Finite Group Databasebeta

← #7652623

Subgroups — #7652623

Order 512.

5840 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42903C214yesmaximal, complemented
2#42895C214yesmaximal, complemented
3#42893C214yesmaximal, complemented
4#42838C214yesmaximal, complemented
5#41962C218yesmaximal, complemented
6#40129C214yesmaximal, complemented
7#40122C214yesmaximal, complemented
8#39790C214yesmaximal, complemented
9#39218C214yesmaximal, complemented
10#38398C218yesmaximal, complemented
11#35677C211yesmaximal, characteristic, complemented
12#35662C211yesmaximal, characteristic, complemented
13#35563C211yesmaximal, characteristic, complemented
14#35540C211yesmaximal, characteristic, complemented
15#35531C211yesmaximal, characteristic, complemented
16#35528C211yesmaximal, characteristic, complemented
17#35285C211yesmaximal, characteristic, complemented
18#35266C211yesmaximal, characteristic, complemented
19#35149C211yesmaximal, characteristic, complemented
20#34814C211yesmaximal, characteristic, complemented
21#34813C211yesmaximal, characteristic, complemented
22C2×#2431C211yesmaximal, characteristic, complemented
23#34276C211yesmaximal, characteristic, complemented
24#34211C211yesmaximal, characteristic, complemented
25#34174C211yesmaximal, characteristic, complemented
26C23×#41C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#535C2211yescharacteristic
29C2×#535C2211yescharacteristic
30C2×#533C2211yescharacteristic
31C22×#127C2211yescharacteristic
32C22×#124C2211yescharacteristic
33C2×#525C2211yescharacteristic
34C22×#121C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C2×#519C2211yescharacteristic
38C2×#518C2211yescharacteristic
39#2860C2214yescomplemented
40#2858C2214yescomplemented
41#2849C2214yes—
42#2829C2218yescomplemented
43#2828C2218yescomplemented
44#2803C2218yescomplemented
45#2803C2218yescomplemented
46#2797C2218yescomplemented
47#2781C2218yescomplemented
48#2780C2218yescomplemented
49#2778C2218yescomplemented
50#2756C2218yescomplemented
51#2750C2218yescomplemented
52#2733C2218yescomplemented
53#2715C2218yescomplemented
54#2714C2218yescomplemented
55#2714C2218yescomplemented
56#2710C2218yescomplemented
57#2708C2218yescomplemented
58#2686C2218yescomplemented
59#2682C2218yescomplemented
60#2662C2218yescomplemented
61#2661C2218yescomplemented
62#2661C2218yescomplemented
63#2649C2218yescomplemented
64#2648C2218yescomplemented
65#2648C2218yescomplemented
66#2644C2214yescomplemented
67#2641C2214yescomplemented
68#2613C2214yes—
69#2597C2218yescomplemented
70#2582C2214yescomplemented
71#2581C2214yescomplemented
72#2576C2218yescomplemented
73#2559C2218yescomplemented
74#2557C2218yescomplemented
75#2555C2218yescomplemented
76#2554C2218yescomplemented
77#2548C2214yescomplemented
78#2548C2214yescomplemented
79#2548C2214yescomplemented
80#2545C2214yescomplemented
81#2544C2212yescomplemented
82#2544C2212yescomplemented
83#2541C2212yescomplemented
84#2541C2212yescomplemented
85#2534C2214yes—
86#2513C2214yescomplemented
87#2512C2214yescomplemented
88#2504C2212yescomplemented
89#2501C2212yescomplemented
90#2500C2212yescomplemented
