Finite Group Databasebeta

← #7652665

Subgroups — #7652665

Order 512.

8004 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3509C211yesmaximal, characteristic, complemented
2C2×#3487C211yesmaximal, characteristic, complemented
3#42889C214yesmaximal, complemented
4#42880C214yesmaximal, complemented
5#42815C214yesmaximal, complemented
6#42800C214yesmaximal, complemented
7#41935C218yesmaximal, complemented
8#39954C214yesmaximal, complemented
9#39854C214yesmaximal, complemented
10#39725C214yesmaximal, complemented
11#39174C214yesmaximal, complemented
12#38367C218yesmaximal, complemented
13#35677C211yesmaximal, characteristic, complemented
14#35666C211yesmaximal, characteristic, complemented
15#35661C211yesmaximal, characteristic, complemented
16#35660C211yesmaximal, characteristic, complemented
17#35634C211yesmaximal, characteristic, complemented
18#35556C211yesmaximal, characteristic, complemented
19#35329C211yesmaximal, characteristic, complemented
20#35256C211yesmaximal, characteristic, complemented
21#35149C211yesmaximal, characteristic, complemented
22#34813C211yesmaximal, characteristic, complemented
23#34743C211yesmaximal, characteristic, complemented
24C2×#2432C211yesmaximal, characteristic, complemented
25#34254C211yesmaximal, characteristic, complemented
26C22×2−1+4C2211yescharacteristic
27C23×#41C2211yescharacteristic
28#3509—216no—
29#3487—216no—
30C2×#557C2214yescomplemented
31C2×#556C2214yescomplemented
32C2×#552C2218yes—
33C2×#550C2214yes—
34C2×#550C2214yes—
35C2×#548C2214yes—
36C2×#548C2214yes—
37C2×#541C2214yescomplemented
38C2×#537C2211yescharacteristic
39C2×#536C2211yescharacteristic
40C2×#536C2211yescharacteristic
41C2×#536C2211yescharacteristic
42C2×#536C2211yescharacteristic
43C2×#535C2211yescharacteristic
44C2×#535C2211yescharacteristic
45C2×#535C2214yes—
46C2×#535C2211yescharacteristic
47C2×#533C2211yescharacteristic
48C2×#533C2214yescomplemented
49C2×#532C2211yescharacteristic
50C22×C4⋊Q8C2211yescharacteristic
51C22×#124C2211yescharacteristic
52C2×#525C2211yescharacteristic
53C2×#525C2211yescharacteristic
54C2×#525C2214yes—
55C2×#525C2211yescharacteristic
56C22×C22⋊Q8C2211yescharacteristic
57C2×#519C2211yescharacteristic
58C2×#519C2211yescharacteristic
59C2×C4×#41C2211yescharacteristic
60#2858C2212yescomplemented
61#2858C2212yescomplemented
62#2856C2212yescomplemented
63#2850C2212yescomplemented
64#2849C2214yes—
65#2820C2218yescomplemented
66#2818C2218yescomplemented
67#2723C2218yescomplemented
68#2720C2218yescomplemented
69#2720C2218yescomplemented
70#2714C2218yescomplemented
71#2714C2218yescomplemented
72#2714C2218yescomplemented
73#2711C2218yescomplemented
74#2711C2218yescomplemented
75#2711C2218yescomplemented
76#2711C2218yescomplemented
77#2711C2218yescomplemented
78#2711C2218yescomplemented
79#2692C2218yescomplemented
80#2676C2218yescomplemented
81#2676C2218yescomplemented
82#2676C2218yescomplemented
83#2662C2218yescomplemented
84#2658C2212yescomplemented
85#2657C2212yescomplemented
86#2641C2218yescomplemented
87#2636C2218yescomplemented
88#2633C2218yescomplemented
89#2632C2218yescomplemented
90#2620C2212yescomplemented
91#2619C2218yescomplemented
92#2619C2212yescomplemented
93#2613C2214yes—
94#2610C2218yescomplemented
95#2603C2218yescomplemented
96#2598C2218yescomplemented
97#2592C2214yescomplemented
98#2580C2218yescomplemented
99#2566C2218yescomplemented
100#2548C2218yescomplemented
101#2548C2214yescomplemented
102#2548C2214yescomplemented
103#2545C2214yescomplemented
