Finite Group Databasebeta

← #7746771

Subgroups — #7746771

Order 512.

4790 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45431C212yesmaximal, complemented
2#45252C214yesmaximal, complemented
3#45250C214yesmaximal, complemented
4#45222C214yesmaximal, complemented
5#45138C212yesmaximal, complemented
6#44902C214yesmaximal, complemented
7#44898C214yesmaximal, complemented
8#42936C214yesmaximal, complemented
9#42470C214yesmaximal, complemented
10#42466C214yesmaximal, complemented
11#36210C212yesmaximal, complemented
12#36209C211yesmaximal, characteristic, complemented
13#36209C211yesmaximal, characteristic, complemented
14#36189C212yesmaximal, complemented
15#36188C211yesmaximal, characteristic, complemented
16#36180C211yesmaximal, characteristic, complemented
17#36030C212yesmaximal, complemented
18#35815C214yesmaximal, complemented
19#35770C214yesmaximal, complemented
20#35738C212yesmaximal, complemented
21#35294C211yesmaximal, characteristic, complemented
22#35279C212yesmaximal, complemented
23#34547C211yesmaximal, characteristic
24#34209C211yesmaximal, characteristic, complemented
25#34188C212yesmaximal, complemented
26C2×#556C2212yes—
27C2×#554C2212yes—
28C22×C4⋊Q8C2211yescharacteristic
29C2×#519C2212yes—
30C2×C4×#41C2212yes—
31#2868C2211yescharacteristic
32#2859C2212yes—
33#2859C2211yescharacteristic
34#2857C2212yes—
35#2857C2212yes—
36#2857C2212yes—
37#2857C2212yes—
38#2831C2218yes—
39#2796C2218yes—
40#2794C2218yes—
41#2773C2218yes—
42#2765C2218yes—
43#2762C2218yes—
44#2761C2218yes—
45#2758C2218yes—
46#2754C2218yes—
47#2750C2218yes—
48#2749C2218yes—
49#2730C2218yes—
50#2721C2218yes—
51#2666C2218yes—
52#2653C2218yes—
53#2634C2214yes—
54#2632C2214yes—
55#2629C2212yes—
56#2628C2212yes—
57#2628C2214yes—
58#2628C2214yes—
59#2611C2214yes—
60#2610C2214yes—
61#2605C2218yes—
62#2599C2214yes—
63#2598C2214yes—
64#2595C2218yes—
65#2589C2218yes—
66#2574C2218yes—
67#2570C2214yes—
68#2570C2218yes—
69#2570C2214yes—
70#2568C2212yes—
71#2568C2214yes—
72#2567C2212yes—
73#2567C2214yes—
74#2563C2214yes—
75#2562C2214yes—
76#2552C2214yes—
77#2550C2214yes—
78#2547C2214yes—
79#2542C2214yes—
80#2536C2212yes—
81#2536C2212yes—
82#2528C2218yes—
83#2517C2218yes—
84#2514C2214yes—
85#2511C2214yes—
86#2509C2214yes—
87#2508C2214yes—
88#2508C2214yes—
89#2507C2214yes—
90#2502C2214yes—
91#2499C2214yes—
92#2497C2214yes—
93#2496C2214yes—
94#2496C2214yes—
95#2495C2214yes—
96#2495C2214yes—
97#2495C2214yes—
98#2494C2214yes—
99#2494C2214yes—
100#2489C2214yes—
101#2489C2214yes—
102#2487C2214yes—
103#2487C2214yes—
104#2487C2214yes—
105#2485C2214yes—
106#2485C2214yes—
107#2485C2214yes—
108#2479C2218yes—
109#2477C2218yes—
110#2469C2218yes—
111#2467C2218yes—
112#2465C2218yes—
113#2442C2214yes—
114#2441C2214yes—
115#2441C2214yes—
116#2440C2214yes—
117#2440C2214yes—
118#2439C2214yes—
119#2423C2218yes—
120#2423C2214yes—
121#2421C2214yes—
122#2417C2214yes—
123#2415C2214yes—
124#2409C2214yes—
125#2409C2214yes—
126#2399C2211yescharacteristic
127#2399C2214yes—
128#2398C2214yes—
129#2398C2212yes—
130#2397C2211yescharacteristic
131#2396C2212yes—
