Finite Group Databasebeta

← #7630960

Subgroups — #7630960

Order 512.

5806 conjugacy classes of subgroups.

The subgroup lattice has 1237 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36640C211yesmaximal, characteristic, complemented
2#36639C211yesmaximal, characteristic, complemented
3#36621C214yesmaximal, complemented
4#36527C214yesmaximal, complemented
5#36526C214yesmaximal, complemented
6#36464C212yesmaximal, complemented
7#36463C212yesmaximal, complemented
8#36454C212yesmaximal, complemented
9#36453C212yesmaximal, complemented
10#36253C214yesmaximal, complemented
11#36252C214yesmaximal, complemented
12#36175C212yesmaximal, complemented
13#36174C212yesmaximal, complemented
14#36115C212yesmaximal, complemented
15#36114C212yesmaximal, complemented
16#35172C211yesmaximal, characteristic, complemented
17#35165C211yesmaximal, characteristic
18#35160C212yesmaximal, complemented
19#35152C212yesmaximal, complemented
20#35043C214yesmaximal, complemented
21#35023C214yesmaximal, complemented
22#34996C214yesmaximal, complemented
23#34265C212yesmaximal, complemented
24#34252C212yesmaximal, complemented
25#34213C211yesmaximal, characteristic, complemented
26#34206C211yesmaximal, characteristic, complemented
27C2×C42×D4C211yesmaximal, characteristic, complemented
28C2×#535C2212yes—
29C2×#533C2211yescharacteristic
30C2×#532C2211yescharacteristic
31C2×#529C2214yescomplemented
32C2×#520C2212yes—
33C22×C4×D4C2211yescharacteristic
34C22×C4×D4C2211yescharacteristic
35C22×C4×D4C2211yescharacteristic
36C23×C42C2212yes—
37#2864C2212yescomplemented
38#2864C2212yescomplemented
39#2862C2211yescharacteristic, complemented
40#2862C2211yescharacteristic, complemented
41#2861C2212yescomplemented
42#2861C2212yescomplemented
43#2859C2211yescharacteristic, complemented
44#2859C2211yescharacteristic, complemented
45#2859C2211yescharacteristic, complemented
46#2859C2211yescharacteristic, complemented
47#2858C2211yescharacteristic, complemented
48#2858C2211yescharacteristic, complemented
49#2855C2214yescomplemented
50#2854C2214yescomplemented
51#2853C2218yescomplemented
52#2852C2218yes—
53#2852C2218yescomplemented
54#2851C2212yes—
55#2851C2212yes—
56#2851C2212yes—
57#2851C2212yes—
58#2851C2214yescomplemented
59#2850C2212yes—
60#2850C2212yes—
61#2850C2212yes—
62#2850C2212yes—
63#2850C2214yescomplemented
64#2849C2218yes—
65#2848C2214yes—
66#2847C2214yes—
67#2643C2218yes—
68#2626C2214yes—
69#2622C2218yes—
70#2617C2214yes—
71#2597C2218yescomplemented
72#2595C2218yescomplemented
73#2580C2214yes—
74#2578C2218yescomplemented
75#2576C2218yescomplemented
76#2576C2218yescomplemented
77#2575C2218yescomplemented
78#2566C2214yes—
79#2563C2212yes—
80#2558C2218yescomplemented
81#2557C2218yescomplemented
82#2547C2212yes—
83#2544C2214yes—
84#2542C2212yes—
85#2541C2212yes—
86#2538C2212yes—
87#2538C2212yes—
88#2537C2212yes—
89#2537C2212yes—
90#2535C2214yes—
91#2527C2218yescomplemented
92#2526C2218yescomplemented
93#2523C2218yescomplemented
94#2518C2218yescomplemented
95#2518C2218yescomplemented
96#2517C2218yescomplemented
97#2514C2214yescomplemented
98#2513C2214yescomplemented
