Finite Group Databasebeta

← #8095538

Subgroups — #8095538

Order 512.

5886 conjugacy classes of subgroups.

The subgroup lattice has 1255 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53088C214yesmaximal, complemented
2#53059C214yesmaximal, complemented
3#53004C214yesmaximal, complemented
4#52960C214yesmaximal, complemented
5#52372C218yesmaximal, complemented
6#46048C214yesmaximal, complemented
7#46010C214yesmaximal, complemented
8#45683C214yesmaximal, complemented
9#45604C214yesmaximal, complemented
10#45529C218yesmaximal, complemented
11#35676C211yesmaximal, characteristic, complemented
12#35676C211yesmaximal, characteristic, complemented
13#35660C211yesmaximal, characteristic, complemented
14#35617C211yesmaximal, characteristic, complemented
15#35541C211yesmaximal, characteristic, complemented
16#35528C211yesmaximal, characteristic, complemented
17#35327C211yesmaximal, characteristic, complemented
18#35313C211yesmaximal, characteristic, complemented
19#35274C211yesmaximal, characteristic, complemented
20#35256C211yesmaximal, characteristic, complemented
21#35168C211yesmaximal, characteristic, complemented
22#35152C211yesmaximal, characteristic, complemented
23C2×#2544C211yesmaximal, characteristic, complemented
24#34816C211yesmaximal, characteristic, complemented
25#34744C211yesmaximal, characteristic, complemented
26C22×2−1+4C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#535C2211yescharacteristic
30C2×#535C2211yescharacteristic
31C2×#535C2211yescharacteristic
32C2×#535C2211yescharacteristic
33C2×#535C2211yescharacteristic
34C2×#535C2211yescharacteristic
35C2×#532C2211yescharacteristic
36C22×#127C2211yescharacteristic
37C22×#124C2211yescharacteristic
38C22×#124C2211yescharacteristic
39C2×#518C2211yescharacteristic
40C2×C4×#41C2211yescharacteristic
41C22×C4×D4C2211yescharacteristic
42#2867C2212yes—
43#2863C2214yescomplemented
44#2858C2212yes—
45#2856C2212yescomplemented
46#2850C2214yescomplemented
47#2850C2212yescomplemented
48#2849C2214yes—
49#2847C2214yes—
50#2830C2218yescomplemented
51#2828C2218yescomplemented
52#2826C2218yescomplemented
53#2825C2218yescomplemented
54#2825C2218yescomplemented
55#2824C2218yescomplemented
56#2824C2218yescomplemented
57#2824C2218yescomplemented
58#2818C2218yescomplemented
59#2813C2218yescomplemented
60#2797C2218yescomplemented
61#2784C2218yescomplemented
62#2778C2218yescomplemented
63#2778C2218yescomplemented
64#2760C2218yescomplemented
65#2749C2218yescomplemented
66#2737C2218yescomplemented
67#2737C2218yescomplemented
68#2709C2218yescomplemented
69#2709C2218yescomplemented
70#2709C2218yescomplemented
71#2703C2218yescomplemented
72#2693C2218yescomplemented
73#2691C2218yescomplemented
74#2688C2218yescomplemented
75#2688C2218yescomplemented
76#2688C2218yescomplemented
77#2673C2218yescomplemented
78#2673C2218yescomplemented
79#2673C2218yescomplemented
80#2657C2212yes—
81#2657C2212yes—
82#2645C2214yescomplemented
83#2622C2214yes—
84#2620C2214yescomplemented
85#2620C2212yescomplemented
86#2619C2212yescomplemented
87#2617C2214yes—
88#2547C2214yescomplemented
89#2545C2214yescomplemented
90#2544C2214yes—
91#2544C2214yes—
92#2544C2214yes—
93#2544C2214yes—
94#2544C2214yes—
95#2544C2214yescomplemented
96#2544C2214yescomplemented
97#2541C2214yes—
