Subgroups — #14557908

Order 2368.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₉₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10596939	C₂	1	2	yes	maximal, complemented
3	#11924532	C₂	1	2	yes	maximal, complemented
4	C₈×Dic₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄×C₃₇	C₂²	1	2	yes	—
7	C₂×C₂²⋊D₃₇	—	2	4	no	—
8	C₂×D₁₄₈	C₂²	1	2	yes	—
9	D₈×C₃₇	—	2	2	no	—
10	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
11	#10596939	—	2	4	no	—
12	C₄×Dic₃₇	C₂²	1	1	yes	characteristic
13	C₂×#64436	C₂²	1	1	yes	characteristic
14	D₂₉₆	—	2	2	no	—
15	C₂³×C₃₇	—	2	2	no	—
16	C₂²×D₃₇	—	2	2	no	—
17	D₄×C₃₇	—	2	2	no	—
18	D₄×C₃₇	—	2	2	no	—
19	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
20	C₂²⋊D₃₇	—	4	8	no	—
21	C₂×Dic₃₇	D₄	1	2	yes	—
22	D₁₄₈	—	2	2	no	—
23	D₁₄₈	—	2	2	no	—
24	C₈×C₃₇	D₄	1	2	yes	complemented
25	#64436	D₄	1	2	yes	complemented
26	C₂²×C₃₇	—	4	2	no	—
27	C₂²×C₃₇	—	4	4	no	—
28	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
29	C₂×D₃₇	—	4	2	no	—
30	C₂×D₃₇	—	4	4	no	—
31	C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
32	C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
33	Dic₃₇	D₈	1	4	yes	complemented
34	C₂×C₃₇	—	8	2	no	—
35	C₂×C₃₇	#127	1	1	yes	characteristic
36	C₂×C₃₇	C₂×D₈	1	2	yes	—
37	D₃₇	—	8	2	no	—
38	#493	—	37	1	no	maximal, Sylow
39	C₃₇	#493	1	1	yes	characteristic, complemented, Sylow
40	C₂×D₈	—	37	2	no	—
41	C₂×D₈	—	37	1	no	—
42	C₂×D₈	D₃₇	1	1	yes	characteristic, complemented
43	#127	—	37	2	no	—
44	C₄×C₈	—	37	1	no	—
45	C₂×D₄	—	37	2	no	—
46	C₂×D₄	—	74	4	no	—
47	C₂×D₄	C₂×D₃₇	1	2	yes	—
48	D₈	—	2	2	no	—
49	D₈	—	74	4	no	—
50	D₈	—	74	2	no	—
51	C₂×C₈	—	37	1	no	—
52	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
53	C₄²	—	37	1	no	—
54	C₂³	—	2	2	no	—
55	C₂³	—	74	2	no	—
56	D₄	—	2	2	no	—
57	D₄	—	2	2	no	—
58	D₄	—	74	2	no	—
59	D₄	—	74	2	no	—
60	D₄	—	148	8	no	—
61	C₂×C₄	—	37	2	no	—
62	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
63	C₈	—	37	2	no	—
64	C₈	C₂²⋊D₃₇	1	2	yes	complemented
65	C₂²	—	4	2	no	—
66	C₂²	—	4	4	no	—
67	C₂²	—	148	2	no	—
68	C₂²	—	148	4	no	—
69	C₂²	D₄×D₃₇	1	1	yes	characteristic
70	C₄	—	37	4	no	—
71	C₄	D₄×D₃₇	1	1	yes	characteristic
72	C₄	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
73	C₂	—	8	2	no	—
74	C₂	—	296	2	no	—
75	C₂	#11924532	1	1	yes	characteristic
76	C₂	D₈×D₃₇	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₃₇
commutator, cosocle	C₂×C₄×C₃₇	C₂³
Frattini	C₂×C₄	C₂²×D₃₇
Fitting	C₂×D₈×C₃₇	C₂
socle	C₂²×C₃₇	C₂×D₄
hypercenter	C₂×D₈	D₃₇
hypocenter	C₃₇	#493
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×D₂₉₆	C₂	semidirect
2. C₂×#10596939	C₂	semidirect
3. #11924532	C₂	semidirect
4. C₈×Dic₃₇	C₂	semidirect
5. C₂×D₈×C₃₇	C₂	semidirect
24. C₈×C₃₇	D₄	semidirect
25. #64436	D₄	semidirect
33. Dic₃₇	D₈	semidirect
39. C₃₇	#493	semidirect
42. C₂×D₈	D₃₇	semidirect
64. C₈	C₂²⋊D₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₂₉₆	2
C₂×#10596939	2
#11924532	2
C₈×Dic₃₇	2
C₂×D₈×C₃₇	2
#493	37