Group #20251819 — subgroups

Subgroups — C₂²×(C₂×D₄₇)⋊C₈ #20251819

Order 6016.

1072 conjugacy classes of subgroups; only the 389 normal subgroups are shown.

normal subgroups only

This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 389 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	C₂³×C₄×D₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×(C₂×D₄₇)⋊C₈	C₂	1	12	yes	maximal, direct product factor
4	C₂³×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁴×D₄₇	C₄	1	1	yes	characteristic
6	C₂³×Dic₄₇	C₄	1	1	yes	characteristic
7	C₂²×C₄×D₄₇	—	2	4	no	—
8	C₂²×C₄×D₄₇	—	2	4	no	—
9	C₂²×C₄×D₄₇	C₄	1	6	yes	—
10	C₂²×C₄×D₄₇	C₂²	1	6	yes	—
11	C₂²×C₄₇⋊C₈	—	2	4	no	—
12	C₂²×C₄₇⋊C₈	C₂²	1	6	yes	complemented
13	(C₂×D₄₇)⋊C₈	C₂²	1	16	yes	direct product factor
14	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₈×C₄₇	—	2	4	no	—
16	C₂²×C₈×C₄₇	C₂²	1	6	yes	complemented
17	C₂⁴×C₄₇	C₂×C₄	1	1	yes	characteristic
18	C₂³×D₄₇	—	2	4	no	—
19	C₂³×D₄₇	—	2	4	no	—
20	C₂³×D₄₇	C₈	1	8	yes	complemented
21	C₂³×D₄₇	C₂×C₄	1	6	yes	—
22	C₂²×C₄×C₄₇	C₂×C₄	1	3	yes	—
23	C₂²×C₄×C₄₇	D₄	1	4	yes	—
24	C₂²×C₄×C₄₇	D₄	1	4	yes	—
25	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
26	C₂²×Dic₄₇	—	2	4	no	—
27	C₂²×Dic₄₇	C₂×C₄	1	6	yes	—
28	C₂×C₄×D₄₇	—	2	24	no	—
29	C₂×C₄×D₄₇	—	2	12	no	—
30	C₂×C₄×D₄₇	—	2	12	no	—
31	C₂×C₄×D₄₇	C₂×C₄	1	12	yes	—
32	C₂×C₄×D₄₇	C₂³	1	4	yes	—
33	C₂×C₈×C₄₇	—	2	12	no	—
34	C₂×C₈×C₄₇	C₂³	1	4	yes	complemented
35	C₂×C₄₇⋊C₈	—	2	12	no	—
36	C₂×C₄₇⋊C₈	C₂³	1	4	yes	complemented
37	C₂³×C₄₇	C₂²⋊C₄	1	4	yes	—
38	C₂³×C₄₇	C₂×C₈	1	4	yes	—
39	C₂³×C₄₇	M₁₆	1	4	yes	—
40	C₂³×C₄₇	C₂²×C₄	1	3	yes	—
41	C₂²×D₄₇	—	2	32	no	—
42	C₂²×D₄₇	—	2	12	no	—
43	C₂²×D₄₇	—	2	12	no	—
44	C₂²×D₄₇	C₂×C₈	1	24	yes	complemented
45	C₂²×D₄₇	C₂²×C₄	1	4	yes	—
46	C₂×C₄×C₄₇	C₂²⋊C₄	1	12	yes	—
47	C₂×C₄×C₄₇	C₂²×C₄	1	3	yes	—
48	C₂×C₄×C₄₇	C₂×D₄	1	6	yes	—
49	C₂×C₄×C₄₇	C₂×D₄	1	6	yes	—
50	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
51	C₂×Dic₄₇	—	2	12	no	—
52	C₂×Dic₄₇	C₂²×C₄	1	4	yes	—
53	C₄×D₄₇	—	2	24	no	—
54	C₄×D₄₇	—	2	4	no	—
55	C₄×D₄₇	—	2	4	no	—
56	C₈×C₄₇	—	2	4	no	—
57	C₄₇⋊C₈	—	2	4	no	—
58	C₂²×C₄₇	C₂²⋊C₈	1	16	yes	complemented
59	C₂²×C₄₇	C₂×C₂²⋊C₄	1	6	yes	—
60	C₂²×C₄₇	C₂²×C₈	1	6	yes	—
61	C₂²×C₄₇	C₂×M₁₆	1	6	yes	—
62	C₂²×C₄₇	C₂³×C₄	1	1	yes	characteristic
63	C₂×D₄₇	—	2	4	no	—
64	C₂×D₄₇	—	2	4	no	—
65	C₂×D₄₇	—	2	48	no	—
66	C₂×D₄₇	C₂²×C₈	1	8	yes	complemented
67	C₄×C₄₇	C₂×C₂²⋊C₄	1	6	yes	—
68	C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
69	C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
70	Dic₄₇	—	2	4	no	—