98#2541C2214yes—
99#2541C2214yes—
100#2534C2218yes—
101#2514C2212yescomplemented
102#2514C2214yescomplemented
103#2513C2212yescomplemented
104#2512C2212yescomplemented
105#2511C2212yescomplemented
106#2511C2214yescomplemented
107#2510C2214yes—
108#2493C2218yes—
109#2481C2214yes—
110#2448C2212yescomplemented
111#2447C2212yescomplemented
112#2447C2214yescomplemented
113#2447C2214yescomplemented
114#2446C2212yescomplemented
115#2445C2214yescomplemented
116#2445C2214yescomplemented
117#2445C2212yescomplemented
118#2444C2214yes—
119#2443C2214yes—
120#2436C2212yescomplemented
121#2436C2214yescomplemented
122#2436C2214yescomplemented
123#2436C2212yescomplemented
124#2436C2214yescomplemented
125#2436C2212yescomplemented
126#2434C2212yescomplemented
127#2433C2218yes—
128#2432C2212yescomplemented
129#2431C2212yescomplemented
130#2431C2214yescomplemented
131#2431C2212yescomplemented
132#2431C2212yescomplemented
133#2431C2214yescomplemented
134#2431C2214yescomplemented
135#2430C2218yes—
136#2428C2214yes—
137#2428C2214yes—
138#2428C2214yescomplemented
139#2428C2214yescomplemented
140#2428C2214yescomplemented
141#2427C2214yescomplemented
142#2427C2214yescomplemented
143#2427C2214yescomplemented
144#2427C2214yescomplemented
145#2426C2214yescomplemented
146#2424C2218yes—
147#2422C2214yescomplemented
148#2422C2214yescomplemented
149#2420C2214yescomplemented
150#2420C2214yescomplemented
151#2412C2214yes—
152#2412C2214yes—
153#2412C2218yes—
154#2410C2218yes—
155#2409C2214yescomplemented
156#2407C2214yescomplemented
157#2404C2214yes—
158#2404C2218yes—
159#2404C2214yes—
160#2401C2214yescomplemented
161#2395C2214yescomplemented
162C2×#394C2214yes—
163#2380C2218yescomplemented
164#2377C2218yescomplemented
165#2317C2211yescharacteristic
166#2316C2211yescharacteristic
167#2311C2211yescharacteristic
168#2310C2211yescharacteristic
169#2310C2211yescharacteristic
170#2309C2211yescharacteristic
171C4×#126C2214yescomplemented
172C4×#123C2214yescomplemented
173#2297C2211yescharacteristic
174#2297C2211yescharacteristic
175#2297C2211yescharacteristic
176#2297C2211yescharacteristic
177#2297C2211yescharacteristic
178#2297C2211yescharacteristic
179#2296C2211yescharacteristic
180#2296C2211yescharacteristic
181C2×#391C2211yescharacteristic
182C2×#390C2211yescharacteristic
183C2×#386C2214yes—
184#2285C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C2×2−1+4—44no—
188C2×2−1+4—44no—
189C2×2−1+4—44no—
190C22×#41C2311yescharacteristic
191C22×#41C2311yescharacteristic
192C22×#41C2311yescharacteristic
193C22×#41C2314yes—
194C22×#41C2312yes—
195C22×#41C2312yes—
196C23×Q8C2311yescharacteristic
197C23×Q8C2312yes—
198C23×Q8C2312yes—
199C23×D4C2311yescharacteristic
200C23×D4C2311yescharacteristic
201C23×D4C2314yes—
202C24×C4C2312yes—
203#537—44no—
204#536—44no—
205#535—44no—
206#535—44no—
207#535—44no—
208#535—44no—
209#535—44no—
210#535—44no—
211#532—44no—
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2312yes—
214C2×#127—44no—
215C2×#127C2318yes—
216C2×#127C2312yes—
217C2×#127C2312yes—
218C2×#127C2311yescharacteristic
219C2×#127C2312yes—
220C2×#127C2312yes—
221C2×#127C2312yes—
222C2×#127C2312yes—
223C2×#127C2312yes—
224C2×#127C2314yes—
225C2×#127C2312yes—
226C2×#127C2318yes—
227C2×#126C2314yes—
228C2×#124—44no—
229C2×#124—44no—
