Finite Group Databasebeta

← #8425073

Subgroups — #8425073

Order 512.

5694 conjugacy classes of subgroups.

The subgroup lattice has 1086 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59419C211yesmaximal, characteristic, complemented
2#59313C211yesmaximal, characteristic, complemented
3#59248C211yesmaximal, characteristic, complemented
4#59051C214yesmaximal, complemented
5#58887C214yesmaximal, complemented
6#58801C214yesmaximal, complemented
7#53059C214yesmaximal, complemented
8#52966C214yesmaximal, complemented
9#52420C214yesmaximal, complemented
10#42618C214yesmaximal, complemented
11#42421C214yesmaximal, complemented
12#40605C214yesmaximal, complemented
13#39341C212yesmaximal, complemented
14#39138C212yesmaximal, complemented
15#39004C214yesmaximal, complemented
16#37780C214yesmaximal, complemented
17#37639C211yesmaximal, characteristic, complemented
18#37620C211yesmaximal, characteristic, complemented
19#37515C214yesmaximal, complemented
20#36453C212yesmaximal, complemented
21#36182C211yesmaximal, characteristic, complemented
22#34925C211yesmaximal, characteristic, complemented
23#34889C212yesmaximal, complemented
24C2×#553C2212yes—
25C2×#550C2212yes—
26C2×#550C2214yes—
27C2×#547C2214yes—
28C2×#537C2214yes—
29C2×#532C2212yes—
30C2×#532C2214yes—
31C2×#529C2212yes—
32#2859C2211yescharacteristic
33#2856C2211yescharacteristic
34#2856C2211yescharacteristic
35#2855C2214yes—
36#2830C2218yes—
37#2825C2218yes—
38#2825C2218yes—
39#2825C2218yes—
40#2823C2214yes—
41#2819C2214yes—
42#2818C2214yes—
43#2815C2214yes—
44#2813C2218yes—
45#2789C2214yes—
46#2765C2218yes—
47#2760C2218yes—
48#2749C2218yes—
49#2714C2218yes—
50#2700C2218yes—
51#2699C2214yes—
52#2699C2218yes—
53#2696C2218yes—
54#2692C2218yes—
55#2691C2218yes—
56#2688C2218yes—
57#2680C2214yes—
58#2676C2218yes—
59#2676C2218yes—
60#2675C2218yes—
61#2673C2218yes—
62#2673C2218yes—
63#2673C2218yes—
64#2673C2218yes—
65#2661C2218yes—
66#2661C2214yes—
67#2653C2218yes—
68#2653C2218yes—
69#2637C2214yes—
70#2629C2214yes—
71#2620C2214yes—
72#2619C2214yes—
73#2619C2214yes—
74#2618C2214yes—
75#2615C2214yes—
76#2615C2214yes—
77#2615C2214yes—
78#2615C2214yes—
79#2599C2214yes—
80#2582C2211yescharacteristic
81#2576C2218yes—
82#2566C2212yes—
83#2563C2214yes—
84#2559C2214yes—
85#2557C2214yes—
86#2555C2214yes—
87#2551C2211yescharacteristic
88#2550C2212yes—
89#2544C2212yes—
90#2543C2214yes—
91#2541C2214yes—
92#2541C2214yes—
93#2541C2212yes—
94#2541C2214yes—
95#2541C2214yes—
96#2540C2212yes—
97#2538C2212yes—
98#2537C2211yescharacteristic
99#2537C2212yes—
100#2537C2211yescharacteristic
101#2535C2212yes—
102#2535C2214yes—
103#2521C2214yes—
104#2514C2214yes—
105#2512C2214yes—
106#2504C2212yes—
107#2500C2212yes—
108#2494C2214yes—
109#2494C2214yes—
