Finite Group Databasebeta

← #7654833

Subgroups — #7654833

Order 512.

5802 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42071C218yesmaximal, complemented
2#41980C214yesmaximal, complemented
3#39562C214yesmaximal, complemented
4#39500C212yesmaximal, complemented
5#39268C214yesmaximal, complemented
6#39185C212yesmaximal, complemented
7#37782C214yesmaximal, complemented
8#37772C214yesmaximal, complemented
9#37669C214yesmaximal, complemented
10#37626C212yesmaximal, complemented
11#37618C211yesmaximal, characteristic, complemented
12#36498C212yesmaximal, complemented
13#36149C212yesmaximal, complemented
14#36147C214yesmaximal, complemented
15#35684C214yesmaximal, complemented
16#35196C212yesmaximal, complemented
17#35192C211yesmaximal, characteristic, complemented
18#35170C212yesmaximal, complemented
19#35165C211yesmaximal, characteristic, complemented
20#34936C211yesmaximal, characteristic, complemented
21#34925C212yesmaximal, complemented
22#34226C211yesmaximal, characteristic, complemented
23#34155C211yesmaximal, characteristic, complemented
24#34126C211yesmaximal, characteristic, complemented
25C2×#542C2214yescomplemented
26C2×#535C2212yes—
27C2×#532C2211yescharacteristic
28C2×#532C2211yescharacteristic
29C2×#532C2214yes—
30C2×#532C2214yescomplemented
31C2×#525C2214yes—
32C22×C4×D4C2211yescharacteristic
33#2864C2212yescomplemented
34#2862C2212yescomplemented
35#2857C2214yescomplemented
36#2855C2214yescomplemented
37#2854C2214yes—
38#2850C2214yescomplemented
39#2847C2214yes—
40#2828C2218yescomplemented
41#2815C2214yes—
42#2808C2218yescomplemented
43#2798C2218yescomplemented
44#2796C2218yescomplemented
45#2733C2218yescomplemented
46#2730C2218yescomplemented
47#2714C2218yescomplemented
48#2712C2218yes—
49#2705C2218yes—
50#2696C2218yes—
51#2678C2218yes—
52#2673C2218yes—
53#2670C2218yes—
54#2665C2214yes—
55#2663C2218yescomplemented
56#2657C2212yescomplemented
57#2649C2218yescomplemented
58#2640C2212yescomplemented
59#2635C2218yescomplemented
60#2631C2214yescomplemented
61#2624C2214yescomplemented
62#2624C2214yescomplemented
63#2619C2214yes—
64#2619C2214yescomplemented
65#2617C2214yes—
66#2615C2214yes—
67#2607C2218yescomplemented
68#2605C2214yescomplemented
69#2597C2218yescomplemented
70#2571C2212yescomplemented
71#2557C2218yes—
72#2555C2218yescomplemented
73#2551C2212yescomplemented
74#2547C2212yes—
75#2547C2212yescomplemented
76#2544C2214yes—
77#2542C2211yescharacteristic
78#2542C2211yescharacteristic
79#2541C2212yes—
80#2541C2211yescharacteristic
81#2541C2211yescharacteristic
82#2541C2212yescomplemented
83#2540C2214yes—
84#2539C2214yes—
85#2537C2212yes—
86#2537C2212yes—
87#2535C2212yes—
88#2535C2212yes—
89#2535C2212yescomplemented
90#2535C2212yescomplemented
91#2521C2218yescomplemented
92#2516C2218yescomplemented
93#2501C2212yes—
94#2497C2214yescomplemented
95#2496C2214yescomplemented
96#2492C2214yescomplemented
97#2491C2214yes—
98#2491C2214yescomplemented
99#2491C2214yescomplemented
100#2467C2218yescomplemented
101#2467C2218yescomplemented
102#2459C2218yes—
103#2459C2218yescomplemented
104#2459C2218yescomplemented
105#2457C2218yes—
106#2457C2218yescomplemented
107#2456C2218yescomplemented
108#2447C2218yescomplemented
109#2444C2218yescomplemented