99#2512C2214yescomplemented
100#2511C2214yescomplemented
101#2497C2214yescomplemented
102#2496C2214yescomplemented
103#2495C2214yescomplemented
104#2495C2214yescomplemented
105#2494C2214yescomplemented
106#2494C2214yescomplemented
107#2490C2214yescomplemented
108#2489C2214yescomplemented
109#2471C2218yescomplemented
110#2470C2218yescomplemented
111#2467C2218yescomplemented
112#2466C2218yescomplemented
113#2460C2218yescomplemented
114#2459C2218yescomplemented
115#2447C2214yes—
116#2447C2214yes—
117#2445C2214yes—
118#2445C2214yes—
119#2427C2214yescomplemented
120#2426C2214yescomplemented
121#2422C2214yes—
122#2422C2214yes—
123#2421C2214yescomplemented
124#2420C2214yes—
125#2420C2214yes—
126#2420C2214yescomplemented
127#2370C2214yescomplemented
128#2369C2212yescomplemented
129#2367C2214yes—
130#2367C2214yes—
131#2367C2214yescomplemented
132#2366C2214yes—
133#2366C2214yes—
134#2366C2212yescomplemented
135#2365C2212yescomplemented
136#2365C2212yescomplemented
137#2363C2214yes—
138#2363C2214yes—
139#2361C2214yes—
140#2361C2214yes—
141#2357C2214yescomplemented
142#2356C2214yescomplemented
143#2355C2212yescomplemented
144#2355C2214yescomplemented
145#2355C2214yescomplemented
146#2354C2214yescomplemented
147#2354C2212yescomplemented
148#2352C2214yescomplemented
149Q8×C4⋊C4C2212yescomplemented
150D4×C4⋊C4C2212yescomplemented
151#2347C2214yescomplemented
152#2346C2214yescomplemented
153#2345C2214yescomplemented
154#2344C2214yescomplemented
155#2329C2214yes—
156#2325C2214yes—
157#2321C2218yes—
158#2318C2218yes—
159#2317C2212yes—
160#2317C2212yes—
161#2311C2212yes—
162#2311C2212yes—
163#2309C2212yes—
164C4×#125C2212yescomplemented
165C4×#125C2212yescomplemented
166C4×#125C2212yescomplemented
167C4×#125C2212yescomplemented
168C4×#124C2212yescomplemented
169C4×#124C2212yescomplemented
170C4×#124C2212yescomplemented
171C4×#124C2212yescomplemented
172C4×C22⋊Q8C2214yes—
173C4×C22⋊Q8C2214yescomplemented
174C4×#123C2218yescomplemented
175C4×#121C2214yes—
176C4×#121C2214yescomplemented
177C4×#120C2218yes—
178#2297C2212yes—
179#2297C2212yes—
180#2296C2212yes—
181#2296C2212yes—
182#2290C2218yes—
183#2290C2218yescomplemented
184#2285C2211yescharacteristic
185#2285C2211yescharacteristic
186#2283C2214yescomplemented
187#2274C2212yes—
188C42×D4C2212yes—
189C42×D4C2212yes—
190C42×D4C2212yes—
191C42×D4C2212yes—
192C42×D4C2212yes—
193C42×D4C2212yes—
194C42×D4C2212yes—
195C42×D4C2212yes—
196C2×C4×C4⋊C4C2211yescharacteristic
197C2×C4×C4⋊C4C2211yescharacteristic
198C2×C4×C4⋊C4C2211yescharacteristic
199C2×C4×C22⋊C4C2212yes—
200C2×C4×C22⋊C4C2212yes—
201C2×C4×C22⋊C4C2212yes—
202C2×C43C2211yescharacteristic
203C22×#41C2312yes—
204C23×D4C2311yescharacteristic
205C24×C4C2312yes—
206C24×C4C2312yes—
207C24×C4C2312yes—
208#535—216no—
209#533—28no—
210#532—28no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#127C2314yes—
216#529—416no—
217C2×#126C2318yes—
218C2×#125C2312yes—
219C2×#125C2312yes—
220C2×#125C2312yes—
221C2×#125C2312yes—
222C2×#125C2312yes—
223C2×#124C2312yes—
224C2×#124C2312yes—
225C2×#124C2314yes—
226C2×#124C2312yes—
227C2×#124C2312yes—
