Finite Group Databasebeta

← #7746778

Subgroups — #7746778

Order 512.

5726 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45423C212yesmaximal, complemented
2#45188C214yesmaximal, complemented
3#45105C214yesmaximal, complemented
4#45043C214yesmaximal, complemented
5#44965C212yesmaximal, complemented
6#44901C214yesmaximal, complemented
7#44887C214yesmaximal, complemented
8#42982C212yesmaximal, complemented
9#42975C212yesmaximal, complemented
10#42471C214yesmaximal, complemented
11#42467C214yesmaximal, complemented
12#36211C212yesmaximal, complemented
13#36187C212yesmaximal, complemented
14#36182C212yesmaximal, complemented
15#36182C212yesmaximal, complemented
16#35830C214yesmaximal, complemented
17#35823C214yesmaximal, complemented
18#35785C214yesmaximal, complemented
19#35294C211yesmaximal, characteristic, complemented
20#35272C212yesmaximal, complemented
21#34547C211yesmaximal, characteristic, complemented
22#34210C211yesmaximal, characteristic, complemented
23#34188C212yesmaximal, complemented
24C2×#555C2214yescomplemented
25C2×#553C2214yescomplemented
26C2×#553C2214yescomplemented
27C2×#535C2214yes—
28C22×#127C2211yescharacteristic
29C2×#518C2212yes—
30C2×C4×#41C2212yes—
31#2868C2211yescharacteristic, complemented
32#2859C2211yescharacteristic, complemented
33#2859C2212yescomplemented
34#2856C2212yes—
35#2856C2212yes—
36#2856C2212yes—
37#2856C2212yes—
38#2830C2214yescomplemented
39#2828C2214yescomplemented
40#2797C2218yescomplemented
41#2786C2218yescomplemented
42#2751C2218yescomplemented
43#2736C2214yes—
44#2735C2214yes—
45#2715C2218yescomplemented
46#2712C2218yescomplemented
47#2709C2218yescomplemented
48#2705C2218yescomplemented
49#2685C2218yes—
50#2684C2218yes—
51#2673C2218yescomplemented
52#2670C2214yes—
53#2668C2214yes—
54#2662C2218yescomplemented
55#2648C2218yescomplemented
56#2630C2218yescomplemented
57#2629C2212yes—
58#2628C2212yes—
59#2619C2214yes—
60#2619C2214yes—
61#2601C2218yescomplemented
62#2595C2218yescomplemented
63#2593C2214yescomplemented
64#2570C2214yescomplemented
65#2566C2214yescomplemented
66#2566C2214yescomplemented
67#2563C2214yescomplemented
68#2557C2218yescomplemented
69#2555C2214yescomplemented
70#2550C2214yescomplemented
71#2548C2214yes—
72#2548C2214yes—
73#2544C2218yescomplemented
74#2541C2214yes—
75#2541C2214yes—
76#2537C2214yescomplemented
77#2537C2214yescomplemented
78#2535C2214yescomplemented
79#2534C2218yes—
80#2513C2214yescomplemented
81#2513C2214yescomplemented
82#2512C2214yescomplemented
83#2512C2214yescomplemented
84#2512C2214yescomplemented
85#2512C2214yescomplemented
86#2504C2214yescomplemented
87#2504C2214yescomplemented
88#2500C2214yescomplemented
89#2500C2214yescomplemented
90#2500C2214yescomplemented
91#2500C2214yescomplemented
92#2491C2214yescomplemented
93#2491C2214yescomplemented
94#2491C2214yescomplemented
95#2491C2214yescomplemented
96#2490C2214yescomplemented
97#2490C2214yescomplemented
98#2480C2218yes—
99#2474C2218yescomplemented
100#2468C2218yescomplemented
101#2467C2218yescomplemented
102#2464C2218yescomplemented
103#2459C2218yescomplemented
104#2441C2214yes—
105#2439C2214yes—
106#2428C2218yescomplemented
107#2424C2218yes—
108#2422C2214yescomplemented
109#2422C2214yescomplemented