71	C₂²×C₂²⋊C₈	—	47	1	no	maximal, Sylow
72	C₂×C₄₇	C₂×C₂²⋊C₈	1	12	yes	complemented
73	C₂×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
74	C₂×C₄₇	C₂³×C₈	1	1	yes	characteristic
75	C₂×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
76	D₄₇	—	2	8	no	—
77	C₂⁴×C₄	—	47	1	no	—
78	C₂³×C₈	—	47	1	no	—
79	C₂³×C₈	D₄₇	1	1	yes	characteristic, complemented
80	C₂×C₂²⋊C₈	—	47	12	no	—
81	C₄₇	C₂²×C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
82	C₂⁵	—	47	1	no	—
83	C₂³×C₄	—	47	1	no	—
84	C₂³×C₄	—	47	6	no	—
85	C₂³×C₄	—	47	6	no	—
86	C₂³×C₄	—	94	4	no	—
87	C₂³×C₄	—	94	4	no	—
88	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
89	C₂²×C₈	—	2	4	no	—
90	C₂²×C₈	—	47	6	no	—
91	C₂²×C₈	—	94	4	no	—
92	C₂²×C₈	C₂×D₄₇	1	6	yes	complemented
93	C₂²⋊C₈	—	47	16	no	—
94	C₂⁴	—	47	8	no	—
95	C₂⁴	—	47	6	no	—
96	C₂⁴	—	94	4	no	—
97	C₂⁴	—	94	4	no	—
98	C₂⁴	C₄×D₄₇	1	1	yes	characteristic
99	C₂²×C₄	—	47	6	no	—
100	C₂²×C₄	—	47	12	no	—
101	C₂²×C₄	—	47	4	no	—
102	C₂²×C₄	—	94	4	no	—
103	C₂²×C₄	—	94	24	no	—
104	C₂²×C₄	—	94	12	no	—
105	C₂²×C₄	—	94	12	no	—
106	C₂²×C₄	C₄×D₄₇	1	3	yes	—
107	C₂²×C₄	D₁₈₈	1	4	yes	—
108	C₂²×C₄	C₂²⋊D₄₇	1	4	yes	—
109	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
110	C₂×C₈	—	2	12	no	—
111	C₂×C₈	—	47	4	no	—
112	C₂×C₈	—	94	12	no	—
113	C₂×C₈	C₂²×D₄₇	1	4	yes	complemented
114	C₂³	—	47	24	no	—
115	C₂³	—	47	4	no	—
116	C₂³	—	94	32	no	—
117	C₂³	—	94	12	no	—
118	C₂³	—	94	12	no	—
119	C₂³	C₈×D₄₇	1	4	yes	—
120	C₂³	#10625324	1	4	yes	—
121	C₂³	(C₂×D₄₇)⋊C₄	1	4	yes	—
122	C₂³	C₂×C₄×D₄₇	1	3	yes	—
123	C₂×C₄	—	47	4	no	—
124	C₂×C₄	—	94	12	no	—
125	C₂×C₄	—	94	24	no	—
126	C₂×C₄	—	94	4	no	—
127	C₂×C₄	—	94	4	no	—
128	C₂×C₄	(C₂×D₄₇)⋊C₄	1	12	yes	—
129	C₂×C₄	C₂×C₄×D₄₇	1	3	yes	—
130	C₂×C₄	C₂×D₁₈₈	1	6	yes	—
131	C₂×C₄	C₂×C₂²⋊D₄₇	1	6	yes	—
132	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
133	C₈	—	2	4	no	—
134	C₈	—	94	4	no	—
135	C₂²	—	47	8	no	—
136	C₂²	—	94	4	no	—
137	C₂²	—	94	48	no	—
138	C₂²	—	94	4	no	—
139	C₂²	(C₂×D₄₇)⋊C₈	1	16	yes	direct product factor
140	C₂²	C₂×(C₂×D₄₇)⋊C₄	1	6	yes	—
141	C₂²	C₂×C₈×D₄₇	1	6	yes	—
142	C₂²	C₂×#10625324	1	6	yes	—
143	C₂²	C₂²×C₄×D₄₇	1	1	yes	characteristic
144	C₄	—	94	4	no	—
145	C₄	C₂×(C₂×D₄₇)⋊C₄	1	6	yes	—
146	C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
147	C₄	C₂²×D₁₈₈	1	1	yes	characteristic
148	C₂	—	94	8	no	—
149	C₂	C₂×(C₂×D₄₇)⋊C₈	1	12	yes	direct product factor
150	C₂	C₂²×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
151	C₂	C₂²×C₈×D₄₇	1	1	yes	characteristic
152	C₂	C₂²×#10625324	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂³×C₄×D₄₇

