Finite Group Databasebeta

← #7647428

Subgroups — #7647428

Order 512.

4924 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42450C214yesmaximal, complemented
2#42448C214yesmaximal, complemented
3#40647C218yesmaximal, complemented
4#39630C212yesmaximal, complemented
5#39607C212yesmaximal, complemented
6#39372C212yesmaximal, complemented
7#39352C212yesmaximal, complemented
8#39188C212yesmaximal, complemented
9#39147C212yesmaximal, complemented
10#38969C212yesmaximal, complemented
11#38932C212yesmaximal, complemented
12#37508C214yesmaximal, complemented
13#36837C214yesmaximal, complemented
14#36828C214yesmaximal, complemented
15#35551C214yesmaximal, complemented
16#35292C211yesmaximal, characteristic, complemented
17#35229C214yesmaximal, complemented
18#35202C211yesmaximal, characteristic, complemented
19#35156C214yesmaximal, complemented
20#34977C211yesmaximal, characteristic, complemented
21#34909C211yesmaximal, characteristic, complemented
22#34236C211yesmaximal, characteristic, complemented
23C4⋊C4×#41C211yesmaximal, characteristic, complemented
24#34060C211yesmaximal, characteristic, complemented
25C2×#540C2214yes—
26C2×#532C2211yescharacteristic
27C2×C4×#41C2211yescharacteristic
28C2×C4×#41C2211yescharacteristic
29C2×C4×#41C2212yes—
30#2864C2212yes—
31#2859C2212yes—
32#2857C2212yes—
33#2856C2212yes—
34#2854C2218yes—
35#2853C2218yes—
36#2827C2218yes—
37#2826C2218yes—
38#2807C2218yes—
39#2803C2218yes—
40#2788C2218yes—
41#2777C2218yes—
42#2764C2218yes—
43#2757C2218yes—
44#2755C2218yes—
45#2751C2218yes—
46#2724C2218yes—
47#2706C2218yes—
48#2704C2218yes—
49#2701C2218yes—
50#2694C2218yes—
51#2687C2218yes—
52#2682C2218yes—
53#2671C2218yes—
54#2667C2214yes—
55#2654C2218yes—
56#2651C2218yes—
57#2647C2214yes—
58#2644C2214yes—
59#2635C2218yes—
60#2633C2218yes—
61#2630C2218yes—
62#2630C2218yes—
63#2629C2214yes—
64#2624C2214yes—
65#2624C2212yes—
66#2615C2212yes—
67#2610C2214yes—
68#2606C2214yes—
69#2600C2214yes—
70#2599C2212yes—
71#2598C2212yes—
72#2592C2212yes—
73#2581C2211yescharacteristic
74#2580C2211yescharacteristic
75#2580C2212yes—
76#2577C2218yes—
77#2567C2211yescharacteristic
78#2566C2214yes—
79#2563C2211yescharacteristic
80#2562C2214yes—
81#2558C2218yes—
82#2552C2212yes—
83#2552C2212yes—
84#2552C2214yes—
85#2548C2211yescharacteristic
86#2541C2211yescharacteristic
87#2540C2212yes—
88#2537C2214yes—
89#2536C2211yescharacteristic
90#2535C2212yes—
91#2535C2211yescharacteristic
92#2522C2218yes—
93#2518C2218yes—
94#2516C2218yes—
95#2513C2214yes—
96#2507C2214yes—
97#2506C2214yes—
98#2505C2218yes—
99#2501C2214yes—
100#2500C2212yes—
101#2497C2214yes—
102#2497C2214yes—
103#2495C2214yes—
104#2495C2214yes—
105#2490C2214yes—
106#2486C2214yes—
107#2485C2212yes—
108#2476C2218yes—
109#2470C2218yes—
110#2460C2218yes—
111#2456C2218yes—
112#2455C2218yes—
113#2454C2214yes—
114#2453C2214yes—
115#2445C2214yes—
116#2442C2214yes—
117#2441C2214yes—
118#2441C2214yes—
119#2431C2212yes—
120#2426C2214yes—
121#2425C2218yes—
122#2425C2218yes—
123#2422C2214yes—
124#2422C2214yes—
125#2422C2214yes—
126#2422C2214yes—
127#2419C2218yes—
128#2416C2214yes—
129#2414C2214yes—
130#2414C2214yes—