104#2542C2214yescomplemented
105#2542C2214yescomplemented
106#2540C2214yescomplemented
107#2540C2214yescomplemented
108#2540C2214yescomplemented
109#2540C2214yescomplemented
110#2539C2218yes—
111#2539C2214yes—
112#2538C2214yescomplemented
113#2536C2214yescomplemented
114#2501C2214yes—
115#2492C2212yescomplemented
116#2491C2212yescomplemented
117#2491C2214yescomplemented
118#2490C2214yescomplemented
119#2490C2212yescomplemented
120#2489C2212yescomplemented
121#2488C2214yes—
122#2472C2214yes—
123#2472C2218yes—
124#2436C2212yescomplemented
125#2434C2214yescomplemented
126#2434C2212yescomplemented
127#2434C2212yescomplemented
128#2434C2212yescomplemented
129#2432C2214yes—
130#2432C2214yes—
131#2432C2214yes—
132#2432C2214yes—
133#2432C2214yes—
134#2432C2212yescomplemented
135#2432C2214yescomplemented
136#2432C2212yescomplemented
137#2432C2212yescomplemented
138#2431C2214yes—
139#2431C2212yescomplemented
140#2430C2218yes—
141#2429C2214yescomplemented
142#2429C2212yescomplemented
143#2428C2214yescomplemented
144#2428C2212yescomplemented
145#2427C2212yescomplemented
146#2426C2212yescomplemented
147#2426C2214yescomplemented
148#2426C2214yescomplemented
149#2426C2214yescomplemented
150#2426C2214yescomplemented
151#2425C2214yes—
152#2424C2214yes—
153#2424C2218yes—
154#2413C2214yes—
155#2411C2214yes—
156#2411C2218yes—
157#2409C2214yescomplemented
158#2407C2214yes—
159#2407C2214yes—
160#2407C2214yescomplemented
161#2406C2218yes—
162#2398C2214yescomplemented
163#2392C2214yescomplemented
164C2×#394C2214yes—
165#2356C2214yescomplemented
166#2355C2214yescomplemented
167#2343C2218yes—
168#2326C2218yescomplemented
169#2324C2218yescomplemented
170#2320C2214yescomplemented
171#2317C2211yescharacteristic
172#2311C2211yescharacteristic
173#2310C2211yescharacteristic
174#2309C2211yescharacteristic
175C4×#124C2214yescomplemented
176C4×#121C2214yescomplemented
177#2297C2211yescharacteristic
178#2297C2211yescharacteristic
179#2297C2211yescharacteristic
180#2296C2211yescharacteristic
181#2295C2214yescomplemented
182C2×#391C2211yescharacteristic
183C2×#390C2211yescharacteristic
184C2×#385C2214yes—
185#2280C2211yescharacteristic
186#2274C2211yescharacteristic
187C4×#117C2211yescharacteristic
188C2×C4×C22⋊C4C2211yescharacteristic
189C2×2−1+4—28no—
190C2×2−1+4—44no—
191C2×2−1+4—44no—
192C22×#41—28no—
193C22×#41—44no—
194C22×#41—44no—
195C22×#41C2311yescharacteristic
196C22×#41C2311yescharacteristic
197C22×#41C2311yescharacteristic
198C22×#41C2314yes—
199C22×#41C2314yes—
200C22×#41C2314yes—
201C22×#41C2312yes—
202C22×#41C2312yes—
203C23×Q8C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C23×Q8C2312yes—
206C23×Q8C2312yes—
207C23×D4C2311yescharacteristic
208C23×D4C2312yes—
209C24×C4C2311yescharacteristic
210C24×C4C2312yes—
211#557—232no—
212#556—232no—
213#552—264no—
214#550—232no—
215#550—232no—
216#548—232no—
217#548—232no—
218#541—232no—
219#537—44no—
220#536—28no—
221#536—28no—
222#536—44no—
223#536—44no—
224#535—28no—
225#535—28no—
226#535—232no—
227#535—44no—
228#533—232no—
229#533—28no—
230#532—44no—
231C2×C4⋊Q8—28no—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2314yes—
236C2×C4⋊Q8C2312yes—
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2312yes—
239C2×C4⋊Q8C2311yescharacteristic
240C2×C4⋊Q8C2312yes—
241C2×#127C2318yes—
242C2×#127C2312yes—
243C2×#127C2312yes—
244C2×#127C2312yes—
245C2×#127C2311yescharacteristic
246C2×#126C2318yes—
247C2×#126C2318yes—
248C2×#125C2318yes—
249C2×#125C2312yes—
250C2×#125C2318yes—
251C2×#125C2318yes—
