Finite Group Databasebeta

← #7647564

Subgroups — #7647564

Order 512.

4994 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42522C214yesmaximal, complemented
2#42521C214yesmaximal, complemented
3#40538C218yesmaximal, complemented
4#40035C214yesmaximal, complemented
5#40029C214yesmaximal, complemented
6#38402C218yesmaximal, complemented
7#37508C214yesmaximal, complemented
8#37355C214yesmaximal, complemented
9#37339C214yesmaximal, complemented
10#35629C211yesmaximal, characteristic, complemented
11#35555C211yesmaximal, characteristic, complemented
12#35541C211yesmaximal, characteristic, complemented
13#35515C211yesmaximal, characteristic, complemented
14#35339C211yesmaximal, characteristic, complemented
15#35280C211yesmaximal, characteristic, complemented
16#35266C211yesmaximal, characteristic, complemented
17#35254C211yesmaximal, characteristic, complemented
18#35252C211yesmaximal, characteristic
19#35157C211yesmaximal, characteristic, complemented
20#35037C214yesmaximal, complemented
21C2×#2500C211yesmaximal, characteristic, complemented
22#34739C211yesmaximal, characteristic, complemented
23#34204C211yesmaximal, characteristic, complemented
24#34136C211yesmaximal, characteristic, complemented
25#34052C211yesmaximal, characteristic, complemented
26C2×#535C2211yescharacteristic
27C2×#533C2211yescharacteristic
28C2×#525C2211yescharacteristic
29C22×#121C2211yescharacteristic
30C2×#518C2211yescharacteristic
31C2×C4×#41C2211yescharacteristic
32C22×#117C2211yescharacteristic
33C22×#117C2211yescharacteristic
34C22×#117C2211yescharacteristic
35#2864C2214yescomplemented
36#2860C2214yescomplemented
37#2857C2214yescomplemented
38#2856C2212yes—
39#2854C2214yescomplemented
40#2853C2214yes—
41#2850C2212yes—
42#2827C2218yescomplemented
43#2826C2218yescomplemented
44#2795C2218yescomplemented
45#2790C2218yescomplemented
46#2786C2218yescomplemented
47#2781C2218yescomplemented
48#2781C2218yescomplemented
49#2775C2218yescomplemented
50#2765C2218yescomplemented
51#2757C2218yescomplemented
52#2746C2218yescomplemented
53#2728C2218yescomplemented
54#2721C2218yescomplemented
55#2711C2218yescomplemented
56#2708C2218yescomplemented
57#2691C2218yescomplemented
58#2681C2218yescomplemented
59#2680C2218yescomplemented
60#2654C2218yescomplemented
61#2653C2218yescomplemented
62#2651C2218yescomplemented
63#2647C2214yescomplemented
64#2644C2214yescomplemented
65#2633C2218yescomplemented
66#2630C2218yescomplemented
67#2630C2218yescomplemented
68#2629C2214yescomplemented
69#2624C2214yescomplemented
70#2622C2214yes—
71#2620C2212yes—
72#2619C2212yes—
73#2594C2218yescomplemented
74#2582C2214yescomplemented
75#2580C2214yescomplemented
76#2577C2218yescomplemented
77#2570C2214yescomplemented
78#2570C2214yescomplemented
79#2570C2214yescomplemented
80#2569C2218yes—
81#2560C2218yescomplemented
82#2558C2218yescomplemented
83#2552C2214yescomplemented
84#2538C2214yescomplemented
85#2538C2214yescomplemented
86#2514C2214yescomplemented
87#2513C2214yescomplemented
88#2513C2214yescomplemented
89#2512C2214yescomplemented
90#2510C2218yes—
91#2507C2214yescomplemented
92#2506C2214yescomplemented
93#2500C2214yes—
94#2500C2214yes—
