Finite Group Databasebeta

← #7652633

Subgroups — #7652633

Order 512.

5862 conjugacy classes of subgroups.

The subgroup lattice has 1207 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42961C214yesmaximal, complemented
2#42872C214yesmaximal, complemented
3#42595C214yesmaximal, complemented
4#42518C214yesmaximal, complemented
5#40696C218yesmaximal, complemented
6#40153C214yesmaximal, complemented
7#40030C214yesmaximal, complemented
8#39768C214yesmaximal, complemented
9#39248C214yesmaximal, complemented
10#38500C218yesmaximal, complemented
11#35676C211yesmaximal, characteristic, complemented
12#35676C211yesmaximal, characteristic, complemented
13#35630C211yesmaximal, characteristic, complemented
14#35626C211yesmaximal, characteristic, complemented
15#35556C211yesmaximal, characteristic, complemented
16#35528C211yesmaximal, characteristic, complemented
17#35338C211yesmaximal, characteristic, complemented
18#35272C211yesmaximal, characteristic, complemented
19#35152C211yesmaximal, characteristic, complemented
20C2×#2544C211yesmaximal, characteristic, complemented
21#34816C211yesmaximal, characteristic, complemented
22#34745C211yesmaximal, characteristic, complemented
23#34275C211yesmaximal, characteristic, complemented
24#34265C211yesmaximal, characteristic, complemented
25#34259C211yesmaximal, characteristic, complemented
26C22×2−1+4C2211yescharacteristic
27C2×#535C2211yescharacteristic
28C2×#535C2211yescharacteristic
29C2×#535C2211yescharacteristic
30C2×#535C2211yescharacteristic
31C2×#533C2211yescharacteristic
32C22×#127C2211yescharacteristic
33C22×#124C2211yescharacteristic
34C22×#124C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C2×#518C2211yescharacteristic
37C2×C4×#41C2211yescharacteristic
38C22×C4×D4C2211yescharacteristic
39#2861C2214yescomplemented
40#2856C2214yes—
41#2849C2214yes—
42#2832C2218yescomplemented
43#2825C2218yescomplemented
44#2808C2218yescomplemented
45#2804C2218yescomplemented
46#2778C2218yescomplemented
47#2760C2218yescomplemented
48#2756C2218yescomplemented
49#2752C2218yescomplemented
50#2751C2218yescomplemented
51#2751C2218yescomplemented
52#2749C2218yescomplemented
53#2749C2218yescomplemented
54#2714C2218yescomplemented
55#2708C2218yescomplemented
56#2703C2218yescomplemented
57#2688C2218yescomplemented
58#2686C2218yescomplemented
59#2676C2218yescomplemented
60#2653C2218yescomplemented
61#2653C2218yescomplemented
62#2648C2218yescomplemented
63#2640C2214yescomplemented
64#2639C2218yescomplemented
65#2635C2218yescomplemented
66#2631C2218yescomplemented
67#2622C2214yes—
68#2619C2214yes—
69#2592C2214yescomplemented
70#2592C2214yescomplemented
71#2592C2214yescomplemented
72#2572C2218yescomplemented
73#2561C2218yes—
74#2559C2218yescomplemented
75#2557C2218yescomplemented
76#2548C2214yes—
77#2548C2214yescomplemented
78#2544C2214yes—
79#2544C2214yes—
80#2544C2214yes—
81#2544C2214yes—
82#2544C2212yes—
83#2544C2212yes—
84#2541C2212yes—
85#2541C2212yes—
86#2541C2214yes—
87#2514C2212yescomplemented
88#2514C2214yescomplemented
89#2514C2214yescomplemented
