Finite Group Databasebeta

← #8425531

Subgroups — #8425531

Order 512.

5816 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59822C211yesmaximal, characteristic, complemented
2#59313C211yesmaximal, characteristic, complemented
3#59233C211yesmaximal, characteristic, complemented
4#59203C214yesmaximal, complemented
5#58384C214yesmaximal, complemented
6#56605C214yesmaximal, complemented
7#53094C214yesmaximal, complemented
8#53055C214yesmaximal, complemented
9#52367C214yesmaximal, complemented
10#42923C214yesmaximal, complemented
11#42736C214yesmaximal, complemented
12#41935C214yesmaximal, complemented
13#39469C212yesmaximal, complemented
14#39339C214yesmaximal, complemented
15#39191C212yesmaximal, complemented
16#37839C214yesmaximal, complemented
17#37639C211yesmaximal, characteristic, complemented
18#37636C211yesmaximal, characteristic, complemented
19#37437C214yesmaximal, complemented
20#36181C211yesmaximal, characteristic, complemented
21#36160C212yesmaximal, complemented
22C2×#2537C211yesmaximal, characteristic, complemented
23#34681C212yesmaximal, complemented
24C2×#555C2212yescomplemented
25C2×#552C2212yes—
26C2×#547C2214yes—
27C2×#535C2214yes—
28C2×#532C2212yescomplemented
29C2×#525C2214yes—
30C22×#121C2214yes—
31C22×C4×D4C2212yes—
32#2859C2211yescharacteristic, complemented
33#2857C2211yescharacteristic
34#2857C2211yescharacteristic, complemented
35#2847C2214yes—
36#2832C2214yescomplemented
37#2832C2218yescomplemented
38#2828C2218yescomplemented
39#2824C2218yescomplemented
40#2820C2214yescomplemented
41#2819C2214yescomplemented
42#2818C2214yescomplemented
43#2816C2218yescomplemented
44#2815C2218yescomplemented
45#2785C2214yescomplemented
46#2753C2218yescomplemented
47#2753C2218yescomplemented
48#2744C2218yescomplemented
49#2737C2218yescomplemented
50#2733C2214yescomplemented
51#2714C2218yescomplemented
52#2712C2218yescomplemented
53#2711C2218yescomplemented
54#2711C2218yescomplemented
55#2706C2218yescomplemented
56#2703C2218yescomplemented
57#2696C2218yescomplemented
58#2692C2218yescomplemented
59#2680C2214yescomplemented
60#2676C2218yescomplemented
61#2676C2218yescomplemented
62#2676C2218yescomplemented
63#2673C2218yescomplemented
64#2673C2218yescomplemented
65#2662C2214yescomplemented
66#2661C2218yescomplemented
67#2661C2218yescomplemented
68#2641C2214yescomplemented
69#2632C2214yescomplemented
70#2628C2214yescomplemented
71#2624C2214yescomplemented
72#2624C2214yescomplemented
73#2619C2214yescomplemented
74#2615C2214yescomplemented
75#2615C2214yescomplemented
76#2615C2214yescomplemented
77#2613C2214yes—
78#2613C2218yes—
79#2610C2214yescomplemented
80#2574C2218yescomplemented
81#2565C2212yescomplemented
82#2563C2212yescomplemented
83#2563C2214yescomplemented
84#2563C2214yescomplemented
85#2561C2218yes—
86#2551C2211yescharacteristic, complemented
87#2548C2214yescomplemented
88#2541C2214yescomplemented
89#2541C2214yescomplemented
90#2539C2218yes—
91#2537C2211yescharacteristic
92#2537C2214yes—
93#2537C2212yes—
94#2537C2214yes—
95#2537C2211yescharacteristic
96#2537C2214yes—
97#2537C2212yescomplemented
98#2537C2211yescharacteristic, complemented
99#2535C2214yescomplemented
100#2531C2218yescomplemented
101#2506C2214yescomplemented
102#2503C2212yes—