132#2396C2212yes—
133#2395C2212yes—
134#2395C2212yes—
135#2392C2211yescharacteristic
136#2392C2212yes—
137#2392C2212yes—
138#2392C2211yescharacteristic
139#2392C2212yes—
140#2388C2212yes—
141#2388C2212yes—
142#2370C2214yes—
143#2365C2214yes—
144#2365C2214yes—
145#2365C2214yes—
146#2362C2214yes—
147#2360C2214yes—
148#2356C2212yes—
149#2356C2212yes—
150#2355C2214yes—
151#2355C2214yes—
152#2354C2214yes—
153#2354C2214yes—
154#2352C2214yes—
155#2352C2214yes—
156#2352C2214yes—
157#2352C2214yes—
158#2352C2214yes—
159D4×C4⋊C4C2214yes—
160#2347C2214yes—
161#2346C2214yes—
162#2346C2214yes—
163#2345C2214yes—
164#2344C2214yes—
165#2344C2214yes—
166#2331C2212yes—
167#2330C2212yes—
168#2327C2212yes—
169#2327C2212yes—
170#2317C2214yes—
171#2314C2214yes—
172#2314C2214yes—
173#2311C2214yes—
174#2311C2214yes—
175#2310C2212yes—
176C4×C4⋊Q8C2211yescharacteristic
177C4×C4⋊Q8C2211yescharacteristic
178C4×C4⋊Q8C2211yescharacteristic
179C4×C4⋊Q8C2211yescharacteristic
180#2285C2212yes—
181#2285C2212yes—
182#2285C2212yes—
183#2285C2211yescharacteristic
184#2285C2212yes—
185C2×#384C2212yes—
186#2274C2214yes—
187C42×D4C2211yescharacteristic
188C42×D4C2211yescharacteristic
189C42×D4C2212yes—
190C4×#117C2211yescharacteristic
191C22×#41C2312yes—
192C23×Q8C2312yes—
193#556—48no—
194#554—48no—
195C2×C4⋊Q8—28no—
196C2×C4⋊Q8C2311yescharacteristic
197C2×C4⋊Q8C2311yescharacteristic
198C2×C4⋊Q8C2314yes—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2314yes—
202C2×#126C2318yes—
203C2×#125C2314yes—
204C2×#125C2312yes—
205C2×#125C2314yes—
206C2×#124C2314yes—
207C2×C22⋊Q8C2314yes—
208C2×C22⋊Q8C2314yes—
209C2×C22⋊Q8C2314yes—
210C2×C22⋊Q8C2314yes—
211C2×C22⋊Q8C2318yes—
212#519—48no—
213C4×#41—216no—
214C2×C4×Q8C2312yes—
215C2×C4×Q8C2312yes—
216C2×C4×Q8C2312yes—
217C2×C4×Q8C2312yes—
218C2×C4×Q8C2312yes—
219C2×C4×Q8C2312yes—
220C2×C4×Q8C2314yes—
221C2×C4×Q8C2314yes—
222C2×C4×Q8C2314yes—
223C2×C4×D4C2312yes—
224C2×C4×D4C2312yes—
225C2×C4×D4C2312yes—
226C2×C4×D4C2312yes—
227C2×C4×D4C2312yes—
228C2×C4×D4C2312yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2312yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2312yes—
237C2×#117C2314yes—
238C2×#117C2312yes—
239C2×#117C2312yes—
240C2×#117C2311yescharacteristic
241C2×#117C2312yes—
242C2×#117C2311yescharacteristic
243C2×#117C2312yes—
244C2×#117C2314yes—
245C2×#117C2314yes—
246C2×#117C2314yes—
247C2×#117C2314yes—
248C2×#117C2314yes—
249C22×C4⋊C4C2314yes—
250C22×C4⋊C4C2314yes—
251C22×C4⋊C4C2314yes—
252C22×C4⋊C4C2314yes—
253C22×C42C2312yes—
254C22×C42C2312yes—
255C22×C42C2311yescharacteristic
256#401C2318yes—
257#400C2318yes—
258#400C2318yes—
259#400C2314yes—
260#400C2314yes—
261#400C2318yes—
262#400C2312yes—
263#400C2314yes—
264#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2312yes—
270#399C2318yes—
271#399C2314yes—
272#399C2318yes—
273#399C2318yes—
274#399C2312yes—
275#399C2312yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2314yes—
282#398C2314yes—
283#398C2311yescharacteristic
284#398C2312yes—
285#398C2312yes—
286#398C2311yescharacteristic
287#398C2312yes—
288#397C2318yes—
289#397C2318yes—