90#2513C2212yescomplemented
91#2512C2212yescomplemented
92#2511C2212yescomplemented
93#2511C2214yescomplemented
94#2511C2214yescomplemented
95#2510C2214yes—
96#2493C2218yes—
97#2491C2214yescomplemented
98#2490C2214yescomplemented
99#2483C2214yes—
100#2483C2214yes—
101#2481C2214yes—
102#2472C2218yes—
103#2456C2218yescomplemented
104#2454C2212yescomplemented
105#2453C2212yescomplemented
106#2452C2212yescomplemented
107#2451C2212yescomplemented
108#2450C2214yes—
109#2449C2214yes—
110#2447C2214yescomplemented
111#2447C2214yescomplemented
112#2447C2214yescomplemented
113#2447C2214yescomplemented
114#2447C2214yescomplemented
115#2445C2214yescomplemented
116#2444C2218yescomplemented
117#2444C2218yescomplemented
118#2436C2212yescomplemented
119#2436C2214yescomplemented
120#2436C2214yescomplemented
121#2436C2214yescomplemented
122#2436C2212yescomplemented
123#2431C2214yescomplemented
124#2431C2214yescomplemented
125#2431C2212yescomplemented
126#2431C2214yescomplemented
127#2431C2212yescomplemented
128#2428C2214yes—
129#2428C2214yes—
130#2422C2214yescomplemented
131#2420C2214yescomplemented
132#2410C2218yes—
133#2408C2218yes—
134#2404C2214yes—
135#2404C2218yes—
136#2404C2214yes—
137#2401C2214yescomplemented
138#2396C2214yescomplemented
139C2×#394C2214yes—
140#2367C2214yescomplemented
141#2366C2214yescomplemented
142#2363C2214yescomplemented
143#2363C2214yescomplemented
144#2361C2214yescomplemented
145#2361C2214yescomplemented
146#2358C2218yes—
147Q8×C22⋊C4C2214yescomplemented
148#2339C2218yes—
149#2339C2214yescomplemented
150#2333C2218yescomplemented
151#2328C2212yescomplemented
152#2326C2212yescomplemented
153#2325C2218yescomplemented
154#2321C2214yes—
155#2317C2211yescharacteristic
156#2311C2211yescharacteristic
157#2311C2212yescomplemented
158#2310C2211yescharacteristic
159#2310C2211yescharacteristic
160#2310C2211yescharacteristic
161#2310C2212yescomplemented
162#2309C2211yescharacteristic
163#2309C2211yescharacteristic
164#2309C2211yescharacteristic
165C4×#127C2212yescomplemented
166C4×#126C2214yescomplemented
167C4×#124C2212yescomplemented
168C4×C22⋊Q8C2214yescomplemented
169C4×#120C2214yes—
170#2297C2211yescharacteristic
171#2297C2211yescharacteristic
172#2297C2211yescharacteristic
173#2297C2211yescharacteristic
174#2297C2211yescharacteristic
175#2297C2212yescomplemented
176#2296C2211yescharacteristic
177#2296C2211yescharacteristic
178#2296C2211yescharacteristic
179C2×#391C2211yescharacteristic
180C2×#391C2212yescomplemented
181C2×#390C2211yescharacteristic
182C2×#386C2214yes—
183#2285C2211yescharacteristic
184#2274C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C2×2−1+4—28no—
188C2×2−1+4—44no—
189C2×2−1+4—44no—
190C22×#41C2311yescharacteristic
191C22×#41C2311yescharacteristic
192C22×#41C2312yes—
193C22×#41C2314yes—
194C22×#41C2312yes—
195C23×Q8C2311yescharacteristic
196C23×Q8C2312yes—
197C23×Q8C2312yes—
198C23×D4C2311yescharacteristic
199C23×D4C2311yescharacteristic
200C23×D4C2314yes—
201C24×C4C2312yes—
202#535—28no—
203#535—28no—
204#535—44no—
205#535—44no—
206#533—44no—
