Group #20251663 — subgroups

Subgroups — #20251663

Order 6016.

340 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689057	C₂	1	4	yes	maximal
2	#15689056	C₂	1	4	yes	maximal
3	#15689055	C₂	1	4	yes	maximal
4	#15688989	C₂	1	2	yes	maximal
5	C₄₇×#382	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₄₇	C₂²	1	4	yes	—
9	C₂×Dic₄₇⋊C₄	C₂²	1	4	yes	—
10	C₂×Dic₄₇⋊C₄	C₂²	1	4	yes	—
11	C₄₇⋊#95	C₂²	1	4	yes	—
12	C₄₇⋊#95	C₂²	1	4	yes	—
13	C₄₇⋊#95	C₂²	1	4	yes	—
14	C₂×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
15	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
16	#95×C₄₇	C₂²	1	4	yes	—
17	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
18	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
19	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
20	C₂²×Dic₄₇	C₂³	1	4	yes	—
21	C₂²×Dic₄₇	C₂³	1	4	yes	—
22	C₄⋊C₄×C₄₇	—	4	2	no	—
23	C₄²×C₄₇	Q₈	1	4	yes	—
24	C₄⋊Dic₄₇	—	4	2	no	—
25	C₄⋊Dic₄₇	—	4	4	no	—
26	C₄⋊Dic₄₇	—	4	2	no	—
27	Dic₄₇⋊C₄	—	4	4	no	—
28	Dic₄₇⋊C₄	—	4	4	no	—
29	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
30	C₂×C₄×C₄₇	—	2	2	no	—
31	C₂×C₄×C₄₇	—	2	1	no	—
32	C₂×C₄×C₄₇	—	2	2	no	—
33	C₂×C₄×C₄₇	—	2	1	no	—
34	C₂×C₄×C₄₇	—	2	4	no	—
35	C₂×C₄×C₄₇	—	2	4	no	—
36	C₂×C₄×C₄₇	—	2	4	no	—
37	C₂×C₄×C₄₇	C₂×Q₈	1	2	yes	—
38	C₂×C₄×C₄₇	C₂×Q₈	1	4	yes	—
39	C₂×Dic₄₇	—	2	4	no	—
40	C₂×Dic₄₇	—	2	4	no	—
41	C₂×Dic₄₇	—	2	4	no	—
42	C₂×Dic₄₇	—	2	4	no	—
43	C₂×Dic₄₇	—	2	4	no	—
44	C₂×Dic₄₇	—	2	4	no	—
45	C₂²×C₄₇	C₂²×Q₈	1	1	yes	characteristic
46	C₂²×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
47	C₂²×C₄₇	H(5,𝔽₂)	1	2	yes	—
48	C₂²×C₄₇	2₋¹⁺⁴	1	2	yes	—
49	C₂²×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
50	C₄×C₄₇	—	2	4	no	—
51	C₄×C₄₇	—	2	2	no	—
52	C₄×C₄₇	—	4	4	no	—
53	Dic₄₇	—	4	4	no	—
54	Dic₄₇	—	4	4	no	—
55	#2845	—	47	1	no	maximal, Sylow
56	C₂×C₄₇	#544	1	2	yes	—
57	C₂×C₄₇	#544	1	1	yes	characteristic
58	C₂×C₄₇	#562	1	2	yes	—
59	C₂×C₄₇	#562	1	1	yes	characteristic
60	C₂×C₄₇	#564	1	1	yes	characteristic
61	#398	—	47	4	no	—
62	#398	—	47	4	no	—
63	#398	—	47	4	no	—
64	#382	—	47	2	no	—
65	#382	D₄₇	1	1	yes	characteristic
66	C₄₇	#2845	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₄⋊C₄	—	47	4	no	—
68	C₂×C₄⋊C₄	—	47	4	no	—
69	C₂×C₄⋊C₄	—	47	2	no	—
70	C₂×C₄⋊C₄	—	47	2	no	—
71	C₂×C₄⋊C₄	—	47	4	no	—
72	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
73	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
74	#95	—	47	4	no	—
75	#95	—	47	4	no	—
76	#95	—	47	4	no	—
77	#95	C₂×D₄₇	1	4	yes	—
78	C₂²×C₄	—	47	4	no	—
79	C₂²×C₄	—	47	4	no	—
80	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
81	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
82	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
83	C₄⋊C₄	—	4	2	no	—
84	C₄⋊C₄	—	188	4	no	—
85	C₄⋊C₄	—	188	4	no	—
86	C₄⋊C₄	—	188	2	no	—
87	C₄⋊C₄	—	188	2	no	—
88	C₄⋊C₄	—	188	4	no	—
89	C₄²	Dic₉₄	1	4	yes	—
90	C₂³	C₂³×D₄₇	1	1	yes	characteristic
91	C₂×C₄	—	2	1	no	—
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	2	1	no	—
95	C₂×C₄	—	2	4	no	—
96	C₂×C₄	—	2	4	no	—
97	C₂×C₄	—	2	4	no	—
98	C₂×C₄	—	94	4	no	—
99	C₂×C₄	—	94	4	no	—
100	C₂×C₄	—	94	4	no	—
101	C₂×C₄	—	94	4	no	—
102	C₂×C₄	—	94	4	no	—
103	C₂×C₄	—	94	4	no	—
104	C₂×C₄	C₂×Dic₉₄	1	4	yes	—
105	C₂×C₄	C₂×Dic₉₄	1	2	yes	—
106	C₂²	C₂²×Dic₉₄	1	1	yes	characteristic
107	C₂²	#13094069	1	1	yes	characteristic
108	C₂²	#13094070	1	2	yes	—
109	C₂²	#13094071	1	2	yes	—
110	C₂²	#13094072	1	1	yes	characteristic
111	C₄	—	2	4	no	—
112	C₄	—	2	2	no	—
113	C₄	—	4	4	no	—
114	C₄	—	188	4	no	—
115	C₄	—	188	4	no	—
116	C₂	#15689751	1	2	yes	—
117	C₂	#15689754	1	1	yes	characteristic
118	C₂	#15689867	1	2	yes	—
119	C₂	#15689871	1	1	yes	characteristic
120	C₂	C₄₇⋊#564	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689057

