Finite Group Databasebeta

← #7650676

Subgroups — #7650676

Order 512.

5166 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42776C214yesmaximal, complemented
2#42669C214yesmaximal, complemented
3#42533C214yesmaximal, complemented
4#42454C214yesmaximal, complemented
5#41555C218yesmaximal, complemented
6#40217C214yesmaximal, complemented
7#39929C214yesmaximal, complemented
8#38998C214yesmaximal, complemented
9#38930C214yesmaximal, complemented
10#37903C218yesmaximal, complemented
11#35673C211yesmaximal, characteristic, complemented
12#35661C211yesmaximal, characteristic, complemented
13#35634C211yesmaximal, characteristic, complemented
14#35627C211yesmaximal, characteristic, complemented
15#35621C211yesmaximal, characteristic, complemented
16#35618C211yesmaximal, characteristic, complemented
17#35328C211yesmaximal, characteristic, complemented
18#35308C211yesmaximal, characteristic, complemented
19#35223C211yesmaximal, characteristic, complemented
20C2×#2503C211yesmaximal, characteristic, complemented
21#34743C211yesmaximal, characteristic, complemented
22#34742C211yesmaximal, characteristic, complemented
23#34268C211yesmaximal, characteristic, complemented
24#34200C211yesmaximal, characteristic, complemented
25#34189C211yesmaximal, 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#2850C2212yescomplemented
43#2850C2212yescomplemented
44#2850C2212yescomplemented
45#2847C2214yes—
46#2837C2218yescomplemented
47#2836C2218yescomplemented
48#2793C2218yescomplemented
49#2791C2218yescomplemented
50#2780C2218yescomplemented
51#2777C2218yescomplemented
52#2761C2218yes—
53#2753C2218yescomplemented
54#2752C2218yes—
55#2749C2218yes—
56#2743C2218yes—
57#2743C2218yescomplemented
58#2743C2218yescomplemented
59#2740C2218yes—
60#2738C2218yes—
61#2738C2218yescomplemented
62#2701C2218yes—
63#2699C2218yes—
64#2667C2218yes—
65#2654C2218yescomplemented
66#2649C2218yescomplemented
67#2648C2218yescomplemented
68#2647C2218yescomplemented
69#2635C2218yes—
70#2621C2212yescomplemented
71#2621C2212yescomplemented
72#2620C2212yescomplemented
73#2619C2212yescomplemented
74#2618C2214yes—
75#2571C2214yescomplemented
76#2570C2214yescomplemented
77#2547C2212yescomplemented
78#2546C2212yescomplemented
79#2545C2212yescomplemented
80#2544C2212yescomplemented
81#2543C2218yes—
82#2542C2214yes—
83#2542C2214yes—
84#2540C2214yes—
85#2540C2214yes—
86#2539C2214yes—
87#2538C2214yes—
88#2536C2214yes—
89#2536C2214yescomplemented
90#2535C2214yescomplemented
91#2526C2218yes—
92#2526C2218yescomplemented
93#2516C2218yes—
94#2509C2214yescomplemented
95#2508C2214yescomplemented
96#2505C2218yes—
97#2504C2212yescomplemented
98#2503C2214yes—
99#2503C2214yes—
100#2503C2214yes—
101#2503C2214yes—
102#2503C2212yescomplemented
103#2501C2214yes—
104#2500C2212yescomplemented
105#2499C2212yescomplemented
106#2498C2218yes—
107#2497C2218yescomplemented
108#2457C2218yes—
109#2448C2214yescomplemented
110#2446C2214yescomplemented
111#2444C2218yes—
112#2429C2212yes—
113#2429C2214yes—
114#2429C2214yescomplemented
115#2428C2212yes—
116#2427C2212yes—
117#2427C2214yescomplemented
118#2426C2214yes—
119#2426C2212yes—
120#2425C2218yes—
121#2425C2218yes—
122#2425C2214yes—
123#2424C2214yes—
124#2423C2212yes—
125#2423C2214yescomplemented
126#2422C2212yes—
127#2421C2212yes—
128#2421C2214yescomplemented
129#2421C2214yescomplemented
130#2420C2218yes—
131#2420C2212yes—
