Finite Group Databasebeta

← #8095667

Subgroups — #8095667

Order 512.

5854 conjugacy classes of subgroups.

The subgroup lattice has 1295 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53129C214yesmaximal, complemented
2#53102C214yesmaximal, complemented
3#53063C214yesmaximal, complemented
4#53053C214yesmaximal, complemented
5#52313C218yesmaximal, complemented
6#45716C214yesmaximal, complemented
7#45655C214yesmaximal, complemented
8#45642C214yesmaximal, complemented
9#45578C218yesmaximal, complemented
10#45515C214yesmaximal, complemented
11#35629C211yesmaximal, characteristic, complemented
12#35565C211yesmaximal, characteristic, complemented
13#35557C211yesmaximal, characteristic, complemented
14#35513C211yesmaximal, characteristic, complemented
15#35513C211yesmaximal, characteristic, complemented
16#35512C211yesmaximal, characteristic, complemented
17#35328C211yesmaximal, characteristic, complemented
18#35273C211yesmaximal, characteristic, complemented
19#35254C211yesmaximal, characteristic, complemented
20#35254C211yesmaximal, characteristic, complemented
21#35150C211yesmaximal, characteristic, complemented
22#35150C211yesmaximal, characteristic, complemented
23C2×#2500C211yesmaximal, characteristic, complemented
24#34743C211yesmaximal, characteristic, complemented
25#34743C211yesmaximal, characteristic, complemented
26C22×H(5,𝔽2)C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#537C2211yescharacteristic
29C2×#537C2211yescharacteristic, complemented
30C2×#535C2211yescharacteristic
31C2×#535C2211yescharacteristic
32C2×#532C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C2×#525C2211yescharacteristic
35C2×#525C2211yescharacteristic
36C2×#525C2211yescharacteristic, complemented
37C2×#525C2211yescharacteristic, complemented
38C22×#121C2211yescharacteristic
39C2×C4×#41C2211yescharacteristic, complemented
40C2×C4×#41C2211yescharacteristic, complemented
41C22×#117C2211yescharacteristic, complemented
42#2857C2212yescomplemented
43#2856C2212yescomplemented
44#2854C2214yescomplemented
45#2854C2214yescomplemented
46#2854C2214yescomplemented
47#2854C2214yescomplemented
48#2850C2212yescomplemented
49#2850C2212yescomplemented
50#2837C2218yescomplemented
51#2829C2218yescomplemented
52#2828C2218yescomplemented
53#2828C2218yescomplemented
54#2828C2218yescomplemented
55#2826C2218yescomplemented
56#2825C2218yescomplemented
57#2818C2218yescomplemented
58#2813C2218yescomplemented
59#2812C2218yescomplemented
60#2807C2218yescomplemented
61#2803C2218yescomplemented
62#2803C2218yescomplemented
63#2803C2218yescomplemented
64#2801C2218yescomplemented
65#2778C2218yescomplemented
66#2778C2218yescomplemented
67#2757C2218yescomplemented
68#2757C2218yescomplemented
69#2756C2218yescomplemented
70#2735C2218yescomplemented
71#2709C2218yescomplemented
72#2705C2218yescomplemented
73#2703C2218yescomplemented
74#2685C2218yescomplemented
75#2685C2218yescomplemented
76#2678C2218yescomplemented
77#2678C2218yescomplemented
78#2673C2218yescomplemented
79#2669C2218yescomplemented
80#2624C2214yescomplemented
81#2624C2214yescomplemented
82#2621C2212yescomplemented
83#2620C2212yescomplemented
84#2620C2212yescomplemented
85#2619C2212yescomplemented
86#2617C2214yescomplemented
87#2617C2214yescomplemented
88#2543C2218yescomplemented
89#2541C2214yescomplemented
90#2541C2214yescomplemented
91#2540C2214yescomplemented
92#2540C2214yescomplemented
93#2539C2214yescomplemented
94#2538C2214yescomplemented
95#2537C2214yescomplemented
