Finite Group Databasebeta

← #8095539

Subgroups — #8095539

Order 512.

5902 conjugacy classes of subgroups.

The subgroup lattice has 1256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53087C214yesmaximal, complemented
2#53073C214yesmaximal, complemented
3#53000C214yesmaximal, complemented
4#52977C214yesmaximal, complemented
5#52345C218yesmaximal, complemented
6#46061C214yesmaximal, complemented
7#46050C214yesmaximal, complemented
8#45647C214yesmaximal, complemented
9#45563C218yesmaximal, complemented
10#45522C214yesmaximal, complemented
11#35677C211yesmaximal, characteristic, complemented
12#35677C211yesmaximal, characteristic, complemented
13#35673C211yesmaximal, characteristic, complemented
14#35616C211yesmaximal, characteristic, complemented
15#35527C211yesmaximal, characteristic, complemented
16#35513C211yesmaximal, characteristic, complemented
17#35329C211yesmaximal, characteristic, complemented
18#35308C211yesmaximal, characteristic, complemented
19#35272C211yesmaximal, characteristic, complemented
20#35266C211yesmaximal, characteristic, complemented
21#35168C211yesmaximal, characteristic, complemented
22#35152C211yesmaximal, characteristic, complemented
23C2×#2544C211yesmaximal, characteristic, complemented
24#34816C211yesmaximal, characteristic, complemented
25#34744C211yesmaximal, characteristic, complemented
26C22×H(5,𝔽2)C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#536C2211yescharacteristic
30C2×#536C2211yescharacteristic, complemented
31C2×#535C2211yescharacteristic
32C2×#535C2211yescharacteristic
33C2×#535C2211yescharacteristic
34C2×#535C2211yescharacteristic, complemented
35C2×#532C2211yescharacteristic
36C22×#127C2211yescharacteristic
37C22×#124C2211yescharacteristic
38C22×#124C2211yescharacteristic, complemented
39C2×#519C2211yescharacteristic, complemented
40C2×C4×#41C2211yescharacteristic, complemented
41C22×C4×D4C2211yescharacteristic, complemented
42#2860C2214yescomplemented
43#2858C2212yescomplemented
44#2858C2212yescomplemented
45#2857C2212yescomplemented
46#2856C2214yescomplemented
47#2850C2212yescomplemented
48#2849C2214yescomplemented
49#2847C2214yescomplemented
50#2829C2218yescomplemented
51#2829C2218yescomplemented
52#2829C2218yescomplemented
53#2828C2218yescomplemented
54#2828C2218yescomplemented
55#2827C2218yescomplemented
56#2826C2218yescomplemented
57#2825C2218yescomplemented
58#2813C2218yescomplemented
59#2812C2218yescomplemented
60#2803C2218yescomplemented
61#2797C2218yescomplemented
62#2796C2218yescomplemented
63#2780C2218yescomplemented
64#2756C2218yescomplemented
65#2752C2218yescomplemented
66#2749C2218yescomplemented
67#2746C2218yescomplemented
68#2714C2218yescomplemented
69#2714C2218yescomplemented
70#2705C2218yescomplemented
71#2703C2218yescomplemented
72#2699C2218yescomplemented
73#2697C2218yescomplemented
74#2691C2218yescomplemented
75#2685C2218yescomplemented
76#2685C2218yescomplemented
77#2678C2218yescomplemented
78#2678C2218yescomplemented
79#2668C2218yescomplemented
80#2658C2212yescomplemented
81#2657C2212yescomplemented
82#2644C2214yescomplemented
83#2622C2214yescomplemented
84#2621C2212yescomplemented
