Finite Group Databasebeta

← #7726887

Subgroups — #7726887

Order 512.

7076 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3558C211yesmaximal, characteristic, complemented
2C22×#542C211yesmaximal, characteristic, complemented
3#51753C214yesmaximal, complemented
4#51752C214yesmaximal, complemented
5#47718C218yesmaximal, complemented
6#45207C214yesmaximal, complemented
7#45049C214yesmaximal, complemented
8#39723C212yesmaximal, complemented
9#39419C214yesmaximal, complemented
10#39374C214yesmaximal, complemented
11#38904C212yesmaximal, complemented
12#38901C214yesmaximal, complemented
13#38023C214yesmaximal, complemented
14#37617C211yesmaximal, characteristic, complemented
15#36967C212yesmaximal, complemented
16#36705C212yesmaximal, complemented
17#36578C212yesmaximal, complemented
18#36236C212yesmaximal, complemented
19#35466C212yesmaximal, complemented
20#35377C212yesmaximal, complemented
21#35301C211yesmaximal, characteristic, complemented
22#35289C211yesmaximal, characteristic, complemented
23#34877C211yesmaximal, characteristic, complemented
24#34240C211yesmaximal, characteristic, complemented
25#3558—216no—
26C2×#562C2212yescomplemented
27C2×H(3,𝔽4)C2212yescomplemented
28C2×#559C2212yescomplemented
29C2×#548C2212yes—
30C2×#546C2214yes—
31C2×#546C2212yescomplemented
32C2×D42C2212yes—
33C2×#542—216no—
34C2×#542C2212yescomplemented
35C2×#542C2214yescomplemented
36C2×#542C2214yescomplemented
37C2×#542C2214yescomplemented
38C2×#542C2214yescomplemented
39C2×#538C2212yes—
40C2×#538C2214yescomplemented
41C2×#535C2212yescomplemented
42C2×#534C2212yes—
43C2×#532C2211yescharacteristic
44C22×C4⋊Q8C2211yescharacteristic, complemented
45C2×#529C2211yescharacteristic
46C22×#126C2212yescomplemented
47C22×#124C2211yescharacteristic
48C22×#124C2212yescomplemented
49C22×#123C2212yescomplemented
50C22×C22⋊Q8C2211yescharacteristic, complemented
51C22×C22⋊Q8C2212yescomplemented
52C22×#121C2211yescharacteristic
53C22×C4×Q8C2211yescharacteristic, complemented
54C22×C4×D4C2211yescharacteristic
55C22×#117C2211yescharacteristic, complemented
56#2862C2212yescomplemented
57#2858C2212yescomplemented
58#2854C2214yescomplemented
59#2854C2212yescomplemented
60#2849C2214yescomplemented
61#2847C2212yescomplemented
62#2821C2214yescomplemented
63#2730C2218yescomplemented
64#2728C2218yescomplemented
65#2710C2218yescomplemented
66#2710C2218yescomplemented
67#2710C2218yescomplemented
68#2706C2218yescomplemented
69#2703C2218yescomplemented
70#2703C2218yescomplemented
71#2695C2218yescomplemented
72#2691C2218yescomplemented
73#2689C2218yescomplemented
74#2689C2218yescomplemented
75#2688C2218yescomplemented
76#2687C2218yescomplemented
77#2685C2218yescomplemented
78#2674C2218yescomplemented
79#2672C2218yescomplemented
80#2670C2218yescomplemented
81#2670C2218yescomplemented
82#2668C2218yescomplemented
83#2658C2212yescomplemented
84#2642C2212yescomplemented
85#2640C2214yescomplemented
86#2628C2212yescomplemented
87#2628C2214yescomplemented
88#2623C2214yescomplemented
89#2622C2214yescomplemented
90#2619C2212yescomplemented
91#2617C2214yescomplemented
92#2611C2212yescomplemented
93#2610C2212yescomplemented
94#2610C2214yescomplemented
95#2601C2214yescomplemented
96#2598C2214yescomplemented
97#2591C2211yescharacteristic
98#2591C2214yescomplemented
99#2591C2212yescomplemented
100#2583C2211yescharacteristic, complemented
101#2579C2214yescomplemented
102#2563C2214yescomplemented
103#2561C2211yescharacteristic, complemented
104#2559C2218yescomplemented