96#2536C2214yescomplemented
97#2535C2214yescomplemented
98#2514C2214yescomplemented
99#2513C2214yescomplemented
100#2512C2214yescomplemented
101#2511C2214yescomplemented
102#2510C2218yescomplemented
103#2500C2214yescomplemented
104#2500C2214yescomplemented
105#2500C2214yescomplemented
106#2500C2214yescomplemented
107#2497C2214yescomplemented
108#2496C2214yescomplemented
109#2495C2214yescomplemented
110#2494C2214yescomplemented
111#2481C2218yescomplemented
112#2448C2214yescomplemented
113#2448C2214yescomplemented
114#2445C2214yescomplemented
115#2445C2214yescomplemented
116#2435C2212yescomplemented
117#2435C2212yescomplemented
118#2433C2212yescomplemented
119#2433C2214yescomplemented
120#2433C2212yescomplemented
121#2432C2212yescomplemented
122#2432C2212yescomplemented
123#2431C2212yescomplemented
124#2431C2212yescomplemented
125#2429C2212yescomplemented
126#2429C2212yescomplemented
127#2428C2212yescomplemented
128#2428C2212yescomplemented
129#2427C2212yescomplemented
130#2427C2212yescomplemented
131#2426C2212yescomplemented
132#2426C2212yescomplemented
133#2425C2214yescomplemented
134#2425C2214yescomplemented
135#2424C2214yescomplemented
136#2424C2214yescomplemented
137#2418C2218yescomplemented
138#2418C2218yescomplemented
139#2416C2218yescomplemented
140#2415C2214yescomplemented
141#2415C2214yescomplemented
142#2415C2214yescomplemented
143#2415C2214yescomplemented
144#2414C2214yescomplemented
145#2414C2214yescomplemented
146#2414C2214yescomplemented
147#2414C2214yescomplemented
148#2410C2218yes—
149#2410C2218yes—
150#2408C2214yes—
151#2408C2214yes—
152#2408C2214yescomplemented
153#2408C2214yescomplemented
154#2407C2214yes—
155#2407C2214yes—
156#2407C2214yescomplemented
157#2407C2214yescomplemented
158#2405C2214yes—
159#2403C2214yes—
160#2392C2214yescomplemented
161#2392C2214yescomplemented
162C2×#394C2214yescomplemented
163#2376C2218yescomplemented
164#2375C2218yescomplemented
165#2316C2211yescharacteristic, complemented
166#2316C2211yescharacteristic, complemented
167#2311C2211yescharacteristic
168#2311C2211yescharacteristic
169#2311C2211yescharacteristic
170#2311C2211yescharacteristic
171#2311C2211yescharacteristic, complemented
172#2311C2211yescharacteristic, complemented
173#2309C2211yescharacteristic
174C4×#121C2214yescomplemented
175C4×#121C2214yescomplemented
176#2297C2211yescharacteristic
177#2297C2211yescharacteristic
178#2296C2211yescharacteristic, complemented
179#2296C2211yescharacteristic, complemented
180C2×#390C2211yescharacteristic
181C2×#390C2211yescharacteristic
182C2×#388C2214yescomplemented
183C2×#384C2211yescharacteristic, complemented
184C2×#382C2211yescharacteristic, complemented
185#2274C2211yescharacteristic, complemented
186C2×C4×C22⋊C4C2211yescharacteristic, complemented
187C2×H(5,𝔽2)—44no—
188C2×H(5,𝔽2)—44no—
189C2×H(5,𝔽2)—44no—
190C22×#41C2311yescharacteristic
191C22×#41C2311yescharacteristic
192C22×#41C2311yescharacteristic
193C22×#41C2311yescharacteristic
194C22×#41C2312yes—
195C22×#41C2312yes—
196C23×D4C2311yescharacteristic
197C23×D4C2314yes—
198C23×D4C2312yes—
199C23×D4C2312yes—
200C23×D4C2312yes—
201C24×C4C2311yescharacteristic
202#537—44no—
203#537—44no—
204#537—44no—
205#535—44no—
206#535—44no—
207#532—44no—
208#532—44no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#127C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#127C2312yes—
214C2×#127C2312yes—
215C2×#127C2318yes—
216C2×#126C2318yes—
