Finite Group Databasebeta

← #7652152

Subgroups — #7652152

Order 512.

5298 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42668C214yesmaximal, complemented
2#42641C214yesmaximal, complemented
3#42550C214yesmaximal, complemented
4#42460C214yesmaximal, complemented
5#40894C218yesmaximal, complemented
6#40054C214yesmaximal, complemented
7#39900C214yesmaximal, complemented
8#39656C214yesmaximal, complemented
9#39606C214yesmaximal, complemented
10#38543C218yesmaximal, complemented
11#35673C211yesmaximal, characteristic, complemented
12#35661C211yesmaximal, characteristic, complemented
13#35634C211yesmaximal, characteristic, complemented
14#35621C211yesmaximal, characteristic, complemented
15#35555C211yesmaximal, characteristic, complemented
16#35530C211yesmaximal, characteristic, complemented
17#35308C211yesmaximal, characteristic, complemented
18#35273C211yesmaximal, characteristic, complemented
19#35223C211yesmaximal, characteristic, complemented
20C2×#2502C211yesmaximal, characteristic, complemented
21#34743C211yesmaximal, characteristic, complemented
22#34742C211yesmaximal, characteristic, complemented
23#34268C211yesmaximal, characteristic, complemented
24#34200C211yesmaximal, characteristic, complemented
25#34188C211yesmaximal, characteristic, complemented
26C2×#537C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#536C2211yescharacteristic
30C2×#536C2211yescharacteristic
31C2×#532C2211yescharacteristic
32C2×#525C2211yescharacteristic
33C2×#525C2211yescharacteristic
34C2×#525C2211yescharacteristic
35C22×C22⋊Q8C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C2×#519C2211yescharacteristic
38C2×C4×#41C2211yescharacteristic
39C2×C4×#41C2211yescharacteristic
40C23×C4⋊C4C2211yescharacteristic
41#2857C2212yescomplemented
42#2857C2212yescomplemented
43#2856C2212yescomplemented
44#2850C2212yescomplemented
45#2847C2214yes—
46#2837C2218yescomplemented
47#2836C2218yescomplemented
48#2797C2218yes—
49#2793C2218yescomplemented
50#2791C2218yescomplemented
51#2786C2218yes—
52#2780C2218yes—
53#2768C2218yes—
54#2768C2218yescomplemented
55#2768C2218yescomplemented
56#2753C2218yes—
57#2748C2218yes—
58#2748C2218yescomplemented
59#2741C2218yescomplemented
60#2711C2218yes—
61#2707C2218yescomplemented
62#2701C2218yescomplemented
63#2671C2218yes—
64#2667C2218yescomplemented
65#2651C2218yescomplemented
66#2651C2218yescomplemented
67#2649C2218yes—
68#2630C2218yes—
69#2629C2218yescomplemented
70#2621C2212yescomplemented
71#2620C2212yescomplemented
72#2620C2212yescomplemented
73#2620C2212yescomplemented
74#2618C2214yes—
75#2570C2214yescomplemented
76#2552C2214yescomplemented
77#2547C2212yescomplemented
78#2546C2212yescomplemented
79#2545C2212yescomplemented
80#2544C2212yescomplemented
81#2542C2214yes—
82#2542C2214yes—
83#2540C2214yes—
84#2540C2214yes—
85#2539C2214yes—
86#2538C2214yes—
87#2538C2214yescomplemented
