Finite Group Databasebeta

← #8093521

Subgroups — #8093521

Order 512.

5630 conjugacy classes of subgroups.

The subgroup lattice has 1254 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53129C214yesmaximal, complemented
2#53095C214yesmaximal, complemented
3#53066C214yesmaximal, complemented
4#53051C214yesmaximal, complemented
5#53047C214yesmaximal, complemented
6#53018C214yesmaximal, complemented
7#52981C214yesmaximal, complemented
8#52977C214yesmaximal, complemented
9#52347C218yesmaximal, complemented
10#52345C218yesmaximal, complemented
11#35677C211yesmaximal, characteristic, complemented
12#35673C211yesmaximal, characteristic, complemented
13#35661C211yesmaximal, characteristic, complemented
14#35634C211yesmaximal, characteristic, complemented
15#35621C211yesmaximal, characteristic, complemented
16#35616C211yesmaximal, characteristic, complemented
17#35563C211yesmaximal, characteristic, complemented
18#35558C211yesmaximal, characteristic, complemented
19#35557C211yesmaximal, characteristic, complemented
20#35530C211yesmaximal, characteristic, complemented
21#35513C211yesmaximal, characteristic, complemented
22#35512C211yesmaximal, characteristic, complemented
23#34635C211yesmaximal, characteristic, complemented
24#34633C211yesmaximal, characteristic, complemented
25C2×#2620C211yesmaximal, characteristic, complemented
26C22×H(5,𝔽2)C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#536C2211yescharacteristic
30C2×#536C2211yescharacteristic, complemented
31C2×#535C2211yescharacteristic
32C2×#532C2211yescharacteristic
33C22×#124C2211yescharacteristic
34C2×#525C2211yescharacteristic
35C2×#525C2211yescharacteristic
36C2×#525C2211yescharacteristic, complemented
37C22×C22⋊Q8C2211yescharacteristic, complemented
38C22×#121C2211yescharacteristic
39C2×#520C2211yescharacteristic, complemented
40C2×#519C2211yescharacteristic, complemented
41C22×#117C2211yescharacteristic, complemented
42#2842C2218yescomplemented
43#2837C2218yescomplemented
44#2837C2218yescomplemented
45#2829C2218yescomplemented
46#2829C2218yescomplemented
47#2829C2218yescomplemented
48#2829C2218yescomplemented
49#2829C2218yescomplemented
50#2828C2218yescomplemented
51#2828C2218yescomplemented
52#2827C2218yescomplemented
53#2827C2218yescomplemented
54#2826C2218yescomplemented
55#2823C2218yescomplemented
56#2813C2218yescomplemented
57#2812C2218yescomplemented
58#2803C2218yescomplemented
59#2797C2218yescomplemented
60#2796C2218yescomplemented
61#2795C2218yescomplemented
62#2790C2218yescomplemented
63#2790C2218yescomplemented
64#2780C2218yescomplemented
65#2735C2218yescomplemented
66#2714C2218yescomplemented
67#2705C2218yescomplemented
68#2697C2218yescomplemented
69#2691C2218yescomplemented
70#2685C2218yescomplemented
71#2685C2218yescomplemented
72#2685C2218yescomplemented
73#2678C2218yescomplemented
74#2625C2212yescomplemented
75#2625C2212yescomplemented
76#2624C2212yescomplemented
77#2624C2212yescomplemented
78#2623C2214yescomplemented
79#2622C2214yescomplemented
80#2621C2212yescomplemented
81#2620C2212yescomplemented
82#2620C2214yescomplemented
83#2620C2214yescomplemented
84#2620C2214yescomplemented
85#2620C2214yescomplemented
86#2620C2212yescomplemented
87#2619C2212yescomplemented
88#2618C2214yescomplemented
89#2617C2214yescomplemented
90#2548C2214yescomplemented
91#2547C2212yescomplemented
92#2546C2212yescomplemented