105#2557C2218yescomplemented
106#2555C2218yescomplemented
107#2547C2214yescomplemented
108#2547C2212yescomplemented
109#2546C2212yescomplemented
110#2539C2211yescharacteristic
111#2539C2218yescomplemented
112#2539C2212yescomplemented
113#2536C2214yescomplemented
114#2535C2214yes—
115#2521C2218yescomplemented
116#2521C2218yescomplemented
117#2504C2212yescomplemented
118#2504C2214yescomplemented
119#2504C2212yescomplemented
120#2491C2218yescomplemented
121#2488C2218yescomplemented
122#2488C2218yescomplemented
123#2488C2218yescomplemented
124#2487C2212yescomplemented
125#2487C2214yescomplemented
126#2487C2212yescomplemented
127#2480C2218yescomplemented
128#2472C2218yescomplemented
129#2472C2218yescomplemented
130#2468C2218yescomplemented
131#2448C2218yescomplemented
132#2448C2214yescomplemented
133#2445C2214yescomplemented
134#2444C2218yescomplemented
135#2436C2212yes—
136#2436C2212yescomplemented
137#2436C2212yescomplemented
138#2434C2212yescomplemented
139#2428C2214yes—
140#2426C2214yescomplemented
141#2425C2218yescomplemented
142#2421C2218yescomplemented
143#2421C2214yescomplemented
144#2421C2214yescomplemented
145#2420C2214yescomplemented
146#2420C2214yescomplemented
147#2418C2218yescomplemented
148#2413C2212yescomplemented
149#2412C2218yescomplemented
150#2412C2214yescomplemented
151#2411C2212yescomplemented
152#2410C2214yescomplemented
153#2408C2214yescomplemented
154#2407C2214yescomplemented
155#2406C2212yescomplemented
156#2405C2214yescomplemented
157#2404C2212yescomplemented
158#2403C2214yescomplemented
159#2396C2212yescomplemented
160#2392C2212yescomplemented
161#2372C2214yescomplemented
162#2367C2214yescomplemented
163#2351C2214yescomplemented
164#2349C2214yescomplemented
165#2342C2214yescomplemented
166#2341C2214yescomplemented
167Q8×C22⋊C4C2212yescomplemented
168D4×C22⋊C4C2212yes—
169D4×C22⋊C4C2214yescomplemented
170#2337C2214yescomplemented
171#2324C2214yescomplemented
172#2321C2214yescomplemented
173#2312C2212yescomplemented
174#2311C2214yescomplemented
175#2308C2214yescomplemented
176C4×#124C2214yescomplemented
177C4×#123C2212yescomplemented
178C4×#123C2214yescomplemented
179C4×#120C2212yescomplemented
180#2293C2214yescomplemented
181C2×#386C2214yescomplemented
182#2283C2211yescharacteristic, complemented
183#2273C2212yescomplemented
184C4×#117C2211yescharacteristic, complemented
185C22×#41C2312yes—
186C22×#41C2312yes—
187C23×Q8C2312yes—
188C23×Q8C2311yescharacteristic
189C23×D4C2314yes—
190C23×D4C2312yes—
191C23×D4C2312yes—
192C23×D4C2311yescharacteristic
193C24×C4C2311yescharacteristic
194C24×C4C2312yes—
195#562—216no—
196H(3,𝔽4)—216no—
197#559—216no—
198#548—216no—
199#546—216no—
200#546—232no—
201D42—216no—
202#542—232no—
203#542—232no—
204#542—232no—
205#542—232no—
206#542—216no—
207#538—232no—
208#538—216no—
209#535—216no—
210#534—216no—
211#532—28no—
212C2×C4⋊Q8—28no—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2312yes—
218C2×C4⋊Q8C2314yes—
219C2×#127C2311yescharacteristic
220C2×#127C2312yes—
221#529—28no—
222C2×#126—216no—
223C2×#126C2312yes—
224C2×#126C2318yes—
225C2×#126C2318yes—
226C2×#126C2314yes—
227C2×#125C2311yescharacteristic
228C2×#124—216no—
229C2×#124D4116yescomplemented
230C2×#124C2312yes—
231C2×#124C2311yescharacteristic
232C2×#124C2318yes—
233C2×#124C2318yes—
234C2×#124C2314yes—
235C2×#124C2312yes—
236C2×#124C2314yes—
237C2×#124C2314yes—
238C2×#124C2314yes—
239C2×#124C2314yes—
240C2×#124C2314yes—
241C2×#124C2312yes—
242C2×#124C2312yes—
243C2×#124C2312yes—
244C2×#124C2312yes—