85#2620C2212yescomplemented
86#2619C2214yescomplemented
87#2617C2214yescomplemented
88#2548C2214yescomplemented
89#2548C2214yescomplemented
90#2548C2214yescomplemented
91#2545C2214yescomplemented
92#2545C2214yescomplemented
93#2544C2214yescomplemented
94#2544C2214yescomplemented
95#2544C2214yescomplemented
96#2544C2214yescomplemented
97#2541C2214yescomplemented
98#2540C2214yescomplemented
99#2540C2214yescomplemented
100#2539C2218yescomplemented
101#2514C2212yescomplemented
102#2513C2212yescomplemented
103#2513C2214yescomplemented
104#2512C2212yescomplemented
105#2512C2214yescomplemented
106#2511C2212yescomplemented
107#2510C2214yescomplemented
108#2498C2218yescomplemented
109#2481C2214yescomplemented
110#2480C2218yescomplemented
111#2448C2214yescomplemented
112#2448C2212yescomplemented
113#2447C2214yescomplemented
114#2447C2212yescomplemented
115#2446C2214yescomplemented
116#2446C2212yescomplemented
117#2445C2212yescomplemented
118#2445C2214yescomplemented
119#2444C2214yescomplemented
120#2443C2214yescomplemented
121#2435C2214yescomplemented
122#2435C2214yescomplemented
123#2435C2212yescomplemented
124#2433C2214yes—
125#2433C2212yes—
126#2433C2212yes—
127#2433C2212yescomplemented
128#2432C2214yescomplemented
129#2432C2214yescomplemented
130#2432C2212yescomplemented
131#2431C2212yes—
132#2431C2214yes—
133#2431C2212yes—
134#2431C2212yescomplemented
135#2429C2214yescomplemented
136#2428C2214yescomplemented
137#2428C2214yescomplemented
138#2427C2214yescomplemented
139#2427C2214yescomplemented
140#2427C2214yescomplemented
141#2426C2214yescomplemented
142#2426C2214yescomplemented
143#2426C2214yescomplemented
144#2426C2214yescomplemented
145#2425C2218yescomplemented
146#2423C2214yescomplemented
147#2422C2214yescomplemented
148#2421C2214yescomplemented
149#2420C2214yescomplemented
150#2411C2214yescomplemented
151#2411C2218yescomplemented
152#2411C2214yescomplemented
153#2410C2218yes—
154#2408C2214yescomplemented
155#2408C2218yescomplemented
156#2407C2214yescomplemented
157#2405C2214yes—
158#2405C2214yes—
159#2403C2218yes—
160#2401C2214yescomplemented
161#2395C2214yescomplemented
162C2×#394C2214yescomplemented
163#2377C2218yescomplemented
164#2375C2218yescomplemented
165#2317C2211yescharacteristic, complemented
166#2316C2211yescharacteristic, complemented
167#2311C2211yescharacteristic
168#2309C2211yescharacteristic
169#2309C2211yescharacteristic
170#2309C2211yescharacteristic, complemented
171C4×#126C2214yescomplemented
172C4×#123C2214yescomplemented
173#2297C2211yescharacteristic
174#2297C2211yescharacteristic
175#2297C2211yescharacteristic
176#2297C2211yescharacteristic
177#2297C2211yescharacteristic
178#2297C2211yescharacteristic, complemented
179#2296C2211yescharacteristic, complemented
180#2296C2211yescharacteristic, complemented
181C2×#391C2211yescharacteristic, complemented
182C2×#390C2211yescharacteristic
183C2×#386C2214yescomplemented
184#2285C2211yescharacteristic, complemented
185C4×#117C2211yescharacteristic, complemented
186C2×C4×C4⋊C4C2211yescharacteristic, 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×D4C2311yescharacteristic
198C23×D4C2314yes—
