Subgroups — #17996389

Order 4736.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11924475	C₂	1	1	yes	maximal, characteristic
2	#108×D₃₇	C₂	1	2	yes	maximal
3	#14557363	C₂	1	1	yes	maximal, characteristic, complemented
4	#14557362	C₂	1	2	yes	maximal, complemented
5	C₃₇×#368	C₂	1	1	yes	maximal, characteristic, complemented
6	M₁₆×D₃₇	—	2	2	no	—
7	C₂×C₈×D₃₇	C₂²	1	1	yes	characteristic
8	#11924475	C₄	1	4	yes	—
9	C₂×#10596925	C₂²	1	1	yes	characteristic
10	#11924472	C₂²	1	2	yes	—
11	#11924471	—	2	2	no	—
12	C₂×C₁₆×C₃₇	C₂²	1	1	yes	characteristic
13	#108×C₃₇	C₂²	1	2	yes	—
14	C₂×C₄×D₃₇	D₄	1	1	yes	characteristic
15	M₁₆×C₃₇	—	2	2	no	—
16	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
17	#10596934	—	2	2	no	—
18	C₂×#64436	D₄	1	1	yes	characteristic
19	#10596929	—	4	2	no	—
20	C₈×D₃₇	—	4	2	no	—
21	C₈×D₃₇	C₂×C₄	1	2	yes	—
22	C₈×D₃₇	Q₈	1	2	yes	—
23	C₁₆×C₃₇	C₂×C₄	1	2	yes	—
24	#10596925	C₂×C₄	1	2	yes	—
25	C₂²×D₃₇	Q₁₆	1	1	yes	characteristic
26	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
27	C₂×Dic₃₇	Q₁₆	1	1	yes	characteristic
28	C₄×D₃₇	C₄⋊C₄	1	2	yes	—
29	C₄×D₃₇	D₈	1	2	yes	—
30	C₈×C₃₇	—	4	2	no	—
31	C₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
32	C₈×C₃₇	C₂×Q₈	1	1	yes	characteristic
33	#64436	—	4	2	no	—
34	#64436	C₄⋊C₄	1	2	yes	—
35	C₂²×C₃₇	C₂×Q₁₆	1	1	yes	characteristic
36	C₂×D₃₇	—	4	1	no	—
37	C₂×D₃₇	#107	1	2	yes	—
38	C₄×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₄×C₃₇	C₂×D₈	1	1	yes	characteristic
40	Dic₃₇	#107	1	2	yes	—
41	#2161	—	37	1	no	maximal, Sylow
42	C₂×C₃₇	—	2	1	no	—
43	C₂×C₃₇	C₂×#107	1	1	yes	characteristic
44	D₃₇	—	2	2	no	—
45	C₂×M₃₂	—	37	1	no	—
46	C₂×#108	—	37	2	no	—
47	#368	—	37	1	no	—
48	#368	—	37	2	no	—
49	#368	D₃₇	1	1	yes	characteristic, complemented
50	C₃₇	#2161	1	1	yes	characteristic, complemented, Sylow
51	C₂×M₁₆	—	74	2	no	—
52	C₂²×C₈	—	37	1	no	—
53	M₃₂	—	37	4	no	—
54	C₂×C₁₆	—	37	1	no	—
55	C₂×C₁₆	C₂×D₃₇	1	1	yes	characteristic
56	#108	—	37	2	no	—
57	#108	—	74	2	no	—
58	#108	C₂×D₃₇	1	2	yes	—
59	C₂²×C₄	—	37	1	no	—
60	M₁₆	—	2	2	no	—
61	M₁₆	—	74	2	no	—
62	M₁₆	—	148	2	no	—
63	C₂×C₈	—	37	1	no	—
64	C₂×C₈	—	37	2	no	—
65	C₂×C₈	—	37	2	no	—
66	C₂×C₈	—	148	2	no	—
67	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
68	C₁₆	—	37	2	no	—
69	C₁₆	C₄×D₃₇	1	2	yes	—
70	C₂³	—	37	1	no	—
71	C₂×C₄	—	37	1	no	—
72	C₂×C₄	—	37	2	no	—
73	C₂×C₄	—	37	2	no	—
74	C₂×C₄	D₄×D₃₇	1	1	yes	characteristic
75	C₈	—	4	2	no	—
76	C₈	—	37	2	no	—
77	C₈	—	148	2	no	—
78	C₈	C₂×C₄×D₃₇	1	1	yes	characteristic
79	C₈	Q₈×D₃₇	1	1	yes	characteristic
80	C₂²	—	37	2	no	—
81	C₂²	—	148	1	no	—
82	C₂²	Q₁₆×D₃₇	1	1	yes	characteristic
83	C₄	—	37	2	no	—
84	C₄	C₄⋊C₄×D₃₇	1	1	yes	characteristic
85	C₄	D₈×D₃₇	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	74	2	no	—
88	C₂	#107×D₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₈×D₃₇
commutator	C₈×C₃₇	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₃₇
Fitting	C₃₇×#368	C₂
socle	C₂×C₃₇	C₂×#107
prime radical	C₂²×D₃₇	Q₁₆
cosocle	C₂×C₈×C₃₇	C₂³
hypercenter	#368	D₃₇
hypocenter	C₃₇	#2161
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #368

Complements

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

N	H ≅ G/N	type
3. #14557363	C₂	semidirect
4. #14557362	C₂	semidirect
5. C₃₇×#368	C₂	semidirect
49. #368	D₃₇	semidirect
50. C₃₇	#2161	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11924475	2
#108×D₃₇	2
#14557363	2
#14557362	2
C₃₇×#368	2
#2161	37