88#2537C2214yescomplemented
89#2536C2214yes—
90#2522C2218yes—
91#2507C2214yescomplemented
92#2507C2218yescomplemented
93#2506C2214yescomplemented
94#2502C2214yes—
95#2502C2214yes—
96#2502C2214yes—
97#2502C2214yes—
98#2502C2212yescomplemented
99#2501C2214yes—
100#2501C2212yescomplemented
101#2500C2212yescomplemented
102#2499C2212yescomplemented
103#2498C2218yes—
104#2476C2218yes—
105#2476C2218yescomplemented
106#2473C2218yes—
107#2464C2218yes—
108#2454C2218yes—
109#2448C2214yescomplemented
110#2446C2214yescomplemented
111#2443C2218yes—
112#2429C2214yes—
113#2429C2212yes—
114#2429C2214yescomplemented
115#2428C2212yes—
116#2427C2212yes—
117#2427C2214yescomplemented
118#2426C2212yes—
119#2426C2214yes—
120#2425C2218yes—
121#2425C2218yes—
122#2425C2214yes—
123#2424C2214yes—
124#2423C2212yes—
125#2423C2214yescomplemented
126#2423C2214yescomplemented
127#2422C2212yes—
128#2422C2214yescomplemented
129#2421C2212yes—
130#2421C2214yescomplemented
131#2420C2212yes—
132#2419C2214yes—
133#2418C2214yes—
134#2417C2214yes—
135#2417C2214yes—
136#2417C2214yescomplemented
137#2416C2214yes—
138#2416C2218yes—
139#2416C2214yes—
140#2415C2214yescomplemented
141#2413C2214yes—
142#2411C2214yes—
143#2395C2214yes—
144#2392C2214yes—
145C2×#398C2214yes—
146#2367C2214yescomplemented
147#2365C2214yescomplemented
148#2361C2214yes—
149#2360C2214yes—
150#2359C2218yes—
151#2355C2214yescomplemented
152#2354C2214yescomplemented
153#2352C2218yes—
154#2352C2214yes—
155D4×C4⋊C4C2214yes—
156#2335C2218yes—
157#2324C2218yes—
158#2323C2214yescomplemented
159#2322C2214yes—
160#2317C2211yescharacteristic
161#2317C2211yescharacteristic
162#2316C2211yescharacteristic
163#2314C2214yescomplemented
164#2311C2211yescharacteristic
165#2311C2211yescharacteristic
166#2311C2211yescharacteristic
167#2311C2211yescharacteristic
168C4×C22⋊Q8C2214yescomplemented
169C4×#123C2214yes—
170C4×#121C2214yes—
171C4×#120C2214yes—
172#2297C2211yescharacteristic
173#2297C2211yescharacteristic
174#2296C2211yescharacteristic
175#2296C2211yescharacteristic
176C2×#391C2211yescharacteristic
177C2×#391C2211yescharacteristic
178C2×#385C2214yes—
179#2285C2211yescharacteristic
180#2285C2214yescomplemented
181C2×#384C2211yescharacteristic
182C2×#384C2211yescharacteristic
183#2280C2211yescharacteristic
184#2274C2211yescharacteristic
185#2274C2211yescharacteristic
186C2×C4×C22⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C22×#41C2311yescharacteristic
190C23×Q8C2311yescharacteristic
191C24×C4C2311yescharacteristic
192C24×C4C2312yes—
193#537—44no—
194#537—44no—
195#536—28no—
196#536—44no—
197#536—44no—
198#532—44no—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2311yescharacteristic
201C2×C4⋊Q8C2312yes—
202C2×C4⋊Q8C2312yes—
203C2×#127C2311yescharacteristic
204C2×#125C2318yes—
205C2×#124C2312yes—
206C2×#124C2311yescharacteristic
207C2×#124C2311yescharacteristic