91#2500C2212yescomplemented
92#2497C2212yescomplemented
93#2496C2212yescomplemented
94#2495C2212yescomplemented
95#2494C2212yescomplemented
96#2493C2214yes—
97#2492C2212yescomplemented
98#2491C2212yescomplemented
99#2490C2212yescomplemented
100#2489C2212yescomplemented
101#2488C2214yes—
102#2483C2214yes—
103#2480C2218yes—
104#2480C2214yes—
105#2472C2214yes—
106#2453C2214yescomplemented
107#2451C2214yescomplemented
108#2448C2214yescomplemented
109#2445C2214yescomplemented
110#2438C2218yes—
111#2435C2218yes—
112#2432C2214yescomplemented
113#2431C2214yes—
114#2431C2214yes—
115#2431C2214yes—
116#2431C2214yes—
117#2431C2214yescomplemented
118#2428C2214yescomplemented
119#2428C2214yescomplemented
120#2428C2214yescomplemented
121#2426C2214yescomplemented
122#2426C2214yescomplemented
123#2426C2214yescomplemented
124#2422C2214yescomplemented
125#2422C2214yescomplemented
126#2420C2214yescomplemented
127#2420C2214yescomplemented
128#2418C2218yes—
129#2416C2214yescomplemented
130#2414C2214yescomplemented
131#2411C2218yes—
132#2410C2218yes—
133#2408C2214yes—
134#2407C2214yescomplemented
135#2407C2214yescomplemented
136#2405C2214yes—
137#2401C2214yescomplemented
138#2398C2214yescomplemented
139C2×#392C2214yes—
140#2367C2214yescomplemented
141#2367C2214yescomplemented
142#2362C2214yescomplemented
143#2360C2214yescomplemented
144#2359C2218yes—
145#2342C2218yes—
146#2341C2214yescomplemented
147#2341C2214yescomplemented
148#2341C2214yescomplemented
149#2341C2214yescomplemented
150#2337C2218yescomplemented
151#2333C2218yescomplemented
152#2327C2212yescomplemented
153#2326C2212yescomplemented
154#2326C2212yescomplemented
155#2326C2212yescomplemented
156#2317C2211yescharacteristic
157#2317C2211yescharacteristic
158#2316C2211yescharacteristic
159#2310C2211yescharacteristic
160#2309C2211yescharacteristic
161#2309C2211yescharacteristic
162#2309C2211yescharacteristic
163#2309C2211yescharacteristic
164#2309C2214yes—
165#2309C2211yescharacteristic
166C4×C4⋊Q8C2212yescomplemented
167C4×#126C2214yescomplemented
168C4×#124C2212yescomplemented
169C4×#124C2214yescomplemented
170C4×#124C2212yescomplemented
171C4×#124C2212yescomplemented
172#2297C2211yescharacteristic
173#2297C2211yescharacteristic
174#2296C2211yescharacteristic
175#2296C2211yescharacteristic
176C2×#391C2211yescharacteristic
177C2×#390C2211yescharacteristic
178C2×#386C2214yes—
179#2285C2211yescharacteristic
180#2280C2211yescharacteristic
181#2280C2211yescharacteristic
182#2280C2211yescharacteristic
183#2280C2214yes—
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C22⋊C4C2211yescharacteristic
187C22×#41—28no—
188C22×#41—44no—
189C22×#41—44no—
190C22×#41C2311yescharacteristic
191C22×#41C2314yes—
192C22×#41C2314yes—
193C23×Q8C2311yescharacteristic
194C23×D4C2311yescharacteristic
195C23×D4C2311yescharacteristic
196C23×D4C2312yes—
197C23×D4C2314yes—
198C23×D4C2312yes—
199C24×C4C2311yescharacteristic
200C24×C4C2312yes—
201#536—28no—
202#535—44no—
203#535—44no—
204#533—44no—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×#127—44no—
208C2×#127C2312yes—
209C2×#127C2312yes—
210C2×#127C2314yes—
