Subgroups — #14558499

Order 2368.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₇⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#11924615	C₂	1	1	yes	maximal, characteristic
3	#11924590	C₂	1	2	yes	maximal, complemented
4	C₈×#3866	C₂	1	2	yes	maximal, complemented
5	M₁₆×D₃₇	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×D₃₇	C₂²	1	1	yes	characteristic
7	C₂²⋊#3866	C₄	1	2	yes	—
8	C₂×#64438	C₄	1	2	yes	complemented
9	C₄⋊#3866	C₄	1	2	yes	—
10	C₄×#3866	C₂²	1	2	yes	—
11	D₃₇⋊C₈	C₄	1	2	yes	complemented
12	D₃₇⋊C₈	C₂²	1	1	yes	characteristic
13	D₃₇⋊C₈	C₂²	1	1	yes	characteristic
14	M₁₆×C₃₇	C₄	1	1	yes	characteristic, complemented
15	#10596934	C₄	1	1	yes	characteristic, complemented
16	#10596929	C₄	1	2	yes	complemented
17	C₈×D₃₇	C₂²	1	2	yes	—
18	C₂²×D₃₇	C₂×C₄	1	1	yes	characteristic
19	C₂×#3866	C₂×C₄	1	4	yes	—
20	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
21	C₂×Dic₃₇	C₂×C₄	1	1	yes	characteristic
22	C₄×D₃₇	C₂×C₄	1	1	yes	characteristic
23	C₄×D₃₇	C₂×C₄	1	1	yes	characteristic
24	C₄×D₃₇	C₂×C₄	1	1	yes	characteristic
25	C₄×D₃₇	C₂³	1	1	yes	characteristic
26	#64438	C₂×C₄	1	2	yes	—
27	#64438	C₂×C₄	1	2	yes	—
28	C₈×C₃₇	C₂×C₄	1	2	yes	—
29	#64436	C₂×C₄	1	2	yes	—
30	C₂²×C₃₇	C₄²	1	1	yes	characteristic
31	C₂×D₃₇	—	2	2	no	—
32	C₂×D₃₇	C₄²	1	1	yes	characteristic
33	C₂×D₃₇	C₂²×C₄	1	1	yes	characteristic
34	#3866	—	2	4	no	—
35	C₄×C₃₇	C₄²	1	1	yes	characteristic
36	C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
37	Dic₃₇	C₄²	1	1	yes	characteristic
38	Dic₃₇	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₃₇	—	2	1	no	—
40	C₂×C₃₇	C₂×C₄²	1	1	yes	characteristic
41	D₃₇	—	2	1	no	—
42	D₃₇	#131	1	2	yes	—
43	#405	—	37	1	no	maximal, Sylow
44	C₃₇	#405	1	1	yes	characteristic, complemented, Sylow
45	C₂×M₁₆	—	37	1	no	—
46	C₂²×C₈	—	37	1	no	—
47	#117	—	37	1	no	—
48	#97	—	37	2	no	—
49	C₄×C₈	—	37	2	no	—
50	C₂²×C₄	—	37	1	no	—
51	M₁₆	—	37	1	no	—
52	M₁₆	—	37	2	no	—
53	M₁₆	#3866	1	1	yes	characteristic, complemented
54	C₂×C₈	—	37	2	no	—
55	C₂×C₈	—	37	1	no	—
56	C₂×C₈	—	37	1	no	—
57	C₂×C₈	—	37	2	no	—
58	C₂×C₈	—	37	2	no	—
59	C₄⋊C₄	—	37	2	no	—
60	C₂²⋊C₄	—	37	2	no	—
61	C₄²	—	37	2	no	—
62	C₂³	—	37	1	no	—
63	C₂×C₄	—	37	1	no	—
64	C₂×C₄	—	37	1	no	—
65	C₂×C₄	—	37	1	no	—
66	C₂×C₄	—	37	1	no	—
67	C₂×C₄	—	37	1	no	—
68	C₂×C₄	—	37	4	no	—
69	C₂×C₄	C₂×#3866	1	1	yes	characteristic
70	C₈	—	37	2	no	—
71	C₈	—	37	2	no	—
72	C₈	—	37	2	no	—
73	C₈	C₂×#3866	1	2	yes	—
74	C₂²	—	37	1	no	—
75	C₂²	—	37	1	no	—
76	C₂²	—	74	2	no	—
77	C₂²	C₄×#3866	1	1	yes	characteristic
78	C₄	—	37	1	no	—
79	C₄	—	37	1	no	—
80	C₄	—	74	4	no	—
81	C₄	C₄×#3866	1	1	yes	characteristic
82	C₄	C₂²×#3866	1	1	yes	characteristic
83	C₂	—	2	1	no	—
84	C₂	—	37	2	no	—
85	C₂	—	74	1	no	—
86	C₂	C₂×C₄×#3866	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂²×#3866
commutator, socle	C₂×C₃₇	C₂×C₄²
Fitting	M₁₆×C₃₇	C₄
prime radical	C₂²×D₃₇	C₂×C₄
cosocle	C₄×D₃₇	C₂³
hypercenter	M₁₆	#3866
hypocenter	C₃₇	#405
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
3. #11924590	C₂	semidirect
4. C₈×#3866	C₂	semidirect
8. C₂×#64438	C₄	semidirect
11. D₃₇⋊C₈	C₄	semidirect
14. M₁₆×C₃₇	C₄	semidirect
15. #10596934	C₄	semidirect
16. #10596929	C₄	semidirect
44. C₃₇	#405	semidirect
53. M₁₆	#3866	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃₇⋊C₈	2
#11924615	2
#11924590	2
C₈×#3866	2
M₁₆×D₃₇	2
#405	37