208C2×#124C2312yes—
209C2×#124C2312yes—
210#525—28no—
211#525—44no—
212#525—44no—
213C2×#123C2312yes—
214C2×#123C2314yes—
215C2×#123C2314yes—
216C2×#123C2312yes—
217C2×#123C2312yes—
218C2×#123C2314yes—
219C2×#123C2314yes—
220C2×#123C2318yes—
221C2×C22⋊Q8—44no—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2312yes—
235C2×#121C2314yes—
236C2×#121C2312yes—
237C2×#121C2314yes—
238C2×#121C2312yes—
239C2×#121C2312yes—
240C2×#121C2312yes—
241C2×#121C2312yes—
242C2×#121C2312yes—
243C2×#121C2314yes—
244C2×#121C2314yes—
245C2×#121C2312yes—
246C2×#121C2318yes—
247C2×#121C2318yes—
248C2×#120C2312yes—
249C2×#120C2312yes—
250C2×#120C2312yes—
251#520—44no—
252#519—44no—
253C4×#41—28no—
254C4×#41—44no—
255C2×C4×Q8C2312yes—
256C2×C4×Q8C2314yes—
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2312yes—
259C2×C4×Q8C2314yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2312yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2312yes—
266C2×C4×D4C2312yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2318yes—
271C2×#117C2311yescharacteristic
272C2×#117C2311yescharacteristic
273C2×#117C2311yescharacteristic
274C2×#117C2312yes—
275C2×#117C2311yescharacteristic
276C2×#117C2312yes—
277C2×#117C2312yes—
278C2×#117C2314yes—
279C2×#117C2318yes—
280C2×#117C2311yescharacteristic
281C22×C4⋊C4—44no—
282C22×C4⋊C4C2311yescharacteristic
283C22×C4⋊C4C2311yescharacteristic
284C22×C4⋊C4C2311yescharacteristic
285C22×C4⋊C4C2312yes—
286C22×C4⋊C4C2312yes—
287C22×C4⋊C4C2314yes—
288C22×C4⋊C4C2314yes—
289C22×C4⋊C4C2312yes—
290C22×C4⋊C4C2314yes—
291C22×C4⋊C4C2314yes—
292C22×C22⋊C4C2312yes—
293C22×C22⋊C4C2312yes—
294C22×C42C2312yes—
295C22×C42C2311yescharacteristic
296C22×C42C2311yescharacteristic
297C22×C42C2312yes—
298#400C2318yes—
299#400C2314yes—
300#400C2318yes—
301#399C2318yes—
302#399C2318yes—
303#399C2318yes—
304#399C2318yes—
305#399C2314yes—
306#399C2318yes—
307#398C2318yes—
308#398C2318yes—
309#398C2318yes—
310#398C2318yes—
311#398C2318yes—
312#398C2318yes—
313#398C2314yes—
314#398C2318yes—
315#398C2318yes—
316#398C2318yes—
317#398C2318yes—
318#398C2318yes—
319#398C2314yes—
320#398C2318yes—
321#398C2318yes—
322#397C2318yes—
323#397C2318yes—
324#397C2318yes—
325#397C2314yes—
326#397C2314yes—
327#397C2318yes—
328#397C2314yes—
329#397C2314yes—
330#396C2314yes—
331#396C2318yes—
332#396C2318yes—
333#396C2318yes—
334#396C2318yes—
335#396C2318yes—
336#396C2318yes—
337#396C2318yes—
338#396C2318yes—
339#396C2314yes—
340#394C2318yes—
341#394C2318yes—
342#394C2318yes—
343#394C2318yes—
344#394C2314yes—
345#394C2314yes—
346#394C2314yes—
347#394C2314yes—
348#394C2318yes—
349#394C2314yes—
350#394C2318yes—
351#394C2318yes—
352#392C2318yes—
353#392C2314yes—
354#391C2312yes—
355#391C2312yes—
356#391C2312yes—
357#391C2312yes—
358#391C2312yes—
359#391C2312yes—
360#391C2311yescharacteristic
361#391C2312yes—
362#391C2314yes—