C₂

yes

maximal, characteristic

C₂³×C₄₇⋊C₈

C₂

yes

maximal, characteristic, complemented

C₂×(C₂×D₄₇)⋊C₈

C₂

yes

maximal, direct product factor

C₂³×C₈×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂⁴×D₄₇

C₄

yes

characteristic

C₂³×Dic₄₇

C₄

yes

characteristic

C₂²×C₄×D₄₇

—

C₂²×C₄×D₄₇

—

C₂²×C₄×D₄₇

C₄

yes

—

C₂²×C₄×D₄₇

C₂²

yes

—

C₂²×C₄₇⋊C₈

—

C₂²×C₄₇⋊C₈

C₂²

yes

complemented

(C₂×D₄₇)⋊C₈

C₂²

yes

direct product factor

C₂³×C₄×C₄₇

C₂²

yes

characteristic

C₂²×C₈×C₄₇

—

C₂²×C₈×C₄₇

C₂²

yes

complemented

C₂⁴×C₄₇

C₂×C₄

yes

characteristic

C₂³×D₄₇

—

C₂³×D₄₇

—

C₂³×D₄₇

C₈

yes

complemented

C₂³×D₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

C₂×C₄

yes

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

C₂×C₄

yes

—

C₂×C₄×D₄₇

C₂³

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂³

yes

complemented

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

C₂³

yes

complemented

C₂³×C₄₇

C₂²⋊C₄

yes

—

C₂³×C₄₇

C₂×C₈

yes

—

C₂³×C₄₇

M₁₆

yes

—

C₂³×C₄₇

C₂²×C₄

yes

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

C₂×C₈

yes

complemented

C₂²×D₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂⁴

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂²×C₄

yes

—

C₄×D₄₇

—

C₄×D₄₇

—

C₄×D₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

C₂²⋊C₈

yes

complemented

C₂²×C₄₇

C₂×C₂²⋊C₄

yes

—

C₂²×C₄₇

C₂²×C₈

yes

—

C₂²×C₄₇

C₂×M₁₆

yes

—

C₂²×C₄₇

C₂³×C₄

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

C₂²×C₈

yes

complemented

C₄×C₄₇

C₂×C₂²⋊C₄

yes

—

C₄×C₄₇

C₂²×D₄

yes

characteristic

C₄×C₄₇

C₂²×D₄

yes

characteristic

Dic₄₇

—

C₂²×C₂²⋊C₈

—

maximal, Sylow

C₂×C₄₇

C₂×C₂²⋊C₈

yes

complemented

C₂×C₄₇

C₂²×C₂²⋊C₄

yes

characteristic

C₂×C₄₇

C₂³×C₈

yes

characteristic

C₂×C₄₇

C₂²×M₁₆

yes

characteristic

D₄₇

—

C₂⁴×C₄

—

C₂³×C₈

—

C₂³×C₈

D₄₇

yes

characteristic, complemented

C₂×C₂²⋊C₈

—

C₄₇

C₂²×C₂²⋊C₈

yes

characteristic, complemented, Sylow

C₂⁵

—

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