228C2×#124C2312yes—
229C2×#123C2318yes—
230C2×#123C2318yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2314yes—
235C2×#121C2312yes—
236C2×#121C2312yes—
237C2×#121C2314yes—
238C2×#121C2314yes—
239C2×#121C2314yes—
240C2×#121C2314yes—
241C2×#120C2318yes—
242#520—216no—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2314yes—
247C2×C4×D4—28no—
248C2×C4×D4—28no—
249C2×C4×D4—28no—
250C2×C4×D4C2312yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2318yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2312yes—
255C2×C4×D4C2312yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2312yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2312yes—
263C2×C4×D4C2312yes—
264C2×C4×D4C2312yes—
265C2×C4×D4C2312yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2318yes—
268C2×C4×D4C2318yes—
269C2×#117C2312yes—
270C2×#117C2312yes—
271C2×#117C2312yes—
272C2×#117C2314yes—
273C2×#117C2318yes—
274C22×C4⋊C4C2311yescharacteristic
275C22×C4⋊C4C2311yescharacteristic
276C22×C4⋊C4C2314yes—
277C22×C4⋊C4C2311yescharacteristic
278C22×C22⋊C4C2312yes—
279C22×C22⋊C4C2312yes—
280C22×C22⋊C4C2312yes—
281C22×C42—48no—
282C22×C42C2311yescharacteristic
283C22×C42C2314yes—
284C22×C42C2311yescharacteristic
285C22×C42C2311yescharacteristic
286C22×C42C2311yescharacteristic
287C22×C42C2311yescharacteristic
288C22×C42C2311yescharacteristic
289C22×C42C2312yes—
290C22×C42C2314yes—
291C22×C42C2314yes—
292C22×C42C2314yes—
293C22×C42C2312yes—
294C22×C42C2312yes—
295C22×C42C2311yescharacteristic
296#401C2318yes—
297#400C2318yes—
298#400C2318yes—
299#400C2318yes—
300#399C2318yes—
301#397C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2318yes—
308#397C2318yes—
309#396C2318yes—
310#396C2318yes—
311#396C2318yes—
312#394C2318yes—
313#394C2318yes—
314#394C2318yes—
315#394C2318yes—
316#394C2318yes—
317#394C2318yes—
318#393C2318yes—
319#392C2318yes—
320#391C2314yes—
321#391C2314yes—
322#391C2318yes—
323#391C2312yes—
324#391C2312yes—
325#391C2312yes—
326#391C2312yes—
327#391C2314yes—
328#391C2312yes—
329#391C2312yes—
330#391C2312yes—
331#391C2312yes—
332#390C2314yes—
333#390C2314yes—
334#390C2314yes—
335#390C2314yes—
336#390C2314yes—
337#390C2314yes—
338#390C2318yes—
339#390C2318yes—
340#390C2312yes—
341#390C2312yes—
342#390C2312yes—
343#390C2312yes—
344#390C2314yes—
345#390C2312yes—
346#390C2312yes—
347#390C2312yes—
348#390C2312yes—
349#389C2312yes—
350#389C2312yes—
351#389C2312yes—
352#389C2312yes—
353#389C2312yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2318yes—
362#389C2314yes—
363#389C2314yes—
364#389C2312yes—
365#389C2312yes—
366#389C2312yes—
367#389C2312yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2314yes—
377#388C2314yes—
378#388C2318yes—
379#388C2318yes—
380#388C2314yes—
381#388C2318yes—
382#388C2314yes—
383#388C2314yes—
384#388C2314yes—
385#388C2314yes—
386#388C2314yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#387C2314yes—
394#387C2314yes—
395#387C2314yes—
396#387C2314yes—
397#387C2314yes—
398#387C2314yes—
399#387C2314yes—
400#387C2314yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#386C2318yes—
413#386C2318yes—
