Finite Group Databasebeta

← #7672500

Subgroups — #7672500

Order 512.

5328 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59684C214yesmaximal, complemented
2#59683C214yesmaximal, complemented
3#59682C214yesmaximal, complemented
4#59585C214yesmaximal, complemented
5#39555C214yesmaximal, complemented
6#39554C214yesmaximal, complemented
7#39184C218yesmaximal, complemented
8#36640C211yesmaximal, characteristic, complemented
9#36520C218yesmaximal, complemented
10#36202C214yesmaximal, complemented
11#36172C214yesmaximal, complemented
12#35630C211yesmaximal, characteristic, complemented
13#35621C211yesmaximal, characteristic, complemented
14#35558C211yesmaximal, characteristic, complemented
15#35533C211yesmaximal, characteristic
16#35327C211yesmaximal, characteristic, complemented
17#35327C211yesmaximal, characteristic, complemented
18#35182C211yesmaximal, characteristic, complemented
19#35152C211yesmaximal, characteristic, complemented
20#34266C211yesmaximal, characteristic, complemented
21#34265C211yesmaximal, characteristic, complemented
22#34189C211yesmaximal, characteristic, complemented
23#34184C211yesmaximal, characteristic, complemented
24C4×#532C211yesmaximal, characteristic, complemented
25C2×C4×#124C211yesmaximal, characteristic, complemented
26C2×#536C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#535C2211yescharacteristic
29C2×#535C2211yescharacteristic
30C2×#532C2211yescharacteristic
31C22×#124C2211yescharacteristic
32C2×#520C2211yescharacteristic
33C2×#520C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C22×C4×Q8C2211yescharacteristic
37C22×C4×D4C2211yescharacteristic
38#2864C2212yescomplemented
39#2864C2212yescomplemented
40#2859C2212yescomplemented
41#2859C2212yescomplemented
42#2853C2214yes—
43#2851C2214yes—
44#2851C2214yes—
45#2850C2212yes—
46#2850C2214yes—
47#2850C2212yes—
48#2849C2214yes—
49#2801C2218yescomplemented
50#2800C2218yescomplemented
51#2779C2218yescomplemented
52#2772C2218yescomplemented
53#2757C2218yescomplemented
54#2753C2218yescomplemented
55#2725C2218yescomplemented
56#2711C2218yescomplemented
57#2623C2214yes—
58#2622C2214yes—
59#2620C2212yes—
60#2620C2214yes—
61#2620C2212yes—
62#2608C2218yescomplemented
63#2602C2218yescomplemented
64#2587C2218yescomplemented
65#2578C2218yescomplemented
66#2576C2218yescomplemented
67#2576C2218yescomplemented
68#2559C2218yescomplemented
69#2558C2218yescomplemented
70#2548C2212yes—
71#2547C2212yescomplemented
72#2546C2212yescomplemented
73#2545C2212yes—
74#2545C2214yes—
75#2545C2214yes—
76#2545C2212yescomplemented
77#2544C2214yes—
78#2544C2214yes—
79#2544C2212yes—
80#2544C2212yescomplemented
81#2541C2212yes—
82#2534C2218yes—
83#2534C2218yes—
84#2531C2218yescomplemented
85#2529C2218yescomplemented
86#2525C2218yescomplemented
87#2518C2218yescomplemented
88#2518C2218yescomplemented
89#2516C2218yescomplemented
90#2515C2218yescomplemented
91#2514C2214yescomplemented
92#2514C2214yescomplemented
93#2513C2214yes—
94#2513C2214yes—
95#2512C2214yes—
96#2512C2214yes—
97#2511C2214yescomplemented
98#2511C2214yescomplemented
