Finite Group Databasebeta

← #7647705

Subgroups — #7647705

Order 512.

5864 conjugacy classes of subgroups.

The subgroup lattice has 1103 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41038C218yesmaximal, complemented
2#41009C218yesmaximal, complemented
3#39438C214yesmaximal, complemented
4#39275C214yesmaximal, complemented
5#37782C214yesmaximal, complemented
6#37772C214yesmaximal, complemented
7#37626C212yesmaximal, complemented
8#37621C211yesmaximal, characteristic, complemented
9#37614C211yesmaximal, characteristic, complemented
10#37334C214yesmaximal, complemented
11#37322C212yesmaximal, complemented
12#37319C212yesmaximal, complemented
13#35524C214yesmaximal, complemented
14#35293C212yesmaximal, complemented
15#35274C211yesmaximal, characteristic, complemented
16#35268C212yesmaximal, complemented
17#35198C212yesmaximal, complemented
18#35197C212yesmaximal, complemented
19#35192C211yesmaximal, characteristic, complemented
20#34925C212yesmaximal, complemented
21#34210C211yesmaximal, characteristic, complemented
22#34151C211yesmaximal, characteristic, complemented
23#34086C211yesmaximal, characteristic, complemented
24C2×#542C2214yescomplemented
25C2×#535C2214yes—
26C2×#532C2211yescharacteristic
27C2×#532C2214yescomplemented
28C2×#532C2214yescomplemented
29C22×#127C2211yescharacteristic
30C2×#529C2211yescharacteristic
31C2×#518C2212yes—
32#2867C2212yes—
33#2864C2212yescomplemented
34#2862C2212yescomplemented
35#2860C2214yescomplemented
36#2858C2212yes—
37#2858C2214yescomplemented
38#2854C2214yescomplemented
39#2850C2214yescomplemented
40#2828C2218yescomplemented
41#2818C2214yes—
42#2813C2214yes—
43#2803C2218yescomplemented
44#2751C2218yescomplemented
45#2733C2218yescomplemented
46#2730C2218yescomplemented
47#2714C2218yescomplemented
48#2712C2218yescomplemented
49#2710C2218yescomplemented
50#2709C2218yescomplemented
51#2709C2218yescomplemented
52#2700C2218yescomplemented
53#2685C2218yes—
54#2684C2218yes—
55#2678C2218yes—
56#2673C2218yescomplemented
57#2673C2218yescomplemented
58#2670C2218yes—
59#2665C2214yes—
60#2662C2214yescomplemented
61#2662C2218yescomplemented
62#2657C2214yes—
63#2657C2212yes—
64#2648C2218yescomplemented
65#2641C2212yes—
66#2635C2218yescomplemented
67#2628C2212yescomplemented
68#2624C2214yescomplemented
69#2624C2214yescomplemented
70#2619C2212yes—
71#2619C2212yes—
72#2619C2214yescomplemented
73#2619C2212yescomplemented
74#2619C2214yescomplemented
75#2616C2212yes—
76#2615C2212yes—
77#2613C2214yes—
78#2605C2214yescomplemented
79#2600C2218yescomplemented
80#2571C2212yescomplemented
81#2562C2212yescomplemented
82#2555C2218yescomplemented
83#2551C2212yescomplemented
84#2548C2212yes—
85#2544C2218yescomplemented
86#2544C2218yescomplemented
87#2541C2214yes—
88#2541C2212yes—
89#2541C2212yes—
90#2541C2212yes—
91#2540C2212yescomplemented
92#2538C2212yescomplemented
93#2537C2212yescomplemented
94#2534C2218yes—
