Group #20250767 — subgroups

Subgroups — #20250767

Order 6016.

520 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 125 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	C₄₇⋊#401	C₂	1	2	yes	maximal, complemented
2	#15689035	C₂	1	3	yes	maximal, complemented
3	#15689003	C₂	1	6	yes	maximal, complemented
4	#15688984	C₂	1	3	yes	maximal, complemented
5	C₄₇×#392	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic
7	C₂³×Dic₄₇	C₂²	1	3	yes	—
8	C₂×C₂²⋊Dic₄₇	C₂²	1	3	yes	—
9	C₂×C₂²⋊Dic₄₇	C₂²	1	6	yes	—
10	C₄₇⋊#95	C₂²	1	3	yes	—
11	C₄₇⋊#95	C₂²	1	6	yes	—
12	C₄₇⋊#95	C₂²	1	6	yes	—
13	C₂²×D₄×C₄₇	C₂²	1	3	yes	—
14	C₂×C₂²⋊C₄×C₄₇	C₂²	1	3	yes	—
15	#95×C₄₇	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄₇	C₂³	1	3	yes	—
17	C₂×D₄×C₄₇	—	2	12	no	—
18	C₂×D₄×C₄₇	—	4	3	no	—
19	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
20	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
21	C₂²×Dic₄₇	—	2	6	no	—
22	C₂²×Dic₄₇	—	4	3	no	—
23	C₂²×Dic₄₇	—	4	3	no	—
24	C₂²×Dic₄₇	C₂³	1	6	yes	—
25	C₂²×Dic₄₇	C₂³	1	2	yes	—
26	C₂×Dic₉₄	—	4	3	no	—
27	C₂²⋊C₄×C₄₇	—	4	3	no	—
28	C₂²⋊Dic₄₇	—	4	6	no	—
29	C₂²⋊Dic₄₇	—	4	3	no	—
30	C₂³×C₄₇	—	2	6	no	—
31	C₂³×C₄₇	—	2	3	no	—
32	C₂³×C₄₇	—	2	6	no	—
33	C₂³×C₄₇	—	2	3	no	—
34	C₂³×C₄₇	#41	1	6	yes	—
35	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
36	D₄×C₄₇	—	4	12	no	—
37	C₂×C₄×C₄₇	—	2	6	no	—
38	C₂×C₄×C₄₇	—	2	3	no	—
39	C₂×C₄×C₄₇	—	2	3	no	—
40	C₂×Dic₄₇	—	2	6	no	—
41	C₂×Dic₄₇	—	2	6	no	—
42	C₂×Dic₄₇	—	2	6	no	—
43	C₂×Dic₄₇	—	2	6	no	—
44	C₂×Dic₄₇	—	4	12	no	—
45	Dic₉₄	—	4	4	no	—
46	C₂²×C₄₇	—	2	6	no	—
47	C₂²×C₄₇	—	2	12	no	—
48	C₂²×C₄₇	—	4	6	no	—
49	C₂²×C₄₇	—	4	3	no	—
50	C₂²×C₄₇	—	4	3	no	—
51	C₂²×C₄₇	C₂×#41	1	3	yes	—
52	C₂²×C₄₇	H(5,𝔽₂)	1	3	yes	—
53	C₂²×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
54	C₄×C₄₇	—	4	3	no	—
55	C₄×C₄₇	—	4	1	no	—
56	Dic₄₇	—	4	6	no	—
57	Dic₄₇	—	4	2	no	—
58	#2760	—	47	1	no	maximal, Sylow
59	C₂×C₄₇	—	4	6	no	—
60	C₂×C₄₇	#538	1	3	yes	—
61	C₂×C₄₇	#551	1	3	yes	—
62	C₂×C₄₇	#560	1	1	yes	characteristic
63	#401	—	47	2	no	—
64	#393	—	47	3	no	—
65	#392	D₄₇	1	1	yes	characteristic
66	#386	—	47	6	no	—
67	#381	—	47	3	no	—
68	C₄₇	#2760	1	1	yes	characteristic, complemented, Sylow
69	C₂²×Q₈	—	47	1	no	—
70	C₂²×D₄	C₂×D₄₇	1	3	yes	—
71	C₂³×C₄	—	47	3	no	—
72	C₂×C₂²⋊C₄	—	47	3	no	—
73	C₂×C₂²⋊C₄	—	47	6	no	—
74	C₂×C₂²⋊C₄	C₂×D₄₇	1	3	yes	—
75	#95	—	47	3	no	—
76	#95	—	47	6	no	—
77	#95	—	47	6	no	—
78	#95	C₂×D₄₇	1	1	yes	characteristic
79	C₂⁴	C₂²×D₄₇	1	3	yes	—
80	C₂×Q₈	—	188	3	no	—
81	C₂×D₄	—	2	12	no	—
82	C₂×D₄	—	4	3	no	—
83	C₂²×C₄	—	47	6	no	—
84	C₂²×C₄	—	47	2	no	—
85	C₂²×C₄	—	94	6	no	—
86	C₂²×C₄	—	188	3	no	—
87	C₂²×C₄	—	188	3	no	—
88	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
89	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
90	C₂²⋊C₄	—	4	3	no	—
91	C₂²⋊C₄	—	188	6	no	—
92	C₂²⋊C₄	—	188	3	no	—
93	C₂³	—	2	6	no	—
94	C₂³	—	2	3	no	—
95	C₂³	—	2	6	no	—
96	C₂³	—	2	3	no	—
97	C₂³	#10625352	1	6	yes	—
98	C₂³	C₂³×D₄₇	1	1	yes	characteristic
99	Q₈	—	188	4	no	—
100	D₄	—	4	12	no	—
101	C₂×C₄	—	2	6	no	—
102	C₂×C₄	—	2	3	no	—
103	C₂×C₄	—	2	3	no	—
104	C₂×C₄	—	94	6	no	—
105	C₂×C₄	—	94	6	no	—
106	C₂×C₄	—	94	6	no	—
107	C₂×C₄	—	94	6	no	—
108	C₂×C₄	—	188	12	no	—
109	C₂²	—	2	12	no	—
110	C₂²	—	2	6	no	—
111	C₂²	—	4	3	no	—
112	C₂²	—	4	3	no	—
113	C₂²	—	4	6	no	—
114	C₂²	C₂×#10625352	1	3	yes	—
115	C₂²	#13094069	1	3	yes	—
116	C₂²	#13094070	1	1	yes	characteristic
117	C₄	—	4	3	no	—
118	C₄	—	4	1	no	—
119	C₄	—	188	2	no	—
120	C₄	—	188	6	no	—
121	C₂	—	4	6	no	—
122	C₂	#15689710	1	3	yes	—
123	C₂	#15689804	1	3	yes	—
124	C₂	#15689860	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄₇⋊#401