414#386C2314yes—
415#386C2318yes—
416#386C2318yes—
417#386C2318yes—
418#386C2314yes—
419#386C2318yes—
420#386C2318yes—
421#386C2318yes—
422#386C2314yes—
423#386C2318yes—
424#386C2314yes—
425#386C2318yes—
426#386C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2314yes—
432#385C2318yes—
433#385C2318yes—
434#385C2314yes—
435#385C2314yes—
436#385C2318yes—
437#385C2314yes—
438#385C2318yes—
439#385C2318yes—
440#384C2314yes—
441#384C2314yes—
442#384C2311yescharacteristic
443#384C2311yescharacteristic
444#384C2311yescharacteristic
445#384C2311yescharacteristic
446#383C2318yes—
447#383C2318yes—
448#382C2312yes—
449#382C2312yes—
450#382C2312yes—
451#382C2312yes—
452#382C2314yes—
453#382C2314yes—
454#382C2318yes—
455#382C2312yes—
456#382C2312yes—
457#382C2312yes—
458#382C2312yes—
459#382C2312yes—
460#382C2312yes—
461#381C2318yes—
462#381C2318yes—
463#381C2318yes—
464#380C2314yes—
465#380C2314yes—
466#380C2314yes—
467#380C2314yes—
468#380C2314yes—
469#380C2314yes—
470#380C2318yes—
471#380C2312yes—
472#380C2312yes—
473#380C2312yes—
474#380C2314yes—
475#380C2314yes—
476#380C2312yes—
477#379C2318yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2318yes—
487C4×C4⋊C4C2318yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C22⋊C4C2318yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2318yes—
511C4×C22⋊C4C2318yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2318yes—
518C4×C22⋊C4C2318yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2314yes—
522C4×C22⋊C4C2314yes—
523C4×C22⋊C4C2314yes—
524C4×C22⋊C4C2314yes—
525C4×C22⋊C4C2314yes—
526C4×C22⋊C4C2314yes—
527#376C2318yes—
528C2×#95C2312yes—
529C2×#95C2312yes—
530C2×#95C2312yes—
531C43C2311yescharacteristic
532C43C2311yescharacteristic
533C43C2311yescharacteristic
534C43C2311yescharacteristic
535C43C2311yescharacteristic
536C43C2311yescharacteristic
537C43C2311yescharacteristic
538C43C2311yescharacteristic
539C25C2412yes—
540C2×#41—28no—
541C2×#41—28no—
542C2×#41—28no—
543C22×Q8C2412yes—
544C22×Q8C2412yes—
545C22×Q8C2412yes—
546C22×D4—24no—
547C22×D4—24no—
548C22×D4#4118yes—
549C22×D4C2412yes—
550C22×D4C2414yes—
551C22×D4C2412yes—
552C22×D4C2412yes—
553C22×D4C2412yes—
554C22×D4C2418yes—
555C22×D4C2418yes—
556C22×D4C2412yes—
557C23×C4—28no—
558C23×C4—28no—
559C23×C4—28no—
560C23×C4—44no—
561C23×C4—44no—
562C23×C4—44no—
563C23×C4—44no—
564C23×C4—44no—
565C23×C4—44no—
566C23×C4C2414yes—
567C23×C4C2414yes—
568C23×C4C2411yescharacteristic
569C23×C4C2411yescharacteristic
570C23×C4C2414yes—
571C23×C4C2414yes—
572C23×C4C2414yes—
573C23×C4C2414yes—
574C23×C4C2411yescharacteristic
575C23×C4C2411yescharacteristic
576C23×C4C2411yescharacteristic
577C23×C4C2412yes—
578C23×C4C2412yes—
579C23×C4C2418yes—
580C23×C4C2414yes—
581C23×C4C2411yescharacteristic
582C23×C4C2412yes—
583C23×C4C2411yescharacteristic
584C4⋊Q8—24no—
585C4⋊Q8—24no—
586C4⋊Q8—24no—
587#127—216no—
588#127—24no—
589#126—416no—
590#125—28no—
591#125—28no—
592#125—44no—
593#125—44no—
594#125—44no—
595#124—216no—
596#124—28no—
597#124—28no—
598#124—44no—
599#124—44no—
600#124—44no—
601#123—416no—
602#123—416no—
603C22⋊Q8—28no—