110#2422C2214yescomplemented
111#2422C2214yescomplemented
112#2420C2214yescomplemented
113#2420C2214yescomplemented
114#2416C2214yescomplemented
115#2416C2214yescomplemented
116#2416C2214yescomplemented
117#2416C2214yescomplemented
118#2414C2214yescomplemented
119#2414C2214yescomplemented
120#2411C2218yes—
121#2408C2214yes—
122#2408C2214yes—
123#2408C2214yes—
124#2408C2214yes—
125#2399C2211yescharacteristic, complemented
126#2398C2212yescomplemented
127#2397C2211yescharacteristic, complemented
128#2396C2212yescomplemented
129#2396C2212yescomplemented
130#2395C2212yes—
131#2395C2212yes—
132#2392C2211yescharacteristic
133#2392C2211yescharacteristic
134#2392C2212yes—
135#2392C2218yescomplemented
136#2392C2212yescomplemented
137#2392C2212yescomplemented
138#2388C2212yes—
139#2388C2212yes—
140#2366C2214yes—
141#2366C2214yes—
142#2363C2214yescomplemented
143#2363C2214yescomplemented
144#2361C2214yescomplemented
145#2361C2214yescomplemented
146#2361C2214yescomplemented
147#2361C2214yescomplemented
148#2357C2214yescomplemented
149#2355C2214yescomplemented
150#2355C2214yescomplemented
151#2354C2214yes—
152#2354C2214yes—
153#2354C2214yescomplemented
154#2354C2214yescomplemented
155#2352C2214yes—
156#2352C2214yes—
157#2352C2214yescomplemented
158#2352C2214yescomplemented
159D4×C22⋊C4C2214yes—
160D4×C22⋊C4C2214yes—
161#2331C2212yescomplemented
162#2330C2212yescomplemented
163#2328C2212yes—
164#2328C2212yes—
165#2314C2214yes—
166#2314C2214yescomplemented
167#2311C2214yes—
168#2309C2214yes—
169#2309C2212yes—
170C4×#127C2212yes—
171C4×#127C2212yes—
172#2285C2211yescharacteristic
173#2285C2212yes—
174#2285C2212yescomplemented
175#2285C2212yescomplemented
176#2285C2212yescomplemented
177C2×#384C2212yescomplemented
178#2274C2214yescomplemented
179C42×D4C2211yescharacteristic, complemented
180C42×D4C2212yescomplemented
181C42×D4C2211yescharacteristic, complemented
182C4×#117C2211yescharacteristic
183C22×#41C2312yes—
184C23×D4C2314yes—
185C23×D4C2312yes—
186#555—416no—
187#553—416no—
188#553—416no—
189#535—416no—
190C2×C4⋊Q8C2314yes—
191C2×C4⋊Q8C2312yes—
192C2×#127—28no—
193C2×#127C2312yes—
194C2×#127C2312yes—
195C2×#127C2314yes—
196C2×#127C2318yes—
197C2×#126C2318yes—
198C2×#126C2318yes—
199C2×#125C2312yes—
200C2×#125C2314yes—
201C2×#124C2318yes—
202C2×#124C2318yes—
203C2×#124C2318yes—
204C2×#123C2318yes—
205C2×#123C2318yes—
206C2×#121C2314yes—
207C2×#121C2314yes—
208C2×#121C2314yes—
209C2×#121C2314yes—
210C2×#121C2314yes—
211C2×#121C2314yes—
212C2×#121C2314yes—
213C2×#121C2314yes—
214C2×#121C2314yes—
215C2×#121C2314yes—
216C2×#121C2314yes—
217C2×#121C2314yes—
218C2×#121C2318yes—
219C2×#121C2318yes—
220C2×#121C2318yes—
221C2×#120C2318yes—
222C2×#120C2318yes—
223#518—48no—
224C4×#41—216no—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2312yes—
227C2×C4×D4C2314yes—
228C2×C4×D4C2312yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2312yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2312yes—
234C2×C4×D4C2312yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2314yes—
242C2×C4×D4C2318yes—
243C2×C4×D4C2318yes—
244C2×C4×D4C2318yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×#117C2312yes—
250C2×#117C2314yes—
251C2×#117C2312yes—
