Subgroups — #14557909

Order 2368.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10596939	C₂	1	4	yes	maximal, complemented
2	#11924533	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#64436	C₂	1	1	yes	maximal, characteristic, complemented
4	#127×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄×C₃₇	—	2	2	no	—
6	C₂×D₄×C₃₇	C₂²	1	2	yes	—
7	C₂×D₁₄₈	—	2	2	no	—
8	C₂×D₁₄₈	C₂²	1	2	yes	—
9	C₄²×C₃₇	C₂²	1	1	yes	characteristic
10	#10596939	—	2	8	no	—
11	C₂×#64436	C₂²	1	2	yes	—
12	C₂³×C₃₇	—	2	2	no	—
13	C₂²×D₃₇	—	2	2	no	—
14	D₄×C₃₇	—	2	4	no	—
15	D₄×C₃₇	—	4	4	no	—
16	C₂×C₄×C₃₇	D₄	1	2	yes	—
17	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
18	D₁₄₈	—	2	4	no	—
19	D₁₄₈	—	4	4	no	—
20	#64436	D₄	1	4	yes	complemented
21	C₂²×C₃₇	—	4	2	no	—
22	C₂²×C₃₇	—	4	4	no	—
23	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
24	C₂×D₃₇	—	4	2	no	—
25	C₂×D₃₇	—	4	4	no	—
26	C₄×C₃₇	D₈	1	4	yes	complemented
27	C₄×C₃₇	C₂×D₄	1	2	yes	—
28	C₂×C₃₇	—	8	2	no	—
29	C₂×C₃₇	#127	1	1	yes	characteristic
30	C₂×C₃₇	C₂×D₈	1	2	yes	—
31	D₃₇	—	8	2	no	—
32	#493	—	37	1	no	maximal, Sylow
33	C₃₇	#493	1	1	yes	characteristic, complemented, Sylow
34	C₂×D₈	—	37	4	no	—
35	#127	—	37	1	no	—
36	#127	D₃₇	1	1	yes	characteristic, complemented
37	C₄×C₈	—	37	1	no	—
38	C₂×D₄	—	2	2	no	—
39	C₂×D₄	—	37	2	no	—
40	C₂×D₄	—	74	2	no	—
41	C₂×D₄	C₂×D₃₇	1	2	yes	—
42	D₈	—	74	8	no	—
43	C₂×C₈	—	37	2	no	—
44	C₄²	C₂×D₃₇	1	1	yes	characteristic
45	C₂³	—	2	2	no	—
46	C₂³	—	74	2	no	—
47	D₄	—	2	4	no	—
48	D₄	—	4	4	no	—
49	D₄	—	74	4	no	—
50	D₄	—	148	4	no	—
51	C₂×C₄	C₂²⋊D₃₇	1	2	yes	—
52	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
53	C₈	—	37	4	no	—
54	C₂²	—	4	2	no	—
55	C₂²	—	4	4	no	—
56	C₂²	—	148	2	no	—
57	C₂²	—	148	4	no	—
58	C₂²	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
59	C₄	#10596939	1	4	yes	complemented
60	C₄	D₄×D₃₇	1	2	yes	—
61	C₂	—	8	2	no	—
62	C₂	—	296	2	no	—
63	C₂	#11924532	1	1	yes	characteristic
64	C₂	C₂×#10596939	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₃₇
commutator, cosocle	C₂×C₄×C₃₇	C₂³
Frattini	C₂×C₄	C₂²×D₃₇
Fitting	#127×C₃₇	C₂
socle	C₂²×C₃₇	C₂×D₄
hypercenter	#127	D₃₇
hypocenter	C₃₇	#493
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #127

Complements

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

N	H ≅ G/N	type
1. C₂×#10596939	C₂	semidirect
2. #11924533	C₂	semidirect
3. C₄×#64436	C₂	semidirect
4. #127×C₃₇	C₂	semidirect
20. #64436	D₄	semidirect
26. C₄×C₃₇	D₈	semidirect
33. C₃₇	#493	semidirect
36. #127	D₃₇	semidirect
59. C₄	#10596939	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10596939	2
#11924533	2
C₄×#64436	2
#127×C₃₇	2
#493	37