Subgroups — #14557826

Order 2368.

96 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	Q₈×Dic₃₇	C₂	1	1	yes	maximal, characteristic
3	#11924470	C₂	1	1	yes	maximal, characteristic
4	#11924469	C₂	1	1	yes	maximal, characteristic
5	#11924465	C₂	1	1	yes	maximal, characteristic
6	#11924460	C₂	1	1	yes	maximal, characteristic
7	#103×C₃₇	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈×C₃₇	C₂²	1	1	yes	characteristic
9	C₂×Dic₇₄	—	2	1	no	—
10	C₂×C₈×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	C₄×Dic₃₇	—	2	1	no	—
17	C₄×Dic₃₇	C₂²	1	1	yes	characteristic
18	C₂×#64436	C₂²	1	1	yes	characteristic
19	Q₈×C₃₇	—	2	1	no	—
20	Q₈×C₃₇	Q₈	1	2	yes	complemented
21	C₂×C₄×C₃₇	—	2	1	no	—
22	C₂×C₄×C₃₇	—	2	1	no	—
23	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
24	C₂×Dic₃₇	—	2	1	no	—
25	C₂×Dic₃₇	—	2	1	no	—
26	C₂×Dic₃₇	D₄	1	1	yes	characteristic
27	C₂×Dic₃₇	D₄	1	1	yes	characteristic
28	Dic₇₄	—	4	2	no	—
29	C₈×C₃₇	—	2	1	no	—
30	#64436	—	2	1	no	—
31	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
32	C₄×C₃₇	—	2	2	no	—
33	C₄×C₃₇	—	4	1	no	—
34	C₄×C₃₇	C₂×Q₈	1	1	yes	characteristic
35	C₄×C₃₇	#41	1	1	yes	characteristic
36	Dic₃₇	—	2	1	no	—
37	Dic₃₇	—	4	1	no	—
38	Dic₃₇	—	4	1	no	—
39	Dic₃₇	Q₁₆	1	2	yes	—
40	C₂×C₃₇	C₂²⋊Q₈	1	1	yes	characteristic
41	C₂×C₃₇	C₂×Q₁₆	1	1	yes	characteristic
42	C₂×C₃₇	AGL(1,ℤ/8)	1	1	yes	characteristic
43	#477	—	37	1	no	maximal, Sylow
44	C₃₇	#477	1	1	yes	characteristic, complemented, Sylow
45	C₄⋊Q₈	—	37	1	no	—
46	C₄×Q₈	—	37	1	no	—
47	#107	—	37	1	no	—
48	#107	—	37	1	no	—
49	C₄⋊C₈	—	37	1	no	—
50	#103	—	37	1	no	—
51	#103	D₃₇	1	1	yes	characteristic
52	C₂×Q₈	—	74	1	no	—
53	C₂×Q₈	C₂×D₃₇	1	1	yes	characteristic
54	C₂×C₈	—	37	1	no	—
55	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
56	C₄⋊C₄	—	37	1	no	—
57	C₄⋊C₄	—	37	1	no	—
58	C₄⋊C₄	—	74	1	no	—
59	C₄⋊C₄	—	74	1	no	—
60	C₄⋊C₄	C₂×D₃₇	1	1	yes	characteristic
61	C₄²	—	37	1	no	—
62	C₄²	—	74	1	no	—
63	Q₈	—	2	1	no	—
64	Q₈	—	148	2	no	—
65	Q₈	Dic₇₄	1	2	yes	complemented
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	37	1	no	—
69	C₂×C₄	—	37	1	no	—
70	C₂×C₄	—	74	1	no	—
71	C₂×C₄	—	74	1	no	—
72	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
73	C₈	—	2	1	no	—
74	C₈	—	74	1	no	—
75	C₂²	D₄×D₃₇	1	1	yes	characteristic
76	C₄	—	2	2	no	—
77	C₄	—	4	1	no	—
78	C₄	—	37	2	no	—
79	C₄	—	74	1	no	—
80	C₄	—	148	1	no	—
81	C₄	—	148	1	no	—
82	C₄	C₂×Dic₇₄	1	1	yes	characteristic
83	C₄	#10596964	1	1	yes	characteristic
84	C₂	#11924513	1	1	yes	characteristic
85	C₂	Q₁₆×D₃₇	1	1	yes	characteristic
86	C₂	#11924563	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₃₇
commutator, cosocle	C₂×C₄×C₃₇	C₂³
Frattini	C₂×C₄	C₂²×D₃₇
Fitting	#103×C₃₇	C₂
socle, prime radical	C₂²×C₃₇	C₂×D₄
hypercenter	#103	D₃₇
hypocenter	C₃₇	#477
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
20. Q₈×C₃₇	Q₈	semidirect
44. C₃₇	#477	semidirect
65. Q₈	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
Q₈×Dic₃₇	2
#11924470	2
#11924469	2
#11924465	2
#11924460	2
#103×C₃₇	2
#477	37