245C2×#123—216no—
246C2×#123C2312yes—
247C2×#123C2318yes—
248C2×#123C2318yes—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×#123C2314yes—
253C2×#123C2312yes—
254C2×#123C2314yes—
255C2×#123C2318yes—
256C2×C22⋊Q8—28no—
257C2×C22⋊Q8—216no—
258C2×C22⋊Q8C2311yescharacteristic
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2318yes—
261C2×C22⋊Q8C2318yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2314yes—
266C2×#121—28no—
267C2×#121C2311yescharacteristic
268C2×#121C2314yes—
269C2×#121C2312yes—
270C2×#121C2312yes—
271C2×#121C2314yes—
272C2×#121C2314yes—
273C2×#121C2314yes—
274C2×#121C2312yes—
275C2×#121C2314yes—
276C2×#121C2314yes—
277C2×#121C2314yes—
278C2×#121C2314yes—
279C2×#121C2318yes—
280C2×#120C2314yes—
281C2×#120C2314yes—
282C2×#120C2314yes—
283C2×#120C2314yes—
284C2×#120C2314yes—
285C2×#120C2314yes—
286C2×#120C2312yes—
287C2×#120C2318yes—
288C2×C4×Q8—28no—
289C2×C4×Q8C2314yes—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2314yes—
293C2×C4×Q8C2314yes—
294C2×C4×D4—28no—
295C2×C4×D4C2312yes—
296C2×C4×D4C2314yes—
297C2×C4×D4C2314yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2311yescharacteristic
301C2×C4×D4C2314yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2314yes—
305C2×C4×D4C2314yes—
306C2×#117—28no—
307C2×#117C2312yes—
308C2×#117C2312yes—
309C2×#117C2312yes—
310C2×#117C2312yes—
311C2×#117C2312yes—
312C2×#117C2312yes—
313C22×C4⋊C4C2312yes—
314C22×C4⋊C4C2312yes—
315C22×C4⋊C4C2311yescharacteristic
316C22×C4⋊C4C2311yescharacteristic
317C22×C4⋊C4C2311yescharacteristic
318C22×C4⋊C4C2311yescharacteristic
319C22×C4⋊C4C2312yes—
320C22×C22⋊C4C2311yescharacteristic
321C22×C22⋊C4C2312yes—
322C22×C22⋊C4C2312yes—
323C22×C22⋊C4C2311yescharacteristic
324C22×C22⋊C4C2312yes—
325C22×C22⋊C4C2314yes—
326C22×C22⋊C4C2314yes—
327C22×C22⋊C4C2318yes—
328C22×C22⋊C4C2312yes—
329C22×C22⋊C4C2312yes—
330C22×C42C2311yescharacteristic
331C22×C42C2312yes—
332C22×C42C2311yescharacteristic
333#400C2314yes—
334#400C2314yes—
335#400C2312yes—
336#400C2314yes—
337#400C2318yes—
338#400C2318yes—
339#400C2318yes—
340#399C2314yes—
341#399C2314yes—
342#399C2314yes—
343#399C2312yes—
344#399C2318yes—
345#399C2318yes—
346#398C2318yes—
347#398C2318yes—
348#398C2312yes—
349#398C2314yes—
350#397C2312yes—
351#397C2318yes—
352#397C2318yes—
353#397C2318yes—
354#397C2318yes—
355#397C2318yes—
356#397C2318yes—
357#397C2318yes—
358#397C2318yes—
359#397C2318yes—
360#396C2318yes—
361#396C2314yes—
362#396C2314yes—
363#395C2318yes—
364#395C2312yes—
365#395C2314yes—
366#394C2312yes—
367#394C2314yes—
368#394C2318yes—
369#394C2314yes—
370#394C2314yes—
371#394C2318yes—
372#394C2318yes—
373#394C2318yes—
374#394C2318yes—
375#394C2318yes—
376#394C2318yes—
377#394C2318yes—
378#394C2318yes—
379#393C2312yes—
380#393C2318yes—
381#393C2318yes—
382#393C2318yes—
383#393C2314yes—
384#392C2314yes—
385#392C2314yes—
386#392C2312yes—
387#392C2318yes—
388#392C2318yes—
389#392C2318yes—
390#392C2318yes—
391#391C2318yes—
392#391C2318yes—
393#391C2314yes—
394#391C2314yes—
395#391C2314yes—
396#391C2314yes—
397#391C2314yes—
398#390C2314yes—
399#390C2314yes—
400#390C2318yes—
401#390C2318yes—
402#390C2314yes—
403#390C2318yes—
404#390C2314yes—
405#390C2318yes—
406#390C2318yes—
407#390C2314yes—
408#390C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2318yes—
412#389C2314yes—
413#389C2314yes—
414#389C2318yes—
415#389C2314yes—
416#388C2314yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2318yes—
422#388C2314yes—
423#388C2318yes—
424#388C2318yes—
425#388C2318yes—
