Subgroups — #14558415

Order 2368.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₇⋊M₁₆	C₂	1	1	yes	maximal, characteristic
2	#11924615	C₂	1	1	yes	maximal, characteristic
3	C₂×#10596929	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×D₃₇	C₂²	1	1	yes	characteristic
5	C₂²⋊#3866	C₄	1	2	yes	—
6	#10596957	C₄	1	2	yes	complemented
7	C₄⋊#3866	—	2	1	no	—
8	C₄×#3866	—	2	1	no	—
9	#10596953	—	2	1	no	—
10	D₃₇⋊C₈	—	2	1	no	—
11	C₂×C₈×C₃₇	C₄	1	1	yes	characteristic, complemented
12	C₂×#64436	C₄	1	1	yes	characteristic, complemented
13	#10596929	—	2	1	no	—
14	#10596929	—	2	1	no	—
15	C₂²×D₃₇	C₂×C₄	1	1	yes	characteristic
16	C₂×#3866	—	2	2	no	—
17	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₃₇	C₂×C₄	1	1	yes	characteristic
19	C₄×D₃₇	D₄	1	1	yes	characteristic
20	C₄×D₃₇	D₄	1	1	yes	characteristic
21	C₄×D₃₇	D₄	1	1	yes	characteristic
22	C₄×D₃₇	Q₈	1	1	yes	characteristic
23	#64438	—	2	2	no	—
24	C₈×C₃₇	—	2	1	no	—
25	#64436	—	2	1	no	—
26	C₂²×C₃₇	C₄²	1	1	yes	characteristic
27	C₂×D₃₇	—	4	1	no	—
28	C₂×D₃₇	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×D₃₇	C₄⋊C₄	1	1	yes	characteristic
30	#3866	—	4	2	no	—
31	C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
32	C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
33	Dic₃₇	C₂²⋊C₄	1	1	yes	characteristic
34	Dic₃₇	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₃₇	—	2	1	no	—
36	C₂×C₃₇	#95	1	1	yes	characteristic
37	D₃₇	—	2	1	no	—
38	D₃₇	—	2	1	no	—
39	#344	—	37	1	no	maximal, Sylow
40	C₃₇	#344	1	1	yes	characteristic, complemented, Sylow
41	C₂×M₁₆	—	37	1	no	—
42	C₂×M₁₆	—	37	1	no	—
43	#117	—	37	1	no	—
44	C₂²×C₄	—	37	1	no	—
45	M₁₆	—	37	2	no	—
46	M₁₆	—	74	1	no	—
47	M₁₆	—	74	1	no	—
48	M₁₆	—	74	1	no	—
49	C₂×C₈	—	37	1	no	—
50	C₂×C₈	—	74	1	no	—
51	C₂×C₈	#3866	1	1	yes	characteristic, complemented
52	C₄⋊C₄	—	74	1	no	—
53	C₂²⋊C₄	—	37	2	no	—
54	C₄²	—	74	1	no	—
55	C₂³	—	37	1	no	—
56	C₂×C₄	—	37	1	no	—
57	C₂×C₄	—	37	1	no	—
58	C₂×C₄	—	37	1	no	—
59	C₂×C₄	—	37	1	no	—
60	C₂×C₄	—	37	1	no	—
61	C₂×C₄	—	74	2	no	—
62	C₂×C₄	C₂×#3866	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	74	2	no	—
65	C₈	—	74	1	no	—
66	C₂²	—	37	1	no	—
67	C₂²	—	37	1	no	—
68	C₂²	—	148	1	no	—
69	C₂²	C₄×#3866	1	1	yes	characteristic
70	C₄	—	37	1	no	—
71	C₄	—	37	1	no	—
72	C₄	—	148	2	no	—
73	C₄	C₄⋊#3866	1	1	yes	characteristic
74	C₄	C₂²⋊#3866	1	1	yes	characteristic
75	C₂	—	2	1	no	—
76	C₂	—	74	1	no	—
77	C₂	—	74	1	no	—
78	C₂	(C₂×#3866)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#3866
commutator	C₂²×C₃₇	C₄²
Frattini	C₂×C₄	C₂×#3866
Fitting	C₂×C₈×C₃₇	C₄
socle	C₂×C₃₇	#95
prime radical	C₂²×D₃₇	C₂×C₄
cosocle	C₂×C₄×D₃₇	C₂²
hypercenter	C₂×C₈	#3866
hypocenter	C₃₇	#344
LCS	G ▷ C₂²×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
6. #10596957	C₄	semidirect
11. C₂×C₈×C₃₇	C₄	semidirect
12. C₂×#64436	C₄	semidirect
40. C₃₇	#344	semidirect
51. 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
D₃₇⋊M₁₆	2
#11924615	2
C₂×#10596929	2
#344	37