Subgroups — #14557905

Order 2368.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10596940	C₂	1	4	yes	maximal, complemented
2	#11924536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#64436	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	C₂×Dic₇₄	C₂²	1	2	yes	—
8	C₄²×C₃₇	C₂²	1	1	yes	characteristic
9	#10596940	—	2	8	no	—
10	C₄⋊Dic₃₇	—	2	2	no	—
11	C₂×#64436	C₂²	1	2	yes	—
12	C₂³×C₃₇	—	2	2	no	—
13	D₄×C₃₇	—	2	4	no	—
14	D₄×C₃₇	—	4	4	no	—
15	C₂×C₄×C₃₇	D₄	1	2	yes	—
16	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
17	C₂×Dic₃₇	—	2	2	no	—
18	Dic₇₄	—	2	4	no	—
19	#64436	D₄	1	4	yes	complemented
20	C₂²×C₃₇	—	4	2	no	—
21	C₂²×C₃₇	—	4	4	no	—
22	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
23	C₄×C₃₇	SD₁₆	1	4	yes	complemented
24	C₄×C₃₇	C₂×D₄	1	2	yes	—
25	Dic₃₇	—	4	2	no	—
26	C₂×C₃₇	—	8	2	no	—
27	C₂×C₃₇	#127	1	1	yes	characteristic
28	C₂×C₃₇	C₂×SD₁₆	1	2	yes	—
29	#492	—	37	1	no	maximal, Sylow
30	C₃₇	#492	1	1	yes	characteristic, complemented, Sylow
31	C₂×SD₁₆	—	37	4	no	—
32	C₄⋊Q₈	—	37	1	no	—
33	#127	D₃₇	1	1	yes	characteristic
34	C₄×C₈	—	37	1	no	—
35	C₂×Q₈	—	37	2	no	—
36	C₂×D₄	—	2	2	no	—
37	C₂×D₄	C₂×D₃₇	1	2	yes	—
38	SD₁₆	—	74	8	no	—
39	C₂×C₈	—	37	2	no	—
40	C₄⋊C₄	—	74	2	no	—
41	C₄²	C₂×D₃₇	1	1	yes	characteristic
42	C₂³	—	2	2	no	—
43	Q₈	—	74	4	no	—
44	D₄	—	2	4	no	—
45	D₄	—	4	4	no	—
46	C₂×C₄	—	74	2	no	—
47	C₂×C₄	C₂²⋊D₃₇	1	2	yes	—
48	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
49	C₈	—	37	4	no	—
50	C₂²	—	4	2	no	—
51	C₂²	—	4	4	no	—
52	C₂²	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
53	C₄	—	148	2	no	—
54	C₄	#10596940	1	4	yes	complemented
55	C₄	D₄×D₃₇	1	2	yes	—
56	C₂	—	8	2	no	—
57	C₂	#11924532	1	1	yes	characteristic
58	C₂	C₂×#10596940	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	#492
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. C₂×#10596940	C₂	semidirect
2. #11924536	C₂	semidirect
3. C₄×#64436	C₂	semidirect
19. #64436	D₄	semidirect
23. C₄×C₃₇	SD₁₆	semidirect
30. C₃₇	#492	semidirect
54. C₄	#10596940	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10596940	2
#11924536	2
C₄×#64436	2
#127×C₃₇	2
#492	37