290#397C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2311yescharacteristic
294#397C2311yescharacteristic
295#397C2312yes—
296#397C2312yes—
297#397C2312yes—
298#397C2318yes—
299#396C2312yes—
300#396C2312yes—
301#396C2318yes—
302#396C2318yes—
303#396C2312yes—
304#396C2312yes—
305#395C2318yes—
306#395C2318yes—
307#395C2314yes—
308#395C2314yes—
309#395C2312yes—
310#395C2314yes—
311#395C2312yes—
312#394C2318yes—
313#394C2312yes—
314#394C2314yes—
315#394C2314yes—
316#394C2311yescharacteristic
317#394C2312yes—
318#394C2312yes—
319#394C2312yes—
320#394C2312yes—
321#394C2312yes—
322#394C2312yes—
323#394C2311yescharacteristic
324#393C2318yes—
325#393C2318yes—
326#393C2312yes—
327#393C2314yes—
328#393C2312yes—
329#392C2311yescharacteristic
330#392C2311yescharacteristic
331#392C2312yes—
332#392C2312yes—
333#392C2312yes—
334#391C2312yes—
335#391C2312yes—
336#391C2312yes—
337#391C2312yes—
338#391C2318yes—
339#391C2318yes—
340#391C2318yes—
341#391C2314yes—
342#391C2314yes—
343#391C2314yes—
344#391C2314yes—
345#391C2318yes—
346#391C2318yes—
347#390C2318yes—
348#390C2318yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2318yes—
358#389C2314yes—
359#389C2318yes—
360#389C2314yes—
361#389C2314yes—
362#389C2318yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2318yes—
371#388C2318yes—
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#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#386C2318yes—
406#386C2318yes—
407#386C2318yes—
408#386C2318yes—
409#386C2318yes—
410#385C2318yes—
411#385C2318yes—
412#385C2318yes—
413#385C2318yes—
414#385C2318yes—
415#384C2311yescharacteristic
416#384C2311yescharacteristic
417#384C2318yes—
418#384C2314yes—
419#384C2314yes—
420#384C2314yes—
421#384C2312yes—
422#384C2312yes—
423#384C2312yes—
424#384C2314yes—
425#383C2314yes—
426#383C2314yes—
427#383C2318yes—
428#382C2318yes—
429#382C2314yes—
430#382C2314yes—
431#382C2314yes—
432#382C2318yes—
433#382C2318yes—
434#382C2314yes—
435#382C2314yes—
436#382C2312yes—
437#382C2312yes—
438#381C2318yes—
439#380C2314yes—
440#380C2314yes—
441#380C2314yes—
442#380C2314yes—
443#380C2314yes—
444#380C2314yes—
445#380C2314yes—
446#380C2314yes—
447#380C2314yes—
448#380C2314yes—
449#380C2314yes—
450#380C2314yes—
451#380C2314yes—
452#380C2318yes—
453#380C2314yes—
454#380C2314yes—
455#380C2314yes—
456#380C2314yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2318yes—
471C4×C4⋊C4C2318yes—
472C4×C4⋊C4C2318yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C22⋊C4C2318yes—
483C4×C22⋊C4C2318yes—
484C4×C22⋊C4C2318yes—
485C4×C22⋊C4C2312yes—
486C4×C22⋊C4C2312yes—
487C4×C22⋊C4C2312yes—
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C2312yes—
490C4×C22⋊C4C2312yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2312yes—
493C4×C22⋊C4C2312yes—
494C4×C22⋊C4C2312yes—
495C4×C22⋊C4C2312yes—
496C4×C22⋊C4C2312yes—
497C4×C22⋊C4C2312yes—
498C4×C22⋊C4C2312yes—
499#376C2311yescharacteristic
500#376C2311yescharacteristic
501#376C2314yes—
502#376C2314yes—
503C43C2311yescharacteristic
504C43C2311yescharacteristic
505C2×#41—28no—
506C2×#41—28no—
