Finite Group Databasebeta

← #7712776

Subgroups — #7712776

Order 512.

4766 conjugacy classes of subgroups.

The subgroup lattice has 1077 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59231C214yesmaximal, complemented
2#59216C214yesmaximal, complemented
3#45664C214yesmaximal, complemented
4#45617C214yesmaximal, complemented
5#40106C214yesmaximal, complemented
6#40083C214yesmaximal, complemented
7#39998C214yesmaximal, complemented
8#39975C214yesmaximal, complemented
9#38215C214yesmaximal, complemented
10#38203C214yesmaximal, complemented
11#37519C212yesmaximal, complemented
12#37382C212yesmaximal, complemented
13#37376C212yesmaximal
14#36635C212yesmaximal, complemented
15#36209C212yesmaximal, complemented
16#36189C212yesmaximal, complemented
17#36151C212yesmaximal, complemented
18#36129C212yesmaximal, complemented
19#35316C211yesmaximal, characteristic, complemented
20#35297C212yesmaximal, complemented
21#35280C211yesmaximal, characteristic, complemented
22#34412C212yesmaximal, complemented
23C4×#532C211yesmaximal, characteristic
24C2×#536C2212yes—
25C2×#533C2212yes—
26C2×#533C2211yescharacteristic
27C2×#532C2211yescharacteristic
28C22×C4⋊Q8C2211yescharacteristic
29C2×C4×#41C2211yescharacteristic
30C2×C4×#41C2211yescharacteristic
31#2864C2214yes—
32#2863C2214yes—
33#2863C2214yes—
34#2862C2212yes—
35#2859C2212yes—
36#2857C2212yes—
37#2857C2212yes—
38#2857C2212yes—
39#2857C2212yes—
40#2857C2212yes—
41#2857C2212yes—
42#2855C2214yes—
43#2855C2214yes—
44#2851C2214yes—
45#2827C2218yes—
46#2802C2218yes—
47#2791C2218yes—
48#2786C2218yes—
49#2772C2218yes—
50#2767C2218yes—
51#2755C2218yes—
52#2754C2218yes—
53#2747C2218yes—
54#2744C2218yes—
55#2740C2218yes—
56#2739C2218yes—
57#2739C2218yes—
58#2734C2214yes—
59#2731C2214yes—
60#2717C2214yes—
61#2709C2214yes—
62#2701C2218yes—
63#2686C2218yes—
64#2666C2218yes—
65#2651C2218yes—
66#2629C2212yes—
67#2629C2212yes—
68#2625C2214yes—
69#2621C2212yes—
70#2621C2212yes—
71#2616C2214yes—
72#2612C2218yes—
73#2606C2218yes—
74#2584C2214yes—
75#2582C2214yes—
76#2581C2214yes—
77#2570C2214yes—
78#2562C2214yes—
79#2550C2214yes—
80#2547C2214yes—
81#2546C2214yes—
82#2538C2214yes—
83#2536C2214yes—
84#2536C2214yes—
85#2536C2214yes—
86#2532C2218yes—
87#2531C2218yes—
88#2526C2218yes—
89#2525C2218yes—
90#2518C2218yes—
91#2515C2218yes—
92#2511C2214yes—
93#2508C2214yes—
94#2508C2214yes—
95#2507C2214yes—
96#2497C2214yes—
97#2495C2218yes—
98#2495C2214yes—
99#2495C2214yes—
100#2492C2214yes—
101#2489C2214yes—
102#2489C2214yes—
103#2489C2214yes—
104#2489C2214yes—
105#2487C2214yes—
106#2486C2214yes—
107#2486C2214yes—
108#2485C2214yes—
109#2485C2214yes—
110#2485C2214yes—
111#2485C2214yes—
112#2453C2214yes—
113#2453C2214yes—
114#2451C2214yes—
115#2446C2214yes—
116#2442C2214yes—
117#2442C2214yes—
118#2441C2214yes—
119#2439C2214yes—
120#2429C2214yes—
121#2423C2214yes—
122#2421C2214yes—
123#2421C2214yes—
124#2417C2214yes—
125#2417C2214yes—
126#2417C2214yes—
127#2417C2214yes—
128#2415C2214yes—
129#2415C2214yes—
130#2415C2214yes—
131#2415C2214yes—
132#2409C2214yes—
133#2379C2214yes—
134#2376C2214yes—
135#2374C2214yes—
136#2372C2214yes—
137#2362C2214yes—
138#2362C2214yes—
139#2360C2214yes—
