Group #20249112 — subgroups

Subgroups — #20249112

Order 6016.

932 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 932 conjugacy classes of subgroups — too many to draw. Only its 181 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	C₂×#13093998	C₂	1	3	yes	maximal, complemented
2	#15689034	C₂	1	2	yes	maximal, complemented
3	#15689031	C₂	1	6	yes	maximal, complemented
4	#15688983	C₂	1	3	yes	maximal, complemented
5	C₂²×#41×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₁₈₈	C₂²	1	1	yes	characteristic
7	C₂²×C₂²⋊D₄₇	C₂²	1	6	yes	—
8	#13093998	—	2	12	no	—
9	C₂×C₄⋊Dic₄₇	C₂²	1	3	yes	—
10	C₂×C₂²⋊Dic₄₇	C₂²	1	6	yes	—
11	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	6	yes	—
12	C₄₇⋊#95	C₂²	1	6	yes	—
13	C₂×#41×C₄₇	—	2	12	no	—
14	C₂²×Q₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×D₄×C₄₇	C₂²	1	3	yes	—
16	C₂³×C₄×C₄₇	C₂²	1	3	yes	—
17	C₂⁴×C₄₇	C₂³	1	3	yes	—
18	C₂³×D₄₇	C₂³	1	2	yes	—
19	#41×C₄₇	—	2	32	no	—
20	C₂×Q₈×C₄₇	—	2	6	no	—
21	C₂×D₄×C₄₇	—	2	12	no	—
22	C₂×D₄×C₄₇	—	2	6	no	—
23	C₂²×C₄×C₄₇	—	2	12	no	—
24	C₂²×C₄×C₄₇	D₄	1	12	yes	complemented
25	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
26	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
27	C₂×C₂²⋊D₄₇	—	2	12	no	—
28	C₂×C₂²⋊D₄₇	—	4	12	no	—
29	C₂²×Dic₄₇	C₂³	1	6	yes	—
30	C₂×D₁₈₈	—	2	6	no	—
31	C₂²⋊Dic₄₇	—	4	6	no	—
32	(C₂×D₄₇)⋊C₄	—	2	12	no	—
33	C₄⋊Dic₄₇	—	2	6	no	—
34	C₂³×C₄₇	—	2	6	no	—
35	C₂³×C₄₇	—	2	3	no	—
36	C₂³×C₄₇	—	2	6	no	—
37	C₂³×C₄₇	—	2	3	no	—
38	C₂³×C₄₇	C₂×D₄	1	6	yes	—
39	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
40	C₂²×D₄₇	—	2	6	no	—
41	C₂²×D₄₇	—	2	6	no	—
42	C₂²×D₄₇	—	2	2	no	—
43	Q₈×C₄₇	—	2	8	no	—
44	D₄×C₄₇	—	2	24	no	—
45	C₂×C₄×C₄₇	—	2	6	no	—
46	C₂×C₄×C₄₇	—	2	24	no	—
47	C₂×C₄×C₄₇	C₂×D₄	1	6	yes	—
48	C₂×C₄×C₄₇	C₂×D₄	1	6	yes	—
49	C₂²⋊D₄₇	—	4	24	no	—
50	C₂×Dic₄₇	—	2	6	no	—
51	C₂×Dic₄₇	—	2	12	no	—
52	D₁₈₈	—	4	4	no	—
53	C₂²×C₄₇	—	2	6	no	—
54	C₂²×C₄₇	—	2	6	no	—
55	C₂²×C₄₇	—	2	6	no	—
56	C₂²×C₄₇	—	4	6	no	—
57	C₂²×C₄₇	—	4	6	no	—
58	C₂²×C₄₇	C₂²×D₄	1	3	yes	—
59	C₂²×C₄₇	H(5,𝔽₂)	1	3	yes	—
60	C₂²×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
61	C₂×D₄₇	—	4	2	no	—
62	C₂×D₄₇	—	4	6	no	—