211C2×#127C2312yes—
212C2×#127C2312yes—
213C2×#126C2314yes—
214C2×#126C2318yes—
215C2×#125C2312yes—
216C2×#124—28no—
217C2×#124C2312yes—
218C2×#124C2312yes—
219C2×#124C2314yes—
220C2×#124C2312yes—
221C2×#124C2318yes—
222C2×#124C2312yes—
223C2×#124C2312yes—
224C2×#124C2314yes—
225C2×#124C2318yes—
226#525—44no—
227C2×#123C2314yes—
228C2×#123C2312yes—
229C2×#123C2318yes—
230C2×#123C2318yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2314yes—
234C2×#121—44no—
235C2×#121C2318yes—
236C2×#121C2312yes—
237C2×#121C2312yes—
238C2×#121C2314yes—
239C2×#121C2314yes—
240C2×#121C2312yes—
241C2×#121C2314yes—
242C2×#121C2318yes—
243C2×#121C2318yes—
244C2×#120C2314yes—
245C2×#120C2312yes—
246C2×#120C2314yes—
247#520—44no—
248#519—44no—
249#519—44no—
250#518—44no—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2314yes—
254C2×C4×Q8C2314yes—
255C2×C4×Q8C2312yes—
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2314yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2312yes—
264C2×C4×D4C2312yes—
265C2×C4×D4C2314yes—
266C2×#117C2311yescharacteristic
267C2×#117C2311yescharacteristic
268C2×#117C2311yescharacteristic
269C2×#117C2311yescharacteristic
270C2×#117C2311yescharacteristic
271C2×#117C2311yescharacteristic
272C2×#117C2311yescharacteristic
273C2×#117C2314yes—
274C2×#117C2314yes—
275C2×#117C2312yes—
276C22×C4⋊C4C2311yescharacteristic
277C22×C4⋊C4C2312yes—
278C22×C22⋊C4C2314yes—
279C22×C22⋊C4C2314yes—
280C22×C22⋊C4C2312yes—
281C22×C22⋊C4C2312yes—
282C22×C22⋊C4C2314yes—
283C22×C42C2311yescharacteristic
284C22×C42C2311yescharacteristic
285#401C2314yes—
286#400C2318yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#399C2318yes—
293#398C2318yes—
294#398C2318yes—
295#397C2314yes—
296#397C2318yes—
297#397C2314yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2314yes—
303#397C2314yes—
304#397C2318yes—
305#397C2314yes—
306#396C2314yes—
307#396C2318yes—
308#396C2318yes—
309#396C2318yes—
310#396C2318yes—
311#395C2318yes—
312#394C2314yes—
313#394C2318yes—
314#394C2318yes—
315#394C2318yes—
316#394C2318yes—
317#394C2318yes—
318#394C2318yes—
319#394C2318yes—
320#394C2318yes—
321#394C2318yes—
322#394C2318yes—
323#394C2318yes—
324#394C2318yes—
325#394C2318yes—
326#394C2318yes—
327#394C2314yes—
328#394C2318yes—
329#394C2318yes—
330#393C2314yes—
331#393C2314yes—
332#392C2318yes—
333#392C2318yes—
334#392C2318yes—
335#392C2318yes—
336#392C2318yes—
337#392C2318yes—
338#392C2318yes—
339#392C2318yes—
340#392C2318yes—
341#391C2311yescharacteristic
342#391C2312yes—
343#391C2312yes—
344#391C2312yes—
345#391C2314yes—
346#391C2314yes—
347#391C2312yes—
348#391C2318yes—
349#391C2311yescharacteristic
350#391C2314yes—
351#391C2312yes—
352#390C2318yes—
353#390C2318yes—
354#390C2312yes—
355#390C2312yes—
356#390C2314yes—
357#390C2314yes—
358#390C2318yes—
359#390C2318yes—
360#390C2312yes—
361#390C2312yes—
362#390C2312yes—
363#390C2312yes—
364#390C2314yes—
365#390C2314yes—
366#390C2314yes—
367#390C2314yes—
368#390C2314yes—
369#390C2311yescharacteristic
370#390C2318yes—
371#390C2318yes—
372#390C2318yes—
373#390C2312yes—
374#390C2312yes—
375#390C2318yes—