95#2521C2218yescomplemented
96#2516C2218yescomplemented
97#2513C2214yescomplemented
98#2491C2214yescomplemented
99#2491C2214yescomplemented
100#2491C2214yescomplemented
101#2472C2218yes—
102#2467C2218yescomplemented
103#2461C2218yescomplemented
104#2459C2218yescomplemented
105#2459C2218yescomplemented
106#2457C2218yescomplemented
107#2456C2218yescomplemented
108#2452C2214yescomplemented
109#2445C2214yescomplemented
110#2445C2214yescomplemented
111#2439C2214yes—
112#2439C2214yes—
113#2435C2212yes—
114#2433C2214yes—
115#2433C2212yes—
116#2433C2214yes—
117#2431C2218yescomplemented
118#2431C2218yescomplemented
119#2428C2214yescomplemented
120#2428C2214yescomplemented
121#2428C2214yescomplemented
122#2428C2214yescomplemented
123#2427C2214yescomplemented
124#2426C2214yescomplemented
125#2424C2218yes—
126#2420C2214yescomplemented
127#2420C2214yescomplemented
128#2420C2214yescomplemented
129#2414C2214yes—
130#2408C2214yes—
131#2407C2218yescomplemented
132#2404C2218yes—
133#2388C2218yescomplemented
134#2374C2214yes—
135#2373C2214yescomplemented
136#2370C2212yescomplemented
137#2367C2212yescomplemented
138#2366C2214yes—
139#2366C2214yes—
140#2363C2212yes—
141#2362C2212yes—
142D4×C22⋊C4C2214yes—
143D4×C22⋊C4C2214yes—
144#2337C2214yescomplemented
145#2333C2214yes—
146#2331C2211yescharacteristic, complemented
147#2331C2211yescharacteristic, complemented
148#2331C2214yescomplemented
149#2328C2212yes—
150#2328C2212yes—
151#2328C2211yescharacteristic, complemented
152#2328C2211yescharacteristic, complemented
153#2328C2214yescomplemented
154#2324C2212yes—
155#2324C2212yes—
156#2324C2214yescomplemented
157#2319C2214yescomplemented
158#2309C2212yes—
159C4×#127C2212yes—
160C4×#127C2212yes—
161C4×#121C2214yescomplemented
162C4×#121C2214yescomplemented
163#2298C2212yescomplemented
164#2297C2214yes—
165#2295C2211yescharacteristic, complemented
166#2293C2212yes—
167#2293C2212yescomplemented
168#2293C2211yescharacteristic, complemented
169#2290C2212yes—
170#2290C2214yescomplemented
171#2285C2211yescharacteristic
172#2283C2211yescharacteristic
173C42×Q8C2211yescharacteristic, complemented
174C42×D4C2212yescomplemented
175C42×D4C2211yescharacteristic, complemented
176C4×#117C2211yescharacteristic
177C4×#117C2211yescharacteristic
178C4×#117C2212yescomplemented
179C22×#41C2312yes—
180C22×#41C2318yes—
181C23×D4C2312yes—
182C23×D4C2312yes—
183C23×D4C2312yes—
184#542—416no—
185#535—416no—
186#532—28no—
187#532—416no—
188#532—416no—
189C2×C4⋊Q8C2311yescharacteristic
190C2×C4⋊Q8C2314yes—
191C2×C4⋊Q8C2314yes—
192C2×#127—28no—
193C2×#127C2312yes—
194C2×#127C2312yes—
195C2×#127C2312yes—
196C2×#127C2311yescharacteristic
197C2×#127C2312yes—
198C2×#127C2314yes—
199C2×#127C2314yes—
200C2×#127C2318yes—
201C2×#127C2314yes—
202C2×#127C2318yes—
203#529—28no—
204C2×#126C2312yes—
205C2×#126C2318yes—
206C2×#125C2311yescharacteristic
207C2×#124C2312yes—
208C2×#124C2311yescharacteristic