363#391C2311yescharacteristic
364#391C2312yes—
365#391C2314yes—
366#391C2312yes—
367#390C2312yes—
368#390C2312yes—
369#390C2312yes—
370#390C2312yes—
371#390C2318yes—
372#390C2318yes—
373#390C2318yes—
374#390C2318yes—
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2318yes—
378#390C2312yes—
379#390C2314yes—
380#389C2312yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2318yes—
386#389C2312yes—
387#389C2318yes—
388#389C2318yes—
389#389C2318yes—
390#389C2318yes—
391#389C2318yes—
392#389C2318yes—
393#389C2312yes—
394#389C2314yes—
395#389C2312yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2314yes—
402#388C2318yes—
403#388C2314yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2314yes—
409#388C2318yes—
410#388C2318yes—
411#388C2314yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2314yes—
422#387C2318yes—
423#387C2314yes—
424#386C2314yes—
425#386C2314yes—
426#386C2314yes—
427#386C2314yes—
428#386C2318yes—
429#386C2318yes—
430#386C2318yes—
431#386C2318yes—
432#386C2318yes—
433#386C2314yes—
434#386C2314yes—
435#386C2314yes—
436#386C2314yes—
437#386C2314yes—
438#385C2314yes—
439#385C2314yes—
440#385C2318yes—
441#385C2318yes—
442#385C2318yes—
443#385C2318yes—
444#385C2314yes—
445#385C2318yes—
446#385C2318yes—
447#385C2314yes—
448#385C2314yes—
449#385C2318yes—
450#385C2318yes—
451#384C2312yes—
452#384C2314yes—
453#384C2312yes—
454#384C2312yes—
455#384C2312yes—
456#384C2314yes—
457#384C2312yes—
458#384C2318yes—
459#384C2312yes—
460#384C2312yes—
461#382C2312yes—
462#382C2312yes—
463#382C2312yes—
464#382C2318yes—
465#381C2312yes—
466#381C2314yes—
467#380C2314yes—
468#380C2314yes—
469#380C2314yes—
470#380C2314yes—
471#380C2314yes—
472#380C2318yes—
473#380C2318yes—
474#380C2318yes—
475#380C2312yes—
476#380C2314yes—
477#380C2312yes—
478#380C2318yes—
479#380C2314yes—
480#380C2318yes—
481#379C2312yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2318yes—
487C4×C4⋊C4C2318yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2318yes—
494C4×C22⋊C4C2318yes—
495C4×C22⋊C4C2314yes—
496C4×C22⋊C4C2314yes—
497C4×C22⋊C4C2312yes—
498C4×C22⋊C4C2312yes—
499C4×C22⋊C4C2312yes—
500C4×C22⋊C4C2314yes—
501C4×C22⋊C4C2312yes—
502C4×C22⋊C4C2312yes—
503C4×C22⋊C4C2312yes—
504C2×#95C2314yes—
505C2×#95C2312yes—
506C2×#95C2314yes—
507C25C2411yescharacteristic
508C2×#41—24no—
509C2×#41—24no—
510C2×#41—24no—
511C2×#41—24no—
512C2×#41—24no—
513C2×#41—24no—
514C2×#41—24no—
515C2×#41—24no—
516C2×#41—24no—
517C22×Q8—24no—
518C22×Q8—24no—
519C22×Q8—24no—
520C22×Q8C2412yes—
521C22×Q8C2411yescharacteristic
522C22×Q8C2412yes—
523C22×Q8C2411yescharacteristic
524C22×Q8C2411yescharacteristic
525C22×D4C2412yes—
526C22×D4C2412yes—
527C22×D4C2412yes—
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C22×D4C2414yes—
532C22×D4C2414yes—
533C22×D4C2414yes—
534C22×D4C2414yes—
535C22×D4C2414yes—
536C22×D4C2414yes—
