Finite Group Databasebeta

← #8095550

Subgroups — #8095550

Order 512.

5494 conjugacy classes of subgroups.

The subgroup lattice has 1209 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53088C214yesmaximal, complemented
2#53073C214yesmaximal, complemented
3#53041C214yesmaximal, complemented
4#53022C214yesmaximal, complemented
5#52375C218yesmaximal, complemented
6#46063C214yesmaximal, complemented
7#46048C214yesmaximal, complemented
8#45669C214yesmaximal, complemented
9#45556C218yesmaximal, complemented
10#45522C214yesmaximal, complemented
11#35676C211yesmaximal, characteristic, complemented
12#35666C211yesmaximal, characteristic, complemented
13#35660C211yesmaximal, characteristic, complemented
14#35617C211yesmaximal, characteristic, complemented
15#35617C211yesmaximal, characteristic, complemented
16#35541C211yesmaximal, characteristic, complemented
17#35329C211yesmaximal, characteristic, complemented
18#35316C211yesmaximal, characteristic, complemented
19#35313C211yesmaximal, characteristic, complemented
20#35256C211yesmaximal, characteristic, complemented
21#35182C211yesmaximal, characteristic, complemented
22#35153C211yesmaximal, characteristic, complemented
23C2×#2545C211yesmaximal, characteristic, complemented
24#34816C211yesmaximal, characteristic, complemented
25#34744C211yesmaximal, characteristic, complemented
26C22×2−1+4C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#536C2211yescharacteristic
30C2×#536C2211yescharacteristic
31C2×#536C2211yescharacteristic
32C2×#535C2211yescharacteristic
33C2×#535C2211yescharacteristic
34C2×#535C2211yescharacteristic
35C2×#532C2211yescharacteristic
36C22×C4⋊Q8C2211yescharacteristic
37C22×#124C2211yescharacteristic
38C22×#124C2211yescharacteristic
39C2×#518C2211yescharacteristic
40C2×C4×#41C2211yescharacteristic
41C22×C4×Q8C2211yescharacteristic
42#2863C2214yescomplemented
43#2858C2212yes—
44#2858C2212yes—
45#2857C2214yescomplemented
46#2856C2212yes—
47#2854C2214yes—
48#2853C2214yes—
49#2850C2212yes—
50#2841C2218yescomplemented
51#2838C2218yescomplemented
52#2838C2218yescomplemented
53#2830C2218yescomplemented
54#2829C2218yescomplemented
55#2828C2218yescomplemented
56#2827C2218yescomplemented
57#2826C2218yescomplemented
58#2825C2218yescomplemented
59#2813C2218yescomplemented
60#2803C2218yescomplemented
61#2797C2218yescomplemented
62#2796C2218yescomplemented
63#2784C2218yescomplemented
64#2780C2218yescomplemented
65#2778C2218yescomplemented
66#2778C2218yescomplemented
67#2757C2218yescomplemented
68#2757C2218yescomplemented
69#2756C2218yescomplemented
70#2749C2218yescomplemented
71#2748C2218yescomplemented
72#2746C2218yescomplemented
73#2742C2218yescomplemented
74#2737C2218yescomplemented
75#2737C2218yescomplemented
76#2705C2218yescomplemented
77#2703C2218yescomplemented
78#2693C2218yescomplemented
79#2691C2218yescomplemented
80#2658C2212yes—
81#2657C2212yes—
82#2645C2214yescomplemented