217C2×#124C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×#124C2312yes—
222C2×#124C2312yes—
223#525—44no—
224#525—44no—
225#525—44no—
226#525—44no—
227C2×#123C2312yes—
228C2×#123C2312yes—
229C2×#123C2312yes—
230C2×#123C2312yes—
231C2×#123C2318yes—
232C2×#123C2318yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2312yes—
238C2×C22⋊Q8C2312yes—
239C2×C22⋊Q8C2312yes—
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2312yes—
243C2×#121—44no—
244C2×#121C2312yes—
245C2×#121C2312yes—
246C2×#121C2314yes—
247C2×#121C2314yes—
248C2×#121C2314yes—
249C2×#121C2314yes—
250C2×#121C2312yes—
251C2×#121C2312yes—
252C2×#121C2314yes—
253C2×#121C2314yes—
254C2×#121C2312yes—
255C2×#121C2312yes—
256C2×#121C2314yes—
257C2×#121C2314yes—
258C2×#121C2312yes—
259C2×#121C2312yes—
260C2×#121C2314yes—
261C2×#121C2312yes—
262C2×#121C2312yes—
263C2×#121C2314yes—
264C2×#121C2314yes—
265C2×#121C2318yes—
266C2×#120C2312yes—
267C2×#120C2312yes—
268C2×#120C2312yes—
269C2×#120C2312yes—
270C2×#120C2318yes—
271C2×#120C2314yes—
272C2×#120C2314yes—
273C2×#120C2318yes—
274C2×#120C2318yes—
275C4×#41—44no—
276C4×#41—44no—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2312yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2314yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2314yes—
283C2×C4×D4C2314yes—
284C2×C4×D4C2314yes—
285C2×C4×D4C2314yes—
286C2×C4×D4C2314yes—
287C2×C4×D4C2312yes—
288C2×C4×D4C2312yes—
289C2×#117—44no—
290C2×#117C2311yescharacteristic
291C2×#117C2311yescharacteristic
292C2×#117C2311yescharacteristic
293C2×#117C2311yescharacteristic
294C2×#117C2312yes—
295C2×#117C2312yes—
296C2×#117C2314yes—
297C2×#117C2314yes—
298C22×C4⋊C4C2311yescharacteristic
299C22×C4⋊C4C2311yescharacteristic
300C22×C4⋊C4C2311yescharacteristic
301C22×C4⋊C4C2314yes—
302C22×C22⋊C4C2312yes—
303C22×C22⋊C4C2312yes—
304C22×C22⋊C4C2314yes—
305C22×C22⋊C4C2312yes—
306C22×C22⋊C4C2314yes—
307C22×C42C2311yescharacteristic
308C22×C42C2311yescharacteristic
309C22×C42C2312yes—
310C22×C42C2312yes—
311C22×C42C2312yes—
312#401C2318yes—
313#400C2318yes—
314#400C2318yes—
315#400C2318yes—
316#399C2318yes—
317#399C2318yes—
318#399C2318yes—
319#398C2318yes—
320#398C2314yes—
321#398C2314yes—
322#397C2318yes—
323#397C2318yes—
324#397C2318yes—
325#397C2318yes—
326#397C2314yes—
327#397C2318yes—
328#397C2318yes—
329#397C2318yes—
330#397C2318yes—
331#397C2314yes—
332#396C2318yes—
333#396C2314yes—
334#396C2318yes—
335#396C2314yes—
336#396C2314yes—
337#396C2314yes—
338#396C2318yes—
339#394C2314yes—
340#394C2318yes—
341#394C2318yes—
342#394C2318yes—
343#394C2318yes—
344#394C2318yes—
345#394C2314yes—
346#394C2318yes—
347#394C2318yes—
348#394C2318yes—
349#394C2318yes—
350#394C2314yes—
351#394C2314yes—
352#394C2318yes—
353#394C2318yes—
354#394C2318yes—
355#394C2318yes—
356#394C2318yes—
357#394C2318yes—
358#394C2318yes—
359#394C2314yes—
360#394C2318yes—
361#394C2318yes—
362#394C2318yes—
363#394C2318yes—
364#394C2314yes—
365#394C2318yes—
366#392C2314yes—
367#392C2318yes—
368#392C2318yes—
369#392C2318yes—
370#392C2318yes—
371#392C2318yes—
372#392C2318yes—
373#392C2318yes—
374#392C2314yes—
375#392C2318yes—
376#392C2318yes—
377#392C2318yes—
378#392C2318yes—
379#392C2318yes—
380#391C2312yes—
381#391C2312yes—
382#391C2312yes—
383#391C2312yes—
384#391C2312yes—
385#391C2312yes—
386#391C2312yes—
387#391C2312yes—
388#390C2314yes—
389#390C2314yes—
390#390C2312yes—
391#390C2312yes—
392#390C2312yes—
393#390C2312yes—
394#390C2312yes—
395#390C2312yes—
396#390C2314yes—
397#390C2318yes—
398#390C2318yes—
