Finite Group Databasebeta

← #7673864

Subgroups — #7673864

Order 512.

5204 conjugacy classes of subgroups.

The subgroup lattice has 1161 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45130C214yesmaximal, complemented
2#45120C214yesmaximal, complemented
3#44922C214yesmaximal, complemented
4#44907C214yesmaximal, complemented
5#39815C218yesmaximal, complemented
6#39813C218yesmaximal, complemented
7#39553C214yesmaximal, complemented
8#39552C214yesmaximal, complemented
9#37945C214yesmaximal, complemented
10#37944C214yesmaximal, complemented
11#35629C211yesmaximal, characteristic, complemented
12#35618C211yesmaximal, characteristic, complemented
13#35557C211yesmaximal, characteristic, complemented
14#35530C211yesmaximal, characteristic, complemented
15#35339C211yesmaximal, characteristic, complemented
16#35328C211yesmaximal, characteristic, complemented
17#35223C211yesmaximal, characteristic, complemented
18#35150C211yesmaximal, characteristic, complemented
19#34633C211yesmaximal, characteristic, complemented
20#34207C211yesmaximal, characteristic, complemented
21#34201C211yesmaximal, characteristic, complemented
22#34200C211yesmaximal, characteristic, complemented
23#34188C211yesmaximal, characteristic, complemented
24#34065C211yesmaximal, characteristic, complemented
25C2×#2317C211yesmaximal, characteristic, complemented
26C2×#537C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#532C2211yescharacteristic
29C2×#525C2211yescharacteristic
30C2×#525C2211yescharacteristic
31C2×#525C2211yescharacteristic
32C2×#520C2211yescharacteristic
33C2×#520C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35C22×#117C2211yescharacteristic
36C22×#117C2211yescharacteristic
37C23×C4⋊C4C2211yescharacteristic
38#2864C2214yescomplemented
39#2854C2214yes—
40#2850C2212yescomplemented
41#2850C2212yescomplemented
42#2847C2214yes—
43#2803C2218yescomplemented
44#2802C2218yescomplemented
45#2800C2218yescomplemented
46#2797C2218yes—
47#2796C2218yes—
48#2787C2218yes—
49#2783C2218yescomplemented
50#2782C2218yes—
51#2781C2218yes—
52#2780C2218yescomplemented
53#2779C2218yescomplemented
54#2778C2218yes—
55#2777C2218yescomplemented
56#2765C2218yescomplemented
57#2714C2218yes—
58#2708C2218yes—
59#2647C2214yescomplemented
60#2621C2212yes—
61#2621C2212yescomplemented
62#2620C2212yes—
63#2620C2212yes—
64#2619C2212yes—
65#2619C2212yescomplemented
66#2618C2214yes—
67#2618C2214yes—
68#2617C2214yes—
69#2617C2214yes—
70#2602C2218yescomplemented
71#2601C2218yescomplemented
72#2600C2218yes—
73#2598C2218yes—
74#2597C2218yes—
75#2595C2218yes—
76#2594C2218yescomplemented
77#2590C2218yescomplemented
78#2587C2218yescomplemented
79#2577C2218yes—
80#2570C2214yescomplemented
81#2570C2214yescomplemented
82#2569C2218yes—
83#2543C2218yes—
84#2536C2214yescomplemented
85#2535C2214yescomplemented
86#2525C2218yescomplemented
87#2514C2214yescomplemented
88#2513C2214yescomplemented
89#2512C2214yescomplemented
90#2511C2214yescomplemented
91#2510C2218yes—
92#2504C2212yescomplemented
