Subgroups — #37589168

Order 24512.

248 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27133888	C₂	1	2	yes	maximal, complemented
2	#27133874	C₂	1	6	yes	maximal, complemented
3	#27133863	C₂	1	3	yes	maximal, complemented
4	C₂×Dic₁₅₃₂	C₂	1	3	yes	maximal, complemented
5	#131×C₃₈₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#20259457	C₂²	1	6	yes	—
7	#20259456	—	2	6	no	—
8	C₂×Dic₇₆₆	C₂²	1	6	yes	—
9	Q₈×D₃₈₃	—	2	2	no	—
10	Dic₁₅₃₂	C₂²	1	3	yes	—
11	Dic₁₅₃₂	C₂²	1	6	yes	—
12	#20259446	C₂²	1	6	yes	—
13	D₃₀₆₄	C₂²	1	1	yes	characteristic
14	#41×C₃₈₃	C₂²	1	1	yes	characteristic
15	M₁₆×C₃₈₃	C₂²	1	3	yes	—
16	C₂×C₈×C₃₈₃	C₂²	1	3	yes	—
17	Dic₇₆₆	—	2	6	no	—
18	Dic₇₆₆	C₂³	1	6	yes	—
19	D₁₅₃₂	C₂³	1	2	yes	—
20	C₂²⋊D₃₈₃	—	2	6	no	—
21	C₂×Dic₃₈₃	—	2	6	no	—
22	C₄×D₃₈₃	—	2	6	no	—
23	Q₈×C₃₈₃	D₄	1	1	yes	characteristic
24	D₄×C₃₈₃	D₄	1	3	yes	—
25	C₂×C₄×C₃₈₃	C₂³	1	3	yes	—
26	C₈×C₃₈₃	C₂³	1	1	yes	characteristic
27	C₈×C₃₈₃	C₂³	1	3	yes	—
28	C₂²×C₃₈₃	C₂×D₄	1	3	yes	—
29	C₂×D₃₈₃	—	2	2	no	—
30	C₄×C₃₈₃	C₂×D₄	1	3	yes	—
31	C₄×C₃₈₃	C₂⁴	1	1	yes	characteristic
32	Dic₃₈₃	—	2	6	no	—
33	C₂×C₃₈₃	—	2	3	no	—
34	C₂×C₃₈₃	C₂²×D₄	1	1	yes	characteristic
35	D₃₈₃	—	4	2	no	—
36	C₃₈₃	#578	1	1	yes	characteristic, complemented, Sylow
37	#578	—	383	1	no	maximal, Sylow
38	2₋¹⁺⁴	—	383	2	no	—
39	#137	—	383	6	no	—
40	#135	—	383	3	no	—
41	C₂×Q₁₆	—	383	3	no	—
42	#131	D₃₈₃	1	1	yes	characteristic, complemented
43	#41	—	383	6	no	—
44	#41	—	766	6	no	—
45	#41	C₂×D₃₈₃	1	1	yes	characteristic
46	C₂×Q₈	—	383	6	no	—
47	C₂×Q₈	—	766	2	no	—
48	Q₁₆	—	383	3	no	—
49	Q₁₆	—	383	6	no	—
50	SD₁₆	—	383	6	no	—
51	D₈	—	383	1	no	—
52	M₁₆	C₂×D₃₈₃	1	3	yes	—
53	C₂×C₈	C₂×D₃₈₃	1	3	yes	—
54	Q₈	—	383	6	no	—
55	Q₈	—	766	6	no	—
56	Q₈	D₁₅₃₂	1	1	yes	characteristic
57	D₄	—	383	2	no	—
58	D₄	—	766	6	no	—
59	D₄	D₁₅₃₂	1	3	yes	—
60	C₂×C₄	—	766	6	no	—
61	C₂×C₄	—	766	6	no	—
62	C₂×C₄	C₂²×D₃₈₃	1	3	yes	—
63	C₈	C₂²×D₃₈₃	1	1	yes	characteristic
64	C₈	C₂²×D₃₈₃	1	3	yes	—
65	C₂²	—	766	2	no	—
66	C₂²	C₂×D₁₅₃₂	1	3	yes	—
67	C₄	—	766	6	no	—
68	C₄	C₂×D₁₅₃₂	1	3	yes	—
69	C₄	C₂³×D₃₈₃	1	1	yes	characteristic
70	C₂	—	2	3	no	—
71	C₂	—	1532	2	no	—
72	C₂	C₂²×D₁₅₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₁₅₃₂
commutator, cosocle	C₄×C₃₈₃	C₂⁴
Frattini	C₄	C₂³×D₃₈₃
Fitting	#131×C₃₈₃	C₂
socle	C₂×C₃₈₃	C₂²×D₄
hypercenter	#131	D₃₈₃
hypocenter	C₃₈₃	#578
LCS	G ▷ C₄×C₃₈₃ ▷ C₂×C₃₈₃ ▷ C₃₈₃
UCS	C₁ ◁ C₂ ◁ #41 ◁ #131

Complements

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

N	H ≅ G/N	type
1. #27133888	C₂	semidirect
2. #27133874	C₂	semidirect
3. #27133863	C₂	semidirect
4. C₂×Dic₁₅₃₂	C₂	semidirect
5. #131×C₃₈₃	C₂	semidirect
36. C₃₈₃	#578	semidirect
42. #131	D₃₈₃	semidirect

Maximal subgroups

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

subgroup	index
#27133888	2
#27133874	2
#27133863	2
C₂×Dic₁₅₃₂	2
#131×C₃₈₃	2
#578	383