103#2499C2212yescomplemented
104#2497C2214yescomplemented
105#2496C2214yescomplemented
106#2495C2214yescomplemented
107#2491C2214yescomplemented
108#2491C2214yescomplemented
109#2488C2218yes—
110#2487C2214yescomplemented
111#2486C2214yes—
112#2486C2214yes—
113#2485C2214yescomplemented
114#2485C2214yescomplemented
115#2485C2214yescomplemented
116#2472C2218yes—
117#2472C2214yes—
118#2464C2214yescomplemented
119#2461C2214yescomplemented
120#2459C2218yescomplemented
121#2452C2212yescomplemented
122#2445C2212yescomplemented
123#2440C2212yes—
124#2440C2214yescomplemented
125#2439C2214yescomplemented
126#2433C2212yes—
127#2430C2214yes—
128#2428C2214yescomplemented
129#2428C2214yescomplemented
130#2428C2212yescomplemented
131#2424C2214yes—
132#2422C2214yescomplemented
133#2422C2212yescomplemented
134#2420C2214yescomplemented
135#2416C2212yes—
136#2416C2214yescomplemented
137#2416C2214yescomplemented
138#2414C2214yescomplemented
139#2414C2214yescomplemented
140#2414C2214yescomplemented
141#2414C2214yescomplemented
142#2414C2214yescomplemented
143#2414C2214yescomplemented
144#2411C2218yes—
145#2408C2212yes—
146#2408C2214yes—
147#2406C2214yes—
148#2404C2218yes—
149#2392C2214yescomplemented
150#2388C2214yescomplemented
151C2×#394C2214yes—
152#2363C2214yescomplemented
153#2354C2212yescomplemented
154#2354C2214yescomplemented
155#2352C2214yes—
156D4×C4⋊C4C2212yescomplemented
157#2346C2214yescomplemented
158#2344C2214yes—
159#2343C2214yes—
160#2324C2214yescomplemented
161#2311C2214yescomplemented
162C4×C4⋊Q8C2211yescharacteristic, complemented
163C4×#127C2212yescomplemented
164C4×#121C2212yes—
165C4×#121C2212yescomplemented
166C4×#120C2214yes—
167#2293C2212yescomplemented
168#2285C2211yescharacteristic, complemented
169C2×#384C2211yescharacteristic
170#2280C2214yes—
171C2×#380C2214yes—
172C42×D4C2211yescharacteristic
173C22×#41C2314yes—
174C22×#41C2314yes—
175C23×D4C2312yes—
176C23×D4C2314yes—
177C24×C4C2314yes—
178#555—48no—
179#552—48no—
180#547—416no—
181#535—416no—
182#532—48no—
183C2×C4⋊Q8C2311yescharacteristic
184C2×C4⋊Q8C2312yes—
185C2×C4⋊Q8C2314yes—
186C2×#127C2312yes—
187C2×#127C2314yes—
188C2×#127C2314yes—
189C2×#127C2312yes—
190C2×#126C2314yes—
191C2×#125C2314yes—
192C2×#125C2312yes—
193C2×#124C2314yes—
194C2×#124C2314yes—
195C2×#124C2314yes—
196C2×#124C2318yes—
197#525—416no—
198C2×#123C2318yes—
199C2×#123C2314yes—
200C2×#123C2314yes—
201C2×#123C2314yes—
202C2×#123C2318yes—
203C2×C22⋊Q8C2314yes—
204C2×C22⋊Q8C2314yes—
205C2×C22⋊Q8C2312yes—
206C2×C22⋊Q8C2312yes—
207C2×C22⋊Q8C2318yes—
208C2×#121—416no—
209C2×#121C2312yes—
210C2×#121C2318yes—
211C2×#121C2314yes—
212C2×#121C2314yes—
213C2×#121C2312yes—
214C2×#121C2312yes—
215C2×#121C2312yes—
216C2×#121C2314yes—
217C2×#121C2314yes—
218C2×#121C2314yes—
219C2×#121C2314yes—
220C2×#121C2314yes—
221C2×#121C2314yes—
222C2×#121C2318yes—
223C2×#121C2314yes—
224C2×#121C2314yes—
225C2×#121C2314yes—
226C2×#121C2314yes—
227C2×#121C2318yes—
228C2×#121C2318yes—
229C2×#120C2314yes—
230C2×#120C2318yes—
231C2×#120C2314yes—
232C2×#120C2314yes—
233C2×C4×Q8C2312yes—
234C2×C4×D4—48no—
235C2×C4×D4C2312yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2314yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C2314yes—
250C2×#117C2314yes—