99#2510C2218yescomplemented
100#2493C2218yes—
101#2480C2218yes—
102#2467C2218yescomplemented
103#2460C2218yescomplemented
104#2457C2218yescomplemented
105#2448C2214yescomplemented
106#2447C2214yes—
107#2446C2214yescomplemented
108#2445C2214yes—
109#2444C2218yescomplemented
110#2425C2218yes—
111#2424C2218yes—
112#2423C2214yescomplemented
113#2422C2214yes—
114#2421C2214yescomplemented
115#2420C2214yes—
116#2417C2214yescomplemented
117#2416C2214yes—
118#2415C2214yescomplemented
119#2414C2214yes—
120#2374C2218yescomplemented
121#2373C2218yescomplemented
122#2367C2214yes—
123#2367C2214yescomplemented
124#2366C2214yes—
125#2365C2214yescomplemented
126#2364C2218yescomplemented
127#2363C2214yes—
128#2362C2214yescomplemented
129#2361C2214yes—
130#2360C2214yescomplemented
131#2357C2214yescomplemented
132#2356C2214yescomplemented
133#2353C2218yes—
134#2353C2218yescomplemented
135#2351C2214yescomplemented
136#2349C2218yes—
137#2349C2214yescomplemented
138#2322C2214yes—
139#2321C2214yes—
140#2317C2211yescharacteristic
141#2317C2211yescharacteristic
142#2317C2212yescomplemented
143#2317C2212yescomplemented
144#2314C2214yescomplemented
145#2311C2211yescharacteristic
146#2311C2211yescharacteristic
147#2310C2211yescharacteristic
148#2310C2211yescharacteristic
149#2309C2211yescharacteristic
150#2309C2211yescharacteristic
151C4×C4⋊Q8C2212yescomplemented
152C4×#127C2212yescomplemented
153C4×#125C2214yescomplemented
154C4×#125C2214yescomplemented
155C4×#124C2214yes—
156C4×#124C2214yes—
157C4×#124C2214yes—
158C4×#124C2214yes—
159C4×#124C2212yescomplemented
160C4×#124C2212yescomplemented
161C4×#123C2214yes—
162C4×#121C2214yes—
163C4×#121C2214yes—
164C4×#120C2214yes—
165#2297C2211yescharacteristic
166#2297C2211yescharacteristic
167#2296C2211yescharacteristic
168#2296C2211yescharacteristic
169#2296C2211yescharacteristic
170#2296C2211yescharacteristic
171C2×#391C2211yescharacteristic
172#2293C2214yescomplemented
173C2×#390C2211yescharacteristic
174C2×#388C2214yes—
175#2285C2211yescharacteristic
176#2285C2211yescharacteristic
177#2285C2211yescharacteristic
178#2285C2212yescomplemented
179#2283C2214yescomplemented
180C2×#382C2211yescharacteristic
181C2×#382C2212yescomplemented
182#2274C2211yescharacteristic
183#2274C2211yescharacteristic
184C42×D4C2214yescomplemented
185C2×C4×C22⋊C4C2214yes—
186C2×C43C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190C23×D4C2311yescharacteristic
191C24×C4C2312yes—
192#536—28no—
193#536—44no—
194#535—28no—
195#535—44no—
196#532—28no—
197C2×C4⋊Q8C2311yescharacteristic
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2312yes—
200C2×#127C2311yescharacteristic
201C2×#127C2312yes—
202C2×#127C2312yes—
203C2×#126C2318yes—
204C2×#125C2314yes—
205C2×#125C2314yes—
206C2×#124—28no—
207C2×#124C2312yes—
208C2×#124C2312yes—
209C2×#124C2312yes—
210C2×#124C2312yes—
211C2×#124C2314yes—
212C2×#124C2311yescharacteristic
213C2×#124C2311yescharacteristic
214C2×#124C2312yes—
215C2×#124C2312yes—
216C2×#123C2314yes—
217C2×#123C2318yes—
218C2×#123C2314yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2312yes—