376#390C2314yes—
377#390C2318yes—
378#390C2314yes—
379#390C2312yes—
380#390C2311yescharacteristic
381#389C2318yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2312yes—
387#389C2312yes—
388#389C2318yes—
389#389C2312yes—
390#389C2312yes—
391#388C2314yes—
392#388C2314yes—
393#388C2314yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2314yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#387C2314yes—
413#387C2314yes—
414#387C2314yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#386C2318yes—
420#386C2318yes—
421#386C2318yes—
422#386C2318yes—
423#386C2318yes—
424#386C2318yes—
425#386C2318yes—
426#386C2318yes—
427#386C2318yes—
428#386C2314yes—
429#386C2318yes—
430#386C2318yes—
431#386C2314yes—
432#385C2314yes—
433#385C2314yes—
434#385C2318yes—
435#385C2318yes—
436#385C2318yes—
437#385C2318yes—
438#385C2318yes—
439#385C2318yes—
440#385C2314yes—
441#385C2314yes—
442#384C2312yes—
443#384C2312yes—
444#384C2311yescharacteristic
445#384C2311yescharacteristic
446#383C2314yes—
447#382C2312yes—
448#382C2312yes—
449#382C2314yes—
450#382C2311yescharacteristic
451#382C2311yescharacteristic
452#381C2314yes—
453#381C2318yes—
454#381C2312yes—
455#381C2312yes—
456#381C2312yes—
457#380C2314yes—
458#380C2312yes—
459#380C2312yes—
460#380C2312yes—
461#380C2312yes—
462#380C2318yes—
463#380C2318yes—
464#380C2314yes—
465#380C2312yes—
466#380C2312yes—
467#379C2312yes—
468#379C2312yes—
469#379C2314yes—
470#379C2314yes—
471#379C2314yes—
472#379C2314yes—
473#379C2314yes—
474#379C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2318yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C22⋊C4C2312yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2318yes—
488C4×C22⋊C4C2318yes—
489C4×C22⋊C4C2318yes—
490C4×C22⋊C4C2318yes—
491C4×C22⋊C4C2318yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2314yes—
495C4×C22⋊C4C2314yes—
496C4×C22⋊C4C2312yes—
497C4×C22⋊C4C2312yes—
498C4×C22⋊C4C2312yes—
499C4×C22⋊C4C2312yes—
500C4×C22⋊C4C2312yes—
501#376C2312yes—
502#376C2312yes—
503C2×#95C2314yes—
504C2×#95C2312yes—
505C43C2312yes—
506C43C2312yes—
507C25C2412yes—
508C25C2411yescharacteristic
509C25C2412yes—
510C2×#41—216no—
511C2×#41—216no—
512C2×#41—24no—
513C2×#41—24no—
514C2×#41—24no—
515C2×#41—48no—
516C2×#41—48no—
517C2×#41—48no—
518C2×#41—48no—
519C2×#41—464no—
520C22×Q8—24no—
521C22×Q8—24no—
522C22×Q8#4118yes—
523C22×Q8C2411yescharacteristic
524C22×Q8C2412yes—
525C22×Q8C2412yes—
526C22×Q8C2414yes—
527C22×D4—24no—
528C22×D4—28no—
529C22×D4—24no—
530C22×D4—24no—
531C22×D4—24no—
532C22×D4—24no—
533C22×D4—24no—
534C22×D4—48no—
535C22×D4—44no—
536C22×D4—44no—
537C22×D4—44no—
538C22×D4—48no—
539C22×D4—84no—
540C22×D4—84no—
541C22×D4C2412yes—
542C22×D4C2412yes—
543C22×D4C2412yes—
544C22×D4C2411yescharacteristic
545C22×D4C2412yes—
546C22×D4C2412yes—
547C22×D4C2418yes—
548C22×D4C2418yes—
549C22×D4C2414yes—
550C22×D4C2418yes—
551C22×D4C2414yes—
552C22×D4C2414yes—
553C22×D4C2418yes—
554C22×D4C2418yes—
555C23×C4—28no—
556C23×C4—24no—
557C23×C4—24no—
558C23×C4—24no—
559C23×C4—44no—
560C23×C4—44no—
561C23×C4C2411yescharacteristic
562C23×C4C2412yes—
563C23×C4C2412yes—