93#2503C2212yescomplemented
94#2502C2212yescomplemented
95#2501C2212yescomplemented
96#2500C2212yescomplemented
97#2500C2212yescomplemented
98#2499C2212yescomplemented
99#2499C2212yescomplemented
100#2497C2214yescomplemented
101#2496C2214yescomplemented
102#2495C2214yescomplemented
103#2494C2214yescomplemented
104#2481C2218yes—
105#2476C2218yes—
106#2470C2218yescomplemented
107#2468C2218yes—
108#2466C2218yescomplemented
109#2456C2218yes—
110#2444C2218yes—
111#2443C2218yes—
112#2423C2214yescomplemented
113#2422C2214yescomplemented
114#2421C2214yescomplemented
115#2420C2214yescomplemented
116#2417C2214yes—
117#2417C2214yes—
118#2416C2214yes—
119#2416C2214yes—
120#2415C2214yes—
121#2415C2214yes—
122#2414C2214yes—
123#2414C2214yes—
124#2392C2214yes—
125#2392C2214yes—
126#2363C2214yes—
127#2362C2214yes—
128#2361C2214yes—
129#2361C2218yes—
130#2360C2214yes—
131#2355C2214yescomplemented
132#2354C2214yes—
133#2354C2214yescomplemented
134#2354C2214yescomplemented
135#2352C2214yes—
136#2352C2214yes—
137#2352C2218yes—
138D4×C4⋊C4C2214yes—
139D4×C4⋊C4C2214yescomplemented
140#2326C2212yescomplemented
141#2326C2212yescomplemented
142#2324C2212yes—
143#2324C2212yes—
144#2323C2212yes—
145#2323C2212yes—
146#2322C2214yes—
147#2322C2214yes—
148#2321C2214yes—
149#2321C2214yes—
150#2317C2214yes—
151#2317C2214yes—
152#2317C2214yes—
153#2317C2214yes—
154#2317C2211yescharacteristic
155#2317C2211yescharacteristic
156#2316C2211yescharacteristic
157#2316C2211yescharacteristic
158#2314C2214yescomplemented
159#2311C2211yescharacteristic
160#2311C2211yescharacteristic
161#2311C2211yescharacteristic
162#2311C2211yescharacteristic
163#2311C2211yescharacteristic
164#2311C2211yescharacteristic
165C4×C4⋊Q8C2212yescomplemented
166C4×#127C2212yescomplemented
167C4×#123C2214yes—
168C4×#120C2214yes—
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2297C2211yescharacteristic
172#2296C2211yescharacteristic
173#2293C2214yes—
174C2×#389C2214yes—
175#2290C2214yes—
176C2×#385C2214yes—
177#2285C2211yescharacteristic
178#2285C2214yescomplemented
179C2×#384C2211yescharacteristic
180C2×#384C2211yescharacteristic
181C2×#382C2211yescharacteristic
182C2×#382C2211yescharacteristic
183#2280C2211yescharacteristic
184#2274C2211yescharacteristic
185#2274C2211yescharacteristic
186C4×#117C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C22×#41C2311yescharacteristic
190C24×C4C2311yescharacteristic
191C24×C4C2312yes—
192#537—44no—
193#537—44no—
194#532—28no—
195C2×C4⋊Q8C2311yescharacteristic
196C2×#127C2311yescharacteristic
197C2×#126C2318yes—
198C2×#124C2311yescharacteristic
199C2×#124C2311yescharacteristic
200#525—28no—
201#525—28no—
202#525—28no—
203C2×#123C2312yes—
204C2×#123C2312yes—
205C2×#123C2312yes—
206C2×#123C2318yes—
207C2×C22⋊Q8C2312yes—
208C2×C22⋊Q8C2312yes—
209C2×C22⋊Q8C2312yes—
210C2×C22⋊Q8C2312yes—
211C2×C22⋊Q8C2312yes—
212C2×C22⋊Q8C2312yes—
213C2×C22⋊Q8C2312yes—
214C2×#121C2312yes—
215C2×#121C2314yes—
216C2×#121C2312yes—
217C2×#121C2312yes—
218C2×#121C2314yes—
219C2×#121C2312yes—
