Subgroups — #18011020

Order 4736.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558466	C₂	1	2	yes	maximal, complemented
2	#14558465	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃₇⋊C₃₂	C₂	1	2	yes	maximal, complemented
4	C₂×#11924586	C₂	1	1	yes	maximal, characteristic, complemented
5	#14557951	C₂	1	1	yes	maximal, characteristic
6	#11924586	C₂²	1	1	yes	characteristic
7	#11924586	C₂²	1	2	yes	—
8	#11924586	C₂²	1	1	yes	characteristic
9	#11924542	C₄	1	1	yes	characteristic
10	#11924475	C₄	1	2	yes	—
11	C₂×#10596925	C₂²	1	1	yes	characteristic
12	C₁₆×D₃₇	C₂²	1	2	yes	—
13	M₃₂×C₃₇	C₄	1	1	yes	characteristic
14	#10596962	C₈	1	1	yes	characteristic
15	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
16	#10596934	C₈	1	1	yes	characteristic
17	#10596929	C₈	1	2	yes	—
18	C₈×D₃₇	C₂×C₄	1	2	yes	—
19	C₁₆×C₃₇	C₂×C₄	1	2	yes	—
20	#10596925	C₂×C₄	1	1	yes	characteristic
21	#10596925	C₂³	1	1	yes	characteristic
22	C₂×C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
23	C₂²⋊D₃₇	C₁₆	1	2	yes	—
24	D₁₄₈	C₁₆	1	1	yes	characteristic
25	C₄×D₃₇	C₂×C₈	1	2	yes	—
26	Dic₇₄	C₁₆	1	1	yes	characteristic
27	C₈×C₃₇	C₂×C₈	1	1	yes	characteristic
28	C₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
29	#64436	C₂×C₈	1	2	yes	—
30	C₂²×C₃₇	C₂×C₁₆	1	1	yes	characteristic
31	C₂×D₃₇	C₂×C₁₆	1	2	yes	—
32	C₄×C₃₇	C₂×C₁₆	1	1	yes	characteristic
33	C₄×C₃₇	C₂²×C₈	1	1	yes	characteristic
34	Dic₃₇	C₂×C₁₆	1	2	yes	—
35	#2258	—	37	1	no	maximal, Sylow
36	C₂×C₃₇	—	2	1	no	—
37	C₂×C₃₇	C₂²×C₁₆	1	1	yes	characteristic
38	D₃₇	—	2	2	no	—
39	#504	—	37	1	no	—
40	M₆₄	—	37	1	no	—
41	M₆₄	—	37	2	no	—
42	C₂×C₃₂	—	37	2	no	—
43	C₂×C₃₂	—	37	1	no	—
44	C₃₇	#2258	1	1	yes	characteristic, complemented, Sylow
45	#131	—	37	1	no	—
46	M₃₂	—	37	2	no	—
47	M₃₂	#3866	1	1	yes	characteristic
48	C₂×C₁₆	—	37	1	no	—
49	C₂×C₁₆	—	37	2	no	—
50	C₃₂	—	37	1	no	—
51	C₃₂	—	37	2	no	—
52	C₃₂	—	37	1	no	—
53	#41	—	37	1	no	—
54	M₁₆	—	37	1	no	—
55	M₁₆	—	37	2	no	—
56	C₂×C₈	—	37	2	no	—
57	C₂×C₈	C₂×#3866	1	1	yes	characteristic
58	C₁₆	—	37	1	no	—
59	C₁₆	—	37	1	no	—
60	C₁₆	C₂×#3866	1	2	yes	—
61	Q₈	—	37	1	no	—
62	D₄	—	37	2	no	—
63	D₄	—	37	1	no	—
64	C₂×C₄	—	37	2	no	—
65	C₂×C₄	D₃₇⋊C₈	1	1	yes	characteristic
66	C₈	—	37	2	no	—
67	C₈	D₃₇⋊C₈	1	1	yes	characteristic
68	C₈	C₂²×#3866	1	1	yes	characteristic
69	C₂²	—	37	2	no	—
70	C₂²	D₃₇⋊C₁₆	1	1	yes	characteristic
71	C₄	—	37	2	no	—
72	C₄	D₃₇⋊C₁₆	1	1	yes	characteristic
73	C₄	C₂×D₃₇⋊C₈	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	74	2	no	—
76	C₂	C₂×D₃₇⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂²×#3866
commutator, socle	C₂×C₃₇	C₂²×C₁₆
Fitting	M₃₂×C₃₇	C₄
prime radical	#10596962	C₈
cosocle	#10596925	C₂³
hypercenter	M₃₂	#3866
hypocenter	C₃₇	#2258
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
1. #14558466	C₂	semidirect
2. #14558465	C₂	semidirect
3. D₃₇⋊C₃₂	C₂	semidirect
4. C₂×#11924586	C₂	semidirect
44. C₃₇	#2258	semidirect

Maximal subgroups

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

subgroup	index
#14558466	2
#14558465	2
D₃₇⋊C₃₂	2
C₂×#11924586	2
#14557951	2
#2258	37