140#2360C2214yes—
141#2356C2214yes—
142#2352C2214yes—
143#2352C2214yes—
144#2351C2214yes—
145#2346C2214yes—
146#2346C2214yes—
147#2345C2214yes—
148Q8×C22⋊C4C2214yes—
149#2335C2218yes—
150#2331C2218yes—
151#2323C2214yes—
152#2323C2214yes—
153#2316C2212yes—
154#2311C2212yes—
155#2310C2212yes—
156C4×C4⋊Q8C2212yes—
157C4×C4⋊Q8C2212yes—
158C4×C4⋊Q8C2212yes—
159C4×#127C2212yes—
160C4×#125C2214yes—
161C4×#124C2212yes—
162C4×#124C2212yes—
163C4×C22⋊Q8C2214yes—
164C4×C22⋊Q8C2214yes—
165C4×#121C2212yes—
166C4×#121C2212yes—
167C4×#121C2212yes—
168C4×#121C2212yes—
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2295C2214yes—
172#2295C2214yes—
173#2293C2212yes—
174#2293C2212yes—
175#2285C2211yescharacteristic
176#2285C2212yes—
177#2285C2211yescharacteristic
178C2×#384C2211yescharacteristic
179#2283C2214yes—
180C42×D4C2212yes—
181C42×D4C2212yes—
182C2×C43C2211yescharacteristic
183C22×#41C2311yescharacteristic
184C22×#41C2311yescharacteristic
185C23×Q8C2312yes—
186#536—216no—
187#533—48no—
188#533—44no—
189#532—28no—
190C2×C4⋊Q8—44no—
191C2×C4⋊Q8C2311yescharacteristic
192C2×C4⋊Q8C2312yes—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2314yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2314yes—
197C2×#127C2311yescharacteristic
198C2×#125C2314yes—
199C2×#125C2314yes—
200C2×#125C2312yes—
201C2×#124C2314yes—
202C2×#124C2311yescharacteristic
203C2×#124C2311yescharacteristic
204C2×#123C2314yes—
205C2×#123C2314yes—
206C2×C22⋊Q8C2314yes—
207C2×C22⋊Q8C2314yes—
208C2×C22⋊Q8C2314yes—
209C2×C22⋊Q8C2314yes—
210C2×C22⋊Q8C2314yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2314yes—
215C2×#121C2312yes—
216C2×#121C2312yes—
217C4×#41—44no—
218C4×#41—44no—
219C2×C4×Q8C2314yes—
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2314yes—
223C2×C4×Q8C2314yes—
224C2×C4×Q8C2314yes—
225C2×C4×Q8C2314yes—
226C2×C4×D4C2312yes—
227C2×C4×D4C2312yes—
228C2×C4×D4C2312yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2312yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2312yes—
234C2×C4×D4C2312yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2312yes—
238C2×#117C2312yes—
239C2×#117C2311yescharacteristic
240C2×#117C2312yes—
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2312yes—
244C2×#117C2314yes—
245C2×#117C2314yes—
246C2×#117C2311yescharacteristic
247C22×C4⋊C4C2312yes—
248C22×C4⋊C4C2314yes—
249C22×C4⋊C4C2314yes—
250C22×C42C2311yescharacteristic
251C22×C42C2311yescharacteristic
252C22×C42C2311yescharacteristic
253C22×C42C2311yescharacteristic
254C22×C42C2312yes—
255C22×C42C2312yes—
256C22×C42C2312yes—
257C22×C42C2311yescharacteristic
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#399C2318yes—
267#398C2318yes—
268#398C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2318yes—
272#398C2318yes—
273#398C2318yes—
274#398C2318yes—
275#398C2318yes—
276#398C2318yes—
277#398C2318yes—
278#397C2318yes—
279#397C2318yes—
280#397C2318yes—
281#397C2318yes—
282#397C2318yes—
283#397C2318yes—
284#397C2318yes—
285#397C2318yes—
286#396C2318yes—
287#396C2318yes—
288#396C2318yes—
289#396C2318yes—
290#395C2318yes—
291#395C2318yes—
292#394C2318yes—
293#394C2318yes—
294#394C2318yes—
295#394C2318yes—
296#394C2318yes—
