Group #20252467 — subgroups

Subgroups — #20252467

Order 6016.

396 conjugacy classes of subgroups; only the 217 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 217 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	C₄×Q₈×D₄₇	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×Dic₉₄	C₂	1	3	yes	maximal, complemented
4	#15689247	C₂	1	3	yes	maximal, complemented
5	#15689175	C₂	1	3	yes	maximal
6	#15689174	C₂	1	3	yes	maximal
7	C₈×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Q₈×D₄₇	C₄	1	1	yes	characteristic
9	Q₈×Dic₄₇	C₄	1	1	yes	characteristic
10	C₄×Dic₉₄	C₂²	1	3	yes	—
11	#13093989	C₄	1	3	yes	—
12	C₄⋊C₄×D₄₇	C₄	1	3	yes	—
13	C₄²×D₄₇	C₂²	1	3	yes	—
14	C₄⋊(C₄₇⋊C₈)	C₂²	1	3	yes	—
15	Dic₄₇⋊C₈	C₂²	1	3	yes	—
16	Dic₄₇⋊C₈	C₂²	1	3	yes	—
17	(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
18	(C₂×D₄₇)⋊C₈	C₂²	1	3	yes	—
19	C₄×C₄₇⋊C₈	C₂²	1	3	yes	—
20	C₈×Dic₄₇	C₂²	1	6	yes	—
21	C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
22	C₄⋊C₈×C₄₇	C₂²	1	3	yes	—
23	C₄×C₈×C₄₇	C₂²	1	3	yes	—
24	C₂×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
25	Q₈×D₄₇	C₈	1	8	yes	complemented
26	C₂×C₄×D₄₇	C₂×C₄	1	3	yes	—
27	C₂×C₄×D₄₇	C₂×C₄	1	3	yes	—
28	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
29	C₂×Dic₉₄	C₂×C₄	1	3	yes	—
30	C₂×C₈×C₄₇	C₂³	1	3	yes	—
31	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
32	C₄⋊C₄×C₄₇	C₂×C₄	1	3	yes	—
33	C₄²×C₄₇	C₂³	1	3	yes	—
34	C₄⋊Dic₄₇	C₂×C₄	1	3	yes	—
35	Dic₄₇⋊C₄	C₂×C₄	1	6	yes	—
36	C₄×Dic₄₇	C₂×C₄	1	3	yes	—
37	C₄×Dic₄₇	C₂×C₄	1	3	yes	—
38	C₄×Dic₄₇	C₂³	1	3	yes	—
39	C₂×C₄₇⋊C₈	C₂³	1	3	yes	—
40	C₂×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
41	C₂²×D₄₇	C₂²×C₄	1	1	yes	characteristic
42	Q₈×C₄₇	C₂×C₈	1	4	yes	—
43	C₂×C₄×C₄₇	C₂²×C₄	1	3	yes	—
44	C₂×C₄×C₄₇	C₂²×C₄	1	3	yes	—
45	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
46	C₂×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
47	C₂×Dic₄₇	C₂²×C₄	1	3	yes	—
48	C₂×Dic₄₇	C₂²×C₄	1	3	yes	—
49	C₄×D₄₇	—	2	1	no	—
50	C₄×D₄₇	—	2	1	no	—
51	C₄×D₄₇	—	4	3	no	—
52	C₄×D₄₇	C₂×C₈	1	12	yes	—
53	Dic₉₄	C₂×C₈	1	12	yes	—
54	C₈×C₄₇	—	2	3	no	—
55	C₈×C₄₇	—	2	1	no	—
56	C₄₇⋊C₈	—	2	1	no	—
57	C₄₇⋊C₈	—	2	3	no	—
58	C₂²×C₄₇	C₂³×C₄	1	1	yes	characteristic
59	C₂×D₄₇	—	2	1	no	—
60	C₂×D₄₇	—	2	1	no	—
61	C₂×D₄₇	C₂²×C₈	1	2	yes	—
62	C₄×C₄₇	—	2	3	no	—
63	C₄×C₄₇	C₂²×C₈	1	6	yes	—