564C23×C4C2412yes—
565C23×C4C2412yes—
566C23×C4C2412yes—
567C23×C4C2412yes—
568C23×C4C2412yes—
569C23×C4C2418yes—
570C23×C4C2414yes—
571C23×C4C2414yes—
572C23×C4C2414yes—
573C23×C4C2411yescharacteristic
574C4⋊Q8—28no—
575C4⋊Q8—44no—
576#127—48no—
577#127—44no—
578#127—44no—
579#127—44no—
580#127—44no—
581#126—48no—
582#126—88no—
583#125—44no—
584#124—28no—
585#124—28no—
586#124—216no—
587#124—28no—
588#124—416no—
589#124—44no—
590#124—44no—
591#124—48no—
592#124—88no—
593#123—216no—
594#123—44no—
595#123—88no—
596#123—88no—
597C22⋊Q8—216no—
598C22⋊Q8—48no—
599C22⋊Q8—44no—
600#121—416no—
601#121—48no—
602#121—48no—
603#121—44no—
604#121—44no—
605#121—44no—
606#121—48no—
607#121—88no—
608#121—88no—
609#120—44no—
610#120—48no—
611#120—48no—
612C4×Q8—48no—
613C4×Q8—44no—
614C4×Q8—44no—
615C4×Q8—44no—
616C4×Q8—44no—
617C4×Q8—48no—
618C4×Q8—48no—
619C4×Q8—44no—
620C4×D4—44no—
621C4×D4—44no—
622C4×D4—44no—
623C4×D4—44no—
624C4×D4—44no—
625C4×D4—48no—
626C4×D4—48no—
627#117—24no—
628#117—24no—
629#117—24no—
630#117—24no—
631#117—24no—
632#117—24no—
633#117—24no—
634#117—48no—
635#117—48no—
636#117—44no—
637C2×C4⋊C4—24no—
638C2×C4⋊C4—44no—
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C22⋊C4—216no—
670C2×C22⋊C4—44no—
671C2×C22⋊C4—48no—
672C2×C22⋊C4—44no—
673C2×C22⋊C4—84no—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2412yes—
681C2×C22⋊C4C2412yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2412yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2412yes—
693C2×C22⋊C4C2412yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2418yes—
709C2×C22⋊C4C2418yes—
710C2×C22⋊C4C2418yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2418yes—
713C2×C22⋊C4C2418yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2418yes—
716C2×C22⋊C4C2418yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C42—24no—
720C2×C42—24no—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2412yes—
729C2×C42C2414yes—
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2412yes—
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2414yes—
736C2×C42C2414yes—
737C2×C42C2414yes—
738C2×C42C2418yes—
739C2×C42C2414yes—
740C2×C42C2414yes—
741C2×C42C2414yes—
742#95C2412yes—
743#95C2412yes—
744#95C2412yes—
745#95C2412yes—
746#95C2418yes—
747#95C2418yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2418yes—
762#95C2418yes—
763#95C2418yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2418yes—
772#95C2418yes—
773C24—22no—
774C24—24no—
775C24—24no—
776C24—24no—
777C24—22no—
778C24—24no—
779C24—22no—
780C24—24no—
781C24—24no—
782C24—42no—
783C24—44no—
784C24—44no—
785C24—42no—
786C24—44no—
787C24—44no—
788C24C2514yes—
789C24C2512yes—
790C24C2514yes—
791C24C2512yes—
792C24C2511yescharacteristic
793#41—464no—
794#41—464no—
795#41—416no—
796C2×Q8—232no—
797C2×Q8—22no—
798C2×Q8—24no—
799C2×Q8—24no—
800C2×Q8—24no—
801C2×Q8—24no—
802C2×Q8—22no—
803C2×Q8—22no—
804C2×Q8—28no—
805C2×Q8—44no—
806C2×Q8—44no—
807C2×Q8C2×#4118yes—
808C2×Q8C2×#4118yes—
809C2×D4—24no—
810C2×D4—24no—
811C2×D4—24no—
812C2×D4—24no—
813C2×D4—24no—
814C2×D4—22no—
815C2×D4—216no—
816C2×D4—24no—