95#2500C2212yes—
96#2500C2212yes—
97#2500C2212yes—
98#2500C2212yes—
99#2500C2212yescomplemented
100#2500C2212yescomplemented
101#2499C2212yescomplemented
102#2499C2212yescomplemented
103#2495C2214yescomplemented
104#2494C2214yescomplemented
105#2485C2214yescomplemented
106#2485C2214yescomplemented
107#2480C2218yes—
108#2473C2218yes—
109#2466C2218yescomplemented
110#2463C2218yescomplemented
111#2454C2214yescomplemented
112#2452C2214yescomplemented
113#2448C2214yescomplemented
114#2447C2214yescomplemented
115#2445C2214yescomplemented
116#2445C2214yescomplemented
117#2442C2212yescomplemented
118#2441C2212yescomplemented
119#2440C2212yescomplemented
120#2439C2212yescomplemented
121#2438C2214yes—
122#2437C2218yes—
123#2437C2214yes—
124#2422C2214yescomplemented
125#2420C2214yescomplemented
126#2418C2218yes—
127#2417C2218yes—
128#2416C2214yes—
129#2414C2214yes—
130#2412C2218yes—
131#2411C2214yes—
132#2410C2214yes—
133#2396C2214yescomplemented
134C2×#394C2214yes—
135#2363C2214yes—
136#2363C2212yescomplemented
137#2362C2212yescomplemented
138#2361C2214yes—
139#2361C2212yescomplemented
140#2360C2212yescomplemented
141#2359C2214yes—
142#2358C2214yes—
143#2342C2214yes—
144D4×C22⋊C4C2214yes—
145#2335C2218yescomplemented
146#2332C2218yescomplemented
147#2324C2214yes—
148#2317C2211yescharacteristic
149#2317C2211yescharacteristic
150#2317C2211yescharacteristic
151#2317C2214yescomplemented
152#2317C2214yescomplemented
153#2316C2211yescharacteristic
154#2316C2211yescharacteristic
155#2316C2211yescharacteristic
156#2316C2211yescharacteristic
157#2316C2211yescharacteristic
158#2315C2214yes—
159#2311C2211yescharacteristic
160#2311C2211yescharacteristic
161#2311C2211yescharacteristic
162#2309C2211yescharacteristic
163#2309C2211yescharacteristic
164C4×C22⋊Q8C2214yescomplemented
165C4×#121C2214yes—
166#2297C2211yescharacteristic
167#2296C2211yescharacteristic
168#2296C2211yescharacteristic
169#2296C2211yescharacteristic
170#2296C2214yescomplemented
171#2296C2214yescomplemented
172#2293C2212yescomplemented
173C2×#390C2211yescharacteristic
174C2×#390C2211yescharacteristic
175#2290C2212yescomplemented
176#2290C2212yescomplemented
177C2×#388C2214yes—
178#2285C2214yes—
179#2285C2211yescharacteristic
180C2×#384C2211yescharacteristic
181C2×#382C2211yescharacteristic
182#2280C2211yescharacteristic
183#2274C2211yescharacteristic
184C42×D4C2212yescomplemented
185C4×#117C2211yescharacteristic
186C2×C4×C22⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C23×D4C2311yescharacteristic
189C23×D4C2312yes—
190C24×C4C2311yescharacteristic
191#535—44no—
192#533—44no—
193C2×C4⋊Q8C2312yes—
194C2×#127C2312yes—
195C2×#126C2318yes—
196C2×#125C2312yes—
197C2×#125C2318yes—
198C2×#124C2312yes—
199#525—28no—
200C2×#123C2312yes—
201C2×#123C2318yes—
202C2×#123C2318yes—
203C2×C22⋊Q8C2311yescharacteristic
204C2×C22⋊Q8C2311yescharacteristic
205C2×C22⋊Q8C2318yes—
206C2×C22⋊Q8C2314yes—
207C2×C22⋊Q8C2314yes—
208C2×C22⋊Q8C2318yes—
209C2×#121—28no—
210C2×#121C2312yes—
211C2×#121C2312yes—
212C2×#121C2311yescharacteristic
213C2×#121C2312yes—
214C2×#121C2311yescharacteristic
215C2×#121C2312yes—
216C2×#121C2314yes—
217C2×#121C2318yes—
218C2×#120C2312yes—
