Subgroups — #14557301

Order 2368.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10596934	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×M₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₃₇	C₂²	1	1	yes	characteristic
5	C₂²×Dic₃₇	C₄	1	2	yes	—
6	M₁₆×C₃₇	—	2	1	no	—
7	M₁₆×C₃₇	C₄	1	2	yes	complemented
8	C₂×C₈×C₃₇	—	2	1	no	—
9	C₄⋊Dic₃₇	—	2	1	no	—
10	C₄⋊Dic₃₇	—	2	1	no	—
11	#10596934	—	2	1	no	—
12	#10596934	C₄	1	2	yes	complemented
13	C₂×#64436	—	2	1	no	—
14	C₂³×C₃₇	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₃₇	D₄	1	1	yes	characteristic
18	C₂×C₄×C₃₇	D₄	1	1	yes	characteristic
19	C₂×C₄×C₃₇	D₄	1	1	yes	characteristic
20	C₂×C₄×C₃₇	Q₈	1	1	yes	characteristic
21	C₂×Dic₃₇	—	2	2	no	—
22	C₂×Dic₃₇	—	4	2	no	—
23	C₈×C₃₇	—	2	2	no	—
24	#64436	—	2	2	no	—
25	C₂²×C₃₇	—	2	1	no	—
26	C₂²×C₃₇	—	2	1	no	—
27	C₂²×C₃₇	C₄²	1	1	yes	characteristic
28	C₂²×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
29	C₂²×C₃₇	C₄⋊C₄	1	1	yes	characteristic
30	C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
31	C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
32	C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
33	C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
34	Dic₃₇	—	4	2	no	—
35	C₂×C₃₇	—	2	1	no	—
36	C₂×C₃₇	—	2	1	no	—
37	C₂×C₃₇	#95	1	1	yes	characteristic
38	C₂×C₃₇	#100	1	1	yes	characteristic
39	C₂×C₃₇	#101	1	1	yes	characteristic
40	#343	—	37	1	no	maximal, Sylow
41	C₃₇	#343	1	1	yes	characteristic, complemented, Sylow
42	C₂×M₁₆	—	37	1	no	—
43	C₂×M₁₆	D₃₇	1	1	yes	characteristic
44	C₂×C₄⋊C₄	—	37	1	no	—
45	C₂²×C₄	—	37	2	no	—
46	C₂²×C₄	C₂×D₃₇	1	1	yes	characteristic
47	M₁₆	—	2	1	no	—
48	M₁₆	—	37	2	no	—
49	M₁₆	—	74	1	no	—
50	M₁₆	Dic₃₇	1	2	yes	complemented
51	C₂×C₈	—	2	1	no	—
52	C₂×C₈	—	74	1	no	—
53	C₄⋊C₄	—	74	1	no	—
54	C₄⋊C₄	—	74	1	no	—
55	C₂³	C₄×D₃₇	1	1	yes	characteristic
56	C₂×C₄	—	74	2	no	—
57	C₂×C₄	—	148	2	no	—
58	C₂×C₄	Dic₇₄	1	1	yes	characteristic
59	C₂×C₄	C₄×D₃₇	1	1	yes	characteristic
60	C₂×C₄	D₁₄₈	1	1	yes	characteristic
61	C₂×C₄	C₂×Dic₃₇	1	1	yes	characteristic
62	C₂×C₄	C₂²⋊D₃₇	1	1	yes	characteristic
63	C₂×C₄	C₂²⋊D₃₇	1	1	yes	characteristic
64	C₈	—	2	2	no	—
65	C₈	—	74	2	no	—
66	C₂²	—	2	1	no	—
67	C₂²	—	2	1	no	—
68	C₂²	C₄×Dic₃₇	1	1	yes	characteristic
69	C₂²	#10596936	1	1	yes	characteristic
70	C₂²	#10596938	1	1	yes	characteristic
71	C₄	—	148	2	no	—
72	C₄	#10596936	1	1	yes	characteristic
73	C₄	C₄⋊Dic₃₇	1	1	yes	characteristic
74	C₄	#10596938	1	1	yes	characteristic
75	C₄	C₂²⋊Dic₃₇	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	2	1	no	—
78	C₂	#11924443	1	1	yes	characteristic
79	C₂	#11924452	1	1	yes	characteristic
80	C₂	#11924454	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10596938
commutator	C₂²×C₃₇	C₄²
Frattini	C₂²×C₄	C₂×D₃₇
Fitting	C₂×M₁₆×C₃₇	C₂
socle	C₂²×C₃₇	C₂²⋊C₄
prime radical	C₂³×C₃₇	C₂×C₄
cosocle	C₂²×C₄×C₃₇	C₂²
hypercenter	C₂×M₁₆	D₃₇
hypocenter	C₃₇	#343
LCS	G ▷ C₂²×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
7. M₁₆×C₃₇	C₄	semidirect
12. #10596934	C₄	semidirect
41. C₃₇	#343	semidirect
50. M₁₆	Dic₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10596934	2
C₂×C₄⋊Dic₃₇	2
C₂×M₁₆×C₃₇	2
#343	37