93#2545C2212yescomplemented
94#2545C2214yescomplemented
95#2544C2212yescomplemented
96#2542C2214yescomplemented
97#2542C2214yescomplemented
98#2540C2214yescomplemented
99#2540C2214yescomplemented
100#2539C2214yescomplemented
101#2538C2214yescomplemented
102#2536C2214yescomplemented
103#2534C2214yescomplemented
104#2513C2214yescomplemented
105#2513C2214yescomplemented
106#2512C2214yescomplemented
107#2512C2214yescomplemented
108#2512C2214yescomplemented
109#2511C2214yescomplemented
110#2502C2212yescomplemented
111#2501C2214yescomplemented
112#2501C2212yescomplemented
113#2500C2212yescomplemented
114#2499C2212yescomplemented
115#2498C2218yescomplemented
116#2497C2214yescomplemented
117#2496C2214yescomplemented
118#2481C2218yescomplemented
119#2480C2218yescomplemented
120#2448C2214yescomplemented
121#2446C2214yescomplemented
122#2443C2218yescomplemented
123#2435C2212yescomplemented
124#2435C2214yescomplemented
125#2435C2212yescomplemented
126#2435C2212yescomplemented
127#2433C2212yescomplemented
128#2432C2214yescomplemented
129#2432C2212yescomplemented
130#2432C2212yescomplemented
131#2432C2212yescomplemented
132#2431C2212yescomplemented
133#2429C2214yescomplemented
134#2428C2214yescomplemented
135#2426C2214yescomplemented
136#2426C2214yescomplemented
137#2426C2214yescomplemented
138#2426C2214yescomplemented
139#2425C2218yescomplemented
140#2423C2214yescomplemented
141#2423C2214yescomplemented
142#2422C2214yescomplemented
143#2421C2214yescomplemented
144#2417C2214yescomplemented
145#2416C2214yescomplemented
146#2415C2214yescomplemented
147#2414C2214yescomplemented
148#2413C2214yescomplemented
149#2411C2214yescomplemented
150#2411C2218yescomplemented
151#2410C2218yes—
152#2408C2214yes—
153#2408C2214yes—
154#2408C2214yescomplemented
155#2408C2214yescomplemented
156#2407C2214yes—
157#2407C2214yes—
158#2407C2214yescomplemented
159#2405C2218yes—
160#2405C2214yes—
161#2403C2214yes—
162#2395C2214yescomplemented
163#2395C2214yescomplemented
164#2392C2214yescomplemented
165#2392C2214yescomplemented
166C2×#396C2214yescomplemented
167C2×#394C2214yescomplemented
168#2317C2211yescharacteristic, complemented
169#2316C2211yescharacteristic, complemented
170#2311C2211yescharacteristic
171#2311C2211yescharacteristic
172#2311C2211yescharacteristic
173#2309C2211yescharacteristic
174#2309C2211yescharacteristic
175#2297C2211yescharacteristic
176#2297C2211yescharacteristic
177#2297C2211yescharacteristic
178#2297C2211yescharacteristic, complemented
179#2296C2211yescharacteristic, complemented
180#2296C2211yescharacteristic, complemented
181C2×#391C2211yescharacteristic, complemented
182C2×#390C2211yescharacteristic
183#2285C2211yescharacteristic, complemented
184C2×#384C2211yescharacteristic, complemented
185#2280C2211yescharacteristic, complemented
186#2274C2211yescharacteristic, complemented
187C2×H(5,𝔽2)—44no—
188C2×H(5,𝔽2)—44no—
189C2×H(5,𝔽2)—44no—
190C22×#41C2311yescharacteristic
191C22×#41C2311yescharacteristic
192C22×#41C2311yescharacteristic
193C22×#41C2312yes—
194C22×#41C2312yes—
195C23×Q8C2311yescharacteristic
196C23×D4C2311yescharacteristic
197C23×D4C2314yes—
198C23×D4C2312yes—
199C23×D4C2312yes—
200C23×D4C2312yes—
201C24×C4C2311yescharacteristic
202#537—44no—
203#536—44no—
204#536—44no—
205#536—44no—
206#535—44no—
207#532—44no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×#127C2311yescharacteristic