604C22⋊Q8—28no—
605C22⋊Q8—48no—
606C22⋊Q8—48no—
607#121—216no—
608#121—216no—
609#121—28no—
610#121—28no—
611#121—48no—
612#121—48no—
613#120—232no—
614C4×Q8—216no—
615C4×Q8—28no—
616C4×Q8—28no—
617C4×Q8—48no—
618C4×D4—28no—
619C4×D4—28no—
620C4×D4—28no—
621C4×D4—28no—
622C4×D4—232no—
623C4×D4—28no—
624C4×D4—28no—
625C4×D4—28no—
626C4×D4—28no—
627C4×D4—216no—
628C4×D4—28no—
629C4×D4—28no—
630C4×D4—28no—
631C4×D4—28no—
632C4×D4—28no—
633C4×D4—28no—
634C4×D4—48no—
635C4×D4—416no—
636C4×D4—416no—
637#117—28no—
638#117—28no—
639#117—28no—
640#117—216no—
641#117—416no—
642C2×C4⋊C4—24no—
643C2×C4⋊C4—24no—
644C2×C4⋊C4—216no—
645C2×C4⋊C4#4118yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2418yes—
672C2×C4⋊C4C2418yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C2418yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2412yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2412yes—
684C2×C4⋊C4C2412yes—
685C2×C22⋊C4—28no—
686C2×C22⋊C4—28no—
687C2×C22⋊C4—28no—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2418yes—
708C2×C22⋊C4C2418yes—
709C2×C22⋊C4C2418yes—
710C2×C22⋊C4C2418yes—
711C2×C22⋊C4C2418yes—
712C2×C22⋊C4C2418yes—
713C2×C22⋊C4C2418yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C42—24no—
719C2×C42—24no—
720C2×C42—216no—
721C2×C42—24no—
722C2×C42—48no—
723C2×C42—48no—
724C2×C42—48no—
725C2×C42—44no—
726C2×C42—44no—
727C2×C42—44no—
728C2×C42—42no—
729C2×C42—42no—
730C2×C42—42no—
731C2×C42#4118yes—
732C2×C42C2414yes—
733C2×C42C2418yes—
734C2×C42C2414yes—
735C2×C42C2414yes—
736C2×C42C2414yes—
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745C2×C42C2414yes—
746C2×C42C2411yescharacteristic
747C2×C42C2411yescharacteristic
748C2×C42C2411yescharacteristic
749C2×C42C2411yescharacteristic
750C2×C42C2411yescharacteristic
751C2×C42C2411yescharacteristic
752C2×C42C2414yes—
753C2×C42C2411yescharacteristic
754C2×C42C2411yescharacteristic
755C2×C42C2411yescharacteristic
756C2×C42C2418yes—
757C2×C42C2418yes—
758C2×C42C2411yescharacteristic
759C2×C42C2411yescharacteristic
760C2×C42C2411yescharacteristic
761C2×C42C2411yescharacteristic
762C2×C42C2411yescharacteristic
763C2×C42C2411yescharacteristic
764C2×C42C2414yes—
765C2×C42C2414yes—
766C2×C42C2414yes—
767C2×C42C2411yescharacteristic
768C2×C42C2411yescharacteristic
769C2×C42C2411yescharacteristic
770C2×C42C2411yescharacteristic
771C2×C42C2411yescharacteristic
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2418yes—
781#95C2418yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2414yes—
788#95C2418yes—
789#95C2414yes—
790#95C2418yes—
791#95C2418yes—
792#95C2418yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2418yes—
799#95C2418yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2418yes—
804#95C2418yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808C24—24no—
809C24—24no—
810C24—42no—
811C24—42no—
812C24—42no—
813C24—42no—
814C24C2×#4118yes—
815C24C2514yes—
816C24C2514yes—
817C24C2511yescharacteristic
818#41—432no—
819C2×Q8—24no—
820C2×Q8—24no—
821C2×Q8—24no—
822C2×Q8—24no—
823C2×Q8—24no—
824C2×Q8—24no—
825C2×Q8—24no—
826C2×Q8—42no—
827C2×Q8—42no—