252C2×#117C2312yes—
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2312yes—
256C2×#117C2314yes—
257C2×#117C2318yes—
258C2×#117C2314yes—
259C2×#117C2314yes—
260C22×C4⋊C4C2314yes—
261C22×C4⋊C4C2314yes—
262C22×C4⋊C4C2314yes—
263C22×C22⋊C4C2318yes—
264C22×C42C2312yes—
265C22×C42C2312yes—
266C22×C42C2311yescharacteristic
267#400C2314yes—
268#400C2312yes—
269#400C2312yes—
270#399C2314yes—
271#399C2312yes—
272#399C2312yes—
273#398C2318yes—
274#398C2311yescharacteristic
275#398C2311yescharacteristic
276#398C2312yes—
277#398C2312yes—
278#398C2312yes—
279#397C2318yes—
280#397C2318yes—
281#397C2318yes—
282#397C2318yes—
283#397C2318yes—
284#397C2318yes—
285#397C2311yescharacteristic
286#397C2312yes—
287#397C2311yescharacteristic
288#397C2312yes—
289#397C2312yes—
290#397C2318yes—
291#396C2318yes—
292#396C2318yes—
293#396C2318yes—
294#396C2318yes—
295#396C2318yes—
296#396C2312yes—
297#396C2312yes—
298#396C2312yes—
299#396C2312yes—
300#395C2314yes—
301#395C2312yes—
302#395C2312yes—
303#394C2311yescharacteristic
304#394C2318yes—
305#394C2318yes—
306#394C2318yes—
307#394C2318yes—
308#394C2318yes—
309#394C2318yes—
310#394C2318yes—
311#394C2318yes—
312#394C2312yes—
313#394C2312yes—
314#394C2312yes—
315#394C2312yes—
316#394C2312yes—
317#394C2312yes—
318#394C2312yes—
319#394C2311yescharacteristic
320#394C2318yes—
321#394C2318yes—
322#394C2318yes—
323#394C2318yes—
324#394C2318yes—
325#394C2318yes—
326#393C2318yes—
327#393C2318yes—
328#393C2314yes—
329#393C2312yes—
330#393C2312yes—
331#392C2318yes—
332#392C2318yes—
333#392C2318yes—
334#392C2318yes—
335#392C2318yes—
336#392C2311yescharacteristic
337#392C2311yescharacteristic
338#392C2312yes—
339#392C2312yes—
340#392C2312yes—
341#391C2318yes—
342#391C2318yes—
343#390C2314yes—
344#390C2314yes—
345#390C2314yes—
346#390C2314yes—
347#390C2314yes—
348#390C2314yes—
349#390C2314yes—
350#390C2314yes—
351#390C2314yes—
352#390C2314yes—
353#390C2314yes—
354#390C2318yes—
355#390C2314yes—
356#390C2314yes—
357#390C2318yes—
358#390C2314yes—
359#390C2314yes—
360#390C2314yes—
361#390C2318yes—
362#390C2314yes—
363#390C2314yes—
364#390C2314yes—
365#390C2314yes—
366#390C2318yes—
367#390C2318yes—
368#389C2314yes—
369#389C2314yes—
370#389C2318yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2314yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#386C2318yes—
398#386C2318yes—
399#386C2318yes—
400#386C2318yes—
401#386C2318yes—
402#386C2318yes—
403#386C2318yes—
404#386C2318yes—
405#386C2318yes—
406#386C2318yes—
407#386C2318yes—
408#386C2318yes—
409#385C2318yes—
410#385C2318yes—
411#385C2318yes—
412#385C2318yes—
413#384C2312yes—
414#384C2314yes—
415#384C2314yes—
416#384C2314yes—
417#384C2314yes—
418#384C2312yes—
419#384C2312yes—
420#384C2312yes—
421#382C2314yes—
422#382C2314yes—
423#382C2314yes—
424#382C2314yes—
425#382C2314yes—
426#382C2312yes—
427#382C2312yes—
428#381C2318yes—
429#380C2318yes—
430#380C2318yes—
431#380C2314yes—
432#380C2314yes—
433#380C2314yes—
434#380C2314yes—
435#380C2314yes—
436#380C2314yes—
437#380C2314yes—
438#380C2314yes—
439#380C2314yes—
440#379C2314yes—
441#379C2314yes—
442#379C2318yes—
443#379C2318yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2318yes—
454C4×C4⋊C4C2318yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C22⋊C4C2312yes—