297#393C2318yes—
298#391C2312yes—
299#391C2314yes—
300#391C2314yes—
301#391C2312yes—
302#391C2314yes—
303#391C2314yes—
304#391C2318yes—
305#391C2314yes—
306#391C2314yes—
307#391C2314yes—
308#391C2314yes—
309#391C2314yes—
310#391C2318yes—
311#391C2318yes—
312#391C2314yes—
313#391C2314yes—
314#391C2314yes—
315#391C2314yes—
316#390C2312yes—
317#390C2312yes—
318#390C2312yes—
319#390C2312yes—
320#390C2312yes—
321#390C2312yes—
322#390C2314yes—
323#389C2314yes—
324#389C2314yes—
325#389C2314yes—
326#389C2314yes—
327#389C2314yes—
328#389C2314yes—
329#389C2312yes—
330#389C2312yes—
331#389C2312yes—
332#389C2312yes—
333#389C2314yes—
334#389C2314yes—
335#389C2314yes—
336#389C2318yes—
337#389C2314yes—
338#389C2318yes—
339#389C2318yes—
340#389C2314yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2318yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2318yes—
352#389C2318yes—
353#389C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2312yes—
369#388C2312yes—
370#388C2312yes—
371#388C2312yes—
372#388C2312yes—
373#388C2312yes—
374#388C2312yes—
375#388C2312yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#386C2314yes—
397#386C2314yes—
398#386C2312yes—
399#386C2318yes—
400#386C2318yes—
401#386C2311yescharacteristic
402#386C2311yescharacteristic
403#386C2311yescharacteristic
404#386C2311yescharacteristic
405#386C2312yes—
406#385C2318yes—
407#385C2318yes—
408#385C2318yes—
409#385C2318yes—
410#384C2312yes—
411#384C2312yes—
412#384C2312yes—
413#384C2314yes—
414#384C2312yes—
415#383C2318yes—
416#383C2318yes—
417#382C2314yes—
418#382C2314yes—
419#382C2314yes—
420#382C2318yes—
421#382C2318yes—
422#382C2314yes—
423#382C2318yes—
424#382C2312yes—
425#382C2312yes—
426#381C2318yes—
427#381C2318yes—
428#380C2314yes—
429#380C2314yes—
430#380C2314yes—
431#380C2314yes—
432#380C2314yes—
433#380C2314yes—
434#380C2318yes—
435#380C2314yes—
436#380C2318yes—
437#380C2314yes—
438#380C2314yes—
439#380C2318yes—
440#380C2314yes—
441#380C2314yes—
442#380C2314yes—
443#380C2314yes—
444#380C2312yes—
445#380C2314yes—
446#380C2314yes—
447#380C2312yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2318yes—
451C4×C4⋊C4C2318yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2312yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2312yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2318yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2312yes—
464C4×C22⋊C4C2318yes—
465C4×C22⋊C4C2318yes—
466C4×C22⋊C4C2312yes—
467C4×C22⋊C4C2312yes—
468C4×C22⋊C4C2312yes—
469C4×C22⋊C4C2312yes—
470C4×C22⋊C4C2312yes—
471C4×C22⋊C4C2312yes—
472C4×C22⋊C4C2318yes—
473C4×C22⋊C4C2312yes—
474C4×C22⋊C4C2312yes—
475C4×C22⋊C4C2312yes—
476C4×C22⋊C4C2312yes—
477C4×C22⋊C4C2312yes—
478C4×C22⋊C4C2312yes—
479#376C2318yes—
480#376C2318yes—
481C43C2312yes—
482C43C2312yes—
483C43C2312yes—
484C43C2312yes—
485C2×#41—24no—
486C2×#41—42no—
487C2×#41—42no—
488C2×#41—42no—
489C2×#41—42no—
490C2×#41#4118yes—
491C22×Q8—28no—
492C22×Q8—44no—
493C22×Q8—44no—
494C22×Q8C2414yes—
495C22×Q8C2414yes—
496C22×Q8C2411yescharacteristic
497C22×Q8C2414yes—
498C22×Q8C2411yescharacteristic
499C22×D4C2412yes—
500C22×D4C2412yes—
501C22×D4C2412yes—
502C22×D4C2411yescharacteristic