213C2×#127C2312yes—
214C2×#126C2318yes—
215C2×#126C2318yes—
216C2×#124—44no—
217C2×#124C2312yes—
218C2×#124C2312yes—
219C2×#124C2314yes—
220C2×#124C2311yescharacteristic
221C2×#124C2311yescharacteristic
222C2×#124C2312yes—
223C2×#124C2312yes—
224C2×#124C2312yes—
225C2×#124C2312yes—
226#525—44no—
227#525—44no—
228#525—44no—
229C2×#123C2312yes—
230C2×#123C2312yes—
231C2×#123C2312yes—
232C2×#123C2314yes—
233C2×#123C2314yes—
234C2×#123C2314yes—
235C2×#123C2318yes—
236C2×C22⋊Q8—44no—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2312yes—
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2312yes—
244C2×C22⋊Q8C2314yes—
245C2×C22⋊Q8C2312yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2312yes—
248C2×#121—44no—
249C2×#121C2314yes—
250C2×#121C2312yes—
251C2×#121C2312yes—
252C2×#121C2314yes—
253C2×#121C2314yes—
254C2×#121C2312yes—
255C2×#121C2314yes—
256C2×#121C2312yes—
257C2×#121C2314yes—
258C2×#121C2312yes—
259C2×#121C2318yes—
260C2×#120C2312yes—
261C2×#120C2312yes—
262C2×#120C2312yes—
263C2×#120C2314yes—
264C2×#120C2318yes—
265C2×#120C2318yes—
266#520—44no—
267#519—44no—
268C2×C4×Q8C2314yes—
269C2×C4×Q8C2314yes—
270C2×C4×Q8C2312yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2314yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2312yes—
277C2×#117—44no—
278C2×#117C2311yescharacteristic
279C2×#117C2311yescharacteristic
280C2×#117C2311yescharacteristic
281C2×#117C2311yescharacteristic
282C2×#117C2311yescharacteristic
283C2×#117C2312yes—
284C2×#117C2312yes—
285C2×#117C2312yes—
286C2×#117C2312yes—
287C2×#117C2314yes—
288C2×#117C2312yes—
289C22×C4⋊C4C2311yescharacteristic
290C22×C4⋊C4C2311yescharacteristic
291C22×C4⋊C4C2312yes—
292C22×C4⋊C4C2312yes—
293C22×C4⋊C4C2312yes—
294C22×C4⋊C4C2314yes—
295C22×C22⋊C4C2312yes—
296C22×C22⋊C4C2312yes—
297C22×C22⋊C4C2314yes—
298C22×C22⋊C4C2312yes—
299C22×C22⋊C4C2314yes—
300C22×C42C2311yescharacteristic
301C22×C42C2311yescharacteristic
302#400C2314yes—
303#400C2318yes—
304#400C2314yes—
305#400C2318yes—
306#400C2318yes—
307#399C2318yes—
308#399C2318yes—
309#399C2318yes—
310#399C2318yes—
311#399C2318yes—
312#399C2314yes—
313#399C2314yes—
314#398C2314yes—
315#398C2318yes—
316#398C2318yes—
317#398C2318yes—
318#398C2318yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#397C2318yes—
323#397C2318yes—
324#397C2314yes—
325#397C2314yes—
326#397C2318yes—
327#397C2318yes—
328#397C2318yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2318yes—
335#397C2318yes—
336#397C2314yes—
337#396C2314yes—
338#396C2318yes—
339#396C2318yes—
340#396C2318yes—
341#396C2318yes—
342#396C2318yes—
343#396C2318yes—
344#396C2314yes—
345#396C2318yes—
346#396C2318yes—
347#396C2318yes—
348#396C2318yes—
349#396C2314yes—
350#396C2318yes—
351#396C2318yes—
352#396C2314yes—
353#394C2318yes—
354#394C2318yes—
355#394C2318yes—
356#394C2314yes—
357#394C2318yes—
358#394C2318yes—
359#394C2318yes—
360#394C2318yes—
361#394C2318yes—
362#394C2314yes—
363#394C2314yes—
364#394C2318yes—
365#394C2318yes—
366#394C2318yes—
367#394C2318yes—
368#394C2318yes—
369#394C2318yes—
370#394C2318yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2318yes—
376#394C2318yes—
377#394C2318yes—
378#394C2318yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#392C2318yes—
383#392C2314yes—
384#392C2318yes—
385#392C2318yes—
386#392C2318yes—
387#392C2318yes—
388#392C2318yes—
389#392C2314yes—
390#391C2312yes—
391#391C2312yes—