110#2494C2214yes—
111#2492C2212yes—
112#2492C2214yes—
113#2491C2214yes—
114#2490C2212yes—
115#2490C2214yes—
116#2486C2214yes—
117#2464C2214yes—
118#2460C2218yes—
119#2456C2218yes—
120#2456C2218yes—
121#2456C2218yes—
122#2452C2214yes—
123#2450C2218yes—
124#2440C2214yes—
125#2431C2214yes—
126#2431C2214yes—
127#2431C2218yes—
128#2430C2214yes—
129#2428C2214yes—
130#2428C2214yes—
131#2428C2212yes—
132#2428C2214yes—
133#2428C2214yes—
134#2427C2214yes—
135#2427C2212yes—
136#2426C2218yes—
137#2422C2214yes—
138#2422C2214yes—
139#2420C2214yes—
140#2420C2214yes—
141#2417C2214yes—
142#2416C2214yes—
143#2416C2214yes—
144#2416C2214yes—
145#2407C2214yes—
146#2407C2214yes—
147#2407C2218yes—
148#2406C2214yes—
149#2395C2214yes—
150#2388C2214yes—
151#2388C2214yes—
152#2365C2214yes—
153#2361C2214yes—
154#2361C2214yes—
155#2355C2212yes—
156D4×C4⋊C4C2212yes—
157#2345C2214yes—
158#2339C2214yes—
159#2324C2214yes—
160#2318C2214yes—
161C4×#127C2211yescharacteristic
162C4×#124C2212yes—
163C4×C22⋊Q8C2212yes—
164C4×#121C2214yes—
165C4×#121C2212yes—
166C4×#121C2214yes—
167C4×#121C2214yes—
168#2297C2214yes—
169#2285C2211yescharacteristic
170C2×#384C2211yescharacteristic
171C42×D4C2211yescharacteristic
172C42×D4C2212yes—
173C22×#41C2314yes—
174C22×#41C2314yes—
175C22×#41C2314yes—
176C22×#41C2314yes—
177#553—48no—
178#550—48no—
179#550—416no—
180#547—416no—
181#537—416no—
182#532—48no—
183#532—416no—
184C2×C4⋊Q8C2314yes—
185C2×C4⋊Q8C2312yes—
186C2×#127C2311yescharacteristic
187C2×#127C2314yes—
188C2×#127C2314yes—
189C2×#127C2318yes—
190C2×#127C2314yes—
191C2×#127C2312yes—
192#529—48no—
193C2×#126C2314yes—
194C2×#126C2314yes—
195C2×#125C2312yes—
196C2×#125C2312yes—
197C2×#124C2314yes—
198C2×#124C2312yes—
199C2×#124C2318yes—
200C2×#124C2312yes—
201C2×#123C2314yes—
202C2×#123C2318yes—
203C2×#123C2314yes—
204C2×#123C2318yes—
205C2×C22⋊Q8C2312yes—
206C2×C22⋊Q8C2314yes—
207C2×C22⋊Q8C2312yes—
208C2×C22⋊Q8C2318yes—
209C2×C22⋊Q8C2318yes—
210C2×#121C2314yes—
211C2×#121C2312yes—
212C2×#121C2314yes—
213C2×#121C2314yes—
214C2×#121C2314yes—
215C2×#121C2312yes—
216C2×#121C2312yes—
217C2×#121C2312yes—
218C2×#121C2312yes—
219C2×#121C2314yes—
220C2×#121C2314yes—
221C2×#121C2314yes—
222C2×#121C2314yes—
223C2×#121C2318yes—
224C2×#121C2314yes—
225C2×#121C2314yes—
226C2×#121C2314yes—
227C2×#121C2314yes—
228C2×#121C2314yes—
229C2×#121C2314yes—
230C2×#121C2318yes—
231C2×#121C2312yes—
232C2×#121C2318yes—
233C2×#121C2318yes—
234C2×#121C2318yes—
235C2×#121C2318yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2314yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2312yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2312yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2318yes—
249C2×C4×D4C2312yes—
