Subgroups — #14557897

Order 2368.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924528	C₂	1	1	yes	maximal, characteristic, complemented
2	#11924457	C₂	1	4	yes	maximal, complemented
3	#11924447	C₂	1	1	yes	maximal, characteristic, complemented
4	#127×C₃₇	C₂	1	1	yes	maximal, characteristic
5	C₂×D₄×C₃₇	—	2	2	no	—
6	C₂×D₄×C₃₇	C₂²	1	2	yes	—
7	C₄²×C₃₇	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₃₇	C₂²	1	2	yes	—
9	#10596936	—	2	2	no	—
10	C₂×#64436	C₂²	1	2	yes	—
11	C₂³×C₃₇	—	2	2	no	—
12	D₄×C₃₇	—	2	4	no	—
13	D₄×C₃₇	—	4	4	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	—	2	2	no	—
18	C₂²×C₃₇	—	4	2	no	—
19	C₂²×C₃₇	—	4	4	no	—
20	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
21	C₄×C₃₇	—	2	2	no	—
22	C₄×C₃₇	#41	1	2	yes	—
23	Dic₃₇	—	4	2	no	—
24	C₂×C₃₇	—	8	2	no	—
25	C₂×C₃₇	#124	1	1	yes	characteristic
26	C₂×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
27	#490	—	37	1	no	maximal, Sylow
28	C₃₇	#490	1	1	yes	characteristic, complemented, Sylow
29	#127	D₃₇	1	1	yes	characteristic
30	#125	—	37	1	no	—
31	#102	—	37	4	no	—
32	#97	—	37	1	no	—
33	C₂×D₄	—	2	2	no	—
34	C₂×D₄	C₂×D₃₇	1	2	yes	—
35	C₂×C₈	—	37	2	no	—
36	C₄⋊C₄	—	37	2	no	—
37	C₄⋊C₄	—	74	2	no	—
38	C₄²	C₂×D₃₇	1	1	yes	characteristic
39	C₂³	—	2	2	no	—
40	D₄	—	2	4	no	—
41	D₄	—	4	4	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	—	74	2	no	—
46	C₂²	—	4	2	no	—
47	C₂²	—	4	4	no	—
48	C₂²	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
49	C₄	—	2	2	no	—
50	C₄	—	148	2	no	—
51	C₄	#10596964	1	2	yes	—
52	C₂	—	8	2	no	—
53	C₂	#11924523	1	1	yes	characteristic
54	C₂	#11924562	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₃₇
commutator, cosocle	C₂×C₄×C₃₇	C₂³
Frattini	C₂×C₄	C₂²×D₃₇
Fitting, prime radical	#127×C₃₇	C₂
socle	C₂²×C₃₇	C₂×D₄
hypercenter	#127	D₃₇
hypocenter	C₃₇	#490
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #127

Complements

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

N	H ≅ G/N	type
1. #11924528	C₂	semidirect
2. #11924457	C₂	semidirect
3. #11924447	C₂	semidirect
28. C₃₇	#490	semidirect

Maximal subgroups

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

subgroup	index
#11924528	2
#11924457	2
#11924447	2
#127×C₃₇	2
#490	37