209C2×#124C2314yes—
210C2×#124C2318yes—
211C2×#124C2318yes—
212C2×#124C2318yes—
213C2×#124C2318yes—
214C2×#124C2318yes—
215C2×#123C2312yes—
216C2×#123C2318yes—
217C2×#123C2318yes—
218C2×C22⋊Q8C2311yescharacteristic
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2318yes—
221C2×#121C2312yes—
222C2×#121C2314yes—
223C2×#121C2312yes—
224C2×#121C2311yescharacteristic
225C2×#121C2314yes—
226C2×#121C2314yes—
227C2×#121C2314yes—
228C2×#121C2314yes—
229C2×#121C2314yes—
230C2×#121C2314yes—
231C2×#121C2314yes—
232C2×#121C2318yes—
233C2×#121C2318yes—
234C2×#121C2318yes—
235C2×#120C2318yes—
236C2×#120C2318yes—
237C2×#120C2318yes—
238#518—48no—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×D4C2314yes—
242C2×C4×D4C2312yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2312yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2314yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2318yes—
253C2×C4×D4C2318yes—
254C2×C4×D4C2318yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2314yes—
257C2×#117C2311yescharacteristic
258C2×#117C2312yes—
259C2×#117C2312yes—
260C2×#117C2311yescharacteristic
261C2×#117C2312yes—
262C2×#117C2314yes—
263C2×#117C2312yes—
264C22×C22⋊C4C2318yes—
265C22×C42C2312yes—
266C22×C42C2314yes—
267C22×C42C2311yescharacteristic
268#400C2314yes—
269#400C2318yes—
270#399C2318yes—
271#399C2314yes—
272#397C2318yes—
273#397C2318yes—
274#397C2318yes—
275#397C2318yes—
276#396C2318yes—
277#396C2318yes—
278#396C2318yes—
279#395C2318yes—
280#395C2314yes—
281#394C2314yes—
282#394C2318yes—
283#394C2318yes—
284#394C2314yes—
285#394C2314yes—
286#394C2318yes—
287#394C2318yes—
288#394C2318yes—
289#394C2318yes—
290#394C2318yes—
291#394C2318yes—
292#394C2314yes—
293#394C2314yes—
294#394C2314yes—
295#394C2318yes—
296#394C2318yes—
297#394C2318yes—
298#394C2318yes—
299#394C2318yes—
300#394C2318yes—
301#394C2318yes—
302#394C2318yes—
303#393C2314yes—
304#393C2318yes—
305#393C2318yes—
306#393C2318yes—
307#392C2318yes—
308#392C2314yes—
309#392C2314yes—
310#392C2318yes—
311#392C2318yes—
312#392C2318yes—
313#392C2318yes—
314#392C2318yes—
315#392C2314yes—
316#392C2314yes—
317#392C2314yes—
318#392C2318yes—
319#392C2318yes—
320#392C2314yes—
321#392C2318yes—
322#392C2318yes—
323#392C2318yes—
324#391C2314yes—
325#391C2314yes—
326#391C2318yes—
327#391C2318yes—
328#391C2312yes—
329#391C2318yes—
330#390C2314yes—
331#390C2314yes—
332#390C2314yes—
333#390C2314yes—
334#390C2314yes—
335#390C2314yes—
336#390C2318yes—
337#390C2314yes—
338#390C2314yes—
339#390C2312yes—
340#390C2312yes—
341#390C2314yes—
342#390C2314yes—
343#390C2314yes—
344#390C2318yes—
345#390C2314yes—
346#390C2314yes—
347#390C2314yes—
348#390C2318yes—
349#390C2318yes—
350#390C2312yes—
351#390C2314yes—
352#390C2314yes—
353#390C2318yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2312yes—
358#389C2312yes—
359#389C2314yes—
360#389C2312yes—
361#389C2314yes—
362#389C2312yes—
363#389C2314yes—