222C2×#121C2314yes—
223C2×#121C2314yes—
224C2×#121C2312yes—
225C2×#121C2312yes—
226C2×#121C2318yes—
227C2×#120C2314yes—
228C2×#120C2314yes—
229#520—44no—
230#520—44no—
231C4×#41—28no—
232C4×#41—28no—
233C2×C4×Q8—44no—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2314yes—
240C2×C4×D4—44no—
241C2×C4×D4C2312yes—
242C2×C4×D4C2312yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2318yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2314yes—
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C2×#117C2312yes—
262C2×#117C2312yes—
263C2×#117C2312yes—
264C2×#117C2312yes—
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2312yes—
269C22×C4⋊C4C2312yes—
270C22×C22⋊C4C2314yes—
271C22×C22⋊C4C2312yes—
272C22×C22⋊C4C2314yes—
273C22×C42C2312yes—
274C22×C42C2312yes—
275C22×C42C2311yescharacteristic
276C22×C42C2311yescharacteristic
277C22×C42C2312yes—
278C22×C42C2312yes—
279C22×C42C2312yes—
280C22×C42C2311yescharacteristic
281#401C2318yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#399C2318yes—
287#398C2318yes—
288#398C2318yes—
289#397C2318yes—
290#397C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#396C2318yes—
297#396C2318yes—
298#396C2318yes—
299#396C2318yes—
300#396C2318yes—
301#396C2318yes—
302#396C2318yes—
303#394C2318yes—
304#394C2318yes—
305#394C2318yes—
306#394C2318yes—
307#394C2318yes—
308#394C2318yes—
309#394C2318yes—
310#394C2318yes—
311#394C2318yes—
312#392C2318yes—
313#391C2312yes—
314#391C2312yes—
315#391C2312yes—
316#391C2312yes—
317#391C2314yes—
318#391C2314yes—
319#391C2314yes—
320#391C2312yes—
321#391C2312yes—
322#391C2314yes—
323#391C2312yes—
324#391C2312yes—
325#390C2314yes—
326#390C2312yes—
327#390C2312yes—
328#390C2314yes—
329#390C2312yes—
330#390C2312yes—
331#390C2314yes—
332#390C2314yes—
333#390C2314yes—
334#390C2312yes—
335#390C2312yes—
336#390C2318yes—
337#390C2318yes—
338#390C2314yes—
339#390C2312yes—
340#390C2312yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2318yes—
350#389C2318yes—
351#389C2318yes—
352#389C2312yes—
353#389C2312yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#389C2312yes—
360#389C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2314yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2314yes—
382#388C2318yes—
383#388C2318yes—
384#388C2314yes—
385#388C2314yes—
386#387C2314yes—
387#387C2314yes—
388#387C2314yes—
389#387C2314yes—
390#387C2314yes—
391#387C2314yes—
392#387C2314yes—
393#387C2314yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#386C2314yes—
404#386C2314yes—
405#386C2318yes—
406#386C2318yes—
407#386C2318yes—
408#386C2318yes—
409#386C2312yes—
410#386C2318yes—
411#386C2318yes—
412#386C2312yes—
413#386C2318yes—
414#386C2318yes—
415#386C2318yes—
416#386C2312yes—
417#386C2312yes—
418#385C2314yes—
419#385C2314yes—
420#385C2318yes—
421#385C2318yes—
422#385C2318yes—
423#385C2312yes—
424#385C2312yes—
425#385C2318yes—
426#385C2318yes—
427#385C2312yes—
428#385C2312yes—
429#385C2314yes—
430#385C2314yes—
431#384C2312yes—
432#384C2312yes—
433#384C2312yes—
434#384C2312yes—
435#384C2311yescharacteristic