503C22×D4C2411yescharacteristic
504C22×D4C2411yescharacteristic
505C22×D4C2411yescharacteristic
506C23×C4C2412yes—
507C23×C4C2412yes—
508C23×C4C2412yes—
509C23×C4C2412yes—
510C23×C4C2412yes—
511C23×C4C2412yes—
512C23×C4C2412yes—
513C23×C4C2411yescharacteristic
514C23×C4C2411yescharacteristic
515C23×C4C2411yescharacteristic
516C23×C4C2411yescharacteristic
517C23×C4C2414yes—
518C23×C4C2414yes—
519C23×C4C2411yescharacteristic
520C4⋊Q8—24no—
521C4⋊Q8—216no—
522C4⋊Q8—28no—
523C4⋊Q8—28no—
524C4⋊Q8—48no—
525C4⋊Q8—44no—
526#127—24no—
527#125—48no—
528#125—44no—
529#125—48no—
530#124—24no—
531#124—24no—
532#124—216no—
533#123—216no—
534#123—216no—
535C22⋊Q8—216no—
536C22⋊Q8—216no—
537C22⋊Q8—48no—
538C22⋊Q8—48no—
539C22⋊Q8—48no—
540C22⋊Q8—48no—
541C22⋊Q8—48no—
542C22⋊Q8—48no—
543C22⋊Q8—48no—
544#121—28no—
545#121—28no—
546C4×Q8—216no—
547C4×Q8—44no—
548C4×Q8—44no—
549C4×Q8—48no—
550C4×Q8—48no—
551C4×Q8—48no—
552C4×Q8—48no—
553C4×D4—28no—
554C4×D4—28no—
555C4×D4—28no—
556C4×D4—28no—
557C4×D4—44no—
558C4×D4—44no—
559C4×D4—44no—
560C4×D4—44no—
561C4×D4—44no—
562C4×D4—44no—
563C4×D4—44no—
564C4×D4—44no—
565#117—28no—
566#117—44no—
567#117—42no—
568#117—42no—
569#117—42no—
570#117—42no—
571#117—48no—
572#117—48no—
573#117—44no—
574C2×C4⋊C4—48no—
575C2×C4⋊C4—44no—
576C2×C4⋊C4—48no—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2418yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2418yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2412yes—
617C2×C22⋊C4C2412yes—
618C2×C22⋊C4C2412yes—
619C2×C22⋊C4C2412yes—
620C2×C22⋊C4C2412yes—
621C2×C22⋊C4C2412yes—
622C2×C22⋊C4C2412yes—
623C2×C22⋊C4C2412yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2412yes—
627C2×C22⋊C4C2411yescharacteristic
628C2×C22⋊C4C2411yescharacteristic
629C2×C22⋊C4C2412yes—
630C2×C22⋊C4C2412yes—
631C2×C22⋊C4C2412yes—
632C2×C22⋊C4C2412yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2412yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2412yes—
639C2×C22⋊C4C2412yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2418yes—
644C2×C42—24no—
645C2×C42—24no—
646C2×C42—24no—
647C2×C42—28no—
648C2×C42—24no—
649C2×C42—28no—
650C2×C42—44no—
651C2×C42—42no—
652C2×C42C2411yescharacteristic
653C2×C42C2412yes—
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2414yes—
657C2×C42C2412yes—
658C2×C42C2412yes—
659C2×C42C2412yes—
660C2×C42C2412yes—
661C2×C42C2412yes—
662C2×C42C2412yes—
663C2×C42C2412yes—
664C2×C42C2412yes—
665C2×C42C2418yes—
666C2×C42C2411yescharacteristic
667C2×C42C2412yes—
668C2×C42C2411yescharacteristic
669C2×C42C2412yes—
670C2×C42C2412yes—
671C2×C42C2412yes—
672C2×C42C2418yes—
673C2×C42C2414yes—
674C2×C42C2418yes—
675C2×C42C2418yes—
676C2×C42C2412yes—
677C2×C42C2412yes—
678C2×C42C2412yes—
679C2×C42C2411yescharacteristic
680C2×C42C2412yes—
681#95C2412yes—
682#95C2418yes—
683#95C2418yes—
684#95C2418yes—
685#95C2418yes—
686#95C2418yes—
687#95C2418yes—
688#95C2418yes—
689#95C2412yes—
690#95C2412yes—
691#95C2412yes—
692#95C2412yes—
693#95C2412yes—
694#95C2412yes—
695#95C2412yes—
696#95C2418yes—
697#95C2412yes—
698#95C2412yes—
699#95C2412yes—
700#95C2412yes—
701#95C2418yes—
702#95C2418yes—
703#95C2418yes—
704#95C2418yes—