537C23×C4—24no—
538C23×C4—24no—
539C23×C4—24no—
540C23×C4—44no—
541C23×C4—84no—
542C23×C4C2412yes—
543C23×C4C2411yescharacteristic
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2412yes—
551C23×C4C2414yes—
552C23×C4C2412yes—
553C23×C4C2412yes—
554C23×C4C2412yes—
555C23×C4C2414yes—
556C23×C4C2418yes—
557C23×C4C2414yes—
558C23×C4C2411yescharacteristic
559C4⋊Q8—28no—
560C4⋊Q8—42no—
561C4⋊Q8—44no—
562C4⋊Q8—44no—
563#127—42no—
564#125—88no—
565#124—28no—
566#124—42no—
567#124—42no—
568#124—44no—
569#124—44no—
570#123—28no—
571#123—216no—
572#123—216no—
573#123—44no—
574#123—44no—
575#123—48no—
576#123—48no—
577#123—88no—
578C22⋊Q8—28no—
579C22⋊Q8—216no—
580C22⋊Q8—48no—
581C22⋊Q8—48no—
582C22⋊Q8—44no—
583C22⋊Q8—44no—
584C22⋊Q8—44no—
585C22⋊Q8—44no—
586C22⋊Q8—48no—
587C22⋊Q8—44no—
588C22⋊Q8—44no—
589C22⋊Q8—44no—
590C22⋊Q8—44no—
591#121—28no—
592#121—216no—
593#121—44no—
594#121—44no—
595#121—44no—
596#121—44no—
597#121—44no—
598#121—44no—
599#121—48no—
600#121—48no—
601#121—48no—
602#121—88no—
603#121—88no—
604#120—28no—
605#120—44no—
606#120—44no—
607C4×Q8—28no—
608C4×Q8—44no—
609C4×Q8—48no—
610C4×Q8—48no—
611C4×Q8—44no—
612C4×D4—28no—
613C4×D4—216no—
614C4×D4—216no—
615C4×D4—44no—
616C4×D4—44no—
617C4×D4—48no—
618C4×D4—48no—
619C4×D4—48no—
620C4×D4—48no—
621C4×D4—48no—
622C4×D4—88no—
623#117—24no—
624#117—24no—
625#117—24no—
626#117—24no—
627#117—28no—
628#117—44no—
629#117—48no—
630#117—44no—
631#117—88no—
632#117#4118yes—
633C2×C4⋊C4—24no—
634C2×C4⋊C4—24no—
635C2×C4⋊C4—24no—
636C2×C4⋊C4—48no—
637C2×C4⋊C4—48no—
638C2×C4⋊C4—44no—
639C2×C4⋊C4—44no—
640C2×C4⋊C4—44no—
641C2×C4⋊C4—84no—
642C2×C4⋊C4—84no—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2418yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2418yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2418yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2412yes—
684C2×C22⋊C4—28no—
685C2×C22⋊C4—44no—
686C2×C22⋊C4C2412yes—
687C2×C22⋊C4C2412yes—
688C2×C22⋊C4C2412yes—
689C2×C22⋊C4C2412yes—
690C2×C22⋊C4C2412yes—
691C2×C22⋊C4C2412yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2412yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2418yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2418yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2418yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2412yes—
724C2×C22⋊C4C2412yes—
725C2×C42—24no—
726C2×C42—24no—
727C2×C42—28no—
728C2×C42—44no—
729C2×C42C2412yes—
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2412yes—
733C2×C42C2412yes—
734C2×C42C2412yes—
735C2×C42C2412yes—
736C2×C42C2412yes—
737C2×C42C2414yes—
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2414yes—
741C2×C42C2418yes—
742C2×C42C2418yes—
743C2×C42C2418yes—
744C2×C42C2414yes—
745C2×C42C2412yes—
746#95C2412yes—
747#95C2412yes—
748#95C2412yes—
749#95C2412yes—
750#95C2418yes—
751#95C2418yes—
752#95C2418yes—