251C2×#117C2314yes—
252C2×#117C2314yes—
253C2×#117C2314yes—
254C2×#117C2314yes—
255C2×#117C2312yes—
256C22×C4⋊C4C2314yes—
257C22×C4⋊C4C2314yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2312yes—
260C22×C22⋊C4C2318yes—
261C22×C22⋊C4C2314yes—
262C22×C42C2311yescharacteristic
263C22×C42C2311yescharacteristic
264#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#399C2318yes—
268#399C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2314yes—
272#397C2318yes—
273#397C2318yes—
274#397C2318yes—
275#397C2318yes—
276#397C2314yes—
277#397C2318yes—
278#397C2318yes—
279#396C2314yes—
280#396C2318yes—
281#396C2318yes—
282#396C2314yes—
283#395C2314yes—
284#395C2314yes—
285#395C2314yes—
286#395C2314yes—
287#394C2314yes—
288#394C2314yes—
289#394C2318yes—
290#394C2318yes—
291#394C2318yes—
292#394C2318yes—
293#394C2314yes—
294#394C2318yes—
295#394C2314yes—
296#394C2318yes—
297#394C2314yes—
298#394C2314yes—
299#394C2318yes—
300#394C2314yes—
301#394C2314yes—
302#394C2318yes—
303#394C2318yes—
304#394C2318yes—
305#394C2314yes—
306#394C2314yes—
307#394C2314yes—
308#394C2314yes—
309#394C2318yes—
310#394C2314yes—
311#394C2318yes—
312#394C2314yes—
313#394C2314yes—
314#393C2318yes—
315#393C2318yes—
316#393C2314yes—
317#393C2318yes—
318#393C2318yes—
319#393C2318yes—
320#393C2314yes—
321#393C2318yes—
322#392C2314yes—
323#392C2314yes—
324#392C2314yes—
325#392C2318yes—
326#392C2318yes—
327#392C2318yes—
328#392C2318yes—
329#392C2318yes—
330#392C2318yes—
331#392C2318yes—
332#392C2314yes—
333#392C2318yes—
334#392C2318yes—
335#392C2314yes—
336#392C2314yes—
337#392C2314yes—
338#392C2318yes—
339#391C2312yes—
340#391C2312yes—
341#391C2312yes—
342#391C2318yes—
343#390C2312yes—
344#390C2312yes—
345#390C2314yes—
346#390C2314yes—
347#390C2318yes—
348#390C2314yes—
349#390C2318yes—
350#390C2318yes—
351#390C2318yes—
352#390C2318yes—
353#390C2314yes—
354#390C2318yes—
355#390C2312yes—
356#390C2318yes—
357#390C2312yes—
358#390C2312yes—
359#390C2312yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2312yes—
366#389C2314yes—
367#389C2314yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2314yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2314yes—
384#388C2314yes—
385#388C2314yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#386C2318yes—
392#386C2318yes—
393#386C2318yes—
394#386C2318yes—
395#386C2318yes—
396#386C2318yes—
397#386C2318yes—
398#386C2318yes—
399#386C2314yes—
400#386C2314yes—
401#386C2314yes—
402#386C2314yes—
403#386C2314yes—
404#385C2318yes—
405#385C2314yes—
406#385C2318yes—
407#385C2314yes—
408#385C2318yes—
409#385C2314yes—
410#384C2312yes—
411#384C2311yescharacteristic
412#384C2312yes—
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#384C2314yes—
416#383C2314yes—
417#382C2314yes—
418#382C2318yes—
419#382C2314yes—
420#382C2312yes—
421#382C2312yes—
422#381C2318yes—
423#381C2314yes—
424#381C2318yes—
425#380C2312yes—
426#380C2314yes—
427#380C2314yes—
428#380C2314yes—
429#380C2314yes—
430#380C2314yes—
431#380C2314yes—
432#380C2314yes—
433#380C2314yes—
434#380C2314yes—
435#380C2314yes—
436#380C2314yes—
437#380C2318yes—
438#380C2314yes—
439#380C2314yes—
440#380C2312yes—
441#380C2318yes—
442#380C2314yes—
443#379C2314yes—
444#379C2318yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2312yes—