219C2×#120C2314yes—
220#518—44no—
221C4×#41—44no—
222C2×C4×Q8C2314yes—
223C2×C4×Q8C2312yes—
224C2×C4×D4C2312yes—
225C2×C4×D4C2312yes—
226C2×C4×D4C2314yes—
227C2×C4×D4C2314yes—
228C2×C4×D4C2314yes—
229C2×C4×D4C2314yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2318yes—
232C2×#117—28no—
233C2×#117—44no—
234C2×#117—44no—
235C2×#117C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2312yes—
243C2×#117C2312yes—
244C2×#117C2312yes—
245C2×#117C2312yes—
246C2×#117C2312yes—
247C2×#117C2312yes—
248C2×#117C2312yes—
249C2×#117C2312yes—
250C2×#117C2312yes—
251C2×#117C2312yes—
252C2×#117C2312yes—
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2312yes—
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2314yes—
259C22×C22⋊C4C2312yes—
260C22×C22⋊C4C2312yes—
261C22×C22⋊C4C2312yes—
262C22×C22⋊C4C2312yes—
263C22×C22⋊C4C2314yes—
264C22×C22⋊C4C2312yes—
265C22×C22⋊C4C2314yes—
266C22×C22⋊C4C2314yes—
267C22×C42C2312yes—
268C22×C42C2311yescharacteristic
269C22×C42C2311yescharacteristic
270C22×C42C2312yes—
271C22×C42C2312yes—
272C22×C42C2312yes—
273#401C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2314yes—
279#399C2314yes—
280#399C2318yes—
281#399C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2314yes—
290#398C2314yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#396C2318yes—
302#396C2318yes—
303#396C2314yes—
304#396C2318yes—
305#396C2318yes—
306#396C2318yes—
307#396C2318yes—
308#396C2314yes—
309#395C2314yes—
310#394C2318yes—
311#394C2318yes—
312#394C2318yes—
313#394C2318yes—
314#394C2318yes—
315#394C2318yes—
316#394C2318yes—
317#394C2318yes—
318#394C2318yes—
319#394C2318yes—
320#394C2318yes—
321#394C2318yes—
322#393C2318yes—
323#393C2314yes—
324#392C2318yes—
325#391C2314yes—
326#391C2312yes—
327#391C2312yes—
328#391C2312yes—
329#391C2318yes—
330#391C2312yes—
331#390C2318yes—
332#390C2314yes—
333#390C2312yes—
334#390C2312yes—
335#390C2314yes—
336#390C2314yes—
337#390C2312yes—
338#390C2312yes—
339#390C2312yes—
340#390C2318yes—
341#390C2314yes—
342#390C2312yes—
343#390C2312yes—
344#390C2314yes—
345#390C2312yes—
346#390C2312yes—
347#390C2312yes—
348#390C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2312yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2312yes—
364#389C2318yes—
365#389C2318yes—
366#389C2312yes—
367#389C2312yes—
368#389C2314yes—
369#389C2312yes—
370#389C2312yes—
371#389C2314yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2314yes—
386#388C2314yes—
387#388C2314yes—
388#388C2314yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2314yes—
399#387C2314yes—
400#387C2318yes—
401#387C2318yes—
402#387C2314yes—
403#387C2318yes—
404#387C2314yes—
405#386C2318yes—
406#386C2314yes—
407#386C2314yes—
408#386C2314yes—
409#386C2314yes—
410#386C2318yes—
411#386C2318yes—
412#386C2318yes—
413#386C2318yes—
414#386C2314yes—
415#386C2314yes—
416#385C2314yes—
417#385C2314yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2318yes—
422#385C2314yes—
423#385C2314yes—
424#385C2318yes—
425#385C2318yes—
426#385C2318yes—
427#385C2318yes—
428#385C2314yes—
429#385C2314yes—
430#385C2314yes—
431#385C2314yes—
432#385C2314yes—
433#385C2314yes—
434#384C2312yes—
435#384C2312yes—