250C2×C4×D4C2314yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2318yes—
253C2×C4×D4C2312yes—
254C2×#117C2314yes—
255C2×#117C2312yes—
256C22×C4⋊C4C2314yes—
257C22×C4⋊C4C2314yes—
258C22×C4⋊C4C2312yes—
259C22×C42C2311yescharacteristic
260C22×C42C2311yescharacteristic
261C22×C42C2314yes—
262#401C2318yes—
263#401C2318yes—
264#400C2314yes—
265#400C2318yes—
266#399C2314yes—
267#398C2314yes—
268#398C2318yes—
269#398C2318yes—
270#398C2314yes—
271#398C2314yes—
272#397C2314yes—
273#397C2314yes—
274#397C2314yes—
275#397C2318yes—
276#397C2318yes—
277#397C2318yes—
278#397C2318yes—
279#397C2318yes—
280#397C2314yes—
281#397C2314yes—
282#396C2318yes—
283#396C2318yes—
284#396C2318yes—
285#396C2318yes—
286#396C2318yes—
287#396C2318yes—
288#395C2314yes—
289#395C2314yes—
290#395C2314yes—
291#394C2314yes—
292#394C2314yes—
293#394C2318yes—
294#394C2314yes—
295#394C2314yes—
296#394C2318yes—
297#394C2314yes—
298#394C2318yes—
299#394C2314yes—
300#394C2314yes—
301#394C2318yes—
302#394C2318yes—
303#394C2318yes—
304#394C2318yes—
305#394C2318yes—
306#394C2318yes—
307#394C2318yes—
308#394C2314yes—
309#394C2314yes—
310#393C2318yes—
311#393C2318yes—
312#393C2318yes—
313#393C2314yes—
314#393C2314yes—
315#393C2314yes—
316#392C2314yes—
317#392C2318yes—
318#392C2314yes—
319#392C2318yes—
320#392C2318yes—
321#392C2318yes—
322#392C2318yes—
323#392C2318yes—
324#392C2318yes—
325#392C2318yes—
326#392C2318yes—
327#392C2318yes—
328#392C2314yes—
329#392C2314yes—
330#392C2314yes—
331#392C2318yes—
332#392C2314yes—
333#392C2314yes—
334#392C2318yes—
335#392C2318yes—
336#392C2318yes—
337#391C2314yes—
338#391C2312yes—
339#391C2314yes—
340#391C2318yes—
341#391C2314yes—
342#391C2314yes—
343#391C2312yes—
344#390C2314yes—
345#390C2312yes—
346#390C2318yes—
347#390C2312yes—
348#390C2312yes—
349#390C2318yes—
350#390C2314yes—
351#390C2314yes—
352#390C2314yes—
353#390C2312yes—
354#390C2314yes—
355#390C2314yes—
356#390C2318yes—
357#390C2314yes—
358#390C2312yes—
359#390C2314yes—
360#389C2312yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2312yes—
367#389C2314yes—
368#389C2314yes—
369#388C2314yes—
370#388C2314yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2314yes—
376#388C2318yes—
377#388C2318yes—
378#388C2314yes—
379#388C2314yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2314yes—
387#386C2318yes—
388#386C2318yes—
389#386C2314yes—
390#386C2314yes—
391#386C2318yes—
392#386C2318yes—
393#386C2318yes—
394#386C2318yes—
395#386C2318yes—
396#386C2318yes—
397#386C2318yes—
398#386C2318yes—
399#386C2318yes—
400#386C2318yes—
401#386C2318yes—
402#386C2314yes—
403#386C2314yes—
404#386C2314yes—
405#386C2314yes—
406#386C2314yes—
407#385C2318yes—
408#385C2318yes—
409#385C2318yes—
410#385C2318yes—
411#385C2314yes—
412#385C2318yes—
413#385C2318yes—
414#384C2311yescharacteristic