207C2×C4⋊Q8C2312yes—
208C2×#127—44no—
209C2×#127C2312yes—
210C2×#127C2312yes—
211C2×#127C2312yes—
212C2×#127C2312yes—
213C2×#127C2314yes—
214C2×#127C2312yes—
215C2×#127C2312yes—
216C2×#126C2314yes—
217C2×#125C2312yes—
218C2×#124—44no—
219C2×#124—44no—
220C2×#124C2312yes—
221C2×#124C2312yes—
222C2×#124C2314yes—
223C2×#124C2312yes—
224C2×#124C2312yes—
225C2×#124C2312yes—
226C2×#124C2314yes—
227C2×#124C2314yes—
228C2×#124C2312yes—
229C2×#124C2318yes—
230C2×#123C2318yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2314yes—
233C2×#121C2314yes—
234C2×#121C2314yes—
235C2×#121C2318yes—
236C2×#121C2318yes—
237C2×#121C2312yes—
238C2×#121C2312yes—
239C2×#121C2314yes—
240C2×#121C2318yes—
241C2×#121C2318yes—
242C2×#120C2314yes—
243C2×#120C2314yes—
244C2×#120C2314yes—
245C2×#120C2314yes—
246#520—44no—
247#518—44no—
248C4×#41—44no—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2312yes—
252C2×C4×D4—44no—
253C2×C4×D4C2312yes—
254C2×C4×D4C2312yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2312yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2312yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2318yes—
264C2×C4×D4C2318yes—
265C2×#117C2311yescharacteristic
266C2×#117C2311yescharacteristic
267C2×#117C2311yescharacteristic
268C2×#117C2311yescharacteristic
269C2×#117C2311yescharacteristic
270C2×#117C2311yescharacteristic
271C2×#117C2312yes—
272C2×#117C2312yes—
273C22×C4⋊C4C2311yescharacteristic
274C22×C4⋊C4C2312yes—
275C22×C4⋊C4C2312yes—
276C22×C22⋊C4C2314yes—
277C22×C22⋊C4C2312yes—
278C22×C22⋊C4C2314yes—
279C22×C22⋊C4C2312yes—
280C22×C22⋊C4C2312yes—
281C22×C22⋊C4C2314yes—
282C22×C42C2311yescharacteristic
283C22×C42C2311yescharacteristic
284C22×C42C2311yescharacteristic
285C22×C42C2312yes—
286#401C2318yes—
287#401C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2318yes—
291#400C2314yes—
292#400C2318yes—
293#400C2318yes—
294#400C2314yes—
295#399C2314yes—
296#398C2314yes—
297#398C2314yes—
298#397C2318yes—
299#397C2318yes—
300#397C2314yes—
301#397C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2318yes—
306#397C2314yes—
307#397C2318yes—
308#397C2318yes—
309#397C2314yes—
310#396C2314yes—
311#396C2314yes—
312#396C2314yes—
313#395C2314yes—
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#393C2318yes—
327#393C2318yes—
328#393C2318yes—
329#393C2318yes—
330#393C2318yes—
331#393C2318yes—
332#393C2318yes—
333#393C2314yes—
334#392C2318yes—
335#392C2318yes—
336#392C2318yes—
337#392C2318yes—
338#392C2318yes—
339#392C2318yes—
340#392C2318yes—
341#392C2318yes—
342#391C2312yes—
343#391C2312yes—
344#391C2314yes—
345#391C2314yes—
346#391C2314yes—
347#391C2312yes—
348#391C2314yes—
349#391C2312yes—
350#391C2311yescharacteristic
351#391C2312yes—
352#391C2312yes—
353#391C2318yes—
354#391C2311yescharacteristic
355#391C2312yes—
356#391C2318yes—
357#391C2314yes—
358#391C2312yes—
359#391C2312yes—
360#391C2311yescharacteristic
361#391C2314yes—
362#391C2312yes—
363#391C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2318yes—
366#390C2312yes—
367#390C2314yes—
368#390C2312yes—
369#390C2312yes—