452C4×C22⋊C4C2318yes—
453C4×C22⋊C4C2318yes—
454C4×C22⋊C4C2312yes—
455C4×C22⋊C4C2314yes—
456C4×C22⋊C4C2314yes—
457C4×C22⋊C4C2312yes—
458C4×C22⋊C4C2314yes—
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461#376C2314yes—
462C2×#95C2314yes—
463C43C2311yescharacteristic
464C25C2414yes—
465C2×#41—48no—
466C2×#41—48no—
467C2×#41—48no—
468C2×#41—48no—
469C2×#41—416no—
470C22×Q8C2412yes—
471C22×Q8C2414yes—
472C22×Q8C2414yes—
473C22×D4—28no—
474C22×D4—44no—
475C22×D4—44no—
476C22×D4—416no—
477C22×D4—48no—
478C22×D4C2411yescharacteristic
479C22×D4C2412yes—
480C22×D4C2412yes—
481C22×D4C2412yes—
482C22×D4C2414yes—
483C22×D4C2414yes—
484C22×D4C2414yes—
485C22×D4C2414yes—
486C22×D4C2414yes—
487C22×D4C2414yes—
488C22×D4C2418yes—
489C22×D4C2418yes—
490C22×D4C2414yes—
491C22×D4C2414yes—
492C22×D4C2418yes—
493C22×D4C2414yes—
494C22×D4C2414yes—
495C22×D4C2414yes—
496C22×D4C2414yes—
497C23×C4—216no—
498C23×C4—48no—
499C23×C4—48no—
500C23×C4C2414yes—
501C23×C4C2414yes—
502C23×C4C2414yes—
503C23×C4C2414yes—
504C23×C4C2412yes—
505C23×C4C2411yescharacteristic
506C23×C4C2411yescharacteristic
507C23×C4C2412yes—
508C23×C4C2414yes—
509C23×C4C2414yes—
510C23×C4C2414yes—
511C23×C4C2418yes—
512C4⋊Q8—24no—
513C4⋊Q8—44no—
514C4⋊Q8—48no—
515#127—44no—
516#127—44no—
517#127—48no—
518#127—48no—
519#126—48no—
520#125—48no—
521#125—44no—
522#124—48no—
523#124—48no—
524#124—48no—
525#124—416no—
526#123—416no—
527#123—48no—
528#123—48no—
529#123—416no—
530#123—48no—
531C22⋊Q8—48no—
532C22⋊Q8—44no—
533C22⋊Q8—416no—
534C22⋊Q8—48no—
535C22⋊Q8—44no—
536#121—28no—
537#121—48no—
538#121—48no—
539#121—416no—
540#121—416no—
541#121—48no—
542#121—48no—
543#121—48no—
544#121—48no—
545#121—416no—
546#121—416no—
547#121—44no—
548#121—48no—
549#121—48no—
550#121—44no—
551#121—44no—
552#121—48no—
553#121—48no—
554#121—48no—
555#121—48no—
556#120—216no—
557#120—48no—
558#120—48no—
559#120—416no—
560C4×Q8—44no—
561C4×D4—28no—
562C4×D4—216no—
563C4×D4—24no—
564C4×D4—28no—
565C4×D4—28no—
566C4×D4—28no—
567C4×D4—48no—
568C4×D4—44no—
569C4×D4—44no—
570C4×D4—48no—
571C4×D4—48no—
572C4×D4—48no—
573C4×D4—48no—
574C4×D4—48no—
575C4×D4—48no—
576#117—216no—
577#117—48no—
578#117—44no—
579#117—48no—
580#117—48no—
581#117—48no—
582C2×C4⋊C4—216no—
583C2×C4⋊C4—44no—
584C2×C4⋊C4—48no—
585C2×C4⋊C4—44no—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2414yes—
617C2×C22⋊C4—48no—
618C2×C22⋊C4—416no—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2412yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2412yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2411yescharacteristic
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2418yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2411yescharacteristic
663C2×C42—24no—
664C2×C42—24no—
665C2×C42C2412yes—
666C2×C42C2414yes—
667C2×C42C2414yes—
668C2×C42C2414yes—
669C2×C42C2412yes—
670C2×C42C2411yescharacteristic
671C2×C42C2412yes—
672C2×C42C2412yes—
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2418yes—
676C2×C42C2418yes—
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679#95C2414yes—
680#95C2414yes—
681#95C2418yes—
682#95C2414yes—
683#95C2414yes—
684#95C2414yes—
685#95C2412yes—
686#95C2412yes—
687#95C2412yes—
688#95C2418yes—