436#384C2314yes—
437#384C2312yes—
438#384C2318yes—
439#384C2312yes—
440#384C2312yes—
441#384C2312yes—
442#383C2318yes—
443#382C2312yes—
444#382C2312yes—
445#382C2312yes—
446#382C2314yes—
447#382C2318yes—
448#382C2312yes—
449#382C2312yes—
450#382C2312yes—
451#381C2318yes—
452#381C2312yes—
453#380C2314yes—
454#380C2314yes—
455#380C2314yes—
456#380C2314yes—
457#380C2314yes—
458#380C2314yes—
459#380C2314yes—
460#380C2314yes—
461#380C2314yes—
462#380C2318yes—
463#380C2312yes—
464#380C2318yes—
465#380C2314yes—
466#380C2312yes—
467#379C2314yes—
468#379C2314yes—
469#379C2312yes—
470C4×C4⋊C4C2318yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2318yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C22⋊C4C2314yes—
483C4×C22⋊C4C2314yes—
484C4×C22⋊C4C2318yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2312yes—
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C2312yes—
490C4×C22⋊C4C2312yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2312yes—
493C4×C22⋊C4C2311yescharacteristic
494C4×C22⋊C4C2311yescharacteristic
495C4×C22⋊C4C2311yescharacteristic
496C4×C22⋊C4C2311yescharacteristic
497#376C2312yes—
498C2×#95C2314yes—
499C2×#95C2312yes—
500C43C2312yes—
501C25C2412yes—
502C25C2411yescharacteristic
503C2×#41—24no—
504C2×#41—24no—
505C2×#41—24no—
506C22×Q8C2411yescharacteristic
507C22×Q8C2414yes—
508C22×D4—28no—
509C22×D4—24no—
510C22×D4—24no—
511C22×D4—24no—
512C22×D4—84no—
513C22×D4C2412yes—
514C22×D4C2412yes—
515C22×D4C2412yes—
516C22×D4C2411yescharacteristic
517C22×D4C2412yes—
518C22×D4C2414yes—
519C22×D4C2412yes—
520C22×D4C2414yes—
521C22×D4C2418yes—
522C23×C4—24no—
523C23×C4—24no—
524C23×C4#4118yes—
525C23×C4C2412yes—
526C23×C4C2412yes—
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C23×C4C2412yes—
533C23×C4C2412yes—
534C23×C4C2412yes—
535C23×C4C2412yes—
536C23×C4C2414yes—
537C23×C4C2414yes—
538C23×C4C2414yes—
539C23×C4C2418yes—
540C23×C4C2411yescharacteristic
541C4⋊Q8—44no—
542#127—44no—
543#126—88no—
544#125—44no—
545#125—88no—
546#124—44no—
547#123—28no—
548#123—416no—
549#123—88no—
550C22⋊Q8—24no—
551C22⋊Q8—24no—
552C22⋊Q8—48no—
553C22⋊Q8—48no—
554C22⋊Q8—416no—
555C22⋊Q8—88no—
556#121—28no—
557#121—28no—
558#121—28no—
559#121—28no—
560#121—24no—
561#121—24no—
562#121—48no—
563#121—88no—
564#120—28no—
565#120—48no—
566C4×Q8—48no—
567C4×Q8—44no—
568C4×D4—28no—
569C4×D4—28no—
570C4×D4—44no—
571C4×D4—48no—
572C4×D4—48no—
573C4×D4—48no—
574C4×D4—48no—
575C4×D4—88no—
576#117—28no—
577#117—28no—
578#117—28no—
579#117—28no—
580#117—24no—
581#117—24no—
582#117—24no—
583#117—24no—
584#117—24no—
585#117—24no—
586#117—24no—
587#117—44no—
588#117—44no—
589#117—44no—
590#117—44no—
591#117—44no—
592#117—44no—
593#117—44no—
594C2×C4⋊C4—24no—
595C2×C4⋊C4—24no—
596C2×C4⋊C4—24no—
597C2×C4⋊C4—44no—
598C2×C4⋊C4—44no—
599C2×C4⋊C4—84no—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2414yes—
640C2×C22⋊C4—28no—
641C2×C22⋊C4—28no—
642C2×C22⋊C4—44no—
643C2×C22⋊C4—48no—
644C2×C22⋊C4—44no—
645C2×C22⋊C4—44no—
646C2×C22⋊C4—48no—
647C2×C22⋊C4—84no—
648C2×C22⋊C4C2412yes—
649C2×C22⋊C4C2412yes—
650C2×C22⋊C4C2412yes—
651C2×C22⋊C4C2412yes—
652C2×C22⋊C4C2412yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2418yes—