110#2439C2214yes—
111#2439C2214yes—
112#2433C2212yes—
113#2431C2214yes—
114#2431C2218yes—
115#2428C2214yes—
116#2428C2214yes—
117#2428C2214yescomplemented
118#2428C2214yescomplemented
119#2427C2218yescomplemented
120#2427C2214yescomplemented
121#2426C2214yescomplemented
122#2424C2218yes—
123#2421C2214yescomplemented
124#2420C2214yes—
125#2420C2214yescomplemented
126#2420C2214yescomplemented
127#2407C2218yescomplemented
128#2404C2218yes—
129#2397C2214yes—
130#2388C2218yescomplemented
131#2372C2212yescomplemented
132#2372C2212yescomplemented
133#2369C2212yescomplemented
134#2367C2214yescomplemented
135#2366C2212yescomplemented
136#2364C2218yescomplemented
137#2363C2212yes—
138#2363C2212yes—
139#2363C2214yes—
140#2363C2214yes—
141#2357C2211yescharacteristic
142#2357C2211yescharacteristic
143#2357C2212yescomplemented
144#2353C2212yes—
145#2353C2212yes—
146#2349C2211yescharacteristic
147#2349C2211yescharacteristic
148#2349C2212yescomplemented
149#2345C2212yes—
150#2342C2214yes—
151#2341C2212yes—
152#2339C2212yes—
153#2339C2218yescomplemented
154D4×C22⋊C4C2212yes—
155#2331C2214yescomplemented
156#2324C2214yes—
157#2324C2214yes—
158#2323C2214yescomplemented
159#2319C2212yescomplemented
160#2314C2214yescomplemented
161#2311C2212yes—
162C4×C4⋊Q8C2212yescomplemented
163C4×#127C2212yes—
164C4×#127C2212yes—
165C4×#127C2212yescomplemented
166C4×#121C2214yescomplemented
167C4×#121C2214yescomplemented
168#2297C2214yes—
169#2293C2212yes—
170#2293C2212yescomplemented
171#2293C2212yescomplemented
172#2290C2214yes—
173#2285C2211yescharacteristic
174#2283C2211yescharacteristic
175#2280C2212yes—
176#2275C2212yescomplemented
177C42×D4C2212yes—
178C42×D4C2212yescomplemented
179C42×D4C2212yescomplemented
180C4×#117C2211yescharacteristic
181C4×#117C2211yescharacteristic
182C2×C4×C22⋊C4C2212yes—
183C22×#41C2312yes—
184C22×#41C2312yes—
185C22×#41C2318yes—
186C23×D4C2311yescharacteristic
187C24×C4C2312yes—
188#542—416no—
189#535—48no—
190#532—28no—
191#532—28no—
192#532—416no—
193#532—416no—
194C2×C4⋊Q8C2311yescharacteristic
195C2×C4⋊Q8C2314yes—
196C2×C4⋊Q8C2311yescharacteristic
197C2×C4⋊Q8C2314yes—
198C2×#127C2312yes—
199C2×#127C2311yescharacteristic
200C2×#127C2311yescharacteristic
201C2×#127C2312yes—
202C2×#127C2314yes—
203C2×#127C2314yes—
204C2×#126C2318yes—
205C2×#124C2312yes—
206C2×#124C2312yes—
207C2×#124C2314yes—
208C2×#124C2318yes—
209C2×#124C2318yes—
210C2×#124C2318yes—
211C2×#124C2314yes—
212#525—416no—
213C2×#123C2318yes—
214C2×#123C2318yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2318yes—
218C2×#121C2312yes—
219C2×#121C2314yes—
220C2×#121C2312yes—
221C2×#121C2312yes—
222C2×#121C2312yes—
223C2×#121C2314yes—
224C2×#121C2314yes—
225C2×#121C2314yes—
226C2×#121C2314yes—
227C2×#121C2314yes—
228C2×#121C2314yes—
229C2×#121C2314yes—
230C2×#121C2318yes—
231C2×#121C2318yes—
232C2×#121C2318yes—
233C2×#120C2318yes—
234C2×#120C2318yes—
235C2×C4×Q8C2314yes—
236C2×C4×D4—28no—
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2312yes—
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2312yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2312yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2312yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C2312yes—
250C2×C4×D4C2318yes—
