Subgroups — #37565198

Order 24256.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20258589	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×D₃₇₉	C₂	1	1	yes	maximal, characteristic
3	#27131288	C₂	1	1	yes	maximal, characteristic
4	#27131242	C₂	1	1	yes	maximal, characteristic, complemented
5	#27131241	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×Dic₃₇₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₈×C₃₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₃₇₉	C₂²	1	1	yes	characteristic
9	#20258589	C₄	1	4	yes	complemented
10	C₂×C₃₇₉⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₃₇₉⋊C₈	C₂²	1	1	yes	characteristic
12	C₈×D₃₇₉	C₄	1	4	yes	complemented
13	Dic₃₇₉⋊C₄	C₄	1	2	yes	—
14	(C₂×D₃₇₉)⋊C₄	C₄	1	2	yes	—
15	C₄×Dic₃₇₉	C₂²	1	1	yes	characteristic
16	C₂×C₈×C₃₇₉	C₂²	1	1	yes	characteristic
17	C₂×C₈×C₃₇₉	C₂²	1	1	yes	characteristic
18	C₄²×C₃₇₉	C₂²	1	1	yes	characteristic
19	C₂²×D₃₇₉	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₃₇₉	C₂×C₄	1	2	yes	—
21	C₂×Dic₃₇₉	C₂×C₄	1	1	yes	characteristic
22	C₄×D₃₇₉	C₂×C₄	1	2	yes	—
23	C₄×D₃₇₉	C₂×C₄	1	2	yes	—
24	C₃₇₉⋊C₈	C₂×C₄	1	2	yes	—
25	C₃₇₉⋊C₈	C₂×C₄	1	2	yes	—
26	C₂×C₄×C₃₇₉	C₂×C₄	1	2	yes	—
27	C₂×C₄×C₃₇₉	C₂³	1	1	yes	characteristic
28	C₈×C₃₇₉	C₂×C₄	1	2	yes	—
29	C₈×C₃₇₉	C₂×C₄	1	2	yes	—
30	C₂²×C₃₇₉	C₂²×C₄	1	1	yes	characteristic
31	C₂×D₃₇₉	—	2	2	no	—
32	C₂×D₃₇₉	C₄²	1	2	yes	—
33	C₄×C₃₇₉	—	2	2	no	—
34	C₄×C₃₇₉	C₂²×C₄	1	1	yes	characteristic
35	C₄×C₃₇₉	C₂²×C₄	1	1	yes	characteristic
36	Dic₃₇₉	—	2	2	no	—
37	Dic₃₇₉	C₄²	1	2	yes	—
38	C₂×C₃₇₉	C₂×C₄²	1	1	yes	characteristic
39	C₂×C₃₇₉	#131	1	2	yes	—
40	D₃₇₉	—	2	2	no	—
41	C₃₇₉	#405	1	1	yes	characteristic, complemented, Sylow
42	#405	—	379	1	no	maximal, Sylow
43	C₂×M₁₆	—	379	1	no	—
44	C₂²×C₈	—	379	1	no	—
45	#117	—	379	1	no	—
46	#97	—	379	1	no	—
47	#97	—	379	1	no	—
48	C₄×C₈	—	379	1	no	—
49	C₄×C₈	D₃₇₉	1	1	yes	characteristic, complemented
50	C₂²×C₄	—	379	1	no	—
51	M₁₆	—	379	4	no	—
52	C₂×C₈	—	379	1	no	—
53	C₂×C₈	—	379	1	no	—
54	C₂×C₈	—	379	4	no	—
55	C₂×C₈	C₂×D₃₇₉	1	1	yes	characteristic
56	C₂×C₈	C₂×D₃₇₉	1	1	yes	characteristic
57	C₄⋊C₄	—	379	2	no	—
58	C₂²⋊C₄	—	379	2	no	—
59	C₄²	—	379	1	no	—
60	C₄²	C₂×D₃₇₉	1	1	yes	characteristic
61	C₂³	—	379	1	no	—
62	C₂×C₄	—	379	1	no	—
63	C₂×C₄	—	379	2	no	—
64	C₂×C₄	—	379	2	no	—
65	C₂×C₄	—	379	2	no	—
66	C₂×C₄	C₄×D₃₇₉	1	2	yes	—
67	C₂×C₄	C₂²×D₃₇₉	1	1	yes	characteristic
68	C₈	—	379	2	no	—
69	C₈	—	379	2	no	—
70	C₈	C₄×D₃₇₉	1	2	yes	—
71	C₈	C₄×D₃₇₉	1	2	yes	—
72	C₂²	—	379	2	no	—
73	C₂²	—	758	2	no	—
74	C₂²	C₂×C₄×D₃₇₉	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	—	379	2	no	—
77	C₄	—	758	2	no	—
78	C₄	C₂×C₄×D₃₇₉	1	1	yes	characteristic
79	C₄	C₂×C₄×D₃₇₉	1	1	yes	characteristic
80	C₂	—	758	2	no	—
81	C₂	C₄²×D₃₇₉	1	1	yes	characteristic
82	C₂	#27131337	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂×D₃₇₉
commutator	C₂×C₃₇₉	C₂×C₄²
Frattini	C₂×C₄	C₂²×D₃₇₉
Fitting	C₄×C₈×C₃₇₉	C₂
socle	C₂²×C₃₇₉	C₂²×C₄
prime radical	C₂²×D₃₇₉	C₂×C₄
cosocle	C₂×C₄×C₃₇₉	C₂³
hypercenter	C₄×C₈	D₃₇₉
hypocenter	C₃₇₉	#405
LCS	G ▷ C₂×C₃₇₉ ▷ C₃₇₉
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
4. #27131242	C₂	semidirect
5. #27131241	C₂	semidirect
6. C₈×Dic₃₇₉	C₂	semidirect
7. C₄×C₈×C₃₇₉	C₂	semidirect
9. #20258589	C₄	semidirect
12. C₈×D₃₇₉	C₄	semidirect
41. C₃₇₉	#405	semidirect
49. C₄×C₈	D₃₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20258589	2
C₂×C₈×D₃₇₉	2
#27131288	2
#27131242	2
#27131241	2
C₈×Dic₃₇₉	2
C₄×C₈×C₃₇₉	2
#405	379