392#391C2312yes—
393#391C2314yes—
394#391C2312yes—
395#391C2312yes—
396#391C2312yes—
397#391C2312yes—
398#391C2312yes—
399#391C2311yescharacteristic
400#391C2311yescharacteristic
401#390C2314yes—
402#390C2314yes—
403#390C2312yes—
404#390C2312yes—
405#390C2314yes—
406#390C2312yes—
407#390C2312yes—
408#390C2312yes—
409#390C2318yes—
410#390C2318yes—
411#390C2318yes—
412#390C2318yes—
413#390C2318yes—
414#390C2318yes—
415#390C2318yes—
416#390C2312yes—
417#390C2312yes—
418#390C2314yes—
419#390C2312yes—
420#390C2312yes—
421#390C2312yes—
422#390C2311yescharacteristic
423#390C2311yescharacteristic
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2318yes—
428#389C2318yes—
429#389C2312yes—
430#389C2312yes—
431#389C2312yes—
432#389C2312yes—
433#388C2318yes—
434#388C2318yes—
435#388C2318yes—
436#388C2318yes—
437#388C2318yes—
438#388C2318yes—
439#388C2318yes—
440#388C2318yes—
441#388C2318yes—
442#388C2318yes—
443#388C2318yes—
444#388C2318yes—
445#388C2318yes—
446#387C2318yes—
447#387C2318yes—
448#387C2318yes—
449#387C2318yes—
450#387C2318yes—
451#386C2314yes—
452#386C2314yes—
453#386C2314yes—
454#386C2318yes—
455#386C2318yes—
456#386C2318yes—
457#386C2318yes—
458#386C2314yes—
459#386C2314yes—
460#386C2314yes—
461#386C2314yes—
462#385C2318yes—
463#385C2318yes—
464#385C2318yes—
465#385C2318yes—
466#385C2318yes—
467#385C2314yes—
468#385C2314yes—
469#385C2314yes—
470#384C2318yes—
471#384C2312yes—
472#384C2314yes—
473#384C2312yes—
474#384C2312yes—
475#384C2312yes—
476#382C2312yes—
477#382C2312yes—
478#381C2312yes—
479#380C2314yes—
480#380C2314yes—
481#380C2314yes—
482#380C2314yes—
483#380C2314yes—
484#380C2312yes—
485#380C2312yes—
486#380C2318yes—
487#379C2314yes—
488#379C2314yes—
489#379C2318yes—
490#379C2318yes—
491#379C2318yes—
492#379C2312yes—
493#379C2318yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2314yes—
500C4×C22⋊C4C2312yes—
501C4×C22⋊C4C2312yes—
502C4×C22⋊C4C2312yes—
503C4×C22⋊C4C2312yes—
504C4×C22⋊C4C2312yes—
505C4×C22⋊C4C2314yes—
506C4×C22⋊C4C2312yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2314yes—
509C2×#95C2314yes—
510C25C2412yes—
511C25C2411yescharacteristic
512C25C2414yes—
513H(5,𝔽2)—464no—
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—24no—
523C2×#41—44no—
524C2×#41—44no—
525C2×#41—44no—
526C2×#41—44no—
527C2×#41—44no—
528C2×#41—44no—
529C22×Q8—24no—
530C22×Q8—24no—
531C22×Q8—24no—
532C22×Q8C2412yes—
533C22×Q8C2412yes—
534C22×Q8C2411yescharacteristic
535C22×Q8C2411yescharacteristic
536C22×Q8C2411yescharacteristic
537C22×D4—24no—
538C22×D4—24no—
539C22×D4—24no—
540C22×D4—44no—
541C22×D4—44no—
542C22×D4—44no—
543C22×D4—44no—
544C22×D4—44no—
545C22×D4—44no—
546C22×D4—44no—
547C22×D4—48no—
548C22×D4—48no—
549C22×D4—48no—
550C22×D4—84no—
551C22×D4C2412yes—
552C22×D4C2411yescharacteristic
553C22×D4C2412yes—
554C22×D4C2412yes—
555C22×D4C2412yes—
556C22×D4C2411yescharacteristic
557C22×D4C2412yes—
558C22×D4C2411yescharacteristic
559C22×D4C2414yes—
560C22×D4C2414yes—
561C22×D4C2414yes—
562C22×D4C2414yes—
563C22×D4C2414yes—
564C22×D4C2418yes—
565C22×D4C2418yes—
566C22×D4C2414yes—
567C22×D4C2414yes—
568C23×C4—24no—
569C23×C4—24no—
570C23×C4—24no—
571C23×C4C2412yes—
572C23×C4C2411yescharacteristic
573C23×C4C2412yes—
574C23×C4C2412yes—
575C23×C4C2412yes—
576C23×C4C2412yes—
577C23×C4C2412yes—
578C23×C4C2412yes—
579C23×C4C2412yes—
580C23×C4C2412yes—
581C23×C4C2412yes—
582C23×C4C2414yes—
