Subgroups — #14558496

Order 2368.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₇⋊M₁₆	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	C₂×C₈×D₃₇	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×D₃₇	C₂²	1	1	yes	characteristic
7	C₂²⋊#3866	C₄	1	2	yes	—
8	#10596957	C₄	1	2	yes	complemented
9	C₄⋊#3866	C₄	1	2	yes	—
10	C₄×#3866	C₂²	1	2	yes	—
11	#10596953	C₄	1	2	yes	complemented
12	D₃₇⋊C₈	C₂²	1	2	yes	—
13	C₂×C₈×C₃₇	C₄	1	1	yes	characteristic, complemented
14	C₂×#64436	C₄	1	1	yes	characteristic, complemented
15	C₈×D₃₇	C₄	1	1	yes	characteristic, complemented
16	C₈×D₃₇	C₄	1	1	yes	characteristic, complemented
17	C₈×D₃₇	C₂²	1	1	yes	characteristic
18	C₈×D₃₇	C₂²	1	1	yes	characteristic
19	C₂²×D₃₇	C₂×C₄	1	1	yes	characteristic
20	C₂×#3866	C₂×C₄	1	4	yes	—
21	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
22	C₂×Dic₃₇	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	C₂×C₄	1	1	yes	characteristic
26	C₄×D₃₇	C₂³	1	1	yes	characteristic
27	#64438	C₂×C₄	1	4	yes	—
28	C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
29	C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
30	#64436	C₂×C₄	1	1	yes	characteristic
31	#64436	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₃₇	C₄²	1	1	yes	characteristic
33	C₂×D₃₇	—	2	2	no	—
34	C₂×D₃₇	C₄²	1	1	yes	characteristic
35	C₂×D₃₇	C₂²×C₄	1	1	yes	characteristic
36	#3866	—	2	4	no	—
37	C₄×C₃₇	C₄²	1	1	yes	characteristic
38	C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
39	Dic₃₇	C₄²	1	1	yes	characteristic
40	Dic₃₇	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₃₇	—	2	1	no	—
42	C₂×C₃₇	C₂×C₄²	1	1	yes	characteristic
43	D₃₇	—	2	1	no	—
44	D₃₇	#131	1	2	yes	—
45	#405	—	37	1	no	maximal, Sylow
46	C₃₇	#405	1	1	yes	characteristic, complemented, Sylow
47	C₂×M₁₆	—	37	1	no	—
48	C₂²×C₈	—	37	1	no	—
49	#117	—	37	1	no	—
50	#97	—	37	2	no	—
51	C₄×C₈	—	37	2	no	—
52	C₂²×C₄	—	37	1	no	—
53	M₁₆	—	37	2	no	—
54	M₁₆	—	37	2	no	—
55	C₂×C₈	—	37	2	no	—
56	C₂×C₈	—	37	1	no	—
57	C₂×C₈	—	37	1	no	—
58	C₂×C₈	—	37	1	no	—
59	C₂×C₈	—	37	1	no	—
60	C₂×C₈	—	37	1	no	—
61	C₂×C₈	#3866	1	1	yes	characteristic, complemented
62	C₄⋊C₄	—	37	2	no	—
63	C₂²⋊C₄	—	37	2	no	—
64	C₄²	—	37	2	no	—
65	C₂³	—	37	1	no	—
66	C₂×C₄	—	37	1	no	—
67	C₂×C₄	—	37	1	no	—
68	C₂×C₄	—	37	1	no	—
69	C₂×C₄	—	37	1	no	—
70	C₂×C₄	—	37	1	no	—
71	C₂×C₄	—	37	4	no	—
72	C₂×C₄	C₂×#3866	1	1	yes	characteristic
73	C₈	—	37	4	no	—
74	C₈	—	37	1	no	—
75	C₈	—	37	1	no	—
76	C₈	C₂×#3866	1	1	yes	characteristic
77	C₈	C₂×#3866	1	1	yes	characteristic
78	C₂²	—	37	1	no	—
79	C₂²	—	37	1	no	—
80	C₂²	—	74	2	no	—
81	C₂²	C₄×#3866	1	1	yes	characteristic
82	C₄	—	37	1	no	—
83	C₄	—	37	1	no	—
84	C₄	—	74	4	no	—
85	C₄	C₄×#3866	1	1	yes	characteristic
86	C₄	C₂²×#3866	1	1	yes	characteristic
87	C₂	—	2	1	no	—
88	C₂	—	37	2	no	—
89	C₂	—	74	1	no	—
90	C₂	C₂×C₄×#3866	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×#3866
commutator, socle	C₂×C₃₇	C₂×C₄²
Frattini	C₄	C₂²×#3866
Fitting	C₂×C₈×C₃₇	C₄
prime radical	C₂²×D₃₇	C₂×C₄
cosocle	C₄×D₃₇	C₂³
hypercenter	C₂×C₈	#3866
hypocenter	C₃₇	#405
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈

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. #10596957	C₄	semidirect
11. #10596953	C₄	semidirect
13. C₂×C₈×C₃₇	C₄	semidirect
14. C₂×#64436	C₄	semidirect
15. C₈×D₃₇	C₄	semidirect
16. C₈×D₃₇	C₄	semidirect
46. C₃₇	#405	semidirect
61. C₂×C₈	#3866	semidirect

Maximal subgroups

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

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