Subgroups — #14557725

Order 2368.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10596939	C₂	1	2	yes	maximal, complemented
2	C₄×D₁₄₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊#64436	C₂	1	1	yes	maximal, characteristic, complemented
4	#11924457	C₂	1	2	yes	maximal, complemented
5	#127×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄×C₃₇	—	2	1	no	—
7	C₂×D₄×C₃₇	—	2	1	no	—
8	C₂×D₄×C₃₇	C₂²	1	2	yes	—
9	C₂×D₁₄₈	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₃₇	—	2	1	no	—
11	C₄²×C₃₇	C₂²	1	1	yes	characteristic
12	#10596939	—	2	4	no	—
13	#10596938	—	2	1	no	—
14	C₄⋊Dic₃₇	C₂²	1	1	yes	characteristic
15	C₂×#64436	C₂²	1	2	yes	—
16	C₂³×C₃₇	—	2	2	no	—
17	C₂²×D₃₇	—	2	1	no	—
18	D₄×C₃₇	—	2	2	no	—
19	D₄×C₃₇	—	2	2	no	—
20	D₄×C₃₇	—	4	2	no	—
21	D₄×C₃₇	—	4	2	no	—
22	C₂×C₄×C₃₇	D₄	1	1	yes	characteristic
23	C₂×C₄×C₃₇	D₄	1	1	yes	characteristic
24	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
25	C₂×Dic₃₇	—	2	1	no	—
26	D₁₄₈	—	2	1	no	—
27	D₁₄₈	D₄	1	2	yes	complemented
28	C₄×D₃₇	—	4	2	no	—
29	#64436	—	2	2	no	—
30	C₂²×C₃₇	—	4	2	no	—
31	C₂²×C₃₇	—	4	2	no	—
32	C₂²×C₃₇	—	4	2	no	—
33	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
34	C₂×D₃₇	—	2	2	no	—
35	C₂×D₃₇	—	4	1	no	—
36	C₂×D₃₇	—	4	1	no	—
37	C₄×C₃₇	—	2	1	no	—
38	C₄×C₃₇	D₈	1	2	yes	complemented
39	C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
40	C₄×C₃₇	#41	1	1	yes	characteristic
41	Dic₃₇	—	4	1	no	—
42	C₂×C₃₇	—	8	2	no	—
43	C₂×C₃₇	#121	1	1	yes	characteristic
44	C₂×C₃₇	C₂×D₈	1	1	yes	characteristic
45	C₂×C₃₇	AGL(1,ℤ/8)	1	1	yes	characteristic
46	D₃₇	—	4	2	no	—
47	#459	—	37	1	no	maximal, Sylow
48	C₃₇	#459	1	1	yes	characteristic, complemented, Sylow
49	C₂×D₈	—	37	2	no	—
50	#127	D₃₇	1	1	yes	characteristic, complemented
51	C₄×D₄	—	37	1	no	—
52	C₄⋊C₈	—	37	1	no	—
53	#102	—	37	2	no	—
54	C₂×D₄	—	2	1	no	—
55	C₂×D₄	—	2	1	no	—
56	C₂×D₄	—	37	1	no	—
57	C₂×D₄	C₂×D₃₇	1	2	yes	—
58	C₂²×C₄	—	74	1	no	—
59	D₈	—	74	4	no	—
60	C₂×C₈	—	37	2	no	—
61	C₄⋊C₄	—	37	1	no	—
62	C₂²⋊C₄	—	74	1	no	—
63	C₄²	C₂×D₃₇	1	1	yes	characteristic
64	C₂³	—	2	2	no	—
65	C₂³	—	74	1	no	—
66	D₄	—	2	2	no	—
67	D₄	—	2	2	no	—
68	D₄	—	4	2	no	—
69	D₄	—	4	2	no	—
70	D₄	—	37	2	no	—
71	D₄	—	74	1	no	—
72	C₂×C₄	—	74	1	no	—
73	C₂×C₄	—	148	2	no	—
74	C₂×C₄	C₂²⋊D₃₇	1	1	yes	characteristic
75	C₂×C₄	C₂²⋊D₃₇	1	1	yes	characteristic
76	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
77	C₈	—	74	2	no	—
78	C₂²	—	4	2	no	—
79	C₂²	—	4	2	no	—
80	C₂²	—	4	2	no	—
81	C₂²	—	74	2	no	—
82	C₂²	—	148	1	no	—
83	C₂²	—	148	1	no	—
84	C₂²	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
85	C₄	—	2	1	no	—
86	C₄	—	148	1	no	—
87	C₄	#10596939	1	2	yes	complemented
88	C₄	D₄×D₃₇	1	1	yes	characteristic
89	C₄	#10596964	1	1	yes	characteristic
90	C₂	—	8	2	no	—
91	C₂	—	148	2	no	—
92	C₂	#11924507	1	1	yes	characteristic
93	C₂	C₂×#10596939	1	1	yes	characteristic
94	C₂	#11924562	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₃₇
commutator, cosocle	C₂×C₄×C₃₇	C₂³
Frattini	C₂×C₄	C₂²×D₃₇
Fitting	#127×C₃₇	C₂
socle	C₂²×C₃₇	C₂×D₄
hypercenter	#127	D₃₇
hypocenter	C₃₇	#459
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #127

Complements

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

N	H ≅ G/N	type
1. C₂×#10596939	C₂	semidirect
2. C₄×D₁₄₈	C₂	semidirect
3. C₄⋊#64436	C₂	semidirect
4. #11924457	C₂	semidirect
5. #127×C₃₇	C₂	semidirect
27. D₁₄₈	D₄	semidirect
38. C₄×C₃₇	D₈	semidirect
48. C₃₇	#459	semidirect
50. #127	D₃₇	semidirect
87. C₄	#10596939	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10596939	2
C₄×D₁₄₈	2
C₄⋊#64436	2
#11924457	2
#127×C₃₇	2
#459	37