828C2×D4—28no—
829C2×D4—28no—
830C2×D4—28no—
831C2×D4—216no—
832C2×D4—216no—
833C2×D4—232no—
834C2×D4—24no—
835C2×D4—24no—
836C2×D4—24no—
837C2×D4—24no—
838C2×D4—24no—
839C2×D4—24no—
840C2×D4—24no—
841C2×D4—24no—
842C2×D4—24no—
843C2×D4—24no—
844C2×D4—24no—
845C2×D4—48no—
846C2×D4—48no—
847C2×D4—48no—
848C2×D4—48no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4C2×#4118yes—
852C2×D4C2×#4118yes—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—24no—
864C22×C4—24no—
865C22×C4—28no—
866C22×C4—28no—
867C22×C4—28no—
868C22×C4—28no—
869C22×C4—28no—
870C22×C4—28no—
871C22×C4—28no—
872C22×C4—28no—
873C22×C4—28no—
874C22×C4—28no—
875C22×C4—28no—
876C22×C4—28no—
877C22×C4—28no—
878C22×C4—28no—
879C22×C4—28no—
880C22×C4—216no—
881C22×C4—42no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—41no—
888C22×C4—41no—
889C22×C4—41no—
890C22×C4—41no—
891C22×C4—41no—
892C22×C4—41no—
893C22×C4—42no—
894C22×C4—44no—
895C22×C4—44no—
896C22×C4—44no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—48no—
900C22×C4—48no—
901C22×C4—432no—
902C22×C4—432no—
903C22×C4—432no—
904C22×C4C2×#4114yes—
905C22×C4C2×#4114yes—
906C22×C4C2×#4118yes—
907C22×C4C2×#4114yes—
908C22×C4C2×#4114yes—
909C22×C4C2×#4114yes—
910C22×C4C2514yes—
911C22×C4C2514yes—
912C22×C4C2511yescharacteristic
913C22×C4C2511yescharacteristic
914C22×C4C2511yescharacteristic
915C22×C4C2511yescharacteristic
916C22×C4C2514yes—
917C22×C4C2514yes—
918C22×C4C2514yes—
919C22×C4C2514yes—
920C22×C4C2514yes—
921C22×C4C2514yes—
922C22×C4C2514yes—
923C22×C4C2511yescharacteristic
924C22×C4C2514yes—
925C22×C4C2511yescharacteristic
926C22×C4C2511yescharacteristic
927C22×C4C2511yescharacteristic
928C22×C4C2511yescharacteristic
929C22×C4C2511yescharacteristic
930C22×C4C2511yescharacteristic
931C22×C4C2511yescharacteristic
932C22×C4C2511yescharacteristic
933C22×C4C2511yescharacteristic
934C4⋊C4—24no—
935C4⋊C4—24no—
936C4⋊C4—24no—
937C4⋊C4—24no—
938C4⋊C4—24no—
939C4⋊C4—216no—
940C4⋊C4—24no—
941C4⋊C4—24no—
942C4⋊C4—24no—
943C4⋊C4—24no—
944C4⋊C4—24no—
945C4⋊C4—24no—
946C4⋊C4—24no—
947C4⋊C4—28no—
948C4⋊C4—28no—
949C4⋊C4—24no—
950C4⋊C4—24no—
951C4⋊C4—28no—
952C4⋊C4—24no—
953C4⋊C4—28no—
954C4⋊C4—24no—
955C4⋊C4—28no—
956C4⋊C4—24no—
957C4⋊C4—24no—
958C4⋊C4—28no—
959C4⋊C4—48no—
960C4⋊C4—48no—
961C4⋊C4—48no—
962C4⋊C4—48no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—44no—
968C4⋊C4—44no—
969C4⋊C4—44no—
970C4⋊C4—44no—
971C4⋊C4C2×#4118yes—
972C4⋊C4C2×#4118yes—
973C22⋊C4—28no—
974C22⋊C4—28no—
975C22⋊C4—28no—
976C22⋊C4—28no—
977C22⋊C4—28no—
978C22⋊C4—216no—
979C22⋊C4—216no—
980C22⋊C4—28no—
981C22⋊C4—28no—
982C22⋊C4—28no—
983C22⋊C4—28no—
984C22⋊C4—216no—
985C22⋊C4—28no—
986C22⋊C4—28no—
987C22⋊C4—28no—
988C22⋊C4—28no—
989C22⋊C4—28no—
990C22⋊C4—28no—
991C22⋊C4—48no—
992C22⋊C4—48no—
993C22⋊C4—48no—
994C22⋊C4—48no—
995C22⋊C4—48no—
996C22⋊C4—48no—
997C22⋊C4—48no—
998C22⋊C4—48no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C42—22no—
1004C42—22no—
1005C42—22no—
1006C42—22no—
1007C42—22no—
1008C42—22no—
1009C42—22no—
1010C42—22no—
1011C42—216no—
1012C42—28no—
1013C42—28no—
1014C42—28no—
1015C42—22no—
