Subgroups — #14557937

Order 2368.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924535	C₂	1	2	yes	maximal
2	#11924470	C₂	1	1	yes	maximal, characteristic
3	#11924469	C₂	1	2	yes	maximal
4	C₈×Dic₃₇	C₂	1	1	yes	maximal, characteristic
5	#107×C₃₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₇₄	—	2	2	no	—
7	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
8	C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
9	C₄⋊Dic₃₇	C₂²	1	2	yes	—
10	#10596936	—	2	2	no	—
11	C₄×Dic₃₇	C₂²	1	1	yes	characteristic
12	C₂×#64436	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₃₇	—	2	2	no	—
14	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
15	C₂×Dic₃₇	—	2	2	no	—
16	C₂×Dic₃₇	D₄	1	1	yes	characteristic
17	C₂×Dic₃₇	D₄	1	1	yes	characteristic
18	Dic₇₄	—	4	4	no	—
19	C₈×C₃₇	Q₈	1	2	yes	complemented
20	#64436	Q₈	1	2	yes	complemented
21	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
22	C₄×C₃₇	—	4	2	no	—
23	C₄×C₃₇	C₂×Q₈	1	1	yes	characteristic
24	C₄×C₃₇	C₂×Q₈	1	1	yes	characteristic
25	Dic₃₇	—	4	2	no	—
26	Dic₃₇	D₈	1	2	yes	—
27	Dic₃₇	Q₁₆	1	2	yes	—
28	C₂×C₃₇	C₄⋊Q₈	1	1	yes	characteristic
29	C₂×C₃₇	C₂×D₈	1	1	yes	characteristic
30	C₂×C₃₇	C₂×Q₁₆	1	1	yes	characteristic
31	#500	—	37	1	no	maximal, Sylow
32	C₃₇	#500	1	1	yes	characteristic, complemented, Sylow
33	C₄⋊Q₈	—	37	2	no	—
34	#107	—	37	1	no	—
35	#107	—	37	2	no	—
36	#107	D₃₇	1	1	yes	characteristic
37	C₄×C₈	—	37	1	no	—
38	C₂×Q₈	—	74	2	no	—
39	C₂×C₈	—	37	1	no	—
40	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
41	C₄⋊C₄	—	37	2	no	—
42	C₄⋊C₄	—	74	2	no	—
43	C₄⋊C₄	C₂×D₃₇	1	2	yes	—
44	C₄²	—	37	1	no	—
45	Q₈	—	148	4	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	—	37	1	no	—
48	C₂×C₄	—	37	1	no	—
49	C₂×C₄	—	74	2	no	—
50	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
51	C₈	—	37	2	no	—
52	C₈	Dic₇₄	1	2	yes	complemented
53	C₂²	D₄×D₃₇	1	1	yes	characteristic
54	C₄	—	4	2	no	—
55	C₄	—	37	2	no	—
56	C₄	—	37	2	no	—
57	C₄	—	148	2	no	—
58	C₄	C₂×Dic₇₄	1	1	yes	characteristic
59	C₄	Q₈×D₃₇	1	1	yes	characteristic
60	C₂	#11924535	1	1	yes	characteristic
61	C₂	D₈×D₃₇	1	1	yes	characteristic
62	C₂	Q₁₆×D₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₃₇
commutator, cosocle	C₂×C₄×C₃₇	C₂³
Frattini	C₂×C₄	C₂²×D₃₇
Fitting	#107×C₃₇	C₂
socle, prime radical	C₂²×C₃₇	C₂×D₄
hypercenter	#107	D₃₇
hypocenter	C₃₇	#500
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
19. C₈×C₃₇	Q₈	semidirect
20. #64436	Q₈	semidirect
32. C₃₇	#500	semidirect
52. C₈	Dic₇₄	semidirect

Maximal subgroups

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

subgroup	index
#11924535	2
#11924470	2
#11924469	2
C₈×Dic₃₇	2
#107×C₃₇	2
#500	37