364#388C2318yes—
365#388C2314yes—
366#388C2314yes—
367#388C2318yes—
368#388C2318yes—
369#388C2314yes—
370#388C2314yes—
371#388C2318yes—
372#388C2314yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2314yes—
379#388C2314yes—
380#388C2314yes—
381#388C2314yes—
382#388C2314yes—
383#388C2318yes—
384#387C2314yes—
385#387C2314yes—
386#387C2318yes—
387#387C2318yes—
388#387C2314yes—
389#387C2318yes—
390#387C2314yes—
391#387C2314yes—
392#387C2314yes—
393#386C2314yes—
394#386C2314yes—
395#386C2318yes—
396#386C2318yes—
397#386C2318yes—
398#386C2318yes—
399#386C2318yes—
400#386C2314yes—
401#386C2314yes—
402#386C2314yes—
403#386C2314yes—
404#386C2318yes—
405#386C2318yes—
406#386C2318yes—
407#386C2318yes—
408#386C2318yes—
409#386C2318yes—
410#386C2314yes—
411#386C2318yes—
412#386C2318yes—
413#386C2318yes—
414#385C2314yes—
415#385C2314yes—
416#385C2318yes—
417#385C2314yes—
418#384C2312yes—
419#383C2312yes—
420#382C2314yes—
421#382C2314yes—
422#382C2312yes—
423#382C2311yescharacteristic
424#382C2311yescharacteristic
425#381C2318yes—
426#381C2312yes—
427#381C2318yes—
428#380C2314yes—
429#380C2314yes—
430#380C2318yes—
431#380C2312yes—
432#380C2312yes—
433#380C2312yes—
434#380C2314yes—
435#379C2318yes—
436#379C2318yes—
437C4×C4⋊C4C2312yes—
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2312yes—
440C4×C4⋊C4C2312yes—
441C4×C4⋊C4C2312yes—
442C4×C4⋊C4C2312yes—
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2312yes—
453C4×C4⋊C4C2311yescharacteristic
454C4×C22⋊C4C2312yes—
455C4×C22⋊C4C2314yes—
456C4×C22⋊C4C2314yes—
457C4×C22⋊C4C2312yes—
458C4×C22⋊C4C2314yes—
459C4×C22⋊C4C2314yes—
460C4×C22⋊C4C2314yes—
461C4×C22⋊C4C2312yes—
462C4×C22⋊C4C2318yes—
463C4×C22⋊C4C2312yes—
464C4×C22⋊C4C2314yes—
465C4×C22⋊C4C2314yes—
466C4×C22⋊C4C2312yes—
467C4×C22⋊C4C2312yes—
468C4×C22⋊C4C2312yes—
469#376C2312yes—
470#376C2311yescharacteristic
471#376C2311yescharacteristic
472#376C2312yes—
473#376C2312yes—
474C43C2311yescharacteristic
475C43C2311yescharacteristic
476C43C2312yes—
477C43C2312yes—
478C25C2414yes—
479C2×#41—28no—
480C2×#41—416no—
481C2×#41—48no—
482C2×#41—416no—
483C2×#41—88no—
484C22×Q8C2411yescharacteristic
485C22×Q8C2418yes—
486C22×Q8C2412yes—
487C22×D4—28no—
488C22×D4—28no—
489C22×D4—28no—
490C22×D4—44no—
491C22×D4—44no—
492C22×D4—48no—
493C22×D4—84no—
494C22×D4C2411yescharacteristic
495C22×D4C2412yes—
496C22×D4C2414yes—
497C22×D4C2414yes—
498C22×D4C2414yes—
499C22×D4C2414yes—
500C22×D4C2412yes—
501C22×D4C2418yes—
502C22×D4C2412yes—
503C22×D4C2414yes—
504C22×D4C2418yes—
505C22×D4C2414yes—
506C22×D4C2412yes—
507C22×D4C2414yes—
508C22×D4C2418yes—
509C22×D4C2418yes—
510C22×D4C2418yes—
511C22×D4C2418yes—
512C22×D4C2418yes—
513C23×C4C2412yes—
514C23×C4C2414yes—
515C23×C4C2414yes—
516C23×C4C2411yescharacteristic
517C23×C4C2411yescharacteristic
518C23×C4C2418yes—
519C23×C4C2414yes—
520C23×C4C2418yes—
521C23×C4C2414yes—
522C23×C4C2411yescharacteristic
523C4⋊Q8—216no—