83#2623C2214yes—
84#2621C2214yescomplemented
85#2620C2212yes—
86#2619C2212yes—
87#2618C2214yes—
88#2547C2214yes—
89#2547C2214yes—
90#2547C2214yescomplemented
91#2546C2214yescomplemented
92#2545C2214yes—
93#2545C2214yes—
94#2545C2214yes—
95#2545C2214yes—
96#2544C2214yes—
97#2544C2214yes—
98#2540C2214yes—
99#2540C2214yes—
100#2539C2218yes—
101#2514C2212yescomplemented
102#2514C2214yescomplemented
103#2513C2212yescomplemented
104#2512C2212yescomplemented
105#2511C2212yescomplemented
106#2511C2214yescomplemented
107#2510C2214yes—
108#2493C2218yes—
109#2486C2218yes—
110#2481C2214yes—
111#2448C2214yescomplemented
112#2448C2212yescomplemented
113#2447C2214yes—
114#2447C2212yescomplemented
115#2446C2212yescomplemented
116#2446C2214yescomplemented
117#2445C2214yes—
118#2445C2212yescomplemented
119#2444C2214yes—
120#2443C2214yes—
121#2436C2214yes—
122#2436C2214yes—
123#2436C2212yescomplemented
124#2434C2212yescomplemented
125#2434C2212yescomplemented
126#2434C2214yescomplemented
127#2434C2212yescomplemented
128#2432C2212yescomplemented
129#2432C2212yescomplemented
130#2432C2214yescomplemented
131#2432C2212yescomplemented
132#2431C2214yes—
133#2431C2214yes—
134#2431C2212yescomplemented
135#2430C2218yes—
136#2429C2214yescomplemented
137#2429C2214yescomplemented
138#2428C2214yes—
139#2427C2214yes—
140#2427C2214yes—
141#2427C2214yes—
142#2427C2214yes—
143#2426C2214yes—
144#2426C2214yescomplemented
145#2426C2214yescomplemented
146#2424C2218yes—
147#2423C2214yescomplemented
148#2422C2214yes—
149#2421C2214yescomplemented
150#2420C2214yes—
151#2412C2214yes—
152#2412C2218yes—
153#2412C2214yes—
154#2412C2218yes—
155#2409C2214yescomplemented
156#2407C2214yescomplemented
157#2406C2218yes—
158#2404C2214yes—
159#2404C2214yes—
160#2401C2214yescomplemented
161#2395C2214yescomplemented
162C2×#396C2214yes—
163#2377C2218yescomplemented
164#2376C2218yescomplemented
165#2317C2211yescharacteristic
166#2316C2211yescharacteristic
167#2311C2211yescharacteristic
168#2310C2211yescharacteristic
169#2310C2211yescharacteristic
170#2310C2211yescharacteristic
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×#388C2214yes—
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×Q8C2311yescharacteristic
198C23×Q8C2312yes—
199C23×Q8C2312yes—
200C23×D4C2311yescharacteristic
201#537—44no—
202#536—44no—
203#536—44no—
204#536—44no—
205#536—44no—
206#535—44no—
207#535—44no—
208#535—44no—
209#532—44no—
210C2×C4⋊Q8—44no—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2314yes—
217C2×C4⋊Q8C2312yes—
218C2×C4⋊Q8C2312yes—
219C2×#127C2312yes—
220C2×#127C2312yes—
221C2×#127C2312yes—
222C2×#127C2311yescharacteristic
223C2×#126C2314yes—
224C2×#124—44no—
225C2×#124—44no—
226C2×#124C2312yes—
227C2×#124C2312yes—
228C2×#124C2311yescharacteristic
229C2×#124C2311yescharacteristic
230C2×#124C2312yes—
231C2×#124C2312yes—
232C2×#124C2312yes—
233C2×#124C2312yes—
234C2×#124C2312yes—