399#390C2318yes—
400#390C2312yes—
401#390C2312yes—
402#390C2318yes—
403#390C2312yes—
404#390C2312yes—
405#390C2318yes—
406#390C2318yes—
407#390C2314yes—
408#390C2314yes—
409#390C2312yes—
410#390C2312yes—
411#390C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2318yes—
417#389C2312yes—
418#389C2312yes—
419#389C2318yes—
420#389C2318yes—
421#389C2312yes—
422#389C2312yes—
423#389C2314yes—
424#389C2314yes—
425#388C2314yes—
426#388C2318yes—
427#388C2318yes—
428#388C2318yes—
429#388C2318yes—
430#388C2318yes—
431#388C2318yes—
432#388C2318yes—
433#388C2318yes—
434#388C2318yes—
435#388C2318yes—
436#388C2318yes—
437#388C2318yes—
438#388C2314yes—
439#388C2318yes—
440#388C2318yes—
441#388C2318yes—
442#388C2318yes—
443#388C2314yes—
444#388C2314yes—
445#388C2318yes—
446#387C2318yes—
447#387C2318yes—
448#387C2318yes—
449#386C2314yes—
450#386C2314yes—
451#386C2314yes—
452#386C2314yes—
453#386C2314yes—
454#386C2314yes—
455#386C2314yes—
456#386C2318yes—
457#386C2318yes—
458#386C2318yes—
459#386C2318yes—
460#386C2318yes—
461#386C2318yes—
462#386C2314yes—
463#386C2318yes—
464#386C2314yes—
465#386C2314yes—
466#386C2314yes—
467#386C2314yes—
468#385C2318yes—
469#385C2318yes—
470#385C2318yes—
471#385C2314yes—
472#385C2314yes—
473#384C2312yes—
474#384C2312yes—
475#384C2314yes—
476#383C2318yes—
477#382C2312yes—
478#382C2312yes—
479#382C2314yes—
480#380C2314yes—
481#380C2314yes—
482#380C2314yes—
483#380C2314yes—
484#380C2314yes—
485#380C2314yes—
486#380C2314yes—
487#380C2314yes—
488#380C2318yes—
489#380C2314yes—
490#380C2314yes—
491#379C2314yes—
492#379C2318yes—
493#379C2318yes—
494#379C2318yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C22⋊C4C2312yes—
500C4×C22⋊C4C2312yes—
501C4×C22⋊C4C2312yes—
502C4×C22⋊C4C2312yes—
503C4×C22⋊C4C2312yes—
504C4×C22⋊C4C2312yes—
505C4×C22⋊C4C2312yes—
506C4×C22⋊C4C2312yes—
507C4×C22⋊C4C2314yes—
508C2×#95C2314yes—
509C2×#95C2312yes—
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—24no—
524C2×#41—24no—
525C2×#41—24no—
526C2×#41—44no—
527C2×#41—44no—
528C2×#41—44no—
529C2×#41—44no—
530C2×#41—44no—
531C2×#41—44no—
532C22×Q8C2411yescharacteristic
533C22×Q8C2411yescharacteristic
534C22×Q8C2411yescharacteristic
535C22×Q8C2411yescharacteristic
536C22×D4—24no—
537C22×D4—24no—
538C22×D4—24no—
539C22×D4—44no—
540C22×D4—44no—
541C22×D4—44no—
542C22×D4—44no—
543C22×D4—44no—
544C22×D4—44no—
545C22×D4—44no—
546C22×D4—48no—
547C22×D4—48no—
548C22×D4—48no—
549C22×D4—84no—
550C22×D4C2412yes—
551C22×D4C2412yes—
552C22×D4C2411yescharacteristic
553C22×D4C2411yescharacteristic
554C22×D4C2412yes—
555C22×D4C2412yes—
556C22×D4C2412yes—
557C22×D4C2412yes—
558C22×D4C2411yescharacteristic
559C22×D4C2411yescharacteristic
560C22×D4C2414yes—
561C22×D4C2414yes—
562C22×D4C2414yes—
563C22×D4C2414yes—
564C22×D4C2414yes—
565C22×D4C2414yes—
566C22×D4C2414yes—
567C22×D4C2414yes—
568C22×D4C2418yes—
569C22×D4C2418yes—
570C22×D4C2418yes—
571C22×D4C2414yes—
572C22×D4C2414yes—
573C22×D4C2414yes—
574C23×C4—24no—
575C23×C4—24no—
576C23×C4—24no—
577C23×C4C2411yescharacteristic
578C23×C4C2412yes—
579C23×C4C2412yes—
580C23×C4C2412yes—
581C23×C4C2412yes—
582C23×C4C2412yes—
583C23×C4C2412yes—
584C23×C4C2412yes—
585C23×C4C2412yes—
586C23×C4C2412yes—
587C23×C4C2412yes—
588C23×C4C2412yes—
589C23×C4C2414yes—
590C23×C4C2414yes—
591C23×C4C2414yes—
592C23×C4C2411yescharacteristic
593C4⋊Q8—42no—
594C4⋊Q8—42no—
595#127—42no—
596#127—42no—
597#127—44no—
598#127—44no—
599#127—88no—
600#126—88no—
601#124—42no—