132#2420C2214yescomplemented
133#2419C2214yes—
134#2418C2214yes—
135#2417C2214yes—
136#2417C2214yes—
137#2417C2214yescomplemented
138#2416C2214yes—
139#2416C2214yes—
140#2415C2214yescomplemented
141#2413C2214yes—
142#2411C2214yes—
143#2395C2214yes—
144C2×#400C2214yes—
145#2392C2214yes—
146#2367C2214yescomplemented
147#2365C2214yescomplemented
148#2361C2214yes—
149#2360C2214yes—
150#2359C2218yes—
151#2357C2214yescomplemented
152#2356C2214yescomplemented
153#2353C2218yes—
154#2352C2214yes—
155D4×C4⋊C4C2214yes—
156#2333C2218yes—
157#2323C2214yescomplemented
158#2322C2214yes—
159#2319C2218yes—
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
178#2285C2211yescharacteristic
179#2283C2214yescomplemented
180C2×#382C2211yescharacteristic
181C2×#382C2211yescharacteristic
182#2280C2211yescharacteristic
183C2×#381C2214yes—
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×#124C2312yes—
205C2×#124C2311yescharacteristic
206C2×#124C2311yescharacteristic
207C2×#124C2312yes—
208C2×#124C2312yes—
209#525—28no—
210#525—44no—
211#525—44no—
212C2×#123C2312yes—
213C2×#123C2314yes—
214C2×#123C2312yes—
215C2×#123C2312yes—
216C2×#123C2314yes—
217C2×#123C2314yes—
218C2×#123C2314yes—
219C2×C22⋊Q8—44no—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2312yes—
233C2×#121C2312yes—
234C2×#121C2318yes—
235C2×#121C2314yes—
236C2×#121C2312yes—
237C2×#121C2312yes—
238C2×#121C2312yes—
239C2×#121C2312yes—
240C2×#121C2312yes—
241C2×#121C2314yes—
242C2×#121C2314yes—
243C2×#121C2314yes—
244C2×#121C2312yes—
245C2×#120C2312yes—
246C2×#120C2312yes—
247C2×#120C2312yes—
248#520—44no—
249#519—44no—
250C4×#41—28no—
251C4×#41—44no—
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2314yes—
254C2×C4×Q8C2312yes—
255C2×C4×Q8C2312yes—
256C2×C4×Q8C2314yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2318yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2312yes—
264C2×C4×D4C2312yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2314yes—
268C2×#117C2311yescharacteristic
269C2×#117C2311yescharacteristic
270C2×#117C2311yescharacteristic
271C2×#117C2312yes—
272C2×#117C2311yescharacteristic
273C2×#117C2312yes—
274C2×#117C2312yes—
275C2×#117C2314yes—
276C2×#117C2311yescharacteristic
277C22×C4⋊C4—44no—
278C22×C4⋊C4C2311yescharacteristic
279C22×C4⋊C4C2311yescharacteristic
280C22×C4⋊C4C2311yescharacteristic
281C22×C4⋊C4C2312yes—
282C22×C4⋊C4C2312yes—
283C22×C4⋊C4C2314yes—
284C22×C4⋊C4C2314yes—
285C22×C4⋊C4C2312yes—
286C22×C22⋊C4C2312yes—
287C22×C22⋊C4C2312yes—
288C22×C42C2312yes—
289C22×C42C2311yescharacteristic
290C22×C42C2311yescharacteristic
291C22×C42C2312yes—
292#400C2318yes—
293#400C2318yes—
294#400C2318yes—
295#400C2318yes—
296#400C2314yes—
297#400C2318yes—
298#400C2318yes—
299#400C2318yes—
300#400C2318yes—
301#400C2318yes—
302#399C2318yes—
303#399C2318yes—
304#399C2318yes—
305#399C2314yes—
306#399C2318yes—
307#398C2318yes—
308#398C2314yes—
309#398C2318yes—
310#398C2318yes—
311#398C2318yes—
312#398C2314yes—
313#398C2318yes—
314#398C2318yes—
315#398C2318yes—
316#397C2314yes—
317#397C2318yes—
318#397C2318yes—
319#397C2318yes—
320#397C2318yes—
321#397C2314yes—
322#397C2314yes—
323#397C2318yes—
324#397C2314yes—
325#397C2318yes—
326#396C2318yes—
327#396C2318yes—
328#396C2318yes—
329#396C2318yes—
330#396C2314yes—
331#396C2314yes—
332#396C2318yes—
333#396C2318yes—
334#394C2314yes—
335#394C2318yes—
336#394C2318yes—
337#394C2318yes—
338#394C2318yes—