370#390C2314yes—
371#390C2314yes—
372#390C2314yes—
373#390C2314yes—
374#390C2312yes—
375#390C2311yescharacteristic
376#390C2318yes—
377#390C2312yes—
378#390C2311yescharacteristic
379#390C2318yes—
380#390C2318yes—
381#390C2314yes—
382#390C2318yes—
383#390C2312yes—
384#390C2312yes—
385#390C2312yes—
386#390C2311yescharacteristic
387#389C2314yes—
388#389C2312yes—
389#389C2312yes—
390#389C2312yes—
391#389C2312yes—
392#389C2312yes—
393#389C2312yes—
394#389C2314yes—
395#388C2314yes—
396#388C2314yes—
397#388C2314yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#387C2314yes—
409#387C2314yes—
410#387C2314yes—
411#387C2318yes—
412#387C2314yes—
413#387C2318yes—
414#387C2314yes—
415#387C2318yes—
416#386C2314yes—
417#386C2318yes—
418#386C2318yes—
419#386C2318yes—
420#386C2318yes—
421#386C2318yes—
422#386C2312yes—
423#386C2318yes—
424#386C2318yes—
425#386C2318yes—
426#386C2318yes—
427#386C2318yes—
428#386C2318yes—
429#386C2318yes—
430#386C2318yes—
431#386C2312yes—
432#386C2314yes—
433#386C2318yes—
434#386C2314yes—
435#386C2318yes—
436#386C2312yes—
437#386C2318yes—
438#386C2318yes—
439#386C2318yes—
440#386C2318yes—
441#386C2318yes—
442#386C2312yes—
443#386C2314yes—
444#386C2318yes—
445#385C2314yes—
446#385C2312yes—
447#385C2318yes—
448#385C2318yes—
449#385C2318yes—
450#385C2312yes—
451#385C2318yes—
452#385C2312yes—
453#385C2318yes—
454#385C2314yes—
455#385C2314yes—
456#385C2314yes—
457#385C2312yes—
458#384C2312yes—
459#384C2312yes—
460#383C2314yes—
461#383C2318yes—
462#382C2312yes—
463#382C2312yes—
464#381C2314yes—
465#381C2314yes—
466#381C2314yes—
467#381C2318yes—
468#381C2318yes—
469#381C2318yes—
470#381C2318yes—
471#380C2314yes—
472#380C2318yes—
473#380C2314yes—
474#380C2314yes—
475#379C2314yes—
476#379C2314yes—
477#379C2314yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2314yes—
495C4×C22⋊C4C2318yes—
496C4×C22⋊C4C2318yes—
497C4×C22⋊C4C2314yes—
498C4×C22⋊C4C2318yes—
499C4×C22⋊C4C2314yes—
500C4×C22⋊C4C2314yes—
501C4×C22⋊C4C2312yes—
502#376C2312yes—
503C2×#95C2318yes—
504C2×#95C2314yes—
505C2×#95C2312yes—
506C43C2312yes—
507C25C2412yes—
508C25C2412yes—
5092−1+4—464no—
510C2×#41—216no—
511C2×#41—28no—
512C2×#41—28no—
513C2×#41—24no—
514C2×#41—24no—
515C2×#41—24no—
516C2×#41—24no—
517C2×#41—24no—
518C2×#41—48no—
519C2×#41—48no—
520C2×#41—44no—
521C2×#41—44no—
522C2×#41—44no—
523C2×#41—44no—
524C2×#41#4118yes—
525C22×Q8—28no—
526C22×Q8—28no—
527C22×Q8—24no—
528C22×Q8—24no—
529C22×Q8—24no—
530C22×Q8—44no—
531C22×Q8—44no—
532C22×Q8—44no—
533C22×Q8—44no—
534C22×Q8C2412yes—
535C22×Q8C2412yes—
536C22×Q8C2411yescharacteristic
537C22×Q8C2411yescharacteristic
538C22×Q8C2414yes—
539C22×Q8C2414yes—
540C22×D4—24no—
541C22×D4—24no—
542C22×D4—24no—
543C22×D4—24no—
544C22×D4—24no—
545C22×D4—24no—
546C22×D4—48no—
547C22×D4—48no—
548C22×D4—84no—
549C22×D4C2412yes—
550C22×D4C2412yes—
551C22×D4C2412yes—
552C22×D4C2412yes—
553C22×D4C2412yes—
554C22×D4C2411yescharacteristic
555C22×D4C2412yes—
556C22×D4C2411yescharacteristic
557C22×D4C2418yes—
558C22×D4C2418yes—
559C22×D4C2418yes—
560C22×D4C2414yes—