230C2×#124C2312yes—
231C2×#124C2312yes—
232C2×#124C2312yes—
233C2×#124C2312yes—
234C2×#124C2312yes—
235C2×#124C2312yes—
236C2×#124C2312yes—
237C2×#124C2311yescharacteristic
238C2×#124C2311yescharacteristic
239C2×#124C2314yes—
240C2×#124C2314yes—
241C2×#124C2314yes—
242C2×#124C2312yes—
243C2×#124C2312yes—
244C2×#123C2314yes—
245C2×#123C2314yes—
246C2×#123C2318yes—
247C2×#123C2318yes—
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2312yes—
250C2×C22⋊Q8C2312yes—
251C2×#121C2314yes—
252C2×#121C2312yes—
253C2×#121C2314yes—
254C2×#121C2312yes—
255C2×#121C2312yes—
256C2×#121C2318yes—
257C2×#121C2314yes—
258C2×#121C2312yes—
259C2×#121C2314yes—
260C2×#121C2312yes—
261C2×#121C2314yes—
262C2×#121C2314yes—
263C2×#121C2312yes—
264C2×#121C2318yes—
265C2×#121C2318yes—
266C2×#121C2318yes—
267C2×#120C2314yes—
268C2×#120C2314yes—
269C2×#120C2314yes—
270C2×#120C2314yes—
271C2×#120C2314yes—
272C2×#120C2314yes—
273#518—44no—
274C4×#41—44no—
275C2×C4×Q8C2312yes—
276C2×C4×D4—44no—
277C2×C4×D4C2314yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2314yes—
281C2×C4×D4C2312yes—
282C2×C4×D4C2314yes—
283C2×C4×D4C2314yes—
284C2×#117C2311yescharacteristic
285C2×#117C2311yescharacteristic
286C2×#117C2311yescharacteristic
287C2×#117C2311yescharacteristic
288C2×#117C2311yescharacteristic
289C2×#117C2312yes—
290C22×C4⋊C4C2311yescharacteristic
291C22×C4⋊C4C2312yes—
292C22×C22⋊C4C2312yes—
293C22×C22⋊C4C2312yes—
294C22×C22⋊C4C2314yes—
295C22×C22⋊C4C2314yes—
296C22×C22⋊C4C2312yes—
297C22×C22⋊C4C2314yes—
298C22×C42C2311yescharacteristic
299C22×C42C2311yescharacteristic
300C22×C42C2311yescharacteristic
301C22×C42C2312yes—
302#401C2318yes—
303#401C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2318yes—
308#400C2318yes—
309#400C2318yes—
310#400C2314yes—
311#399C2314yes—
312#398C2314yes—
313#397C2314yes—
314#397C2314yes—
315#397C2318yes—
316#397C2318yes—
317#397C2318yes—
318#397C2318yes—
319#397C2314yes—
320#397C2314yes—
321#397C2318yes—
322#397C2318yes—
323#397C2318yes—
324#397C2314yes—
325#397C2314yes—
326#396C2314yes—
327#396C2318yes—
328#396C2318yes—
329#396C2318yes—
330#395C2318yes—
331#394C2314yes—
332#394C2318yes—
333#394C2318yes—
334#394C2318yes—
335#394C2318yes—
336#394C2318yes—
337#394C2318yes—
338#394C2318yes—
339#394C2318yes—
340#394C2318yes—
341#394C2318yes—
342#394C2318yes—
343#394C2318yes—
344#394C2318yes—
345#394C2318yes—
346#394C2318yes—
347#394C2318yes—
348#394C2318yes—
349#394C2318yes—
350#394C2318yes—
351#394C2314yes—
352#393C2318yes—
353#393C2318yes—
354#393C2318yes—
355#393C2318yes—
356#393C2318yes—
357#392C2318yes—
358#392C2318yes—
359#392C2318yes—
360#392C2318yes—
361#392C2318yes—
362#392C2318yes—
363#392C2318yes—
364#392C2318yes—
365#392C2318yes—
366#392C2318yes—
367#392C2318yes—
368#392C2318yes—
369#392C2318yes—
370#391C2314yes—
371#391C2314yes—
372#391C2314yes—
373#391C2312yes—
374#391C2312yes—
375#391C2312yes—
376#391C2311yescharacteristic
377#391C2312yes—
378#391C2311yescharacteristic
379#391C2312yes—
380#391C2314yes—
381#391C2312yes—
382#391C2312yes—
383#391C2312yes—
384#391C2312yes—
385#391C2312yes—
386#390C2314yes—
387#390C2314yes—
388#390C2312yes—
389#390C2318yes—
390#390C2318yes—
391#390C2312yes—
392#390C2311yescharacteristic
393#390C2318yes—
394#390C2311yescharacteristic
395#390C2312yes—