465C4×C22⋊C4C2312yes—
466C4×C22⋊C4C2318yes—
467C4×C22⋊C4C2318yes—
468C4×C22⋊C4C2318yes—
469C4×C22⋊C4C2312yes—
470C4×C22⋊C4C2312yes—
471C4×C22⋊C4C2312yes—
472C4×C22⋊C4C2312yes—
473C4×C22⋊C4C2312yes—
474C4×C22⋊C4C2312yes—
475C4×C22⋊C4C2312yes—
476C4×C22⋊C4C2312yes—
477C4×C22⋊C4C2312yes—
478C4×C22⋊C4C2312yes—
479C4×C22⋊C4C2312yes—
480C4×C22⋊C4C2312yes—
481#376C2311yescharacteristic
482#376C2311yescharacteristic
483C43C2311yescharacteristic
484C43C2311yescharacteristic
485C25C2414yes—
486C2×#41—28no—
487C2×#41—28no—
488C2×#41—44no—
489C22×Q8C2412yes—
490C22×Q8C2414yes—
491C22×D4—28no—
492C22×D4—216no—
493C22×D4—44no—
494C22×D4—44no—
495C22×D4—48no—
496C22×D4—48no—
497C22×D4C2414yes—
498C22×D4C2414yes—
499C22×D4C2414yes—
500C22×D4C2411yescharacteristic
501C22×D4C2412yes—
502C22×D4C2412yes—
503C22×D4C2412yes—
504C22×D4C2412yes—
505C22×D4C2414yes—
506C22×D4C2418yes—
507C22×D4C2418yes—
508C22×D4C2418yes—
509C22×D4C2411yescharacteristic
510C22×D4C2418yes—
511C22×D4C2418yes—
512C23×C4C2412yes—
513C23×C4C2412yes—
514C23×C4C2412yes—
515C23×C4C2412yes—
516C23×C4C2412yes—
517C23×C4C2411yescharacteristic
518C23×C4C2412yes—
519C23×C4C2412yes—
520C23×C4C2418yes—
521C23×C4C2418yes—
522C23×C4C2418yes—
523C4⋊Q8—44no—
524C4⋊Q8—48no—
525#127—28no—
526#127—216no—
527#127—28no—
528#127—416no—
529#126—416no—
530#126—416no—
531#125—28no—
532#125—48no—
533#124—416no—
534#124—416no—
535#124—416no—
536#123—416no—
537#123—416no—
538#121—216no—
539#121—216no—
540#121—416no—
541#121—416no—
542#121—416no—
543#121—48no—
544#121—48no—
545#121—48no—
546#121—48no—
547#121—48no—
548#121—48no—
549#121—48no—
550#121—48no—
551#121—48no—
552#121—48no—
553#120—416no—
554#120—416no—
555C4×Q8—28no—
556C4×Q8—28no—
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—216no—
566C4×D4—28no—
567C4×D4—416no—
568C4×D4—48no—
569C4×D4—48no—
570C4×D4—48no—
571C4×D4—48no—
572C4×D4—48no—
573C4×D4—42no—
574C4×D4—42no—
575C4×D4—44no—
576C4×D4—44no—
577C4×D4—416no—
578C4×D4—416no—
579#117—28no—
580#117—216no—
581#117—28no—
582#117—28no—
583#117—24no—
584#117—42no—
585#117—416no—
586#117—44no—
587#117—48no—
588#117—48no—
589#117—48no—
590C2×C4⋊C4—48no—
591C2×C4⋊C4—48no—
592C2×C4⋊C4—48no—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2414yes—
626C2×C22⋊C4—416no—
627C2×C22⋊C4C2412yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2412yes—
630C2×C22⋊C4C2412yes—
631C2×C22⋊C4C2412yes—
632C2×C22⋊C4C2412yes—
633C2×C22⋊C4C2412yes—
634C2×C22⋊C4C2412yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2412yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2412yes—
641C2×C22⋊C4C2412yes—
642C2×C22⋊C4C2412yes—
643C2×C22⋊C4C2412yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2411yescharacteristic
651C2×C22⋊C4C2411yescharacteristic
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2412yes—
660C2×C22⋊C4C2412yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2418yes—
671C2×C42—28no—
672C2×C42—28no—
673C2×C42#4118yes—
674C2×C42C2418yes—
675C2×C42C2412yes—
676C2×C42C2412yes—
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2412yes—
681C2×C42C2412yes—
682C2×C42C2412yes—
683C2×C42C2412yes—
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2412yes—