426#388C2318yes—
427#388C2318yes—
428#388C2318yes—
429#388C2318yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2318yes—
434#387C2318yes—
435#387C2314yes—
436#387C2318yes—
437#386C2312yes—
438#386C2314yes—
439#386C2314yes—
440#386C2314yes—
441#386C2318yes—
442#386C2318yes—
443#386C2314yes—
444#386C2314yes—
445#386C2314yes—
446#386C2318yes—
447#386C2318yes—
448#386C2312yes—
449#386C2314yes—
450#386C2314yes—
451#386C2318yes—
452#386C2318yes—
453#386C2318yes—
454#386C2318yes—
455#386C2314yes—
456#386C2318yes—
457#386C2318yes—
458#386C2318yes—
459#386C2318yes—
460#385C2314yes—
461#385C2312yes—
462#385C2318yes—
463#385C2318yes—
464#385C2312yes—
465#385C2318yes—
466#385C2318yes—
467#385C2314yes—
468#385C2318yes—
469#385C2314yes—
470#383C2312yes—
471#382C2314yes—
472#382C2314yes—
473#382C2318yes—
474#382C2312yes—
475#381C2312yes—
476#381C2318yes—
477#381C2318yes—
478#381C2312yes—
479#380C2318yes—
480#380C2318yes—
481#380C2314yes—
482#380C2314yes—
483#380C2312yes—
484#380C2314yes—
485#380C2314yes—
486#380C2318yes—
487#380C2318yes—
488#379C2312yes—
489#379C2318yes—
490#379C2314yes—
491#379C2318yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2318yes—
497C4×C22⋊C4C2311yescharacteristic
498C4×C22⋊C4C2311yescharacteristic
499C4×C22⋊C4C2312yes—
500C4×C22⋊C4C2314yes—
501C4×C22⋊C4C2318yes—
502C4×C22⋊C4C2312yes—
503C4×C22⋊C4C2314yes—
504C4×C22⋊C4C2318yes—
505C4×C22⋊C4C2318yes—
506C4×C22⋊C4C2318yes—
507C4×C22⋊C4C2314yes—
508#376C2312yes—
509#376C2312yes—
510C2×#95C2318yes—
511C43C2312yes—
512C25C2411yescharacteristic
513C25C2412yes—
514C25C2414yes—
515C2×#41—28no—
516C2×#41—28no—
517C2×#41—48no—
518C2×#41—48no—
519C22×Q8—28no—
520C22×Q8—44no—
521C22×Q8—84no—
522C22×Q8C2×D418yes—
523C22×Q8C2412yes—
524C22×Q8C2411yescharacteristic
525C22×Q8C2414yes—
526C22×Q8C2414yes—
527C22×Q8C2412yes—
528C22×Q8C2412yes—
529C22×D4—28no—
530C22×D4—216no—
531C22×D4—28no—
532C22×D4—44no—
533C22×D4—48no—
534C22×D4—48no—
535C22×D4—48no—
536C22×D4—84no—
537C22×D4C2×D418yes—
538C22×D4C2414yes—
539C22×D4C2412yes—
540C22×D4C2412yes—
541C22×D4C2412yes—
542C22×D4C2411yescharacteristic
543C22×D4C2414yes—
544C22×D4C2412yes—
545C22×D4C2414yes—
546C22×D4C2414yes—
547C22×D4C2412yes—
548C22×D4C2414yes—
549C22×D4C2418yes—
550C22×D4C2414yes—
551C22×D4C2414yes—
552C22×D4C2418yes—
553C22×D4C2412yes—
554C23×C4—28no—
555C23×C4—24no—
556C23×C4—44no—
557C23×C4—84no—
558C23×C4C2411yescharacteristic
559C23×C4C2412yes—
560C23×C4C2412yes—
561C23×C4C2411yescharacteristic
562C23×C4C2411yescharacteristic
563C23×C4C2411yescharacteristic
564C23×C4C2412yes—
565C23×C4C2411yescharacteristic
566C23×C4C2412yes—
567C23×C4C2414yes—
568C23×C4C2418yes—
569C23×C4C2414yes—
570C23×C4C2412yes—
571C23×C4C2414yes—
572C23×C4C2418yes—
573C23×C4C2412yes—
574C23×C4C2411yescharacteristic
575C4⋊Q8—28no—
576C4⋊Q8—28no—
577C4⋊Q8—28no—
578C4⋊Q8—28no—
579C4⋊Q8—24no—
580C4⋊Q8—84no—
581#127—28no—
582#127—24no—
583#126—232no—
584#126—232no—
585#126—216no—
586#126—28no—
587#125—24no—
588#124—28no—
589#124—216no—
590#124—232no—
591#124—232no—
592#124—216no—
593#124—216no—
594#124—24no—
595#124—28no—
596#124—84no—
597#124—84no—
598#124—84no—
599#124C2×D4116yes—
600#124C2×D4116yes—
601#124C2×D4116yes—
602#124C2×D4116yes—
603#123—28no—
604#123—232no—
605#123—232no—
606#123—216no—
607#123—216no—
608#123—216no—
609#123—216no—
610#123—48no—
611#123—44no—
612#123—88no—
613C22⋊Q8—216no—
614C22⋊Q8—216no—
615C22⋊Q8—216no—
616C22⋊Q8—28no—
617C22⋊Q8—24no—
618C22⋊Q8—232no—
619C22⋊Q8—232no—
620C22⋊Q8—216no—
621#121—216no—