817C2×D4—24no—
818C2×D4—24no—
819C2×D4—24no—
820C2×D4—22no—
821C2×D4—24no—
822C2×D4—22no—
823C2×D4—24no—
824C2×D4—24no—
825C2×D4—24no—
826C2×D4—24no—
827C2×D4—24no—
828C2×D4—216no—
829C2×D4—48no—
830C2×D4—48no—
831C2×D4—432no—
832C2×D4—44no—
833C2×D4—48no—
834C2×D4—44no—
835C2×D4—48no—
836C2×D4—48no—
837C2×D4—48no—
838C2×D4—44no—
839C2×D4—48no—
840C2×D4—48no—
841C2×D4—48no—
842C2×D4—48no—
843C2×D4—48no—
844C2×D4—44no—
845C2×D4—44no—
846C2×D4—48no—
847C2×D4—48no—
848C2×D4—48no—
849C2×D4—48no—
850C2×D4—416no—
851C2×D4—416no—
852C2×D4—832no—
853C2×D4—816no—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—22no—
857C22×C4—24no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—24no—
861C22×C4—24no—
862C22×C4—24no—
863C22×C4—216no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—24no—
867C22×C4—24no—
868C22×C4—24no—
869C22×C4—24no—
870C22×C4—24no—
871C22×C4—24no—
872C22×C4—24no—
873C22×C4—48no—
874C22×C4—48no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—48no—
883C22×C4—48no—
884C22×C4—48no—
885C22×C4—432no—
886C22×C4—416no—
887C22×C4C2×#4118yes—
888C22×C4C2×#4114yes—
889C22×C4H(5,𝔽2)14yes—
890C22×C4H(5,𝔽2)14yes—
891C22×C4C2512yes—
892C22×C4C2512yes—
893C22×C4C2512yes—
894C22×C4C2512yes—
895C22×C4C2512yes—
896C22×C4C2512yes—
897C22×C4C2512yes—
898C22×C4C2514yes—
899C22×C4C2514yes—
900C22×C4C2514yes—
901C22×C4C2514yes—
902C22×C4C2512yes—
903C22×C4C2512yes—
904C22×C4C2512yes—
905C22×C4C2512yes—
906C22×C4C2514yes—
907C22×C4C2514yes—
908C22×C4C2512yes—
909C22×C4C2511yescharacteristic
910C22×C4C2511yescharacteristic
911C4⋊C4—24no—
912C4⋊C4—216no—
913C4⋊C4—24no—
914C4⋊C4—24no—
915C4⋊C4—22no—
916C4⋊C4—22no—
917C4⋊C4—22no—
918C4⋊C4—22no—
919C4⋊C4—22no—
920C4⋊C4—22no—
921C4⋊C4—24no—
922C4⋊C4—24no—
923C4⋊C4—24no—
924C4⋊C4—28no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—48no—
929C4⋊C4—44no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—44no—
933C4⋊C4—44no—
934C4⋊C4—48no—
935C4⋊C4—44no—
936C4⋊C4—48no—
937C4⋊C4—48no—
938C4⋊C4—44no—
939C4⋊C4—44no—
940C4⋊C4—44no—
941C22⋊C4—24no—
942C22⋊C4—24no—
943C22⋊C4—24no—
944C22⋊C4—24no—
945C22⋊C4—24no—
946C22⋊C4—24no—
947C22⋊C4—24no—
948C22⋊C4—216no—
949C22⋊C4—216no—
950C22⋊C4—216no—
951C22⋊C4—24no—
952C22⋊C4—24no—
953C22⋊C4—28no—
954C22⋊C4—42no—
955C22⋊C4—42no—
956C22⋊C4—44no—
957C22⋊C4—44no—
958C22⋊C4—48no—
959C22⋊C4—48no—
960C22⋊C4—48no—
961C22⋊C4—44no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—48no—
965C22⋊C4—44no—
966C22⋊C4—44no—
967C22⋊C4—48no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—48no—
971C22⋊C4—48no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—48no—
976C22⋊C4—48no—
977C22⋊C4—48no—
978C22⋊C4—48no—
979C22⋊C4—48no—
980C22⋊C4—48no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—48no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C42—24no—
987C42—22no—
988C42—22no—
989C42—24no—
990C42—24no—
991C42—22no—
992C42—22no—
993C42—24no—
994C42—24no—
995C42—24no—
996C42—24no—
997C42—24no—
998C42—24no—
999C42—28no—
1000C42—44no—
1001C42—44no—
1002C42—44no—
1003C42—48no—
1004C42—44no—
1005C42—44no—
1006C42—44no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—24no—