220C2×#121C2312yes—
221C2×#121C2314yes—
222C2×#121C2312yes—
223C2×#121C2312yes—
224C2×#121C2318yes—
225C2×#120C2312yes—
226C2×#120C2312yes—
227C2×#120C2312yes—
228#520—44no—
229#520—44no—
230C4×#41—28no—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2312yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2312yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2318yes—
245C2×C4×D4C2318yes—
246C2×#117—28no—
247C2×#117—44no—
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2312yes—
253C2×#117C2312yes—
254C2×#117C2312yes—
255C2×#117C2312yes—
256C2×#117C2312yes—
257C2×#117C2311yescharacteristic
258C2×#117C2314yes—
259C2×#117C2314yes—
260C2×#117C2312yes—
261C2×#117C2312yes—
262C2×#117C2318yes—
263C22×C4⋊C4—44no—
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2312yes—
269C22×C4⋊C4C2314yes—
270C22×C4⋊C4C2314yes—
271C22×C4⋊C4C2312yes—
272C22×C4⋊C4C2312yes—
273C22×C4⋊C4C2312yes—
274C22×C4⋊C4C2314yes—
275C22×C4⋊C4C2314yes—
276C22×C22⋊C4C2312yes—
277C22×C22⋊C4C2312yes—
278C22×C42C2312yes—
279C22×C42C2311yescharacteristic
280C22×C42C2312yes—
281C22×C42C2311yescharacteristic
282#401C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2318yes—
287#400C2318yes—
288#400C2318yes—
289#399C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2314yes—
294#398C2318yes—
295#398C2314yes—
296#398C2318yes—
297#397C2314yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2314yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#396C2314yes—
308#396C2318yes—
309#396C2318yes—
310#396C2314yes—
311#396C2314yes—
312#396C2314yes—
313#396C2318yes—
314#394C2314yes—
315#394C2318yes—
316#394C2314yes—
317#394C2318yes—
318#394C2318yes—
319#394C2318yes—
320#394C2314yes—
321#394C2318yes—
322#394C2314yes—
323#394C2314yes—
324#394C2314yes—
325#394C2318yes—
326#392C2318yes—
327#392C2314yes—
328#392C2318yes—
329#392C2314yes—
330#391C2312yes—
331#391C2312yes—
332#391C2312yes—
333#391C2312yes—
334#391C2312yes—
335#391C2312yes—
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#391C2312yes—
339#391C2312yes—
340#390C2312yes—
341#390C2312yes—
342#390C2318yes—
343#390C2312yes—
344#390C2312yes—
345#390C2312yes—
346#390C2312yes—
347#390C2314yes—
348#390C2314yes—
349#390C2318yes—
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2318yes—
353#390C2312yes—
354#390C2312yes—
355#389C2318yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2318yes—
361#389C2318yes—
362#389C2318yes—
363#389C2318yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2318yes—
369#389C2312yes—
370#389C2312yes—
371#389C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2314yes—
375#388C2318yes—
376#388C2314yes—
377#388C2314yes—
378#388C2314yes—
379#388C2318yes—
380#388C2314yes—
381#388C2314yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2314yes—
404#387C2314yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#386C2314yes—
411#386C2314yes—
412#386C2314yes—
413#386C2314yes—
414#386C2314yes—
415#386C2314yes—
416#386C2314yes—
417#386C2314yes—
418#386C2314yes—
419#386C2318yes—
420#386C2318yes—