252C2×#124—44no—
253C2×#124C2318yes—
254C2×#124C2312yes—
255C2×#124C2312yes—
256C2×#124C2312yes—
257C2×#124C2312yes—
258C2×#124C2318yes—
259C2×#124C2312yes—
260C2×#124C2311yescharacteristic
261C2×#124C2311yescharacteristic
262C2×#124C2312yes—
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×#124C2314yes—
266C2×#124C2314yes—
267C2×#124C2312yes—
268#525—28no—
269#525—28no—
270#525—232no—
271#525—44no—
272C2×#123C2314yes—
273C2×#123C2312yes—
274C2×#123C2312yes—
275C2×#123C2314yes—
276C2×#123C2312yes—
277C2×#123C2314yes—
278C2×#123C2314yes—
279C2×C22⋊Q8—44no—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2318yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2318yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×#121C2318yes—
296C2×#121C2312yes—
297C2×#121C2312yes—
298C2×#121C2318yes—
299C2×#121C2318yes—
300C2×#121C2314yes—
301C2×#121C2314yes—
302C2×#121C2318yes—
303C2×#121C2312yes—
304C2×#121C2312yes—
305C2×#121C2312yes—
306C2×#121C2314yes—
307C2×#121C2312yes—
308C2×#121C2314yes—
309C2×#121C2314yes—
310C2×#121C2312yes—
311C2×#120C2312yes—
312C2×#120C2314yes—
313C2×#120C2312yes—
314C2×#120C2314yes—
315C2×#120C2314yes—
316C2×#120C2312yes—
317#519—28no—
318#519D4116yescomplemented
319C4×#41—28no—
320C2×C4×Q8C2318yes—
321C2×C4×Q8C2314yes—
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2314yes—
324C2×C4×Q8C2314yes—
325C2×C4×Q8C2314yes—
326C2×C4×Q8C2314yes—
327C2×C4×D4C2318yes—
328C2×C4×D4C2318yes—
329C2×C4×D4C2314yes—
330C2×C4×D4C2314yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2314yes—
335C2×#117C2311yescharacteristic
336C2×#117C2311yescharacteristic
337C2×#117C2311yescharacteristic
338C2×#117C2318yes—
339C2×#117C2312yes—
340C2×#117C2314yes—
341C2×#117C2311yescharacteristic
342C2×#117C2314yes—
343C2×#117C2311yescharacteristic
344C22×C4⋊C4C2311yescharacteristic
345C22×C4⋊C4C2314yes—
346C22×C4⋊C4C2312yes—
347C22×C22⋊C4C2312yes—
348C22×C22⋊C4C2312yes—
349C22×C22⋊C4C2314yes—
350C22×C22⋊C4C2314yes—
351C22×C42C2312yes—
352C22×C42C2311yescharacteristic
353C22×C42C2311yescharacteristic
354#400C2314yes—
355#400C2314yes—
356#399C2318yes—
357#399C2318yes—
358#399C2318yes—
359#399C2318yes—
360#399C2318yes—
361#398C2318yes—
362#398C2314yes—
363#397C2314yes—
364#397C2318yes—
365#397C2314yes—
366#397C2314yes—
367#396C2314yes—
368#396C2318yes—
369#396C2318yes—
370#396C2318yes—
371#396C2314yes—
372#396C2318yes—
373#396C2318yes—
374#395C2318yes—
375#395C2318yes—
376#395C2318yes—
377#394C2314yes—
378#394C2318yes—
379#394C2318yes—
380#394C2318yes—
381#394C2318yes—
382#394C2318yes—
383#394C2318yes—
384#394C2318yes—
385#394C2318yes—
386#394C2318yes—
387#394C2318yes—
388#394C2314yes—
389#394C2318yes—
390#394C2318yes—
391#394C2318yes—
392#394C2318yes—
393#394C2314yes—
394#394C2314yes—
395#394C2318yes—
396#394C2318yes—
397#394C2314yes—
398#393C2314yes—
399#393C2318yes—
400#393C2318yes—
401#393C2314yes—
402#392C2314yes—
403#392C2318yes—
404#392C2318yes—
405#392C2318yes—
406#392C2318yes—
407#392C2318yes—
408#392C2318yes—
409#392C2318yes—
410#391C2314yes—
411#391C2312yes—
412#391C2312yes—
413#391C2312yes—
414#391C2312yes—
415#391C2314yes—
416#391C2312yes—
417#391C2311yescharacteristic
418#391C2314yes—
419#391C2311yescharacteristic
420#391C2312yes—
421#391C2312yes—
422#390C2314yes—
423#390C2314yes—
424#390C2318yes—
425#390C2318yes—
426#390C2312yes—
427#390C2318yes—
428#390C2318yes—
429#390C2318yes—
430#390C2318yes—
431#390C2318yes—
432#390C2318yes—
433#390C2314yes—
434#390C2312yes—
435#390C2311yescharacteristic
