Subgroups — #14557932

Order 2368.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924528	C₂	1	1	yes	maximal, characteristic
2	#11924469	C₂	1	2	yes	maximal
3	#11924467	C₂	1	2	yes	maximal
4	C₄×#64436	C₂	1	1	yes	maximal, characteristic
5	#125×C₃₇	C₂	1	1	yes	maximal, characteristic
6	C₄⋊C₄×C₃₇	—	2	2	no	—
7	C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
8	C₄²×C₃₇	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₃₇	C₂²	1	2	yes	—
10	#10596936	—	2	2	no	—
11	C₂×#64436	C₂²	1	1	yes	characteristic
12	C₂×#64436	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₃₇	—	2	2	no	—
14	C₂×C₄×C₃₇	D₄	1	2	yes	—
15	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
16	C₂×Dic₃₇	—	2	2	no	—
17	#64436	Q₈	1	2	yes	—
18	#64436	Q₈	1	2	yes	—
19	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
20	C₄×C₃₇	—	2	2	no	—
21	C₄×C₃₇	—	4	2	no	—
22	C₄×C₃₇	C₂×Q₈	1	1	yes	characteristic
23	C₄×C₃₇	C₂×Q₈	1	1	yes	characteristic
24	Dic₃₇	—	4	2	no	—
25	C₂×C₃₇	C₄⋊Q₈	1	1	yes	characteristic
26	C₂×C₃₇	#135	1	2	yes	—
27	#499	—	37	1	no	maximal, Sylow
28	C₃₇	#499	1	1	yes	characteristic, complemented, Sylow
29	#125	—	37	1	no	—
30	#125	D₃₇	1	1	yes	characteristic
31	#107	—	37	2	no	—
32	#106	—	37	2	no	—
33	C₄×C₈	—	37	1	no	—
34	C₂×C₈	—	37	1	no	—
35	C₂×C₈	—	37	1	no	—
36	C₄⋊C₄	—	2	2	no	—
37	C₄⋊C₄	—	37	2	no	—
38	C₄⋊C₄	—	74	2	no	—
39	C₄⋊C₄	C₂×D₃₇	1	2	yes	—
40	C₄²	C₂×D₃₇	1	1	yes	characteristic
41	C₂×C₄	—	2	2	no	—
42	C₂×C₄	—	74	2	no	—
43	C₂×C₄	C₂²⋊D₃₇	1	2	yes	—
44	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
45	C₈	—	37	2	no	—
46	C₈	—	37	2	no	—
47	C₂²	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
48	C₄	—	2	2	no	—
49	C₄	—	4	2	no	—
50	C₄	—	148	2	no	—
51	C₄	Q₈×D₃₇	1	1	yes	characteristic
52	C₄	Q₈×D₃₇	1	1	yes	characteristic
53	C₂	#11924534	1	1	yes	characteristic
54	C₂	#11924556	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₃₇
commutator, cosocle	C₂×C₄×C₃₇	C₂³
Frattini	C₂×C₄	C₂²×D₃₇
Fitting	#125×C₃₇	C₂
socle, prime radical	C₂²×C₃₇	C₂×D₄
hypercenter	#125	D₃₇
hypocenter	C₃₇	#499
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
28. C₃₇	#499	semidirect

Maximal subgroups

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

subgroup	index
#11924528	2
#11924469	2
#11924467	2
C₄×#64436	2
#125×C₃₇	2
#499	37