131#2407C2212yes—
132#2407C2214yes—
133#2395C2212yes—
134#2388C2212yes—
135#2388C2214yes—
136#2369C2212yes—
137#2366C2212yes—
138#2361C2214yes—
139#2357C2212yes—
140#2351C2212yes—
141Q8×C4⋊C4C2212yes—
142#2349C2212yes—
143#2349C2214yes—
144#2349C2212yes—
145D4×C4⋊C4C2212yes—
146D4×C4⋊C4C2214yes—
147#2339C2214yes—
148#2337C2214yes—
149#2330C2214yes—
150#2326C2214yes—
151#2324C2214yes—
152#2323C2214yes—
153#2320C2212yes—
154#2319C2212yes—
155#2319C2214yes—
156#2319C2212yes—
157#2318C2214yes—
158#2317C2212yes—
159#2314C2212yes—
160#2314C2212yes—
161#2311C2212yes—
162C4×#127C2212yes—
163C4×#124C2212yes—
164C4×C22⋊Q8C2212yes—
165C4×#121C2212yes—
166C4×#121C2214yes—
167C4×#121C2214yes—
168#2296C2212yes—
169#2296C2214yes—
170#2295C2212yes—
171#2293C2212yes—
172#2290C2214yes—
173#2290C2214yes—
174#2285C2212yes—
175#2285C2211yescharacteristic
176#2285C2212yes—
177#2283C2212yes—
178#2283C2211yescharacteristic
179#2275C2212yes—
180C4×#117C2211yescharacteristic
181C2×C4×C4⋊C4C2211yescharacteristic
182C2×C4×C4⋊C4C2212yes—
183C22×#41C2311yescharacteristic
184C22×#41C2311yescharacteristic
185C22×#41C2312yes—
186#540—416no—
187#532—28no—
188C2×C4⋊Q8C2311yescharacteristic
189C2×#127C2312yes—
190C2×#127C2311yescharacteristic
191C2×#125C2314yes—
192C2×#125C2314yes—
193C2×#125C2318yes—
194C2×#124C2312yes—
195C2×#124C2312yes—
196C2×#123C2318yes—
197C2×#123C2318yes—
198C2×#123C2318yes—
199C2×#123C2318yes—
200C2×#123C2318yes—
201C2×C22⋊Q8C2312yes—
202C2×C22⋊Q8C2314yes—
203C2×#121C2312yes—
204C2×#121C2312yes—
205C2×#121C2312yes—
206C2×#121C2314yes—
207C2×#121C2318yes—
208C2×#121C2314yes—
209C2×#121C2314yes—
210C2×#121C2318yes—
211C2×#121C2314yes—
212C4×#41—28no—
213C4×#41—28no—
214C4×#41—48no—
215C2×C4×Q8C2311yescharacteristic
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2314yes—
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2312yes—
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2312yes—
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2312yes—
226C2×C4×D4C2314yes—
227C2×C4×D4C2312yes—
228C2×C4×D4C2312yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2314yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2318yes—
235C2×C4×D4C2318yes—
236C2×C4×D4C2318yes—
237C2×#117C2312yes—
238C2×#117C2311yescharacteristic
239C2×#117C2312yes—
240C2×#117C2311yescharacteristic
241C2×#117C2312yes—
242C2×#117C2314yes—
243C2×#117C2312yes—
244C2×#117C2314yes—
245C22×C4⋊C4C2312yes—
246C22×C4⋊C4C2314yes—
247C22×C42C2312yes—
248C22×C42C2312yes—
249C22×C42C2314yes—
250C22×C42C2312yes—
251C22×C42C2311yescharacteristic
252#400C2318yes—
253#400C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2312yes—
257#400C2318yes—
258#399C2318yes—
259#399C2318yes—
260#399C2312yes—
261#399C2314yes—
262#399C2318yes—
263#398C2318yes—
264#398C2318yes—
265#398C2312yes—
266#398C2318yes—
267#398C2318yes—
268#398C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2318yes—
272#397C2318yes—
273#397C2318yes—
274#397C2314yes—
275#397C2318yes—
276#397C2318yes—
277#397C2314yes—
278#397C2312yes—
279#397C2318yes—
280#397C2318yes—
281#397C2318yes—
282#396C2318yes—
283#396C2318yes—