436#390C2318yes—
437#390C2318yes—
438#390C2311yescharacteristic
439#390C2312yes—
440#390C2318yes—
441#390C2314yes—
442#390C2318yes—
443#390C2312yes—
444#390C2314yes—
445#390C2312yes—
446#389C2314yes—
447#389C2312yes—
448#389C2318yes—
449#389C2314yes—
450#389C2312yes—
451#388C2314yes—
452#388C2318yes—
453#388C2314yes—
454#388C2318yes—
455#388C2318yes—
456#388C2318yes—
457#388C2318yes—
458#388C2318yes—
459#388C2314yes—
460#388C2314yes—
461#388C2318yes—
462#388C2314yes—
463#388C2314yes—
464#387C2318yes—
465#387C2318yes—
466#387C2318yes—
467#387C2318yes—
468#386C2314yes—
469#386C2318yes—
470#386C2318yes—
471#386C2318yes—
472#386C2318yes—
473#386C2314yes—
474#386C2318yes—
475#386C2314yes—
476#386C2314yes—
477#386C2314yes—
478#386C2314yes—
479#385C2318yes—
480#385C2318yes—
481#385C2318yes—
482#385C2318yes—
483#385C2314yes—
484#385C2318yes—
485#385C2318yes—
486#385C2318yes—
487#385C2318yes—
488#385C2318yes—
489#385C2318yes—
490#385C2314yes—
491#385C2318yes—
492#385C2318yes—
493#384C2318yes—
494#384C2312yes—
495#383C2318yes—
496#382C2318yes—
497#382C2314yes—
498#382C2312yes—
499#381C2314yes—
500#381C2312yes—
501#380C2314yes—
502#380C2314yes—
503#380C2312yes—
504#380C2312yes—
505#379C2314yes—
506#379C2312yes—
507C4×C4⋊C4C2318yes—
508C4×C4⋊C4C2314yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2314yes—
511C4×C4⋊C4C2314yes—
512C4×C4⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2312yes—
522C4×C22⋊C4C2312yes—
523C4×C22⋊C4C2312yes—
524C4×C22⋊C4C2312yes—
525#376C2312yes—
526#376C2318yes—
527C2×#95C2314yes—
528C2×#95C2312yes—
529C43C2312yes—
530C25C2411yescharacteristic
531C25C2412yes—
5322−1+4—464no—
533C2×#41—216no—
534C2×#41—216no—
535C2×#41—28no—
536C2×#41—28no—
537C2×#41—24no—
538C2×#41—216no—
539C2×#41—24no—
540C2×#41—24no—
541C2×#41—24no—
542C2×#41—24no—
543C2×#41—24no—
544C2×#41—24no—
545C2×#41—24no—
546C2×#41—24no—
547C2×#41—48no—
548C2×#41—48no—
549C2×#41—48no—
550C2×#41—48no—
551C2×#41—48no—
552C2×#41—48no—
553C2×#41—44no—
554C2×#41—44no—
555C2×#41—44no—
556C2×#41—44no—
557C2×#41—464no—
558C22×Q8—28no—
559C22×Q8—28no—
560C22×Q8—24no—
561C22×Q8—24no—
562C22×Q8—24no—
563C22×Q8—24no—
564C22×Q8—24no—
565C22×Q8—44no—
566C22×Q8—44no—
567C22×Q8—44no—
568C22×Q8—44no—
569C22×Q8C2×D418yes—
570C22×Q8C2412yes—
571C22×Q8C2412yes—
572C22×Q8C2411yescharacteristic
573C22×Q8C2411yescharacteristic
574C22×Q8C2411yescharacteristic
575C22×Q8C2414yes—
576C22×Q8C2412yes—
577C22×Q8C2412yes—
578C22×Q8C2414yes—
579C22×D4—28no—
580C22×D4—24no—
581C22×D4—24no—
582C22×D4—24no—
583C22×D4—44no—
584C22×D4—44no—
585C22×D4C2412yes—
586C22×D4C2411yescharacteristic
587C22×D4C2412yes—
588C22×D4C2412yes—
589C22×D4C2412yes—
590C22×D4C2411yescharacteristic
591C22×D4C2412yes—
592C22×D4C2411yescharacteristic
593C22×D4C2418yes—
594C22×D4C2414yes—
595C22×D4C2418yes—
596C22×D4C2414yes—
597C22×D4C2418yes—
598C22×D4C2414yes—
599C22×D4C2414yes—
600C22×D4C2414yes—
601C22×D4C2414yes—
602C22×D4C2414yes—
603C22×D4C2414yes—
604C23×C4—28no—
605C23×C4—24no—
606C23×C4—24no—
607C23×C4—24no—
608C23×C4—44no—
609C23×C4—44no—
610C23×C4C2412yes—
611C23×C4C2411yescharacteristic
612C23×C4C2412yes—
613C23×C4C2412yes—
614C23×C4C2412yes—
615C23×C4C2412yes—
616C23×C4C2412yes—
617C23×C4C2412yes—
618C23×C4C2414yes—
619C23×C4C2412yes—
620C23×C4C2412yes—
621C23×C4C2412yes—
622C23×C4C2414yes—
623C23×C4C2414yes—
624C23×C4C2418yes—
625C23×C4C2411yescharacteristic
626C4⋊Q8—28no—
627C4⋊Q8—28no—
628C4⋊Q8—216no—
629C4⋊Q8—28no—
630C4⋊Q8—28no—
631C4⋊Q8—28no—
632C4⋊Q8—42no—
633C4⋊Q8—44no—