524C4⋊Q8—24no—
525C4⋊Q8—48no—
526#127—28no—
527#127—28no—
528#127—28no—
529#127—28no—
530#127—24no—
531#127—48no—
532#127—48no—
533#127—48no—
534#127—416no—
535#127—88no—
536#126—28no—
537#126—416no—
538#125—24no—
539#124—24no—
540#124—28no—
541#124—416no—
542#124—416no—
543#124—48no—
544#124—416no—
545#124—416no—
546#124—88no—
547#123—28no—
548#123—416no—
549#123—88no—
550C22⋊Q8—24no—
551C22⋊Q8—416no—
552C22⋊Q8—48no—
553#121—24no—
554#121—28no—
555#121—28no—
556#121—216no—
557#121—216no—
558#121—416no—
559#121—416no—
560#121—48no—
561#121—48no—
562#121—48no—
563#121—48no—
564#121—48no—
565#121—48no—
566#121—88no—
567#120—416no—
568#120—416no—
569#120—88no—
570C4×Q8—28no—
571C4×Q8—24no—
572C4×D4—28no—
573C4×D4—28no—
574C4×D4—24no—
575C4×D4—28no—
576C4×D4—28no—
577C4×D4—216no—
578C4×D4—28no—
579C4×D4—44no—
580C4×D4—48no—
581C4×D4—48no—
582C4×D4—48no—
583C4×D4—416no—
584C4×D4—416no—
585C4×D4—416no—
586C4×D4—84no—
587C4×D4—84no—
588#117—28no—
589#117—28no—
590#117—24no—
591#117—42no—
592#117—44no—
593#117—48no—
594#117—44no—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2418yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2412yes—
621C2×C22⋊C4—416no—
622C2×C22⋊C4C2412yes—
623C2×C22⋊C4C2418yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2412yes—
626C2×C22⋊C4C2412yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2412yes—
633C2×C22⋊C4C2412yes—
634C2×C22⋊C4C2412yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2418yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2412yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2418yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2414yes—
663C2×C42—28no—
664C2×C42—48no—
665C2×C42#4118yescomplemented
666C2×C42C2411yescharacteristic
667C2×C42C2412yes—
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2412yes—
671C2×C42C2414yes—
672C2×C42C2414yes—
673C2×C42C2412yes—
674C2×C42C2412yes—
675C2×C42C2414yes—
676C2×C42C2414yes—
677C2×C42C2412yes—
678C2×C42C2414yes—
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2414yes—
682C2×C42C2414yes—
683C2×C42C2414yes—
684C2×C42C2414yes—
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690#95C2412yes—
691#95C2412yes—
692#95C2412yes—
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696#95C2412yes—
697#95C2412yes—
698#95C2412yes—
699#95C2414yes—
700#95C2412yes—
701#95C2412yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2418yes—
707#95C2414yes—
708#95C2414yes—
709#95C2412yes—
710#95C2412yes—
711#95C2418yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2418yes—
718#95C2418yes—
719#95C2418yes—
720#95C2418yes—
721C24—28no—
722C24—44no—
723C24—44no—
724C24—48no—
725C24—48no—
726C24C2518yes—
727C24C2512yes—
728C24C2514yes—
729C24C2511yescharacteristic
730#41—816no—
731#41—864no—
732C2×Q8—22no—
733C2×Q8—24no—
734C2×Q8—24no—
735C2×Q8—216no—
736C2×Q8—44no—
737C2×Q8—48no—
738C2×Q8—48no—
739C2×D4—24no—
740C2×D4—28no—