753#95C2418yes—
754#95C2414yes—
755#95C2418yes—
756#95C2418yes—
757#95C2414yes—
758#95C2418yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2418yes—
763#95C2414yes—
764#95C2414yes—
765#95C2418yes—
766#95C2418yes—
767#95C2418yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2418yes—
774#95C2418yes—
775C24—22no—
776C24—24no—
777C24—22no—
778C24—22no—
779C24—42no—
780C24C2512yes—
781C24C2512yes—
782C24C2512yes—
783C24C2512yes—
784C24C2511yescharacteristic
785#41—416no—
786#41—416no—
787#41—416no—
788C2×Q8—22no—
789C2×Q8—24no—
790C2×Q8—22no—
791C2×Q8—24no—
792C2×Q8—22no—
793C2×Q8—24no—
794C2×Q8—22no—
795C2×Q8—22no—
796C2×Q8—24no—
797C2×Q8—24no—
798C2×Q8—22no—
799C2×Q8—24no—
800C2×Q8—22no—
801C2×Q8—22no—
802C2×Q8—22no—
803C2×Q8—416no—
804C2×D4—24no—
805C2×D4—24no—
806C2×D4—24no—
807C2×D4—24no—
808C2×D4—24no—
809C2×D4—24no—
810C2×D4—24no—
811C2×D4—24no—
812C2×D4—24no—
813C2×D4—28no—
814C2×D4—28no—
815C2×D4—28no—
816C2×D4—22no—
817C2×D4—28no—
818C2×D4—22no—
819C2×D4—22no—
820C2×D4—22no—
821C2×D4—22no—
822C2×D4—22no—
823C2×D4—22no—
824C2×D4—22no—
825C2×D4—22no—
826C2×D4—28no—
827C2×D4—44no—
828C2×D4—44no—
829C2×D4—44no—
830C2×D4—44no—
831C2×D4—44no—
832C2×D4—44no—
833C2×D4—44no—
834C2×D4—44no—
835C2×D4—44no—
836C2×D4—48no—
837C2×D4—48no—
838C22×C4—24no—
839C22×C4—22no—
840C22×C4—24no—
841C22×C4—24no—
842C22×C4—24no—
843C22×C4—22no—
844C22×C4—24no—
845C22×C4—22no—
846C22×C4—24no—
847C22×C4—24no—
848C22×C4—24no—
849C22×C4—24no—
850C22×C4—28no—
851C22×C4—24no—
852C22×C4—24no—
853C22×C4—24no—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—24no—
857C22×C4—24no—
858C22×C4—24no—
859C22×C4—24no—
860C22×C4—24no—
861C22×C4—24no—
862C22×C4—24no—
863C22×C4—24no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—24no—
867C22×C4—28no—
868C22×C4—28no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—48no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—48no—
878C22×C4—44no—
879C22×C4—48no—
880C22×C4—44no—
881C22×C4—48no—
882C22×C4—416no—
883C22×C4—816no—
884C22×C4C2×#4114yes—
885C22×C4H(5,𝔽2)14yes—
886C22×C4H(5,𝔽2)14yes—
887C22×C4C2512yes—
888C22×C4C2512yes—
889C22×C4C2514yes—
890C22×C4C2514yes—
891C22×C4C2514yes—
892C22×C4C2514yes—
893C22×C4C2512yes—
894C22×C4C2514yes—
895C22×C4C2514yes—
896C22×C4C2512yes—
897C22×C4C2512yes—
898C22×C4C2512yes—
899C22×C4C2512yes—
900C22×C4C2514yes—
901C22×C4C2512yes—
902C22×C4C2514yes—
903C22×C4C2512yes—
904C22×C4C2512yes—
905C22×C4C2511yescharacteristic
906C22×C4C2511yescharacteristic
907C4⋊C4—28no—
908C4⋊C4—28no—
909C4⋊C4—216no—
910C4⋊C4—24no—
911C4⋊C4—24no—
912C4⋊C4—24no—
913C4⋊C4—24no—
914C4⋊C4—24no—
915C4⋊C4—24no—
916C4⋊C4—22no—
917C4⋊C4—22no—
918C4⋊C4—24no—
919C4⋊C4—24no—
920C4⋊C4—24no—
921C4⋊C4—28no—
922C4⋊C4—28no—
923C4⋊C4—28no—
924C4⋊C4—48no—
925C4⋊C4—44no—
926C4⋊C4—48no—
927C4⋊C4—48no—
928C4⋊C4—48no—
929C4⋊C4—48no—
930C4⋊C4—48no—
931C4⋊C4—44no—