63	C₂×D₄₇	—	4	6	no	—
64	C₄×C₄₇	—	2	6	no	—
65	C₄×C₄₇	#120	1	4	yes	—
66	Dic₄₇	—	4	6	no	—
67	#2615	—	47	1	no	maximal, Sylow
68	C₂×C₄₇	—	4	6	no	—
69	C₂×C₄₇	C₂×#120	1	1	yes	characteristic
70	C₂×C₄₇	#535	1	3	yes	—
71	C₂×C₄₇	#537	1	3	yes	—
72	D₄₇	—	8	2	no	—
73	C₂²×#41	D₄₇	1	1	yes	characteristic, complemented
74	C₂×#121	—	47	3	no	—
75	#393	—	47	2	no	—
76	#392	—	47	6	no	—
77	#380	—	47	3	no	—
78	C₄₇	#2615	1	1	yes	characteristic, complemented, Sylow
79	C₂×#41	—	2	12	no	—
80	C₂²×Q₈	C₂×D₄₇	1	1	yes	characteristic
81	C₂²×D₄	—	47	6	no	—
82	C₂²×D₄	—	47	1	no	—
83	C₂²×D₄	C₂×D₄₇	1	3	yes	—
84	C₂³×C₄	C₂×D₄₇	1	3	yes	—
85	#121	—	94	12	no	—
86	C₂×C₄⋊C₄	—	47	3	no	—
87	C₂×C₂²⋊C₄	—	47	6	no	—
88	C₂×C₂²⋊C₄	—	47	6	no	—
89	#95	—	47	6	no	—
90	C₂⁴	—	47	2	no	—
91	C₂⁴	C₂²×D₄₇	1	3	yes	—
92	#41	—	2	32	no	—
93	C₂×Q₈	—	2	6	no	—
94	C₂×D₄	—	2	12	no	—
95	C₂×D₄	—	2	6	no	—
96	C₂×D₄	—	94	12	no	—
97	C₂×D₄	—	94	6	no	—
98	C₂×D₄	—	188	12	no	—
99	C₂²×C₄	—	2	12	no	—
100	C₂²×C₄	—	47	6	no	—
101	C₂²×C₄	C₂²⋊D₄₇	1	12	yes	complemented
102	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
103	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
104	C₄⋊C₄	—	94	6	no	—
105	C₂²⋊C₄	—	94	12	no	—
106	C₂²⋊C₄	—	188	6	no	—
107	C₂³	—	2	6	no	—
108	C₂³	—	2	3	no	—
109	C₂³	—	2	6	no	—
110	C₂³	—	2	3	no	—
111	C₂³	—	94	6	no	—
112	C₂³	—	94	6	no	—
113	C₂³	—	94	2	no	—
114	C₂³	C₂×C₂²⋊D₄₇	1	6	yes	—
115	C₂³	C₂³×D₄₇	1	1	yes	characteristic
116	Q₈	—	2	8	no	—
117	D₄	—	2	24	no	—
118	D₄	—	188	24	no	—
119	D₄	—	188	4	no	—
120	C₂×C₄	—	2	6	no	—
121	C₂×C₄	—	2	24	no	—
122	C₂×C₄	—	94	6	no	—
123	C₂×C₄	—	94	12	no	—
124	C₂×C₄	C₂×C₂²⋊D₄₇	1	6	yes	—
125	C₂×C₄	C₂×C₂²⋊D₄₇	1	6	yes	—
126	C₂²	—	2	6	no	—
127	C₂²	—	2	6	no	—
128	C₂²	—	2	6	no	—
129	C₂²	—	4	6	no	—
130	C₂²	—	4	6	no	—
131	C₂²	—	188	2	no	—
132	C₂²	—	188	6	no	—
133	C₂²	—	188	6	no	—
134	C₂²	C₂²×C₂²⋊D₄₇	1	3	yes	—
135	C₂²	#13094070	1	3	yes	—
136	C₂²	#13094071	1	1	yes	characteristic
137	C₄	—	2	6	no	—
138	C₄	—	188	6	no	—
139	C₄	#13093993	1	4	yes	—
140	C₂	—	4	6	no	—
141	C₂	—	376	2	no	—
142	C₂	C₂×#13093993	1	1	yes	characteristic
143	C₂	#15689687	1	3	yes	—
144	C₂	#15689701	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093998