199C23×D4C2312yes—
200C23×D4C2312yes—
201C23×D4C2314yes—
202C24×C4C2312yes—
203#537—44no—
204#536—44no—
205#536—44no—
206#536—44no—
207#535—44no—
208#535—44no—
209#535—44no—
210#535—44no—
211#532—44no—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2311yescharacteristic
216C2×#127—44no—
217C2×#127C2312yes—
218C2×#127C2312yes—
219C2×#127C2312yes—
220C2×#127C2312yes—
221C2×#127C2311yescharacteristic
222C2×#127C2314yes—
223C2×#127C2312yes—
224C2×#127C2312yes—
225C2×#126C2314yes—
226C2×#126C2318yes—
227C2×#124—44no—
228C2×#124—44no—
229C2×#124C2312yes—
230C2×#124C2312yes—
231C2×#124C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#124C2312yes—
234C2×#124C2312yes—
235C2×#124C2312yes—
236C2×#124C2312yes—
237C2×#124C2312yes—
238C2×#124C2314yes—
239C2×#124C2314yes—
240C2×#124C2314yes—
241C2×#124C2312yes—
242C2×#124C2312yes—
243C2×#123C2314yes—
244C2×#123C2314yes—
245C2×#123C2314yes—
246C2×#123C2314yes—
247C2×#123C2318yes—
248C2×C22⋊Q8C2312yes—
249C2×C22⋊Q8C2312yes—
250C2×C22⋊Q8C2312yes—
251C2×C22⋊Q8C2314yes—
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2312yes—
254C2×#121C2314yes—
255C2×#121C2312yes—
256C2×#121C2314yes—
257C2×#121C2314yes—
258C2×#121C2318yes—
259C2×#121C2314yes—
260C2×#121C2312yes—
261C2×#121C2312yes—
262C2×#121C2314yes—
263C2×#121C2312yes—
264C2×#121C2318yes—
265C2×#121C2318yes—
266C2×#120C2314yes—
267C2×#120C2314yes—
268C2×#120C2314yes—
269C2×#120C2318yes—
270C2×#120C2314yes—
271C2×#120C2318yes—
272C2×#120C2318yes—
273#519—44no—
274C4×#41—44no—
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2314yes—
277C2×C4×Q8C2314yes—
278C2×C4×D4—44no—
279C2×C4×D4C2314yes—
280C2×C4×D4C2314yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2314yes—
283C2×C4×D4C2312yes—
284C2×#117C2311yescharacteristic
285C2×#117C2311yescharacteristic
286C2×#117C2311yescharacteristic
287C2×#117C2311yescharacteristic
288C2×#117C2311yescharacteristic
289C2×#117C2312yes—
290C2×#117C2314yes—
291C22×C4⋊C4C2311yescharacteristic
292C22×C4⋊C4C2312yes—
293C22×C22⋊C4C2312yes—
294C22×C22⋊C4C2312yes—
295C22×C22⋊C4C2314yes—
296C22×C22⋊C4C2312yes—
297C22×C22⋊C4C2314yes—
298C22×C42C2311yescharacteristic
299C22×C42C2311yescharacteristic
300C22×C42C2311yescharacteristic
301C22×C42C2312yes—
302#401C2314yes—
303#400C2314yes—
304#400C2318yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#399C2318yes—
309#399C2318yes—
310#399C2314yes—
311#399C2318yes—
312#398C2314yes—
313#398C2318yes—
314#398C2318yes—
315#397C2318yes—
316#397C2318yes—
317#397C2318yes—
318#397C2314yes—
319#397C2318yes—
320#397C2318yes—
321#397C2318yes—
322#397C2314yes—
323#397C2318yes—
324#397C2318yes—
325#397C2314yes—
326#397C2314yes—
327#397C2314yes—
328#397C2314yes—
329#396C2318yes—
330#396C2318yes—
331#396C2318yes—
332#396C2318yes—
333#396C2314yes—
334#396C2318yes—
335#396C2318yes—
336#394C2314yes—
337#394C2318yes—
338#394C2318yes—
339#394C2318yes—
340#394C2318yes—
341#394C2318yes—
342#394C2318yes—
343#394C2318yes—
344#394C2314yes—
345#394C2318yes—
346#394C2318yes—
347#394C2318yes—
348#394C2318yes—
349#394C2318yes—
350#394C2318yes—
351#394C2318yes—
352#394C2318yes—
353#394C2318yes—
354#394C2318yes—
355#394C2318yes—