660C2×C22⋊C4C2412yes—
661C2×C22⋊C4C2412yes—
662C2×C22⋊C4C2412yes—
663C2×C22⋊C4C2412yes—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2418yes—
687C2×C42—28no—
688C2×C42—24no—
689C2×C42—24no—
690C2×C42—44no—
691C2×C42—44no—
692C2×C42—44no—
693C2×C42C2412yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2411yescharacteristic
698C2×C42C2414yes—
699C2×C42C2414yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2412yes—
708C2×C42C2414yes—
709C2×C42C2414yes—
710C2×C42C2414yes—
711C2×C42C2418yes—
712C2×C42C2414yes—
713C2×C42C2414yes—
714#95C2412yes—
715#95C2412yes—
716#95C2412yes—
717#95C2412yes—
718#95C2418yes—
719#95C2418yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2418yes—
726#95C2418yes—
727#95C2414yes—
728#95C2414yes—
729#95C2418yes—
730#95C2418yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2418yes—
735#95C2418yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2418yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746C24—22no—
747C24—22no—
748C24—24no—
749C24—24no—
750C24—24no—
751C24—42no—
752C24—42no—
753C24—44no—
754C24—44no—
755C24C2×#4114yes—
756C24C2514yes—
757C24C2512yes—
758C24C2511yescharacteristic
759C24C2511yescharacteristic
760C24C2511yescharacteristic
761#41—416no—
762C2×Q8—22no—
763C2×Q8—22no—
764C2×Q8—22no—
765C2×Q8—28no—
766C2×Q8—44no—
767C2×Q8—44no—
768C2×D4—24no—
769C2×D4—24no—
770C2×D4—28no—
771C2×D4—24no—
772C2×D4—24no—
773C2×D4—24no—
774C2×D4—28no—
775C2×D4—24no—
776C2×D4—24no—
777C2×D4—22no—
778C2×D4—24no—
779C2×D4—24no—
780C2×D4—22no—
781C2×D4—24no—
782C2×D4—24no—
783C2×D4—22no—
784C2×D4—44no—
785C2×D4—48no—
786C2×D4—44no—
787C2×D4—48no—
788C2×D4—48no—
789C2×D4—48no—
790C2×D4—48no—
791C2×D4—416no—
792C2×D4—816no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—232no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—28no—
814C22×C4—42no—
815C22×C4—44no—
816C22×C4—44no—
817C22×C4—44no—
818C22×C4—42no—
819C22×C4—44no—
820C22×C4—42no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—48no—
829C22×C4—48no—
830C22×C4—48no—
831C22×C4C2×#4114yes—
832C22×C4C2×#4114yes—
833C22×C4C2×#4114yes—
834C22×C4C2×#4114yes—
835C22×C4C2×#4114yes—
836C22×C4C2×#4114yes—
837C22×C4H(5,𝔽2)14yes—
838C22×C42−1+414yes—
839C22×C4C2512yes—
840C22×C4C2512yes—
841C22×C4C2512yes—
842C22×C4C2514yes—
843C22×C4C2512yes—
844C22×C4C2514yes—
845C22×C4C2514yes—
846C22×C4C2514yes—
847C22×C4C2514yes—
848C22×C4C2514yes—
849C22×C4C2514yes—
850C22×C4C2512yes—
851C22×C4C2514yes—
852C22×C4C2514yes—
853C22×C4C2512yes—
854C22×C4C2511yescharacteristic
855C22×C4C2511yescharacteristic
856C22×C4C2512yes—
857C22×C4C2511yescharacteristic
858C22×C4C2511yescharacteristic
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—24no—
865C4⋊C4—22no—
866C4⋊C4—22no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—48no—
880C4⋊C4—48no—
881C4⋊C4—44no—
882C4⋊C4—48no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—48no—
887C4⋊C4—48no—
888C4⋊C4—48no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—48no—
892C4⋊C4—48no—
893C4⋊C4—44no—
894C4⋊C4—48no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—48no—
898C4⋊C4—44no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—24no—