C₂

yes

maximal, complemented

#15689034

C₂

yes

maximal, complemented

#15689031

C₂

yes

maximal, complemented

#15688983

C₂

yes

maximal, complemented

C₂²×#41×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₈₈

C₂²

yes

characteristic

C₂²×C₂²⋊D₄₇

C₂²

yes

—

#13093998

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₂×(C₂×D₄₇)⋊C₄

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂×#41×C₄₇

—

C₂²×Q₈×C₄₇

C₂²

yes

characteristic

C₂²×D₄×C₄₇

C₂²

yes

—

C₂³×C₄×C₄₇

C₂²

yes

—

C₂⁴×C₄₇

C₂³

yes

—

C₂³×D₄₇

C₂³

yes

—

#41×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

D₄

yes

complemented

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂×C₂²⋊D₄₇

—

C₂×C₂²⋊D₄₇

—

C₂²×Dic₄₇

C₂³

yes

—

C₂×D₁₈₈

—

C₂²⋊Dic₄₇

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

Q₈×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂²⋊D₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂²×D₄

yes

—

C₂²×C₄₇

H(5,𝔽₂)

yes

—

C₂²×C₄₇

2₋¹⁺⁴

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#120

yes

—

Dic₄₇

—

#2615

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

C₂×#120

yes

characteristic

C₂×C₄₇

#535

yes

—

C₂×C₄₇

#537

yes

—

D₄₇

—

C₂²×#41

D₄₇

yes

characteristic, complemented

—

—

—

—

C₄₇

#2615

yes

characteristic, complemented, Sylow

C₂×#41

—

C₂²×Q₈

C₂×D₄₇

yes

characteristic

C₂²×D₄

—

C₂²×D₄

—

C₂²×D₄

C₂×D₄₇

yes

—

C₂³×C₄

C₂×D₄₇

yes

—

#121

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

#95

—

C₂⁴

—

C₂⁴

C₂²×D₄₇

yes

—

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

188

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

C₂²⋊D₄₇

yes

complemented

102

C₂²×C₄

C₂²×D₄₇

yes

—

103

C₂²×C₄

C₂²×D₄₇

yes

characteristic

104

C₄⋊C₄

—

105

C₂²⋊C₄

—

106

C₂²⋊C₄

—

188

—

107

C₂³

—

108

C₂³

—

109

C₂³

—

110

C₂³

—

111

C₂³

—

112

C₂³

—

113

C₂³

—

114

C₂³

C₂×C₂²⋊D₄₇

yes

—

115

C₂³

C₂³×D₄₇

yes

characteristic

116

Q₈

—

117

D₄

—

118

D₄

—

188

—

119

D₄

—

188

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

125

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

—

188

—

132

C₂²

—

188

—

133

C₂²

—

188

—

134

C₂²

C₂²×C₂²⋊D₄₇

yes

—

135

C₂²

#13094070

yes

—

136

C₂²

#13094071

yes

characteristic

137

C₄

—

138

C₄

—

188

—

139

C₄

#13093993

yes

—

140

C₂

—

141

C₂

—

376

—

142

C₂

C₂×#13093993

yes

characteristic

143

C₂

#15689687

yes

—

144

C₂

#15689701

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₂²×#41×C₄₇	C₂
hypercenter	C₂²×#41	D₄₇
hypocenter	C₄₇	#2615
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×#41

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₂²×#41×C₄₇

C₂

hypercenter

C₂²×#41

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ C₂²×#41

N	H ≅ G/N	type
1. C₂×#13093998	C₂	semidirect
2. #15689034	C₂	semidirect
3. #15689031	C₂	semidirect
4. #15688983	C₂	semidirect
5. C₂²×#41×C₄₇	C₂	semidirect
24. C₂²×C₄×C₄₇	D₄	semidirect
73. C₂²×#41	D₄₇	semidirect
78. C₄₇	#2615	semidirect
101. C₂²×C₄	C₂²⋊D₄₇	semidirect

H ≅ G/N

type

1. C₂×#13093998

C₂

semidirect

2. #15689034

C₂

semidirect

3. #15689031

C₂

semidirect

4. #15688983

C₂

semidirect

5. C₂²×#41×C₄₇

C₂

semidirect

24. C₂²×C₄×C₄₇

D₄

semidirect

73. C₂²×#41

D₄₇

semidirect

78. C₄₇

#2615

semidirect

101. C₂²×C₄

C₂²⋊D₄₇

semidirect

Subgroups — #20249112

Conjugacy classes of subgroups

Complements