421#386C2318yes—
422#386C2318yes—
423#386C2318yes—
424#386C2318yes—
425#386C2318yes—
426#386C2314yes—
427#386C2314yes—
428#385C2314yes—
429#385C2314yes—
430#385C2318yes—
431#385C2318yes—
432#385C2318yes—
433#385C2318yes—
434#385C2314yes—
435#385C2314yes—
436#385C2314yes—
437#385C2318yes—
438#385C2318yes—
439#385C2318yes—
440#385C2318yes—
441#385C2318yes—
442#384C2312yes—
443#384C2312yes—
444#384C2312yes—
445#384C2312yes—
446#384C2314yes—
447#384C2314yes—
448#384C2312yes—
449#384C2312yes—
450#384C2312yes—
451#383C2318yes—
452#382C2312yes—
453#382C2314yes—
454#382C2312yes—
455#382C2312yes—
456#382C2312yes—
457#382C2312yes—
458#382C2314yes—
459#382C2312yes—
460#382C2312yes—
461#382C2318yes—
462#381C2312yes—
463#381C2318yes—
464#380C2314yes—
465#380C2314yes—
466#380C2314yes—
467#380C2314yes—
468#380C2314yes—
469#380C2314yes—
470#380C2314yes—
471#380C2314yes—
472#380C2314yes—
473#380C2318yes—
474#380C2312yes—
475#380C2312yes—
476#380C2318yes—
477#379C2312yes—
478C4×C4⋊C4C2318yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2318yes—
485C4×C4⋊C4C2318yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2318yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2318yes—
494C4×C22⋊C4C2314yes—
495C4×C22⋊C4C2312yes—
496C4×C22⋊C4C2312yes—
497C4×C22⋊C4C2312yes—
498C4×C22⋊C4C2312yes—
499C4×C22⋊C4C2314yes—
500#376C2312yes—
501C2×#95C2314yes—
502C2×#95C2314yes—
503C43C2312yes—
504C25C2411yescharacteristic
505C2×#41—24no—
506C2×#41—24no—
507C2×#41—24no—
508C2×#41—24no—
509C2×#41—24no—
510C2×#41—24no—
511C2×#41—24no—
512C2×#41—24no—
513C2×#41—24no—
514C22×Q8C2411yescharacteristic
515C22×Q8C2411yescharacteristic
516C22×Q8C2411yescharacteristic
517C22×D4C2412yes—
518C22×D4C2412yes—
519C22×D4C2412yes—
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C22×D4C2414yes—
524C22×D4C2414yes—
525C22×D4C2414yes—
526C22×D4C2414yes—
527C22×D4C2414yes—
528C22×D4C2414yes—
529C23×C4—24no—
530C23×C4—24no—
531C23×C4—44no—
532C23×C4—84no—
533C23×C4#4118yes—
534C23×C4C2412yes—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2411yescharacteristic
538C23×C4C2412yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C23×C4C2414yes—
546C23×C4C2418yes—
547C23×C4C2414yes—
548C23×C4C2414yes—
549C23×C4C2412yes—
550C23×C4C2411yescharacteristic
551C4⋊Q8—24no—
552#127—24no—
553#126—88no—
554#124—24no—
555#124—24no—
556#123—28no—
557#123—28no—
558#123—28no—
559#123—88no—
560C22⋊Q8—28no—
561C22⋊Q8—28no—
562C22⋊Q8—28no—
563C22⋊Q8—44no—
564C22⋊Q8—44no—
565C22⋊Q8—44no—
566C22⋊Q8—44no—
567#121—28no—
568#121—28no—
569#121—28no—
570#121—216no—
571#121—44no—
572#121—44no—
573#121—44no—
574#121—44no—
575#121—48no—
576#121—48no—
577#121—88no—
578#120—28no—
579#120—28no—
580#120—28no—
581C4×Q8—28no—
582C4×Q8—44no—
583C4×Q8—44no—
584C4×D4—216no—
585C4×D4—216no—
586C4×D4—216no—
587C4×D4—216no—
588C4×D4—28no—
589C4×D4—216no—
590C4×D4—44no—
591C4×D4—44no—
592C4×D4—48no—
593C4×D4—48no—
594C4×D4—88no—
595C4×D4—88no—
596#117—24no—
597#117—24no—
598#117—24no—
599#117—24no—
600#117—24no—
601#117—28no—