689#95C2418yes—
690#95C2418yes—
691#95C2414yes—
692#95C2414yes—
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696#95C2418yes—
697#95C2418yes—
698#95C2418yes—
699#95C2414yes—
700#95C2418yes—
701#95C2418yes—
702#95C2418yes—
703#95C2418yes—
704C24—28no—
705C24—28no—
706C24—28no—
707C24—44no—
708C24—44no—
709C24—44no—
710C24—44no—
711C24C2514yes—
712C24C2514yes—
713C24C2511yescharacteristic
714C24C2514yes—
715C24C2511yescharacteristic
716#41—832no—
717#41—832no—
718C2×Q8—24no—
719C2×Q8—42no—
720C2×Q8—44no—
721C2×Q8—48no—
722C2×Q8—44no—
723C2×Q8—44no—
724C2×Q8—42no—
725C2×Q8—44no—
726C2×D4—24no—
727C2×D4—28no—
728C2×D4—22no—
729C2×D4—28no—
730C2×D4—28no—
731C2×D4—24no—
732C2×D4—24no—
733C2×D4—24no—
734C2×D4—24no—
735C2×D4—28no—
736C2×D4—24no—
737C2×D4—24no—
738C2×D4—28no—
739C2×D4—28no—
740C2×D4—24no—
741C2×D4—24no—
742C2×D4—24no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—432no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—44no—
758C2×D4—44no—
759C2×D4—44no—
760C2×D4—48no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—44no—
768C2×D4—44no—
769C2×D4—44no—
770C2×D4—44no—
771C2×D4—44no—
772C2×D4—44no—
773C2×D4—44no—
774C2×D4—48no—
775C2×D4—48no—
776C2×D4—48no—
777C2×D4—48no—
778C2×D4—48no—
779C2×D4—48no—
780C2×D4—832no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—216no—
784C22×C4—22no—
785C22×C4—28no—
786C22×C4—28no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—24no—
790C22×C4—28no—
791C22×C4—22no—
792C22×C4—28no—
793C22×C4—28no—
794C22×C4—28no—
795C22×C4—28no—
796C22×C4—24no—
797C22×C4—28no—
798C22×C4—28no—
799C22×C4—28no—
800C22×C4—28no—
801C22×C4—24no—
802C22×C4—28no—
803C22×C4—28no—
804C22×C4—41no—
805C22×C4—41no—
806C22×C4—44no—
807C22×C4—48no—
808C22×C4—44no—
809C22×C4—44no—
810C22×C4—48no—
811C22×C4—48no—
812C22×C4—44no—
813C22×C4—44no—
814C22×C4—44no—
815C22×C4—832no—
816C22×C4H(5,𝔽2)18yes—
817C22×C4C2512yes—
818C22×C4C2512yes—
819C22×C4C2514yes—
820C22×C4C2514yes—
821C22×C4C2514yes—
822C22×C4C2514yes—
823C22×C4C2514yes—
824C22×C4C2514yes—
825C22×C4C2514yes—
826C22×C4C2514yes—
827C22×C4C2514yes—
828C22×C4C2511yescharacteristic
829C22×C4C2511yescharacteristic
830C22×C4C2512yes—
831C22×C4C2511yescharacteristic
832C22×C4C2511yescharacteristic
833C22×C4C2511yescharacteristic
834C22×C4C2512yes—
835C4⋊C4—28no—
836C4⋊C4—28no—
837C4⋊C4—216no—
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—24no—
841C4⋊C4—28no—
842C4⋊C4—28no—
843C4⋊C4—24no—
844C4⋊C4—28no—
845C4⋊C4—28no—
846C4⋊C4—24no—
847C4⋊C4—22no—
848C4⋊C4—24no—
849C4⋊C4—28no—
850C4⋊C4—42no—
851C4⋊C4—44no—
852C4⋊C4—48no—
853C4⋊C4—42no—
854C4⋊C4—44no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4—42no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4—44no—
863C4⋊C4—44no—
864C4⋊C4—48no—
865C4⋊C4—44no—
866C22⋊C4—28no—
867C22⋊C4—24no—
868C22⋊C4—28no—
869C22⋊C4—28no—
870C22⋊C4—28no—
871C22⋊C4—24no—
872C22⋊C4—28no—
873C22⋊C4—28no—
874C22⋊C4—22no—
875C22⋊C4—28no—
876C22⋊C4—28no—
877C22⋊C4—28no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—48no—
881C22⋊C4—48no—
882C22⋊C4—48no—
883C22⋊C4—48no—
884C22⋊C4—44no—
885C22⋊C4—44no—
886C22⋊C4—48no—
887C22⋊C4—48no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—48no—
891C22⋊C4—48no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—48no—