235C2×#124C2314yes—
236C2×#124C2314yes—
237C2×#124C2314yes—
238C2×#124C2312yes—
239C2×#124C2312yes—
240C2×#123C2314yes—
241C2×#123C2314yes—
242C2×#123C2314yes—
243C2×#123C2318yes—
244C2×#123C2314yes—
245C2×#123C2314yes—
246C2×C22⋊Q8C2312yes—
247C2×C22⋊Q8C2314yes—
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2312yes—
250C2×C22⋊Q8C2312yes—
251C2×C22⋊Q8C2314yes—
252C2×C22⋊Q8C2312yes—
253C2×#121C2312yes—
254C2×#121C2314yes—
255C2×#121C2312yes—
256C2×#121C2312yes—
257C2×#121C2318yes—
258C2×#121C2314yes—
259C2×#121C2314yes—
260C2×#121C2314yes—
261C2×#121C2312yes—
262C2×#120C2314yes—
263C2×#120C2314yes—
264C2×#120C2314yes—
265#518—44no—
266C4×#41—44no—
267C2×C4×Q8—44no—
268C2×C4×Q8C2314yes—
269C2×C4×Q8C2314yes—
270C2×C4×Q8C2312yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2314yes—
276C2×#117C2311yescharacteristic
277C2×#117C2311yescharacteristic
278C2×#117C2311yescharacteristic
279C2×#117C2311yescharacteristic
280C2×#117C2311yescharacteristic
281C2×#117C2312yes—
282C22×C4⋊C4C2311yescharacteristic
283C22×C4⋊C4C2312yes—
284C22×C4⋊C4C2312yes—
285C22×C4⋊C4C2314yes—
286C22×C22⋊C4C2312yes—
287C22×C22⋊C4C2314yes—
288C22×C22⋊C4C2314yes—
289C22×C22⋊C4C2314yes—
290C22×C22⋊C4C2312yes—
291C22×C42C2311yescharacteristic
292C22×C42C2311yescharacteristic
293C22×C42C2311yescharacteristic
294C22×C42C2312yes—
295C22×C42C2312yes—
296#401C2318yes—
297#401C2314yes—
298#400C2314yes—
299#400C2318yes—
300#400C2318yes—
301#400C2318yes—
302#400C2314yes—
303#400C2314yes—
304#400C2318yes—
305#400C2314yes—
306#399C2318yes—
307#399C2318yes—
308#399C2314yes—
309#399C2318yes—
310#398C2314yes—
311#398C2318yes—
312#398C2318yes—
313#398C2318yes—
314#398C2318yes—
315#397C2314yes—
316#397C2318yes—
317#397C2318yes—
318#397C2318yes—
319#397C2318yes—
320#397C2318yes—
321#397C2318yes—
322#397C2314yes—
323#397C2314yes—
324#397C2318yes—
325#397C2318yes—
326#397C2318yes—
327#397C2314yes—
328#397C2314yes—
329#397C2314yes—
330#396C2318yes—
331#396C2318yes—
332#396C2318yes—
333#396C2318yes—
334#396C2318yes—
335#396C2318yes—
336#396C2318yes—
337#396C2314yes—
338#395C2318yes—
339#395C2318yes—
340#395C2318yes—
341#394C2314yes—
342#394C2318yes—
343#394C2318yes—
344#394C2318yes—
345#394C2318yes—
346#394C2318yes—
347#394C2318yes—
348#394C2318yes—
349#394C2314yes—
350#394C2318yes—
351#394C2318yes—
352#394C2318yes—
353#394C2318yes—
354#394C2318yes—
355#393C2318yes—
356#393C2318yes—
357#393C2318yes—
358#392C2318yes—
359#392C2318yes—
360#392C2318yes—
361#392C2318yes—
362#392C2318yes—
363#392C2318yes—
364#391C2314yes—
365#391C2314yes—
366#391C2314yes—
367#391C2314yes—
368#391C2312yes—
369#391C2312yes—
370#391C2314yes—
371#391C2312yes—
372#391C2311yescharacteristic
373#391C2312yes—
374#391C2311yescharacteristic
375#391C2312yes—
376#391C2314yes—
377#391C2312yes—
378#391C2312yes—
379#391C2312yes—
380#391C2312yes—
381#391C2312yes—
382#390C2312yes—
383#390C2318yes—
384#390C2318yes—