415#384C2312yes—
416#384C2311yescharacteristic
417#384C2311yescharacteristic
418#384C2314yes—
419#383C2314yes—
420#382C2314yes—
421#382C2312yes—
422#382C2312yes—
423#382C2314yes—
424#382C2312yes—
425#381C2314yes—
426#381C2318yes—
427#381C2318yes—
428#380C2314yes—
429#380C2314yes—
430#380C2314yes—
431#380C2314yes—
432#380C2314yes—
433#380C2318yes—
434#380C2314yes—
435#380C2314yes—
436#380C2312yes—
437#380C2314yes—
438#380C2314yes—
439#380C2312yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2312yes—
448C4×C4⋊C4C2312yes—
449C4×C22⋊C4C2314yes—
450C4×C22⋊C4C2314yes—
451C4×C22⋊C4C2318yes—
452C4×C22⋊C4C2314yes—
453C4×C22⋊C4C2314yes—
454C4×C22⋊C4C2312yes—
455C4×C22⋊C4C2314yes—
456C4×C22⋊C4C2314yes—
457C4×C22⋊C4C2314yes—
458C4×C22⋊C4C2314yes—
459C4×C22⋊C4C2312yes—
460C4×C22⋊C4C2311yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
462C2×#95C2314yes—
463C43C2311yescharacteristic
464C2×#41—48no—
465C2×#41—48no—
466C2×#41—48no—
467C2×#41—48no—
468C2×#41—48no—
469C2×#41—416no—
470C2×#41—48no—
471C2×#41—416no—
472C2×#41—48no—
473C2×#41—48no—
474C22×Q8C2412yes—
475C22×Q8C2414yes—
476C22×Q8C2414yes—
477C22×D4C2412yes—
478C22×D4C2412yes—
479C22×D4C2414yes—
480C22×D4C2414yes—
481C22×D4C2411yescharacteristic
482C22×D4C2412yes—
483C22×D4C2414yes—
484C22×D4C2414yes—
485C22×D4C2414yes—
486C22×D4C2418yes—
487C22×D4C2418yes—
488C22×D4C2418yes—
489C22×D4C2414yes—
490C22×D4C2414yes—
491C22×D4C2418yes—
492C22×D4C2414yes—
493C22×D4C2414yes—
494C22×D4C2414yes—
495C22×D4C2418yes—
496C22×D4C2414yes—
497C23×C4C2412yes—
498C23×C4C2414yes—
499C23×C4C2414yes—
500C23×C4C2412yes—
501C23×C4C2411yescharacteristic
502C23×C4C2411yescharacteristic
503C23×C4C2414yes—
504C23×C4C2414yes—
505C23×C4C2418yes—
506C23×C4C2414yes—
507C23×C4C2418yes—
508C23×C4C2414yes—
509C4⋊Q8—216no—
510C4⋊Q8—44no—
511#127—24no—
512#127—44no—
513#127—48no—
514#127—48no—
515#127—48no—
516#127—416no—
517#126—48no—
518#126—48no—
519#125—44no—
520#125—44no—
521#124—48no—
522#124—44no—
523#124—44no—
524#124—416no—
525#123—48no—
526#123—416no—
527#123—48no—
528#123—416no—
529C22⋊Q8—28no—
530C22⋊Q8—416no—
531C22⋊Q8—416no—
532C22⋊Q8—44no—
533C22⋊Q8—48no—
534#121—216no—
535#121—28no—
536#121—216no—
537#121—48no—
538#121—416no—
539#121—48no—
540#121—44no—
541#121—416no—
542#121—416no—
543#121—416no—
544#121—416no—
545#121—48no—
546#121—48no—
547#121—48no—
548#121—48no—
549#121—44no—
550#121—48no—
551#121—44no—
552#121—44no—
553#121—48no—
554#121—416no—
555#121—48no—
556#121—48no—
557#121—48no—
558#121—48no—
559#121—44no—
560C4×Q8—28no—
561C4×Q8—48no—
562C4×D4—28no—
563C4×D4—216no—
564C4×D4—24no—
565C4×D4—28no—
566C4×D4—28no—
567C4×D4—44no—
568C4×D4—48no—
569C4×D4—48no—
570C4×D4—48no—
571C4×D4—44no—
572C4×D4—48no—
573C4×D4—48no—
574C4×D4—48no—
