Subgroups — #14557304

Order 2368.

90 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	#11924495	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	M₁₆×C₃₇	—	2	1	no	—
6	M₁₆×C₃₇	—	2	1	no	—
7	C₂×C₈×C₃₇	C₄	1	2	yes	complemented
8	C₂²⋊Dic₃₇	C₄	1	2	yes	—
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	C₈×C₃₇	—	2	2	no	—
23	#64436	—	2	2	no	—
24	C₂²×C₃₇	—	4	1	no	—
25	C₂²×C₃₇	C₄²	1	1	yes	characteristic
26	C₂²×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
27	C₂²×C₃₇	C₄⋊C₄	1	1	yes	characteristic
28	C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
29	C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
30	C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
31	C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
32	Dic₃₇	—	4	2	no	—
33	C₂×C₃₇	—	2	1	no	—
34	C₂×C₃₇	—	2	1	no	—
35	C₂×C₃₇	—	2	1	no	—
36	C₂×C₃₇	#95	1	1	yes	characteristic
37	#344	—	37	1	no	maximal, Sylow
38	C₃₇	#344	1	1	yes	characteristic, complemented, Sylow
39	C₂×M₁₆	—	37	1	no	—
40	C₂×M₁₆	D₃₇	1	1	yes	characteristic
41	#117	—	37	1	no	—
42	C₂²×C₄	C₂×D₃₇	1	1	yes	characteristic
43	M₁₆	—	2	1	no	—
44	M₁₆	—	2	1	no	—
45	M₁₆	—	37	2	no	—
46	M₁₆	—	74	1	no	—
47	C₂×C₈	—	74	1	no	—
48	C₂×C₈	Dic₃₇	1	2	yes	complemented
49	C₄⋊C₄	—	74	1	no	—
50	C₂²⋊C₄	—	37	2	no	—
51	C₄²	—	74	1	no	—
52	C₂³	C₄×D₃₇	1	1	yes	characteristic
53	C₂×C₄	—	74	2	no	—
54	C₂×C₄	Dic₇₄	1	1	yes	characteristic
55	C₂×C₄	C₄×D₃₇	1	1	yes	characteristic
56	C₂×C₄	D₁₄₈	1	1	yes	characteristic
57	C₂×C₄	C₂×Dic₃₇	1	1	yes	characteristic
58	C₂×C₄	C₂²⋊D₃₇	1	1	yes	characteristic
59	C₂×C₄	C₂²⋊D₃₇	1	1	yes	characteristic
60	C₈	—	2	2	no	—
61	C₈	—	74	2	no	—
62	C₂²	—	4	1	no	—
63	C₂²	C₄×Dic₃₇	1	1	yes	characteristic
64	C₂²	#10596936	1	1	yes	characteristic
65	C₂²	#10596938	1	1	yes	characteristic
66	C₄	—	148	2	no	—
67	C₄	#10596936	1	1	yes	characteristic
68	C₄	C₄⋊Dic₃₇	1	1	yes	characteristic
69	C₄	#10596938	1	1	yes	characteristic
70	C₄	C₂²⋊Dic₃₇	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	—	2	1	no	—
73	C₂	—	2	1	no	—
74	C₂	#11924443	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊Dic₃₇
commutator	C₂²×C₃₇	C₄²
Frattini	C₂²×C₄	C₂×D₃₇
Fitting	C₂×M₁₆×C₃₇	C₂
socle	C₂×C₃₇	#95
prime radical	C₂³×C₃₇	C₂×C₄
cosocle	C₂²×C₄×C₃₇	C₂²
hypercenter	C₂×M₁₆	D₃₇
hypocenter	C₃₇	#344
LCS	G ▷ C₂²×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
7. C₂×C₈×C₃₇	C₄	semidirect
12. #10596934	C₄	semidirect
38. C₃₇	#344	semidirect
48. C₂×C₈	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
#11924495	2
C₂×M₁₆×C₃₇	2
#344	37