741C2×D4—22no—
742C2×D4—24no—
743C2×D4—28no—
744C2×D4—28no—
745C2×D4—28no—
746C2×D4—28no—
747C2×D4—24no—
748C2×D4—24no—
749C2×D4—28no—
750C2×D4—28no—
751C2×D4—28no—
752C2×D4—24no—
753C2×D4—24no—
754C2×D4—28no—
755C2×D4—28no—
756C2×D4—216no—
757C2×D4—216no—
758C2×D4—24no—
759C2×D4—28no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—432no—
765C2×D4—48no—
766C2×D4—48no—
767C2×D4—44no—
768C2×D4—44no—
769C2×D4—44no—
770C2×D4—48no—
771C2×D4—48no—
772C2×D4—48no—
773C2×D4—48no—
774C2×D4—48no—
775C2×D4—48no—
776C2×D4—48no—
777C2×D4—48no—
778C2×D4—48no—
779C2×D4—48no—
780C2×D4—48no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—48no—
784C2×D4—48no—
785C2×D4—48no—
786C2×D4—48no—
787C2×D4—48no—
788C2×D4—48no—
789C2×D4—48no—
790C2×D4—48no—
791C2×D4—816no—
792C2×D4—816no—
793C22×C4—22no—
794C22×C4—24no—
795C22×C4—22no—
796C22×C4—24no—
797C22×C4—28no—
798C22×C4—24no—
799C22×C4—28no—
800C22×C4—28no—
801C22×C4—28no—
802C22×C4—28no—
803C22×C4—28no—
804C22×C4—24no—
805C22×C4—216no—
806C22×C4—44no—
807C22×C4—42no—
808C22×C4—44no—
809C22×C4—44no—
810C22×C4—44no—
811C22×C4—48no—
812C22×C4—44no—
813C22×C4—48no—
814C22×C4—44no—
815C22×C4—48no—
816C22×C4—48no—
817C22×C4—48no—
818C22×C4C2×#4114yes—
819C22×C4C2×#4114yes—
820C22×C4C2×#4114yes—
821C22×C4C2514yes—
822C22×C4C2514yes—
823C22×C4C2514yes—
824C22×C4C2512yes—
825C22×C4C2512yes—
826C22×C4C2512yes—
827C22×C4C2512yes—
828C22×C4C2514yes—
829C22×C4C2518yes—
830C22×C4C2512yes—
831C22×C4C2512yes—
832C22×C4C2511yescharacteristic
833C22×C4C2511yescharacteristic
834C22×C4C2511yescharacteristic
835C22×C4C2511yescharacteristic
836C22×C4C2512yes—
837C22×C4C2514yes—
838C22×C4C2511yescharacteristic
839C22×C4C2511yescharacteristic
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—24no—
844C4⋊C4—22no—
845C4⋊C4—24no—
846C4⋊C4—22no—
847C4⋊C4—24no—
848C4⋊C4—24no—
849C4⋊C4—24no—
850C4⋊C4—28no—
851C4⋊C4—24no—
852C4⋊C4—28no—
853C4⋊C4—216no—
854C4⋊C4—28no—
855C4⋊C4—24no—
856C4⋊C4—42no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C4⋊C4—48no—
861C4⋊C4—44no—
862C4⋊C4—48no—
863C4⋊C4—48no—
864C4⋊C4—44no—
865C4⋊C4H(5,𝔽2)18yes—
866C22⋊C4—24no—
867C22⋊C4—24no—
868C22⋊C4—24no—
869C22⋊C4—28no—
870C22⋊C4—28no—
871C22⋊C4—24no—
872C22⋊C4—24no—
873C22⋊C4—24no—
874C22⋊C4—216no—
875C22⋊C4—28no—
876C22⋊C4—28no—
877C22⋊C4—28no—
878C22⋊C4—216no—
879C22⋊C4—216no—
880C22⋊C4—44no—
881C22⋊C4—48no—
882C22⋊C4—42no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C22⋊C4—44no—
886C22⋊C4—44no—
887C22⋊C4—48no—
888C22⋊C4—48no—
889C22⋊C4—48no—
890C22⋊C4—48no—
891C22⋊C4—48no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C22⋊C4—44no—
897C22⋊C4—48no—
898C22⋊C4—48no—
899C22⋊C4—48no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C22⋊C4—48no—
903C22⋊C4—48no—
904C22⋊C4—48no—
905C22⋊C4—48no—
906C22⋊C4—44no—
907C42—24no—
908C42—28no—
909C42—24no—
910C42—24no—
911C42—28no—
912C42—22no—
913C42—28no—
914C42—24no—
915C42—28no—
