Subgroups — #14557940

Order 2368.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924535	C₂	1	1	yes	maximal, characteristic
2	#11924527	C₂	1	1	yes	maximal, characteristic
3	#11924470	C₂	1	1	yes	maximal, characteristic
4	#11924469	C₂	1	1	yes	maximal, characteristic
5	#11924467	C₂	1	1	yes	maximal, characteristic
6	#11924446	C₂	1	1	yes	maximal, characteristic
7	#106×C₃₇	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₇₄	—	2	1	no	—
9	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₃₇	—	2	1	no	—
13	C₄⋊Dic₃₇	C₂²	1	1	yes	characteristic
14	C₄⋊Dic₃₇	C₂²	1	1	yes	characteristic
15	#10596936	—	2	1	no	—
16	#10596936	—	2	1	no	—
17	C₄×Dic₃₇	C₂²	1	1	yes	characteristic
18	C₂×#64436	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₃₇	—	2	1	no	—
20	C₂×C₄×C₃₇	—	2	1	no	—
21	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
22	C₂×Dic₃₇	—	2	1	no	—
23	C₂×Dic₃₇	—	2	1	no	—
24	C₂×Dic₃₇	D₄	1	1	yes	characteristic
25	C₂×Dic₃₇	D₄	1	1	yes	characteristic
26	Dic₇₄	—	4	2	no	—
27	C₈×C₃₇	Q₈	1	2	yes	complemented
28	#64436	Q₈	1	2	yes	complemented
29	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
30	C₄×C₃₇	—	4	1	no	—
31	C₄×C₃₇	—	4	1	no	—
32	C₄×C₃₇	C₂×Q₈	1	1	yes	characteristic
33	C₄×C₃₇	C₂×Q₈	1	1	yes	characteristic
34	Dic₃₇	—	2	1	no	—
35	Dic₃₇	—	2	1	no	—
36	Dic₃₇	—	4	1	no	—
37	Dic₃₇	—	4	1	no	—
38	C₂×C₃₇	C₄⋊Q₈	1	1	yes	characteristic
39	C₂×C₃₇	AGL(1,ℤ/8)	1	1	yes	characteristic
40	C₂×C₃₇	#137	1	1	yes	characteristic
41	#501	—	37	1	no	maximal, Sylow
42	C₃₇	#501	1	1	yes	characteristic, complemented, Sylow
43	C₄⋊Q₈	—	37	1	no	—
44	#125	—	37	1	no	—
45	#107	—	37	1	no	—
46	#107	—	37	1	no	—
47	#106	—	37	1	no	—
48	#106	D₃₇	1	1	yes	characteristic
49	#97	—	37	1	no	—
50	C₂×Q₈	—	74	1	no	—
51	C₂×C₈	—	37	1	no	—
52	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
53	C₄⋊C₄	—	37	1	no	—
54	C₄⋊C₄	—	37	1	no	—
55	C₄⋊C₄	—	74	1	no	—
56	C₄⋊C₄	—	74	1	no	—
57	C₄⋊C₄	—	74	1	no	—
58	C₄⋊C₄	C₂×D₃₇	1	1	yes	characteristic
59	C₄⋊C₄	C₂×D₃₇	1	1	yes	characteristic
60	C₄²	—	37	1	no	—
61	Q₈	—	148	2	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	37	1	no	—
65	C₂×C₄	—	37	1	no	—
66	C₂×C₄	—	74	1	no	—
67	C₂×C₄	—	74	1	no	—
68	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
69	C₈	—	37	2	no	—
70	C₈	Dic₇₄	1	2	yes	complemented
71	C₂²	D₄×D₃₇	1	1	yes	characteristic
72	C₄	—	4	1	no	—
73	C₄	—	4	1	no	—
74	C₄	—	74	1	no	—
75	C₄	—	74	1	no	—
76	C₄	—	148	1	no	—
77	C₄	—	148	1	no	—
78	C₄	C₂×Dic₇₄	1	1	yes	characteristic
79	C₄	Q₈×D₃₇	1	1	yes	characteristic
80	C₂	#11924535	1	1	yes	characteristic
81	C₂	#11924563	1	1	yes	characteristic
82	C₂	#11924565	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₃₇
commutator, cosocle	C₂×C₄×C₃₇	C₂³
Frattini	C₂×C₄	C₂²×D₃₇
Fitting	#106×C₃₇	C₂
socle, prime radical	C₂²×C₃₇	C₂×D₄
hypercenter	#106	D₃₇
hypocenter	C₃₇	#501
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
27. C₈×C₃₇	Q₈	semidirect
28. #64436	Q₈	semidirect
42. C₃₇	#501	semidirect
70. 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
#11924527	2
#11924470	2
#11924469	2
#11924467	2
#11924446	2
#106×C₃₇	2
#501	37