602#124—42no—
603#124—42no—
604#124—42no—
605#124—44no—
606#124—44no—
607#123—416no—
608#123—44no—
609#123—44no—
610#123—44no—
611#123—44no—
612#123—88no—
613C22⋊Q8—44no—
614C22⋊Q8—44no—
615C22⋊Q8—44no—
616C22⋊Q8—44no—
617C22⋊Q8—44no—
618C22⋊Q8—44no—
619C22⋊Q8—44no—
620C22⋊Q8—44no—
621C22⋊Q8—44no—
622C22⋊Q8—44no—
623#121—48no—
624#121—48no—
625#121—48no—
626#121—48no—
627#121—44no—
628#121—44no—
629#121—44no—
630#121—44no—
631#121—48no—
632#121—48no—
633#121—44no—
634#121—44no—
635#121—44no—
636#121—44no—
637#121—44no—
638#121—44no—
639#121—48no—
640#121—48no—
641#121—48no—
642#121—48no—
643#121—48no—
644#121—88no—
645#120—416no—
646#120—44no—
647#120—44no—
648#120—44no—
649#120—44no—
650#120—48no—
651#120—48no—
652#120—88no—
653#120—88no—
654C4×Q8—44no—
655C4×Q8—44no—
656C4×D4—44no—
657C4×D4—44no—
658C4×D4—48no—
659C4×D4—48no—
660C4×D4—48no—
661C4×D4—48no—
662C4×D4—48no—
663C4×D4—48no—
664C4×D4—48no—
665C4×D4—48no—
666#117—24no—
667#117—24no—
668#117—24no—
669#117—24no—
670#117—44no—
671#117—44no—
672#117—48no—
673#117—48no—
674C2×C4⋊C4—24no—
675C2×C4⋊C4—24no—
676C2×C4⋊C4—24no—
677C2×C4⋊C4—84no—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2412yes—
680C2×C4⋊C4C2412yes—
681C2×C4⋊C4C2412yes—
682C2×C4⋊C4C2412yes—
683C2×C4⋊C4C2412yes—
684C2×C4⋊C4C2412yes—
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2412yes—
687C2×C4⋊C4C2412yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2418yes—
690C2×C4⋊C4C2418yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2418yes—
705C2×C4⋊C4C2418yes—
706C2×C4⋊C4C2414yes—
707C2×C22⋊C4—48no—
708C2×C22⋊C4—44no—
709C2×C22⋊C4—44no—
710C2×C22⋊C4—44no—
711C2×C22⋊C4—84no—
712C2×C22⋊C4C2418yes—
713C2×C22⋊C4C2412yes—
714C2×C22⋊C4C2412yes—
715C2×C22⋊C4C2412yes—
716C2×C22⋊C4C2412yes—
717C2×C22⋊C4C2412yes—
718C2×C22⋊C4C2412yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2418yes—
721C2×C22⋊C4C2418yes—
722C2×C22⋊C4C2418yes—
723C2×C22⋊C4C2418yes—
724C2×C22⋊C4C2412yes—
725C2×C22⋊C4C2412yes—
726C2×C22⋊C4C2418yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2414yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2418yes—
743C2×C22⋊C4C2418yes—
744C2×C22⋊C4C2418yes—
745C2×C22⋊C4C2418yes—
746C2×C22⋊C4C2418yes—
747C2×C22⋊C4C2418yes—
748C2×C22⋊C4C2418yes—
749C2×C22⋊C4C2414yes—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2418yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2418yes—
758C2×C22⋊C4C2418yes—
759C2×C22⋊C4C2414yes—
760C2×C42—24no—
761C2×C42—24no—
762C2×C42—44no—
763C2×C42—44no—
764C2×C42—44no—
765C2×C42C2412yes—
766C2×C42C2412yes—
767C2×C42C2411yescharacteristic
768C2×C42C2411yescharacteristic
769C2×C42C2412yes—
770C2×C42C2412yes—
771C2×C42C2412yes—
772C2×C42C2412yes—
773C2×C42C2411yescharacteristic
774C2×C42C2411yescharacteristic
775C2×C42C2418yes—
776C2×C42C2414yes—
777C2×C42C2414yes—
778C2×C42C2418yes—
779#95C2412yes—
780#95C2412yes—
781#95C2412yes—
782#95C2412yes—
783#95C2418yes—
784#95C2418yes—
785#95C2418yes—
786#95C2414yes—
787#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2418yes—
795#95C2418yes—
796#95C2418yes—
797#95C2418yes—
798#95C2418yes—
799#95C2418yes—
800#95C2418yes—
801#95C2418yes—
802C24—22no—
803C24—24no—
804C24—22no—
805C24—22no—
806C24—24no—
807C24—24no—
808C24—42no—
809C24—42no—
810C24—44no—
811C24—44no—
812C24—44no—
813C24—44no—
814C24—44no—
815C24—48no—
816C24—48no—
817C24C2512yes—
818C24C2512yes—
819C24C2514yes—
820C24C2512yes—
821C24C2512yes—
822C24C2512yes—
823C24C2511yescharacteristic
824#41—432no—