396#390C2312yes—
397#390C2314yes—
398#390C2312yes—
399#390C2312yes—
400#390C2312yes—
401#390C2312yes—
402#389C2314yes—
403#389C2314yes—
404#389C2314yes—
405#389C2312yes—
406#389C2312yes—
407#389C2312yes—
408#389C2312yes—
409#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#388C2314yes—
413#388C2318yes—
414#388C2318yes—
415#388C2318yes—
416#388C2314yes—
417#387C2314yes—
418#387C2314yes—
419#387C2314yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2314yes—
424#387C2314yes—
425#386C2314yes—
426#386C2318yes—
427#386C2318yes—
428#386C2318yes—
429#386C2318yes—
430#386C2318yes—
431#386C2318yes—
432#386C2318yes—
433#386C2318yes—
434#386C2318yes—
435#386C2318yes—
436#386C2318yes—
437#386C2318yes—
438#386C2318yes—
439#386C2312yes—
440#386C2312yes—
441#386C2312yes—
442#386C2318yes—
443#386C2312yes—
444#386C2312yes—
445#386C2312yes—
446#386C2318yes—
447#386C2318yes—
448#386C2318yes—
449#386C2314yes—
450#386C2318yes—
451#386C2318yes—
452#386C2318yes—
453#386C2318yes—
454#386C2318yes—
455#386C2318yes—
456#386C2314yes—
457#386C2314yes—
458#386C2314yes—
459#386C2318yes—
460#386C2318yes—
461#385C2314yes—
462#385C2318yes—
463#385C2318yes—
464#385C2318yes—
465#385C2314yes—
466#385C2312yes—
467#385C2312yes—
468#385C2318yes—
469#385C2314yes—
470#384C2312yes—
471#384C2312yes—
472#383C2314yes—
473#383C2318yes—
474#382C2312yes—
475#382C2312yes—
476#381C2314yes—
477#381C2314yes—
478#381C2318yes—
479#381C2318yes—
480#381C2314yes—
481#380C2314yes—
482#380C2314yes—
483#380C2318yes—
484#380C2318yes—
485#380C2314yes—
486#380C2318yes—
487#379C2314yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C22⋊C4C2312yes—
498C4×C22⋊C4C2314yes—
499C4×C22⋊C4C2314yes—
500C4×C22⋊C4C2312yes—
501C4×C22⋊C4C2314yes—
502C4×C22⋊C4C2314yes—
503C4×C22⋊C4C2312yes—
504C4×C22⋊C4C2312yes—
505C4×C22⋊C4C2314yes—
506#376C2312yes—
507C2×#95C2314yes—
508C2×#95C2312yes—
509C43C2312yes—
510C25C2412yes—
511C25C2412yes—
5122−1+4—464no—
513C2×#41—24no—
514C2×#41—24no—
515C2×#41—24no—
516C2×#41—24no—
517C2×#41—24no—
518C2×#41—24no—
519C2×#41—24no—
520C2×#41—24no—
521C2×#41—24no—
522C2×#41—48no—
523C2×#41—48no—
524C2×#41—48no—
525C2×#41—44no—
526C2×#41—44no—
527C2×#41—44no—
528C2×#41—44no—
529C2×#41—44no—
530C2×#41—44no—
531C22×Q8—24no—
532C22×Q8—24no—
533C22×Q8—24no—
534C22×Q8—44no—
535C22×Q8—44no—
536C22×Q8—44no—
537C22×Q8—44no—
538C22×Q8—44no—
539C22×Q8—44no—
540C22×Q8C2411yescharacteristic
541C22×Q8C2412yes—
542C22×Q8C2411yescharacteristic
543C22×Q8C2412yes—
544C22×Q8C2411yescharacteristic
545C22×Q8C2414yes—
546C22×D4—24no—
547C22×D4—24no—
548C22×D4—24no—
549C22×D4—24no—
550C22×D4—24no—
551C22×D4—24no—
552C22×D4—48no—
553C22×D4—48no—
554C22×D4—84no—
555C22×D4C2412yes—
556C22×D4C2412yes—
557C22×D4C2412yes—
558C22×D4C2412yes—
559C22×D4C2412yes—
560C22×D4C2411yescharacteristic
561C22×D4C2412yes—
562C22×D4C2412yes—
563C22×D4C2411yescharacteristic
564C22×D4C2411yescharacteristic
565C22×D4C2414yes—
566C22×D4C2418yes—
567C22×D4C2418yes—
568C22×D4C2418yes—
569C22×D4C2414yes—
570C22×D4C2418yes—
571C22×D4C2414yes—
572C22×D4C2418yes—
573C22×D4C2414yes—
574C22×D4C2414yes—
575C22×D4C2414yes—
576C22×D4C2418yes—
577C22×D4C2414yes—
578C23×C4—44no—
579C23×C4—84no—
580C23×C4C2412yes—
581C23×C4C2412yes—
582C23×C4C2412yes—
583C23×C4C2412yes—
584C23×C4C2412yes—
