Subgroups — #14557951

Order 2368.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924542	C₂	1	1	yes	maximal, characteristic
2	#11924475	C₂	1	2	yes	maximal, complemented
3	C₂×#10596925	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₆×D₃₇	C₂	1	2	yes	maximal, complemented
5	M₃₂×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#10596962	C₄	1	1	yes	characteristic
7	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
8	#10596934	C₄	1	1	yes	characteristic
9	#10596929	C₄	1	2	yes	—
10	C₈×D₃₇	C₂²	1	2	yes	—
11	C₁₆×C₃₇	C₂²	1	2	yes	—
12	#10596925	C₂²	1	1	yes	characteristic
13	#10596925	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
15	C₂²⋊D₃₇	C₈	1	2	yes	—
16	D₁₄₈	C₈	1	1	yes	characteristic
17	C₄×D₃₇	C₂×C₄	1	2	yes	—
18	Dic₇₄	C₈	1	1	yes	characteristic
19	C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
20	C₈×C₃₇	C₂³	1	1	yes	characteristic
21	#64436	C₂×C₄	1	2	yes	—
22	C₂²×C₃₇	C₂×C₈	1	1	yes	characteristic
23	C₂×D₃₇	C₂×C₈	1	2	yes	—
24	C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
25	C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
26	Dic₃₇	C₂×C₈	1	2	yes	—
27	C₂×C₃₇	—	2	1	no	—
28	C₂×C₃₇	C₂²×C₈	1	1	yes	characteristic
29	D₃₇	—	2	2	no	—
30	#504	—	37	1	no	maximal, Sylow
31	C₃₇	#504	1	1	yes	characteristic, complemented, Sylow
32	#131	—	37	1	no	—
33	M₃₂	—	37	2	no	—
34	M₃₂	D₃₇	1	1	yes	characteristic, complemented
35	C₂×C₁₆	—	37	1	no	—
36	C₂×C₁₆	—	37	2	no	—
37	#41	—	37	1	no	—
38	M₁₆	—	37	1	no	—
39	M₁₆	—	37	2	no	—
40	C₂×C₈	—	37	2	no	—
41	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
42	C₁₆	—	37	1	no	—
43	C₁₆	—	37	1	no	—
44	C₁₆	C₂×D₃₇	1	2	yes	—
45	Q₈	—	37	1	no	—
46	D₄	—	37	2	no	—
47	D₄	—	37	1	no	—
48	C₂×C₄	—	37	2	no	—
49	C₂×C₄	C₄×D₃₇	1	1	yes	characteristic
50	C₈	—	37	2	no	—
51	C₈	C₄×D₃₇	1	1	yes	characteristic
52	C₈	C₂²×D₃₇	1	1	yes	characteristic
53	C₂²	—	37	2	no	—
54	C₂²	C₈×D₃₇	1	1	yes	characteristic
55	C₄	—	37	2	no	—
56	C₄	C₈×D₃₇	1	1	yes	characteristic
57	C₄	C₂×C₄×D₃₇	1	1	yes	characteristic
58	C₂	—	2	1	no	—
59	C₂	—	74	2	no	—
60	C₂	C₂×C₈×D₃₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂²×D₃₇
commutator, socle	C₂×C₃₇	C₂²×C₈
Fitting	M₃₂×C₃₇	C₂
prime radical	#10596962	C₄
cosocle	C₈×C₃₇	C₂³
hypercenter	M₃₂	D₃₇
hypocenter	C₃₇	#504
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. #11924475	C₂	semidirect
3. C₂×#10596925	C₂	semidirect
4. C₁₆×D₃₇	C₂	semidirect
5. M₃₂×C₃₇	C₂	semidirect
31. C₃₇	#504	semidirect
34. M₃₂	D₃₇	semidirect

Maximal subgroups

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

subgroup	index
#11924542	2
#11924475	2
C₂×#10596925	2
C₁₆×D₃₇	2
M₃₂×C₃₇	2
#504	37