339#394C2314yes—
340#394C2318yes—
341#394C2314yes—
342#394C2314yes—
343#394C2318yes—
344#394C2314yes—
345#392C2318yes—
346#392C2314yes—
347#392C2318yes—
348#391C2312yes—
349#391C2312yes—
350#391C2312yes—
351#391C2312yes—
352#391C2312yes—
353#391C2312yes—
354#391C2311yescharacteristic
355#391C2312yes—
356#391C2314yes—
357#391C2311yescharacteristic
358#391C2312yes—
359#391C2314yes—
360#391C2312yes—
361#390C2312yes—
362#390C2312yes—
363#390C2312yes—
364#390C2312yes—
365#390C2314yes—
366#390C2318yes—
367#390C2318yes—
368#390C2318yes—
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2318yes—
372#390C2312yes—
373#389C2312yes—
374#389C2314yes—
375#389C2312yes—
376#389C2318yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2318yes—
381#389C2318yes—
382#389C2312yes—
383#389C2318yes—
384#389C2314yes—
385#389C2318yes—
386#389C2318yes—
387#389C2312yes—
388#388C2318yes—
389#388C2318yes—
390#388C2314yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2314yes—
404#388C2314yes—
405#388C2314yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2314yes—
416#387C2318yes—
417#387C2314yes—
418#386C2314yes—
419#386C2314yes—
420#386C2314yes—
421#386C2314yes—
422#386C2314yes—
423#386C2314yes—
424#386C2318yes—
425#386C2318yes—
426#386C2318yes—
427#386C2318yes—
428#386C2318yes—
429#386C2318yes—
430#386C2318yes—
431#386C2318yes—
432#386C2314yes—
433#386C2314yes—
434#386C2314yes—
435#385C2314yes—
436#385C2314yes—
437#385C2318yes—
438#385C2318yes—
439#385C2314yes—
440#385C2318yes—
441#385C2314yes—
442#385C2314yes—
443#384C2312yes—
444#384C2312yes—
445#384C2312yes—
446#384C2318yes—
447#383C2318yes—
448#382C2312yes—
449#382C2312yes—
450#382C2314yes—
451#382C2312yes—
452#382C2318yes—
453#382C2312yes—
454#382C2314yes—
455#382C2312yes—
456#382C2312yes—
457#382C2312yes—
458#381C2318yes—
459#381C2318yes—
460#381C2312yes—
461#381C2318yes—
462#381C2318yes—
463#381C2314yes—
464#381C2318yes—
465#381C2318yes—
466#380C2314yes—
467#380C2314yes—
468#380C2314yes—
469#380C2314yes—
470#380C2314yes—
471#380C2318yes—
472#380C2318yes—
473#380C2318yes—
474#380C2312yes—
475#380C2312yes—
476#380C2314yes—
477#380C2314yes—
478#379C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2318yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C22⋊C4C2314yes—
489C4×C22⋊C4C2318yes—
490C4×C22⋊C4C2318yes—
491C4×C22⋊C4C2318yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2312yes—
495C4×C22⋊C4C2312yes—
496C4×C22⋊C4C2312yes—
497C4×C22⋊C4C2314yes—
498C4×C22⋊C4C2312yes—
499C4×C22⋊C4C2312yes—
500C4×C22⋊C4C2312yes—
501#376C2318yes—
502C2×#95C2314yes—
503C2×#95C2314yes—
504C2×#95C2312yes—
505C2×#95C2314yes—
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—48no—
542C23×C4C2412yes—
543C23×C4C2411yescharacteristic
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2412yes—
551C23×C4C2412yes—
552C23×C4C2412yes—
553C23×C4C2418yes—
554C23×C4C2412yes—
555C23×C4C2414yes—
556C23×C4C2414yes—
557C23×C4C2414yes—
558C23×C4C2411yescharacteristic
559C4⋊Q8—28no—
560C4⋊Q8—42no—
561C4⋊Q8—44no—
562C4⋊Q8—44no—
563#127—42no—
564#124—28no—
565#124—42no—
566#124—42no—
567#124—44no—
568#124—44no—
569#123—28no—
570#123—216no—
571#123—48no—
572#123—44no—
573#123—44no—
574#123—48no—
575#123—48no—
576C22⋊Q8—28no—
577C22⋊Q8—216no—
578C22⋊Q8—48no—
579C22⋊Q8—48no—
580C22⋊Q8—44no—
581C22⋊Q8—44no—
582C22⋊Q8—44no—
583C22⋊Q8—44no—
584C22⋊Q8—48no—
585C22⋊Q8—44no—
586C22⋊Q8—44no—