585C23×C4C2411yescharacteristic
586C23×C4C2412yes—
587C23×C4C2412yes—
588C23×C4C2411yescharacteristic
589C23×C4C2418yes—
590C23×C4C2414yes—
591C23×C4C2418yes—
592C23×C4C2414yes—
593C23×C4C2414yes—
594C23×C4C2411yescharacteristic
595C4⋊Q8—42no—
596C4⋊Q8—44no—
597#127—48no—
598#127—44no—
599#127—44no—
600#127—416no—
601#127—42no—
602#127—44no—
603#127—44no—
604#127—44no—
605#127—44no—
606#127—44no—
607#127—44no—
608#127—88no—
609#126—48no—
610#124—44no—
611#124—44no—
612#124—48no—
613#124—48no—
614#124—48no—
615#124—42no—
616#124—42no—
617#124—44no—
618#124—44no—
619#124—44no—
620#124—44no—
621#124—44no—
622#124—44no—
623#124—44no—
624#123—48no—
625#123—48no—
626#123—88no—
627#123—88no—
628C22⋊Q8—48no—
629C22⋊Q8—44no—
630C22⋊Q8—44no—
631#121—416no—
632#121—48no—
633#121—48no—
634#121—44no—
635#121—44no—
636#121—48no—
637#121—44no—
638#121—48no—
639#121—44no—
640#121—44no—
641#121—44no—
642#121—48no—
643#121—48no—
644#121—88no—
645#121—88no—
646#121—88no—
647#120—48no—
648#120—48no—
649#120—48no—
650#120—48no—
651#120—48no—
652#120—48no—
653C4×Q8—44no—
654C4×D4—48no—
655C4×D4—48no—
656C4×D4—44no—
657C4×D4—48no—
658C4×D4—48no—
659C4×D4—48no—
660C4×D4—48no—
661#117—24no—
662#117—24no—
663#117—24no—
664#117—24no—
665#117—24no—
666#117—44no—
667C2×C4⋊C4—24no—
668C2×C4⋊C4—44no—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2412yes—
681C2×C4⋊C4C2412yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2418yes—
687C2×C4⋊C4C2418yes—
688C2×C4⋊C4C2418yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C22⋊C4—48no—
694C2×C22⋊C4—44no—
695C2×C22⋊C4—44no—
696C2×C22⋊C4—44no—
697C2×C22⋊C4—48no—
698C2×C22⋊C4—84no—
699C2×C22⋊C4C2412yes—
700C2×C22⋊C4C2412yes—
701C2×C22⋊C4C2412yes—
702C2×C22⋊C4C2412yes—
703C2×C22⋊C4C2412yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2418yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2418yes—
708C2×C22⋊C4C2418yes—
709C2×C22⋊C4C2418yes—
710C2×C22⋊C4C2418yes—
711C2×C22⋊C4C2418yes—
712C2×C22⋊C4C2418yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2418yes—
719C2×C22⋊C4C2418yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2418yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2418yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2418yes—
731C2×C22⋊C4C2418yes—
732C2×C22⋊C4C2418yes—
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2418yes—
736C2×C22⋊C4C2414yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2414yes—
741C2×C42—24no—
742C2×C42—24no—
743C2×C42—24no—
744C2×C42—44no—
745C2×C42C2411yescharacteristic
746C2×C42C2412yes—
747C2×C42C2412yes—
748C2×C42C2412yes—
749C2×C42C2412yes—
750C2×C42C2412yes—
751C2×C42C2412yes—
752C2×C42C2412yes—
753C2×C42C2412yes—
754C2×C42C2412yes—
755C2×C42C2411yescharacteristic
756C2×C42C2411yescharacteristic
757C2×C42C2414yes—
758C2×C42C2411yescharacteristic
759C2×C42C2414yes—
760C2×C42C2414yes—
761#95C2412yes—
762#95C2412yes—
763#95C2412yes—
764#95C2412yes—
765#95C2418yes—
766#95C2418yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2418yes—
788#95C2418yes—
789#95C2418yes—
790#95C2418yes—
791#95C2418yes—
792#95C2418yes—
793#95C2418yes—
794C24—24no—
795C24—24no—
796C24—24no—
797C24—24no—
798C24—24no—
799C24—24no—
800C24—44no—
801C24—44no—
802C24—44no—
803C24—44no—
804C24C2514yes—
805C24C2514yes—
806C24C2512yes—