634C4⋊Q8—44no—
635#127—28no—
636#127—232no—
637#127—28no—
638#127—42no—
639#127—44no—
640#126—232no—
641#126—232no—
642#125—28no—
643#125—232no—
644#125—232no—
645#125—232no—
646#124—28no—
647#124—28no—
648#124—232no—
649#124—28no—
650#124—28no—
651#124—48no—
652#124—44no—
653#124—44no—
654#124—42no—
655#124—42no—
656#124—44no—
657#124—44no—
658#124—44no—
659#124—416no—
660#124—48no—
661#123—216no—
662#123—28no—
663#123—28no—
664#123—216no—
665#123—44no—
666#123—48no—
667#123—48no—
668C22⋊Q8—216no—
669C22⋊Q8—28no—
670C22⋊Q8—28no—
671C22⋊Q8—232no—
672C22⋊Q8—216no—
673C22⋊Q8—232no—
674C22⋊Q8—216no—
675C22⋊Q8—48no—
676C22⋊Q8—48no—
677C22⋊Q8—44no—
678C22⋊Q8—44no—
679C22⋊Q8—44no—
680C22⋊Q8—48no—
681C22⋊Q8—44no—
682C22⋊Q8—44no—
683#121—28no—
684#121—28no—
685#121—232no—
686#121—216no—
687#121—216no—
688#121—232no—
689#121—232no—
690#121—48no—
691#121—416no—
692#121—44no—
693#121—44no—
694#121—44no—
695#121—44no—
696#121—44no—
697#121—48no—
698#121—48no—
699#120—28no—
700#120—216no—
701#120—28no—
702#120—216no—
703#120—44no—
704#120—48no—
705C4×Q8—28no—
706C4×Q8—216no—
707C4×Q8—216no—
708C4×Q8—232no—
709C4×Q8—216no—
710C4×Q8C2×D4132yes—
711C4×Q8C2×D4132yes—
712C4×D4—28no—
713C4×D4—216no—
714C4×D4—216no—
715C4×D4—232no—
716C4×D4—232no—
717C4×D4—216no—
718C4×D4—48no—
719C4×D4—48no—
720#117—24no—
721#117—24no—
722#117—24no—
723#117—216no—
724#117—28no—
725#117—232no—
726#117C2×D418yes—
727#117C2×D418yes—
728#117C2×D4132yes—
729C2×C4⋊C4—216no—
730C2×C4⋊C4—24no—
731C2×C4⋊C4—44no—
732C2×C4⋊C4C2418yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2418yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2418yes—
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2418yes—
746C2×C4⋊C4C2418yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2418yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2418yes—
755C2×C4⋊C4C2418yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2418yes—
762C2×C22⋊C4—44no—
763C2×C22⋊C4—48no—
764C2×C22⋊C4—44no—
765C2×C22⋊C4—48no—
766C2×C22⋊C4C2412yes—
767C2×C22⋊C4C2418yes—
768C2×C22⋊C4C2412yes—
769C2×C22⋊C4C2412yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2412yes—
772C2×C22⋊C4C2412yes—
773C2×C22⋊C4C2418yes—
774C2×C22⋊C4C2418yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2418yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2418yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2418yes—
784C2×C22⋊C4C2418yes—
785C2×C22⋊C4C2418yes—
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2418yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2418yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2418yes—
803C2×C22⋊C4C2418yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2418yes—
809C2×C22⋊C4C2412yes—
810C2×C22⋊C4C2412yes—
811C2×C42—24no—
812C2×C42—24no—
813C2×C42—28no—
814C2×C42C2418yes—
815C2×C42C2411yescharacteristic
816C2×C42C2412yes—
817C2×C42C2412yes—
818C2×C42C2412yes—
819C2×C42C2412yes—
820C2×C42C2414yes—
821C2×C42C2412yes—
822C2×C42C2411yescharacteristic
823C2×C42C2411yescharacteristic
824C2×C42C2411yescharacteristic
825C2×C42C2414yes—
826C2×C42C2418yes—
827C2×C42C2414yes—
828C2×C42C2412yes—
829C2×C42C2418yes—
830C2×C42C2412yes—
831#95C2418yes—
832#95C2412yes—
833#95C2412yes—
834#95C2412yes—
835#95C2412yes—
836#95C2418yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2418yes—
841#95C2418yes—
842#95C2418yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2418yes—
852#95C2414yes—
853#95C2418yes—
854C24—22no—
855C24—24no—
856C24—24no—
857C24—22no—
858C24—22no—