385#390C2318yes—
386#390C2312yes—
387#390C2311yescharacteristic
388#390C2318yes—
389#390C2318yes—
390#390C2318yes—
391#390C2311yescharacteristic
392#390C2312yes—
393#390C2312yes—
394#390C2314yes—
395#390C2312yes—
396#390C2312yes—
397#390C2312yes—
398#390C2312yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2318yes—
403#389C2318yes—
404#389C2318yes—
405#389C2312yes—
406#389C2312yes—
407#389C2312yes—
408#389C2312yes—
409#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#388C2318yes—
413#388C2318yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2314yes—
419#388C2318yes—
420#388C2314yes—
421#388C2318yes—
422#388C2318yes—
423#387C2314yes—
424#387C2314yes—
425#387C2314yes—
426#387C2318yes—
427#387C2318yes—
428#387C2314yes—
429#387C2318yes—
430#387C2318yes—
431#387C2318yes—
432#387C2314yes—
433#386C2314yes—
434#386C2318yes—
435#386C2318yes—
436#386C2318yes—
437#386C2318yes—
438#386C2318yes—
439#386C2318yes—
440#386C2318yes—
441#386C2312yes—
442#386C2312yes—
443#386C2312yes—
444#386C2312yes—
445#386C2312yes—
446#386C2312yes—
447#386C2318yes—
448#386C2318yes—
449#386C2318yes—
450#386C2318yes—
451#386C2318yes—
452#386C2314yes—
453#386C2314yes—
454#386C2314yes—
455#386C2314yes—
456#385C2318yes—
457#385C2318yes—
458#385C2318yes—
459#385C2314yes—
460#385C2312yes—
461#385C2312yes—
462#385C2318yes—
463#385C2318yes—
464#385C2318yes—
465#385C2318yes—
466#385C2314yes—
467#385C2314yes—
468#384C2312yes—
469#384C2312yes—
470#383C2314yes—
471#383C2318yes—
472#382C2312yes—
473#382C2312yes—
474#381C2314yes—
475#381C2314yes—
476#381C2314yes—
477#381C2318yes—
478#381C2314yes—
479#380C2314yes—
480#380C2314yes—
481#380C2318yes—
482#380C2318yes—
483#380C2318yes—
484#380C2318yes—
485#380C2318yes—
486#380C2318yes—
487#380C2314yes—
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—
5112−1+4—464no—
512C2×#41—24no—
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—48no—
522C2×#41—48no—
523C2×#41—48no—
524C2×#41—44no—
525C2×#41—44no—
526C2×#41—44no—
527C2×#41—44no—
528C2×#41—44no—
529C2×#41—44no—
530C22×Q8—24no—
531C22×Q8—24no—
532C22×Q8—24no—
533C22×Q8—24no—
534C22×Q8—24no—
535C22×Q8—24no—
536C22×Q8—44no—
537C22×Q8—44no—
538C22×Q8—44no—
539C22×Q8—44no—
540C22×Q8—44no—
541C22×Q8—44no—
542C22×Q8C2412yes—
543C22×Q8C2412yes—
544C22×Q8C2411yescharacteristic
545C22×Q8C2412yes—
546C22×Q8C2411yescharacteristic
547C22×Q8C2412yes—
548C22×Q8C2411yescharacteristic
549C22×Q8C2414yes—
550C22×D4—24no—
551C22×D4—24no—
552C22×D4—24no—
553C22×D4C2412yes—
554C22×D4C2412yes—
555C22×D4C2412yes—
556C22×D4C2411yescharacteristic
557C22×D4C2412yes—
558C22×D4C2412yes—
559C22×D4C2411yescharacteristic
560C22×D4C2411yescharacteristic
561C22×D4C2414yes—
562C22×D4C2414yes—
563C22×D4C2418yes—
564C22×D4C2418yes—
565C22×D4C2414yes—
566C22×D4C2414yes—
567C22×D4C2414yes—
568C23×C4C2412yes—
569C23×C4C2412yes—
570C23×C4C2412yes—
571C23×C4C2412yes—
572C23×C4C2412yes—
573C23×C4C2412yes—