622#121—216no—
623#121—216no—
624#121—28no—
625#121—24no—
626#121—28no—
627#121—28no—
628#121—216no—
629#121—216no—
630#121—216no—
631#121—216no—
632#121—48no—
633#121—88no—
634#120—216no—
635#120—216no—
636#120—216no—
637#120—216no—
638#120—216no—
639#120—48no—
640#120—44no—
641#120—88no—
642C4×Q8—216no—
643C4×Q8—216no—
644C4×Q8—28no—
645C4×Q8—24no—
646C4×Q8—48no—
647C4×D4—216no—
648C4×D4—216no—
649C4×D4—28no—
650C4×D4—28no—
651C4×D4—216no—
652C4×D4—216no—
653C4×D4—24no—
654C4×D4—28no—
655C4×D4—28no—
656C4×D4—48no—
657C4×D4—48no—
658#117—28no—
659#117—28no—
660#117—28no—
661#117—28no—
662#117—28no—
663#117—44no—
664C2×C4⋊C4—24no—
665C2×C4⋊C4—24no—
666C2×C4⋊C4—24no—
667C2×C4⋊C4—24no—
668C2×C4⋊C4—28no—
669C2×C4⋊C4—28no—
670C2×C4⋊C4—28no—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2418yes—
680C2×C4⋊C4C2418yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2412yes—
684C2×C4⋊C4C2412yes—
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2412yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2412yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2412yes—
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2411yescharacteristic
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2418yes—
697C2×C4⋊C4C2418yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2418yes—
700C2×C4⋊C4C2418yes—
701C2×C4⋊C4C2414yes—
702C2×C22⋊C4—28no—
703C2×C22⋊C4—28no—
704C2×C22⋊C4—24no—
705C2×C22⋊C4—24no—
706C2×C22⋊C4—28no—
707C2×C22⋊C4—216no—
708C2×C22⋊C4—48no—
709C2×C22⋊C4—88no—
710C2×C22⋊C4C2×D4116yes—
711C2×C22⋊C4C2×D4116yes—
712C2×C22⋊C4C2412yes—
713C2×C22⋊C4C2412yes—
714C2×C22⋊C4C2412yes—
715C2×C22⋊C4C2412yes—
716C2×C22⋊C4C2412yes—
717C2×C22⋊C4C2412yes—
718C2×C22⋊C4C2418yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2418yes—
723C2×C22⋊C4C2418yes—
724C2×C22⋊C4C2412yes—
725C2×C22⋊C4C2412yes—
726C2×C22⋊C4C2412yes—
727C2×C22⋊C4C2412yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2412yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2418yes—
736C2×C22⋊C4C2418yes—
737C2×C22⋊C4C2418yes—
738C2×C22⋊C4C2418yes—
739C2×C22⋊C4C2418yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2418yes—
743C2×C22⋊C4C2418yes—
744C2×C22⋊C4C2418yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2418yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C2418yes—
749C2×C22⋊C4C2418yes—
750C2×C22⋊C4C2418yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2418yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2414yes—
757C2×C42—24no—
758C2×C42—28no—
759C2×C42C2×D418yes—
760C2×C42C2412yes—
761C2×C42C2412yes—
762C2×C42C2412yes—
763C2×C42C2414yes—
764C2×C42C2414yes—
765C2×C42C2418yes—
766C2×C42C2414yes—
767C2×C42C2418yes—
768C2×C42C2412yes—
769C2×C42C2412yes—
770C2×C42C2414yes—
771C2×C42C2411yescharacteristic
772C2×C42C2411yescharacteristic
773C2×C42C2411yescharacteristic
774C2×C42C2411yescharacteristic
775#95C2414yes—
776#95C2418yes—
777#95C2418yes—
778#95C2418yes—
779#95C2412yes—
780#95C2414yes—
781#95C2414yes—
782#95C2412yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2418yes—
787#95C2414yes—
788#95C2418yes—
789#95C2418yes—
790#95C2414yes—
791#95C2414yes—
792#95C2414yes—
793#95C2418yes—
794#95C2414yes—
795#95C2418yes—
796#95C2418yes—
797#95C2418yes—
798#95C2418yes—
799#95C2418yes—
800C24—28no—
801C24—22no—
802C24—24no—
803C24—28no—
804C24—42no—
805C24—44no—
806C24—44no—
807C24—42no—
808C24—44no—
809C24—48no—
810C24—48no—
811C24—44no—
812C24C22×D418yes—
813C24C2512yes—
814C24C2512yes—
815C24C2514yes—
816C24C2514yes—