825#41—432no—
826#41—416no—
827#41—416no—
828#41—416no—
829#41—416no—
830C2×Q8—22no—
831C2×Q8—22no—
832C2×Q8—22no—
833C2×Q8—22no—
834C2×Q8—22no—
835C2×Q8—22no—
836C2×Q8—22no—
837C2×Q8—22no—
838C2×Q8—22no—
839C2×Q8—22no—
840C2×Q8—22no—
841C2×Q8—22no—
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—24no—
851C2×D4—24no—
852C2×D4—24no—
853C2×D4—24no—
854C2×D4—22no—
855C2×D4—22no—
856C2×D4—22no—
857C2×D4—22no—
858C2×D4—22no—
859C2×D4—22no—
860C2×D4—24no—
861C2×D4—24no—
862C2×D4—24no—
863C2×D4—24no—
864C2×D4—22no—
865C2×D4—22no—
866C2×D4—22no—
867C2×D4—22no—
868C2×D4—24no—
869C2×D4—24no—
870C2×D4—22no—
871C2×D4—22no—
872C2×D4—28no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—48no—
889C2×D4—48no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—48no—
899C2×D4—48no—
900C2×D4—48no—
901C2×D4—48no—
902C2×D4—48no—
903C2×D4—48no—
904C2×D4—48no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—48no—
909C2×D4—48no—
910C2×D4—48no—
911C2×D4—464no—
912C2×D4—432no—
913C2×D4—432no—
914C2×D4—416no—
915C2×D4—816no—
916C22×C4—24no—
917C22×C4—22no—
918C22×C4—22no—
919C22×C4—22no—
920C22×C4—24no—
921C22×C4—24no—
922C22×C4—24no—
923C22×C4—24no—
924C22×C4—24no—
925C22×C4—24no—
926C22×C4—24no—
927C22×C4—24no—
928C22×C4—24no—
929C22×C4—24no—
930C22×C4—24no—
931C22×C4—24no—
932C22×C4—24no—
933C22×C4—24no—
934C22×C4—24no—
935C22×C4—24no—
936C22×C4—24no—
937C22×C4—24no—
938C22×C4—24no—
939C22×C4—24no—
940C22×C4—24no—
941C22×C4—24no—
942C22×C4—24no—
943C22×C4—28no—
944C22×C4—42no—
945C22×C4—44no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4—44no—
949C22×C4—44no—
950C22×C4—44no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—44no—
954C22×C4—44no—
955C22×C4—44no—
956C22×C4—44no—
957C22×C4—44no—
958C22×C4—416no—
959C22×C4H(5,𝔽2)14yes—
960C22×C4H(5,𝔽2)14yes—
961C22×C4H(5,𝔽2)14yes—
962C22×C4C2512yes—
963C22×C4C2512yes—
964C22×C4C2512yes—
965C22×C4C2514yes—
966C22×C4C2514yes—
967C22×C4C2514yes—
968C22×C4C2512yes—
969C22×C4C2514yes—
970C22×C4C2514yes—
971C22×C4C2514yes—
972C22×C4C2512yes—
973C22×C4C2514yes—
974C22×C4C2512yes—
975C22×C4C2512yes—
976C22×C4C2512yes—
977C22×C4C2512yes—
978C22×C4C2511yescharacteristic
979C22×C4C2511yescharacteristic
980C4⋊C4—24no—
981C4⋊C4—24no—
982C4⋊C4—24no—
983C4⋊C4—24no—
984C4⋊C4—24no—
985C4⋊C4—24no—
986C4⋊C4—24no—
987C4⋊C4—24no—
988C4⋊C4—24no—
989C4⋊C4—24no—
990C4⋊C4—28no—
991C4⋊C4—48no—
992C4⋊C4—48no—
993C4⋊C4—44no—
994C4⋊C4—44no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—44no—
1003C4⋊C4—44no—
1004C4⋊C4—44no—
1005C4⋊C4—48no—
1006C4⋊C4—44no—
1007C4⋊C4—48no—
1008C4⋊C4—44no—
1009C22⋊C4—24no—
1010C22⋊C4—24no—
1011C22⋊C4—24no—
1012C22⋊C4—24no—
1013C22⋊C4—216no—
1014C22⋊C4—24no—
1015C22⋊C4—24no—
1016C22⋊C4—28no—
1017C22⋊C4—48no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
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—
1031C22⋊C4—44no—
1032C22⋊C4—44no—
1033C22⋊C4—44no—
1034C22⋊C4—44no—
1035C22⋊C4—44no—
1036C22⋊C4—44no—
1037C22⋊C4—44no—
1038C22⋊C4—48no—
1039C22⋊C4—48no—
1040C22⋊C4—48no—
1041C22⋊C4—44no—
1042C22⋊C4—48no—
1043C22⋊C4—48no—
1044C22⋊C4—48no—
1045C22⋊C4—48no—
1046C22⋊C4—44no—
1047C22⋊C4—44no—
1048C22⋊C4—44no—
1049C22⋊C4—44no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C22⋊C4—44no—
1053C22⋊C4—48no—
1054C22⋊C4—48no—
1055C22⋊C4—48no—
1056C22⋊C4—44no—
1057C42—22no—
1058C42—22no—
1059C42—22no—
1060C42—22no—
1061C42—24no—
1062C42—24no—
1063C42—24no—
1064C42—24no—
1065C42—24no—
1066C42—24no—
1067C42—48no—
1068C42—44no—
1069C42—44no—