583C23×C4C2414yes—
584C23×C4C2411yescharacteristic
585C4⋊Q8—42no—
586C4⋊Q8—44no—
587C4⋊Q8—44no—
588C4⋊Q8—44no—
589#127—42no—
590#127—44no—
591#126—88no—
592#126—88no—
593#124—44no—
594#124—44no—
595#124—48no—
596#124—42no—
597#124—42no—
598#124—44no—
599#124—44no—
600#124—44no—
601#124—44no—
602#123—44no—
603#123—44no—
604#123—44no—
605#123—48no—
606#123—48no—
607#123—48no—
608#123—88no—
609C22⋊Q8—48no—
610C22⋊Q8—48no—
611C22⋊Q8—44no—
612C22⋊Q8—44no—
613C22⋊Q8—44no—
614C22⋊Q8—44no—
615C22⋊Q8—44no—
616C22⋊Q8—48no—
617C22⋊Q8—48no—
618C22⋊Q8—44no—
619C22⋊Q8—44no—
620#121—48no—
621#121—48no—
622#121—44no—
623#121—44no—
624#121—44no—
625#121—48no—
626#121—44no—
627#121—44no—
628#121—48no—
629#121—48no—
630#121—88no—
631#120—44no—
632#120—44no—
633#120—44no—
634#120—48no—
635#120—88no—
636#120—88no—
637C4×Q8—48no—
638C4×Q8—48no—
639C4×Q8—44no—
640C4×D4—44no—
641C4×D4—48no—
642C4×D4—48no—
643C4×D4—48no—
644C4×D4—48no—
645C4×D4—48no—
646#117—24no—
647#117—24no—
648#117—24no—
649#117—24no—
650#117—24no—
651#117—44no—
652#117—44no—
653#117—44no—
654#117—44no—
655#117—48no—
656#117—44no—
657C2×C4⋊C4—24no—
658C2×C4⋊C4—24no—
659C2×C4⋊C4—44no—
660C2×C4⋊C4—44no—
661C2×C4⋊C4—44no—
662C2×C4⋊C4—84no—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2418yes—
679C2×C4⋊C4C2418yes—
680C2×C4⋊C4C2418yes—
681C2×C4⋊C4C2418yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2418yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2418yes—
690C2×C4⋊C4C2418yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2418yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C22⋊C4—44no—
700C2×C22⋊C4—44no—
701C2×C22⋊C4—44no—
702C2×C22⋊C4—48no—
703C2×C22⋊C4—84no—
704C2×C22⋊C4C2412yes—
705C2×C22⋊C4C2412yes—
706C2×C22⋊C4C2412yes—
707C2×C22⋊C4C2412yes—
708C2×C22⋊C4C2412yes—
709C2×C22⋊C4C2412yes—
710C2×C22⋊C4C2412yes—
711C2×C22⋊C4C2412yes—
712C2×C22⋊C4C2412yes—
713C2×C22⋊C4C2418yes—
714C2×C22⋊C4C2418yes—
715C2×C22⋊C4C2418yes—
716C2×C22⋊C4C2418yes—
717C2×C22⋊C4C2418yes—
718C2×C22⋊C4C2418yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2418yes—
730C2×C22⋊C4C2418yes—
731C2×C22⋊C4C2418yes—
732C2×C22⋊C4C2418yes—
733C2×C22⋊C4C2418yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2414yes—
737C2×C22⋊C4C2418yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2418yes—
741C2×C22⋊C4C2418yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C2414yes—
749C2×C22⋊C4C2414yes—
750C2×C22⋊C4C2418yes—
751C2×C22⋊C4C2418yes—
752C2×C42—24no—
753C2×C42—24no—
754C2×C42C2412yes—
755C2×C42C2411yescharacteristic
756C2×C42C2411yescharacteristic
757C2×C42C2412yes—
758C2×C42C2411yescharacteristic
759C2×C42C2411yescharacteristic
760C2×C42C2412yes—
761C2×C42C2412yes—
762C2×C42C2412yes—
763C2×C42C2412yes—
764C2×C42C2412yes—
765C2×C42C2414yes—
766C2×C42C2418yes—
767C2×C42C2418yes—
768#95C2418yes—
769#95C2418yes—
770#95C2418yes—
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—
792C24—22no—
793C24—22no—
794C24—24no—
795C24—24no—
796C24—22no—
797C24—24no—
798C24—42no—
799C24—42no—
800C24—44no—
801C24—44no—
802C24—44no—
803C24—44no—
804C24—44no—
805C24—48no—
806C24—48no—
807C24C2512yes—
808C24C2512yes—
809C24C2514yes—
810C24C2512yes—
811C24C2512yes—
812C24C2511yescharacteristic
813#41—432no—
814#41—432no—
815#41—416no—
816#41—416no—
817#41—416no—
818C2×Q8—24no—
819C2×Q8—22no—
820C2×Q8—24no—
821C2×Q8—24no—
822C2×Q8—24no—
823C2×Q8—22no—
824C2×Q8—24no—
