Subgroups — #14558432

Order 2368.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924610	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10596927	C₂	1	1	yes	maximal, characteristic, complemented
3	#11924544	C₂	1	1	yes	maximal, characteristic
4	#10596962	C₄	1	1	yes	characteristic
5	M₁₆×C₃₇	C₄	1	1	yes	characteristic
6	C₂×#64436	C₂²	1	1	yes	characteristic
7	#10596929	—	2	1	no	—
8	C₈×D₃₇	—	2	1	no	—
9	#10596927	—	2	1	no	—
10	#10596927	—	2	1	no	—
11	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
12	C₂²⋊D₃₇	—	2	1	no	—
13	D₁₄₈	C₈	1	1	yes	characteristic
14	C₄×D₃₇	—	2	1	no	—
15	Dic₇₄	C₈	1	1	yes	characteristic
16	C₈×C₃₇	—	2	1	no	—
17	#64436	D₄	1	1	yes	characteristic
18	#64436	D₄	1	1	yes	characteristic
19	C₂²×C₃₇	M₁₆	1	1	yes	characteristic
20	C₂×D₃₇	—	2	1	no	—
21	C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
23	Dic₃₇	—	2	1	no	—
24	C₂×C₃₇	—	2	1	no	—
25	C₂×C₃₇	C₂²⋊C₈	1	1	yes	characteristic
26	D₃₇	—	4	1	no	—
27	#350	—	37	1	no	maximal, Sylow
28	C₃₇	#350	1	1	yes	characteristic, complemented, Sylow
29	#131	—	37	1	no	—
30	M₃₂	—	37	1	no	—
31	C₂×C₁₆	—	37	1	no	—
32	#41	—	37	1	no	—
33	M₁₆	—	74	1	no	—
34	M₁₆	#3866	1	1	yes	characteristic
35	C₂×C₈	—	37	1	no	—
36	C₂×C₈	—	74	1	no	—
37	C₁₆	—	74	1	no	—
38	C₁₆	—	74	1	no	—
39	Q₈	—	37	1	no	—
40	D₄	—	37	1	no	—
41	D₄	—	74	1	no	—
42	C₂×C₄	—	74	1	no	—
43	C₂×C₄	C₂×#3866	1	1	yes	characteristic
44	C₈	—	2	1	no	—
45	C₈	—	37	1	no	—
46	C₈	—	37	1	no	—
47	C₂²	—	74	1	no	—
48	C₂²	#10596953	1	1	yes	characteristic
49	C₄	—	74	1	no	—
50	C₄	D₃₇⋊C₈	1	1	yes	characteristic
51	C₄	C₂²⋊#3866	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	148	1	no	—
54	C₂	#11924593	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#3866
commutator	C₄×C₃₇	C₂×C₈
Frattini	C₂×C₄	C₂×#3866
Fitting	M₁₆×C₃₇	C₄
socle	C₂×C₃₇	C₂²⋊C₈
prime radical	#10596962	C₄
cosocle	C₂×#64436	C₂²
hypercenter	M₁₆	#3866
hypocenter	C₃₇	#350
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
1. #11924610	C₂	semidirect
2. C₂×#10596927	C₂	semidirect
28. C₃₇	#350	semidirect

Maximal subgroups

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

subgroup	index
#11924610	2
C₂×#10596927	2
#11924544	2
#350	37