561C22×D4C2414yes—
562C22×D4C2418yes—
563C22×D4C2414yes—
564C22×D4C2418yes—
565C23×C4—44no—
566C23×C4—84no—
567C23×C4C2412yes—
568C23×C4C2412yes—
569C23×C4C2412yes—
570C23×C4C2412yes—
571C23×C4C2411yescharacteristic
572C23×C4C2412yes—
573C23×C4C2412yes—
574C23×C4C2411yescharacteristic
575C23×C4C2414yes—
576C23×C4C2414yes—
577C23×C4C2414yes—
578C23×C4C2414yes—
579C23×C4C2414yes—
580C23×C4C2414yes—
581C23×C4C2418yes—
582C23×C4C2411yescharacteristic
583C4⋊Q8—44no—
584#127—28no—
585#127—28no—
586#127—44no—
587#127—44no—
588#127—48no—
589#127—44no—
590#127—44no—
591#126—48no—
592#125—44no—
593#124—28no—
594#124—28no—
595#124—48no—
596#124—48no—
597#124—48no—
598#124—44no—
599#124—44no—
600#124—44no—
601#124—44no—
602#124—88no—
603#123—88no—
604C22⋊Q8—48no—
605C22⋊Q8—48no—
606#121—216no—
607#121—216no—
608#121—416no—
609#121—416no—
610#121—44no—
611#121—44no—
612#121—48no—
613#121—88no—
614#121—88no—
615#120—216no—
616#120—216no—
617#120—48no—
618#120—48no—
619C4×Q8—48no—
620C4×Q8—44no—
621C4×Q8—44no—
622C4×D4—48no—
623C4×D4—48no—
624C4×D4—44no—
625C4×D4—44no—
626C4×D4—44no—
627C4×D4—44no—
628C4×D4—44no—
629C4×D4—44no—
630C4×D4—48no—
631C4×D4—48no—
632C4×D4—88no—
633C4×D4—88no—
634#117—24no—
635#117—24no—
636#117—24no—
637#117—24no—
638#117—24no—
639#117—24no—
640#117—44no—
641#117—44no—
642C2×C4⋊C4—24no—
643C2×C4⋊C4—44no—
644C2×C4⋊C4—44no—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C22⋊C4—48no—
674C2×C22⋊C4—44no—
675C2×C22⋊C4—44no—
676C2×C22⋊C4—44no—
677C2×C22⋊C4—48no—
678C2×C22⋊C4—84no—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2412yes—
681C2×C22⋊C4C2412yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2412yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2418yes—
708C2×C22⋊C4C2418yes—
709C2×C22⋊C4C2418yes—
710C2×C22⋊C4C2418yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2418yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C42—24no—
719C2×C42—24no—
720C2×C42—24no—
721C2×C42—44no—
722C2×C42C2412yes—
723C2×C42C2411yescharacteristic
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2412yes—
729C2×C42C2412yes—
730C2×C42C2412yes—
731C2×C42C2412yes—
732C2×C42C2412yes—
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2414yes—
737C2×C42C2414yes—
738C2×C42C2414yes—
739C2×C42C2418yes—
740C2×C42C2414yes—
741#95C2414yes—
742#95C2418yes—
743#95C2412yes—
744#95C2412yes—
745#95C2412yes—
746#95C2412yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2418yes—
756#95C2418yes—
757#95C2414yes—
758#95C2414yes—
759#95C2418yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2418yes—
773#95C2418yes—
774#95C2418yes—
775#95C2418yes—
776C24—24no—
777C24—24no—
778C24—24no—
779C24—24no—
780C24—24no—
781C24—24no—
782C24—44no—
783C24—44no—
784C24—44no—
785C24—44no—
786C24C2514yes—
787C24C2514yes—
788C24C2512yes—
789C24C2512yes—
790C24C2511yescharacteristic
791#41—232no—
792#41—432no—
793#41—464no—
794#41—432no—
795#41—416no—
796C2×Q8—28no—
797C2×Q8—24no—
798C2×Q8—24no—
799C2×Q8—22no—
800C2×Q8—22no—
801C2×Q8—22no—
802C2×Q8—24no—
803C2×Q8—24no—
804C2×Q8—24no—
805C2×Q8—24no—