436#384C2311yescharacteristic
437#383C2318yes—
438#383C2318yes—
439#382C2314yes—
440#382C2314yes—
441#382C2312yes—
442#382C2312yes—
443#382C2312yes—
444#382C2318yes—
445#382C2311yescharacteristic
446#382C2312yes—
447#382C2311yescharacteristic
448#382C2314yes—
449#382C2312yes—
450#382C2312yes—
451#381C2314yes—
452#381C2314yes—
453#381C2318yes—
454#381C2318yes—
455#380C2314yes—
456#380C2314yes—
457#380C2318yes—
458#380C2314yes—
459#380C2314yes—
460#380C2318yes—
461#380C2314yes—
462#379C2314yes—
463#379C2314yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2318yes—
477C4×C4⋊C4C2318yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C22⋊C4C2314yes—
482C4×C22⋊C4C2318yes—
483C4×C22⋊C4C2318yes—
484C4×C22⋊C4C2318yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2318yes—
489C4×C22⋊C4C2318yes—
490C4×C22⋊C4C2318yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2318yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2314yes—
495C4×C22⋊C4C2314yes—
496#376C2318yes—
497C2×#95C2314yes—
498C2×#95C2318yes—
499C2×#95C2314yes—
500C43C2312yes—
501C43C2312yes—
502C43C2312yes—
503C43C2312yes—
504C25C2412yes—
505C2×#41—24no—
506C2×#41—24no—
507C2×#41—24no—
508C2×#41—24no—
509C2×#41—24no—
510C2×#41#4118yes—
511C22×Q8—24no—
512C22×Q8—24no—
513C22×Q8—24no—
514C22×Q8C2412yes—
515C22×Q8C2412yes—
516C22×Q8C2411yescharacteristic
517C22×Q8C2411yescharacteristic
518C22×D4—24no—
519C22×D4—24no—
520C22×D4—24no—
521C22×D4C2412yes—
522C22×D4C2412yes—
523C22×D4C2412yes—
524C22×D4C2411yescharacteristic
525C22×D4C2414yes—
526C22×D4C2412yes—
527C22×D4C2411yescharacteristic
528C22×D4C2418yes—
529C22×D4C2414yes—
530C22×D4C2414yes—
531C23×C4—48no—
532C23×C4—44no—
533C23×C4C2412yes—
534C23×C4C2412yes—
535C23×C4C2411yescharacteristic
536C23×C4C2412yes—
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2411yescharacteristic
540C23×C4C2412yes—
541C23×C4C2414yes—
542C23×C4C2414yes—
543C23×C4C2418yes—
544C23×C4C2414yes—
545C23×C4C2414yes—
546C23×C4C2412yes—
547C23×C4C2411yescharacteristic
548C4⋊Q8—24no—
549C4⋊Q8—28no—
550C4⋊Q8—44no—
551#127—24no—
552#127—28no—
553#127—44no—
554#126—416no—
555#125—48no—
556#125—48no—
557#124—24no—
558#124—28no—
559#124—24no—
560#124—28no—
561#124—28no—
562#124—28no—
563#124—216no—
564#124—44no—
565#124—44no—
566#123—216no—
567#123—416no—
568#123—48no—
569C22⋊Q8—216no—
570C22⋊Q8—44no—
571C22⋊Q8—44no—
572#121—216no—
573#121—216no—
574#121—416no—
575#121—44no—
576#121—44no—
577#120—216no—
578#120—48no—
579C4×Q8—28no—
580C4×Q8—28no—
581C4×Q8—48no—
582C4×Q8—48no—
583C4×Q8—44no—
584C4×Q8—44no—
585C4×D4—216no—
586C4×D4—216no—
587C4×D4—216no—
588C4×D4—28no—
589C4×D4—28no—
590C4×D4—48no—
591C4×D4—48no—
592C4×D4—48no—
593C4×D4—48no—
594C4×D4—44no—
595C4×D4—44no—
596C4×D4—416no—
597C4×D4—48no—
598C4×D4—48no—
599#117—24no—
600#117—24no—
601#117—24no—
602#117—24no—
603#117—24no—
604#117—24no—
605#117—28no—
606#117—28no—
607#117—44no—
608#117—44no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—44no—
612C2×C4⋊C4—44no—
613C2×C4⋊C4—44no—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2418yes—
