Subgroups — #14558543

Order 2368.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924615	C₂	1	2	yes	maximal
2	#11924605	C₂	1	2	yes	maximal, complemented
3	#11924604	C₂	1	2	yes	maximal, complemented
4	C₂×C₈×D₃₇	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×D₃₇	C₂²	1	1	yes	characteristic
6	C₂²⋊#3866	—	2	2	no	—
7	C₄⋊#3866	C₂²	1	4	yes	—
8	C₄×#3866	—	2	2	no	—
9	C₂×C₈×C₃₇	C₄	1	1	yes	characteristic, complemented
10	C₂×#64436	C₄	1	1	yes	characteristic, complemented
11	C₈×D₃₇	C₄	1	1	yes	characteristic, complemented
12	C₈×D₃₇	C₄	1	1	yes	characteristic, complemented
13	C₈×D₃₇	C₂²	1	1	yes	characteristic
14	C₈×D₃₇	C₂²	1	1	yes	characteristic
15	C₂²×D₃₇	D₄	1	1	yes	characteristic
16	C₂×#3866	—	2	4	no	—
17	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₃₇	Q₈	1	1	yes	characteristic
19	C₄×D₃₇	C₂×C₄	1	1	yes	characteristic
20	C₄×D₃₇	D₄	1	1	yes	characteristic
21	C₄×D₃₇	Q₈	1	1	yes	characteristic
22	C₄×D₃₇	C₂³	1	1	yes	characteristic
23	C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
24	C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
25	#64436	C₂×C₄	1	1	yes	characteristic
26	#64436	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₃₇	C₄⋊C₄	1	1	yes	characteristic
28	C₂×D₃₇	—	2	2	no	—
29	C₂×D₃₇	C₄⋊C₄	1	1	yes	characteristic
30	C₂×D₃₇	C₂×D₄	1	1	yes	characteristic
31	#3866	—	4	4	no	—
32	C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
33	C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
34	Dic₃₇	C₄⋊C₄	1	1	yes	characteristic
35	Dic₃₇	C₂×Q₈	1	1	yes	characteristic
36	C₂×C₃₇	—	2	1	no	—
37	C₂×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
38	D₃₇	—	2	1	no	—
39	D₃₇	#135	1	2	yes	—
40	#427	—	37	1	no	maximal, Sylow
41	C₃₇	#427	1	1	yes	characteristic, complemented, Sylow
42	C₂²×C₈	—	37	1	no	—
43	#117	—	37	2	no	—
44	#107	—	37	2	no	—
45	#106	—	37	2	no	—
46	C₂²×C₄	—	37	1	no	—
47	C₂×C₈	—	37	1	no	—
48	C₂×C₈	—	37	1	no	—
49	C₂×C₈	—	37	1	no	—
50	C₂×C₈	—	37	1	no	—
51	C₂×C₈	—	37	1	no	—
52	C₂×C₈	#3866	1	1	yes	characteristic, complemented
53	C₄⋊C₄	—	37	4	no	—
54	C₂²⋊C₄	—	74	2	no	—
55	C₄²	—	74	2	no	—
56	C₂³	—	37	1	no	—
57	C₂×C₄	—	37	1	no	—
58	C₂×C₄	—	37	1	no	—
59	C₂×C₄	—	37	1	no	—
60	C₂×C₄	—	37	1	no	—
61	C₂×C₄	—	37	1	no	—
62	C₂×C₄	—	74	4	no	—
63	C₂×C₄	C₂×#3866	1	1	yes	characteristic
64	C₈	—	37	1	no	—
65	C₈	—	37	1	no	—
66	C₈	C₂×#3866	1	1	yes	characteristic
67	C₈	C₂×#3866	1	1	yes	characteristic
68	C₂²	—	37	1	no	—
69	C₂²	—	37	1	no	—
70	C₂²	—	74	2	no	—
71	C₂²	C₄⋊#3866	1	1	yes	characteristic
72	C₄	—	37	1	no	—
73	C₄	—	37	1	no	—
74	C₄	—	148	4	no	—
75	C₄	C₄⋊#3866	1	1	yes	characteristic
76	C₄	C₂²×#3866	1	1	yes	characteristic
77	C₂	—	2	1	no	—
78	C₂	—	37	2	no	—
79	C₂	—	74	1	no	—
80	C₂	C₂×C₄⋊#3866	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄⋊#3866
commutator	C₄×C₃₇	C₂²×C₄
Frattini	C₄	C₂²×#3866
Fitting	C₂×C₈×C₃₇	C₄
socle	C₂×C₃₇	C₂×C₄⋊C₄
prime radical	C₂²×D₃₇	D₄
cosocle	C₄×D₃₇	C₂³
hypercenter	C₂×C₈	#3866
hypocenter	C₃₇	#427
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. #11924605	C₂	semidirect
3. #11924604	C₂	semidirect
9. C₂×C₈×C₃₇	C₄	semidirect
10. C₂×#64436	C₄	semidirect
11. C₈×D₃₇	C₄	semidirect
12. C₈×D₃₇	C₄	semidirect
41. C₃₇	#427	semidirect
52. 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
#11924615	2
#11924605	2
#11924604	2
C₂×C₈×D₃₇	2
#427	37