64	C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
65	C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
66	Dic₄₇	—	2	1	no	—
67	Dic₄₇	—	2	3	no	—
68	Dic₄₇	C₂²×C₈	1	6	yes	—
69	#2982	—	47	1	no	maximal, Sylow
70	C₂×C₄₇	#519	1	1	yes	characteristic
71	C₂×C₄₇	C₂³×C₈	1	1	yes	characteristic
72	C₂×C₄₇	#568	1	1	yes	characteristic
73	D₄₇	—	2	2	no	—
74	C₂×C₄×Q₈	—	47	1	no	—
75	C₈×Q₈	—	47	1	no	—
76	C₈×Q₈	—	47	3	no	—
77	C₈×Q₈	—	47	3	no	—
78	C₈×Q₈	D₄₇	1	1	yes	characteristic, complemented
79	#431	—	47	3	no	—
80	#431	—	47	3	no	—
81	C₄₇	#2982	1	1	yes	characteristic, complemented, Sylow
82	C₂²×Q₈	—	47	1	no	—
83	C₄×Q₈	—	47	1	no	—
84	C₄×Q₈	—	47	3	no	—
85	C₄×Q₈	—	47	3	no	—
86	C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
87	C₂×C₄⋊C₄	—	47	3	no	—
88	C₂×C₄²	—	47	3	no	—
89	C₄⋊C₈	—	47	3	no	—
90	C₄⋊C₈	—	47	3	no	—
91	C₄⋊C₈	—	47	3	no	—
92	C₄⋊C₈	C₂×D₄₇	1	3	yes	—
93	C₂²⋊C₈	—	47	3	no	—
94	C₂²⋊C₈	—	47	1	no	—
95	C₄×C₈	—	47	6	no	—
96	C₄×C₈	—	47	3	no	—
97	C₄×C₈	C₂×D₄₇	1	3	yes	—
98	C₂×Q₈	—	47	8	no	—
99	C₂×Q₈	—	47	3	no	—
100	C₂×Q₈	C₄×D₄₇	1	1	yes	characteristic
101	C₂²×C₄	—	47	3	no	—
102	C₂²×C₄	—	47	1	no	—
103	C₂²×C₄	—	47	3	no	—
104	C₂×C₈	—	47	1	no	—
105	C₂×C₈	—	47	3	no	—
106	C₂×C₈	C₂²×D₄₇	1	3	yes	—
107	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
108	C₄⋊C₄	—	47	6	no	—
109	C₄⋊C₄	—	47	3	no	—
110	C₄⋊C₄	C₄×D₄₇	1	3	yes	—
111	C₄²	—	47	3	no	—
112	C₄²	—	47	3	no	—
113	C₄²	—	47	3	no	—
114	C₄²	C₂²×D₄₇	1	3	yes	—
115	C₂³	—	47	1	no	—
116	Q₈	—	47	12	no	—
117	Q₈	C₈×D₄₇	1	4	yes	—
118	C₂×C₄	—	47	3	no	—
119	C₂×C₄	—	47	12	no	—
120	C₂×C₄	—	47	1	no	—
121	C₂×C₄	—	47	3	no	—
122	C₂×C₄	—	94	1	no	—
123	C₂×C₄	—	94	1	no	—
124	C₂×C₄	—	188	3	no	—
125	C₂×C₄	C₂×C₄×D₄₇	1	3	yes	—
126	C₂×C₄	C₂×C₄×D₄₇	1	3	yes	—
127	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
128	C₈	—	2	3	no	—
129	C₈	—	2	1	no	—
130	C₈	—	94	1	no	—
131	C₈	—	94	3	no	—
132	C₂²	—	47	2	no	—
133	C₂²	—	94	1	no	—
134	C₂²	—	94	1	no	—
135	C₂²	C₂²×C₄×D₄₇	1	1	yes	characteristic
136	C₄	—	2	3	no	—
137	C₄	—	47	6	no	—
138	C₄	—	94	1	no	—
139	C₄	—	94	3	no	—
140	C₄	C₂×C₈×D₄₇	1	6	yes	—
141	C₄	#13094071	1	1	yes	characteristic
142	C₄	#13094072	1	1	yes	characteristic
143	C₂	—	94	2	no	—
144	C₂	#15689599	1	1	yes	characteristic
145	C₂	C₂²×C₈×D₄₇	1	1	yes	characteristic
146	C₂	#15689888	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×Q₈×D₄₇