902C22⋊C4—48no—
903C22⋊C4—48no—
904C22⋊C4—44no—
905C22⋊C4—48no—
906C22⋊C4—48no—
907C22⋊C4—48no—
908C22⋊C4—44no—
909C22⋊C4H(5,𝔽2)14yes—
910C42—22no—
911C42—24no—
912C42—24no—
913C42—22no—
914C42—28no—
915C42—28no—
916C42—24no—
917C42—28no—
918C42—22no—
919C42—24no—
920C42—41no—
921C42—48no—
922C42—48no—
923C42H(5,𝔽2)14yes—
924C23—21no—
925C23—22no—
926C23—21no—
927C23—21no—
928C23—24no—
929C23—24no—
930C23—24no—
931C23—24no—
932C23—22no—
933C23—24no—
934C23—24no—
935C23—24no—
936C23—24no—
937C23—24no—
938C23—24no—
939C23—24no—
940C23—21no—
941C23—24no—
942C23—24no—
943C23—24no—
944C23—24no—
945C23—24no—
946C23—24no—
947C23—24no—
948C23—22no—
949C23—24no—
950C23—24no—
951C23—21no—
952C23—24no—
953C23—416no—
954C23—416no—
955C23—416no—
956C23—88no—
957C23—88no—
958C23—88no—
959C23—88no—
960C23C2×H(5,𝔽2)12yes—
961C23C2×H(5,𝔽2)14yes—
962C23C2611yescharacteristic
963Q8—84no—
964Q8—88no—
965Q8—88no—
966D4—416no—
967D4—44no—
968D4—416no—
969D4—48no—
970D4—48no—
971D4—48no—
972D4—88no—
973D4—88no—
974D4—88no—
975D4—88no—
976D4—816no—
977D4—88no—
978D4—88no—
979D4—88no—
980D4—88no—
981D4—88no—
982D4—88no—
983D4—168no—
984D4—168no—
985C2×C4—21no—
986C2×C4—22no—
987C2×C4—21no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—216no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—22no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—21no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—22no—
1010C2×C4—21no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—28no—
1015C2×C4—28no—
1016C2×C4—24no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—28no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—21no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—44no—
1029C2×C4—44no—
1030C2×C4—416no—
1031C2×C4—416no—
1032C2×C4—416no—
1033C2×C4—416no—
1034C2×C4—48no—
1035C2×C4—88no—
1036C2×C4—88no—
1037C2×C4—88no—
1038C2×C4—816no—
1039C2×C4C2×H(5,𝔽2)12yes—
1040C2×C4C2×H(5,𝔽2)12yes—
1041C2×C4C2×H(5,𝔽2)12yes—
1042C2×C4C2×H(5,𝔽2)14yes—
1043C2×C4C2×H(5,𝔽2)14yes—
1044C2×C4C2×H(5,𝔽2)14yes—
1045C2×C4#58514yes—
1046C22—22no—
1047C22—22no—
1048C22—24no—
1049C22—24no—
1050C22—44no—
1051C22—41no—
1052C22—44no—
1053C22—44no—
1054C22—44no—
1055C22—44no—
1056C22—44no—
1057C22—41no—
1058C22—41no—
1059C22—44no—
1060C22—44no—
1061C22—44no—
1062C22—42no—
1063C22—44no—
1064C22—44no—
1065C22—44no—
1066C22—44no—
1067C22—44no—
1068C22—44no—
1069C22—44no—
1070C22—44no—
1071C22—42no—
1072C22—44no—
1073C22—44no—
1074C22—44no—
1075C22—44no—
1076C22—832no—
1077C22#354914yes—
1078C22C22×H(5,𝔽2)11yescharacteristic
1079C22C22×H(5,𝔽2)12yes—
1080C22C22×H(5,𝔽2)11yescharacteristic
1081C22C2×#58512yes—
1082C222−1+611yescharacteristic
1083C4—22no—
1084C4—22no—
1085C4—22no—
1086C4—24no—
1087C4—44no—
1088C4—44no—
1089C4—44no—
1090C4—41no—
1091C4—44no—
1092C4—41no—
1093C4—44no—
1094C4—44no—
1095C4—42no—
1096C4—44no—
1097C4—44no—
1098C4—42no—
1099C4—44no—
1100C4#354218yes—
1101C2—24no—
1102C2—84no—
1103C2—81no—
1104C2—84no—
1105C2—84no—
1106C2C2×#354212yes—
1107C2C2×#354911yescharacteristic
1108C2#6291411yescharacteristic
1109C2#6292512yes—
1110C2#6302411yescharacteristic
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. #59822C2semidirect
2. #59313C2semidirect