284#396C2318yes—
285#396C2318yes—
286#396C2318yes—
287#396C2318yes—
288#395C2314yes—
289#395C2312yes—
290#394C2318yes—
291#394C2314yes—
292#394C2318yes—
293#394C2318yes—
294#394C2318yes—
295#394C2318yes—
296#394C2312yes—
297#394C2314yes—
298#394C2314yes—
299#394C2318yes—
300#394C2318yes—
301#394C2318yes—
302#394C2318yes—
303#393C2314yes—
304#393C2314yes—
305#393C2312yes—
306#392C2318yes—
307#392C2312yes—
308#392C2314yes—
309#392C2314yes—
310#392C2314yes—
311#392C2318yes—
312#391C2314yes—
313#391C2312yes—
314#391C2312yes—
315#391C2314yes—
316#391C2318yes—
317#390C2312yes—
318#390C2318yes—
319#390C2312yes—
320#390C2314yes—
321#390C2314yes—
322#390C2314yes—
323#390C2312yes—
324#390C2314yes—
325#390C2318yes—
326#390C2314yes—
327#390C2314yes—
328#390C2318yes—
329#390C2314yes—
330#390C2312yes—
331#389C2314yes—
332#389C2314yes—
333#389C2314yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2318yes—
339#389C2314yes—
340#389C2312yes—
341#389C2312yes—
342#389C2318yes—
343#389C2318yes—
344#389C2314yes—
345#389C2314yes—
346#389C2318yes—
347#389C2318yes—
348#389C2314yes—
349#389C2318yes—
350#389C2314yes—
351#389C2318yes—
352#389C2314yes—
353#388C2318yes—
354#388C2318yes—
355#388C2314yes—
356#388C2314yes—
357#388C2314yes—
358#388C2314yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2314yes—
370#388C2314yes—
371#388C2314yes—
372#388C2318yes—
373#387C2314yes—
374#387C2314yes—
375#387C2314yes—
376#387C2314yes—
377#387C2314yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2314yes—
382#387C2318yes—
383#387C2318yes—
384#387C2314yes—
385#387C2318yes—
386#386C2314yes—
387#386C2314yes—
388#386C2318yes—
389#386C2318yes—
390#386C2318yes—
391#386C2318yes—
392#386C2318yes—
393#386C2314yes—
394#386C2314yes—
395#386C2314yes—
396#385C2318yes—
397#385C2318yes—
398#385C2318yes—
399#385C2314yes—
400#385C2314yes—
401#385C2318yes—
402#385C2314yes—
403#385C2318yes—
404#385C2318yes—
405#385C2314yes—
406#385C2318yes—
407#385C2314yes—
408#385C2318yes—
409#385C2318yes—
410#385C2318yes—
411#384C2312yes—
412#384C2314yes—
413#384C2312yes—
414#384C2312yes—
415#384C2314yes—
416#384C2314yes—
417#384C2312yes—
418#383C2314yes—
419#383C2318yes—
420#383C2312yes—
421#382C2312yes—
422#382C2312yes—
423#382C2312yes—
424#382C2314yes—
425#382C2312yes—
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#382C2314yes—
429#381C2314yes—
430#381C2314yes—
431#381C2318yes—
432#381C2312yes—
433#380C2312yes—
434#380C2314yes—
435#380C2314yes—
436#380C2314yes—
437#380C2312yes—
438#380C2312yes—
439#380C2312yes—
440#380C2314yes—
441#380C2314yes—
442#380C2318yes—
443#380C2318yes—
444#380C2314yes—
445#380C2312yes—
446#380C2312yes—
447#380C2314yes—
448#380C2312yes—
449#380C2312yes—
450#380C2312yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2312yes—
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2314yes—
470C4×C22⋊C4C2312yes—
471C4×C22⋊C4C2318yes—
472C4×C22⋊C4C2314yes—
473C4×C22⋊C4C2312yes—
474C4×C22⋊C4C2314yes—
475C4×C22⋊C4C2318yes—
476C4×C22⋊C4C2314yes—
477C4×C22⋊C4C2314yes—
478C4×C22⋊C4C2312yes—
479#376C2312yes—
480#376C2314yes—
481#376C2312yes—
482C2×#95C2312yes—
483C2×#95C2314yes—
484C2×#95C2314yes—