C₂

yes

maximal, complemented

#15689035

C₂

yes

maximal, complemented

#15689003

C₂

yes

maximal, complemented

#15688984

C₂

yes

maximal, complemented

C₄₇×#392

C₂

yes

maximal, characteristic

C₂²×Dic₉₄

C₂²

yes

characteristic

C₂³×Dic₄₇

C₂²

yes

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂²×D₄×C₄₇

C₂²

yes

—

C₂×C₂²⋊C₄×C₄₇

C₂²

yes

—

#95×C₄₇

C₂²

yes

characteristic

C₂⁴×C₄₇

C₂³

yes

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂×Dic₉₄

—

C₂²⋊C₄×C₄₇

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

#41

yes

—

C₂³×C₄₇

C₂⁴

yes

characteristic

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×#41

yes

—

C₂²×C₄₇

H(5,𝔽₂)

yes

—

C₂²×C₄₇

H(5,𝔽₂)

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

Dic₄₇

—

Dic₄₇

—

#2760

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

#538

yes

—

C₂×C₄₇

#551

yes

—

C₂×C₄₇

yes

—

—

D₄₇

yes

characteristic

#386

—

#381

—

C₄₇

#2760

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×D₄

C₂×D₄₇

yes

—

C₂³×C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₄₇

yes

—

—

—

—

C₂×D₄₇

yes

characteristic

C₂⁴

C₂²×D₄₇

yes

—

C₂×Q₈

—

188

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

188

—

C₂²×C₄

—

188

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₂²⋊C₄

—

C₂²⋊C₄

—

188

—

C₂²⋊C₄

—

188

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

#10625352

yes

—

C₂³

C₂³×D₄₇

yes

characteristic

Q₈

—

188

—

100

D₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

188

—

109

C₂²

—

110

C₂²

—

111

C₂²

—

112

C₂²

—

113

C₂²

—

114

C₂²

C₂×#10625352

yes

—

115

C₂²

#13094069

yes

—

116

C₂²

#13094070

yes

characteristic

117

C₄

—

118

C₄

—

119

C₄

—

188

—

120

C₄

—

188

—

121

C₂

—

122

C₂

#15689710

yes

—

123

C₂

#15689804

yes

—

124

C₂

#15689860

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₄₇×#392	C₂
hypercenter	#392	D₄₇
hypocenter	C₄₇	#2760
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ #392

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₄₇×#392

C₂

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ #392

N	H ≅ G/N	type
1. C₄₇⋊#401	C₂	semidirect
2. #15689035	C₂	semidirect
3. #15689003	C₂	semidirect
4. #15688984	C₂	semidirect
68. C₄₇	#2760	semidirect

H ≅ G/N

type

1. C₄₇⋊#401

C₂

semidirect

2. #15689035

C₂

semidirect

3. #15689003

C₂

semidirect

4. #15688984

C₂

semidirect

68. C₄₇

#2760

semidirect

Subgroups — #20250767

Conjugacy classes of subgroups

Complements