825C2×Q8—22no—
826C2×Q8—22no—
827C2×Q8—22no—
828C2×Q8—24no—
829C2×Q8—22no—
830C2×Q8—22no—
831C2×Q8—22no—
832C2×Q8—22no—
833C2×Q8—416no—
834C2×D4—24no—
835C2×D4—24no—
836C2×D4—24no—
837C2×D4—24no—
838C2×D4—24no—
839C2×D4—24no—
840C2×D4—24no—
841C2×D4—24no—
842C2×D4—24no—
843C2×D4—22no—
844C2×D4—22no—
845C2×D4—24no—
846C2×D4—24no—
847C2×D4—24no—
848C2×D4—22no—
849C2×D4—22no—
850C2×D4—22no—
851C2×D4—22no—
852C2×D4—24no—
853C2×D4—24no—
854C2×D4—22no—
855C2×D4—22no—
856C2×D4—24no—
857C2×D4—22no—
858C2×D4—44no—
859C2×D4—44no—
860C2×D4—44no—
861C2×D4—44no—
862C2×D4—44no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—48no—
872C2×D4—48no—
873C2×D4—44no—
874C2×D4—48no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—48no—
880C2×D4—48no—
881C2×D4—48no—
882C2×D4—44no—
883C2×D4—48no—
884C2×D4—464no—
885C2×D4—432no—
886C2×D4—432no—
887C2×D4—416no—
888C2×D4—816no—
889C22×C4—24no—
890C22×C4—22no—
891C22×C4—24no—
892C22×C4—24no—
893C22×C4—22no—
894C22×C4—24no—
895C22×C4—22no—
896C22×C4—24no—
897C22×C4—24no—
898C22×C4—24no—
899C22×C4—24no—
900C22×C4—24no—
901C22×C4—24no—
902C22×C4—24no—
903C22×C4—24no—
904C22×C4—24no—
905C22×C4—24no—
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—42no—
915C22×C4—42no—
916C22×C4—44no—
917C22×C4—44no—
918C22×C4—44no—
919C22×C4—42no—
920C22×C4—44no—
921C22×C4—44no—
922C22×C4—42no—
923C22×C4—44no—
924C22×C4—48no—
925C22×C4—416no—
926C22×C4H(5,𝔽2)14yes—
927C22×C4H(5,𝔽2)14yes—
928C22×C4H(5,𝔽2)14yes—
929C22×C4C2512yes—
930C22×C4C2512yes—
931C22×C4C2512yes—
932C22×C4C2512yes—
933C22×C4C2514yes—
934C22×C4C2514yes—
935C22×C4C2514yes—
936C22×C4C2514yes—
937C22×C4C2514yes—
938C22×C4C2512yes—
939C22×C4C2512yes—
940C22×C4C2512yes—
941C22×C4C2514yes—
942C22×C4C2512yes—
943C22×C4C2514yes—
944C22×C4C2512yes—
945C22×C4C2512yes—
946C22×C4C2511yescharacteristic
947C22×C4C2511yescharacteristic
948C4⋊C4—24no—
949C4⋊C4—24no—
950C4⋊C4—24no—
951C4⋊C4—24no—
952C4⋊C4—22no—
953C4⋊C4—22no—
954C4⋊C4—24no—
955C4⋊C4—24no—
956C4⋊C4—24no—
957C4⋊C4—24no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—44no—
963C4⋊C4—48no—
964C4⋊C4—48no—
965C4⋊C4—48no—
966C4⋊C4—44no—
967C4⋊C4—44no—
968C4⋊C4—44no—
969C4⋊C4—48no—
970C4⋊C4—44no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C4⋊C4—44no—
975C4⋊C4—48no—
976C4⋊C4—44no—
977C4⋊C4—48no—
978C4⋊C4—48no—
979C4⋊C4—44no—
980C4⋊C4—48no—
981C4⋊C4—44no—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C22⋊C4—24no—
985C22⋊C4—24no—
986C22⋊C4—24no—
987C22⋊C4—24no—
988C22⋊C4—24no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—48no—
994C22⋊C4—48no—
995C22⋊C4—48no—
996C22⋊C4—48no—
997C22⋊C4—48no—
998C22⋊C4—48no—
999C22⋊C4—44no—
1000C22⋊C4—48no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—48no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C22⋊C4—44no—
1015C22⋊C4—48no—
1016C22⋊C4—44no—
1017C22⋊C4—48no—
1018C22⋊C4—48no—
1019C22⋊C4—48no—
1020C22⋊C4—48no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C4—48no—
1025C22⋊C4—44no—
1026C22⋊C4—48no—
1027C22⋊C4—48no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C42—24no—
1033C42—24no—
1034C42—22no—
1035C42—22no—
1036C42—22no—
1037C42—22no—
1038C42—24no—
1039C42—24no—
1040C42—24no—
1041C42—24no—
1042C42—24no—
1043C42—44no—
1044C42—48no—
1045C42—48no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—24no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—24no—
1062C23—24no—
1063C23—24no—