1016C42—22no—
1017C42—22no—
1018C42—28no—
1019C42—28no—
1020C42—28no—
1021C42—22no—
1022C42—22no—
1023C42—22no—
1024C42—22no—
1025C42—22no—
1026C42—22no—
1027C42—44no—
1028C42—44no—
1029C42—44no—
1030C42—41no—
1031C42—41no—
1032C42—41no—
1033C42—41no—
1034C42—41no—
1035C42—41no—
1036C42—48no—
1037C42—48no—
1038C42C2×#4114yes—
1039C42C2×#4114yes—
1040C42C2×#4114yes—
1041C42C2×#4114yes—
1042C42H(5,𝔽2)14yes—
1043C23—21no—
1044C23—21no—
1045C23—21no—
1046C23—21no—
1047C23—24no—
1048C23—24no—
1049C23—24no—
1050C23—24no—
1051C23—24no—
1052C23—24no—
1053C23—216no—
1054C23—24no—
1055C23—24no—
1056C23—24no—
1057C23—24no—
1058C23—24no—
1059C23—24no—
1060C23—24no—
1061C23—48no—
1062C23—48no—
1063C23—48no—
1064C23—48no—
1065C23—48no—
1066C23—48no—
1067C23C22×#4118yes—
1068C23C22×#4112yes—
1069C23C22×#4112yes—
1070C23C22×#4112yes—
1071C23C2611yescharacteristic
1072Q8—48no—
1073Q8—48no—
1074Q8—84no—
1075D4—216no—
1076D4—216no—
1077D4—416no—
1078D4—48no—
1079D4—48no—
1080D4—84no—
1081D4—816no—
1082D4—816no—
1083C2×C4—28no—
1084C2×C4—28no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—24no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—24no—
1101C2×C4—28no—
1102C2×C4—24no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—48no—
1142C2×C4—44no—
1143C2×C4—416no—
1144C2×C4—416no—
1145C2×C4—416no—
1146C2×C4—416no—
1147C2×C4—416no—
1148C2×C4—44no—
1149C2×C4—44no—
1150C2×C4—48no—
1151C2×C4—48no—
1152C2×C4—416no—
1153C2×C4—416no—
1154C2×C4—816no—
1155C2×C4#529116yescomplemented
1156C2×C4C22×#4118yes—
1157C2×C4C22×#4112yes—
1158C2×C4C22×#4112yes—
1159C2×C4C22×#4112yes—
1160C2×C4C22×#4112yes—
1161C2×C4C22×#4112yes—
1162C2×C4C22×#4112yes—
1163C2×C4C22×#4112yes—
1164C2×C4C22×#4112yes—
1165C2×C4C22×#4112yes—
1166C2×C4C22×#4112yes—
1167C2×C4C2×H(5,𝔽2)12yes—
1168C2×C4C2×H(5,𝔽2)12yes—
1169C2×C4C2×H(5,𝔽2)12yes—
1170C2×C4#58512yes—
1171C2×C4#58512yes—
1172C2×C4#58512yes—
1173C22—22no—
1174C22—22no—
1175C22—22no—
1176C22—22no—
1177C22—22no—
1178C22—22no—
1179C22—28no—
1180C22—28no—
1181C22—28no—
1182C22—432no—
1183C22—44no—
1184C22—44no—
1185C22—44no—
1186C22—44no—
1187C22—44no—
1188C22—44no—
1189C22—44no—
1190C22—44no—
1191C22—44no—
1192C22—44no—
1193C22—44no—
1194C22C2×#52914yes—
1195C22C23×#4111yescharacteristic
1196C22C23×#4111yescharacteristic
1197C22C23×#4111yescharacteristic
1198C22C22×H(5,𝔽2)11yescharacteristic
1199C22C2×#58511yescharacteristic
1200C22C2×#58511yescharacteristic
1201C22C2×#58511yescharacteristic
1202C4—22no—
1203C4—22no—
1204C4—22no—
1205C4—22no—
1206C4—22no—
1207C4—28no—
1208C4—22no—
1209C4—22no—
1210C4—44no—
1211C4—44no—
1212C4—44no—
1213C4—44no—
1214C4—44no—
1215C4—41no—
1216C4—41no—
1217C4—44no—
1218C4—44no—
1219C4—41no—
1220C4—41no—
1221C4—44no—
1222C4—44no—
1223C4C2×#52914yes—
1224C4C2×#52914yes—
1225C4#350614yes—
1226C2—24no—
1227C2—48no—
1228C2—84no—
1229C2C22×#52911yescharacteristic
1230C2C2×#350611yescharacteristic
1231C2#6277311yescharacteristic
1232C2#6277311yescharacteristic
1233C2#6278111yescharacteristic
1234C2#6279311yescharacteristic
1235C2#6281511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35165C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36640C2semidirect