356#394C2318yes—
357#394C2318yes—
358#394C2318yes—
359#392C2318yes—
360#392C2318yes—
361#392C2318yes—
362#392C2318yes—
363#392C2318yes—
364#392C2318yes—
365#392C2318yes—
366#392C2318yes—
367#392C2318yes—
368#392C2318yes—
369#392C2318yes—
370#391C2312yes—
371#391C2312yes—
372#391C2311yescharacteristic
373#391C2312yes—
374#391C2311yescharacteristic
375#391C2312yes—
376#391C2312yes—
377#391C2312yes—
378#391C2314yes—
379#391C2312yes—
380#391C2312yes—
381#390C2314yes—
382#390C2314yes—
383#390C2314yes—
384#390C2312yes—
385#390C2312yes—
386#390C2314yes—
387#390C2314yes—
388#390C2312yes—
389#390C2318yes—
390#390C2318yes—
391#390C2318yes—
392#390C2318yes—
393#390C2318yes—
394#390C2311yescharacteristic
395#390C2318yes—
396#390C2318yes—
397#390C2318yes—
398#390C2312yes—
399#390C2311yescharacteristic
400#390C2318yes—
401#390C2318yes—
402#390C2312yes—
403#390C2314yes—
404#390C2312yes—
405#390C2312yes—
406#390C2312yes—
407#390C2312yes—
408#390C2312yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2318yes—
413#389C2312yes—
414#389C2312yes—
415#389C2312yes—
416#389C2312yes—
417#388C2314yes—
418#388C2314yes—
419#388C2314yes—
420#388C2318yes—
421#388C2318yes—
422#388C2318yes—
423#388C2318yes—
424#388C2318yes—
425#388C2318yes—
426#388C2318yes—
427#388C2314yes—
428#388C2318yes—
429#388C2318yes—
430#388C2318yes—
431#388C2314yes—
432#387C2314yes—
433#387C2314yes—
434#387C2314yes—
435#387C2314yes—
436#387C2318yes—
437#387C2318yes—
438#387C2314yes—
439#386C2314yes—
440#386C2318yes—
441#386C2318yes—
442#386C2318yes—
443#386C2318yes—
444#386C2318yes—
445#386C2312yes—
446#386C2312yes—
447#386C2312yes—
448#386C2318yes—
449#386C2312yes—
450#386C2312yes—
451#386C2312yes—
452#386C2318yes—
453#386C2318yes—
454#386C2318yes—
455#386C2314yes—
456#386C2314yes—
457#386C2314yes—
458#386C2314yes—
459#386C2318yes—
460#386C2318yes—
461#385C2318yes—
462#385C2318yes—
463#385C2318yes—
464#385C2314yes—
465#385C2312yes—
466#385C2312yes—
467#385C2318yes—
468#385C2314yes—
469#385C2314yes—
470#384C2312yes—
471#384C2312yes—
472#383C2314yes—
473#382C2312yes—
474#382C2312yes—
475#381C2318yes—
476#381C2314yes—
477#380C2314yes—
478#380C2314yes—
479#380C2318yes—
480#380C2318yes—
481#380C2314yes—
482#379C2314yes—
483#379C2314yes—
484#379C2314yes—
485#379C2318yes—
486#379C2318yes—
487#379C2318yes—
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—
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—24no—
541C22×D4—24no—
542C22×D4—24no—
543C22×D4—44no—
544C22×D4—44no—
545C22×D4—44no—
546C22×D4—44no—
547C22×D4—44no—
548C22×D4—44no—
549C22×D4—48no—
550C22×D4—48no—
551C22×D4—48no—
552C22×D4—48no—
553C22×D4—48no—
554C22×D4—84no—
555C22×D4C2412yes—
556C22×D4C2412yes—
557C22×D4C2412yes—
558C22×D4C2411yescharacteristic
559C22×D4C2412yes—
560C22×D4C2412yes—
561C22×D4C2412yes—
562C22×D4C2411yescharacteristic
563C22×D4C2412yes—
564C22×D4C2411yescharacteristic
565C22×D4C2418yes—
566C22×D4C2414yes—
567C22×D4C2418yes—
568C22×D4C2414yes—
569C22×D4C2414yes—
570C22×D4C2414yes—
571C22×D4C2418yes—
572C22×D4C2418yes—
573C22×D4C2418yes—
574C22×D4C2414yes—
575C22×D4C2414yes—
576C23×C4—44no—
577C23×C4—84no—
578C23×C4C2412yes—