932C4⋊C4—48no—
933C4⋊C4—44no—
934C4⋊C4—44no—
935C4⋊C4—44no—
936C4⋊C4—44no—
937C4⋊C4—48no—
938C4⋊C4—44no—
939C4⋊C4—44no—
940C4⋊C4—48no—
941C4⋊C4—44no—
942C4⋊C4—48no—
943C4⋊C4—44no—
944C4⋊C4—48no—
945C4⋊C4—44no—
946C4⋊C4—44no—
947C4⋊C4C2×#4118yes—
948C22⋊C4—24no—
949C22⋊C4—24no—
950C22⋊C4—24no—
951C22⋊C4—24no—
952C22⋊C4—24no—
953C22⋊C4—28no—
954C22⋊C4—28no—
955C22⋊C4—28no—
956C22⋊C4—28no—
957C22⋊C4—216no—
958C22⋊C4—24no—
959C22⋊C4—24no—
960C22⋊C4—28no—
961C22⋊C4—28no—
962C22⋊C4—48no—
963C22⋊C4—44no—
964C22⋊C4—44no—
965C22⋊C4—48no—
966C22⋊C4—48no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C22⋊C4—48no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—48no—
980C22⋊C4—44no—
981C22⋊C4—48no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4C2×#4118yes—
986C22⋊C42−1+418yes—
987C42—22no—
988C42—22no—
989C42—24no—
990C42—28no—
991C42—22no—
992C42—22no—
993C42—24no—
994C42—24no—
995C42—24no—
996C42—24no—
997C42—24no—
998C42—44no—
999C42—44no—
1000C42—48no—
1001C42—48no—
1002C42—48no—
1003C42C2×#4118yes—
1004C23—22no—
1005C23—22no—
1006C23—28no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—24no—
1023C23—24no—
1024C23—24no—
1025C23—24no—
1026C23—24no—
1027C23—24no—
1028C23—48no—
1029C23—48no—
1030C23—44no—
1031C23—44no—
1032C23C22×#4112yes—
1033C23C2×H(5,𝔽2)12yes—
1034C23C2×H(5,𝔽2)12yes—
1035C23C2×2−1+414yes—
1036C23C2611yescharacteristic
1037Q8—48no—
1038Q8—48no—
1039Q8—44no—
1040Q8—44no—
1041Q8—44no—
1042D4—416no—
1043D4—48no—
1044D4—48no—
1045D4—48no—
1046D4—44no—
1047D4—44no—
1048D4—44no—
1049D4—88no—
1050D4—88no—
1051D4—88no—
1052D4—164no—
1053D4—164no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—24no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—24no—
1068C2×C4—22no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—24no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—28no—
1094C2×C4—28no—
1095C2×C4—22no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—28no—
1099C2×C4—22no—
1100C2×C4—416no—
1101C2×C4—48no—
1102C2×C4—48no—
1103C2×C4—44no—
1104C2×C4—48no—
1105C2×C4—48no—
1106C2×C4—48no—
1107C2×C4—48no—
1108C2×C4—48no—
1109C2×C4—48no—
1110C2×C4—88no—
1111C2×C4—84no—
1112C2×C4—84no—
1113C2×C4—84no—
1114C2×C4—816no—
1115C2×C4—164no—
1116C2×C4#540116yes—
1117C2×C4C22×#4118yes—
1118C2×C4C22×#4112yes—
1119C2×C4C22×#4112yes—
1120C2×C4C2×H(5,𝔽2)12yes—
1121C2×C4C2×H(5,𝔽2)12yes—
1122C2×C4C2×H(5,𝔽2)12yes—
1123C2×C4C2×H(5,𝔽2)12yes—
1124C2×C4C2×2−1+414yes—
1125C2×C4C2×2−1+414yes—
1126C22—24no—
1127C22—22no—
1128C22—22no—
1129C22—24no—
1130C22—24no—
1131C22—24no—
1132C22—24no—
1133C22—416no—
1134C22—42no—
1135C22—42no—
1136C22—42no—
1137C22—42no—
1138C22—44no—
1139C22—44no—
1140C22—44no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—42no—
1147C22—42no—
1148C22—42no—
1149C22—42no—
1150C22—44no—
1151C22—44no—
1152C22—44no—
1153C22C2×#54014yes—