817C24C2511yescharacteristic
818#41—816no—
819#41—816no—
820C2×Q8—22no—
821C2×Q8—24no—
822C2×Q8—28no—
823C2×Q8—28no—
824C2×Q8—28no—
825C2×Q8—44no—
826C2×Q8—44no—
827C2×Q8—44no—
828C2×Q8—44no—
829C2×Q8—42no—
830C2×Q8—44no—
831C2×Q8—44no—
832C2×Q8—416no—
833C2×Q8—816no—
834C2×Q8C22×D418yes—
835C2×Q8C22×D418yes—
836C2×D4—28no—
837C2×D4—24no—
838C2×D4—24no—
839C2×D4—28no—
840C2×D4—24no—
841C2×D4—28no—
842C2×D4—28no—
843C2×D4—28no—
844C2×D4—28no—
845C2×D4—28no—
846C2×D4—216no—
847C2×D4—24no—
848C2×D4—22no—
849C2×D4—24no—
850C2×D4—28no—
851C2×D4—24no—
852C2×D4—28no—
853C2×D4—28no—
854C2×D4—416no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—44no—
858C2×D4—44no—
859C2×D4—48no—
860C2×D4—48no—
861C2×D4—48no—
862C2×D4—44no—
863C2×D4—42no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—48no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—48no—
871C2×D4—48no—
872C2×D4—48no—
873C2×D4—48no—
874C2×D4—816no—
875C2×D4—816no—
876C2×D4—832no—
877C2×D4C22×D418yes—
878C2×D4C22×D418yes—
879C22×C4—24no—
880C22×C4—24no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—24no—
884C22×C4—22no—
885C22×C4—24no—
886C22×C4—24no—
887C22×C4—28no—
888C22×C4—216no—
889C22×C4—24no—
890C22×C4—24no—
891C22×C4—24no—
892C22×C4—24no—
893C22×C4—28no—
894C22×C4—24no—
895C22×C4—28no—
896C22×C4—28no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—44no—
902C22×C4—44no—
903C22×C4—44no—
904C22×C4—42no—
905C22×C4—48no—
906C22×C4—48no—
907C22×C4—44no—
908C22×C4—44no—
909C22×C4—48no—
910C22×C4—44no—
911C22×C4—44no—
912C22×C4—48no—
913C22×C4—48no—
914C22×C4—48no—
915C22×C4—416no—
916C22×C4—816no—
917C22×C4C22×D414yes—
918C22×C4C22×D414yes—
919C22×C4C22×D418yes—
920C22×C4C22×D414yes—
921C22×C4C2514yes—
922C22×C4C2518yes—
923C22×C4C2514yes—
924C22×C4C2512yes—
925C22×C4C2512yes—
926C22×C4C2514yes—
927C22×C4C2512yes—
928C22×C4C2514yes—
929C22×C4C2512yes—
930C22×C4C2514yes—
931C22×C4C2512yes—
932C22×C4C2512yes—
933C22×C4C2511yescharacteristic
934C22×C4C2511yescharacteristic
935C22×C4C2511yescharacteristic
936C22×C4C2511yescharacteristic
937C22×C4C2514yes—
938C22×C4C2511yescharacteristic
939C22×C4C2511yescharacteristic
940C4⋊C4—24no—
941C4⋊C4—24no—
942C4⋊C4—24no—
943C4⋊C4—24no—
944C4⋊C4—24no—
945C4⋊C4—24no—
946C4⋊C4—24no—
947C4⋊C4—24no—
948C4⋊C4—216no—
949C4⋊C4—216no—
950C4⋊C4—28no—
951C4⋊C4—28no—
952C4⋊C4—24no—
953C4⋊C4—24no—
954C4⋊C4—24no—
955C4⋊C4—24no—
956C4⋊C4—24no—
957C4⋊C4—28no—
958C4⋊C4—24no—
959C4⋊C4—22no—
960C4⋊C4—28no—
961C4⋊C4—22no—
962C4⋊C4—28no—
963C4⋊C4—44no—
964C4⋊C4—44no—
965C4⋊C4—48no—
966C4⋊C4—48no—
967C4⋊C4—44no—
968C4⋊C4—48no—
969C4⋊C4—44no—
970C4⋊C4—48no—
971C22⋊C4—216no—
972C22⋊C4—28no—
973C22⋊C4—216no—
974C22⋊C4—24no—
975C22⋊C4—28no—
976C22⋊C4—24no—
977C22⋊C4—28no—
978C22⋊C4—24no—
979C22⋊C4—24no—
980C22⋊C4—24no—
981C22⋊C4—24no—
982C22⋊C4—24no—
983C22⋊C4—24no—
984C22⋊C4—28no—
985C22⋊C4—216no—
986C22⋊C4—24no—
987C22⋊C4—24no—
988C22⋊C4—24no—
989C22⋊C4—28no—
990C22⋊C4—28no—
991C22⋊C4—28no—
992C22⋊C4—28no—
993C22⋊C4—48no—
994C22⋊C4—44no—
995C22⋊C4—48no—
996C22⋊C4—48no—
997C22⋊C4—48no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—48no—
1001C22⋊C4—44no—
1002C22⋊C4—48no—
1003C22⋊C4—48no—
1004C22⋊C4—48no—
1005C22⋊C4—48no—
1006C22⋊C4—48no—
1007C22⋊C4—44no—
1008C22⋊C4—48no—
1009C22⋊C4—44no—
1010C22⋊C4—48no—
1011C22⋊C4—48no—
1012C22⋊C4C22×D4116yes—
1013C22⋊C4C22×D4116yes—
1014C22⋊C4C22×D4116yes—
1015C22⋊C4C22×D4116yes—
1016C42—24no—
1017C42—24no—
1018C42—216no—
1019C42—24no—
1020C42—28no—
1021C42—28no—
1022C42—44no—
1023C42—48no—
