Subgroups — #14557887

Order 2368.

96 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	#11924460	C₂	1	2	yes	maximal, complemented
3	#11924457	C₂	1	2	yes	maximal
4	C₄×#64436	C₂	1	1	yes	maximal, characteristic, complemented
5	#124×C₃₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×C₃₇	C₂²	1	1	yes	characteristic
7	C₂×D₄×C₃₇	C₂²	1	1	yes	characteristic
8	C₂²⋊C₄×C₃₇	—	2	2	no	—
9	C₄²×C₃₇	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₃₇	C₂²	1	2	yes	—
11	#10596936	—	2	2	no	—
12	C₂×#64436	C₂²	1	2	yes	—
13	C₂³×C₃₇	—	2	1	no	—
14	Q₈×C₃₇	—	2	2	no	—
15	D₄×C₃₇	—	2	2	no	—
16	C₂×C₄×C₃₇	—	2	1	no	—
17	C₂×C₄×C₃₇	D₄	1	2	yes	—
18	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
19	C₂×Dic₃₇	—	2	2	no	—
20	#64436	—	2	2	no	—
21	C₂²×C₃₇	—	4	1	no	—
22	C₂²×C₃₇	—	4	2	no	—
23	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
24	C₄×C₃₇	—	2	2	no	—
25	C₄×C₃₇	—	4	1	no	—
26	C₄×C₃₇	#41	1	2	yes	—
27	Dic₃₇	—	4	2	no	—
28	C₂×C₃₇	—	8	1	no	—
29	C₂×C₃₇	#124	1	1	yes	characteristic
30	C₂×C₃₇	#135	1	2	yes	—
31	#488	—	37	1	no	maximal, Sylow
32	C₃₇	#488	1	1	yes	characteristic, complemented, Sylow
33	#125	—	37	1	no	—
34	#124	D₃₇	1	1	yes	characteristic
35	#103	—	37	2	no	—
36	#102	—	37	2	no	—
37	C₄×C₈	—	37	1	no	—
38	C₂×Q₈	C₂×D₃₇	1	1	yes	characteristic
39	C₂×D₄	C₂×D₃₇	1	1	yes	characteristic
40	C₂×C₈	—	37	2	no	—
41	C₄⋊C₄	—	37	2	no	—
42	C₄⋊C₄	—	74	2	no	—
43	C₂²⋊C₄	—	2	2	no	—
44	C₄²	C₂×D₃₇	1	1	yes	characteristic
45	C₂³	—	2	1	no	—
46	Q₈	—	2	2	no	—
47	D₄	—	2	2	no	—
48	C₂×C₄	—	2	1	no	—
49	C₂×C₄	—	74	2	no	—
50	C₂×C₄	C₂²⋊D₃₇	1	2	yes	—
51	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
52	C₈	—	74	2	no	—
53	C₂²	—	4	1	no	—
54	C₂²	—	4	2	no	—
55	C₂²	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
56	C₄	—	2	2	no	—
57	C₄	—	4	1	no	—
58	C₄	—	148	2	no	—
59	C₄	#10596964	1	2	yes	—
60	C₂	—	8	1	no	—
61	C₂	#11924523	1	1	yes	characteristic
62	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	#124×C₃₇	C₂
socle	C₂²×C₃₇	C₂×D₄
prime radical	C₂×D₄×C₃₇	C₂²
hypercenter	#124	D₃₇
hypocenter	C₃₇	#488
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #124

Complements

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

N	H ≅ G/N	type
1. #11924528	C₂	semidirect
2. #11924460	C₂	semidirect
4. C₄×#64436	C₂	semidirect
32. C₃₇	#488	semidirect

Maximal subgroups

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

subgroup	index
#11924528	2
#11924460	2
#11924457	2
C₄×#64436	2
#124×C₃₇	2
#488	37