Subgroups — #14557580

Order 2368.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10596929	C₂	1	1	yes	maximal, characteristic
2	M₁₆×D₃₇	C₂	1	2	yes	maximal
3	#11924472	C₂	1	1	yes	maximal, characteristic, complemented
4	#11924471	C₂	1	2	yes	maximal, complemented
5	#108×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₃₇	C₂²	1	1	yes	characteristic
7	M₁₆×C₃₇	C₂²	1	2	yes	—
8	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
9	#10596934	C₂²	1	2	yes	—
10	C₂×#64436	C₂²	1	1	yes	characteristic
11	#10596929	—	2	2	no	—
12	#10596929	C₄	1	4	yes	—
13	C₈×D₃₇	—	2	2	no	—
14	C₂²×D₃₇	Q₈	1	1	yes	characteristic
15	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
16	C₂×Dic₃₇	Q₈	1	1	yes	characteristic
17	C₄×D₃₇	C₂×C₄	1	2	yes	—
18	C₄×D₃₇	D₄	1	2	yes	—
19	C₈×C₃₇	—	2	2	no	—
20	C₈×C₃₇	C₂×C₄	1	2	yes	—
21	#64436	—	2	2	no	—
22	#64436	C₂×C₄	1	2	yes	—
23	C₂²×C₃₇	C₂×Q₈	1	1	yes	characteristic
24	C₂×D₃₇	—	4	1	no	—
25	C₂×D₃₇	C₄⋊C₄	1	2	yes	—
26	C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
27	C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
28	Dic₃₇	C₄⋊C₄	1	2	yes	—
29	C₂×C₃₇	—	2	1	no	—
30	C₂×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
31	D₃₇	—	2	2	no	—
32	#430	—	37	1	no	maximal, Sylow
33	C₃₇	#430	1	1	yes	characteristic, complemented, Sylow
34	C₂×M₁₆	—	37	1	no	—
35	C₂×M₁₆	—	37	2	no	—
36	#108	—	37	2	no	—
37	#108	—	37	1	no	—
38	#108	D₃₇	1	1	yes	characteristic, complemented
39	C₂²×C₄	—	37	1	no	—
40	M₁₆	—	37	4	no	—
41	M₁₆	—	37	2	no	—
42	M₁₆	—	74	2	no	—
43	M₁₆	C₂×D₃₇	1	2	yes	—
44	C₂×C₈	—	37	1	no	—
45	C₂×C₈	—	74	2	no	—
46	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
47	C₂³	—	37	1	no	—
48	C₂×C₄	—	37	1	no	—
49	C₂×C₄	—	37	2	no	—
50	C₂×C₄	—	37	2	no	—
51	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
52	C₈	—	2	2	no	—
53	C₈	—	37	2	no	—
54	C₈	—	74	2	no	—
55	C₈	C₄×D₃₇	1	2	yes	—
56	C₂²	—	37	2	no	—
57	C₂²	—	148	1	no	—
58	C₂²	Q₈×D₃₇	1	1	yes	characteristic
59	C₄	—	37	2	no	—
60	C₄	C₂×C₄×D₃₇	1	1	yes	characteristic
61	C₄	D₄×D₃₇	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	74	2	no	—
64	C₂	C₄⋊C₄×D₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×D₃₇
commutator	C₄×C₃₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃₇
Fitting	#108×C₃₇	C₂
socle	C₂×C₃₇	C₂×C₄⋊C₄
prime radical	C₂²×D₃₇	Q₈
cosocle	C₂×C₄×C₃₇	C₂³
hypercenter	#108	D₃₇
hypocenter	C₃₇	#430
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
3. #11924472	C₂	semidirect
4. #11924471	C₂	semidirect
5. #108×C₃₇	C₂	semidirect
33. C₃₇	#430	semidirect
38. #108	D₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10596929	2
M₁₆×D₃₇	2
#11924472	2
#11924471	2
#108×C₃₇	2
#430	37