1070C42—48no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—24no—
1089C23—24no—
1090C23—24no—
1091C23—28no—
1092C23—22no—
1093C23—22no—
1094C23—24no—
1095C23—24no—
1096C23—24no—
1097C23—24no—
1098C23—24no—
1099C23—28no—
1100C23—24no—
1101C23—24no—
1102C23—24no—
1103C23—22no—
1104C23—22no—
1105C23—44no—
1106C23—44no—
1107C23—416no—
1108C23—44no—
1109C23—48no—
1110C23—84no—
1111C23—84no—
1112C23—84no—
1113C23—84no—
1114C23—88no—
1115C23—88no—
1116C23—164no—
1117C23—164no—
1118C23—168no—
1119C23—168no—
1120C23C2×H(5,𝔽2)12yes—
1121C23C2×H(5,𝔽2)12yes—
1122C23C2×H(5,𝔽2)12yes—
1123C23C2611yescharacteristic
1124Q8—44no—
1125Q8—44no—
1126Q8—44no—
1127Q8—44no—
1128D4—416no—
1129D4—416no—
1130D4—48no—
1131D4—48no—
1132D4—48no—
1133D4—48no—
1134D4—48no—
1135D4—48no—
1136D4—44no—
1137D4—44no—
1138D4—44no—
1139D4—44no—
1140D4—88no—
1141D4—88no—
1142D4—88no—
1143D4—88no—
1144D4—88no—
1145D4—88no—
1146D4—816no—
1147D4—164no—
1148D4—164no—
1149D4—164no—
1150D4—168no—
1151D4—168no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—24no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—28no—
1180C2×C4—22no—
1181C2×C4—24no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—28no—
1190C2×C4—24no—
1191C2×C4—22no—
1192C2×C4—28no—
1193C2×C4—24no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—48no—
1197C2×C4—416no—
1198C2×C4—44no—
1199C2×C4—48no—
1200C2×C4—48no—
1201C2×C4—48no—
1202C2×C4—48no—
1203C2×C4—48no—
1204C2×C4—48no—
1205C2×C4—88no—
1206C2×C4—84no—
1207C2×C4—84no—
1208C2×C4—84no—
1209C2×C4—84no—
1210C2×C4—88no—
1211C2×C4#560116yes—
1212C2×C4C2×H(5,𝔽2)12yes—
1213C2×C4C2×H(5,𝔽2)12yes—
1214C2×C4C2×H(5,𝔽2)12yes—
1215C2×C4C2×H(5,𝔽2)12yes—
1216C2×C4C2×H(5,𝔽2)12yes—
1217C2×C4C2×H(5,𝔽2)12yes—
1218C2×C4#58514yes—
1219C22—22no—
1220C22—22no—
1221C22—24no—
1222C22—24no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—44no—
1228C22—42no—
1229C22—42no—
1230C22—44no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—44no—
1236C22—44no—
1237C22—42no—
1238C22—42no—
1239C22—44no—
1240C22—44no—
1241C22—48no—
1242C22—42no—
1243C22—44no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—44no—
1249C22—44no—
1250C22—42no—
1251C22—42no—
1252C22—44no—
1253C22—44no—
1254C22—48no—
1255C22—88no—
1256C22—168no—
1257C22—1616no—
1258C22C2×#56014yes—
1259C22C22×H(5,𝔽2)11yescharacteristic
1260C22C22×H(5,𝔽2)11yescharacteristic
1261C22C22×H(5,𝔽2)11yescharacteristic
1262C22C2×#58512yes—
1263C22H(7,𝔽2)12yes—
1264C4—24no—
1265C4—44no—
1266C4—44no—
1267C4—44no—
1268C4—42no—
1269C4—44no—
1270C4—42no—
1271C4—44no—
1272C4—42no—
1273C4—42no—
1274C4—42no—
1275C4—42no—
1276C4—42no—
1277C4—42no—
1278C4—44no—
1279C4—44no—
1280C4C2×#56014yes—
1281C4C2×#56014yes—
1282C2—24no—
1283C2—82no—
1284C2—82no—
1285C2—82no—
1286C2—82no—
1287C2—84no—
1288C2—82no—
1289C2C22×#56011yescharacteristic
1290C2#6283611yescharacteristic
1291C2#6287611yescharacteristic
1292C2#6293012yes—
1293C2#6295712yes—
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. #53102C2semidirect
3. #53063C2semidirect
4. #53053C2semidirect
5. #52313C2semidirect
6. #45716C2semidirect
7. #45655C2semidirect
8. #45642C2semidirect
9. #45578C2semidirect
10. #45515C2semidirect
11. #35629C2semidirect
12. #35565C2semidirect
13. #35557C2semidirect
14. #35513C2semidirect
15. #35513C2semidirect
16. #35512C2semidirect
17. #35328C2semidirect
18. #35273C2semidirect
19. #35254C2semidirect
20. #35254C2semidirect
21. #35150C2semidirect
22. #35150C2semidirect
23. C2×#2500C2semidirect