687C2×C42C2412yes—
688C2×C42C2418yes—
689C2×C42C2414yes—
690C2×C42C2418yes—
691C2×C42C2418yes—
692C2×C42C2412yes—
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696#95C2412yes—
697#95C2412yes—
698#95C2412yes—
699#95C2412yes—
700#95C2412yes—
701#95C2412yes—
702#95C2412yes—
703#95C2412yes—
704#95C2412yes—
705#95C2412yes—
706#95C2411yescharacteristic
707#95C2412yes—
708#95C2411yescharacteristic
709#95C2412yes—
710#95C2412yes—
711#95C2411yescharacteristic
712#95C2412yes—
713#95C2411yescharacteristic
714#95C2418yes—
715#95C2418yes—
716#95C2418yes—
717#95C2418yes—
718#95C2418yes—
719#95C2418yes—
720#95C2418yes—
721#95C2418yes—
722#95C2418yes—
723#95C2418yes—
724#95C2414yes—
725#95C2414yes—
726#95C2418yes—
727C24—28no—
728C24—44no—
729C24—44no—
730C24—48no—
731C24—48no—
732C24C2518yes—
733C24C2512yes—
734C24C2511yescharacteristic
735C24C2512yes—
736#41—432no—
737C2×Q8—24no—
738C2×Q8—24no—
739C2×Q8—42no—
740C2×Q8—48no—
741C2×Q8—44no—
742C2×D4—24no—
743C2×D4—24no—
744C2×D4—24no—
745C2×D4—24no—
746C2×D4—24no—
747C2×D4—24no—
748C2×D4—216no—
749C2×D4—216no—
750C2×D4—24no—
751C2×D4—28no—
752C2×D4—28no—
753C2×D4—28no—
754C2×D4—28no—
755C2×D4—216no—
756C2×D4—28no—
757C2×D4—24no—
758C2×D4—28no—
759C2×D4—28no—
760C2×D4—24no—
761C2×D4—28no—
762C2×D4—28no—
763C2×D4—28no—
764C2×D4—44no—
765C2×D4—42no—
766C2×D4—42no—
767C2×D4—41no—
768C2×D4—41no—
769C2×D4—44no—
770C2×D4—42no—
771C2×D4—42no—
772C2×D4—42no—
773C2×D4—432no—
774C2×D4—48no—
775C2×D4—48no—
776C2×D4—48no—
777C2×D4—48no—
778C2×D4—48no—
779C2×D4—48no—
780C2×D4—48no—
781C2×D4—48no—
782C2×D4—48no—
783C2×D4—48no—
784C2×D4—48no—
785C2×D4—48no—
786C2×D4—832no—
787C22×C4—24no—
788C22×C4—22no—
789C22×C4—24no—
790C22×C4—24no—
791C22×C4—22no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—216no—
809C22×C4—48no—
810C22×C4—48no—
811C22×C4—48no—
812C22×C4—48no—
813C22×C4—48no—
814C22×C4—48no—
815C22×C4—48no—
816C22×C4—48no—
817C22×C4C2×#4118yes—
818C22×C4C2×#4114yes—
819C22×C4H(5,𝔽2)18yes—
820C22×C4C2511yescharacteristic
821C22×C4C2512yes—
822C22×C4C2511yescharacteristic
823C22×C4C2511yescharacteristic
824C22×C4C2512yes—
825C22×C4C2512yes—
826C22×C4C2512yes—
827C22×C4C2518yes—
828C22×C4C2518yes—
829C22×C4C2512yes—
830C22×C4C2512yes—
831C22×C4C2518yes—
832C22×C4C2511yescharacteristic
833C22×C4C2512yes—
834C22×C4C2511yescharacteristic
835C22×C4C2512yes—
836C22×C4C2512yes—
837C22×C4C2512yes—
838C22×C4C2511yescharacteristic
839C4⋊C4—24no—
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—24no—
844C4⋊C4—24no—
845C4⋊C4—28no—
846C4⋊C4—28no—
847C4⋊C4—28no—
848C4⋊C4—28no—
849C4⋊C4—24no—
850C4⋊C4—28no—
851C4⋊C4—24no—
852C4⋊C4—28no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—216no—
856C4⋊C4—28no—
857C4⋊C4—28no—
858C4⋊C4—28no—
859C4⋊C4—48no—
860C4⋊C4—48no—
861C4⋊C4—48no—
862C4⋊C4—41no—
863C4⋊C4—41no—
864C4⋊C4—48no—
865C4⋊C4—42no—
866C4⋊C4—42no—
867C4⋊C4—41no—
868C4⋊C4—41no—
869C4⋊C4—48no—
870C4⋊C4—48no—
871C4⋊C4—44no—
872C22⋊C4—24no—
873C22⋊C4—24no—
874C22⋊C4—216no—
875C22⋊C4—24no—
876C22⋊C4—24no—
877C22⋊C4—24no—
878C22⋊C4—24no—
879C22⋊C4—24no—
880C22⋊C4—24no—
881C22⋊C4—24no—
882C22⋊C4—216no—
883C22⋊C4—216no—
884C22⋊C4—24no—
885C22⋊C4—24no—
886C22⋊C4—24no—
887C22⋊C4—24no—
888C22⋊C4—216no—
