Subgroups — #14558402

Order 2368.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₇⋊M₁₆	C₂	1	2	yes	maximal
2	C₂×#10596929	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×D₃₇	C₂²	1	1	yes	characteristic
4	#10596957	—	2	2	no	—
5	#10596953	—	2	2	no	—
6	D₃₇⋊C₈	C₄	1	4	yes	—
7	C₂×C₈×C₃₇	C₄	1	1	yes	characteristic
8	C₂×#64436	C₄	1	1	yes	characteristic
9	#10596929	—	2	2	no	—
10	C₂²×D₃₇	Q₈	1	1	yes	characteristic
11	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
12	C₂×Dic₃₇	D₄	1	1	yes	characteristic
13	C₄×D₃₇	C₂×C₄	1	2	yes	—
14	C₄×D₃₇	D₄	1	2	yes	—
15	#64438	—	2	4	no	—
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	C₄⋊C₄	1	2	yes	—
21	C₄×C₃₇	C₄²	1	1	yes	characteristic
22	C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
23	Dic₃₇	C₂²⋊C₄	1	2	yes	—
24	C₂×C₃₇	—	2	1	no	—
25	C₂×C₃₇	#95	1	1	yes	characteristic
26	D₃₇	—	2	2	no	—
27	#338	—	37	1	no	maximal, Sylow
28	C₃₇	#338	1	1	yes	characteristic, complemented, Sylow
29	C₂×M₁₆	—	37	2	no	—
30	C₂×M₁₆	—	37	1	no	—
31	C₂²×C₄	—	37	1	no	—
32	M₁₆	—	74	2	no	—
33	M₁₆	—	74	2	no	—
34	M₁₆	—	74	2	no	—
35	C₂×C₈	—	37	4	no	—
36	C₂×C₈	—	37	1	no	—
37	C₂×C₈	#3866	1	1	yes	characteristic
38	C₂³	—	37	1	no	—
39	C₂×C₄	—	37	1	no	—
40	C₂×C₄	—	37	2	no	—
41	C₂×C₄	—	37	2	no	—
42	C₂×C₄	C₂×#3866	1	1	yes	characteristic
43	C₈	—	2	1	no	—
44	C₈	—	74	4	no	—
45	C₈	—	74	1	no	—
46	C₂²	—	37	2	no	—
47	C₂²	—	148	1	no	—
48	C₂²	C₄⋊#3866	1	1	yes	characteristic
49	C₄	—	37	2	no	—
50	C₄	C₄×#3866	1	1	yes	characteristic
51	C₄	C₂²⋊#3866	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	74	2	no	—
54	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	Q₈
cosocle	C₂×C₄×D₃₇	C₂²
hypercenter	C₂×C₈	#3866
hypocenter	C₃₇	#338
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
28. C₃₇	#338	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
C₂×#10596929	2
#338	37