916C42—22no—
917C42—22no—
918C42—24no—
919C42—44no—
920C42—44no—
921C42—44no—
922C42—42no—
923C42—42no—
924C42—44no—
925C42—44no—
926C42C2×#4114yes—
927C42C2×#4114yes—
928C42C2×#4114yes—
929C42C2×#4114yes—
930C42H(5,𝔽2)14yes—
931C23—21no—
932C23—22no—
933C23—21no—
934C23—22no—
935C23—22no—
936C23—24no—
937C23—28no—
938C23—28no—
939C23—28no—
940C23—24no—
941C23—24no—
942C23—28no—
943C23—24no—
944C23—22no—
945C23—24no—
946C23—22no—
947C23—24no—
948C23—28no—
949C23—24no—
950C23—28no—
951C23—28no—
952C23—24no—
953C23—24no—
954C23—416no—
955C23—88no—
956C23—88no—
957C23—168no—
958C23—168no—
959C23C22×#4112yes—
960C23C2611yescharacteristic
961Q8—44no—
962Q8—84no—
963Q8—816no—
964D4—416no—
965D4—416no—
966D4—48no—
967D4—416no—
968D4—44no—
969D4—416no—
970D4—84no—
971D4—816no—
972D4—88no—
973D4—88no—
974D4—84no—
975D4—816no—
976D4—84no—
977D4—88no—
978D4—816no—
979D4—816no—
980D4—816no—
981D4—168no—
982D4—168no—
983C2×C4—24no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—24no—
991C2×C4—22no—
992C2×C4—28no—
993C2×C4—28no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—22no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—22no—
1007C2×C4—24no—
1008C2×C4—28no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—28no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—24no—
1015C2×C4—22no—
1016C2×C4—24no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—28no—
1025C2×C4—44no—
1026C2×C4—416no—
1027C2×C4—416no—
1028C2×C4—48no—
1029C2×C4—416no—
1030C2×C4—816no—
1031C2×C4—88no—
1032C2×C4—168no—
1033C2×C4C22×#4112yes—
1034C2×C4C22×#4112yes—
1035C2×C4C22×#4112yes—
1036C2×C4C22×#4112yes—
1037C2×C4C22×#4112yes—
1038C2×C4C22×#4112yes—
1039C2×C4C2×H(5,𝔽2)14yes—
1040C2×C4C2×H(5,𝔽2)18yes—
1041C2×C4C2×H(5,𝔽2)12yes—
1042C2×C4C2×H(5,𝔽2)14yes—
1043C2×C4#58512yes—
1044C22—22no—
1045C22—22no—
1046C22—22no—
1047C22—42no—
1048C22—42no—
1049C22—44no—
1050C22—48no—
1051C22—42no—
1052C22—48no—
1053C22—44no—
1054C22—42no—
1055C22—44no—
1056C22—44no—
1057C22—48no—
1058C22—48no—
1059C22—44no—
1060C22—44no—
1061C22—44no—
1062C22—48no—
1063C22—44no—
1064C22—48no—
1065C22—42no—
1066C22—48no—
1067C22—44no—
1068C22—1616no—
1069C22C23×#4111yescharacteristic
1070C22C22×H(5,𝔽2)12yes—
1071C22C22×H(5,𝔽2)11yescharacteristic
1072C22C2×#58511yescharacteristic
1073C22H(7,𝔽2)12yes—
1074C4—22no—
1075C4—22no—
1076C4—22no—
1077C4—24no—
1078C4—28no—
1079C4—22no—
1080C4—44no—
1081C4—42no—
1082C4—42no—
1083C4—44no—
1084C4—48no—
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—44no—
1089C4—44no—
1090C4—42no—
1091C4#346014yes—
1092C4#350814yes—
1093C2—42no—
1094C2—84no—
1095C2—82no—
1096C2—88no—
1097C2C2×#346011yescharacteristic
1098C2C2×#350811yescharacteristic
1099C2#6285511yescharacteristic
1100C2#6291212yes—
1101C2#6292312yes—
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. #41038C2semidirect
2. #41009C2semidirect
3. #39438C2semidirect
4. #39275C2semidirect