889C22⋊C4—44no—
890C22⋊C4—48no—
891C22⋊C4—41no—
892C22⋊C4—41no—
893C22⋊C4—48no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C22⋊C4—48no—
897C22⋊C4—42no—
898C22⋊C4—48no—
899C22⋊C4—42no—
900C22⋊C4—48no—
901C22⋊C4—42no—
902C22⋊C4—42no—
903C22⋊C4—42no—
904C22⋊C4—42no—
905C22⋊C4—48no—
906C22⋊C4—48no—
907C22⋊C4—48no—
908C22⋊C4—48no—
909C22⋊C4—48no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C42—24no—
917C42—24no—
918C42—24no—
919C42—24no—
920C42—24no—
921C42—24no—
922C42—216no—
923C42—22no—
924C42—24no—
925C42—24no—
926C42—22no—
927C42—22no—
928C42—24no—
929C42—24no—
930C42—48no—
931C42—44no—
932C42—48no—
933C42—48no—
934C42C2×#4114yes—
935C42C2×#4118yes—
936C42C2×#4114yes—
937C42H(5,𝔽2)14yes—
938C23—22no—
939C23—21no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—21no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—28no—
950C23—22no—
951C23—22no—
952C23—28no—
953C23—28no—
954C23—28no—
955C23—22no—
956C23—22no—
957C23—28no—
958C23—28no—
959C23—28no—
960C23—22no—
961C23—22no—
962C23—416no—
963C23—816no—
964C23—168no—
965C23—164no—
966C23—164no—
967C23C22×#4112yes—
968C23C2×H(5,𝔽2)14yes—
969C23C2611yescharacteristic
970Q8—48no—
971Q8—164no—
972D4—48no—
973D4—48no—
974D4—48no—
975D4—416no—
976D4—44no—
977D4—48no—
978D4—44no—
979D4—416no—
980D4—416no—
981D4—416no—
982D4—816no—
983D4—816no—
984D4—816no—
985D4—168no—
986D4—168no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—21no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—216no—
996C2×C4—216no—
997C2×C4—28no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—28no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—28no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—28no—
1012C2×C4—28no—
1013C2×C4—28no—
1014C2×C4—28no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—22no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—28no—
1030C2×C4—28no—
1031C2×C4—28no—
1032C2×C4—22no—
1033C2×C4—48no—
1034C2×C4—48no—
1035C2×C4—48no—
1036C2×C4—48no—
1037C2×C4—48no—
1038C2×C4—816no—
1039C2×C4—168no—
1040C2×C4—168no—
1041C2×C4C22×#4112yes—
1042C2×C4C22×#4114yes—
1043C2×C4C22×#4114yes—
1044C2×C4C22×#4112yes—
1045C2×C4C2×H(5,𝔽2)14yes—
1046C2×C4C2×H(5,𝔽2)14yes—
1047C2×C4C2×H(5,𝔽2)14yes—
1048C2×C4C2×H(5,𝔽2)12yes—
1049C2×C4#58514yes—
1050C2×C4#58512yes—
1051C22—22no—
1052C22—24no—
1053C22—24no—
1054C22—24no—
1055C22—24no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—41no—
1061C22—42no—
1062C22—41no—
1063C22—42no—
1064C22—48no—
1065C22—42no—
1066C22—42no—
1067C22—48no—
1068C22—48no—
1069C22—48no—
1070C22—48no—
1071C22—42no—
1072C22—48no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—48no—
1077C22—1616no—
1078C22C23×#4111yescharacteristic
1079C22C22×H(5,𝔽2)11yescharacteristic
1080C22C22×H(5,𝔽2)12yes—
1081C22C2×#58511yescharacteristic
1082C22C2×#58512yes—
1083C4—22no—
1084C4—24no—
1085C4—24no—
1086C4—24no—
1087C4—42no—
1088C4—42no—
1089C4—42no—
1090C4—42no—
1091C4—42no—
1092C4—48no—
1093C4—42no—
1094C4—48no—
1095C4—41no—
1096C4—48no—
1097C4—41no—
1098C4—41no—
1099C4—41no—
1100C4#349418yes—
1101C4#350614yes—
1102C2—44no—
1103C2—42no—
1104C2—82no—
1105C2—88no—
1106C2C2×#350611yescharacteristic
1107C2C2×#349412yes—
1108C2#6283412yes—
1109C2#6283411yescharacteristic
