Subgroups — #14558492

Order 2368.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₇⋊C₈	C₂	1	2	yes	maximal
2	#11924591	C₂	1	4	yes	maximal, complemented
3	C₄²×D₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×D₃₇	C₄	1	2	yes	—
5	C₂×C₄×D₃₇	C₂²	1	1	yes	characteristic
6	C₂×#64438	C₂²	1	4	yes	—
7	D₃₇⋊C₈	C₄	1	8	yes	complemented
8	C₄²×C₃₇	C₄	1	1	yes	characteristic
9	C₄×Dic₃₇	C₄	1	1	yes	characteristic
10	C₄×Dic₃₇	C₂²	1	2	yes	—
11	C₂²×D₃₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₃₇	C₂×C₄	1	2	yes	—
13	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
14	C₂×Dic₃₇	C₂×C₄	1	2	yes	—
15	C₂×Dic₃₇	C₂³	1	1	yes	characteristic
16	C₄×D₃₇	—	2	4	no	—
17	C₄×D₃₇	C₂×C₄	1	4	yes	—
18	#64438	C₂×C₄	1	8	yes	complemented
19	C₂²×C₃₇	C₂²×C₄	1	1	yes	characteristic
20	C₂×D₃₇	C₄²	1	2	yes	—
21	C₂×D₃₇	M₁₆	1	4	yes	—
22	C₄×C₃₇	—	2	2	no	—
23	C₄×C₃₇	C₄²	1	2	yes	—
24	Dic₃₇	—	2	2	no	—
25	Dic₃₇	C₂²×C₄	1	2	yes	—
26	C₂×C₃₇	C₂×C₄²	1	1	yes	characteristic
27	C₂×C₃₇	C₂×M₁₆	1	2	yes	—
28	D₃₇	#97	1	4	yes	complemented
29	C₂×#97	—	37	1	no	maximal, Sylow
30	C₃₇	C₂×#97	1	1	yes	characteristic, complemented, Sylow
31	C₂²×C₈	—	37	2	no	—
32	C₂×C₄²	—	37	1	no	—
33	#97	—	37	4	no	—
34	C₂²×C₄	—	37	1	no	—
35	C₂²×C₄	—	37	2	no	—
36	C₂×C₈	—	37	8	no	—
37	C₂×C₈	—	37	4	no	—
38	C₄²	—	37	2	no	—
39	C₄²	—	37	1	no	—
40	C₄²	#3866	1	1	yes	characteristic
41	C₂³	—	37	1	no	—
42	C₂×C₄	—	37	1	no	—
43	C₂×C₄	—	37	4	no	—
44	C₂×C₄	—	37	2	no	—
45	C₂×C₄	—	74	4	no	—
46	C₂×C₄	C₂×#3866	1	2	yes	—
47	C₂×C₄	C₂×#3866	1	1	yes	characteristic
48	C₈	—	37	8	no	—
49	C₂²	—	37	2	no	—
50	C₂²	—	37	4	no	—
51	C₂²	C₂²×#3866	1	1	yes	characteristic
52	C₄	—	2	2	no	—
53	C₄	—	37	2	no	—
54	C₄	—	74	2	no	—
55	C₄	C₄×#3866	1	2	yes	—
56	C₂	—	37	4	no	—
57	C₂	C₂×C₄×#3866	1	1	yes	characteristic
58	C₂	D₃₇⋊M₁₆	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×#3866
commutator	C₂×C₃₇	C₂×C₄²
Frattini	C₂²	C₂²×#3866
Fitting	C₄²×C₃₇	C₄
socle	C₂²×C₃₇	C₂²×C₄
prime radical	C₂²×D₃₇	C₂×C₄
cosocle	C₂×Dic₃₇	C₂³
hypercenter	C₄²	#3866
hypocenter	C₃₇	C₂×#97
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
2. #11924591	C₂	semidirect
7. D₃₇⋊C₈	C₄	semidirect
18. #64438	C₂×C₄	semidirect
28. D₃₇	#97	semidirect
30. C₃₇	C₂×#97	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃₇⋊C₈	2
#11924591	2
C₄²×D₃₇	2
C₂×#97	37