574C23×C4C2411yescharacteristic
575C23×C4C2412yes—
576C23×C4C2412yes—
577C23×C4C2411yescharacteristic
578C23×C4C2414yes—
579C23×C4C2418yes—
580C23×C4C2414yes—
581C23×C4C2414yes—
582C23×C4C2411yescharacteristic
583C4⋊Q8—44no—
584C4⋊Q8—44no—
585C4⋊Q8—48no—
586C4⋊Q8—42no—
587C4⋊Q8—44no—
588C4⋊Q8—44no—
589C4⋊Q8—44no—
590C4⋊Q8—44no—
591#127—42no—
592#127—44no—
593#127—44no—
594#127—44no—
595#126—48no—
596#124—48no—
597#124—48no—
598#124—48no—
599#124—44no—
600#124—44no—
601#124—42no—
602#124—42no—
603#124—44no—
604#124—44no—
605#124—44no—
606#124—44no—
607#124—44no—
608#124—44no—
609#124—44no—
610#123—416no—
611#123—48no—
612#123—48no—
613#123—48no—
614#123—48no—
615#123—48no—
616C22⋊Q8—48no—
617C22⋊Q8—48no—
618C22⋊Q8—48no—
619C22⋊Q8—44no—
620C22⋊Q8—44no—
621C22⋊Q8—44no—
622C22⋊Q8—44no—
623#121—416no—
624#121—48no—
625#121—44no—
626#121—44no—
627#121—48no—
628#121—44no—
629#121—44no—
630#121—48no—
631#121—48no—
632#120—48no—
633#120—48no—
634#120—48no—
635C4×Q8—48no—
636C4×Q8—48no—
637C4×Q8—44no—
638C4×D4—44no—
639C4×D4—48no—
640C4×D4—48no—
641C4×D4—48no—
642C4×D4—48no—
643#117—24no—
644#117—24no—
645#117—24no—
646#117—24no—
647#117—24no—
648#117—44no—
649C2×C4⋊C4—24no—
650C2×C4⋊C4—44no—
651C2×C4⋊C4—44no—
652C2×C4⋊C4—48no—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2418yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C2418yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2418yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2418yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C22⋊C4—48no—
685C2×C22⋊C4—48no—
686C2×C22⋊C4—44no—
687C2×C22⋊C4—44no—
688C2×C22⋊C4—48no—
689C2×C22⋊C4C2412yes—
690C2×C22⋊C4C2412yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2412yes—
693C2×C22⋊C4C2412yes—
694C2×C22⋊C4C2412yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2418yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2418yes—
713C2×C22⋊C4C2418yes—
714C2×C22⋊C4C2418yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2418yes—
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×C42—24no—
729C2×C42—24no—
730C2×C42—24no—
731C2×C42—44no—
732C2×C42—44no—
733C2×C42C2412yes—
734C2×C42C2411yescharacteristic
735C2×C42C2412yes—
736C2×C42C2412yes—
737C2×C42C2412yes—
738C2×C42C2412yes—
739C2×C42C2412yes—
740C2×C42C2412yes—
741C2×C42C2412yes—
742C2×C42C2412yes—
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2414yes—
747C2×C42C2418yes—
748C2×C42C2414yes—
749C2×C42C2414yes—
750#95C2412yes—
751#95C2412yes—
752#95C2412yes—
753#95C2412yes—
754#95C2418yes—
755#95C2418yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2418yes—
777#95C2418yes—
778#95C2418yes—
779#95C2418yes—
780#95C2418yes—
781#95C2418yes—
782#95C2418yes—
783#95C2418yes—
784#95C2418yes—
785C24—24no—
786C24—24no—
787C24—24no—
788C24—44no—
789C24—44no—
790C24C2514yes—
791C24C2512yes—
792C24C2512yes—
793C24C2512yes—
794C24C2511yescharacteristic
795#41—464no—