575C4×D4—44no—
576C4×D4—416no—
577C4×D4—416no—
578#117—48no—
579#117—44no—
580C2×C4⋊C4—216no—
581C2×C4⋊C4—48no—
582C2×C4⋊C4—44no—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2418yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2418yes—
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2412yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2411yescharacteristic
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2412yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2411yescharacteristic
653C2×C42—24no—
654C2×C42—24no—
655C2×C42—48no—
656C2×C42C2412yes—
657C2×C42C2414yes—
658C2×C42C2414yes—
659C2×C42C2411yescharacteristic
660C2×C42C2412yes—
661C2×C42C2412yes—
662C2×C42C2414yes—
663C2×C42C2412yes—
664C2×C42C2411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2414yes—
667C2×C42C2418yes—
668C2×C42C2414yes—
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671#95C2414yes—
672#95C2414yes—
673#95C2414yes—
674#95C2412yes—
675#95C2414yes—
676#95C2414yes—
677#95C2412yes—
678#95C2414yes—
679#95C2412yes—
680#95C2414yes—
681#95C2414yes—
682#95C2418yes—
683#95C2414yes—
684#95C2414yes—
685#95C2418yes—
686#95C2414yes—
687#95C2414yes—
688#95C2414yes—
689#95C2414yes—
690#95C2414yes—
691#95C2418yes—
692#95C2418yes—
693#95C2414yes—
694#95C2418yes—
695#95C2414yes—
696#95C2418yes—
697#95C2418yes—
698#95C2418yes—
699#95C2418yes—
700C24C2511yescharacteristic
701C24C2514yes—
702C24C2514yes—
703C24C2514yes—
704C24C2511yescharacteristic
705#41—832no—
706#41—832no—
707#41—832no—
708#41—832no—
709C2×Q8—24no—
710C2×Q8—24no—
711C2×Q8—216no—
712C2×Q8—24no—
713C2×Q8—44no—
714C2×Q8—44no—
715C2×Q8—44no—
716C2×Q8—44no—
717C2×D4—22no—
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—24no—
722C2×D4—24no—
723C2×D4—24no—
724C2×D4—24no—
725C2×D4—28no—
726C2×D4—28no—
727C2×D4—28no—
728C2×D4—216no—
729C2×D4—28no—
730C2×D4—24no—
731C2×D4—24no—
732C2×D4—24no—
733C2×D4—28no—
734C2×D4—42no—
735C2×D4—44no—
736C2×D4—42no—
737C2×D4—44no—
738C2×D4—44no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—48no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—48no—
748C2×D4—48no—
749C2×D4—48no—
750C2×D4—48no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—48no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—48no—
758C2×D4—44no—
759C2×D4—42no—
760C2×D4—44no—
761C2×D4—48no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—48no—
766C2×D4—44no—
767C2×D4—48no—
768C2×D4—44no—
769C2×D4—48no—
770C2×D4—48no—
771C2×D4—48no—
772C22×C4—22no—
773C22×C4—28no—
774C22×C4—24no—
775C22×C4—22no—
776C22×C4—24no—
777C22×C4—22no—
778C22×C4—28no—
779C22×C4—28no—
780C22×C4—24no—
781C22×C4—22no—
782C22×C4—28no—
783C22×C4—28no—
784C22×C4—28no—
785C22×C4—28no—
786C22×C4—24no—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—28no—