859C24—24no—
860C24—42no—
861C24—44no—
862C24—42no—
863C24—44no—
864C24C2512yes—
865C24C2514yes—
866C24C2512yes—
867C24C2512yes—
868C24C2512yes—
869C24C2511yescharacteristic
870#41—464no—
871#41—464no—
872#41—464no—
873#41—432no—
874#41—432no—
875#41—416no—
876#41—416no—
877#41—416no—
878C2×Q8—232no—
879C2×Q8—28no—
880C2×Q8—24no—
881C2×Q8—24no—
882C2×Q8—22no—
883C2×Q8—28no—
884C2×Q8—22no—
885C2×Q8—22no—
886C2×Q8—24no—
887C2×Q8—24no—
888C2×Q8—24no—
889C2×Q8—24no—
890C2×Q8—24no—
891C2×Q8—24no—
892C2×Q8—22no—
893C2×Q8—24no—
894C2×Q8—22no—
895C2×Q8—22no—
896C2×Q8—24no—
897C2×Q8—22no—
898C2×Q8—22no—
899C2×Q8—22no—
900C2×Q8—28no—
901C2×Q8—44no—
902C2×Q8—44no—
903C2×Q8—44no—
904C2×Q8—432no—
905C2×Q8—432no—
906C2×Q8—416no—
907C2×Q8C22×D418yes—
908C2×Q8C22×D418yes—
909C2×D4—24no—
910C2×D4—24no—
911C2×D4—24no—
912C2×D4—24no—
913C2×D4—24no—
914C2×D4—24no—
915C2×D4—24no—
916C2×D4—24no—
917C2×D4—24no—
918C2×D4—22no—
919C2×D4—216no—
920C2×D4—24no—
921C2×D4—24no—
922C2×D4—28no—
923C2×D4—22no—
924C2×D4—22no—
925C2×D4—28no—
926C2×D4—216no—
927C2×D4—216no—
928C2×D4—28no—
929C2×D4—22no—
930C2×D4—22no—
931C2×D4—24no—
932C2×D4—22no—
933C2×D4—24no—
934C2×D4—24no—
935C2×D4—22no—
936C2×D4—22no—
937C2×D4—24no—
938C2×D4—22no—
939C2×D4—48no—
940C2×D4—48no—
941C2×D4—44no—
942C2×D4—44no—
943C2×D4—432no—
944C2×D4—44no—
945C2×D4—44no—
946C2×D4—44no—
947C2×D4—48no—
948C2×D4—44no—
949C2×D4—44no—
950C2×D4—44no—
951C2×D4—48no—
952C2×D4—44no—
953C2×D4—48no—
954C2×D4—48no—
955C2×D4—44no—
956C2×D4—44no—
957C2×D4—44no—
958C2×D4—44no—
959C2×D4—44no—
960C2×D4—44no—
961C2×D4—48no—
962C2×D4—48no—
963C2×D4—48no—
964C2×D4—416no—
965C22×C4—24no—
966C22×C4—24no—
967C22×C4—24no—
968C22×C4—24no—
969C22×C4—22no—
970C22×C4—24no—
971C22×C4—24no—
972C22×C4—22no—
973C22×C4—22no—
974C22×C4—24no—
975C22×C4—24no—
976C22×C4—28no—
977C22×C4—24no—
978C22×C4—28no—
979C22×C4—28no—
980C22×C4—24no—
981C22×C4—24no—
982C22×C4—216no—
983C22×C4—24no—
984C22×C4—24no—
985C22×C4—24no—
986C22×C4—24no—
987C22×C4—24no—
988C22×C4—24no—
989C22×C4—24no—
990C22×C4—24no—
991C22×C4—24no—
992C22×C4—24no—
993C22×C4—24no—
994C22×C4—24no—
995C22×C4—24no—
996C22×C4—28no—
997C22×C4—48no—
998C22×C4—48no—
999C22×C4—44no—
1000C22×C4—42no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4—42no—
1006C22×C4—44no—
1007C22×C4—42no—
1008C22×C4—432no—
1009C22×C4—416no—
1010C22×C4C22×D418yes—
1011C22×C4C22×D414yes—
1012C22×C4H(5,𝔽2)14yes—
1013C22×C4H(5,𝔽2)14yes—
1014C22×C4C2512yes—
1015C22×C4C2512yes—
1016C22×C4C2512yes—
1017C22×C4C2514yes—
1018C22×C4C2512yes—
1019C22×C4C2514yes—
1020C22×C4C2512yes—
1021C22×C4C2512yes—
1022C22×C4C2512yes—
1023C22×C4C2514yes—
1024C22×C4C2512yes—
1025C22×C4C2514yes—
1026C22×C4C2512yes—
1027C22×C4C2514yes—
1028C22×C4C2514yes—
1029C22×C4C2514yes—
1030C22×C4C2512yes—
1031C22×C4C2511yescharacteristic
1032C22×C4C2511yescharacteristic
1033C4⋊C4—216no—
1034C4⋊C4—216no—
1035C4⋊C4—28no—
1036C4⋊C4—28no—
1037C4⋊C4—24no—
1038C4⋊C4—216no—
1039C4⋊C4—28no—
1040C4⋊C4—28no—
1041C4⋊C4—216no—
1042C4⋊C4—216no—
1043C4⋊C4—28no—
1044C4⋊C4—28no—
1045C4⋊C4—24no—
1046C4⋊C4—24no—
1047C4⋊C4—22no—
1048C4⋊C4—22no—
1049C4⋊C4—24no—
1050C4⋊C4—48no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—48no—
1056C4⋊C4—44no—
1057C4⋊C4—48no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4C22×D418yes—
1061C4⋊C4C22×D418yes—
1062C4⋊C4C22×D4132yes—
1063C22⋊C4—24no—
1064C22⋊C4—24no—
1065C22⋊C4—24no—
1066C22⋊C4—28no—
1067C22⋊C4—216no—
1068C22⋊C4—216no—
1069C22⋊C4—28no—
1070C22⋊C4—28no—
1071C22⋊C4—216no—