602#117—28no—
603#117—28no—
604#117—28no—
605#117—28no—
606#117—48no—
607#117—48no—
608#117—44no—
609#117—44no—
610#117—88no—
611C2×C4⋊C4—28no—
612C2×C4⋊C4—24no—
613C2×C4⋊C4—24no—
614C2×C4⋊C4—24no—
615C2×C4⋊C4—24no—
616C2×C4⋊C4—48no—
617C2×C4⋊C4—48no—
618C2×C4⋊C4—44no—
619C2×C4⋊C4—44no—
620C2×C4⋊C4—44no—
621C2×C4⋊C4—84no—
622C2×C4⋊C4—84no—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2418yes—
663C2×C22⋊C4—28no—
664C2×C22⋊C4—44no—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C42—24no—
705C2×C42—28no—
706C2×C42—44no—
707C2×C42#4118yes—
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2412yes—
716C2×C42C2414yes—
717C2×C42C2418yes—
718C2×C42C2414yes—
719C2×C42C2414yes—
720C2×C42C2418yes—
721C2×C42C2418yes—
722C2×C42C2414yes—
723C2×C42C2414yes—
724C2×C42C2411yescharacteristic
725C2×C42C2412yes—
726C2×C42C2411yescharacteristic
727#95C2418yes—
728#95C2418yes—
729#95C2418yes—
730#95C2418yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2418yes—
736#95C2418yes—
737#95C2418yes—
738#95C2414yes—
739#95C2418yes—
740#95C2418yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2414yes—
750#95C2414yes—
751#95C2418yes—
752#95C2418yes—
753#95C2414yes—
754#95C2414yes—
755#95C2418yes—
756#95C2418yes—
757C24—22no—
758C24—22no—
759C24—42no—
760C24—42no—
761C24C2×#4114yes—
762C24C2512yes—
763C24C2512yes—
764C24C2512yes—
765C24C2512yes—
766C24C2511yescharacteristic
767#41—416no—
768#41—416no—
769#41—416no—
770C2×Q8—22no—
771C2×Q8—22no—
772C2×Q8—22no—
773C2×Q8—22no—
774C2×Q8—22no—
775C2×Q8—22no—
776C2×Q8—22no—
777C2×Q8—22no—
778C2×Q8—22no—
779C2×D4—24no—
780C2×D4—28no—
781C2×D4—24no—
782C2×D4—24no—
783C2×D4—24no—
784C2×D4—24no—
785C2×D4—24no—
786C2×D4—24no—
787C2×D4—24no—
788C2×D4—24no—
789C2×D4—28no—
790C2×D4—28no—
791C2×D4—22no—
792C2×D4—28no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—22no—
798C2×D4—22no—
799C2×D4—22no—
800C2×D4—22no—
801C2×D4—44no—
802C2×D4—44no—
803C2×D4—44no—
804C2×D4—44no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—44no—
810C2×D4—44no—
811C2×D4—48no—
812C2×D4—48no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—232no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—28no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4—44no—
838C22×C4—42no—
839C22×C4—44no—
840C22×C4—42no—
841C22×C4—48no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—48no—
846C22×C4—48no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4—48no—
851C22×C4—48no—
852C22×C4—816no—
853C22×C4C2×#4118yes—
854C22×C4C2×#4118yes—
855C22×C4C2×#4114yes—
856C22×C4C2×#4118yes—
857C22×C4C2×#4114yes—
858C22×C4C2×#4114yes—
859C22×C4H(5,𝔽2)14yes—
860C22×C4C2514yes—
861C22×C4C2514yes—
862C22×C4C2514yes—
863C22×C4C2514yes—
864C22×C4C2514yes—
865C22×C4C2512yes—
866C22×C4C2512yes—
867C22×C4C2512yes—
868C22×C4C2512yes—
869C22×C4C2512yes—
870C22×C4C2512yes—
871C22×C4C2512yes—
872C22×C4C2514yes—
873C22×C4C2514yes—
874C22×C4C2514yes—
875C22×C4C2512yes—
876C22×C4C2512yes—
877C22×C4C2512yes—
878C22×C4C2511yescharacteristic
879C22×C4C2511yescharacteristic