806C2×Q8—22no—
807C2×Q8—22no—
808C2×Q8—44no—
809C2×Q8—44no—
810C2×Q8—44no—
811C2×Q8—44no—
812C2×Q8—44no—
813C2×Q8—432no—
814C2×Q8—432no—
815C2×Q8—416no—
816C2×Q8C2×#4114yes—
817C2×D4—24no—
818C2×D4—24no—
819C2×D4—28no—
820C2×D4—24no—
821C2×D4—24no—
822C2×D4—24no—
823C2×D4—216no—
824C2×D4—216no—
825C2×D4—24no—
826C2×D4—24no—
827C2×D4—24no—
828C2×D4—24no—
829C2×D4—22no—
830C2×D4—22no—
831C2×D4—22no—
832C2×D4—24no—
833C2×D4—24no—
834C2×D4—24no—
835C2×D4—24no—
836C2×D4—24no—
837C2×D4—24no—
838C2×D4—24no—
839C2×D4—24no—
840C2×D4—22no—
841C2×D4—22no—
842C2×D4—216no—
843C2×D4—44no—
844C2×D4—44no—
845C2×D4—48no—
846C2×D4—48no—
847C2×D4—48no—
848C2×D4—48no—
849C2×D4—48no—
850C2×D4—48no—
851C2×D4—48no—
852C2×D4—48no—
853C2×D4—48no—
854C2×D4—44no—
855C2×D4—44no—
856C2×D4—48no—
857C2×D4—48no—
858C2×D4—48no—
859C2×D4—48no—
860C2×D4—48no—
861C2×D4—416no—
862C2×D4—416no—
863C2×D4—832no—
864C2×D4C2×#4118yes—
865C2×D4C2×#4114yes—
866C22×C4—24no—
867C22×C4—24no—
868C22×C4—28no—
869C22×C4—24no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—24no—
873C22×C4—24no—
874C22×C4—24no—
875C22×C4—24no—
876C22×C4—24no—
877C22×C4—28no—
878C22×C4—24no—
879C22×C4—24no—
880C22×C4—24no—
881C22×C4—24no—
882C22×C4—28no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4—42no—
892C22×C4—44no—
893C22×C4—42no—
894C22×C4—48no—
895C22×C4—48no—
896C22×C4—44no—
897C22×C4—48no—
898C22×C4—44no—
899C22×C4—44no—
900C22×C4—44no—
901C22×C4—48no—
902C22×C4—48no—
903C22×C4—48no—
904C22×C4—816no—
905C22×C4C2×#4118yes—
906C22×C4C2×#4114yes—
907C22×C4H(5,𝔽2)14yes—
908C22×C4H(5,𝔽2)14yes—
909C22×C4C2512yes—
910C22×C4C2514yes—
911C22×C4C2512yes—
912C22×C4C2512yes—
913C22×C4C2514yes—
914C22×C4C2514yes—
915C22×C4C2512yes—
916C22×C4C2512yes—
917C22×C4C2514yes—
918C22×C4C2512yes—
919C22×C4C2514yes—
920C22×C4C2512yes—
921C22×C4C2512yes—
922C22×C4C2512yes—
923C22×C4C2514yes—
924C22×C4C2512yes—
925C22×C4C2512yes—
926C22×C4C2512yes—
927C22×C4C2511yescharacteristic
928C22×C4C2511yescharacteristic
929C4⋊C4—24no—
930C4⋊C4—24no—
931C4⋊C4—24no—
932C4⋊C4—24no—
933C4⋊C4—22no—
934C4⋊C4—22no—
935C4⋊C4—22no—
936C4⋊C4—22no—
937C4⋊C4—24no—
938C4⋊C4—24no—
939C4⋊C4—24no—
940C4⋊C4—24no—
941C4⋊C4—28no—
942C4⋊C4—28no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—44no—
946C4⋊C4—44no—
947C4⋊C4—44no—
948C4⋊C4—48no—
949C4⋊C4—44no—
950C4⋊C4—44no—
951C4⋊C4—44no—
952C4⋊C4—44no—
953C4⋊C4—44no—
954C4⋊C4—44no—
955C4⋊C4—44no—
956C4⋊C4—44no—
957C22⋊C4—24no—
958C22⋊C4—24no—
959C22⋊C4—24no—
960C22⋊C4—24no—
961C22⋊C4—24no—
962C22⋊C4—24no—
963C22⋊C4—216no—
964C22⋊C4—216no—
965C22⋊C4—28no—
966C22⋊C4—48no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—48no—
970C22⋊C4—48no—
971C22⋊C4—48no—
972C22⋊C4—48no—
973C22⋊C4—48no—
974C22⋊C4—48no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—48no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—48no—
983C22⋊C4—48no—
984C22⋊C4—48no—
985C22⋊C4—48no—
986C22⋊C4—44no—
987C22⋊C4—48no—
988C22⋊C4—48no—
989C22⋊C4—44no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—48no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C42—24no—