587C22⋊Q8—44no—
588C22⋊Q8—44no—
589#121—28no—
590#121—48no—
591#121—44no—
592#121—44no—
593#121—44no—
594#121—44no—
595#121—44no—
596#121—44no—
597#121—416no—
598#121—48no—
599#121—48no—
600#121—48no—
601#120—28no—
602#120—44no—
603#120—44no—
604C4×Q8—28no—
605C4×Q8—44no—
606C4×Q8—48no—
607C4×Q8—48no—
608C4×Q8—44no—
609C4×D4—28no—
610C4×D4—216no—
611C4×D4—216no—
612C4×D4—44no—
613C4×D4—44no—
614C4×D4—48no—
615C4×D4—48no—
616C4×D4—48no—
617C4×D4—416no—
618C4×D4—48no—
619C4×D4—48no—
620#117—24no—
621#117—24no—
622#117—24no—
623#117—24no—
624#117—28no—
625#117—44no—
626#117—48no—
627#117—44no—
628#117#4118yes—
629C2×C4⋊C4—24no—
630C2×C4⋊C4—24no—
631C2×C4⋊C4—24no—
632C2×C4⋊C4—48no—
633C2×C4⋊C4—48no—
634C2×C4⋊C4—44no—
635C2×C4⋊C4—44no—
636C2×C4⋊C4—44no—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2418yes—
673C2×C4⋊C4C2412yes—
674C2×C22⋊C4—44no—
675C2×C22⋊C4—44no—
676C2×C22⋊C4C2412yes—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2412yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2412yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2412yes—
689C2×C22⋊C4C2412yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2418yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2418yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2412yes—
715C2×C42—24no—
716C2×C42—24no—
717C2×C42—28no—
718C2×C42—44no—
719C2×C42C2412yes—
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2414yes—
727C2×C42C2412yes—
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2414yes—
731C2×C42C2418yes—
732C2×C42C2414yes—
733C2×C42C2418yes—
734C2×C42C2418yes—
735C2×C42C2412yes—
736#95C2418yes—
737#95C2412yes—
738#95C2412yes—
739#95C2412yes—
740#95C2412yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748#95C2414yes—
749#95C2418yes—
750#95C2418yes—
751#95C2414yes—
752#95C2414yes—
753#95C2418yes—
754#95C2418yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2418yes—
759#95C2414yes—
760#95C2418yes—
761#95C2414yes—
762#95C2414yes—
763#95C2418yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2418yes—
768#95C2418yes—
769C24—22no—
770C24—24no—
771C24—22no—
772C24—22no—
773C24—42no—
774C24C2512yes—
775C24C2512yes—
776C24C2512yes—
777C24C2512yes—
778C24C2511yescharacteristic
779#41—416no—
780#41—416no—
781#41—416no—
782C2×Q8—22no—
783C2×Q8—24no—
784C2×Q8—22no—
785C2×Q8—24no—
786C2×Q8—22no—
787C2×Q8—24no—
788C2×Q8—22no—
789C2×Q8—22no—
790C2×Q8—24no—
791C2×Q8—24no—
792C2×Q8—22no—
793C2×Q8—24no—
794C2×Q8—22no—
795C2×Q8—22no—
796C2×Q8—22no—
797C2×Q8—416no—
798C2×D4—24no—
799C2×D4—24no—
800C2×D4—24no—
801C2×D4—24no—
802C2×D4—24no—
803C2×D4—24no—
804C2×D4—24no—
805C2×D4—24no—
806C2×D4—24no—
807C2×D4—28no—
808C2×D4—28no—
809C2×D4—28no—
810C2×D4—22no—
811C2×D4—28no—
812C2×D4—22no—
813C2×D4—22no—
814C2×D4—22no—
815C2×D4—22no—
816C2×D4—22no—
817C2×D4—22no—
818C2×D4—22no—
819C2×D4—22no—
820C2×D4—44no—
821C2×D4—44no—
822C2×D4—44no—
823C2×D4—44no—
824C2×D4—44no—
825C2×D4—44no—
826C2×D4—44no—
827C2×D4—44no—
828C2×D4—44no—
829C2×D4—44no—
830C2×D4—48no—
831C2×D4—48no—
832C22×C4—22no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—22no—
836C22×C4—24no—
837C22×C4—22no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—24no—
841C22×C4—24no—
842C22×C4—24no—
843C22×C4—216no—
844C22×C4—24no—
845C22×C4—24no—
846C22×C4—24no—
847C22×C4—24no—
848C22×C4—24no—
849C22×C4—24no—
850C22×C4—24no—
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—28no—