C₂

yes

maximal, characteristic

Q₈×C₄₇⋊C₈

C₂

yes

maximal, characteristic, complemented

C₈×Dic₉₄

C₂

yes

maximal, complemented

#15689247

C₂

yes

maximal, complemented

#15689175

C₂

yes

maximal

#15689174

C₂

yes

maximal

C₈×Q₈×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×D₄₇

C₄

yes

characteristic

Q₈×Dic₄₇

C₄

yes

characteristic

C₄×Dic₉₄

C₂²

yes

—

#13093989

C₄

yes

—

C₄⋊C₄×D₄₇

C₄

yes

—

C₄²×D₄₇

C₂²

yes

—

C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

Dic₄₇⋊C₈

C₂²

yes

—

Dic₄₇⋊C₈

C₂²

yes

—

(C₂×D₄₇)⋊C₈

C₂²

yes

characteristic

(C₂×D₄₇)⋊C₈

C₂²

yes

—

C₄×C₄₇⋊C₈

C₂²

yes

—

C₈×Dic₄₇

C₂²

yes

—

C₄×Q₈×C₄₇

C₂²

yes

characteristic

C₄⋊C₈×C₄₇

C₂²

yes

—

C₄×C₈×C₄₇

C₂²

yes

—

C₂×Q₈×C₄₇

C₂×C₄

yes

characteristic

Q₈×D₄₇

C₈

yes

complemented

C₂×C₄×D₄₇

C₂×C₄

yes

—

C₂×C₄×D₄₇

C₂×C₄

yes

—

C₂×C₄×D₄₇

C₂³

yes

characteristic

C₂×Dic₉₄

C₂×C₄

yes

—

C₂×C₈×C₄₇

C₂³

yes

—

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄⋊C₄×C₄₇

C₂×C₄

yes

—

C₄²×C₄₇

C₂³

yes

—

C₄⋊Dic₄₇

C₂×C₄

yes

—

Dic₄₇⋊C₄

C₂×C₄

yes

—

C₄×Dic₄₇

C₂×C₄

yes

—

C₄×Dic₄₇

C₂×C₄

yes

—

C₄×Dic₄₇

C₂³

yes

—

C₂×C₄₇⋊C₈

C₂³

yes

—

C₂×C₄₇⋊C₈

C₂³

yes

characteristic

C₂²×D₄₇

C₂²×C₄

yes

characteristic

Q₈×C₄₇

C₂×C₈

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂⁴

yes

characteristic

C₂×Dic₄₇

C₂²×C₄

yes

characteristic

C₂×Dic₄₇

C₂²×C₄

yes

—

C₂×Dic₄₇

C₂²×C₄

yes

—

C₄×D₄₇

—

C₄×D₄₇

—

C₄×D₄₇

—

C₄×D₄₇

C₂×C₈

yes

—

Dic₉₄

C₂×C₈

yes

—

C₈×C₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₂²×C₄₇

C₂³×C₄

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

C₂²×C₈

yes

—

C₄×C₄₇

—

C₄×C₄₇

C₂²×C₈

yes

—

C₄×C₄₇

2₋¹⁺⁴

yes

characteristic

C₄×C₄₇

2₋¹⁺⁴

yes

characteristic

Dic₄₇

—

Dic₄₇

—

Dic₄₇

C₂²×C₈

yes

—

—

C₂×C₄₇

yes

C₂×C₄₇

C₂³×C₈

yes

characteristic

C₂×C₄₇

#568

yes

characteristic

D₄₇

—

C₂×C₄×Q₈

—

C₈×Q₈

—

C₈×Q₈

—

C₈×Q₈

—

C₈×Q₈

D₄₇

yes

characteristic, complemented

#431

—

#431

—

C₄₇

#2982

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

C₂×D₄₇

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₇

yes

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₄₇

yes

—

C₂×Q₈

—

C₂×Q₈

—

100

C₂×Q₈

C₄×D₄₇

yes

characteristic

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

C₂²×D₄₇

yes

—

107

C₂×C₈

C₂²×D₄₇

yes

characteristic

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄⋊C₄

C₄×D₄₇

yes

—

111

C₄²

—

112

C₄²

—

113

C₄²

—

114

C₄²

C₂²×D₄₇

yes

—

115

C₂³

—

116

Q₈

—

117

Q₈

C₈×D₄₇

yes

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

188

—

125

C₂×C₄

C₂×C₄×D₄₇

yes

—

126

C₂×C₄

C₂×C₄×D₄₇

yes

—

127

C₂×C₄

C₂³×D₄₇

yes

characteristic

128

C₈

—

129

C₈

—

130

C₈

—

131

C₈

—

132

C₂²

—

133

C₂²

—

134

C₂²

—

135

C₂²

C₂²×C₄×D₄₇

yes

characteristic

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

C₂×C₈×D₄₇

yes

—

141

C₄

#13094071

yes

characteristic

142

C₄

#13094072

yes

characteristic

143

C₂

—

144

C₂

#15689599

yes

characteristic

145

C₂

C₂²×C₈×D₄₇

yes

characteristic

146

C₂

#15689888

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₄₇
commutator	C₂×C₄₇	C₂³×C₈
Fitting	C₈×Q₈×C₄₇	C₂
socle	C₂²×C₄₇	C₂³×C₄
hypercenter	C₈×Q₈	D₄₇
hypocenter	C₄₇	#2982
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₈×Q₈

subgroup

G/H

center, Frattini

C₂×C₄

C₂³×D₄₇

commutator

C₂×C₄₇

C₂³×C₈

Fitting

C₈×Q₈×C₄₇

C₂

socle

C₂²×C₄₇

C₂³×C₄

hypercenter

C₈×Q₈

D₄₇

C₄₇

G ▷ C₂×C₄₇ ▷ C₄₇

C₁ ◁ C₂×C₄ ◁ C₈×Q₈

N	H ≅ G/N	type
2. Q₈×C₄₇⋊C₈	C₂	semidirect
3. C₈×Dic₉₄	C₂	semidirect
4. #15689247	C₂	semidirect
7. C₈×Q₈×C₄₇	C₂	semidirect
25. Q₈×D₄₇	C₈	semidirect
78. C₈×Q₈	D₄₇	semidirect
81. C₄₇	#2982	semidirect

H ≅ G/N

type

2. Q₈×C₄₇⋊C₈

C₂

semidirect

3. C₈×Dic₉₄

C₂

semidirect

4. #15689247

C₂

semidirect

7. C₈×Q₈×C₄₇

C₂

semidirect

25. Q₈×D₄₇

C₈

semidirect

78. C₈×Q₈

D₄₇

semidirect

81. C₄₇

#2982

semidirect

Subgroups — #20252467

Conjugacy classes of subgroups

Complements