997C42—24no—
998C42—22no—
999C42—22no—
1000C42—24no—
1001C42—24no—
1002C42—24no—
1003C42—24no—
1004C42—22no—
1005C42—22no—
1006C42—24no—
1007C42—24no—
1008C42—24no—
1009C42—24no—
1010C42—44no—
1011C42—44no—
1012C42—44no—
1013C42—48no—
1014C42—44no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—24no—
1020C23—24no—
1021C23—24no—
1022C23—24no—
1023C23—22no—
1024C23—24no—
1025C23—24no—
1026C23—24no—
1027C23—24no—
1028C23—22no—
1029C23—22no—
1030C23—24no—
1031C23—28no—
1032C23—28no—
1033C23—24no—
1034C23—28no—
1035C23—28no—
1036C23—416no—
1037C23—48no—
1038C23—48no—
1039C23—84no—
1040C23—88no—
1041C23—84no—
1042C23—88no—
1043C23—88no—
1044C23—84no—
1045C23—84no—
1046C23C22×#4114yes—
1047C23C22×#4112yes—
1048C23C2×H(5,𝔽2)12yes—
1049C23C2×H(5,𝔽2)12yes—
1050C23C2611yescharacteristic
1051Q8—28no—
1052Q8—416no—
1053Q8—48no—
1054Q8—44no—
1055Q8—48no—
1056Q8—88no—
1057D4—216no—
1058D4—28no—
1059D4—416no—
1060D4—48no—
1061D4—48no—
1062D4—48no—
1063D4—48no—
1064D4—48no—
1065D4—44no—
1066D4—816no—
1067D4—816no—
1068D4—816no—
1069D4—816no—
1070D4—164no—
1071D4—164no—
1072D4—168no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—216no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—22no—
1081C2×C4—24no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—24no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—24no—
1092C2×C4—22no—
1093C2×C4—24no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—22no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—24no—
1113C2×C4—28no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—24no—
1121C2×C4—48no—
1122C2×C4—416no—
1123C2×C4—44no—
1124C2×C4—44no—
1125C2×C4—416no—
1126C2×C4—48no—
1127C2×C4—48no—
1128C2×C4—88no—
1129C2×C4—84no—
1130C2×C4—84no—
1131C2×C4—816no—
1132C2×C4—164no—
1133C2×C4—164no—
1134C2×C4—164no—
1135C2×C4#538116yes—
1136C2×C4C22×#4114yes—
1137C2×C4C22×#4112yes—
1138C2×C4C22×#4112yes—
1139C2×C4C2×H(5,𝔽2)12yes—
1140C2×C4C2×H(5,𝔽2)12yes—
1141C2×C4C2×H(5,𝔽2)12yes—
1142C2×C4C2×H(5,𝔽2)12yes—
1143C2×C4#58514yes—
1144C22—24no—
1145C22—22no—
1146C22—22no—
1147C22—24no—
1148C22—28no—
1149C22—24no—
1150C22—42no—
1151C22—42no—
1152C22—44no—
1153C22—48no—
1154C22—48no—
1155C22—44no—
1156C22—44no—
1157C22—42no—
1158C22—44no—
1159C22—44no—
1160C22—44no—
1161C22—42no—
1162C22—48no—
1163C22—48no—
1164C22—44no—
1165C22—42no—
1166C22—44no—
1167C22—44no—
1168C22—816no—
1169C22—168no—
1170C22C2×#53814yes—
1171C22C23×#4111yescharacteristic
1172C22C22×H(5,𝔽2)11yescharacteristic
1173C22C22×H(5,𝔽2)11yescharacteristic
1174C22C2×#58512yes—
1175C22H(7,𝔽2)12yes—
1176C4—24no—
1177C4—24no—
1178C4—44no—
1179C4—44no—
1180C4—42no—
1181C4—42no—
1182C4—42no—
1183C4—42no—
1184C4—44no—
1185C4—42no—
1186C4—42no—
1187C4—42no—
1188C4—42no—
1189C4—44no—
1190C4—42no—
1191C4—44no—
1192C4—42no—
1193C4—44no—
1194C4C2×#53814yes—
1195C4C2×#53814yes—
1196C2—24no—
1197C2—44no—
1198C2—82no—
1199C2—84no—
1200C2—84no—
1201C2C22×#53811yescharacteristic
1202C2#6283611yescharacteristic
1203C2#6287611yescharacteristic
1204C2#6292412yes—
1205C2#6301012yes—