1011C23—22no—
1012C23—24no—
1013C23—24no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—24no—
1018C23—24no—
1019C23—22no—
1020C23—24no—
1021C23—22no—
1022C23—22no—
1023C23—24no—
1024C23—28no—
1025C23—28no—
1026C23—28no—
1027C23—22no—
1028C23—24no—
1029C23—28no—
1030C23—22no—
1031C23—44no—
1032C23—416no—
1033C23—44no—
1034C23—48no—
1035C23—44no—
1036C23—48no—
1037C23—84no—
1038C23—88no—
1039C23—84no—
1040C23—84no—
1041C23—84no—
1042C23—84no—
1043C23—88no—
1044C23—88no—
1045C23—84no—
1046C23C22×#4112yes—
1047C23C2×H(5,𝔽2)12yes—
1048C23C2×H(5,𝔽2)12yes—
1049C23C2611yescharacteristic
1050Q8—216no—
1051Q8—216no—
1052Q8—44no—
1053Q8—88no—
1054D4—432no—
1055D4—48no—
1056D4—48no—
1057D4—48no—
1058D4—48no—
1059D4—48no—
1060D4—44no—
1061D4—816no—
1062D4—88no—
1063D4—816no—
1064D4—816no—
1065D4—164no—
1066D4—164no—
1067D4—168no—
1068C2×C4—22no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—22no—
1072C2×C4—216no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—24no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—24no—
1088C2×C4—22no—
1089C2×C4—24no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—22no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—22no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—22no—
1102C2×C4—24no—
1103C2×C4—22no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—22no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—28no—
1112C2×C4—22no—
1113C2×C4—24no—
1114C2×C4—48no—
1115C2×C4—432no—
1116C2×C4—44no—
1117C2×C4—48no—
1118C2×C4—48no—
1119C2×C4—48no—
1120C2×C4—84no—
1121C2×C4—84no—
1122C2×C4—164no—
1123C2×C4—164no—
1124C2×C4—164no—
1125C2×C4#538116yes—
1126C2×C4C22×#4118yes—
1127C2×C4C22×#4112yes—
1128C2×C4C22×#4112yes—
1129C2×C4C2×H(5,𝔽2)12yes—
1130C2×C4C2×H(5,𝔽2)12yes—
1131C2×C4C2×H(5,𝔽2)12yes—
1132C2×C4C2×H(5,𝔽2)12yes—
1133C2×C4#58514yes—
1134C22—24no—
1135C22—22no—
1136C22—22no—
1137C22—24no—
1138C22—44no—
1139C22—42no—
1140C22—42no—
1141C22—48no—
1142C22—48no—
1143C22—44no—
1144C22—42no—
1145C22—44no—
1146C22—42no—
1147C22—42no—
1148C22—44no—
1149C22—42no—
1150C22—44no—
1151C22—48no—
1152C22—48no—
1153C22—42no—
1154C22—44no—
1155C22—42no—
1156C22—44no—
1157C22—42no—
1158C22—42no—
1159C22—44no—
1160C22—88no—
1161C22—816no—
1162C22—168no—
1163C22C2×#53814yes—
1164C22C23×#4111yescharacteristic
1165C22C22×H(5,𝔽2)11yescharacteristic
1166C22C22×H(5,𝔽2)11yescharacteristic
1167C22C2×#58512yes—
1168C22H(7,𝔽2)12yes—
1169C4—24no—
1170C4—28no—
1171C4—44no—
1172C4—42no—
1173C4—42no—
1174C4—42no—
1175C4—42no—
1176C4—42no—
1177C4—44no—
1178C4—42no—
1179C4—42no—
1180C4—42no—
1181C4—42no—
1182C4—44no—
1183C4—44no—
1184C4—44no—
1185C4—42no—
1186C4—42no—
1187C4C2×#53814yes—
1188C4C2×#53814yes—
1189C2—24no—
1190C2—82no—
1191C2—84no—
1192C2—82no—
1193C2—84no—
1194C2C22×#53811yescharacteristic
1195C2#6283611yescharacteristic
1196C2#6287611yescharacteristic
1197C2#6292412yes—
1198C2#6300612yes—
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. #42903C2semidirect
2. #42895C2semidirect
3. #42893C2semidirect
4. #42838C2semidirect
5. #41962C2semidirect
6. #40129C2semidirect