651C2×C22⋊C4—216no—
652C2×C22⋊C4—48no—
653C2×C22⋊C4—44no—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2412yes—
660C2×C22⋊C4C2412yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2412yes—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2418yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2418yes—
687C2×C42—24no—
688C2×C42—24no—
689C2×C42—28no—
690C2×C42—28no—
691C2×C42—44no—
692C2×C42—44no—
693C2×C42—44no—
694C2×C42#4118yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2412yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2414yes—
707C2×C42C2414yes—
708C2×C42C2411yescharacteristic
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2411yescharacteristic
712C2×C42C2414yes—
713C2×C42C2414yes—
714C2×C42C2418yes—
715C2×C42C2418yes—
716C2×C42C2418yes—
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2412yes—
721C2×C42C2411yescharacteristic
722C2×C42C2412yes—
723C2×C42C2411yescharacteristic
724#95C2418yes—
725#95C2414yes—
726#95C2418yes—
727#95C2418yes—
728#95C2418yes—
729#95C2418yes—
730#95C2418yes—
731#95C2414yes—
732#95C2418yes—
733#95C2418yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2414yes—
747#95C2418yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2418yes—
755#95C2418yes—
756C24—24no—
757C24—24no—
758C24—24no—
759C24—44no—
760C24—44no—
761C24C2514yes—
762C24C2512yes—
763C24C2512yes—
764C24C2511yescharacteristic
765#41—232no—
766#41—416no—
767C2×Q8—22no—
768C2×Q8—22no—
769C2×Q8—24no—
770C2×Q8—24no—
771C2×Q8—24no—
772C2×Q8—24no—
773C2×Q8—22no—
774C2×Q8—22no—
775C2×Q8—24no—
776C2×Q8—24no—
777C2×Q8—22no—
778C2×Q8—416no—
779C2×Q8C2×#4114yes—
780C2×D4—24no—
781C2×D4—24no—
782C2×D4—24no—
783C2×D4—28no—
784C2×D4—24no—
785C2×D4—24no—
786C2×D4—216no—
787C2×D4—22no—
788C2×D4—22no—
789C2×D4—24no—
790C2×D4—24no—
791C2×D4—24no—
792C2×D4—24no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—24no—
796C2×D4—24no—
797C2×D4—22no—
798C2×D4—28no—
799C2×D4—44no—
800C2×D4—48no—
801C2×D4—48no—
802C2×D4—44no—
803C2×D4—44no—
804C2×D4—48no—
805C2×D4—48no—
806C2×D4—416no—
807C2×D4C2×#4118yes—
808C2×D4C2×#4114yes—
809C22×C4—22no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—22no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—28no—
825C22×C4—28no—
826C22×C4—216no—
827C22×C4—42no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—44no—
832C22×C4—48no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—48no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—48no—
842C22×C4—48no—
843C22×C4—816no—
844C22×C4C2×#4118yes—
845C22×C4C2×#4118yes—
846C22×C4C2×#4114yes—
847C22×C4C2×#4114yes—
848C22×C4H(5,𝔽2)14yes—
849C22×C4C2514yes—
850C22×C4C2514yes—
851C22×C4C2512yes—
852C22×C4C2512yes—
853C22×C4C2514yes—
854C22×C4C2514yes—
855C22×C4C2514yes—
856C22×C4C2512yes—
857C22×C4C2514yes—
858C22×C4C2514yes—
859C22×C4C2512yes—
860C22×C4C2512yes—
861C22×C4C2512yes—
862C22×C4C2512yes—
863C22×C4C2512yes—
864C22×C4C2512yes—
865C22×C4C2512yes—
866C22×C4C2512yes—
867C22×C4C2512yes—
868C22×C4C2511yescharacteristic
869C22×C4C2511yescharacteristic