507C2×#41—44no—
508C22×Q8—28no—
509C22×Q8—44no—
510C22×Q8—44no—
511C22×Q8C2412yes—
512C22×Q8C2412yes—
513C22×Q8C2412yes—
514C22×Q8C2414yes—
515C22×Q8C2414yes—
516C22×D4C2411yescharacteristic
517C22×D4C2412yes—
518C22×D4C2412yes—
519C22×D4C2412yes—
520C22×D4C2411yescharacteristic
521C22×D4C2412yes—
522C23×C4C2412yes—
523C23×C4C2412yes—
524C23×C4C2412yes—
525C23×C4C2412yes—
526C23×C4C2412yes—
527C23×C4C2412yes—
528C23×C4C2411yescharacteristic
529C23×C4C2412yes—
530C23×C4C2414yes—
531C23×C4C2418yes—
532C4⋊Q8—24no—
533C4⋊Q8—24no—
534C4⋊Q8—216no—
535C4⋊Q8—28no—
536C4⋊Q8—28no—
537C4⋊Q8—48no—
538#126—416no—
539#125—44no—
540#125—48no—
541#125—48no—
542#124—48no—
543C22⋊Q8—416no—
544C22⋊Q8—48no—
545C22⋊Q8—48no—
546C22⋊Q8—48no—
547C22⋊Q8—48no—
548C4×Q8—28no—
549C4×Q8—28no—
550C4×Q8—28no—
551C4×Q8—28no—
552C4×Q8—48no—
553C4×Q8—48no—
554C4×Q8—44no—
555C4×Q8—44no—
556C4×Q8—48no—
557C4×D4—28no—
558C4×D4—28no—
559C4×D4—28no—
560C4×D4—28no—
561C4×D4—28no—
562C4×D4—28no—
563C4×D4—28no—
564C4×D4—28no—
565C4×D4—24no—
566C4×D4—24no—
567C4×D4—48no—
568C4×D4—44no—
569C4×D4—44no—
570C4×D4—44no—
571#117—28no—
572#117—216no—
573#117—28no—
574#117—28no—
575#117—24no—
576#117—42no—
577#117—48no—
578#117—48no—
579#117—48no—
580#117—48no—
581#117—44no—
582#117—48no—
583C2×C4⋊C4—216no—
584C2×C4⋊C4—48no—
585C2×C4⋊C4—48no—
586C2×C4⋊C4—48no—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C22⋊C4C2411yescharacteristic
633C2×C22⋊C4C2411yescharacteristic
634C2×C22⋊C4C2412yes—
635C2×C22⋊C4C2412yes—
636C2×C22⋊C4C2412yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2412yes—
639C2×C22⋊C4C2412yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2412yes—
642C2×C22⋊C4C2412yes—
643C2×C22⋊C4C2412yes—
644C2×C22⋊C4C2412yes—
645C2×C22⋊C4C2412yes—
646C2×C22⋊C4C2412yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2412yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2412yes—
654C2×C22⋊C4C2412yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2418yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2418yes—
662C2×C42—28no—
663C2×C42—28no—
664C2×C42#4118yes—
665C2×C42C2412yes—
666C2×C42C2412yes—
667C2×C42C2411yescharacteristic
668C2×C42C2414yes—
669C2×C42C2411yescharacteristic
670C2×C42C2414yes—
671C2×C42C2411yescharacteristic
672C2×C42C2418yes—
673C2×C42C2412yes—
674C2×C42C2412yes—
675C2×C42C2412yes—
676C2×C42C2412yes—
677C2×C42C2412yes—
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2414yes—
682C2×C42C2414yes—
683C2×C42C2414yes—
684C2×C42C2418yes—
685C2×C42C2418yes—
686C2×C42C2418yes—
687C2×C42C2412yes—
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691#95C2411yescharacteristic
692#95C2411yescharacteristic
693#95C2412yes—
694#95C2412yes—
695#95C2412yes—
696#95C2412yes—
697#95C2418yes—
698#95C2418yes—
699#95C2414yes—
700#95C2414yes—
701#95C2412yes—
702#95C2412yes—
703#95C2412yes—
704#95C2411yescharacteristic
705#95C2412yes—
706#95C2411yescharacteristic
707#95C2412yes—
708#95C2412yes—
709#95C2412yes—
710#95C2412yes—
711#95C2412yes—
712#95C2412yes—
713#95C2418yes—
714#95C2418yes—
715#95C2418yes—
716#95C2418yes—
717#95C2418yes—