790C22×C4—28no—
791C22×C4—216no—
792C22×C4—28no—
793C22×C4—44no—
794C22×C4—41no—
795C22×C4—41no—
796C22×C4—44no—
797C22×C4—48no—
798C22×C4—48no—
799C22×C4—48no—
800C22×C4—48no—
801C22×C4—48no—
802C22×C4—44no—
803C22×C4—48no—
804C22×C4—44no—
805C22×C4—48no—
806C22×C4C2514yes—
807C22×C4C2512yes—
808C22×C4C2514yes—
809C22×C4C2512yes—
810C22×C4C2514yes—
811C22×C4C2514yes—
812C22×C4C2514yes—
813C22×C4C2511yescharacteristic
814C22×C4C2514yes—
815C22×C4C2514yes—
816C22×C4C2511yescharacteristic
817C22×C4C2514yes—
818C22×C4C2512yes—
819C22×C4C2511yescharacteristic
820C22×C4C2511yescharacteristic
821C22×C4C2514yes—
822C22×C4C2511yescharacteristic
823C22×C4C2512yes—
824C4⋊C4—28no—
825C4⋊C4—216no—
826C4⋊C4—28no—
827C4⋊C4—24no—
828C4⋊C4—28no—
829C4⋊C4—24no—
830C4⋊C4—22no—
831C4⋊C4—216no—
832C4⋊C4—24no—
833C4⋊C4—28no—
834C4⋊C4—28no—
835C4⋊C4—28no—
836C4⋊C4—24no—
837C4⋊C4—28no—
838C4⋊C4—42no—
839C4⋊C4—42no—
840C4⋊C4—48no—
841C4⋊C4—44no—
842C4⋊C4—42no—
843C4⋊C4—44no—
844C4⋊C4—44no—
845C4⋊C4—42no—
846C4⋊C4—44no—
847C4⋊C4—44no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—48no—
851C4⋊C4—44no—
852C4⋊C4H(5,𝔽2)18yes—
853C22⋊C4—28no—
854C22⋊C4—28no—
855C22⋊C4—28no—
856C22⋊C4—28no—
857C22⋊C4—22no—
858C22⋊C4—28no—
859C22⋊C4—216no—
860C22⋊C4—28no—
861C22⋊C4—28no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—44no—
865C22⋊C4—44no—
866C22⋊C4—44no—
867C22⋊C4—44no—
868C22⋊C4—44no—
869C22⋊C4—42no—
870C22⋊C4—42no—
871C22⋊C4—48no—
872C22⋊C4—48no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—48no—
876C22⋊C4—48no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—48no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—48no—
884C22⋊C4—48no—
885C22⋊C4—48no—
886C22⋊C4—48no—
887C22⋊C4—48no—
888C22⋊C4—48no—
889C22⋊C4—48no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4H(5,𝔽2)14yes—
894C42—24no—
895C42—24no—
896C42—22no—
897C42—22no—
898C42—24no—
899C42—28no—
900C42—28no—
901C42—28no—
902C42—22no—
903C42—24no—
904C42—44no—
905C42—44no—
906C42—41no—
907C42—48no—
908C42H(5,𝔽2)14yes—
909C23—21no—
910C23—22no—
911C23—22no—
912C23—21no—
913C23—22no—
914C23—24no—
915C23—21no—
916C23—24no—
917C23—24no—
918C23—24no—
919C23—28no—
920C23—24no—
921C23—24no—
922C23—24no—
923C23—24no—
924C23—24no—
925C23—24no—
926C23—21no—
927C23—24no—
928C23—24no—
929C23—28no—
930C23—22no—
931C23—24no—
932C23—24no—
933C23—21no—
934C23—24no—
935C23—24no—
936C23—24no—
937C23C2×H(5,𝔽2)12yes—
938C23C2611yescharacteristic
939Q8—416no—
940Q8—48no—
941Q8—88no—
942D4—416no—
943D4—44no—
944D4—48no—
945D4—48no—
946D4—416no—
947D4—84no—
948D4—88no—
949D4—816no—
950D4—88no—
951D4—88no—
952D4—816no—
953D4—816no—
954D4—88no—
955D4—88no—
956D4—88no—
957D4—816no—
958D4—88no—
959D4—88no—
960D4—164no—
961D4—168no—
962C2×C4—21no—