579C23×C4C2412yes—
580C23×C4C2412yes—
581C23×C4C2412yes—
582C23×C4C2412yes—
583C23×C4C2411yescharacteristic
584C23×C4C2412yes—
585C23×C4C2412yes—
586C23×C4C2411yescharacteristic
587C23×C4C2414yes—
588C23×C4C2418yes—
589C23×C4C2414yes—
590C23×C4C2411yescharacteristic
591C4⋊Q8—42no—
592C4⋊Q8—44no—
593C4⋊Q8—44no—
594C4⋊Q8—44no—
595#127—44no—
596#127—44no—
597#127—48no—
598#127—42no—
599#127—44no—
600#127—44no—
601#127—44no—
602#127—44no—
603#126—48no—
604#126—88no—
605#124—48no—
606#124—48no—
607#124—48no—
608#124—44no—
609#124—44no—
610#124—42no—
611#124—42no—
612#124—44no—
613#124—44no—
614#124—44no—
615#124—44no—
616#124—44no—
617#124—44no—
618#124—44no—
619#123—48no—
620#123—48no—
621#123—48no—
622#123—48no—
623#123—88no—
624C22⋊Q8—48no—
625C22⋊Q8—44no—
626C22⋊Q8—44no—
627C22⋊Q8—48no—
628C22⋊Q8—44no—
629C22⋊Q8—44no—
630#121—416no—
631#121—48no—
632#121—48no—
633#121—48no—
634#121—44no—
635#121—44no—
636#121—44no—
637#121—44no—
638#121—48no—
639#121—48no—
640#121—88no—
641#121—88no—
642#120—416no—
643#120—48no—
644#120—48no—
645#120—48no—
646#120—48no—
647#120—88no—
648#120—88no—
649C4×Q8—44no—
650C4×Q8—48no—
651C4×Q8—48no—
652C4×D4—48no—
653C4×D4—48no—
654C4×D4—44no—
655C4×D4—48no—
656C4×D4—48no—
657#117—24no—
658#117—24no—
659#117—24no—
660#117—24no—
661#117—24no—
662#117—44no—
663#117—48no—
664C2×C4⋊C4—24no—
665C2×C4⋊C4—44no—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2418yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2418yes—
685C2×C4⋊C4C2418yes—
686C2×C4⋊C4C2418yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2418yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
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⋊C4C2414yes—
719C2×C22⋊C4C2418yes—
720C2×C22⋊C4C2418yes—
721C2×C22⋊C4C2418yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2418yes—
725C2×C22⋊C4C2418yes—
726C2×C22⋊C4C2418yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2418yes—
732C2×C22⋊C4C2418yes—
733C2×C22⋊C4C2418yes—
734C2×C22⋊C4C2418yes—
735C2×C22⋊C4C2418yes—
736C2×C22⋊C4C2418yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
744C2×C42—24no—
745C2×C42—24no—
746C2×C42—24no—
747C2×C42—44no—
748C2×C42C2412yes—
749C2×C42C2411yescharacteristic
750C2×C42C2412yes—
751C2×C42C2412yes—
752C2×C42C2412yes—
753C2×C42C2412yes—
754C2×C42C2412yes—
755C2×C42C2412yes—
756C2×C42C2412yes—
757C2×C42C2412yes—
758C2×C42C2411yescharacteristic
759C2×C42C2411yescharacteristic
760C2×C42C2411yescharacteristic
761C2×C42C2418yes—
762C2×C42C2414yes—
763C2×C42C2414yes—
764C2×C42C2414yes—
765#95C2412yes—
766#95C2412yes—
767#95C2412yes—
768#95C2412yes—
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#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
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—
804C24—44no—
805C24—44no—
806C24—44no—
807C24—48no—
808C24—48no—
809C24C2512yes—
810C24C2512yes—
811C24C2514yes—
812C24C2514yes—
813C24C2512yes—
814C24C2511yescharacteristic
815#41—432no—
816#41—432no—
817#41—416no—
818#41—416no—
819#41—416no—
820C2×Q8—24no—
821C2×Q8—24no—
822C2×Q8—22no—
823C2×Q8—24no—
824C2×Q8—24no—
825C2×Q8—22no—
826C2×Q8—22no—
827C2×Q8—22no—
828C2×Q8—24no—