485C43C2312yes—
486C2×#41—24no—
487C2×#41—24no—
488C2×#41—24no—
489C2×#41—24no—
490C2×#41—28no—
491C2×#41—44no—
492C2×#41—84no—
493C22×Q8C2411yescharacteristic
494C22×Q8C2411yescharacteristic
495C22×Q8C2412yes—
496C22×D4C2412yes—
497C22×D4C2412yes—
498C22×D4C2412yes—
499C22×D4C2411yescharacteristic
500C22×D4C2414yes—
501C22×D4C2412yes—
502C22×D4C2411yescharacteristic
503C22×D4C2414yes—
504C22×D4C2418yes—
505C22×D4C2412yes—
506C22×D4C2418yes—
507C23×C4C2412yes—
508C23×C4C2412yes—
509C23×C4C2412yes—
510C23×C4C2412yes—
511C23×C4C2411yescharacteristic
512C23×C4C2411yescharacteristic
513C23×C4C2418yes—
514C23×C4C2412yes—
515C23×C4C2414yes—
516C23×C4C2412yes—
517C23×C4C2414yes—
518C23×C4C2418yes—
519C23×C4C2411yescharacteristic
520C4⋊Q8—24no—
521#127—28no—
522#127—24no—
523#125—48no—
524#125—48no—
525#125—88no—
526#124—28no—
527#124—28no—
528#123—416no—
529#123—416no—
530#123—88no—
531#123—88no—
532#123—88no—
533C22⋊Q8—28no—
534C22⋊Q8—84no—
535#121—28no—
536#121—28no—
537#121—28no—
538#121—416no—
539#121—48no—
540#121—48no—
541#121—48no—
542#121—416no—
543#121—84no—
544C4×Q8—24no—
545C4×Q8—24no—
546C4×Q8—24no—
547C4×Q8—24no—
548C4×Q8—48no—
549C4×D4—216no—
550C4×D4—28no—
551C4×D4—28no—
552C4×D4—28no—
553C4×D4—28no—
554C4×D4—24no—
555C4×D4—24no—
556C4×D4—24no—
557C4×D4—24no—
558C4×D4—28no—
559C4×D4—28no—
560C4×D4—48no—
561C4×D4—48no—
562C4×D4—48no—
563C4×D4—416no—
564C4×D4—88no—
565C4×D4—88no—
566#117—24no—
567#117—24no—
568#117—28no—
569#117—28no—
570#117—48no—
571#117—48no—
572#117—44no—
573#117—44no—
574C2×C4⋊C4—44no—
575C2×C4⋊C4—48no—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2418yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2418yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2412yes—
617C2×C22⋊C4C2412yes—
618C2×C22⋊C4C2412yes—
619C2×C22⋊C4C2412yes—
620C2×C22⋊C4C2412yes—
621C2×C22⋊C4C2412yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C42—28no—
649C2×C42—28no—
650C2×C42—44no—
651C2×C42—48no—
652C2×C42#4118yes—
653C2×C42C2412yes—
654C2×C42C2412yes—
655C2×C42C2412yes—
656C2×C42C2414yes—
657C2×C42C2414yes—
658C2×C42C2412yes—
659C2×C42C2412yes—
660C2×C42C2412yes—
661C2×C42C2412yes—
662C2×C42C2412yes—
663C2×C42C2412yes—
664C2×C42C2414yes—
665C2×C42C2414yes—
666C2×C42C2414yes—
667C2×C42C2418yes—
668C2×C42C2418yes—
669C2×C42C2412yes—
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674#95C2412yes—
675#95C2412yes—
676#95C2412yes—
677#95C2418yes—
678#95C2414yes—
679#95C2414yes—
680#95C2418yes—
681#95C2414yes—
682#95C2412yes—
683#95C2412yes—
684#95C2412yes—
685#95C2414yes—
686#95C2414yes—
687#95C2414yes—
688#95C2414yes—
689#95C2414yes—
690#95C2418yes—
691#95C2414yes—
692#95C2414yes—
693#95C2412yes—
694#95C2414yes—
695#95C2412yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2418yes—
700#95C2414yes—
701#95C2418yes—
702#95C2418yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2418yes—
709#95C2418yes—
710#95C2418yes—
711#95C2418yes—
712C24C2512yes—
713C24C2514yes—
714C24C2511yescharacteristic
715C24C2512yes—
716#41—232no—
717#41—416no—
718#41—816no—
719C2×Q8—22no—
720C2×Q8—22no—
721C2×Q8—24no—
722C2×Q8—22no—
723C2×Q8—42no—