860C22×C4—44no—
861C22×C4—42no—
862C22×C4—42no—
863C22×C4—48no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—48no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—44no—
875C22×C4—48no—
876C22×C4—416no—
877C22×C4—816no—
878C22×C4C2×#4114yes—
879C22×C4H(5,𝔽2)14yes—
880C22×C4H(5,𝔽2)14yes—
881C22×C4C2512yes—
882C22×C4C2512yes—
883C22×C4C2514yes—
884C22×C4C2512yes—
885C22×C4C2514yes—
886C22×C4C2512yes—
887C22×C4C2514yes—
888C22×C4C2514yes—
889C22×C4C2512yes—
890C22×C4C2514yes—
891C22×C4C2514yes—
892C22×C4C2512yes—
893C22×C4C2514yes—
894C22×C4C2512yes—
895C22×C4C2512yes—
896C22×C4C2512yes—
897C22×C4C2512yes—
898C22×C4C2514yes—
899C22×C4C2511yescharacteristic
900C22×C4C2511yescharacteristic
901C4⋊C4—28no—
902C4⋊C4—28no—
903C4⋊C4—216no—
904C4⋊C4—24no—
905C4⋊C4—24no—
906C4⋊C4—24no—
907C4⋊C4—24no—
908C4⋊C4—24no—
909C4⋊C4—24no—
910C4⋊C4—22no—
911C4⋊C4—22no—
912C4⋊C4—24no—
913C4⋊C4—24no—
914C4⋊C4—24no—
915C4⋊C4—48no—
916C4⋊C4—44no—
917C4⋊C4—48no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—48no—
922C4⋊C4—44no—
923C4⋊C4—48no—
924C4⋊C4—48no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—48no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—44no—
933C4⋊C4—48no—
934C4⋊C4—44no—
935C4⋊C4—44no—
936C4⋊C4—44no—
937C4⋊C4C2×#4118yes—
938C22⋊C4—24no—
939C22⋊C4—24no—
940C22⋊C4—24no—
941C22⋊C4—24no—
942C22⋊C4—24no—
943C22⋊C4—24no—
944C22⋊C4—28no—
945C22⋊C4—28no—
946C22⋊C4—28no—
947C22⋊C4—28no—
948C22⋊C4—216no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C22⋊C4—48no—
952C22⋊C4—48no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—44no—
957C22⋊C4—44no—
958C22⋊C4—48no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4—44no—
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—48no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4C2×#4118yes—
977C42—22no—
978C42—22no—
979C42—24no—
980C42—28no—
981C42—22no—
982C42—22no—
983C42—24no—
984C42—24no—
985C42—24no—
986C42—24no—
987C42—24no—
988C42—44no—
989C42—48no—
990C42—44no—
991C42—48no—
992C42—48no—
993C42C2×#4118yes—
994C23—22no—
995C23—22no—
996C23—28no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—24no—
1013C23—24no—
1014C23—24no—
1015C23—24no—
1016C23—24no—
1017C23—24no—
1018C23—48no—
1019C23—48no—
1020C23—44no—
1021C23—44no—
1022C23C22×#4112yes—
1023C23C2×H(5,𝔽2)12yes—
1024C23C2×H(5,𝔽2)12yes—
1025C23#58514yes—
1026C23C2611yescharacteristic
1027Q8—48no—
1028Q8—48no—
1029Q8—44no—
1030Q8—44no—
1031Q8—44no—
1032D4—416no—
1033D4—48no—
1034D4—48no—
1035D4—48no—
1036D4—44no—
1037D4—44no—
1038D4—44no—
1039D4—88no—
1040D4—88no—
1041D4—88no—
1042D4—164no—
1043D4—164no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—24no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—24no—
1056C2×C4—22no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—24no—
1074C2×C4—28no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—24no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—28no—
1083C2×C4—24no—
1084C2×C4—28no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—24no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—44no—
1093C2×C4—48no—
1094C2×C4—48no—
1095C2×C4—48no—
1096C2×C4—48no—
1097C2×C4—48no—
1098C2×C4—48no—
1099C2×C4—88no—
1100C2×C4—84no—
1101C2×C4—84no—
1102C2×C4—84no—
1103C2×C4—84no—
1104C2×C4—816no—
1105C2×C4—84no—
1106C2×C4—88no—
1107C2×C4—164no—
1108C2×C4#540116yes—
1109C2×C4C22×#4118yes—