902C22⋊C4—24no—
903C22⋊C4—24no—
904C22⋊C4—24no—
905C22⋊C4—24no—
906C22⋊C4—24no—
907C22⋊C4—24no—
908C22⋊C4—24no—
909C22⋊C4—24no—
910C22⋊C4—28no—
911C22⋊C4—28no—
912C22⋊C4—24no—
913C22⋊C4—24no—
914C22⋊C4—24no—
915C22⋊C4—24no—
916C22⋊C4—216no—
917C22⋊C4—42no—
918C22⋊C4—48no—
919C22⋊C4—42no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—48no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4—48no—
931C22⋊C4—48no—
932C22⋊C4—48no—
933C22⋊C4—44no—
934C22⋊C4—48no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—44no—
938C42—28no—
939C42—28no—
940C42—24no—
941C42—22no—
942C42—22no—
943C42—24no—
944C42—24no—
945C42—24no—
946C42—24no—
947C42—24no—
948C42—24no—
949C42—24no—
950C42—22no—
951C42—22no—
952C42—24no—
953C42—44no—
954C42—44no—
955C42—44no—
956C42—44no—
957C42—48no—
958C42—44no—
959C23—22no—
960C23—22no—
961C23—21no—
962C23—21no—
963C23—21no—
964C23—21no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—28no—
970C23—22no—
971C23—24no—
972C23—24no—
973C23—22no—
974C23—22no—
975C23—24no—
976C23—28no—
977C23—24no—
978C23—24no—
979C23—28no—
980C23—44no—
981C23—44no—
982C23—48no—
983C23—84no—
984C23—84no—
985C23—84no—
986C23—84no—
987C23—88no—
988C23—88no—
989C23C22×#4112yes—
990C23C22×#4112yes—
991C23C22×#4112yes—
992C23C2×H(5,𝔽2)12yes—
993C23C2×2−1+412yes—
994C23C2611yescharacteristic
995Q8—44no—
996Q8—88no—
997D4—48no—
998D4—416no—
999D4—48no—
1000D4—48no—
1001D4—48no—
1002D4—44no—
1003D4—84no—
1004D4—88no—
1005D4—168no—
1006C2×C4—22no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—22no—
1012C2×C4—28no—
1013C2×C4—28no—
1014C2×C4—28no—
1015C2×C4—28no—
1016C2×C4—28no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—24no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—28no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—22no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—28no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—28no—
1054C2×C4—24no—
1055C2×C4—22no—
1056C2×C4—24no—
1057C2×C4—48no—
1058C2×C4—48no—
1059C2×C4—88no—
1060C2×C4—84no—
1061C2×C4—84no—
1062C2×C4—84no—
1063C2×C4—84no—
1064C2×C4—88no—
1065C2×C4—88no—
1066C2×C4—168no—
1067C2×C4#539116yes—
1068C2×C4C22×#4112yes—
1069C2×C4C22×#4112yes—
1070C2×C4C22×#4112yes—
1071C2×C4C22×#4112yes—
1072C2×C4C2×H(5,𝔽2)12yes—
1073C2×C4C2×H(5,𝔽2)12yes—
1074C2×C4C2×2−1+412yes—
1075C2×C4C2×2−1+412yes—
1076C2×C4#58514yes—
1077C22—22no—
1078C22—22no—
1079C22—24no—
1080C22—24no—
1081C22—22no—
1082C22—22no—
1083C22—22no—
1084C22—22no—
1085C22—22no—
1086C22—22no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—44no—
1093C22—44no—
1094C22—42no—
1095C22—42no—
1096C22—44no—
1097C22—44no—
1098C22—48no—
1099C22—44no—
1100C22—48no—
1101C22—88no—
1102C22—168no—
1103C22C2×#53914yes—
1104C22C23×#4111yescharacteristic
1105C22C22×H(5,𝔽2)11yescharacteristic
1106C22C22×2−1+411yescharacteristic
1107C22C2×#58512yes—
1108C22H(7,𝔽2)12yes—
1109C4—22no—
1110C4—22no—
1111C4—24no—
1112C4—44no—
1113C4—42no—
1114C4—44no—
1115C4—44no—
1116C4—42no—
1117C4—42no—
1118C4—44no—
1119C4—42no—
1120C4—42no—
1121C4—42no—
1122C4—44no—
1123C4—44no—
1124C4—44no—
1125C4—44no—
1126C4—44no—
1127C4C2×#53914yes—
1128C4C2×#53914yes—