1072C22⋊C4—28no—
1073C22⋊C4—216no—
1074C22⋊C4—28no—
1075C22⋊C4—24no—
1076C22⋊C4—216no—
1077C22⋊C4—24no—
1078C22⋊C4—28no—
1079C22⋊C4—28no—
1080C22⋊C4—42no—
1081C22⋊C4—48no—
1082C22⋊C4—42no—
1083C22⋊C4—48no—
1084C22⋊C4—48no—
1085C22⋊C4—48no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—48no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—48no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—48no—
1104C22⋊C4—48no—
1105C22⋊C4—44no—
1106C22⋊C4C22×D418yes—
1107C22⋊C4C22×D418yes—
1108C42—22no—
1109C42—22no—
1110C42—28no—
1111C42—24no—
1112C42—216no—
1113C42—24no—
1114C42—24no—
1115C42—22no—
1116C42—22no—
1117C42—24no—
1118C42—24no—
1119C42—44no—
1120C42—44no—
1121C42—48no—
1122C42C22×D418yes—
1123C42C22×D4132yes—
1124C42C22×D418yes—
1125C23—22no—
1126C23—22no—
1127C23—22no—
1128C23—22no—
1129C23—24no—
1130C23—22no—
1131C23—22no—
1132C23—22no—
1133C23—22no—
1134C23—22no—
1135C23—22no—
1136C23—24no—
1137C23—22no—
1138C23—22no—
1139C23—22no—
1140C23—22no—
1141C23—24no—
1142C23—22no—
1143C23—24no—
1144C23—28no—
1145C23—24no—
1146C23—22no—
1147C23—24no—
1148C23—24no—
1149C23—22no—
1150C23—24no—
1151C23—28no—
1152C23—24no—
1153C23—22no—
1154C23—44no—
1155C23—44no—
1156C23—416no—
1157C23—48no—
1158C23—44no—
1159C23—84no—
1160C23—88no—
1161C23—84no—
1162C23—84no—
1163C23—84no—
1164C23C23×D412yes—
1165C23C2×H(5,𝔽2)12yes—
1166C23C2×H(5,𝔽2)12yes—
1167C23C2611yescharacteristic
1168Q8—216no—
1169Q8—216no—
1170Q8—416no—
1171Q8—416no—
1172Q8—48no—
1173Q8—48no—
1174Q8—44no—
1175Q8—44no—
1176Q8—44no—
1177D4—432no—
1178D4—416no—
1179D4—48no—
1180D4—48no—
1181D4—48no—
1182D4—48no—
1183D4—48no—
1184D4—44no—
1185D4—44no—
1186D4—44no—
1187D4—88no—
1188D4—816no—
1189D4—816no—
1190D4—88no—
1191D4—88no—
1192D4—88no—
1193D4—164no—
1194D4—164no—
1195D4—164no—
1196C2×C4—22no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—22no—
1204C2×C4—216no—
1205C2×C4—24no—
1206C2×C4—22no—
1207C2×C4—24no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—24no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—22no—
1221C2×C4—24no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—24no—
1230C2×C4—28no—
1231C2×C4—24no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—24no—
1235C2×C4—22no—
1236C2×C4—24no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—22no—
1241C2×C4—416no—
1242C2×C4—48no—
1243C2×C4—432no—
1244C2×C4—416no—
1245C2×C4—416no—
1246C2×C4—44no—
1247C2×C4—48no—
1248C2×C4—48no—
1249C2×C4—48no—
1250C2×C4—48no—
1251C2×C4—48no—
1252C2×C4—48no—
1253C2×C4—84no—
1254C2×C4—84no—
1255C2×C4#535116yes—
1256C2×C4C23×D418yes—
1257C2×C4C23×D418yes—
1258C2×C4C23×D418yes—
1259C2×C4C23×D412yes—
1260C2×C4C23×D412yes—
1261C2×C4C2×H(5,𝔽2)12yes—
1262C2×C4C2×H(5,𝔽2)12yes—
1263C2×C4C2×H(5,𝔽2)12yes—
1264C2×C4C2×H(5,𝔽2)12yes—
1265C2×C4#58514yes—
1266C22—24no—
1267C22—22no—
1268C22—22no—
1269C22—24no—
1270C22—44no—
1271C22—44no—
1272C22—44no—
1273C22—42no—
1274C22—48no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—44no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—44no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—44no—
1287C22—42no—
1288C22—44no—
1289C22—44no—
1290C22—48no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—44no—
1295C22—42no—
1296C22—42no—
1297C22—816no—
1298C22—88no—
1299C22C2×#53514yes—
1300C22C24×D411yescharacteristic
1301C22C22×H(5,𝔽2)11yescharacteristic
1302C22C22×H(5,𝔽2)11yescharacteristic
1303C22C2×#58512yes—
1304C222−1+612yes—
1305C4—24no—
1306C4—28no—
1307C4—28no—
1308C4—28no—
1309C4—42no—
1310C4—44no—