1024C42—42no—
1025C42—42no—
1026C42—44no—
1027C42C22×D414yes—
1028C42C22×D414yes—
1029C42C22×D414yes—
1030C42C22×D414yes—
1031C23—22no—
1032C23—22no—
1033C23—24no—
1034C23—28no—
1035C23—24no—
1036C23—28no—
1037C23—216no—
1038C23—22no—
1039C23—22no—
1040C23—24no—
1041C23—24no—
1042C23—22no—
1043C23—24no—
1044C23—22no—
1045C23—24no—
1046C23—28no—
1047C23—22no—
1048C23—24no—
1049C23—22no—
1050C23—28no—
1051C23—24no—
1052C23—24no—
1053C23—48no—
1054C23—48no—
1055C23—44no—
1056C23—44no—
1057C23—44no—
1058C23—816no—
1059C23—88no—
1060C23—88no—
1061C23—88no—
1062C23—88no—
1063C23—816no—
1064C23—168no—
1065C23C23×D418yes—
1066C23C23×D412yes—
1067C23#58514yes—
1068C23C2611yescharacteristic
1069Q8—216no—
1070Q8—48no—
1071Q8—82no—
1072Q8—88no—
1073Q8—88no—
1074Q8—84no—
1075D4—216no—
1076D4—48no—
1077D4—48no—
1078D4—416no—
1079D4—48no—
1080D4—84no—
1081D4—82no—
1082D4—88no—
1083D4—84no—
1084D4—88no—
1085D4—88no—
1086D4—88no—
1087D4—88no—
1088D4—816no—
1089D4—88no—
1090D4—168no—
1091C2×C4—22no—
1092C2×C4—28no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—28no—
1098C2×C4—28no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—28no—
1113C2×C4—28no—
1114C2×C4—22no—
1115C2×C4—24no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—22no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—28no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—48no—
1132C2×C4—44no—
1133C2×C4—48no—
1134C2×C4—44no—
1135C2×C4—44no—
1136C2×C4—48no—
1137C2×C4—48no—
1138C2×C4—44no—
1139C2×C4—48no—
1140C2×C4—48no—
1141C2×C4—88no—
1142C2×C4—88no—
1143C2×C4—816no—
1144C2×C4—88no—
1145C2×C4—168no—
1146C2×C4C23×D418yes—
1147C2×C4C23×D412yes—
1148C2×C4C23×D412yes—
1149C2×C4C23×D412yes—
1150C2×C4C23×D412yes—
1151C2×C4C23×D412yes—
1152C2×C4C23×D412yes—
1153C2×C4#58514yes—
1154C22—22no—
1155C22—22no—
1156C22—28no—
1157C22—28no—
1158C22—28no—
1159C22—28no—
1160C22—48no—
1161C22—48no—
1162C22—42no—
1163C22—42no—
1164C22—44no—
1165C22—44no—
1166C22—42no—
1167C22—42no—
1168C22—42no—
1169C22—44no—
1170C22—42no—
1171C22—44no—
1172C22—44no—
1173C22—44no—
1174C22—48no—
1175C22—44no—
1176C22—48no—
1177C22—816no—
1178C22—88no—
1179C22—1616no—
1180C22#350014yes—
1181C22C24×D411yescharacteristic
1182C22C2×#58512yes—
1183C22C2×#58512yes—
1184C22H(7,𝔽2)12yes—
1185C4—22no—
1186C4—28no—
1187C4—22no—
1188C4—22no—
1189C4—22no—
1190C4—22no—
1191C4—42no—
1192C4—42no—
1193C4—42no—
1194C4—42no—
1195C4—44no—
1196C4—42no—
1197C4—44no—
1198C4—44no—
1199C4—42no—
1200C4—44no—
1201C4—48no—
1202C4—44no—
1203C4#348514yes—
1204C2—24no—
1205C2—48no—
1206C2—82no—
1207C2—84no—
1208C2—82no—
1209C2C2×#348511yescharacteristic
1210C2C2×#350011yescharacteristic
1211C2#6285211yescharacteristic
1212C2#6297014yes—
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×#3558C2semidirect
2. C22×#542C2semidirect
3. #51753C2semidirect
4. #51752C2semidirect
5. #47718C2semidirect
6. #45207C2semidirect
7. #45049C2semidirect
8. #39723C2semidirect
9. #39419C2semidirect
10. #39374C2semidirect
11. #38904C2semidirect
12. #38901C2semidirect
13. #38023C2semidirect
14. #37617C2semidirect
15. #36967C2semidirect
16. #36705C2semidirect
17. #36578C2semidirect
18. #36236C2semidirect
19. #35466C2semidirect
20. #35377C2semidirect
21. #35301C2semidirect
22. #35289C2semidirect
23. #34877C2semidirect
24. #34240C2semidirect
26. C2×#562C22semidirect
27. C2×H(3,𝔽4)C22semidirect
28. C2×#559C22semidirect
31. C2×#546C22semidirect
34. C2×#542C22semidirect
35. C2×#542C22semidirect
36. C2×#542C22semidirect
37. C2×#542C22semidirect