1110C2×C4C22×#4112yes—
1111C2×C4C22×#4112yes—
1112C2×C4C2×H(5,𝔽2)12yes—
1113C2×C4C2×H(5,𝔽2)12yes—
1114C2×C4C2×H(5,𝔽2)12yes—
1115C2×C4C2×H(5,𝔽2)12yes—
1116C22—24no—
1117C22—22no—
1118C22—22no—
1119C22—24no—
1120C22—24no—
1121C22—24no—
1122C22—24no—
1123C22—416no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—44no—
1129C22—44no—
1130C22—44no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22—42no—
1137C22—44no—
1138C22—44no—
1139C22—44no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22C2×#54014yes—
1144C22C23×#4111yescharacteristic
1145C22C22×H(5,𝔽2)11yescharacteristic
1146C22C22×H(5,𝔽2)11yescharacteristic
1147C22C2×#58512yes—
1148C222−1+612yes—
1149C4—28no—
1150C4—42no—
1151C4—42no—
1152C4—44no—
1153C4—44no—
1154C4—42no—
1155C4—42no—
1156C4—44no—
1157C4—44no—
1158C4—42no—
1159C4—42no—
1160C4—44no—
1161C4—44no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—44no—
1167C4C2×#54014yes—
1168C4C2×#54014yes—
1169C2—24no—
1170C2—44no—
1171C2—82no—
1172C2—82no—
1173C2—82no—
1174C2C22×#54011yescharacteristic
1175C2#6282411yescharacteristic
1176C2#6288711yescharacteristic
1177C2#6292712yes—
1178C2#6299312yes—
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. #42776C2semidirect
2. #42669C2semidirect
3. #42533C2semidirect
4. #42454C2semidirect
5. #41555C2semidirect
6. #40217C2semidirect
7. #39929C2semidirect
8. #38998C2semidirect
9. #38930C2semidirect
10. #37903C2semidirect
11. #35673C2semidirect
12. #35661C2semidirect
13. #35634C2semidirect
14. #35627C2semidirect
15. #35621C2semidirect
16. #35618C2semidirect
17. #35328C2semidirect
18. #35308C2semidirect
19. #35223C2semidirect
20. C2×#2503C2semidirect
21. #34743C2semidirect
22. #34742C2semidirect
23. #34268C2semidirect
24. #34200C2semidirect
25. #34189C2semidirect
41. #2857C22semidirect
42. #2850C22semidirect
43. #2850C22semidirect
44. #2850C22semidirect
46. #2837C22semidirect
47. #2836C22semidirect
48. #2793C22semidirect
49. #2791C22semidirect
50. #2780C22semidirect
51. #2777C22semidirect
53. #2753C22semidirect
57. #2743C22semidirect
58. #2743C22semidirect
61. #2738C22semidirect
65. #2654C22semidirect
66. #2649C22semidirect
67. #2648C22semidirect
68. #2647C22semidirect
70. #2621C22semidirect
71. #2621C22semidirect
72. #2620C22semidirect
73. #2619C22semidirect
75. #2571C22semidirect
76. #2570C22semidirect
77. #2547C22semidirect
78. #2546C22semidirect
79. #2545C22semidirect
80. #2544C22semidirect
89. #2536C22semidirect
90. #2535C22semidirect
92. #2526C22semidirect
94. #2509C22semidirect
95. #2508C22semidirect
97. #2504C22semidirect
102. #2503C22semidirect
104. #2500C22semidirect
105. #2499C22semidirect
107. #2497C22semidirect
109. #2448C22semidirect
110. #2446C22semidirect
114. #2429C22semidirect
117. #2427C22semidirect
125. #2423C22semidirect
128. #2421C22semidirect
129. #2421C22semidirect
132. #2420C22semidirect
137. #2417C22semidirect
140. #2415C22semidirect
146. #2367C22semidirect
147. #2365C22semidirect
151. #2357C22semidirect
152. #2356C22semidirect
157. #2323C22semidirect
163. #2314C22semidirect
168. C4×C22⋊Q8C22semidirect
179. #2283C22semidirect

Maximal subgroups

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

subgroupindex
#427762
#426692
#425332
#424542
#415552
#402172
#399292
#389982
#389302
#379032
#356732
#356612
#356342
#356272
#356212
#356182
#353282
#353082
#352232
C2×#25032
#347432
#347422
#342682
#342002
#341892