829C2×Q8—24no—
830C2×Q8—22no—
831C2×Q8—22no—
832C2×Q8—22no—
833C2×Q8—22no—
834C2×Q8—22no—
835C2×Q8—416no—
836C2×D4—24no—
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—22no—
848C2×D4—22no—
849C2×D4—24no—
850C2×D4—24no—
851C2×D4—24no—
852C2×D4—22no—
853C2×D4—24no—
854C2×D4—24no—
855C2×D4—24no—
856C2×D4—24no—
857C2×D4—22no—
858C2×D4—22no—
859C2×D4—24no—
860C2×D4—22no—
861C2×D4—22no—
862C2×D4—24no—
863C2×D4—24no—
864C2×D4—22no—
865C2×D4—22no—
866C2×D4—216no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—48no—
876C2×D4—48no—
877C2×D4—44no—
878C2×D4—48no—
879C2×D4—48no—
880C2×D4—48no—
881C2×D4—48no—
882C2×D4—48no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—48no—
886C2×D4—48no—
887C2×D4—48no—
888C2×D4—48no—
889C2×D4—48no—
890C2×D4—48no—
891C2×D4—48no—
892C2×D4—44no—
893C2×D4—48no—
894C2×D4—48no—
895C2×D4—48no—
896C2×D4—464no—
897C2×D4—432no—
898C2×D4—432no—
899C2×D4—416no—
900C2×D4—416no—
901C2×D4—832no—
902C22×C4—22no—
903C22×C4—22no—
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—24no—
915C22×C4—24no—
916C22×C4—24no—
917C22×C4—24no—
918C22×C4—24no—
919C22×C4—24no—
920C22×C4—28no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—44no—
924C22×C4—44no—
925C22×C4—44no—
926C22×C4—42no—
927C22×C4—44no—
928C22×C4—42no—
929C22×C4—44no—
930C22×C4—42no—
931C22×C4—48no—
932C22×C4—44no—
933C22×C4—48no—
934C22×C4—48no—
935C22×C4—816no—
936C22×C4H(5,𝔽2)14yes—
937C22×C4H(5,𝔽2)14yes—
938C22×C4H(5,𝔽2)14yes—
939C22×C4C2512yes—
940C22×C4C2512yes—
941C22×C4C2512yes—
942C22×C4C2512yes—
943C22×C4C2512yes—
944C22×C4C2512yes—
945C22×C4C2514yes—
946C22×C4C2514yes—
947C22×C4C2514yes—
948C22×C4C2514yes—
949C22×C4C2512yes—
950C22×C4C2512yes—
951C22×C4C2512yes—
952C22×C4C2514yes—
953C22×C4C2514yes—
954C22×C4C2512yes—
955C22×C4C2512yes—
956C22×C4C2511yescharacteristic
957C22×C4C2511yescharacteristic
958C4⋊C4—24no—
959C4⋊C4—24no—
960C4⋊C4—24no—
961C4⋊C4—24no—
962C4⋊C4—24no—
963C4⋊C4—22no—
964C4⋊C4—24no—
965C4⋊C4—22no—
966C4⋊C4—24no—
967C4⋊C4—24no—
968C4⋊C4—28no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—44no—
972C4⋊C4—48no—
973C4⋊C4—44no—
974C4⋊C4—44no—
975C4⋊C4—44no—
976C4⋊C4—48no—
977C4⋊C4—48no—
978C4⋊C4—48no—
979C4⋊C4—44no—
980C4⋊C4—44no—
981C4⋊C4—44no—
982C4⋊C4—44no—
983C4⋊C4—48no—
984C4⋊C4—44no—
985C4⋊C4—44no—
986C22⋊C4—24no—
987C22⋊C4—24no—
988C22⋊C4—24no—
989C22⋊C4—24no—
990C22⋊C4—24no—
991C22⋊C4—28no—
992C22⋊C4—28no—
993C22⋊C4—48no—
994C22⋊C4—48no—
995C22⋊C4—48no—
996C22⋊C4—48no—
997C22⋊C4—48no—
998C22⋊C4—48no—
999C22⋊C4—48no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—48no—
1004C22⋊C4—48no—
1005C22⋊C4—48no—
1006C22⋊C4—48no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—48no—
1013C22⋊C4—48no—
1014C22⋊C4—48no—
1015C22⋊C4—48no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—48no—
1021C22⋊C4—48no—
1022C22⋊C4—48no—
1023C22⋊C4—48no—
1024C22⋊C4—44no—
1025C22⋊C4—44no—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C42—22no—
1032C42—22no—
1033C42—24no—
1034C42—24no—
1035C42—24no—
1036C42—24no—
1037C42—22no—
1038C42—22no—
1039C42—24no—
1040C42—24no—
1041C42—24no—
1042C42—24no—
1043C42—24no—
1044C42—44no—
1045C42—48no—
1046C42—44no—