1154C22C23×#4111yescharacteristic
1155C22C22×H(5,𝔽2)11yescharacteristic
1156C22C22×H(5,𝔽2)11yescharacteristic
1157C22C22×2−1+412yes—
1158C22H(7,𝔽2)12yes—
1159C4—24no—
1160C4—28no—
1161C4—24no—
1162C4—42no—
1163C4—42no—
1164C4—44no—
1165C4—44no—
1166C4—44no—
1167C4—42no—
1168C4—42no—
1169C4—42no—
1170C4—42no—
1171C4—42no—
1172C4—44no—
1173C4—42no—
1174C4—44no—
1175C4—44no—
1176C4—44no—
1177C4C2×#54014yes—
1178C4C2×#54014yes—
1179C2—24no—
1180C2—44no—
1181C2—82no—
1182C2—82no—
1183C2—82no—
1184C2C22×#54011yescharacteristic
1185C2#6283311yescharacteristic
1186C2#6287611yescharacteristic
1187C2#6294412yes—
1188C2#6300012yes—
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. #42668C2semidirect
2. #42641C2semidirect
3. #42550C2semidirect
4. #42460C2semidirect
5. #40894C2semidirect
6. #40054C2semidirect
7. #39900C2semidirect
8. #39656C2semidirect
9. #39606C2semidirect
10. #38543C2semidirect
11. #35673C2semidirect
12. #35661C2semidirect
13. #35634C2semidirect
14. #35621C2semidirect
15. #35555C2semidirect
16. #35530C2semidirect
17. #35308C2semidirect
18. #35273C2semidirect
19. #35223C2semidirect
20. C2×#2502C2semidirect
21. #34743C2semidirect
22. #34742C2semidirect
23. #34268C2semidirect
24. #34200C2semidirect
25. #34188C2semidirect
41. #2857C22semidirect
42. #2857C22semidirect
43. #2856C22semidirect
44. #2850C22semidirect
46. #2837C22semidirect
47. #2836C22semidirect
49. #2793C22semidirect
50. #2791C22semidirect
54. #2768C22semidirect
55. #2768C22semidirect
58. #2748C22semidirect
59. #2741C22semidirect
61. #2707C22semidirect
62. #2701C22semidirect
64. #2667C22semidirect
65. #2651C22semidirect
66. #2651C22semidirect
69. #2629C22semidirect
70. #2621C22semidirect
71. #2620C22semidirect
72. #2620C22semidirect
73. #2620C22semidirect
75. #2570C22semidirect
76. #2552C22semidirect
77. #2547C22semidirect
78. #2546C22semidirect
79. #2545C22semidirect
80. #2544C22semidirect
87. #2538C22semidirect
88. #2537C22semidirect
91. #2507C22semidirect
92. #2507C22semidirect
93. #2506C22semidirect
98. #2502C22semidirect
100. #2501C22semidirect
101. #2500C22semidirect
102. #2499C22semidirect
105. #2476C22semidirect
109. #2448C22semidirect
110. #2446C22semidirect
114. #2429C22semidirect
117. #2427C22semidirect
125. #2423C22semidirect
126. #2423C22semidirect
128. #2422C22semidirect
130. #2421C22semidirect
136. #2417C22semidirect
140. #2415C22semidirect
146. #2367C22semidirect
147. #2365C22semidirect
151. #2355C22semidirect
152. #2354C22semidirect
158. #2323C22semidirect
163. #2314C22semidirect
168. C4×C22⋊Q8C22semidirect
180. #2285C22semidirect

Maximal subgroups

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

subgroupindex
#426682
#426412
#425502
#424602
#408942
#400542
#399002
#396562
#396062
#385432
#356732
#356612
#356342
#356212
#355552
#355302
#353082
#352732
#352232
C2×#25022
#347432
#347422
#342682
#342002
#341882