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—28no—
886C4⋊C4—24no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—28no—
890C4⋊C4—28no—
891C4⋊C4—28no—
892C4⋊C4—28no—
893C4⋊C4—24no—
894C4⋊C4—24no—
895C4⋊C4—24no—
896C4⋊C4—24no—
897C4⋊C4—24no—
898C4⋊C4—24no—
899C4⋊C4—24no—
900C4⋊C4—24no—
901C4⋊C4—22no—
902C4⋊C4—22no—
903C4⋊C4—48no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—48no—
907C4⋊C4—48no—
908C4⋊C4—48no—
909C4⋊C4—48no—
910C4⋊C4—44no—
911C4⋊C4—48no—
912C4⋊C4—44no—
913C4⋊C4—48no—
914C4⋊C4—44no—
915C4⋊C4—48no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—48no—
919C4⋊C4—44no—
920C22⋊C4—24no—
921C22⋊C4—24no—
922C22⋊C4—24no—
923C22⋊C4—24no—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—28no—
927C22⋊C4—24no—
928C22⋊C4—24no—
929C22⋊C4—24no—
930C22⋊C4—24no—
931C22⋊C4—24no—
932C22⋊C4—28no—
933C22⋊C4—28no—
934C22⋊C4—28no—
935C22⋊C4—28no—
936C22⋊C4—28no—
937C22⋊C4—28no—
938C22⋊C4—48no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—48no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—48no—
947C22⋊C4—48no—
948C22⋊C4—44no—
949C22⋊C4—48no—
950C22⋊C4—48no—
951C22⋊C4—48no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—44no—
957C22⋊C4—44no—
958C22⋊C4—44no—
959C42—24no—
960C42—24no—
961C42—22no—
962C42—22no—
963C42—28no—
964C42—24no—
965C42—24no—
966C42—24no—
967C42—24no—
968C42—48no—
969C42—44no—
970C42—44no—
971C42—44no—
972C42—48no—
973C42—48no—
974C42—44no—
975C42C2×#4114yes—
976C42C2×#4114yes—
977C42C2×#4118yes—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—28no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—48no—
1003C23—44no—
1004C23—48no—
1005C23—44no—
1006C23C22×#4114yes—
1007C23C22×#4112yes—
1008C23C22×#4112yes—
1009C23C2×H(5,𝔽2)12yes—
1010C23C2611yescharacteristic
1011Q8—44no—
1012Q8—44no—
1013Q8—44no—
1014D4—416no—
1015D4—416no—
1016D4—48no—
1017D4—48no—
1018D4—48no—
1019D4—44no—
1020D4—44no—
1021D4—44no—
1022D4—88no—
1023D4—88no—
1024D4—164no—
1025D4—164no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—28no—
1033C2×C4—216no—
1034C2×C4—216no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—24no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—28no—
1061C2×C4—28no—
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—28no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—22no—
1069C2×C4—24no—
1070C2×C4—22no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—28no—
1074C2×C4—48no—
1075C2×C4—416no—
1076C2×C4—48no—
1077C2×C4—48no—
1078C2×C4—48no—
1079C2×C4—48no—
1080C2×C4—84no—
1081C2×C4—84no—
1082C2×C4—84no—
1083C2×C4—84no—
1084C2×C4—816no—
1085C2×C4—164no—
1086C2×C4—164no—
1087C2×C4#553116yes—
1088C2×C4C22×#4114yes—
1089C2×C4C22×#4114yes—
1090C2×C4C22×#4114yes—
1091C2×C4C22×#4112yes—
1092C2×C4C22×#4112yes—
1093C2×C4C22×#4112yes—
1094C2×C4C22×#4112yes—
1095C2×C4C2×H(5,𝔽2)12yes—
1096C2×C4C2×H(5,𝔽2)12yes—
1097C22—24no—
1098C22—24no—
1099C22—22no—
1100C22—22no—
1101C22—24no—
1102C22—24no—
1103C22—24no—
1104C22—416no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—44no—