251C2×C4×D4C2318yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2312yes—
256C2×C4×D4C2318yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2318yes—
259C2×#117C2312yes—
260C2×#117C2312yes—
261C2×#117C2314yes—
262C2×#117C2314yes—
263C2×#117C2312yes—
264C22×C4⋊C4C2311yescharacteristic
265C22×C22⋊C4C2312yes—
266C22×C22⋊C4C2314yes—
267C22×C42C2314yes—
268C22×C42C2314yes—
269C22×C42C2311yescharacteristic
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#399C2318yes—
274#399C2318yes—
275#399C2314yes—
276#399C2314yes—
277#397C2318yes—
278#397C2318yes—
279#397C2314yes—
280#397C2314yes—
281#397C2314yes—
282#397C2318yes—
283#397C2314yes—
284#397C2318yes—
285#397C2318yes—
286#396C2318yes—
287#396C2318yes—
288#395C2318yes—
289#394C2318yes—
290#394C2318yes—
291#394C2318yes—
292#394C2318yes—
293#394C2318yes—
294#394C2318yes—
295#394C2318yes—
296#394C2318yes—
297#394C2318yes—
298#394C2318yes—
299#394C2318yes—
300#394C2318yes—
301#393C2318yes—
302#393C2318yes—
303#393C2318yes—
304#393C2318yes—
305#392C2314yes—
306#392C2318yes—
307#392C2318yes—
308#392C2318yes—
309#392C2318yes—
310#392C2318yes—
311#392C2318yes—
312#392C2314yes—
313#392C2314yes—
314#392C2318yes—
315#392C2314yes—
316#392C2318yes—
317#392C2318yes—
318#392C2314yes—
319#392C2314yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C2318yes—
324#391C2318yes—
325#391C2318yes—
326#391C2318yes—
327#391C2314yes—
328#391C2314yes—
329#390C2312yes—
330#390C2318yes—
331#390C2312yes—
332#390C2312yes—
333#390C2318yes—
334#390C2312yes—
335#390C2314yes—
336#390C2314yes—
337#390C2314yes—
338#390C2314yes—
339#390C2318yes—
340#390C2318yes—
341#390C2312yes—
342#390C2312yes—
343#390C2312yes—
344#390C2314yes—
345#390C2314yes—
346#390C2312yes—
347#390C2314yes—
348#390C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2318yes—
355#389C2314yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#389C2312yes—
360#389C2314yes—
361#388C2318yes—
362#388C2318yes—
363#388C2314yes—
364#388C2314yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2314yes—
372#388C2318yes—
373#388C2318yes—
374#388C2314yes—
375#388C2314yes—
376#388C2314yes—
377#388C2314yes—
378#388C2314yes—
379#388C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2314yes—
387#387C2314yes—
388#387C2318yes—
389#386C2318yes—
390#386C2318yes—
391#386C2318yes—
392#386C2318yes—
393#386C2318yes—
394#386C2314yes—
395#386C2314yes—
396#386C2318yes—
397#386C2318yes—
398#386C2318yes—
399#386C2318yes—
400#386C2318yes—
401#386C2314yes—
402#386C2314yes—
403#386C2318yes—
404#386C2314yes—
405#386C2314yes—
406#386C2318yes—
407#386C2318yes—
408#385C2318yes—
409#385C2318yes—
410#385C2314yes—
411#385C2314yes—
412#384C2312yes—
413#384C2312yes—
414#384C2312yes—
415#383C2312yes—
416#382C2314yes—
417#382C2314yes—
418#382C2311yescharacteristic
419#382C2311yescharacteristic
420#382C2312yes—
421#381C2314yes—
422#381C2318yes—
423#381C2318yes—
424#381C2312yes—
425#381C2312yes—
426#381C2312yes—
427#380C2314yes—
428#380C2314yes—
429#380C2314yes—
430#380C2314yes—
431#380C2314yes—
432#380C2312yes—
433#380C2314yes—
434#380C2312yes—
435#380C2314yes—
436#380C2312yes—
437#380C2318yes—
438#380C2314yes—
439#380C2312yes—
440#380C2312yes—
441#379C2314yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2312yes—
