Subgroups — #14557741

Order 2368.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10596942	C₂	1	1	yes	maximal, characteristic
2	#11924534	C₂	1	1	yes	maximal, characteristic
3	Q₈×Dic₃₇	C₂	1	1	yes	maximal, characteristic
4	#11924465	C₂	1	1	yes	maximal, characteristic
5	#11924461	C₂	1	1	yes	maximal, characteristic
6	#11924460	C₂	1	1	yes	maximal, characteristic
7	C₂×Q₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈×C₃₇	C₂²	1	1	yes	characteristic
9	C₂×Q₈×C₃₇	C₂²	1	1	yes	characteristic
10	C₂×Dic₇₄	C₂²	1	1	yes	characteristic
11	Q₁₆×C₃₇	—	2	2	no	—
12	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
13	#10596942	—	2	2	no	—
14	C₄⋊Dic₃₇	—	2	1	no	—
15	C₄⋊Dic₃₇	C₂²	1	1	yes	characteristic
16	#10596936	—	2	1	no	—
17	#10596936	—	2	1	no	—
18	C₄×Dic₃₇	—	2	1	no	—
19	C₄×Dic₃₇	C₂²	1	1	yes	characteristic
20	C₂×#64436	C₂²	1	1	yes	characteristic
21	Q₈×C₃₇	—	2	1	no	—
22	Q₈×C₃₇	—	2	1	no	—
23	Q₈×C₃₇	—	2	1	no	—
24	Q₈×C₃₇	D₄	1	2	yes	—
25	C₂×C₄×C₃₇	—	2	1	no	—
26	C₂×C₄×C₃₇	—	2	1	no	—
27	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
28	C₂×Dic₃₇	—	2	1	no	—
29	C₂×Dic₃₇	—	2	1	no	—
30	C₂×Dic₃₇	D₄	1	1	yes	characteristic
31	C₂×Dic₃₇	D₄	1	1	yes	characteristic
32	Dic₇₄	—	2	1	no	—
33	Dic₇₄	—	2	1	no	—
34	C₈×C₃₇	—	2	1	no	—
35	#64436	—	2	1	no	—
36	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
37	C₄×C₃₇	—	2	2	no	—
38	C₄×C₃₇	—	4	1	no	—
39	C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
40	C₄×C₃₇	#41	1	1	yes	characteristic
41	Dic₃₇	—	2	1	no	—
42	Dic₃₇	—	4	1	no	—
43	Dic₃₇	—	4	1	no	—
44	Dic₃₇	Q₁₆	1	2	yes	complemented
45	C₂×C₃₇	#121	1	1	yes	characteristic
46	C₂×C₃₇	C₂×Q₁₆	1	1	yes	characteristic
47	C₂×C₃₇	#137	1	1	yes	characteristic
48	#462	—	37	1	no	maximal, Sylow
49	C₃₇	#462	1	1	yes	characteristic, complemented, Sylow
50	C₂×Q₁₆	—	37	1	no	—
51	C₂×Q₁₆	D₃₇	1	1	yes	characteristic
52	C₄⋊Q₈	—	37	1	no	—
53	C₄×Q₈	—	37	1	no	—
54	C₄⋊C₈	—	37	1	no	—
55	#103	—	37	1	no	—
56	#103	—	37	1	no	—
57	C₂×Q₈	—	37	1	no	—
58	C₂×Q₈	C₂×D₃₇	1	1	yes	characteristic
59	C₂×Q₈	C₂×D₃₇	1	1	yes	characteristic
60	Q₁₆	—	2	2	no	—
61	Q₁₆	—	74	2	no	—
62	C₂×C₈	—	37	1	no	—
63	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
64	C₄⋊C₄	—	37	1	no	—
65	C₄⋊C₄	—	74	1	no	—
66	C₄⋊C₄	—	74	1	no	—
67	C₄⋊C₄	—	74	1	no	—
68	C₄²	—	37	1	no	—
69	C₄²	—	74	1	no	—
70	Q₈	—	2	1	no	—
71	Q₈	—	2	1	no	—
72	Q₈	—	2	1	no	—
73	Q₈	—	74	1	no	—
74	Q₈	—	74	1	no	—
75	Q₈	C₂²⋊D₃₇	1	2	yes	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	37	1	no	—
79	C₂×C₄	—	37	1	no	—
80	C₂×C₄	—	74	1	no	—
81	C₂×C₄	—	74	1	no	—
82	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	74	1	no	—
85	C₂²	D₄×D₃₇	1	1	yes	characteristic
86	C₄	—	2	2	no	—
87	C₄	—	4	1	no	—
88	C₄	—	37	2	no	—
89	C₄	—	74	1	no	—
90	C₄	—	148	1	no	—
91	C₄	—	148	1	no	—
92	C₄	#10596964	1	1	yes	characteristic
93	C₄	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
94	C₂	#11924508	1	1	yes	characteristic
95	C₂	Q₁₆×D₃₇	1	1	yes	characteristic
96	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	C₂×Q₁₆×C₃₇	C₂
socle, prime radical	C₂²×C₃₇	C₂×D₄
hypercenter	C₂×Q₁₆	D₃₇
hypocenter	C₃₇	#462
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
44. Dic₃₇	Q₁₆	semidirect
49. C₃₇	#462	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10596942	2
#11924534	2
Q₈×Dic₃₇	2
#11924465	2
#11924461	2
#11924460	2
C₂×Q₁₆×C₃₇	2
#462	37