C₂

yes

maximal

#15689056

C₂

yes

maximal

#15689055

C₂

yes

maximal

#15688989

C₂

yes

maximal

C₄₇×#382

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

#95×C₄₇

C₂²

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

Q₈

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×Q₈

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂²×C₄₇

C₂²×Q₈

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

—

C₂²×C₄₇

2₋¹⁺⁴

yes

—

C₂²×C₄₇

2₋¹⁺⁴

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

Dic₄₇

—

Dic₄₇

—

#2845

—

maximal, Sylow

C₂×C₄₇

#544

yes

—

C₂×C₄₇

#544

yes

characteristic

C₂×C₄₇

#562

yes

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

—

—

—

D₄₇

yes

characteristic

C₄₇

#2845

yes

characteristic, complemented, Sylow

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

C₂×C₄²

C₂×D₄₇

yes

—

—

—

C₂×D₄₇

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₂²×C₄

C₂²×D₄₇

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

188

—

C₄⋊C₄

—

188

—

C₄⋊C₄

—

188

—

C₄⋊C₄

—

188

—

C₄⋊C₄

—

188

—

C₄²

Dic₉₄

yes

—

C₂³

C₂³×D₄₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

C₂×Dic₉₄

yes

—

105

C₂×C₄

C₂×Dic₉₄

yes

—

106

C₂²

C₂²×Dic₉₄

yes

characteristic

107

C₂²

#13094069

yes

characteristic

108

C₂²

#13094070

yes

—

109

C₂²

#13094071

yes

—

110

C₂²

#13094072

yes

characteristic

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

—

188

—

115

C₄

—

188

—

116

C₂

#15689751

yes

—

117

C₂

#15689754

yes

characteristic

118

C₂

#15689867

yes

—

119

C₂

#15689871

yes

characteristic

120

C₂

C₄₇⋊#564

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₄₇×#382	C₂
hypercenter	#382	D₄₇
hypocenter	C₄₇	#2845
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ #382

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₄₇×#382

C₂

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ #382

N	H ≅ G/N	type
66. C₄₇	#2845	semidirect

H ≅ G/N

type

66. C₄₇

#2845

semidirect

Subgroups — #20251663

Conjugacy classes of subgroups

Complements