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. #42961C2semidirect
2. #42872C2semidirect
3. #42595C2semidirect
4. #42518C2semidirect
5. #40696C2semidirect
6. #40153C2semidirect
7. #40030C2semidirect
8. #39768C2semidirect
9. #39248C2semidirect
10. #38500C2semidirect
11. #35676C2semidirect
12. #35676C2semidirect
13. #35630C2semidirect
14. #35626C2semidirect
15. #35556C2semidirect
16. #35528C2semidirect
17. #35338C2semidirect
18. #35272C2semidirect
19. #35152C2semidirect
20. C2×#2544C2semidirect
21. #34816C2semidirect
22. #34745C2semidirect
23. #34275C2semidirect
24. #34265C2semidirect
25. #34259C2semidirect
39. #2861C22semidirect
42. #2832C22semidirect
43. #2825C22semidirect
44. #2808C22semidirect
45. #2804C22semidirect
46. #2778C22semidirect
47. #2760C22semidirect
48. #2756C22semidirect
49. #2752C22semidirect
50. #2751C22semidirect
51. #2751C22semidirect
52. #2749C22semidirect
53. #2749C22semidirect
54. #2714C22semidirect
55. #2708C22semidirect
56. #2703C22semidirect
57. #2688C22semidirect
58. #2686C22semidirect
59. #2676C22semidirect
60. #2653C22semidirect
61. #2653C22semidirect
62. #2648C22semidirect
63. #2640C22semidirect
64. #2639C22semidirect
65. #2635C22semidirect
66. #2631C22semidirect
69. #2592C22semidirect
70. #2592C22semidirect
71. #2592C22semidirect
72. #2572C22semidirect
74. #2559C22semidirect
75. #2557C22semidirect
77. #2548C22semidirect
87. #2514C22semidirect
88. #2514C22semidirect
89. #2514C22semidirect
90. #2513C22semidirect
91. #2512C22semidirect
92. #2511C22semidirect
93. #2511C22semidirect
94. #2511C22semidirect
97. #2491C22semidirect
98. #2490C22semidirect
103. #2456C22semidirect
104. #2454C22semidirect
105. #2453C22semidirect
106. #2452C22semidirect
107. #2451C22semidirect
110. #2447C22semidirect
111. #2447C22semidirect
112. #2447C22semidirect
113. #2447C22semidirect
114. #2447C22semidirect
115. #2445C22semidirect
116. #2444C22semidirect
117. #2444C22semidirect
118. #2436C22semidirect
119. #2436C22semidirect
120. #2436C22semidirect
121. #2436C22semidirect
122. #2436C22semidirect
123. #2431C22semidirect
124. #2431C22semidirect
125. #2431C22semidirect
126. #2431C22semidirect
127. #2431C22semidirect
130. #2422C22semidirect
131. #2420C22semidirect
137. #2401C22semidirect
138. #2396C22semidirect
140. #2367C22semidirect
141. #2366C22semidirect
142. #2363C22semidirect
143. #2363C22semidirect
144. #2361C22semidirect
145. #2361C22semidirect
147. Q8×C22⋊C4C22semidirect
149. #2339C22semidirect
150. #2333C22semidirect
151. #2328C22semidirect
152. #2326C22semidirect
153. #2325C22semidirect
157. #2311C22semidirect
161. #2310C22semidirect
165. C4×#127C22semidirect
166. C4×#126C22semidirect
167. C4×#124C22semidirect
168. C4×C22⋊Q8C22semidirect
175. #2297C22semidirect
180. C2×#391C22semidirect

Maximal subgroups

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

subgroupindex
#429612
#428722
#425952
#425182
#406962
#401532
#400302
#397682
#392482
#385002
#356762
#356302
#356262
#355562
#355282
#353382
#352722
#351522
C2×#25442
#348162
#347452
#342752
#342652
#342592