1311C4—44no—
1312C4—42no—
1313C4—42no—
1314C4—42no—
1315C4—42no—
1316C4—44no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—42no—
1321C4—44no—
1322C4C2×#53514yes—
1323C4C2×#53514yes—
1324C2—24no—
1325C2—82no—
1326C2—82no—
1327C2—82no—
1328C2—84no—
1329C2—82no—
1330C2C22×#53511yescharacteristic
1331C2#6283611yescharacteristic
1332C2#6288711yescharacteristic
1333C2#6292512yes—
1334C2#6300212yes—
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. C2×#3509C2semidirect
2. C2×#3487C2semidirect
3. #42889C2semidirect
4. #42880C2semidirect
5. #42815C2semidirect
6. #42800C2semidirect
7. #41935C2semidirect
8. #39954C2semidirect
9. #39854C2semidirect
10. #39725C2semidirect
11. #39174C2semidirect
12. #38367C2semidirect
13. #35677C2semidirect
14. #35666C2semidirect
15. #35661C2semidirect
16. #35660C2semidirect
17. #35634C2semidirect
18. #35556C2semidirect
19. #35329C2semidirect
20. #35256C2semidirect
21. #35149C2semidirect
22. #34813C2semidirect
23. #34743C2semidirect
24. C2×#2432C2semidirect
25. #34254C2semidirect
30. C2×#557C22semidirect
31. C2×#556C22semidirect
37. C2×#541C22semidirect
48. C2×#533C22semidirect
60. #2858C22semidirect
61. #2858C22semidirect
62. #2856C22semidirect
63. #2850C22semidirect
65. #2820C22semidirect
66. #2818C22semidirect
67. #2723C22semidirect
68. #2720C22semidirect
69. #2720C22semidirect
70. #2714C22semidirect
71. #2714C22semidirect
72. #2714C22semidirect
73. #2711C22semidirect
74. #2711C22semidirect
75. #2711C22semidirect
76. #2711C22semidirect
77. #2711C22semidirect
78. #2711C22semidirect
79. #2692C22semidirect
80. #2676C22semidirect
81. #2676C22semidirect
82. #2676C22semidirect
83. #2662C22semidirect
84. #2658C22semidirect
85. #2657C22semidirect
86. #2641C22semidirect
87. #2636C22semidirect
88. #2633C22semidirect
89. #2632C22semidirect
90. #2620C22semidirect
91. #2619C22semidirect
92. #2619C22semidirect
94. #2610C22semidirect
95. #2603C22semidirect
96. #2598C22semidirect
97. #2592C22semidirect
98. #2580C22semidirect
99. #2566C22semidirect
100. #2548C22semidirect
101. #2548C22semidirect
102. #2548C22semidirect
103. #2545C22semidirect
104. #2542C22semidirect
105. #2542C22semidirect
106. #2540C22semidirect
107. #2540C22semidirect
108. #2540C22semidirect
109. #2540C22semidirect
112. #2538C22semidirect
113. #2536C22semidirect
115. #2492C22semidirect
116. #2491C22semidirect
117. #2491C22semidirect
118. #2490C22semidirect
119. #2490C22semidirect
120. #2489C22semidirect
124. #2436C22semidirect
125. #2434C22semidirect
126. #2434C22semidirect
127. #2434C22semidirect
128. #2434C22semidirect
134. #2432C22semidirect
135. #2432C22semidirect
136. #2432C22semidirect
137. #2432C22semidirect
139. #2431C22semidirect
141. #2429C22semidirect
142. #2429C22semidirect
143. #2428C22semidirect
144. #2428C22semidirect
145. #2427C22semidirect
146. #2426C22semidirect
147. #2426C22semidirect
148. #2426C22semidirect
149. #2426C22semidirect
150. #2426C22semidirect
157. #2409C22semidirect
160. #2407C22semidirect
162. #2398C22semidirect
163. #2392C22semidirect
165. #2356C22semidirect
166. #2355C22semidirect
168. #2326C22semidirect
169. #2324C22semidirect
170. #2320C22semidirect
175. C4×#124C22semidirect
176. C4×#121C22semidirect
181. #2295C22semidirect
318. #519D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35092
C2×#34872
#428892
#428802
#428152
#428002
#419352
#399542
#398542
#397252
#391742
#383672
#356772
#356662
#356612
#356602
#356342
#355562
#353292
#352562
#351492
#348132
#347432
C2×#24322
#342542