1064C23—24no—
1065C23—28no—
1066C23—22no—
1067C23—24no—
1068C23—22no—
1069C23—22no—
1070C23—24no—
1071C23—28no—
1072C23—24no—
1073C23—24no—
1074C23—22no—
1075C23—44no—
1076C23—44no—
1077C23—416no—
1078C23—44no—
1079C23—48no—
1080C23—84no—
1081C23—84no—
1082C23—84no—
1083C23—88no—
1084C23—88no—
1085C23—84no—
1086C23—168no—
1087C23—164no—
1088C23—168no—
1089C23—164no—
1090C23C2×H(5,𝔽2)12yes—
1091C23C2×H(5,𝔽2)12yes—
1092C23C2×H(5,𝔽2)12yes—
1093C23C2611yescharacteristic
1094Q8—48no—
1095Q8—48no—
1096Q8—44no—
1097Q8—44no—
1098Q8—44no—
1099D4—416no—
1100D4—416no—
1101D4—48no—
1102D4—48no—
1103D4—48no—
1104D4—48no—
1105D4—44no—
1106D4—48no—
1107D4—44no—
1108D4—44no—
1109D4—88no—
1110D4—88no—
1111D4—88no—
1112D4—88no—
1113D4—816no—
1114D4—164no—
1115D4—168no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—22no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—24no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—28no—
1146C2×C4—22no—
1147C2×C4—24no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—22no—
1153C2×C4—28no—
1154C2×C4—24no—
1155C2×C4—22no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—22no—
1163C2×C4—48no—
1164C2×C4—416no—
1165C2×C4—44no—
1166C2×C4—48no—
1167C2×C4—48no—
1168C2×C4—48no—
1169C2×C4—48no—
1170C2×C4—48no—
1171C2×C4—48no—
1172C2×C4—84no—
1173C2×C4—84no—
1174C2×C4—84no—
1175C2×C4—164no—
1176C2×C4#560116yes—
1177C2×C4C2×H(5,𝔽2)12yes—
1178C2×C4C2×H(5,𝔽2)12yes—
1179C2×C4C2×H(5,𝔽2)12yes—
1180C2×C4C2×H(5,𝔽2)12yes—
1181C2×C4C2×H(5,𝔽2)12yes—
1182C2×C4C2×H(5,𝔽2)12yes—
1183C22—24no—
1184C22—22no—
1185C22—24no—
1186C22—22no—
1187C22—42no—
1188C22—44no—
1189C22—44no—
1190C22—44no—
1191C22—42no—
1192C22—48no—
1193C22—42no—
1194C22—42no—
1195C22—44no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—44no—
1201C22—44no—
1202C22—48no—
1203C22—44no—
1204C22—42no—
1205C22—42no—
1206C22—44no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—44no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—88no—
1215C22—168no—
1216C22—1616no—
1217C22C2×#56014yes—
1218C22C22×H(5,𝔽2)11yescharacteristic
1219C22C22×H(5,𝔽2)11yescharacteristic
1220C22C22×H(5,𝔽2)11yescharacteristic
1221C22H(7,𝔽2)12yes—
1222C222−1+612yes—
1223C4—42no—
1224C4—42no—
1225C4—42no—
1226C4—42no—
1227C4—44no—
1228C4—44no—
1229C4—44no—
1230C4—42no—
1231C4—44no—
1232C4—44no—
1233C4—44no—
1234C4—42no—
1235C4—42no—
1236C4—42no—
1237C4—42no—
1238C4—42no—
1239C4—44no—
1240C4C2×#56014yes—
1241C4C2×#56014yes—
1242C2—24no—
1243C2—82no—
1244C2—82no—
1245C2—82no—
1246C2—82no—
1247C2—84no—
1248C2C22×#56011yescharacteristic
1249C2#6287512yes—
1250C2#6287611yescharacteristic
1251C2#6287812yes—
1252C2#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. #53129C2semidirect
2. #53095C2semidirect
3. #53066C2semidirect
4. #53051C2semidirect
5. #53047C2semidirect
6. #53018C2semidirect
7. #52981C2semidirect
8. #52977C2semidirect
9. #52347C2semidirect
10. #52345C2semidirect
11. #35677C2semidirect
12. #35673C2semidirect
13. #35661C2semidirect
14. #35634C2semidirect
15. #35621C2semidirect
16. #35616C2semidirect
17. #35563C2semidirect
18. #35558C2semidirect
19. #35557C2semidirect
20. #35530C2semidirect
21. #35513C2semidirect
22. #35512C2semidirect
23. #34635C2semidirect
24. #34633C2semidirect
25. C2×#2620C2semidirect
30. C2×#536C22semidirect
36. C2×#525C22semidirect
37. C22×C22⋊Q8C22semidirect
39. C2×#520C22semidirect
