Subgroups — #14557582

Order 2368.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10596934	C₂	1	2	yes	maximal
2	#11924472	C₂	1	4	yes	maximal, complemented
3	C₂×M₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₃₇	C₂²	1	1	yes	characteristic
5	M₁₆×C₃₇	C₄	1	4	yes	—
6	C₂×C₈×C₃₇	C₂²	1	2	yes	—
7	#10596934	—	2	2	no	—
8	#10596934	C₂²	1	4	yes	—
9	C₂×#64436	—	2	2	no	—
10	C₂³×C₃₇	Q₈	1	1	yes	characteristic
11	C₂×C₄×C₃₇	C₂×C₄	1	2	yes	—
12	C₂×C₄×C₃₇	D₄	1	2	yes	—
13	C₂×C₄×C₃₇	Q₈	1	1	yes	characteristic
14	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
15	C₈×C₃₇	C₂×C₄	1	4	yes	—
16	#64436	—	2	4	no	—
17	C₂²×C₃₇	—	4	1	no	—
18	C₂²×C₃₇	C₄⋊C₄	1	2	yes	—
19	C₂²×C₃₇	C₂×Q₈	1	1	yes	characteristic
20	C₄×C₃₇	C₄⋊C₄	1	2	yes	—
21	C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
22	C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
23	C₂×C₃₇	—	2	2	no	—
24	C₂×C₃₇	—	2	1	no	—
25	C₂×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
26	#430	—	37	1	no	maximal, Sylow
27	C₃₇	#430	1	1	yes	characteristic, complemented, Sylow
28	C₂×M₁₆	—	37	2	no	—
29	C₂×M₁₆	D₃₇	1	1	yes	characteristic
30	#108	—	37	4	no	—
31	C₂²×C₄	C₂×D₃₇	1	1	yes	characteristic
32	M₁₆	—	37	4	no	—
33	M₁₆	—	74	2	no	—
34	M₁₆	Dic₃₇	1	4	yes	—
35	C₂×C₈	—	74	2	no	—
36	C₂×C₈	C₂×D₃₇	1	2	yes	—
37	C₂³	Dic₇₄	1	1	yes	characteristic
38	C₂×C₄	Dic₇₄	1	1	yes	characteristic
39	C₂×C₄	D₁₄₈	1	2	yes	—
40	C₂×C₄	C₂×Dic₃₇	1	2	yes	—
41	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
42	C₈	—	74	4	no	—
43	C₈	C₂×Dic₃₇	1	4	yes	—
44	C₂²	—	4	1	no	—
45	C₂²	C₄⋊Dic₃₇	1	2	yes	—
46	C₂²	C₂×Dic₇₄	1	1	yes	characteristic
47	C₄	C₄⋊Dic₃₇	1	2	yes	—
48	C₄	C₂×D₁₄₈	1	1	yes	characteristic
49	C₄	C₂²×Dic₃₇	1	1	yes	characteristic
50	C₂	—	2	2	no	—
51	C₂	—	2	1	no	—
52	C₂	C₂×C₄⋊Dic₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₁₄₈
commutator	C₄×C₃₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃₇
Fitting	C₂×M₁₆×C₃₇	C₂
socle	C₂×C₃₇	C₂×C₄⋊C₄
prime radical	C₂³×C₃₇	Q₈
cosocle	C₂×C₄×C₃₇	C₂³
hypercenter	C₂×M₁₆	D₃₇
hypocenter	C₃₇	#430
LCS	G ▷ C₄×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
2. #11924472	C₂	semidirect
27. C₃₇	#430	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
#11924472	2
C₂×M₁₆×C₃₇	2
#430	37