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2312yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2312yes—
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2312yes—
456C4×C4⋊C4C2312yes—
457C4×C4⋊C4C2311yescharacteristic
458C4×C22⋊C4C2312yes—
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2314yes—
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2314yes—
463C4×C22⋊C4C2318yes—
464C4×C22⋊C4C2314yes—
465C4×C22⋊C4C2314yes—
466C4×C22⋊C4C2314yes—
467C4×C22⋊C4C2318yes—
468C4×C22⋊C4C2312yes—
469C4×C22⋊C4C2312yes—
470C4×C22⋊C4C2312yes—
471C4×C22⋊C4C2314yes—
472C4×C22⋊C4C2314yes—
473C4×C22⋊C4C2314yes—
474C4×C22⋊C4C2314yes—
475C4×C22⋊C4C2314yes—
476C4×C22⋊C4C2314yes—
477C4×C22⋊C4C2314yes—
478C4×C22⋊C4C2312yes—
479C4×C22⋊C4C2312yes—
480#376C2311yescharacteristic
481#376C2312yes—
482#376C2312yes—
483#376C2311yescharacteristic
484C2×#95C2314yes—
485C2×#95C2312yes—
486C2×#95C2312yes—
487C43C2312yes—
488C43C2312yes—
489C25C2412yes—
490C2×#41—28no—
491C2×#41—28no—
492C2×#41—44no—
493C2×#41—44no—
494C2×#41—416no—
495C2×#41—416no—
496C2×#41—48no—
497C2×#41—416no—
498C22×Q8C2412yes—
499C22×Q8C2418yes—
500C22×Q8C2412yes—
501C22×D4—24no—
502C22×D4—24no—
503C22×D4—42no—
504C22×D4C2412yes—
505C22×D4C2412yes—
506C22×D4C2412yes—
507C22×D4C2411yescharacteristic
508C22×D4C2418yes—
509C22×D4C2412yes—
510C22×D4C2411yescharacteristic
511C22×D4C2412yes—
512C22×D4C2412yes—
513C22×D4C2414yes—
514C22×D4C2414yes—
515C22×D4C2418yes—
516C22×D4C2412yes—
517C22×D4C2418yes—
518C22×D4C2418yes—
519C22×D4C2418yes—
520C22×D4C2418yes—
521C23×C4—28no—
522C23×C4—48no—
523C23×C4C2412yes—
524C23×C4C2414yes—
525C23×C4C2412yes—
526C23×C4C2414yes—
527C23×C4C2414yes—
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2412yes—
531C23×C4C2412yes—
532C23×C4C2412yes—
533C23×C4C2414yes—
534C23×C4C2418yes—
535C23×C4C2414yes—
536C23×C4C2414yes—
537C23×C4C2411yescharacteristic
538C4⋊Q8—216no—
539C4⋊Q8—24no—
540C4⋊Q8—24no—
541C4⋊Q8—48no—
542#127—28no—
543#127—24no—
544#127—24no—
545#127—44no—
546#127—48no—
547#127—48no—
548#126—416no—
549#124—28no—
550#124—28no—
551#124—48no—
552#124—416no—
553#124—48no—
554#124—416no—
555#124—416no—
556#123—416no—
557#123—416no—
558C22⋊Q8—216no—
559C22⋊Q8—48no—
560C22⋊Q8—416no—
561#121—216no—
562#121—28no—
563#121—28no—
564#121—28no—
565#121—28no—
566#121—216no—
567#121—416no—
568#121—416no—
569#121—416no—
570#121—48no—
571#121—48no—
572#121—48no—
573#121—48no—
574#121—48no—
575#121—48no—
576#120—416no—
577#120—416no—
578C4×Q8—48no—
579C4×D4—28no—
580C4×D4—28no—
581C4×D4—28no—
582C4×D4—24no—
583C4×D4—24no—
584C4×D4—28no—
585C4×D4—24no—
586C4×D4—24no—
587C4×D4—28no—
588C4×D4—28no—
589C4×D4—28no—
590C4×D4—28no—
591C4×D4—28no—
592C4×D4—416no—
593C4×D4—44no—
594C4×D4—416no—
595C4×D4—48no—
596C4×D4—48no—
597C4×D4—48no—
598C4×D4—48no—
599C4×D4—416no—
600C4×D4—416no—
601#117—28no—
602#117—48no—
603#117—48no—
604#117—44no—
605#117—44no—
606C2×C4⋊C4—24no—
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2412yes—
633C2×C22⋊C4—28no—
634C2×C22⋊C4—48no—
635C2×C22⋊C4C2412yes—
636C2×C22⋊C4C2412yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2412yes—
639C2×C22⋊C4C2412yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2418yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2418yes—