963C2×C4—22no—
964C2×C4—24no—
965C2×C4—21no—
966C2×C4—24no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—22no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—21no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—22no—
982C2×C4—21no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—22no—
988C2×C4—28no—
989C2×C4—24no—
990C2×C4—28no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—28no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—21no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—44no—
1005C2×C4—416no—
1006C2×C4—44no—
1007C2×C4—48no—
1008C2×C4—416no—
1009C2×C4—416no—
1010C2×C4—48no—
1011C2×C4—88no—
1012C2×C4—816no—
1013C2×C4—88no—
1014C2×C4—88no—
1015C2×C4—816no—
1016C2×C4C2×H(5,𝔽2)12yes—
1017C2×C4C2×H(5,𝔽2)12yes—
1018C2×C4C2×H(5,𝔽2)12yes—
1019C2×C4C2×H(5,𝔽2)18yes—
1020C2×C4C2×H(5,𝔽2)14yes—
1021C2×C4C2×H(5,𝔽2)14yes—
1022C2×C4#58514yes—
1023C22—22no—
1024C22—22no—
1025C22—22no—
1026C22—42no—
1027C22—42no—
1028C22—42no—
1029C22—44no—
1030C22—44no—
1031C22—48no—
1032C22—44no—
1033C22—44no—
1034C22—44no—
1035C22—44no—
1036C22—44no—
1037C22—41no—
1038C22—41no—
1039C22—44no—
1040C22—44no—
1041C22—44no—
1042C22—41no—
1043C22—44no—
1044C22—44no—
1045C22—44no—
1046C22—44no—
1047C22—44no—
1048C22—48no—
1049C22—42no—
1050C22—44no—
1051C22—44no—
1052C22C22×H(5,𝔽2)11yescharacteristic
1053C22C22×H(5,𝔽2)12yes—
1054C22C22×H(5,𝔽2)11yescharacteristic
1055C22C2×#58512yes—
1056C222−1+611yescharacteristic
1057C4—22no—
1058C4—28no—
1059C4—22no—
1060C4—22no—
1061C4—42no—
1062C4—44no—
1063C4—42no—
1064C4—44no—
1065C4—44no—
1066C4—44no—
1067C4—44no—
1068C4—41no—
1069C4—44no—
1070C4—41no—
1071C4—44no—
1072C4—42no—
1073C4—44no—
1074C4#354618yes—
1075C2—42no—
1076C2—81no—
1077C2—84no—
1078C2—84no—
1079C2—84no—
1080C2C2×#354612yes—
1081C2#6275911yescharacteristic
1082C2#6291411yescharacteristic
1083C2#6292212yes—
1084C2#6301111yescharacteristic
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. #59419C2semidirect
2. #59313C2semidirect
3. #59248C2semidirect
4. #59051C2semidirect
5. #58887C2semidirect
6. #58801C2semidirect
7. #53059C2semidirect
8. #52966C2semidirect
9. #52420C2semidirect
10. #42618C2semidirect
11. #42421C2semidirect
12. #40605C2semidirect
13. #39341C2semidirect
14. #39138C2semidirect
15. #39004C2semidirect
16. #37780C2semidirect
17. #37639C2semidirect
18. #37620C2semidirect
19. #37515C2semidirect
20. #36453C2semidirect
21. #36182C2semidirect
22. #34925C2semidirect
23. #34889C2semidirect

Maximal subgroups

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

subgroupindex
#594192
#593132
#592482
#590512
#588872
#588012
#530592
#529662
#524202
#426182
#424212
#406052
#393412
#391382
#390042
#377802
#376392
#376202
#375152
#364532
#361822
#349252
#348892