Subgroups — #17992783

Order 4736.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557367	C₂	1	1	yes	maximal, characteristic, complemented
2	#14557361	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#508	C₂	1	1	yes	maximal, characteristic
4	#11924470	—	2	1	no	—
5	#11924442	—	2	1	no	—
6	#135×C₃₇	—	2	1	no	—
7	Q₃₂×C₃₇	C₄	1	1	yes	characteristic, complemented
8	SD₃₂×C₃₇	—	2	1	no	—
9	D₁₆×C₃₇	C₄	1	1	yes	characteristic, complemented
10	C₂×C₁₆×C₃₇	C₂²	1	1	yes	characteristic
11	#41×C₃₇	—	4	1	no	—
12	Q₁₆×C₃₇	—	2	1	no	—
13	SD₁₆×C₃₇	—	4	1	no	—
14	D₈×C₃₇	—	2	1	no	—
15	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
16	C₄⋊Dic₃₇	—	4	1	no	—
17	C₁₆×C₃₇	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₃₇	D₄	1	1	yes	characteristic
19	Q₈×C₃₇	—	4	1	no	—
20	D₄×C₃₇	—	4	1	no	—
21	D₄×C₃₇	—	8	1	no	—
22	C₂×C₄×C₃₇	—	8	1	no	—
23	C₂×C₄×C₃₇	D₈	1	1	yes	characteristic
24	C₂×Dic₃₇	—	8	1	no	—
25	C₈×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₃₇	SD₁₆	1	1	yes	characteristic
27	C₂²×C₃₇	—	8	1	no	—
28	C₂²×C₃₇	D₁₆	1	1	yes	characteristic
29	C₄×C₃₇	—	8	1	no	—
30	C₄×C₃₇	#102	1	1	yes	characteristic
31	C₄×C₃₇	SD₃₂	1	1	yes	characteristic
32	Dic₃₇	—	16	1	no	—
33	#1418	—	37	1	no	maximal, Sylow
34	C₂×C₃₇	—	2	1	no	—
35	C₂×C₃₇	—	16	1	no	—
36	C₂×C₃₇	#357	1	1	yes	characteristic
37	#508	D₃₇	1	1	yes	characteristic
38	M₆₄	—	37	1	no	—
39	#367	—	37	1	no	—
40	C₃₇	#1418	1	1	yes	characteristic, complemented, Sylow
41	#135	—	2	1	no	—
42	Q₃₂	Dic₃₇	1	1	yes	characteristic, complemented
43	SD₃₂	—	2	1	no	—
44	D₁₆	Dic₃₇	1	1	yes	characteristic, complemented
45	C₂×C₁₆	C₂×D₃₇	1	1	yes	characteristic
46	#107	—	74	1	no	—
47	C₃₂	—	74	1	no	—
48	#41	—	4	1	no	—
49	Q₁₆	—	2	1	no	—
50	SD₁₆	—	4	1	no	—
51	D₈	—	2	1	no	—
52	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
53	C₄⋊C₄	—	148	1	no	—
54	C₁₆	C₂×Dic₃₇	1	1	yes	characteristic
55	C₁₆	C₂²⋊D₃₇	1	1	yes	characteristic
56	Q₈	—	4	1	no	—
57	D₄	—	4	1	no	—
58	D₄	—	8	1	no	—
59	C₂×C₄	—	8	1	no	—
60	C₂×C₄	—	296	1	no	—
61	C₂×C₄	#10596939	1	1	yes	characteristic
62	C₈	#10596940	1	1	yes	characteristic
63	C₈	C₂²⋊Dic₃₇	1	1	yes	characteristic
64	C₂²	—	8	1	no	—
65	C₂²	#11924477	1	1	yes	characteristic
66	C₄	—	8	1	no	—
67	C₄	—	592	1	no	—
68	C₄	#11924457	1	1	yes	characteristic
69	C₄	#11924480	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	16	1	no	—
72	C₂	#14557334	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14557334
commutator	C₁₆×C₃₇	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₃₇
Fitting, prime radical	C₃₇×#508	C₂
socle	C₂×C₃₇	#357
cosocle	C₂×C₁₆×C₃₇	C₂²
hypercenter	#508	D₃₇
hypocenter	C₃₇	#1418
LCS	G ▷ C₁₆×C₃₇ ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #508

Complements

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

N	H ≅ G/N	type
1. #14557367	C₂	semidirect
2. #14557361	C₂	semidirect
7. Q₃₂×C₃₇	C₄	semidirect
9. D₁₆×C₃₇	C₄	semidirect
40. C₃₇	#1418	semidirect
42. Q₃₂	Dic₃₇	semidirect
44. D₁₆	Dic₃₇	semidirect

Maximal subgroups

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

subgroup	index
#14557367	2
#14557361	2
C₃₇×#508	2
#1418	37