3. #59233C2semidirect
4. #59203C2semidirect
5. #58384C2semidirect
6. #56605C2semidirect
7. #53094C2semidirect
8. #53055C2semidirect
9. #52367C2semidirect
10. #42923C2semidirect
11. #42736C2semidirect
12. #41935C2semidirect
13. #39469C2semidirect
14. #39339C2semidirect
15. #39191C2semidirect
16. #37839C2semidirect
17. #37639C2semidirect
18. #37636C2semidirect
19. #37437C2semidirect
20. #36181C2semidirect
21. #36160C2semidirect
22. C2×#2537C2semidirect
23. #34681C2semidirect
24. C2×#555C22semidirect
28. C2×#532C22semidirect
32. #2859C22semidirect
34. #2857C22semidirect
36. #2832C22semidirect
37. #2832C22semidirect
38. #2828C22semidirect
39. #2824C22semidirect
40. #2820C22semidirect
41. #2819C22semidirect
42. #2818C22semidirect
43. #2816C22semidirect
44. #2815C22semidirect
45. #2785C22semidirect
46. #2753C22semidirect
47. #2753C22semidirect
48. #2744C22semidirect
49. #2737C22semidirect
50. #2733C22semidirect
51. #2714C22semidirect
52. #2712C22semidirect
53. #2711C22semidirect
54. #2711C22semidirect
55. #2706C22semidirect
56. #2703C22semidirect
57. #2696C22semidirect
58. #2692C22semidirect
59. #2680C22semidirect
60. #2676C22semidirect
61. #2676C22semidirect
62. #2676C22semidirect
63. #2673C22semidirect
64. #2673C22semidirect
65. #2662C22semidirect
66. #2661C22semidirect
67. #2661C22semidirect
68. #2641C22semidirect
69. #2632C22semidirect
70. #2628C22semidirect
71. #2624C22semidirect
72. #2624C22semidirect
73. #2619C22semidirect
74. #2615C22semidirect
75. #2615C22semidirect
76. #2615C22semidirect
79. #2610C22semidirect
80. #2574C22semidirect
81. #2565C22semidirect
82. #2563C22semidirect
83. #2563C22semidirect
84. #2563C22semidirect
86. #2551C22semidirect
87. #2548C22semidirect
88. #2541C22semidirect
89. #2541C22semidirect
97. #2537C22semidirect
98. #2537C22semidirect
99. #2535C22semidirect
100. #2531C22semidirect
101. #2506C22semidirect
103. #2499C22semidirect
104. #2497C22semidirect
105. #2496C22semidirect
106. #2495C22semidirect
107. #2491C22semidirect
108. #2491C22semidirect
110. #2487C22semidirect
113. #2485C22semidirect
114. #2485C22semidirect
115. #2485C22semidirect
118. #2464C22semidirect
119. #2461C22semidirect
120. #2459C22semidirect
121. #2452C22semidirect
122. #2445C22semidirect
124. #2440C22semidirect
125. #2439C22semidirect
128. #2428C22semidirect
129. #2428C22semidirect
130. #2428C22semidirect
132. #2422C22semidirect
133. #2422C22semidirect
134. #2420C22semidirect
136. #2416C22semidirect
137. #2416C22semidirect
138. #2414C22semidirect
139. #2414C22semidirect
140. #2414C22semidirect
141. #2414C22semidirect
142. #2414C22semidirect
143. #2414C22semidirect
149. #2392C22semidirect
150. #2388C22semidirect
152. #2363C22semidirect
153. #2354C22semidirect
154. #2354C22semidirect
156. D4×C4⋊C4C22semidirect
157. #2346C22semidirect
160. #2324C22semidirect
161. #2311C22semidirect
162. C4×C4⋊Q8C22semidirect
163. C4×#127C22semidirect
165. C4×#121C22semidirect
167. #2293C22semidirect
168. #2285C22semidirect

Maximal subgroups

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

subgroupindex
#598222
#593132
#592332
#592032
#583842
#566052
#530942
#530552
#523672
#429232
#427362
#419352
#394692
#393392
#391912
#378392
#376392
#376362
#374372
#361812
#361602
C2×#25372
#346812