705#95C2418yes—
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709#95C2418yes—
710#95C2418yes—
711#95C2418yes—
712#95C2418yes—
713#95C2418yes—
714#95C2418yes—
715#95C2418yes—
716#95C2418yes—
717#95C2418yes—
718C24C2512yes—
719C24C2511yescharacteristic
720C24C2511yescharacteristic
721C24C2511yescharacteristic
722#41—416no—
723#41—416no—
724C2×Q8—28no—
725C2×Q8—22no—
726C2×Q8—28no—
727C2×Q8—28no—
728C2×Q8—28no—
729C2×Q8—28no—
730C2×Q8—28no—
731C2×Q8—28no—
732C2×Q8—41no—
733C2×Q8—41no—
734C2×Q8—41no—
735C2×Q8—41no—
736C2×Q8—44no—
737C2×Q8—44no—
738C2×Q8—816no—
739C2×Q8C2×#4114yes—
740C2×D4—24no—
741C2×D4—24no—
742C2×D4—24no—
743C2×D4—22no—
744C2×D4—24no—
745C2×D4—24no—
746C2×D4—41no—
747C2×D4—41no—
748C2×D4—41no—
749C2×D4—41no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—42no—
753C2×D4—41no—
754C2×D4—41no—
755C2×D4—41no—
756C2×D4—41no—
757C2×D4—42no—
758C2×D4C2×#4114yes—
759C2×D4C2×#4114yes—
760C2×D4C2×#4114yes—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—24no—
768C22×C4—28no—
769C22×C4—24no—
770C22×C4—24no—
771C22×C4—24no—
772C22×C4—24no—
773C22×C4—24no—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—24no—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—24no—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—41no—
790C22×C4—42no—
791C22×C4—42no—
792C22×C4—41no—
793C22×C4—44no—
794C22×C4—44no—
795C22×C4—48no—
796C22×C4—44no—
797C22×C4C2×#4114yes—
798C22×C4C2×#4114yes—
799C22×C4C2×#4114yes—
800C22×C4C2512yes—
801C22×C4C2518yes—
802C22×C4C2512yes—
803C22×C4C2512yes—
804C22×C4C2512yes—
805C22×C4C2512yes—
806C22×C4C2518yes—
807C22×C4C2512yes—
808C22×C4C2512yes—
809C22×C4C2518yes—
810C22×C4C2518yes—
811C22×C4C2512yes—
812C22×C4C2511yescharacteristic
813C22×C4C2511yescharacteristic
814C22×C4C2511yescharacteristic
815C22×C4C2512yes—
816C22×C4C2512yes—
817C22×C4C2511yescharacteristic
818C22×C4C2512yes—
819C4⋊C4—28no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—216no—
823C4⋊C4—216no—
824C4⋊C4—28no—
825C4⋊C4—28no—
826C4⋊C4—28no—
827C4⋊C4—28no—
828C4⋊C4—24no—
829C4⋊C4—24no—
830C4⋊C4—28no—
831C4⋊C4—216no—
832C4⋊C4—28no—
833C4⋊C4—28no—
834C4⋊C4—28no—
835C4⋊C4—28no—
836C4⋊C4—44no—
837C4⋊C4—48no—
838C4⋊C4—48no—
839C4⋊C4—42no—
840C4⋊C4—42no—
841C4⋊C4—42no—
842C4⋊C4—42no—
843C4⋊C4—42no—
844C4⋊C4—42no—
845C4⋊C4—42no—
846C4⋊C4—42no—
847C4⋊C4—48no—
848C4⋊C4—48no—
849C4⋊C4—48no—
850C4⋊C4—48no—
851C4⋊C4—48no—
852C4⋊C4—48no—
853C4⋊C4—48no—
854C4⋊C4—48no—
855C4⋊C4—48no—
856C4⋊C4—48no—
857C22⋊C4—28no—
858C22⋊C4—24no—
859C22⋊C4—24no—
860C22⋊C4—216no—
861C22⋊C4—216no—
862C22⋊C4—24no—
863C22⋊C4—24no—
864C22⋊C4—24no—
865C22⋊C4—24no—
866C22⋊C4—24no—
867C22⋊C4—24no—
868C22⋊C4—48no—
869C22⋊C4—41no—
870C22⋊C4—42no—
871C22⋊C4—42no—
872C22⋊C4—42no—
873C22⋊C4—42no—
874C22⋊C4—41no—
875C22⋊C4—42no—
876C22⋊C4—44no—
877C22⋊C4—48no—
878C22⋊C4—42no—
879C22⋊C4—42no—
880C22⋊C4—42no—
881C22⋊C4—42no—
882C22⋊C4—48no—
883C22⋊C4—48no—
884C22⋊C4—48no—
885C22⋊C4—48no—
886C42—24no—
887C42—22no—
888C42—22no—
889C42—28no—
890C42—22no—
891C42—24no—
892C42—22no—
893C42—22no—
894C42—24no—
895C42—24no—
896C42—24no—
897C42—24no—
898C42—24no—
899C42—24no—
900C42—24no—
901C42—24no—
902C42—216no—
903C42—24no—
904C42—24no—