5. #37782C2semidirect
6. #37772C2semidirect
7. #37626C2semidirect
8. #37621C2semidirect
9. #37614C2semidirect
10. #37334C2semidirect
11. #37322C2semidirect
12. #37319C2semidirect
13. #35524C2semidirect
14. #35293C2semidirect
15. #35274C2semidirect
16. #35268C2semidirect
17. #35198C2semidirect
18. #35197C2semidirect
19. #35192C2semidirect
20. #34925C2semidirect
21. #34210C2semidirect
22. #34151C2semidirect
23. #34086C2semidirect
24. C2×#542C22semidirect
27. C2×#532C22semidirect
28. C2×#532C22semidirect
33. #2864C22semidirect
34. #2862C22semidirect
35. #2860C22semidirect
37. #2858C22semidirect
38. #2854C22semidirect
39. #2850C22semidirect
40. #2828C22semidirect
43. #2803C22semidirect
44. #2751C22semidirect
45. #2733C22semidirect
46. #2730C22semidirect
47. #2714C22semidirect
48. #2712C22semidirect
49. #2710C22semidirect
50. #2709C22semidirect
51. #2709C22semidirect
52. #2700C22semidirect
56. #2673C22semidirect
57. #2673C22semidirect
60. #2662C22semidirect
61. #2662C22semidirect
64. #2648C22semidirect
66. #2635C22semidirect
67. #2628C22semidirect
68. #2624C22semidirect
69. #2624C22semidirect
72. #2619C22semidirect
73. #2619C22semidirect
74. #2619C22semidirect
78. #2605C22semidirect
79. #2600C22semidirect
80. #2571C22semidirect
81. #2562C22semidirect
82. #2555C22semidirect
83. #2551C22semidirect
85. #2544C22semidirect
86. #2544C22semidirect
91. #2540C22semidirect
92. #2538C22semidirect
93. #2537C22semidirect
95. #2521C22semidirect
96. #2516C22semidirect
97. #2513C22semidirect
98. #2491C22semidirect
99. #2491C22semidirect
100. #2491C22semidirect
102. #2467C22semidirect
103. #2461C22semidirect
104. #2459C22semidirect
105. #2459C22semidirect
106. #2457C22semidirect
107. #2456C22semidirect
108. #2452C22semidirect
109. #2445C22semidirect
110. #2445C22semidirect
117. #2431C22semidirect
118. #2431C22semidirect
119. #2428C22semidirect
120. #2428C22semidirect
121. #2428C22semidirect
122. #2428C22semidirect
123. #2427C22semidirect
124. #2426C22semidirect
126. #2420C22semidirect
127. #2420C22semidirect
128. #2420C22semidirect
131. #2407C22semidirect
133. #2388C22semidirect
135. #2373C22semidirect
136. #2370C22semidirect
137. #2367C22semidirect
144. #2337C22semidirect
146. #2331C22semidirect
147. #2331C22semidirect
148. #2331C22semidirect
151. #2328C22semidirect
152. #2328C22semidirect
153. #2328C22semidirect
156. #2324C22semidirect
157. #2319C22semidirect
161. C4×#121C22semidirect
162. C4×#121C22semidirect
163. #2298C22semidirect
165. #2295C22semidirect
167. #2293C22semidirect
168. #2293C22semidirect
170. #2290C22semidirect
173. C42×Q8C22semidirect
174. C42×D4C22semidirect
175. C42×D4C22semidirect
178. C4×#117C22semidirect
665. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
#410382
#410092
#394382
#392752
#377822
#377722
#376262
#376212
#376142
#373342
#373222
#373192
#355242
#352932
#352742
#352682
#351982
#351972
#351922
#349252
#342102
#341512
#340862