807C24C2512yes—
808C24C2512yes—
809C24C2511yescharacteristic
810#41—464no—
811#41—432no—
812#41—432no—
813#41—416no—
814#41—416no—
815#41—416no—
816C2×Q8—22no—
817C2×Q8—22no—
818C2×Q8—24no—
819C2×Q8—22no—
820C2×Q8—22no—
821C2×Q8—24no—
822C2×Q8—24no—
823C2×Q8—24no—
824C2×Q8—24no—
825C2×Q8—22no—
826C2×Q8—22no—
827C2×Q8—22no—
828C2×Q8—22no—
829C2×Q8—24no—
830C2×Q8—22no—
831C2×Q8—44no—
832C2×Q8—44no—
833C2×Q8—44no—
834C2×Q8—432no—
835C2×Q8—432no—
836C2×Q8—416no—
837C2×D4—24no—
838C2×D4—24no—
839C2×D4—24no—
840C2×D4—24no—
841C2×D4—24no—
842C2×D4—24no—
843C2×D4—24no—
844C2×D4—24no—
845C2×D4—24no—
846C2×D4—24no—
847C2×D4—24no—
848C2×D4—24no—
849C2×D4—24no—
850C2×D4—22no—
851C2×D4—24no—
852C2×D4—24no—
853C2×D4—24no—
854C2×D4—24no—
855C2×D4—22no—
856C2×D4—22no—
857C2×D4—24no—
858C2×D4—24no—
859C2×D4—24no—
860C2×D4—22no—
861C2×D4—24no—
862C2×D4—22no—
863C2×D4—22no—
864C2×D4—22no—
865C2×D4—22no—
866C2×D4—22no—
867C2×D4—216no—
868C2×D4—28no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—48no—
874C2×D4—48no—
875C2×D4—48no—
876C2×D4—44no—
877C2×D4—48no—
878C2×D4—48no—
879C2×D4—48no—
880C2×D4—48no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—48no—
884C2×D4—44no—
885C2×D4—48no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—48no—
889C2×D4—48no—
890C2×D4—48no—
891C2×D4—48no—
892C2×D4—48no—
893C2×D4—48no—
894C2×D4—48no—
895C2×D4—48no—
896C2×D4—48no—
897C2×D4—48no—
898C2×D4—48no—
899C2×D4—48no—
900C2×D4—48no—
901C2×D4—416no—
902C2×D4—416no—
903C2×D4—832no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—24no—
907C22×C4—24no—
908C22×C4—24no—
909C22×C4—24no—
910C22×C4—24no—
911C22×C4—24no—
912C22×C4—24no—
913C22×C4—24no—
914C22×C4—24no—
915C22×C4—24no—
916C22×C4—24no—
917C22×C4—24no—
918C22×C4—24no—
919C22×C4—24no—
920C22×C4—24no—
921C22×C4—24no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—44no—
926C22×C4—44no—
927C22×C4—44no—
928C22×C4—44no—
929C22×C4—44no—
930C22×C4—44no—
931C22×C4—44no—
932C22×C4—42no—
933C22×C4—44no—
934C22×C4—42no—
935C22×C4—48no—
936C22×C4—44no—
937C22×C4—48no—
938C22×C4—44no—
939C22×C4—48no—
940C22×C4—48no—
941C22×C4—48no—
942C22×C4—48no—
943C22×C4—816no—
944C22×C4H(5,𝔽2)14yes—
945C22×C4H(5,𝔽2)14yes—
946C22×C4H(5,𝔽2)14yes—
947C22×C4C2512yes—
948C22×C4C2512yes—
949C22×C4C2514yes—
950C22×C4C2512yes—
951C22×C4C2514yes—
952C22×C4C2512yes—
953C22×C4C2512yes—
954C22×C4C2514yes—
955C22×C4C2512yes—
956C22×C4C2512yes—
957C22×C4C2514yes—
958C22×C4C2514yes—
959C22×C4C2512yes—
960C22×C4C2514yes—
961C22×C4C2512yes—
962C22×C4C2512yes—
963C22×C4C2512yes—
964C22×C4C2511yescharacteristic
965C22×C4C2511yescharacteristic
966C4⋊C4—24no—
967C4⋊C4—24no—
968C4⋊C4—24no—
969C4⋊C4—24no—
970C4⋊C4—24no—
971C4⋊C4—22no—
972C4⋊C4—24no—
973C4⋊C4—22no—
974C4⋊C4—24no—
975C4⋊C4—24no—
976C4⋊C4—28no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—44no—
980C4⋊C4—44no—
981C4⋊C4—44no—
982C4⋊C4—44no—
983C4⋊C4—48no—
984C4⋊C4—48no—
985C4⋊C4—48no—
986C4⋊C4—44no—
987C4⋊C4—44no—
988C4⋊C4—44no—
989C4⋊C4—44no—
990C22⋊C4—24no—
991C22⋊C4—24no—
992C22⋊C4—24no—
993C22⋊C4—24no—
994C22⋊C4—24no—
995C22⋊C4—28no—
996C22⋊C4—48no—
997C22⋊C4—48no—
998C22⋊C4—48no—
999C22⋊C4—48no—
1000C22⋊C4—48no—
1001C22⋊C4—48no—
1002C22⋊C4—48no—
1003C22⋊C4—48no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C22⋊C4—48no—
