Subgroups — #14557900

Order 2368.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924534	C₂	1	1	yes	maximal, characteristic
2	#11924527	C₂	1	1	yes	maximal, characteristic
3	#11924461	C₂	1	1	yes	maximal, characteristic
4	#11924460	C₂	1	1	yes	maximal, characteristic
5	#11924459	C₂	1	1	yes	maximal, characteristic
6	#11924446	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	C₂²	1	1	yes	characteristic
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	#10596936	—	2	1	no	—
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	Q₈×C₃₇	—	2	1	no	—
20	Q₈×C₃₇	—	2	1	no	—
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	—	2	1	no	—
29	Dic₇₄	—	2	1	no	—
30	C₈×C₃₇	—	2	1	no	—
31	#64436	—	2	1	no	—
32	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
33	C₄×C₃₇	—	4	1	no	—
34	C₄×C₃₇	—	4	1	no	—
35	C₄×C₃₇	#41	1	1	yes	characteristic
36	C₄×C₃₇	#41	1	1	yes	characteristic
37	Dic₃₇	—	2	1	no	—
38	Dic₃₇	—	2	1	no	—
39	Dic₃₇	—	4	1	no	—
40	Dic₃₇	—	4	1	no	—
41	C₂×C₃₇	#124	1	1	yes	characteristic
42	C₂×C₃₇	#137	1	1	yes	characteristic
43	C₂×C₃₇	#137	1	1	yes	characteristic
44	#491	—	37	1	no	maximal, Sylow
45	C₃₇	#491	1	1	yes	characteristic, complemented, Sylow
46	C₄⋊Q₈	—	37	1	no	—
47	#125	—	37	1	no	—
48	#103	—	37	1	no	—
49	#103	—	37	1	no	—
50	#103	—	37	1	no	—
51	#103	D₃₇	1	1	yes	characteristic
52	#97	—	37	1	no	—
53	C₂×Q₈	—	37	1	no	—
54	C₂×Q₈	C₂×D₃₇	1	1	yes	characteristic
55	C₂×C₈	—	37	1	no	—
56	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
57	C₄⋊C₄	—	37	1	no	—
58	C₄⋊C₄	—	74	1	no	—
59	C₄⋊C₄	—	74	1	no	—
60	C₄⋊C₄	—	74	1	no	—
61	C₄⋊C₄	—	74	1	no	—
62	C₄⋊C₄	C₂×D₃₇	1	1	yes	characteristic
63	C₄²	—	37	1	no	—
64	Q₈	—	2	1	no	—
65	Q₈	—	2	1	no	—
66	Q₈	—	74	1	no	—
67	Q₈	—	74	1	no	—
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	37	1	no	—
71	C₂×C₄	—	37	1	no	—
72	C₂×C₄	—	74	1	no	—
73	C₂×C₄	—	74	1	no	—
74	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
75	C₈	—	2	1	no	—
76	C₈	—	74	1	no	—
77	C₂²	D₄×D₃₇	1	1	yes	characteristic
78	C₄	—	4	1	no	—
79	C₄	—	4	1	no	—
80	C₄	—	74	1	no	—
81	C₄	—	74	1	no	—
82	C₄	—	148	1	no	—
83	C₄	—	148	1	no	—
84	C₄	#10596962	1	1	yes	characteristic
85	C₄	#10596964	1	1	yes	characteristic
86	C₂	#11924522	1	1	yes	characteristic
87	C₂	#11924565	1	1	yes	characteristic
88	C₂	#11924568	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	#491
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
45. C₃₇	#491	semidirect

Maximal subgroups

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

subgroup	index
#11924534	2
#11924527	2
#11924461	2
#11924460	2
#11924459	2
#11924446	2
#103×C₃₇	2
#491	37