1047C42—44no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—24no—
1055C23—24no—
1056C23—24no—
1057C23—24no—
1058C23—22no—
1059C23—22no—
1060C23—24no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—24no—
1065C23—24no—
1066C23—24no—
1067C23—28no—
1068C23—24no—
1069C23—28no—
1070C23—24no—
1071C23—28no—
1072C23—24no—
1073C23—28no—
1074C23—24no—
1075C23—416no—
1076C23—416no—
1077C23—48no—
1078C23—48no—
1079C23—84no—
1080C23—84no—
1081C23—88no—
1082C23—88no—
1083C23—84no—
1084C23—84no—
1085C23—88no—
1086C23—164no—
1087C23—164no—
1088C23—168no—
1089C23—168no—
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—48no—
1106D4—48no—
1107D4—44no—
1108D4—48no—
1109D4—44no—
1110D4—44no—
1111D4—816no—
1112D4—88no—
1113D4—816no—
1114D4—164no—
1115D4—164no—
1116D4—164no—
1117D4—168no—
1118D4—168no—
1119D4—168no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—24no—
1133C2×C4—22no—
1134C2×C4—24no—
1135C2×C4—22no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—22no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—22no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—28no—
1166C2×C4—22no—
1167C2×C4—48no—
1168C2×C4—44no—
1169C2×C4—44no—
1170C2×C4—416no—
1171C2×C4—48no—
1172C2×C4—48no—
1173C2×C4—48no—
1174C2×C4—48no—
1175C2×C4—88no—
1176C2×C4—84no—
1177C2×C4—84no—
1178C2×C4—816no—
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—44no—
1193C22—42no—
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—44no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—44no—
1211C22—44no—
1212C22—48no—
1213C22—44no—
1214C22—48no—
1215C22—44no—
1216C22—816no—
1217C22—168no—
1218C22—1616no—
1219C22C2×#56014yes—
1220C22C22×H(5,𝔽2)11yescharacteristic
1221C22C22×H(5,𝔽2)11yescharacteristic
1222C22C22×H(5,𝔽2)11yescharacteristic
1223C22C2×#58512yes—
1224C22H(7,𝔽2)12yes—
1225C4—24no—
1226C4—42no—
1227C4—42no—
1228C4—42no—
1229C4—44no—
1230C4—42no—
1231C4—42no—
1232C4—42no—
1233C4—44no—
1234C4—42no—
1235C4—42no—
1236C4—42no—
1237C4—42no—
1238C4—44no—
1239C4—44no—
1240C4—44no—
1241C4—44no—
1242C4C2×#56014yes—
1243C4C2×#56014yes—
1244C2—24no—
1245C2—82no—
1246C2—84no—
1247C2—82no—
1248C2—84no—
1249C2—82no—
1250C2C22×#56011yescharacteristic
1251C2#6283611yescharacteristic
1252C2#6287611yescharacteristic
1253C2#6292412yes—
1254C2#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. #53087C2semidirect
2. #53073C2semidirect
3. #53000C2semidirect
4. #52977C2semidirect
5. #52345C2semidirect
6. #46061C2semidirect
7. #46050C2semidirect
8. #45647C2semidirect
9. #45563C2semidirect
10. #45522C2semidirect
11. #35677C2semidirect
12. #35677C2semidirect
13. #35673C2semidirect
14. #35616C2semidirect
15. #35527C2semidirect
16. #35513C2semidirect
17. #35329C2semidirect
18. #35308C2semidirect
19. #35272C2semidirect
20. #35266C2semidirect
21. #35168C2semidirect
22. #35152C2semidirect
23. C2×#2544C2semidirect
24. #34816C2semidirect
25. #34744C2semidirect
30. C2×#536C22semidirect
34. C2×#535C22semidirect
38. C22×#124C22semidirect
39. C2×#519C22semidirect
40. C2×C4×#41C22semidirect
41. C22×C4×D4C22semidirect
42. #2860C22semidirect
43. #2858C22semidirect
44. #2858C22semidirect
45. #2857C22semidirect