905C42—24no—
906C42—42no—
907C42—42no—
908C42—42no—
909C42—48no—
910C42—44no—
911C42—48no—
912C42—48no—
913C42H(5,𝔽2)14yes—
914C422−1+418yes—
915C23—21no—
916C23—21no—
917C23—21no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—21no—
925C23—21no—
926C23—21no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23C22×#4112yes—
935C23C22×#4112yes—
936C23C22×#4112yes—
937C23C2611yescharacteristic
938Q8—44no—
939Q8—44no—
940Q8—416no—
941Q8—416no—
942Q8—88no—
943D4—44no—
944D4—44no—
945D4—44no—
946D4—48no—
947D4—48no—
948D4—44no—
949D4—48no—
950C2×C4—22no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—28no—
961C2×C4—28no—
962C2×C4—28no—
963C2×C4—22no—
964C2×C4—28no—
965C2×C4—22no—
966C2×C4—28no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—28no—
974C2×C4—28no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—28no—
978C2×C4—28no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—28no—
990C2×C4—28no—
991C2×C4—28no—
992C2×C4—28no—
993C2×C4—28no—
994C2×C4—28no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—44no—
1000C2×C4—48no—
1001C2×C4—44no—
1002C2×C4—48no—
1003C2×C4—48no—
1004C2×C4—48no—
1005C2×C4—48no—
1006C2×C4—48no—
1007C2×C4—48no—
1008C2×C4—88no—
1009C2×C4—164no—
1010C2×C4C22×#4112yes—
1011C2×C4C22×#4112yes—
1012C2×C4C22×#4112yes—
1013C2×C4C22×#4112yes—
1014C2×C4C2×H(5,𝔽2)12yes—
1015C2×C4C2×H(5,𝔽2)14yes—
1016C2×C4C2×2−1+414yes—
1017C2×C4C2×2−1+414yes—
1018C2×C4C2×2−1+414yes—
1019C2×C4#58512yes—
1020C2×C4#58514yes—
1021C22—22no—
1022C22—22no—
1023C22—22no—
1024C22—24no—
1025C22—24no—
1026C22—24no—
1027C22—42no—
1028C22—42no—
1029C22—42no—
1030C22—41no—
1031C22—41no—
1032C22—41no—
1033C22—41no—
1034C22—41no—
1035C22—41no—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22C23×#4111yescharacteristic
1044C22C22×H(5,𝔽2)11yescharacteristic
1045C22C22×2−1+412yes—
1046C22C2×#58512yes—
1047C22C2×#58511yescharacteristic
1048C4—22no—
1049C4—22no—
1050C4—22no—
1051C4—24no—
1052C4—24no—
1053C4—42no—
1054C4—42no—
1055C4—42no—
1056C4—42no—
1057C4—42no—
1058C4—48no—
1059C4—42no—
1060C4—48no—
1061C4—48no—
1062C4—42no—
1063C4—42no—
1064C4—48no—
1065C4#350514yes—
1066C4#354718yes—
1067C2—42no—
1068C2—42no—
1069C2—42no—
1070C2—82no—
1071C2C2×#354712yes—
1072C2C2×#350511yescharacteristic
1073C2#6280512yes—
1074C2#6283711yescharacteristic
1075C2#6283911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#532C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #59231C2semidirect
2. #59216C2semidirect
3. #45664C2semidirect
4. #45617C2semidirect
5. #40106C2semidirect
6. #40083C2semidirect
7. #39998C2semidirect
8. #39975C2semidirect
9. #38215C2semidirect
10. #38203C2semidirect
11. #37519C2semidirect
12. #37382C2semidirect
14. #36635C2semidirect
15. #36209C2semidirect
16. #36189C2semidirect
17. #36151C2semidirect
18. #36129C2semidirect
19. #35316C2semidirect
20. #35297C2semidirect
21. #35280C2semidirect
22. #34412C2semidirect

Maximal subgroups

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

subgroupindex
#592312
#592162
#456642
#456172
#401062
#400832
#399982
#399752
#382152
#382032
#375192
#373822
#373762
#366352
#362092
#361892
#361512
#361292
#353162
#352972
#352802
#344122
C4×#5322