796#41—432no—
797#41—432no—
798#41—416no—
799#41—416no—
800#41—416no—
801C2×Q8—24no—
802C2×Q8—24no—
803C2×Q8—22no—
804C2×Q8—22no—
805C2×Q8—24no—
806C2×Q8—24no—
807C2×Q8—24no—
808C2×Q8—22no—
809C2×Q8—24no—
810C2×Q8—24no—
811C2×Q8—24no—
812C2×Q8—24no—
813C2×Q8—22no—
814C2×Q8—22no—
815C2×Q8—24no—
816C2×Q8—22no—
817C2×Q8—22no—
818C2×Q8—24no—
819C2×Q8—24no—
820C2×Q8—22no—
821C2×Q8—22no—
822C2×Q8—44no—
823C2×Q8—44no—
824C2×Q8—44no—
825C2×Q8—432no—
826C2×Q8—432no—
827C2×Q8—416no—
828C2×Q8—416no—
829C2×D4—24no—
830C2×D4—24no—
831C2×D4—24no—
832C2×D4—24no—
833C2×D4—24no—
834C2×D4—24no—
835C2×D4—24no—
836C2×D4—24no—
837C2×D4—24no—
838C2×D4—24no—
839C2×D4—24no—
840C2×D4—22no—
841C2×D4—24no—
842C2×D4—24no—
843C2×D4—22no—
844C2×D4—22no—
845C2×D4—22no—
846C2×D4—24no—
847C2×D4—24no—
848C2×D4—22no—
849C2×D4—22no—
850C2×D4—22no—
851C2×D4—22no—
852C2×D4—22no—
853C2×D4—44no—
854C2×D4—44no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—44no—
858C2×D4—44no—
859C2×D4—48no—
860C2×D4—44no—
861C2×D4—44no—
862C2×D4—48no—
863C2×D4—44no—
864C2×D4—48no—
865C2×D4—48no—
866C2×D4—48no—
867C2×D4—48no—
868C2×D4—48no—
869C2×D4—48no—
870C2×D4—48no—
871C2×D4—416no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—24no—
875C22×C4—24no—
876C22×C4—24no—
877C22×C4—24no—
878C22×C4—24no—
879C22×C4—24no—
880C22×C4—24no—
881C22×C4—24no—
882C22×C4—24no—
883C22×C4—24no—
884C22×C4—24no—
885C22×C4—24no—
886C22×C4—24no—
887C22×C4—24no—
888C22×C4—24no—
889C22×C4—24no—
890C22×C4—24no—
891C22×C4—24no—
892C22×C4—24no—
893C22×C4—28no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—44no—
898C22×C4—44no—
899C22×C4—44no—
900C22×C4—44no—
901C22×C4—44no—
902C22×C4—44no—
903C22×C4—44no—
904C22×C4—44no—
905C22×C4—42no—
906C22×C4—44no—
907C22×C4—42no—
908C22×C4—48no—
909C22×C4—48no—
910C22×C4—48no—
911C22×C4H(5,𝔽2)14yes—
912C22×C4H(5,𝔽2)14yes—
913C22×C4H(5,𝔽2)14yes—
914C22×C4C2512yes—
915C22×C4C2512yes—
916C22×C4C2514yes—
917C22×C4C2512yes—
918C22×C4C2514yes—
919C22×C4C2514yes—
920C22×C4C2514yes—
921C22×C4C2512yes—
922C22×C4C2512yes—
923C22×C4C2514yes—
924C22×C4C2512yes—
925C22×C4C2512yes—
926C22×C4C2512yes—
927C22×C4C2514yes—
928C22×C4C2512yes—
929C22×C4C2514yes—
930C22×C4C2512yes—
931C22×C4C2512yes—
932C22×C4C2511yescharacteristic
933C22×C4C2511yescharacteristic
934C4⋊C4—24no—
935C4⋊C4—24no—
936C4⋊C4—24no—
937C4⋊C4—24no—
938C4⋊C4—24no—
939C4⋊C4—22no—
940C4⋊C4—24no—
941C4⋊C4—22no—
942C4⋊C4—24no—
943C4⋊C4—24no—
944C4⋊C4—28no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—48no—
948C4⋊C4—48no—
949C4⋊C4—48no—
950C4⋊C4—44no—
951C4⋊C4—44no—
952C4⋊C4—44no—
953C4⋊C4—44no—
954C4⋊C4—44no—
955C4⋊C4—48no—
956C4⋊C4—44no—
957C4⋊C4—48no—
958C4⋊C4—48no—
959C4⋊C4—44no—
960C4⋊C4—44no—
961C4⋊C4—48no—
962C4⋊C4—48no—
963C4⋊C4—44no—
964C4⋊C4—44no—
965C22⋊C4—24no—
966C22⋊C4—24no—
967C22⋊C4—24no—
968C22⋊C4—24no—
969C22⋊C4—24no—
970C22⋊C4—216no—
971C22⋊C4—28no—
972C22⋊C4—28no—
973C22⋊C4—48no—
974C22⋊C4—48no—