46. #2856C22semidirect
47. #2850C22semidirect
48. #2849C22semidirect
49. #2847C22semidirect
50. #2829C22semidirect
51. #2829C22semidirect
52. #2829C22semidirect
53. #2828C22semidirect
54. #2828C22semidirect
55. #2827C22semidirect
56. #2826C22semidirect
57. #2825C22semidirect
58. #2813C22semidirect
59. #2812C22semidirect
60. #2803C22semidirect
61. #2797C22semidirect
62. #2796C22semidirect
63. #2780C22semidirect
64. #2756C22semidirect
65. #2752C22semidirect
66. #2749C22semidirect
67. #2746C22semidirect
68. #2714C22semidirect
69. #2714C22semidirect
70. #2705C22semidirect
71. #2703C22semidirect
72. #2699C22semidirect
73. #2697C22semidirect
74. #2691C22semidirect
75. #2685C22semidirect
76. #2685C22semidirect
77. #2678C22semidirect
78. #2678C22semidirect
79. #2668C22semidirect
80. #2658C22semidirect
81. #2657C22semidirect
82. #2644C22semidirect
83. #2622C22semidirect
84. #2621C22semidirect
85. #2620C22semidirect
86. #2619C22semidirect
87. #2617C22semidirect
88. #2548C22semidirect
89. #2548C22semidirect
90. #2548C22semidirect
91. #2545C22semidirect
92. #2545C22semidirect
93. #2544C22semidirect
94. #2544C22semidirect
95. #2544C22semidirect
96. #2544C22semidirect
97. #2541C22semidirect
98. #2540C22semidirect
99. #2540C22semidirect
100. #2539C22semidirect
101. #2514C22semidirect
102. #2513C22semidirect
103. #2513C22semidirect
104. #2512C22semidirect
105. #2512C22semidirect
106. #2511C22semidirect
107. #2510C22semidirect
108. #2498C22semidirect
109. #2481C22semidirect
110. #2480C22semidirect
111. #2448C22semidirect
112. #2448C22semidirect
113. #2447C22semidirect
114. #2447C22semidirect
115. #2446C22semidirect
116. #2446C22semidirect
117. #2445C22semidirect
118. #2445C22semidirect
119. #2444C22semidirect
120. #2443C22semidirect
121. #2435C22semidirect
122. #2435C22semidirect
123. #2435C22semidirect
127. #2433C22semidirect
128. #2432C22semidirect
129. #2432C22semidirect
130. #2432C22semidirect
134. #2431C22semidirect
135. #2429C22semidirect
136. #2428C22semidirect
137. #2428C22semidirect
138. #2427C22semidirect
139. #2427C22semidirect
140. #2427C22semidirect
141. #2426C22semidirect
142. #2426C22semidirect
143. #2426C22semidirect
144. #2426C22semidirect
145. #2425C22semidirect
146. #2423C22semidirect
147. #2422C22semidirect
148. #2421C22semidirect
149. #2420C22semidirect
150. #2411C22semidirect
151. #2411C22semidirect
152. #2411C22semidirect
154. #2408C22semidirect
155. #2408C22semidirect
156. #2407C22semidirect
160. #2401C22semidirect
161. #2395C22semidirect
162. C2×#394C22semidirect
163. #2377C22semidirect
164. #2375C22semidirect
165. #2317C22semidirect
166. #2316C22semidirect
170. #2309C22semidirect
171. C4×#126C22semidirect
172. C4×#123C22semidirect
178. #2297C22semidirect
179. #2296C22semidirect
180. #2296C22semidirect
181. C2×#391C22semidirect
183. C2×#386C22semidirect
184. #2285C22semidirect
185. C4×#117C22semidirect
186. C2×C4×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#530872
#530732
#530002
#529772
#523452
#460612
#460502
#456472
#455632
#455222
#356772
#356732
#356162
#355272
#355132
#353292
#353082
#352722
#352662
#351682
#351522
C2×#25442
#348162
#347442