870C4⋊C4—28no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—28no—
874C4⋊C4—24no—
875C4⋊C4—24no—
876C4⋊C4—28no—
877C4⋊C4—216no—
878C4⋊C4—24no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—22no—
883C4⋊C4—22no—
884C4⋊C4—22no—
885C4⋊C4—22no—
886C4⋊C4—28no—
887C4⋊C4—28no—
888C4⋊C4—28no—
889C4⋊C4—28no—
890C4⋊C4—28no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—48no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—48no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—48no—
907C22⋊C4—24no—
908C22⋊C4—24no—
909C22⋊C4—24no—
910C22⋊C4—24no—
911C22⋊C4—28no—
912C22⋊C4—216no—
913C22⋊C4—24no—
914C22⋊C4—24no—
915C22⋊C4—216no—
916C22⋊C4—216no—
917C22⋊C4—28no—
918C22⋊C4—28no—
919C22⋊C4—28no—
920C22⋊C4—216no—
921C22⋊C4—216no—
922C22⋊C4—28no—
923C22⋊C4—28no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—48no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—48no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C42—24no—
941C42—24no—
942C42—24no—
943C42—28no—
944C42—28no—
945C42—22no—
946C42—22no—
947C42—24no—
948C42—24no—
949C42—24no—
950C42—24no—
951C42—24no—
952C42—24no—
953C42—24no—
954C42—24no—
955C42—24no—
956C42—24no—
957C42—42no—
958C42—42no—
959C42—42no—
960C42—42no—
961C42—48no—
962C42—44no—
963C42—44no—
964C42—48no—
965C42—48no—
966C42C2×#4114yes—
967C42C2×#4114yes—
968C42C2×#4118yes—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—22no—
977C23—22no—
978C23—24no—
979C23—22no—
980C23—24no—
981C23—28no—
982C23—24no—
983C23—24no—
984C23—28no—
985C23—416no—
986C23—48no—
987C23—84no—
988C23—88no—
989C23—84no—
990C23C22×#4114yes—
991C23C22×#4112yes—
992C23C22×#4112yes—
993C23C2×H(5,𝔽2)12yes—
994C23C2611yescharacteristic
995Q8—28no—
996Q8—48no—
997Q8—48no—
998Q8—44no—
999D4—216no—
1000D4—28no—
1001D4—416no—
1002D4—48no—
1003D4—48no—
1004D4—48no—
1005D4—44no—
1006D4—816no—
1007D4—164no—
1008D4—164no—
1009C2×C4—28no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—216no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—22no—
1029C2×C4—24no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—28no—
1048C2×C4—28no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—48no—
1058C2×C4—48no—
1059C2×C4—44no—
1060C2×C4—48no—
1061C2×C4—48no—
1062C2×C4—88no—
1063C2×C4—88no—
1064C2×C4—816no—
1065C2×C4—84no—
1066C2×C4—84no—
1067C2×C4—164no—
1068C2×C4—164no—
1069C2×C4#553116yes—
1070C2×C4C22×#4114yes—
1071C2×C4C22×#4114yes—
1072C2×C4C22×#4114yes—
1073C2×C4C22×#4112yes—
1074C2×C4C22×#4112yes—
1075C2×C4C22×#4112yes—
1076C2×C4C22×#4112yes—
1077C2×C4C2×H(5,𝔽2)12yes—
1078C2×C4C2×H(5,𝔽2)12yes—
1079C2×C4#58514yes—
1080C2×C4#58514yes—
1081C22—24no—
1082C22—24no—
1083C22—22no—
1084C22—22no—
1085C22—28no—
1086C22—24no—
1087C22—44no—
1088C22—42no—
1089C22—42no—
1090C22—44no—
1091C22—48no—
1092C22—44no—
1093C22—48no—
1094C22—44no—
1095C22—42no—
1096C22—42no—
1097C22—44no—
1098C22—42no—
1099C22—44no—
1100C22—816no—
1101C22C2×#55314yes—
1102C22C23×#4111yescharacteristic
1103C22C23×#4111yescharacteristic
1104C22C22×H(5,𝔽2)11yescharacteristic
1105C22C2×#58512yes—
1106C22C2×#58512yes—
1107C4—24no—