718#95C2418yes—
719#95C2418yes—
720#95C2418yes—
721#95C2418yes—
722#95C2418yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728#95C2418yes—
729#95C2418yes—
730#95C2418yes—
731#95C2418yes—
732#95C2418yes—
733#95C2418yes—
734C24C2512yes—
735C24C2511yescharacteristic
736C24C2512yes—
737#41—432no—
738C2×Q8—24no—
739C2×Q8—28no—
740C2×Q8—24no—
741C2×Q8—24no—
742C2×Q8—24no—
743C2×Q8—24no—
744C2×Q8—28no—
745C2×Q8—24no—
746C2×Q8—24no—
747C2×Q8—24no—
748C2×Q8—44no—
749C2×Q8—44no—
750C2×Q8—42no—
751C2×Q8—48no—
752C2×Q8—432no—
753C2×D4—24no—
754C2×D4—24no—
755C2×D4—24no—
756C2×D4—24no—
757C2×D4—24no—
758C2×D4—24no—
759C2×D4—24no—
760C2×D4—22no—
761C2×D4—22no—
762C2×D4—24no—
763C2×D4—42no—
764C2×D4—42no—
765C2×D4—42no—
766C2×D4—42no—
767C2×D4—42no—
768C2×D4—42no—
769C22×C4—24no—
770C22×C4—22no—
771C22×C4—24no—
772C22×C4—24no—
773C22×C4—24no—
774C22×C4—22no—
775C22×C4—28no—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—24no—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—24no—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—24no—
790C22×C4—24no—
791C22×C4—44no—
792C22×C4—44no—
793C22×C4—48no—
794C22×C4—48no—
795C22×C4—48no—
796C22×C4C2×#4118yes—
797C22×C4C2×#4114yes—
798C22×C42−1+418yes—
799C22×C4C2512yes—
800C22×C4C2512yes—
801C22×C4C2512yes—
802C22×C4C2512yes—
803C22×C4C2511yescharacteristic
804C22×C4C2514yes—
805C22×C4C2512yes—
806C22×C4C2518yes—
807C22×C4C2514yes—
808C22×C4C2514yes—
809C22×C4C2514yes—
810C22×C4C2518yes—
811C22×C4C2512yes—
812C22×C4C2512yes—
813C22×C4C2511yescharacteristic
814C22×C4C2512yes—
815C22×C4C2511yescharacteristic
816C22×C4C2511yescharacteristic
817C22×C4C2511yescharacteristic
818C22×C4C2512yes—
819C22×C4C2511yescharacteristic
820C22×C4C2512yes—
821C4⋊C4—216no—
822C4⋊C4—28no—
823C4⋊C4—28no—
824C4⋊C4—24no—
825C4⋊C4—24no—
826C4⋊C4—24no—
827C4⋊C4—24no—
828C4⋊C4—24no—
829C4⋊C4—24no—
830C4⋊C4—24no—
831C4⋊C4—28no—
832C4⋊C4—22no—
833C4⋊C4—22no—
834C4⋊C4—24no—
835C4⋊C4—28no—
836C4⋊C4—28no—
837C4⋊C4—22no—
838C4⋊C4—22no—
839C4⋊C4—28no—
840C4⋊C4—28no—
841C4⋊C4—28no—
842C4⋊C4—24no—
843C4⋊C4—24no—
844C4⋊C4—28no—
845C4⋊C4—28no—
846C4⋊C4—28no—
847C4⋊C4—28no—
848C4⋊C4—28no—
849C4⋊C4—48no—
850C4⋊C4—48no—
851C4⋊C4—48no—
852C4⋊C4—42no—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C4⋊C4—42no—
856C4⋊C4—42no—
857C4⋊C4—42no—
858C4⋊C4—48no—
859C4⋊C4—48no—
860C4⋊C4—48no—
861C4⋊C4—48no—
862C4⋊C4—48no—
863C4⋊C4—48no—
864C4⋊C4—48no—
865C4⋊C4—48no—
866C22⋊C4—24no—
867C22⋊C4—24no—
868C22⋊C4—216no—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—24no—
872C22⋊C4—24no—
873C22⋊C4—24no—
874C22⋊C4—24no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—24no—
878C22⋊C4—24no—
879C22⋊C4—24no—
880C22⋊C4—24no—
881C22⋊C4—42no—
882C22⋊C4—48no—
883C22⋊C4—48no—
884C22⋊C4—44no—
885C22⋊C4—48no—
886C22⋊C4—42no—
887C22⋊C4—42no—
888C22⋊C4—42no—
889C22⋊C4—42no—
890C22⋊C4—42no—
891C22⋊C4—42no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C42—24no—
897C42—24no—
898C42—24no—
899C42—24no—
900C42—24no—
901C42—24no—
902C42—22no—
903C42—28no—
904C42—28no—
905C42—216no—
906C42—24no—
907C42—24no—
908C42—22no—