38. C2×#542C22semidirect
40. C2×#538C22semidirect
41. C2×#535C22semidirect
44. C22×C4⋊Q8C22semidirect
46. C22×#126C22semidirect
48. C22×#124C22semidirect
49. C22×#123C22semidirect
50. C22×C22⋊Q8C22semidirect
51. C22×C22⋊Q8C22semidirect
53. C22×C4×Q8C22semidirect
55. C22×#117C22semidirect
56. #2862C22semidirect
57. #2858C22semidirect
58. #2854C22semidirect
59. #2854C22semidirect
60. #2849C22semidirect
61. #2847C22semidirect
62. #2821C22semidirect
63. #2730C22semidirect
64. #2728C22semidirect
65. #2710C22semidirect
66. #2710C22semidirect
67. #2710C22semidirect
68. #2706C22semidirect
69. #2703C22semidirect
70. #2703C22semidirect
71. #2695C22semidirect
72. #2691C22semidirect
73. #2689C22semidirect
74. #2689C22semidirect
75. #2688C22semidirect
76. #2687C22semidirect
77. #2685C22semidirect
78. #2674C22semidirect
79. #2672C22semidirect
80. #2670C22semidirect
81. #2670C22semidirect
82. #2668C22semidirect
83. #2658C22semidirect
84. #2642C22semidirect
85. #2640C22semidirect
86. #2628C22semidirect
87. #2628C22semidirect
88. #2623C22semidirect
89. #2622C22semidirect
90. #2619C22semidirect
91. #2617C22semidirect
92. #2611C22semidirect
93. #2610C22semidirect
94. #2610C22semidirect
95. #2601C22semidirect
96. #2598C22semidirect
98. #2591C22semidirect
99. #2591C22semidirect
100. #2583C22semidirect
101. #2579C22semidirect
102. #2563C22semidirect
103. #2561C22semidirect
104. #2559C22semidirect
105. #2557C22semidirect
106. #2555C22semidirect
107. #2547C22semidirect
108. #2547C22semidirect
109. #2546C22semidirect
111. #2539C22semidirect
112. #2539C22semidirect
113. #2536C22semidirect
115. #2521C22semidirect
116. #2521C22semidirect
117. #2504C22semidirect
118. #2504C22semidirect
119. #2504C22semidirect
120. #2491C22semidirect
121. #2488C22semidirect
122. #2488C22semidirect
123. #2488C22semidirect
124. #2487C22semidirect
125. #2487C22semidirect
126. #2487C22semidirect
127. #2480C22semidirect
128. #2472C22semidirect
129. #2472C22semidirect
130. #2468C22semidirect
131. #2448C22semidirect
132. #2448C22semidirect
133. #2445C22semidirect
134. #2444C22semidirect
136. #2436C22semidirect
137. #2436C22semidirect
138. #2434C22semidirect
140. #2426C22semidirect
141. #2425C22semidirect
142. #2421C22semidirect
143. #2421C22semidirect
144. #2421C22semidirect
145. #2420C22semidirect
146. #2420C22semidirect
147. #2418C22semidirect
148. #2413C22semidirect
149. #2412C22semidirect
150. #2412C22semidirect
151. #2411C22semidirect
152. #2410C22semidirect
153. #2408C22semidirect
154. #2407C22semidirect
155. #2406C22semidirect
156. #2405C22semidirect
157. #2404C22semidirect
158. #2403C22semidirect
159. #2396C22semidirect
160. #2392C22semidirect
161. #2372C22semidirect
162. #2367C22semidirect
163. #2351C22semidirect
164. #2349C22semidirect
165. #2342C22semidirect
166. #2341C22semidirect
167. Q8×C22⋊C4C22semidirect
169. D4×C22⋊C4C22semidirect
170. #2337C22semidirect
171. #2324C22semidirect
172. #2321C22semidirect
173. #2312C22semidirect
174. #2311C22semidirect
175. #2308C22semidirect
176. C4×#124C22semidirect
177. C4×#123C22semidirect
178. C4×#123C22semidirect
179. C4×#120C22semidirect
180. #2293C22semidirect
181. C2×#386C22semidirect
182. #2283C22semidirect
183. #2273C22semidirect
184. C4×#117C22semidirect
229. C2×#124D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35582
C22×#5422
#517532
#517522
#477182
#452072
#450492
#397232
#394192
#393742
#389042
#389012
#380232
#376172
#369672
#367052
#365782
#362362
#354662
#353772
#353012
#352892
#348772
#342402