724C2×Q8—44no—
725C2×Q82−1+414yes—
726C2×D4—24no—
727C2×D4—24no—
728C2×D4—24no—
729C2×D4—28no—
730C2×D4—28no—
731C2×D4—216no—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—24no—
735C2×D4—24no—
736C2×D4—24no—
737C2×D4—24no—
738C2×D4—24no—
739C2×D4—22no—
740C2×D4—24no—
741C2×D4—28no—
742C2×D4—48no—
743C2×D4—42no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—44no—
747C2×D4—48no—
748C2×D4—48no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—48no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4H(5,𝔽2)14yes—
755C22×C4—24no—
756C22×C4—24no—
757C22×C4—22no—
758C22×C4—24no—
759C22×C4—22no—
760C22×C4—24no—
761C22×C4—216no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—28no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—24no—
771C22×C4—24no—
772C22×C4—28no—
773C22×C4—42no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—48no—
777C22×C4—44no—
778C22×C4—44no—
779C22×C4—48no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—48no—
783C22×C4—48no—
784C22×C4—48no—
785C22×C4—48no—
786C22×C4C2×#4114yes—
787C22×C4C2×#4114yes—
788C22×C4C2×#4114yes—
789C22×C4C2512yes—
790C22×C4C2514yes—
791C22×C4C2514yes—
792C22×C4C2512yes—
793C22×C4C2512yes—
794C22×C4C2514yes—
795C22×C4C2514yes—
796C22×C4C2514yes—
797C22×C4C2514yes—
798C22×C4C2514yes—
799C22×C4C2512yes—
800C22×C4C2512yes—
801C22×C4C2518yes—
802C22×C4C2511yescharacteristic
803C22×C4C2511yescharacteristic
804C22×C4C2511yescharacteristic
805C22×C4C2511yescharacteristic
806C22×C4C2512yes—
807C22×C4C2511yescharacteristic
808C22×C4C2511yescharacteristic
809C4⋊C4—24no—
810C4⋊C4—24no—
811C4⋊C4—22no—
812C4⋊C4—22no—
813C4⋊C4—22no—
814C4⋊C4—22no—
815C4⋊C4—24no—
816C4⋊C4—24no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—28no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—28no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—28no—
826C4⋊C4—24no—
827C4⋊C4—24no—
828C4⋊C4—44no—
829C4⋊C4—48no—
830C4⋊C4—48no—
831C4⋊C4—44no—
832C4⋊C4—44no—
833C4⋊C4—44no—
834C4⋊C4—48no—
835C4⋊C4—48no—
836C4⋊C4—48no—
837C4⋊C4—48no—
838C4⋊C4—44no—
839C4⋊C4—48no—
840C4⋊C4—48no—
841C4⋊C4—44no—
842C4⋊C4—48no—
843C4⋊C4—48no—
844C4⋊C4—48no—
845C4⋊C4—48no—
846C4⋊C4—44no—
847C4⋊C4—44no—
848C22⋊C4—24no—
849C22⋊C4—24no—
850C22⋊C4—216no—
851C22⋊C4—28no—
852C22⋊C4—24no—
853C22⋊C4—24no—
854C22⋊C4—24no—
855C22⋊C4—24no—
856C22⋊C4—28no—
857C22⋊C4—28no—
858C22⋊C4—28no—
859C22⋊C4—216no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—44no—
865C22⋊C4—48no—
866C22⋊C4—44no—
867C22⋊C4—48no—
868C22⋊C4—44no—
869C22⋊C4—48no—
870C22⋊C4—48no—
871C22⋊C4—48no—
872C22⋊C4—48no—
873C22⋊C4—48no—
874C22⋊C4—48no—
875C22⋊C4—48no—
876C22⋊C4—48no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C42—24no—
882C42—24no—
883C42—24no—
884C42—24no—
885C42—24no—
886C42—24no—
887C42—28no—
888C42—24no—
889C42—24no—
890C42—28no—
891C42—42no—
892C42—42no—
893C42—44no—
894C42—48no—
895C42—44no—
896C42—44no—
897C42—48no—
898C42C2×#4114yes—
899C42C2×#4114yes—
900C42C2×#4114yes—
901C42C2×#4114yes—
902C23—22no—
903C23—21no—
904C23—21no—
905C23—22no—
906C23—22no—
907C23—24no—
908C23—24no—
909C23—22no—
910C23—22no—
911C23—24no—
912C23—22no—
913C23—24no—