975C22⋊C4—48no—
976C22⋊C4—48no—
977C22⋊C4—48no—
978C22⋊C4—48no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—48no—
989C22⋊C4—44no—
990C22⋊C4—44no—
991C22⋊C4—48no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—48no—
995C22⋊C4—48no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—48no—
999C22⋊C4—48no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C42—22no—
1005C42—22no—
1006C42—24no—
1007C42—24no—
1008C42—24no—
1009C42—24no—
1010C42—22no—
1011C42—22no—
1012C42—24no—
1013C42—24no—
1014C42—24no—
1015C42—24no—
1016C42—24no—
1017C42—44no—
1018C42—48no—
1019C42—44no—
1020C42—44no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—24no—
1025C23—24no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—24no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—24no—
1036C23—24no—
1037C23—28no—
1038C23—24no—
1039C23—24no—
1040C23—24no—
1041C23—24no—
1042C23—28no—
1043C23—48no—
1044C23—84no—
1045C23—84no—
1046C23—88no—
1047C23—88no—
1048C23C2×H(5,𝔽2)12yes—
1049C23C2×H(5,𝔽2)12yes—
1050C23C2×H(5,𝔽2)12yes—
1051C23C2611yescharacteristic
1052Q8—416no—
1053Q8—48no—
1054Q8—48no—
1055Q8—48no—
1056Q8—44no—
1057Q8—48no—
1058Q8—44no—
1059Q8—44no—
1060D4—416no—
1061D4—48no—
1062D4—48no—
1063D4—48no—
1064D4—48no—
1065D4—48no—
1066D4—44no—
1067D4—44no—
1068D4—44no—
1069D4—88no—
1070D4—164no—
1071D4—164no—
1072D4—164no—
1073D4—168no—
1074D4—168no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—22no—
1090C2×C4—24no—
1091C2×C4—22no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—24no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—24no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—28no—
1108C2×C4—24no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—24no—
1112C2×C4—22no—
1113C2×C4—24no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—24no—
1122C2×C4—22no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—48no—
1126C2×C4—44no—
1127C2×C4—44no—
1128C2×C4—416no—
1129C2×C4—416no—
1130C2×C4—48no—
1131C2×C4—48no—
1132C2×C4—48no—
1133C2×C4—48no—
1134C2×C4—48no—
1135C2×C4—88no—
1136C2×C4—84no—
1137C2×C4—84no—
1138C2×C4—168no—
1139C2×C4#560116yes—
1140C2×C4C2×H(5,𝔽2)12yes—
1141C2×C4C2×H(5,𝔽2)12yes—
1142C2×C4C2×H(5,𝔽2)12yes—
1143C2×C4C2×H(5,𝔽2)12yes—
1144C2×C4C2×H(5,𝔽2)12yes—
1145C2×C4C2×H(5,𝔽2)12yes—
1146C2×C4#58514yes—
1147C22—22no—
1148C22—22no—
1149C22—24no—
1150C22—24no—
1151C22—42no—
1152C22—42no—
1153C22—44no—
1154C22—42no—
1155C22—42no—
1156C22—44no—
1157C22—42no—
1158C22—42no—
1159C22—48no—
1160C22—44no—
1161C22—44no—
1162C22—44no—
1163C22—42no—
1164C22—42no—
1165C22—42no—
1166C22—44no—
1167C22—44no—
1168C22—44no—
1169C22—44no—
1170C22—48no—
1171C22—168no—
1172C22C2×#56014yes—
1173C22C22×H(5,𝔽2)11yescharacteristic
1174C22C22×H(5,𝔽2)11yescharacteristic
1175C22C22×H(5,𝔽2)11yescharacteristic
1176C22C2×#58512yes—
1177C222−1+612yes—
1178C4—24no—
1179C4—42no—
1180C4—44no—
1181C4—42no—
1182C4—42no—
1183C4—42no—
