Subgroups — #37565620

Order 24256.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20258591	C₂	1	4	yes	maximal, complemented
2	#27131328	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₃₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#127×C₃₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₁₅₁₆	—	2	2	no	—
6	C₂×D₁₅₁₆	C₂²	1	2	yes	—
7	#20258591	—	2	8	no	—
8	C₂×C₃₇₉⋊C₈	C₂²	1	2	yes	—
9	C₂×D₄×C₃₇₉	—	2	2	no	—
10	C₂×D₄×C₃₇₉	C₂²	1	2	yes	—
11	C₄²×C₃₇₉	C₂²	1	1	yes	characteristic
12	C₂²×D₃₇₉	—	2	2	no	—
13	D₁₅₁₆	—	2	4	no	—
14	D₁₅₁₆	—	4	4	no	—
15	C₃₇₉⋊C₈	D₄	1	4	yes	complemented
16	C₂³×C₃₇₉	—	2	2	no	—
17	D₄×C₃₇₉	—	2	4	no	—
18	D₄×C₃₇₉	—	4	4	no	—
19	C₂×C₄×C₃₇₉	D₄	1	2	yes	—
20	C₂×C₄×C₃₇₉	C₂³	1	1	yes	characteristic
21	C₂²×C₃₇₉	—	4	2	no	—
22	C₂²×C₃₇₉	—	4	4	no	—
23	C₂²×C₃₇₉	C₂×D₄	1	1	yes	characteristic
24	C₂×D₃₇₉	—	4	2	no	—
25	C₂×D₃₇₉	—	4	4	no	—
26	C₄×C₃₇₉	D₈	1	4	yes	complemented
27	C₄×C₃₇₉	C₂×D₄	1	2	yes	—
28	C₂×C₃₇₉	—	8	2	no	—
29	C₂×C₃₇₉	#127	1	1	yes	characteristic
30	C₂×C₃₇₉	C₂×D₈	1	2	yes	—
31	D₃₇₉	—	8	2	no	—
32	C₃₇₉	#493	1	1	yes	characteristic, complemented, Sylow
33	#493	—	379	1	no	maximal, Sylow
34	C₂×D₈	—	379	4	no	—
35	#127	—	379	1	no	—
36	#127	D₃₇₉	1	1	yes	characteristic, complemented
37	C₄×C₈	—	379	1	no	—
38	C₂×D₄	—	2	2	no	—
39	C₂×D₄	—	379	2	no	—
40	C₂×D₄	—	758	2	no	—
41	C₂×D₄	C₂×D₃₇₉	1	2	yes	—
42	D₈	—	758	8	no	—
43	C₂×C₈	—	379	2	no	—
44	C₄²	C₂×D₃₇₉	1	1	yes	characteristic
45	C₂³	—	2	2	no	—
46	C₂³	—	758	2	no	—
47	D₄	—	2	4	no	—
48	D₄	—	4	4	no	—
49	D₄	—	1516	4	no	—
50	D₄	—	758	4	no	—
51	C₂×C₄	C₂²⋊D₃₇₉	1	2	yes	—
52	C₂×C₄	C₂²×D₃₇₉	1	1	yes	characteristic
53	C₈	—	379	4	no	—
54	C₂²	—	4	2	no	—
55	C₂²	—	4	4	no	—
56	C₂²	—	1516	2	no	—
57	C₂²	—	1516	4	no	—
58	C₂²	C₂×C₂²⋊D₃₇₉	1	1	yes	characteristic
59	C₄	#20258591	1	4	yes	complemented
60	C₄	D₄×D₃₇₉	1	2	yes	—
61	C₂	—	8	2	no	—
62	C₂	—	3032	2	no	—
63	C₂	#27131327	1	1	yes	characteristic
64	C₂	C₂×#20258591	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₃₇₉
commutator, cosocle	C₂×C₄×C₃₇₉	C₂³
Frattini	C₂×C₄	C₂²×D₃₇₉
Fitting	#127×C₃₇₉	C₂
socle	C₂²×C₃₇₉	C₂×D₄
hypercenter	#127	D₃₇₉
hypocenter	C₃₇₉	#493
LCS	G ▷ C₂×C₄×C₃₇₉ ▷ C₂×C₃₇₉ ▷ C₃₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #127

Complements

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

N	H ≅ G/N	type
1. C₂×#20258591	C₂	semidirect
2. #27131328	C₂	semidirect
3. C₄×C₃₇₉⋊C₈	C₂	semidirect
4. #127×C₃₇₉	C₂	semidirect
15. C₃₇₉⋊C₈	D₄	semidirect
26. C₄×C₃₇₉	D₈	semidirect
32. C₃₇₉	#493	semidirect
36. #127	D₃₇₉	semidirect
59. C₄	#20258591	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20258591	2
#27131328	2
C₄×C₃₇₉⋊C₈	2
#127×C₃₇₉	2
#493	379