914C23—22no—
915C23—24no—
916C23—28no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—28no—
922C23C22×#4112yes—
923C23C2×H(5,𝔽2)14yes—
924C23C2611yescharacteristic
925Q8—28no—
926Q8—44no—
927Q8—84no—
928D4—216no—
929D4—28no—
930D4—44no—
931D4—48no—
932D4—416no—
933D4—48no—
934D4—48no—
935D4—84no—
936D4—88no—
937D4—816no—
938D4—168no—
939C2×C4—216no—
940C2×C4—22no—
941C2×C4—21no—
942C2×C4—22no—
943C2×C4—21no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—28no—
948C2×C4—28no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—28no—
959C2×C4—22no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—22no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—22no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—22no—
972C2×C4—28no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—28no—
978C2×C4—24no—
979C2×C4—22no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—28no—
983C2×C4—24no—
984C2×C4—22no—
985C2×C4—44no—
986C2×C4—48no—
987C2×C4—48no—
988C2×C4—48no—
989C2×C4—84no—
990C2×C4—84no—
991C2×C4—88no—
992C2×C4—816no—
993C2×C4—88no—
994C2×C4—168no—
995C2×C4C22×#4112yes—
996C2×C4C22×#4112yes—
997C2×C4C22×#4112yes—
998C2×C4C22×#4112yes—
999C2×C4C22×#4112yes—
1000C2×C4C22×#4112yes—
1001C2×C4C2×H(5,𝔽2)12yes—
1002C2×C4C2×2−1+414yes—
1003C2×C4C2×2−1+412yes—
1004C2×C4#58514yes—
1005C22—22no—
1006C22—24no—
1007C22—22no—
1008C22—28no—
1009C22—22no—
1010C22—42no—
1011C22—42no—
1012C22—42no—
1013C22—42no—
1014C22—44no—
1015C22—42no—
1016C22—44no—
1017C22—44no—
1018C22—42no—
1019C22—48no—
1020C22—42no—
1021C22—42no—
1022C22—42no—
1023C22—44no—
1024C22—42no—
1025C22—42no—
1026C22—48no—
1027C22C23×#4111yescharacteristic
1028C22C22×H(5,𝔽2)11yescharacteristic
1029C22C22×2−1+411yescharacteristic
1030C22C2×#58512yes—
1031C22H(7,𝔽2)12yes—
1032C4—22no—
1033C4—24no—
1034C4—22no—
1035C4—22no—
1036C4—22no—
1037C4—42no—
1038C4—42no—
1039C4—42no—
1040C4—44no—
1041C4—44no—
1042C4—44no—
1043C4—48no—
1044C4—44no—
1045C4—44no—
1046C4—42no—
1047C4—42no—
1048C4—44no—
1049C4—44no—
1050C4#345514yes—
1051C4#349214yes—
1052C2—42no—
1053C2—44no—
1054C2—82no—
1055C2—84no—
1056C2C2×#345511yescharacteristic
1057C2C2×#349211yescharacteristic
1058C2#6285511yescharacteristic
1059C2#6292012yes—
1060C2#6295212yes—
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. #42450C2semidirect
2. #42448C2semidirect
3. #40647C2semidirect
4. #39630C2semidirect
5. #39607C2semidirect
6. #39372C2semidirect
7. #39352C2semidirect
8. #39188C2semidirect
9. #39147C2semidirect
10. #38969C2semidirect
11. #38932C2semidirect
12. #37508C2semidirect
13. #36837C2semidirect
14. #36828C2semidirect
15. #35551C2semidirect
16. #35292C2semidirect
17. #35229C2semidirect
18. #35202C2semidirect
19. #35156C2semidirect
20. #34977C2semidirect
21. #34909C2semidirect
22. #34236C2semidirect
23. C4⋊C4×#41C2semidirect
24. #34060C2semidirect

Maximal subgroups

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

subgroupindex
#424502
#424482
#406472
#396302
#396072
#393722
#393522
#391882
#391472
#389692
#389322
#375082
#368372
#368282
#355512
#352922
#352292
#352022
#351562
#349772
#349092
#342362
C4⋊C4×#412
#340602