2. #36639C2semidirect
3. #36621C2semidirect
4. #36527C2semidirect
5. #36526C2semidirect
6. #36464C2semidirect
7. #36463C2semidirect
8. #36454C2semidirect
9. #36453C2semidirect
10. #36253C2semidirect
11. #36252C2semidirect
12. #36175C2semidirect
13. #36174C2semidirect
14. #36115C2semidirect
15. #36114C2semidirect
16. #35172C2semidirect
18. #35160C2semidirect
19. #35152C2semidirect
20. #35043C2semidirect
21. #35023C2semidirect
22. #34996C2semidirect
23. #34265C2semidirect
24. #34252C2semidirect
25. #34213C2semidirect
26. #34206C2semidirect
27. C2×C42×D4C2semidirect
31. C2×#529C22semidirect
37. #2864C22semidirect
38. #2864C22semidirect
39. #2862C22semidirect
40. #2862C22semidirect
41. #2861C22semidirect
42. #2861C22semidirect
43. #2859C22semidirect
44. #2859C22semidirect
45. #2859C22semidirect
46. #2859C22semidirect
47. #2858C22semidirect
48. #2858C22semidirect
49. #2855C22semidirect
50. #2854C22semidirect
51. #2853C22semidirect
53. #2852C22semidirect
58. #2851C22semidirect
63. #2850C22semidirect
71. #2597C22semidirect
72. #2595C22semidirect
74. #2578C22semidirect
75. #2576C22semidirect
76. #2576C22semidirect
77. #2575C22semidirect
80. #2558C22semidirect
81. #2557C22semidirect
91. #2527C22semidirect
92. #2526C22semidirect
93. #2523C22semidirect
94. #2518C22semidirect
95. #2518C22semidirect
96. #2517C22semidirect
97. #2514C22semidirect
98. #2513C22semidirect
99. #2512C22semidirect
100. #2511C22semidirect
101. #2497C22semidirect
102. #2496C22semidirect
103. #2495C22semidirect
104. #2495C22semidirect
105. #2494C22semidirect
106. #2494C22semidirect
107. #2490C22semidirect
108. #2489C22semidirect
109. #2471C22semidirect
110. #2470C22semidirect
111. #2467C22semidirect
112. #2466C22semidirect
113. #2460C22semidirect
114. #2459C22semidirect
119. #2427C22semidirect
120. #2426C22semidirect
123. #2421C22semidirect
126. #2420C22semidirect
127. #2370C22semidirect
128. #2369C22semidirect
131. #2367C22semidirect
134. #2366C22semidirect
135. #2365C22semidirect
136. #2365C22semidirect
141. #2357C22semidirect
142. #2356C22semidirect
143. #2355C22semidirect
144. #2355C22semidirect
145. #2355C22semidirect
146. #2354C22semidirect
147. #2354C22semidirect
148. #2352C22semidirect
149. Q8×C4⋊C4C22semidirect
150. D4×C4⋊C4C22semidirect
151. #2347C22semidirect
152. #2346C22semidirect
153. #2345C22semidirect
154. #2344C22semidirect
164. C4×#125C22semidirect
165. C4×#125C22semidirect
166. C4×#125C22semidirect
167. C4×#125C22semidirect
168. C4×#124C22semidirect
169. C4×#124C22semidirect
170. C4×#124C22semidirect
171. C4×#124C22semidirect
173. C4×C22⋊Q8C22semidirect
174. C4×#123C22semidirect
176. C4×#121C22semidirect
183. #2290C22semidirect
186. #2283C22semidirect
1155. C2×C4#529semidirect

Maximal subgroups

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

subgroupindex
#366402
#366392
#366212
#365272
#365262
#364642
#364632
#364542
#364532
#362532
#362522
#361752
#361742
#361152
#361142
#351722
#351652
#351602
#351522
#350432
#350232
#349962
#342652
#342522
#342132
#342062
C2×C42×D42