1008C22⋊C4—48no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—48no—
1012C22⋊C4—44no—
1013C22⋊C4—48no—
1014C22⋊C4—44no—
1015C22⋊C4—48no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C22⋊C4—44no—
1022C22⋊C4—48no—
1023C22⋊C4—48no—
1024C22⋊C4—44no—
1025C22⋊C4—44no—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
1028C22⋊C4—48no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C42—22no—
1033C42—22no—
1034C42—24no—
1035C42—24no—
1036C42—24no—
1037C42—24no—
1038C42—22no—
1039C42—22no—
1040C42—24no—
1041C42—24no—
1042C42—24no—
1043C42—24no—
1044C42—24no—
1045C42—28no—
1046C42—44no—
1047C42—44no—
1048C23—22no—
1049C23—22no—
1050C23—24no—
1051C23—22no—
1052C23—22no—
1053C23—24no—
1054C23—24no—
1055C23—24no—
1056C23—24no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—24no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—24no—
1066C23—24no—
1067C23—24no—
1068C23—28no—
1069C23—28no—
1070C23—24no—
1071C23—24no—
1072C23—28no—
1073C23—28no—
1074C23—24no—
1075C23—416no—
1076C23—48no—
1077C23—48no—
1078C23—84no—
1079C23—84no—
1080C23—88no—
1081C23—88no—
1082C23—84no—
1083C23—84no—
1084C23—88no—
1085C23C2×H(5,𝔽2)12yes—
1086C23C2×H(5,𝔽2)12yes—
1087C23C2×H(5,𝔽2)12yes—
1088C23C2611yescharacteristic
1089Q8—416no—
1090Q8—48no—
1091Q8—44no—
1092Q8—48no—
1093Q8—44no—
1094Q8—44no—
1095D4—416no—
1096D4—48no—
1097D4—48no—
1098D4—48no—
1099D4—48no—
1100D4—48no—
1101D4—48no—
1102D4—48no—
1103D4—44no—
1104D4—44no—
1105D4—44no—
1106D4—88no—
1107D4—816no—
1108D4—816no—
1109D4—164no—
1110D4—164no—
1111D4—164no—
1112D4—164no—
1113D4—164no—
1114D4—168no—
1115D4—168no—
1116D4—168no—
1117D4—168no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—24no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—24no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—22no—
1148C2×C4—24no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—24no—
1159C2×C4—22no—
1160C2×C4—24no—
1161C2×C4—28no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—48no—
1166C2×C4—44no—
1167C2×C4—44no—
1168C2×C4—416no—
1169C2×C4—416no—
1170C2×C4—48no—
1171C2×C4—48no—
1172C2×C4—48no—
1173C2×C4—48no—
1174C2×C4—84no—
1175C2×C4—84no—
1176C2×C4—88no—
1177C2×C4—816no—
1178C2×C4—168no—
1179C2×C4#560116yes—
1180C2×C4C2×H(5,𝔽2)12yes—
1181C2×C4C2×H(5,𝔽2)12yes—
1182C2×C4C2×H(5,𝔽2)12yes—
1183C2×C4C2×H(5,𝔽2)12yes—
1184C2×C4C2×H(5,𝔽2)12yes—
1185C2×C4C2×H(5,𝔽2)12yes—
1186C2×C4#58514yes—
1187C22—22no—
1188C22—22no—
1189C22—24no—
1190C22—24no—
1191C22—42no—
1192C22—42no—
1193C22—44no—
1194C22—44no—
1195C22—42no—
1196C22—44no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—44no—
1201C22—44no—
1202C22—48no—
1203C22—48no—
1204C22—44no—
1205C22—44no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—44no—
1210C22—44no—
1211C22—48no—
1212C22—44no—
1213C22—44no—
1214C22—44no—
1215C22—48no—
1216C22—816no—
1217C22—168no—
1218C22C2×#56014yes—
1219C22C22×H(5,𝔽2)11yescharacteristic
1220C22C22×H(5,𝔽2)11yescharacteristic
1221C22C22×H(5,𝔽2)11yescharacteristic
1222C22C2×#58512yes—
1223C22H(7,𝔽2)12yes—
1224C4—24no—
1225C4—42no—
1226C4—42no—
1227C4—42no—
1228C4—44no—
1229C4—42no—
1230C4—42no—
1231C4—42no—
1232C4—42no—
1233C4—44no—
1234C4—42no—
1235C4—42no—
1236C4—44no—
1237C4—42no—
1238C4—44no—
1239C4—44no—
1240C4—44no—
1241C4C2×#56014yes—