675C2×C42—48no—
676C2×C42—48no—
677C2×C42#4118yescomplemented
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2414yes—
682C2×C42C2412yes—
683C2×C42C2414yes—
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2412yes—
687C2×C42C2414yes—
688C2×C42C2412yes—
689C2×C42C2414yes—
690C2×C42C2414yes—
691C2×C42C2414yes—
692C2×C42C2418yes—
693C2×C42C2414yes—
694C2×C42C2414yes—
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699#95C2411yescharacteristic
700#95C2411yescharacteristic
701#95C2414yes—
702#95C2412yes—
703#95C2412yes—
704#95C2414yes—
705#95C2414yes—
706#95C2418yes—
707#95C2411yescharacteristic
708#95C2411yescharacteristic
709#95C2412yes—
710#95C2412yes—
711#95C2412yes—
712#95C2414yes—
713#95C2412yes—
714#95C2414yes—
715#95C2412yes—
716#95C2412yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2418yes—
725#95C2418yes—
726#95C2414yes—
727#95C2418yes—
728#95C2418yes—
729#95C2418yes—
730#95C2418yes—
731#95C2418yes—
732#95C2418yes—
733#95C2418yes—
734C24—24no—
735C24—24no—
736C24—44no—
737C24—42no—
738C24—44no—
739C24C2512yes—
740C24C2514yes—
741C24C2514yes—
742C24C2511yescharacteristic
743C24C2512yes—
744#41—816no—
745#41—816no—
746#41—864no—
747C2×Q8—24no—
748C2×Q8—24no—
749C2×Q8—28no—
750C2×Q8—216no—
751C2×Q8—42no—
752C2×Q8—48no—
753C2×Q8—48no—
754C2×Q8—42no—
755C2×D4—216no—
756C2×D4—24no—
757C2×D4—28no—
758C2×D4—28no—
759C2×D4—216no—
760C2×D4—22no—
761C2×D4—24no—
762C2×D4—22no—
763C2×D4—24no—
764C2×D4—24no—
765C2×D4—24no—
766C2×D4—24no—
767C2×D4—24no—
768C2×D4—24no—
769C2×D4—24no—
770C2×D4—24no—
771C2×D4—24no—
772C2×D4—216no—
773C2×D4—28no—
774C2×D4—22no—
775C2×D4—22no—
776C2×D4—24no—
777C2×D4—22no—
778C2×D4—416no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—42no—
782C2×D4—48no—
783C2×D4—48no—
784C2×D4—48no—
785C2×D4—44no—
786C2×D4—48no—
787C2×D4—48no—
788C2×D4—48no—
789C2×D4—48no—
790C2×D4—48no—
791C2×D4—48no—
792C2×D4—48no—
793C2×D4—42no—
794C2×D4—48no—
795C2×D4—42no—
796C2×D4—44no—
797C2×D4—48no—
798C2×D4—48no—
799C2×D4—48no—
800C2×D4—48no—
801C2×D4—48no—
802C2×D4H(5,𝔽2)14yes—
803C22×C4—24no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—28no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—28no—
811C22×C4—28no—
812C22×C4—28no—
813C22×C4—28no—
814C22×C4—28no—
815C22×C4—28no—
816C22×C4—28no—
817C22×C4—28no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—28no—
821C22×C4—28no—
822C22×C4—216no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—42no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—48no—
832C22×C4—48no—
833C22×C4—48no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—816no—
838C22×C4C2×#4114yes—
839C22×C4C2×#4114yes—
840C22×C4C2×#4114yes—
841C22×C4C2514yes—
842C22×C4C2514yes—
843C22×C4C2514yes—
844C22×C4C2512yes—
845C22×C4C2514yes—
846C22×C4C2518yes—
847C22×C4C2512yes—
848C22×C4C2514yes—
849C22×C4C2512yes—
850C22×C4C2512yes—
851C22×C4C2512yes—
852C22×C4C2511yescharacteristic
853C22×C4C2511yescharacteristic
854C22×C4C2511yescharacteristic
855C22×C4C2511yescharacteristic
856C22×C4C2514yes—
857C22×C4C2512yes—
858C22×C4C2511yescharacteristic
859C22×C4C2511yescharacteristic
860C4⋊C4—24no—
861C4⋊C4—22no—
862C4⋊C4—22no—
863C4⋊C4—24no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—28no—