24. #34743C2semidirect
25. #34743C2semidirect
29. C2×#537C22semidirect
36. C2×#525C22semidirect
37. C2×#525C22semidirect
39. C2×C4×#41C22semidirect
40. C2×C4×#41C22semidirect
41. C22×#117C22semidirect
42. #2857C22semidirect
43. #2856C22semidirect
44. #2854C22semidirect
45. #2854C22semidirect
46. #2854C22semidirect
47. #2854C22semidirect
48. #2850C22semidirect
49. #2850C22semidirect
50. #2837C22semidirect
51. #2829C22semidirect
52. #2828C22semidirect
53. #2828C22semidirect
54. #2828C22semidirect
55. #2826C22semidirect
56. #2825C22semidirect
57. #2818C22semidirect
58. #2813C22semidirect
59. #2812C22semidirect
60. #2807C22semidirect
61. #2803C22semidirect
62. #2803C22semidirect
63. #2803C22semidirect
64. #2801C22semidirect
65. #2778C22semidirect
66. #2778C22semidirect
67. #2757C22semidirect
68. #2757C22semidirect
69. #2756C22semidirect
70. #2735C22semidirect
71. #2709C22semidirect
72. #2705C22semidirect
73. #2703C22semidirect
74. #2685C22semidirect
75. #2685C22semidirect
76. #2678C22semidirect
77. #2678C22semidirect
78. #2673C22semidirect
79. #2669C22semidirect
80. #2624C22semidirect
81. #2624C22semidirect
82. #2621C22semidirect
83. #2620C22semidirect
84. #2620C22semidirect
85. #2619C22semidirect
86. #2617C22semidirect
87. #2617C22semidirect
88. #2543C22semidirect
89. #2541C22semidirect
90. #2541C22semidirect
91. #2540C22semidirect
92. #2540C22semidirect
93. #2539C22semidirect
94. #2538C22semidirect
95. #2537C22semidirect
96. #2536C22semidirect
97. #2535C22semidirect
98. #2514C22semidirect
99. #2513C22semidirect
100. #2512C22semidirect
101. #2511C22semidirect
102. #2510C22semidirect
103. #2500C22semidirect
104. #2500C22semidirect
105. #2500C22semidirect
106. #2500C22semidirect
107. #2497C22semidirect
108. #2496C22semidirect
109. #2495C22semidirect
110. #2494C22semidirect
111. #2481C22semidirect
112. #2448C22semidirect
113. #2448C22semidirect
114. #2445C22semidirect
115. #2445C22semidirect
116. #2435C22semidirect
117. #2435C22semidirect
118. #2433C22semidirect
119. #2433C22semidirect
120. #2433C22semidirect
121. #2432C22semidirect
122. #2432C22semidirect
123. #2431C22semidirect
124. #2431C22semidirect
125. #2429C22semidirect
126. #2429C22semidirect
127. #2428C22semidirect
128. #2428C22semidirect
129. #2427C22semidirect
130. #2427C22semidirect
131. #2426C22semidirect
132. #2426C22semidirect
133. #2425C22semidirect
134. #2425C22semidirect
135. #2424C22semidirect
136. #2424C22semidirect
137. #2418C22semidirect
138. #2418C22semidirect
139. #2416C22semidirect
140. #2415C22semidirect
141. #2415C22semidirect
142. #2415C22semidirect
143. #2415C22semidirect
144. #2414C22semidirect
145. #2414C22semidirect
146. #2414C22semidirect
147. #2414C22semidirect
152. #2408C22semidirect
153. #2408C22semidirect
156. #2407C22semidirect
157. #2407C22semidirect
160. #2392C22semidirect
161. #2392C22semidirect
162. C2×#394C22semidirect
163. #2376C22semidirect
164. #2375C22semidirect
165. #2316C22semidirect
166. #2316C22semidirect
171. #2311C22semidirect
172. #2311C22semidirect
174. C4×#121C22semidirect
175. C4×#121C22semidirect
178. #2296C22semidirect
179. #2296C22semidirect
182. C2×#388C22semidirect
183. C2×#384C22semidirect
184. C2×#382C22semidirect
185. #2274C22semidirect
186. C2×C4×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#531292
#531022
#530632
#530532
#523132
#457162
#456552
#456422
#455782
#455152
#356292
#355652
#355572
#355132
#355122
#353282
#352732
#352542
#351502
C2×#25002
#347432