1184C4—44no—
1185C4—44no—
1186C4—44no—
1187C4—42no—
1188C4—42no—
1189C4—44no—
1190C4—42no—
1191C4—44no—
1192C4—42no—
1193C4—42no—
1194C4—42no—
1195C4—44no—
1196C4C2×#56014yes—
1197C4C2×#56014yes—
1198C2—24no—
1199C2—82no—
1200C2—82no—
1201C2—82no—
1202C2—84no—
1203C2C22×#56011yescharacteristic
1204C2#6283611yescharacteristic
1205C2#6288711yescharacteristic
1206C2#6293112yes—
1207C2#6295412yes—
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. #53073C2semidirect
3. #53041C2semidirect
4. #53022C2semidirect
5. #52375C2semidirect
6. #46063C2semidirect
7. #46048C2semidirect
8. #45669C2semidirect
9. #45556C2semidirect
10. #45522C2semidirect
11. #35676C2semidirect
12. #35666C2semidirect
13. #35660C2semidirect
14. #35617C2semidirect
15. #35617C2semidirect
16. #35541C2semidirect
17. #35329C2semidirect
18. #35316C2semidirect
19. #35313C2semidirect
20. #35256C2semidirect
21. #35182C2semidirect
22. #35153C2semidirect
23. C2×#2545C2semidirect
24. #34816C2semidirect
25. #34744C2semidirect
42. #2863C22semidirect
45. #2857C22semidirect
50. #2841C22semidirect
51. #2838C22semidirect
52. #2838C22semidirect
53. #2830C22semidirect
54. #2829C22semidirect
55. #2828C22semidirect
56. #2827C22semidirect
57. #2826C22semidirect
58. #2825C22semidirect
59. #2813C22semidirect
60. #2803C22semidirect
61. #2797C22semidirect
62. #2796C22semidirect
63. #2784C22semidirect
64. #2780C22semidirect
65. #2778C22semidirect
66. #2778C22semidirect
67. #2757C22semidirect
68. #2757C22semidirect
69. #2756C22semidirect
70. #2749C22semidirect
71. #2748C22semidirect
72. #2746C22semidirect
73. #2742C22semidirect
74. #2737C22semidirect
75. #2737C22semidirect
76. #2705C22semidirect
77. #2703C22semidirect
78. #2693C22semidirect
79. #2691C22semidirect
82. #2645C22semidirect
84. #2621C22semidirect
90. #2547C22semidirect
91. #2546C22semidirect
101. #2514C22semidirect
102. #2514C22semidirect
103. #2513C22semidirect
104. #2512C22semidirect
105. #2511C22semidirect
106. #2511C22semidirect
111. #2448C22semidirect
112. #2448C22semidirect
114. #2447C22semidirect
115. #2446C22semidirect
116. #2446C22semidirect
118. #2445C22semidirect
123. #2436C22semidirect
124. #2434C22semidirect
125. #2434C22semidirect
126. #2434C22semidirect
127. #2434C22semidirect
128. #2432C22semidirect
129. #2432C22semidirect
130. #2432C22semidirect
131. #2432C22semidirect
134. #2431C22semidirect
136. #2429C22semidirect
137. #2429C22semidirect
144. #2426C22semidirect
145. #2426C22semidirect
147. #2423C22semidirect
149. #2421C22semidirect
155. #2409C22semidirect
156. #2407C22semidirect
160. #2401C22semidirect
161. #2395C22semidirect
163. #2377C22semidirect
164. #2376C22semidirect
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
#530732
#530412
#530222
#523752
#460632
#460482
#456692
#455562
#455222
#356762
#356662
#356602
#356172
#355412
#353292
#353162
#353132
#352562
#351822
#351532
C2×#25452
#348162
#347442