869C4⋊C4—24no—
870C4⋊C4—28no—
871C4⋊C4—216no—
872C4⋊C4—216no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—42no—
876C4⋊C4—44no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—48no—
882C4⋊C4—48no—
883C4⋊C4—48no—
884C4⋊C4—48no—
885C4⋊C4H(5,𝔽2)18yes—
886C22⋊C4—28no—
887C22⋊C4—216no—
888C22⋊C4—24no—
889C22⋊C4—24no—
890C22⋊C4—24no—
891C22⋊C4—24no—
892C22⋊C4—28no—
893C22⋊C4—28no—
894C22⋊C4—28no—
895C22⋊C4—28no—
896C22⋊C4—28no—
897C22⋊C4—28no—
898C22⋊C4—28no—
899C22⋊C4—216no—
900C22⋊C4—216no—
901C22⋊C4—24no—
902C22⋊C4—28no—
903C22⋊C4—28no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—42no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—48no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C22⋊C4—48no—
916C22⋊C4—48no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—48no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C42—24no—
927C42—24no—
928C42—24no—
929C42—28no—
930C42—28no—
931C42—24no—
932C42—24no—
933C42—24no—
934C42—24no—
935C42—44no—
936C42—44no—
937C42—44no—
938C42—44no—
939C42—42no—
940C42—44no—
941C42—44no—
942C42—48no—
943C42C2×#4114yes—
944C42C2×#4114yes—
945C42C2×#4114yes—
946C42C2×#4114yes—
947C23—22no—
948C23—22no—
949C23—21no—
950C23—24no—
951C23—22no—
952C23—22no—
953C23—24no—
954C23—21no—
955C23—22no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—28no—
962C23—24no—
963C23—22no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—28no—
971C23—22no—
972C23—48no—
973C23—48no—
974C23—84no—
975C23—88no—
976C23—88no—
977C23C22×#4112yes—
978C23C2×H(5,𝔽2)14yes—
979C23C2611yescharacteristic
980Q8—48no—
981Q8—816no—
982Q8—84no—
983D4—28no—
984D4—48no—
985D4—432no—
986D4—48no—
987D4—48no—
988D4—48no—
989D4—44no—
990D4—48no—
991D4—48no—
992D4—84no—
993D4—816no—
994D4—88no—
995D4—88no—
996D4—816no—
997D4—816no—
998D4—816no—
999D4—168no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—21no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—24no—
1008C2×C4—21no—
1009C2×C4—28no—
1010C2×C4—28no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—28no—
1025C2×C4—28no—
1026C2×C4—28no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—24no—
1033C2×C4—22no—
1034C2×C4—24no—
1035C2×C4—22no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—28no—
1041C2×C4—44no—
1042C2×C4—416no—
1043C2×C4—416no—
1044C2×C4—416no—
1045C2×C4—48no—
1046C2×C4—48no—
1047C2×C4—88no—
1048C2×C4—84no—
1049C2×C4—84no—
1050C2×C4—816no—
1051C2×C4—88no—
1052C2×C4—84no—
1053C2×C4—88no—
1054C2×C4C22×#4112yes—
1055C2×C4C22×#4112yes—
1056C2×C4C22×#4112yes—
1057C2×C4C22×#4112yes—
1058C2×C4C22×#4112yes—
1059C2×C4C22×#4112yes—
1060C2×C4C2×H(5,𝔽2)18yes—
1061C2×C4C2×H(5,𝔽2)12yes—
1062C2×C4C2×H(5,𝔽2)14yes—
1063C2×C4#58514yes—
1064C2×C4#58512yes—
1065C22—28no—
1066C22—22no—
1067C22—24no—
1068C22—22no—
1069C22—22no—
1070C22—42no—
1071C22—44no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—44no—
1076C22—48no—
1077C22—44no—
1078C22—44no—
1079C22—44no—
1080C22—48no—
1081C22—44no—
1082C22—44no—
1083C22—44no—
1084C22—42no—
1085C22—44no—
1086C22—42no—
1087C22—44no—
1088C22—44no—
1089C22—44no—
1090C22—44no—
1091C22—42no—
1092C22—816no—
1093C22C23×#4111yescharacteristic
1094C22C22×H(5,𝔽2)11yescharacteristic
1095C22C22×H(5,𝔽2)12yes—
1096C22C2×#58512yes—
