Subgroups — #17992656

Order 4736.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557935	C₂	1	1	yes	maximal, characteristic
2	#14557354	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#364	C₂	1	1	yes	maximal, characteristic
4	#11924528	C₄	1	2	yes	—
5	#11924476	—	2	1	no	—
6	#11924470	—	2	1	no	—
7	#11924468	—	2	1	no	—
8	M₃₂×C₃₇	—	2	1	no	—
9	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
11	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
12	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
13	C₄⋊Dic₃₇	—	2	2	no	—
14	#10596936	—	4	2	no	—
15	C₁₆×C₃₇	—	4	1	no	—
16	#10596925	—	4	1	no	—
17	C₂×C₄×C₃₇	—	2	1	no	—
18	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×Dic₃₇	—	4	2	no	—
20	C₈×C₃₇	SD₁₆	1	1	yes	characteristic
21	C₈×C₃₇	SD₁₆	1	1	yes	characteristic
22	C₈×C₃₇	Q₁₆	1	1	yes	characteristic
23	C₈×C₃₇	Q₁₆	1	1	yes	characteristic
24	C₂²×C₃₇	#100	1	1	yes	characteristic
25	C₄×C₃₇	—	4	1	no	—
26	C₄×C₃₇	#103	1	1	yes	characteristic
27	C₄×C₃₇	#103	1	1	yes	characteristic
28	Dic₃₇	—	8	2	no	—
29	#1366	—	37	1	no	maximal, Sylow
30	C₂×C₃₇	—	2	1	no	—
31	C₂×C₃₇	#333	1	1	yes	characteristic
32	#499	—	37	1	no	—
33	#364	—	37	1	no	—
34	#364	D₃₇	1	1	yes	characteristic
35	C₃₇	#1366	1	1	yes	characteristic, complemented, Sylow
36	#125	—	37	2	no	—
37	M₃₂	—	2	1	no	—
38	M₃₂	—	74	1	no	—
39	#107	—	74	1	no	—
40	#106	—	74	1	no	—
41	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
42	C₂×C₈	D₁₄₈	1	1	yes	characteristic
43	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
44	C₄⋊C₄	—	74	2	no	—
45	C₄⋊C₄	—	148	2	no	—
46	C₄²	C₄×D₃₇	1	1	yes	characteristic
47	C₁₆	—	4	1	no	—
48	C₁₆	—	148	1	no	—
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	148	2	no	—
51	C₂×C₄	#10596938	1	1	yes	characteristic
52	C₈	#10596930	1	1	yes	characteristic
53	C₈	Dic₁₄₈	1	1	yes	characteristic
54	C₈	#10596940	1	1	yes	characteristic
55	C₈	#10596942	1	1	yes	characteristic
56	C₂²	#11924452	1	1	yes	characteristic
57	C₄	—	4	1	no	—
58	C₄	—	296	2	no	—
59	C₄	#11924459	1	1	yes	characteristic
60	C₄	#11924461	1	1	yes	characteristic
61	C₂	—	2	1	no	—
62	C₂	#14557281	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14557281
commutator	C₄²×C₃₇	C₂×C₄
Frattini	C₄×C₈	C₂×D₃₇
Fitting	C₃₇×#364	C₂
socle	C₂×C₃₇	#333
prime radical	C₂²×C₃₇	#100
cosocle	C₄×C₈×C₃₇	C₂²
hypercenter	#364	D₃₇
hypocenter	C₃₇	#1366
LCS	G ▷ C₄²×C₃₇ ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
35. C₃₇	#1366	semidirect

Maximal subgroups

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

subgroup	index
#14557935	2
#14557354	2
C₃₇×#364	2
#1366	37