Subgroups — #14558401

Order 2368.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924615	C₂	1	2	yes	maximal
2	C₂×#10596929	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×D₃₇	C₂²	1	1	yes	characteristic
4	C₂²⋊#3866	—	2	2	no	—
5	C₄⋊#3866	—	2	2	no	—
6	C₄×#3866	C₄	1	4	yes	complemented
7	C₂×C₈×C₃₇	C₄	1	1	yes	characteristic, complemented
8	C₂×#64436	C₄	1	1	yes	characteristic, complemented
9	#10596929	—	2	2	no	—
10	C₂²×D₃₇	D₄	1	1	yes	characteristic
11	C₂×#3866	—	2	4	no	—
12	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
13	C₂×Dic₃₇	Q₈	1	1	yes	characteristic
14	C₄×D₃₇	C₂×C₄	1	2	yes	—
15	C₄×D₃₇	D₄	1	2	yes	—
16	C₈×C₃₇	—	2	1	no	—
17	#64436	—	2	1	no	—
18	C₂²×C₃₇	C₄⋊C₄	1	1	yes	characteristic
19	C₂×D₃₇	—	4	1	no	—
20	C₂×D₃₇	C₂²⋊C₄	1	2	yes	—
21	#3866	—	4	4	no	—
22	C₄×C₃₇	C₄²	1	1	yes	characteristic
23	C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
24	Dic₃₇	C₄⋊C₄	1	2	yes	—
25	C₂×C₃₇	—	2	1	no	—
26	C₂×C₃₇	#95	1	1	yes	characteristic
27	D₃₇	—	2	2	no	—
28	H(3,ℤ/4)	—	37	1	no	maximal, Sylow
29	C₃₇	H(3,ℤ/4)	1	1	yes	characteristic, complemented, Sylow
30	C₂×M₁₆	—	37	1	no	—
31	#117	—	37	2	no	—
32	C₂²×C₄	—	37	1	no	—
33	M₁₆	—	74	2	no	—
34	C₂×C₈	—	37	1	no	—
35	C₂×C₈	#3866	1	1	yes	characteristic, complemented
36	C₄⋊C₄	—	74	2	no	—
37	C₂²⋊C₄	—	74	2	no	—
38	C₄²	—	37	4	no	—
39	C₂³	—	37	1	no	—
40	C₂×C₄	—	37	1	no	—
41	C₂×C₄	—	37	2	no	—
42	C₂×C₄	—	37	2	no	—
43	C₂×C₄	—	74	4	no	—
44	C₂×C₄	C₂×#3866	1	1	yes	characteristic
45	C₈	—	2	1	no	—
46	C₈	—	74	1	no	—
47	C₂²	—	37	2	no	—
48	C₂²	—	148	1	no	—
49	C₂²	C₄⋊#3866	1	1	yes	characteristic
50	C₄	—	37	2	no	—
51	C₄	—	148	4	no	—
52	C₄	C₄×#3866	1	1	yes	characteristic
53	C₄	C₂²⋊#3866	1	1	yes	characteristic
54	C₂	—	2	1	no	—
55	C₂	—	74	2	no	—
56	C₂	(C₂×#3866)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄×#3866
commutator	C₄×C₃₇	C₄²
Frattini	C₂×C₄	C₂×#3866
Fitting	C₂×C₈×C₃₇	C₄
socle	C₂×C₃₇	#95
prime radical	C₂²×D₃₇	D₄
cosocle	C₂×C₄×D₃₇	C₂²
hypercenter	C₂×C₈	#3866
hypocenter	C₃₇	H(3,ℤ/4)
LCS	G ▷ C₄×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
6. C₄×#3866	C₄	semidirect
7. C₂×C₈×C₃₇	C₄	semidirect
8. C₂×#64436	C₄	semidirect
29. C₃₇	H(3,ℤ/4)	semidirect
35. C₂×C₈	#3866	semidirect

Maximal subgroups

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

subgroup	index
#11924615	2
C₂×#10596929	2
H(3,ℤ/4)	37