1110C2#6283911yescharacteristic
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. #45423C2semidirect
2. #45188C2semidirect
3. #45105C2semidirect
4. #45043C2semidirect
5. #44965C2semidirect
6. #44901C2semidirect
7. #44887C2semidirect
8. #42982C2semidirect
9. #42975C2semidirect
10. #42471C2semidirect
11. #42467C2semidirect
12. #36211C2semidirect
13. #36187C2semidirect
14. #36182C2semidirect
15. #36182C2semidirect
16. #35830C2semidirect
17. #35823C2semidirect
18. #35785C2semidirect
19. #35294C2semidirect
20. #35272C2semidirect
21. #34547C2semidirect
22. #34210C2semidirect
23. #34188C2semidirect
24. C2×#555C22semidirect
25. C2×#553C22semidirect
26. C2×#553C22semidirect
31. #2868C22semidirect
32. #2859C22semidirect
33. #2859C22semidirect
38. #2830C22semidirect
39. #2828C22semidirect
40. #2797C22semidirect
41. #2786C22semidirect
42. #2751C22semidirect
45. #2715C22semidirect
46. #2712C22semidirect
47. #2709C22semidirect
48. #2705C22semidirect
51. #2673C22semidirect
54. #2662C22semidirect
55. #2648C22semidirect
56. #2630C22semidirect
61. #2601C22semidirect
62. #2595C22semidirect
63. #2593C22semidirect
64. #2570C22semidirect
65. #2566C22semidirect
66. #2566C22semidirect
67. #2563C22semidirect
68. #2557C22semidirect
69. #2555C22semidirect
70. #2550C22semidirect
73. #2544C22semidirect
76. #2537C22semidirect
77. #2537C22semidirect
78. #2535C22semidirect
80. #2513C22semidirect
81. #2513C22semidirect
82. #2512C22semidirect
83. #2512C22semidirect
84. #2512C22semidirect
85. #2512C22semidirect
86. #2504C22semidirect
87. #2504C22semidirect
88. #2500C22semidirect
89. #2500C22semidirect
90. #2500C22semidirect
91. #2500C22semidirect
92. #2491C22semidirect
93. #2491C22semidirect
94. #2491C22semidirect
95. #2491C22semidirect
96. #2490C22semidirect
97. #2490C22semidirect
99. #2474C22semidirect
100. #2468C22semidirect
101. #2467C22semidirect
102. #2464C22semidirect
103. #2459C22semidirect
106. #2428C22semidirect
108. #2422C22semidirect
109. #2422C22semidirect
110. #2422C22semidirect
111. #2422C22semidirect
112. #2420C22semidirect
113. #2420C22semidirect
114. #2416C22semidirect
115. #2416C22semidirect
116. #2416C22semidirect
117. #2416C22semidirect
118. #2414C22semidirect
119. #2414C22semidirect
125. #2399C22semidirect
126. #2398C22semidirect
127. #2397C22semidirect
128. #2396C22semidirect
129. #2396C22semidirect
135. #2392C22semidirect
136. #2392C22semidirect
137. #2392C22semidirect
142. #2363C22semidirect
143. #2363C22semidirect
144. #2361C22semidirect
145. #2361C22semidirect
146. #2361C22semidirect
147. #2361C22semidirect
148. #2357C22semidirect
149. #2355C22semidirect
150. #2355C22semidirect
153. #2354C22semidirect
154. #2354C22semidirect
157. #2352C22semidirect
158. #2352C22semidirect
161. #2331C22semidirect
162. #2330C22semidirect
166. #2314C22semidirect
174. #2285C22semidirect
175. #2285C22semidirect
176. #2285C22semidirect
177. C2×#384C22semidirect
178. #2274C22semidirect
179. C42×D4C22semidirect
180. C42×D4C22semidirect
181. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#454232
#451882
#451052
#450432
#449652
#449012
#448872
#429822
#429752
#424712
#424672
#362112
#361872
#361822
#358302
#358232
#357852
#352942
#352722
#345472
#342102
#341882