1097C22C2×#58511yescharacteristic
1098C4—24no—
1099C4—28no—
1100C4—22no—
1101C4—22no—
1102C4—22no—
1103C4—22no—
1104C4—44no—
1105C4—42no—
1106C4—48no—
1107C4—42no—
1108C4—42no—
1109C4—44no—
1110C4—44no—
1111C4—44no—
1112C4—42no—
1113C4—42no—
1114C4—44no—
1115C4#349414yes—
1116C4#350814yes—
1117C2—44no—
1118C2—42no—
1119C2—84no—
1120C2—84no—
1121C2—82no—
1122C2#6268611yescharacteristic
1123C2C2×#349411yescharacteristic
1124C2C2×#350811yescharacteristic
1125C2#6301212yes—
1126C2#6302212yes—
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. #42071C2semidirect
2. #41980C2semidirect
3. #39562C2semidirect
4. #39500C2semidirect
5. #39268C2semidirect
6. #39185C2semidirect
7. #37782C2semidirect
8. #37772C2semidirect
9. #37669C2semidirect
10. #37626C2semidirect
11. #37618C2semidirect
12. #36498C2semidirect
13. #36149C2semidirect
14. #36147C2semidirect
15. #35684C2semidirect
16. #35196C2semidirect
17. #35192C2semidirect
18. #35170C2semidirect
19. #35165C2semidirect
20. #34936C2semidirect
21. #34925C2semidirect
22. #34226C2semidirect
23. #34155C2semidirect
24. #34126C2semidirect
25. C2×#542C22semidirect
30. C2×#532C22semidirect
33. #2864C22semidirect
34. #2862C22semidirect
35. #2857C22semidirect
36. #2855C22semidirect
38. #2850C22semidirect
40. #2828C22semidirect
42. #2808C22semidirect
43. #2798C22semidirect
44. #2796C22semidirect
45. #2733C22semidirect
46. #2730C22semidirect
47. #2714C22semidirect
55. #2663C22semidirect
56. #2657C22semidirect
57. #2649C22semidirect
58. #2640C22semidirect
59. #2635C22semidirect
60. #2631C22semidirect
61. #2624C22semidirect
62. #2624C22semidirect
64. #2619C22semidirect
67. #2607C22semidirect
68. #2605C22semidirect
69. #2597C22semidirect
70. #2571C22semidirect
72. #2555C22semidirect
73. #2551C22semidirect
75. #2547C22semidirect
82. #2541C22semidirect
89. #2535C22semidirect
90. #2535C22semidirect
91. #2521C22semidirect
92. #2516C22semidirect
94. #2497C22semidirect
95. #2496C22semidirect
96. #2492C22semidirect
98. #2491C22semidirect
99. #2491C22semidirect
100. #2467C22semidirect
101. #2467C22semidirect
103. #2459C22semidirect
104. #2459C22semidirect
106. #2457C22semidirect
107. #2456C22semidirect
108. #2447C22semidirect
109. #2444C22semidirect
117. #2428C22semidirect
118. #2428C22semidirect
119. #2427C22semidirect
120. #2427C22semidirect
121. #2426C22semidirect
123. #2421C22semidirect
125. #2420C22semidirect
126. #2420C22semidirect
127. #2407C22semidirect
130. #2388C22semidirect
131. #2372C22semidirect
132. #2372C22semidirect
133. #2369C22semidirect
134. #2367C22semidirect
135. #2366C22semidirect
136. #2364C22semidirect
143. #2357C22semidirect
148. #2349C22semidirect
153. #2339C22semidirect
155. #2331C22semidirect
158. #2323C22semidirect
159. #2319C22semidirect
160. #2314C22semidirect
162. C4×C4⋊Q8C22semidirect
165. C4×#127C22semidirect
166. C4×#121C22semidirect
167. C4×#121C22semidirect
170. #2293C22semidirect
171. #2293C22semidirect
176. #2275C22semidirect
178. C42×D4C22semidirect
179. C42×D4C22semidirect
677. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
#420712
#419802
#395622
#395002
#392682
#391852
#377822
#377722
#376692
#376262
#376182
#364982
#361492
#361472
#356842
#351962
#351922
#351702
#351652
#349362
#349252
#342262
#341552
#341262