1110C22—44no—
1111C22—44no—
1112C22—44no—
1113C22—44no—
1114C22—44no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22C2×#55314yes—
1125C22C23×#4111yescharacteristic
1126C22C23×#4111yescharacteristic
1127C22C22×H(5,𝔽2)11yescharacteristic
1128C22H(7,𝔽2)12yes—
1129C222−1+612yes—
1130C4—24no—
1131C4—24no—
1132C4—24no—
1133C4—44no—
1134C4—42no—
1135C4—42no—
1136C4—44no—
1137C4—44no—
1138C4—44no—
1139C4—44no—
1140C4—44no—
1141C4—44no—
1142C4—42no—
1143C4—42no—
1144C4—44no—
1145C4—42no—
1146C4—42no—
1147C4—42no—
1148C4C2×#55314yes—
1149C4C2×#55314yes—
1150C2—24no—
1151C2—44no—
1152C2—82no—
1153C2—82no—
1154C2—82no—
1155C2C22×#55311yescharacteristic
1156C2#6284512yes—
1157C2#6285612yes—
1158C2#6287611yescharacteristic
1159C2#6288711yescharacteristic
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. #45130C2semidirect
2. #45120C2semidirect
3. #44922C2semidirect
4. #44907C2semidirect
5. #39815C2semidirect
6. #39813C2semidirect
7. #39553C2semidirect
8. #39552C2semidirect
9. #37945C2semidirect
10. #37944C2semidirect
11. #35629C2semidirect
12. #35618C2semidirect
13. #35557C2semidirect
14. #35530C2semidirect
15. #35339C2semidirect
16. #35328C2semidirect
17. #35223C2semidirect
18. #35150C2semidirect
19. #34633C2semidirect
20. #34207C2semidirect
21. #34201C2semidirect
22. #34200C2semidirect
23. #34188C2semidirect
24. #34065C2semidirect
25. C2×#2317C2semidirect
38. #2864C22semidirect
40. #2850C22semidirect
41. #2850C22semidirect
43. #2803C22semidirect
44. #2802C22semidirect
45. #2800C22semidirect
49. #2783C22semidirect
52. #2780C22semidirect
53. #2779C22semidirect
55. #2777C22semidirect
56. #2765C22semidirect
59. #2647C22semidirect
61. #2621C22semidirect
65. #2619C22semidirect
70. #2602C22semidirect
71. #2601C22semidirect
76. #2594C22semidirect
77. #2590C22semidirect
78. #2587C22semidirect
80. #2570C22semidirect
81. #2570C22semidirect
84. #2536C22semidirect
85. #2535C22semidirect
86. #2525C22semidirect
87. #2514C22semidirect
88. #2513C22semidirect
89. #2512C22semidirect
90. #2511C22semidirect
92. #2504C22semidirect
93. #2503C22semidirect
94. #2502C22semidirect
95. #2501C22semidirect
96. #2500C22semidirect
97. #2500C22semidirect
98. #2499C22semidirect
99. #2499C22semidirect
100. #2497C22semidirect
101. #2496C22semidirect
102. #2495C22semidirect
103. #2494C22semidirect
106. #2470C22semidirect
108. #2466C22semidirect
112. #2423C22semidirect
113. #2422C22semidirect
114. #2421C22semidirect
115. #2420C22semidirect
131. #2355C22semidirect
133. #2354C22semidirect
134. #2354C22semidirect
139. D4×C4⋊C4C22semidirect
140. #2326C22semidirect
141. #2326C22semidirect
158. #2314C22semidirect
165. C4×C4⋊Q8C22semidirect
166. C4×#127C22semidirect
178. #2285C22semidirect

Maximal subgroups

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

subgroupindex
#451302
#451202
#449222
#449072
#398152
#398132
#395532
#395522
#379452
#379442
#356292
#356182
#355572
#355302
#353392
#353282
#352232
#351502
#346332
#342072
#342012
#342002
#341882
#340652
C2×#23172