1129C2—24no—
1130C2—42no—
1131C2—42no—
1132C2—82no—
1133C2—84no—
1134C2C22×#53911yescharacteristic
1135C2#6281511yescharacteristic
1136C2#6285511yescharacteristic
1137C2#6292912yes—
1138C2#6295712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35252C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #42522C2semidirect
2. #42521C2semidirect
3. #40538C2semidirect
4. #40035C2semidirect
5. #40029C2semidirect
6. #38402C2semidirect
7. #37508C2semidirect
8. #37355C2semidirect
9. #37339C2semidirect
10. #35629C2semidirect
11. #35555C2semidirect
12. #35541C2semidirect
13. #35515C2semidirect
14. #35339C2semidirect
15. #35280C2semidirect
16. #35266C2semidirect
17. #35254C2semidirect
19. #35157C2semidirect
20. #35037C2semidirect
21. C2×#2500C2semidirect
22. #34739C2semidirect
23. #34204C2semidirect
24. #34136C2semidirect
25. #34052C2semidirect
35. #2864C22semidirect
36. #2860C22semidirect
37. #2857C22semidirect
39. #2854C22semidirect
42. #2827C22semidirect
43. #2826C22semidirect
44. #2795C22semidirect
45. #2790C22semidirect
46. #2786C22semidirect
47. #2781C22semidirect
48. #2781C22semidirect
49. #2775C22semidirect
50. #2765C22semidirect
51. #2757C22semidirect
52. #2746C22semidirect
53. #2728C22semidirect
54. #2721C22semidirect
55. #2711C22semidirect
56. #2708C22semidirect
57. #2691C22semidirect
58. #2681C22semidirect
59. #2680C22semidirect
60. #2654C22semidirect
61. #2653C22semidirect
62. #2651C22semidirect
63. #2647C22semidirect
64. #2644C22semidirect
65. #2633C22semidirect
66. #2630C22semidirect
67. #2630C22semidirect
68. #2629C22semidirect
69. #2624C22semidirect
73. #2594C22semidirect
74. #2582C22semidirect
75. #2580C22semidirect
76. #2577C22semidirect
77. #2570C22semidirect
78. #2570C22semidirect
79. #2570C22semidirect
81. #2560C22semidirect
82. #2558C22semidirect
83. #2552C22semidirect
84. #2538C22semidirect
85. #2538C22semidirect
86. #2514C22semidirect
87. #2513C22semidirect
88. #2513C22semidirect
89. #2512C22semidirect
91. #2507C22semidirect
92. #2506C22semidirect
99. #2500C22semidirect
100. #2500C22semidirect
101. #2499C22semidirect
102. #2499C22semidirect
103. #2495C22semidirect
104. #2494C22semidirect
105. #2485C22semidirect
106. #2485C22semidirect
109. #2466C22semidirect
110. #2463C22semidirect
111. #2454C22semidirect
112. #2452C22semidirect
113. #2448C22semidirect
114. #2447C22semidirect
115. #2445C22semidirect
116. #2445C22semidirect
117. #2442C22semidirect
118. #2441C22semidirect
119. #2440C22semidirect
120. #2439C22semidirect
124. #2422C22semidirect
125. #2420C22semidirect
133. #2396C22semidirect
136. #2363C22semidirect
137. #2362C22semidirect
139. #2361C22semidirect
140. #2360C22semidirect
145. #2335C22semidirect
146. #2332C22semidirect
151. #2317C22semidirect
152. #2317C22semidirect
164. C4×C22⋊Q8C22semidirect
170. #2296C22semidirect
171. #2296C22semidirect
172. #2293C22semidirect
175. #2290C22semidirect
176. #2290C22semidirect
184. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#425222
#425212
#405382
#400352
#400292
#384022
#375082
#373552
#373392
#356292
#355552
#355412
#355152
#353392
#352802
#352662
#352542
#352522
#351572
#350372
C2×#25002
#347392
#342042
#341362
#340522