #2856C22semidirect
37. #2856C22semidirect
38. #2854C22semidirect
39. #2854C22semidirect
40. #2829C22semidirect
43. #2803C22semidirect
44. #2797C22semidirect
45. #2796C22semidirect
46. #2715C22semidirect
47. #2714C22semidirect
48. #2710C22semidirect
49. #2709C22semidirect
50. #2709C22semidirect
51. #2705C22semidirect
54. #2682C22semidirect
56. #2673C22semidirect
57. #2673C22semidirect
60. #2662C22semidirect
61. #2661C22semidirect
62. #2661C22semidirect
65. #2644C22semidirect
67. #2641C22semidirect
68. #2630C22semidirect
69. #2628C22semidirect
70. #2624C22semidirect
71. #2620C22semidirect
74. #2619C22semidirect
78. #2606C22semidirect
79. #2602C22semidirect
80. #2595C22semidirect
81. #2562C22semidirect
82. #2557C22semidirect
83. #2554C22semidirect
84. #2552C22semidirect
85. #2552C22semidirect
91. #2540C22semidirect
93. #2538C22semidirect
94. #2537C22semidirect
95. #2512C22semidirect
96. #2490C22semidirect
97. #2490C22semidirect
98. #2490C22semidirect
99. #2474C22semidirect
100. #2471C22semidirect
101. #2464C22semidirect
102. #2464C22semidirect
103. #2456C22semidirect
104. #2455C22semidirect
105. #2454C22semidirect
106. #2445C22semidirect
107. #2445C22semidirect
108. #2445C22semidirect
109. #2445C22semidirect
116. #2428C22semidirect
117. #2428C22semidirect
118. #2428C22semidirect
119. #2428C22semidirect
120. #2428C22semidirect
121. #2428C22semidirect
122. #2427C22semidirect
123. #2426C22semidirect
125. #2422C22semidirect
126. #2422C22semidirect
127. #2422C22semidirect
130. #2414C22semidirect
133. #2392C22semidirect
135. #2373C22semidirect
136. #2370C22semidirect
137. #2367C22semidirect
144. #2337C22semidirect
146. #2331C22semidirect
147. #2331C22semidirect
148. #2330C22semidirect
151. #2328C22semidirect
152. #2328C22semidirect
155. #2324C22semidirect
156. #2324C22semidirect
160. C4×#127C22semidirect
161. C4×#121C22semidirect
162. #2298C22semidirect
164. #2295C22semidirect
166. #2293C22semidirect
167. #2293C22semidirect
168. #2293C22semidirect
170. #2290C22semidirect
173. C42×Q8C22semidirect
174. C42×D4C22semidirect
175. C42×D4C22semidirect
178. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#410582
#410212
#394342
#392702
#377862
#377752
#376252
#376212
#376142
#373312
#373212
#373192
#355382
#352962
#352782
#352742
#352022
#351712
#349342
#342102
#341512
#340862