7. #40122C2semidirect
8. #39790C2semidirect
9. #39218C2semidirect
10. #38398C2semidirect
11. #35677C2semidirect
12. #35662C2semidirect
13. #35563C2semidirect
14. #35540C2semidirect
15. #35531C2semidirect
16. #35528C2semidirect
17. #35285C2semidirect
18. #35266C2semidirect
19. #35149C2semidirect
20. #34814C2semidirect
21. #34813C2semidirect
22. C2×#2431C2semidirect
23. #34276C2semidirect
24. #34211C2semidirect
25. #34174C2semidirect
39. #2860C22semidirect
40. #2858C22semidirect
42. #2829C22semidirect
43. #2828C22semidirect
44. #2803C22semidirect
45. #2803C22semidirect
46. #2797C22semidirect
47. #2781C22semidirect
48. #2780C22semidirect
49. #2778C22semidirect
50. #2756C22semidirect
51. #2750C22semidirect
52. #2733C22semidirect
53. #2715C22semidirect
54. #2714C22semidirect
55. #2714C22semidirect
56. #2710C22semidirect
57. #2708C22semidirect
58. #2686C22semidirect
59. #2682C22semidirect
60. #2662C22semidirect
61. #2661C22semidirect
62. #2661C22semidirect
63. #2649C22semidirect
64. #2648C22semidirect
65. #2648C22semidirect
66. #2644C22semidirect
67. #2641C22semidirect
69. #2597C22semidirect
70. #2582C22semidirect
71. #2581C22semidirect
72. #2576C22semidirect
73. #2559C22semidirect
74. #2557C22semidirect
75. #2555C22semidirect
76. #2554C22semidirect
77. #2548C22semidirect
78. #2548C22semidirect
79. #2548C22semidirect
80. #2545C22semidirect
81. #2544C22semidirect
82. #2544C22semidirect
83. #2541C22semidirect
84. #2541C22semidirect
86. #2513C22semidirect
87. #2512C22semidirect
88. #2504C22semidirect
89. #2501C22semidirect
90. #2500C22semidirect
91. #2500C22semidirect
92. #2497C22semidirect
93. #2496C22semidirect
94. #2495C22semidirect
95. #2494C22semidirect
97. #2492C22semidirect
98. #2491C22semidirect
99. #2490C22semidirect
100. #2489C22semidirect
106. #2453C22semidirect
107. #2451C22semidirect
108. #2448C22semidirect
109. #2445C22semidirect
112. #2432C22semidirect
117. #2431C22semidirect
118. #2428C22semidirect
119. #2428C22semidirect
120. #2428C22semidirect
121. #2426C22semidirect
122. #2426C22semidirect
123. #2426C22semidirect
124. #2422C22semidirect
125. #2422C22semidirect
126. #2420C22semidirect
127. #2420C22semidirect
129. #2416C22semidirect
130. #2414C22semidirect
134. #2407C22semidirect
135. #2407C22semidirect
137. #2401C22semidirect
138. #2398C22semidirect
140. #2367C22semidirect
141. #2367C22semidirect
142. #2362C22semidirect
143. #2360C22semidirect
146. #2341C22semidirect
147. #2341C22semidirect
148. #2341C22semidirect
149. #2341C22semidirect
150. #2337C22semidirect
151. #2333C22semidirect
152. #2327C22semidirect
153. #2326C22semidirect
154. #2326C22semidirect
155. #2326C22semidirect
166. C4×C4⋊Q8C22semidirect
167. C4×#126C22semidirect
168. C4×#124C22semidirect
169. C4×#124C22semidirect
170. C4×#124C22semidirect
171. C4×#124C22semidirect

Maximal subgroups

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

subgroupindex
#429032
#428952
#428932
#428382
#419622
#401292
#401222
#397902
#392182
#383982
#356772
#356622
#355632
#355402
#355312
#355282
#352852
#352662
#351492
#348142
#348132
C2×#24312
#342762
#342112
#341742