1242C4C2×#56014yes—
1243C2—24no—
1244C2—82no—
1245C2—82no—
1246C2—82no—
1247C2—84no—
1248C2—84no—
1249C2C22×#56011yescharacteristic
1250C2#6283611yescharacteristic
1251C2#6287611yescharacteristic
1252C2#6292412yes—
1253C2#6296112yes—
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. #53088C2semidirect
2. #53059C2semidirect
3. #53004C2semidirect
4. #52960C2semidirect
5. #52372C2semidirect
6. #46048C2semidirect
7. #46010C2semidirect
8. #45683C2semidirect
9. #45604C2semidirect
10. #45529C2semidirect
11. #35676C2semidirect
12. #35676C2semidirect
13. #35660C2semidirect
14. #35617C2semidirect
15. #35541C2semidirect
16. #35528C2semidirect
17. #35327C2semidirect
18. #35313C2semidirect
19. #35274C2semidirect
20. #35256C2semidirect
21. #35168C2semidirect
22. #35152C2semidirect
23. C2×#2544C2semidirect
24. #34816C2semidirect
25. #34744C2semidirect
43. #2863C22semidirect
45. #2856C22semidirect
46. #2850C22semidirect
47. #2850C22semidirect
50. #2830C22semidirect
51. #2828C22semidirect
52. #2826C22semidirect
53. #2825C22semidirect
54. #2825C22semidirect
55. #2824C22semidirect
56. #2824C22semidirect
57. #2824C22semidirect
58. #2818C22semidirect
59. #2813C22semidirect
60. #2797C22semidirect
61. #2784C22semidirect
62. #2778C22semidirect
63. #2778C22semidirect
64. #2760C22semidirect
65. #2749C22semidirect
66. #2737C22semidirect
67. #2737C22semidirect
68. #2709C22semidirect
69. #2709C22semidirect
70. #2709C22semidirect
71. #2703C22semidirect
72. #2693C22semidirect
73. #2691C22semidirect
74. #2688C22semidirect
75. #2688C22semidirect
76. #2688C22semidirect
77. #2673C22semidirect
78. #2673C22semidirect
79. #2673C22semidirect
82. #2645C22semidirect
84. #2620C22semidirect
85. #2620C22semidirect
86. #2619C22semidirect
88. #2547C22semidirect
89. #2545C22semidirect
95. #2544C22semidirect
96. #2544C22semidirect
101. #2514C22semidirect
102. #2514C22semidirect
103. #2513C22semidirect
104. #2512C22semidirect
105. #2511C22semidirect
106. #2511C22semidirect
110. #2448C22semidirect
111. #2447C22semidirect
112. #2447C22semidirect
113. #2447C22semidirect
114. #2446C22semidirect
115. #2445C22semidirect
116. #2445C22semidirect
117. #2445C22semidirect
120. #2436C22semidirect
121. #2436C22semidirect
122. #2436C22semidirect
123. #2436C22semidirect
124. #2436C22semidirect
125. #2436C22semidirect
126. #2434C22semidirect
128. #2432C22semidirect
129. #2431C22semidirect
130. #2431C22semidirect
131. #2431C22semidirect
132. #2431C22semidirect
133. #2431C22semidirect
134. #2431C22semidirect
138. #2428C22semidirect
139. #2428C22semidirect
140. #2428C22semidirect
141. #2427C22semidirect
142. #2427C22semidirect
143. #2427C22semidirect
144. #2427C22semidirect
145. #2426C22semidirect
147. #2422C22semidirect
148. #2422C22semidirect
149. #2420C22semidirect
150. #2420C22semidirect
155. #2409C22semidirect
156. #2407C22semidirect
160. #2401C22semidirect
161. #2395C22semidirect
163. #2380C22semidirect
164. #2377C22semidirect
171. C4×#126C22semidirect
172. C4×#123C22semidirect

Maximal subgroups

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

subgroupindex
#530882
#530592
#530042
#529602
#523722
#460482
#460102
#456832
#456042
#455292
#356762
#356602
#356172
#355412
#355282
#353272
#353132
#352742
#352562
#351682
#351522
C2×#25442
#348162
#347442