909C42—22no—
910C42—24no—
911C42—24no—
912C42—48no—
913C42—48no—
914C42—44no—
915C42—44no—
916C42—44no—
917C42—48no—
918C42C2×#4114yes—
919C42C2×#4118yes—
920C42C2×#4114yes—
921C42H(5,𝔽2)14yes—
922C23—22no—
923C23—21no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—21no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23C22×#4112yes—
940C23C2×2−1+414yes—
941C23C2611yescharacteristic
942Q8—48no—
943Q8—416no—
944Q8—48no—
945Q8—48no—
946Q8—88no—
947D4—28no—
948D4—48no—
949D4—48no—
950D4—44no—
951D4—48no—
952D4—48no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—21no—
961C2×C4—216no—
962C2×C4—216no—
963C2×C4—28no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—22no—
978C2×C4—28no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—28no—
983C2×C4—28no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—28no—
995C2×C4—28no—
996C2×C4—28no—
997C2×C4—28no—
998C2×C4—22no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—28no—
1005C2×C4—416no—
1006C2×C4—48no—
1007C2×C4—48no—
1008C2×C4—48no—
1009C2×C4—48no—
1010C2×C4—48no—
1011C2×C4—168no—
1012C2×C4C22×#4112yes—
1013C2×C4C22×#4114yes—
1014C2×C4C22×#4114yes—
1015C2×C4C22×#4112yes—
1016C2×C4C2×H(5,𝔽2)12yes—
1017C2×C4C2×H(5,𝔽2)12yes—
1018C2×C4C2×H(5,𝔽2)12yes—
1019C2×C4C2×2−1+414yes—
1020C2×C4C2×2−1+414yes—
1021C2×C4#58514yes—
1022C2×C4#58512yes—
1023C22—22no—
1024C22—24no—
1025C22—24no—
1026C22—24no—
1027C22—24no—
1028C22—42no—
1029C22—42no—
1030C22—41no—
1031C22—42no—
1032C22—41no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22C23×#4111yescharacteristic
1043C22C22×H(5,𝔽2)11yescharacteristic
1044C22C22×2−1+412yes—
1045C22C2×#58511yescharacteristic
1046C22C2×#58512yes—
1047C4—22no—
1048C4—24no—
1049C4—24no—
1050C4—22no—
1051C4—22no—
1052C4—42no—
1053C4—42no—
1054C4—44no—
1055C4—44no—
1056C4—42no—
1057C4—42no—
1058C4—42no—
1059C4—41no—
1060C4—44no—
1061C4—41no—
1062C4—44no—
1063C4—48no—
1064C4—42no—
1065C4—48no—
1066C4—42no—
1067C4#349518yes—
1068C4#350614yes—
1069C2—42no—
1070C2—44no—
1071C2—82no—
1072C2C2×#350611yescharacteristic
1073C2C2×#349512yes—
1074C2#6283311yescharacteristic
1075C2#6283611yescharacteristic
1076C2#6283812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34547C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45431C2semidirect
2. #45252C2semidirect
3. #45250C2semidirect
4. #45222C2semidirect
5. #45138C2semidirect
6. #44902C2semidirect
7. #44898C2semidirect
8. #42936C2semidirect
9. #42470C2semidirect
10. #42466C2semidirect
11. #36210C2semidirect
12. #36209C2semidirect
13. #36209C2semidirect
14. #36189C2semidirect
15. #36188C2semidirect
16. #36180C2semidirect
17. #36030C2semidirect
18. #35815C2semidirect
19. #35770C2semidirect
20. #35738C2semidirect
21. #35294C2semidirect
22. #35279C2semidirect
24. #34209C2semidirect
25. #34188C2semidirect

Maximal subgroups

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

subgroupindex
#454312
#452522
#452502
#452222
#451382
#449022
#448982
#429362
#424702
#424662
#362102
#362092
#361892
#361882
#361802
#360302
#358152
#357702
#357382
#352942
#352792
#345472
#342092
#341882