40. C2×#519C22semidirect
41. C22×#117C22semidirect
42. #2842C22semidirect
43. #2837C22semidirect
44. #2837C22semidirect
45. #2829C22semidirect
46. #2829C22semidirect
47. #2829C22semidirect
48. #2829C22semidirect
49. #2829C22semidirect
50. #2828C22semidirect
51. #2828C22semidirect
52. #2827C22semidirect
53. #2827C22semidirect
54. #2826C22semidirect
55. #2823C22semidirect
56. #2813C22semidirect
57. #2812C22semidirect
58. #2803C22semidirect
59. #2797C22semidirect
60. #2796C22semidirect
61. #2795C22semidirect
62. #2790C22semidirect
63. #2790C22semidirect
64. #2780C22semidirect
65. #2735C22semidirect
66. #2714C22semidirect
67. #2705C22semidirect
68. #2697C22semidirect
69. #2691C22semidirect
70. #2685C22semidirect
71. #2685C22semidirect
72. #2685C22semidirect
73. #2678C22semidirect
74. #2625C22semidirect
75. #2625C22semidirect
76. #2624C22semidirect
77. #2624C22semidirect
78. #2623C22semidirect
79. #2622C22semidirect
80. #2621C22semidirect
81. #2620C22semidirect
82. #2620C22semidirect
83. #2620C22semidirect
84. #2620C22semidirect
85. #2620C22semidirect
86. #2620C22semidirect
87. #2619C22semidirect
88. #2618C22semidirect
89. #2617C22semidirect
90. #2548C22semidirect
91. #2547C22semidirect
92. #2546C22semidirect
93. #2545C22semidirect
94. #2545C22semidirect
95. #2544C22semidirect
96. #2542C22semidirect
97. #2542C22semidirect
98. #2540C22semidirect
99. #2540C22semidirect
100. #2539C22semidirect
101. #2538C22semidirect
102. #2536C22semidirect
103. #2534C22semidirect
104. #2513C22semidirect
105. #2513C22semidirect
106. #2512C22semidirect
107. #2512C22semidirect
108. #2512C22semidirect
109. #2511C22semidirect
110. #2502C22semidirect
111. #2501C22semidirect
112. #2501C22semidirect
113. #2500C22semidirect
114. #2499C22semidirect
115. #2498C22semidirect
116. #2497C22semidirect
117. #2496C22semidirect
118. #2481C22semidirect
119. #2480C22semidirect
120. #2448C22semidirect
121. #2446C22semidirect
122. #2443C22semidirect
123. #2435C22semidirect
124. #2435C22semidirect
125. #2435C22semidirect
126. #2435C22semidirect
127. #2433C22semidirect
128. #2432C22semidirect
129. #2432C22semidirect
130. #2432C22semidirect
131. #2432C22semidirect
132. #2431C22semidirect
133. #2429C22semidirect
134. #2428C22semidirect
135. #2426C22semidirect
136. #2426C22semidirect
137. #2426C22semidirect
138. #2426C22semidirect
139. #2425C22semidirect
140. #2423C22semidirect
141. #2423C22semidirect
142. #2422C22semidirect
143. #2421C22semidirect
144. #2417C22semidirect
145. #2416C22semidirect
146. #2415C22semidirect
147. #2414C22semidirect
148. #2413C22semidirect
149. #2411C22semidirect
150. #2411C22semidirect
154. #2408C22semidirect
155. #2408C22semidirect
158. #2407C22semidirect
162. #2395C22semidirect
163. #2395C22semidirect
164. #2392C22semidirect
165. #2392C22semidirect
166. C2×#396C22semidirect
167. C2×#394C22semidirect
168. #2317C22semidirect
169. #2316C22semidirect
178. #2297C22semidirect
179. #2296C22semidirect
180. #2296C22semidirect
181. C2×#391C22semidirect
183. #2285C22semidirect
184. C2×#384C22semidirect
185. #2280C22semidirect
186. #2274C22semidirect

Maximal subgroups

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

subgroupindex
#531292
#530952
#530662
#530512
#530472
#530182
#529812
#529772
#523472
#523452
#356772
#356732
#356612
#356342
#356212
#356162
#355632
#355582
#355572
#355302
#355132
#355122
#346352
#346332
C2×#26202