1108C4—24no—
1109C4—24no—
1110C4—24no—
1111C4—24no—
1112C4—44no—
1113C4—42no—
1114C4—44no—
1115C4—44no—
1116C4—44no—
1117C4—44no—
1118C4—42no—
1119C4—42no—
1120C4—42no—
1121C4—42no—
1122C4—44no—
1123C4—42no—
1124C4—42no—
1125C4—44no—
1126C4C2×#55314yes—
1127C4C2×#55314yes—
1128C2—24no—
1129C2—44no—
1130C2—82no—
1131C2—84no—
1132C2C22×#55311yescharacteristic
1133C2#6281012yes—
1134C2#6281512yes—
1135C2#6282411yescharacteristic
1136C2#6283611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35533C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59684C2semidirect
2. #59683C2semidirect
3. #59682C2semidirect
4. #59585C2semidirect
5. #39555C2semidirect
6. #39554C2semidirect
7. #39184C2semidirect
8. #36640C2semidirect
9. #36520C2semidirect
10. #36202C2semidirect
11. #36172C2semidirect
12. #35630C2semidirect
13. #35621C2semidirect
14. #35558C2semidirect
16. #35327C2semidirect
17. #35327C2semidirect
18. #35182C2semidirect
19. #35152C2semidirect
20. #34266C2semidirect
21. #34265C2semidirect
22. #34189C2semidirect
23. #34184C2semidirect
24. C4×#532C2semidirect
25. C2×C4×#124C2semidirect
38. #2864C22semidirect
39. #2864C22semidirect
40. #2859C22semidirect
41. #2859C22semidirect
49. #2801C22semidirect
50. #2800C22semidirect
51. #2779C22semidirect
52. #2772C22semidirect
53. #2757C22semidirect
54. #2753C22semidirect
55. #2725C22semidirect
56. #2711C22semidirect
62. #2608C22semidirect
63. #2602C22semidirect
64. #2587C22semidirect
65. #2578C22semidirect
66. #2576C22semidirect
67. #2576C22semidirect
68. #2559C22semidirect
69. #2558C22semidirect
71. #2547C22semidirect
72. #2546C22semidirect
76. #2545C22semidirect
80. #2544C22semidirect
84. #2531C22semidirect
85. #2529C22semidirect
86. #2525C22semidirect
87. #2518C22semidirect
88. #2518C22semidirect
89. #2516C22semidirect
90. #2515C22semidirect
91. #2514C22semidirect
92. #2514C22semidirect
97. #2511C22semidirect
98. #2511C22semidirect
99. #2510C22semidirect
102. #2467C22semidirect
103. #2460C22semidirect
104. #2457C22semidirect
105. #2448C22semidirect
107. #2446C22semidirect
109. #2444C22semidirect
112. #2423C22semidirect
114. #2421C22semidirect
116. #2417C22semidirect
118. #2415C22semidirect
120. #2374C22semidirect
121. #2373C22semidirect
123. #2367C22semidirect
125. #2365C22semidirect
126. #2364C22semidirect
128. #2362C22semidirect
130. #2360C22semidirect
131. #2357C22semidirect
132. #2356C22semidirect
134. #2353C22semidirect
135. #2351C22semidirect
137. #2349C22semidirect
142. #2317C22semidirect
143. #2317C22semidirect
144. #2314C22semidirect
151. C4×C4⋊Q8C22semidirect
152. C4×#127C22semidirect
153. C4×#125C22semidirect
154. C4×#125C22semidirect
159. C4×#124C22semidirect
160. C4×#124C22semidirect
172. #2293C22semidirect
178. #2285C22semidirect
179. #2283C22semidirect
181. C2×#382C22semidirect
184. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#596842
#596832
#596822
#595852
#395552
#395542
#391842
#366402
#365202
#362022
#361722
#356302
#356212
#355582
#355332
#353272
#351822
#351522
#342662
#342652
#341892
#341842
C4×#5322
C2×C4×#1242