C₂×D₄₇

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×D₄₇

yes

complemented

C₂²⋊C₈

—

C₂⁴

—

C₂⁴

—

C₂⁴

—

C₂⁴

—

C₂⁴

C₄×D₄₇

yes

characteristic

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

C₄×D₄₇

yes

—

107

C₂²×C₄

D₁₈₈

yes

—

108

C₂²×C₄

C₂²⋊D₄₇

yes

—

109

C₂²×C₄

C₂²×D₄₇

yes

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

C₂²×D₄₇

yes

complemented

114

C₂³

—

115

C₂³

—

116

C₂³

—

117

C₂³

—

118

C₂³

—

119

C₂³

C₈×D₄₇

yes

—

120

C₂³

#10625324

yes

—

121

C₂³

(C₂×D₄₇)⋊C₄

yes

—

122

C₂³

C₂×C₄×D₄₇

yes

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

(C₂×D₄₇)⋊C₄

yes

—

129

C₂×C₄

C₂×C₄×D₄₇

yes

—

130

C₂×C₄

C₂×D₁₈₈

yes

—

131

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

132

C₂×C₄

C₂³×D₄₇

yes

characteristic

133

C₈

—

134

C₈

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

138

C₂²

—

139

C₂²

(C₂×D₄₇)⋊C₈

yes

direct product factor

140

C₂²

C₂×(C₂×D₄₇)⋊C₄

yes

—

141

C₂²

C₂×C₈×D₄₇

yes

—

142

C₂²

C₂×#10625324

yes

—

143

C₂²

C₂²×C₄×D₄₇

yes

characteristic

144

C₄

—

145

C₄

C₂×(C₂×D₄₇)⋊C₄

yes

—

146

C₄

C₂²×C₂²⋊D₄₇

yes

characteristic

147

C₄

C₂²×D₁₈₈

yes

characteristic

148

C₂

—

149

C₂

C₂×(C₂×D₄₇)⋊C₈

yes

direct product factor

150

C₂

C₂²×(C₂×D₄₇)⋊C₄

yes

characteristic

151

C₂

C₂²×C₈×D₄₇

yes

characteristic

152

C₂

C₂²×#10625324

yes

characteristic

	subgroup	G/H
center	C₂³×C₄	C₂×D₄₇
commutator	C₂×C₄₇	C₂³×C₈
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₂³×C₈×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂×C₄
hypercenter	C₂³×C₈	D₄₇
hypocenter	C₄₇	C₂²×C₂²⋊C₈
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₂³×C₈

subgroup

G/H

center

C₂³×C₄

C₂×D₄₇

commutator

C₂×C₄₇

C₂³×C₈

Frattini

C₂×C₄

C₂³×D₄₇

Fitting

C₂³×C₈×C₄₇

C₂

socle

C₂⁴×C₄₇

C₂×C₄

hypercenter

C₂³×C₈

D₄₇

hypocenter

C₄₇

C₂²×C₂²⋊C₈

LCS

G ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³×C₄ ◁ C₂³×C₈

N	H ≅ G/N	type
2. C₂³×C₄₇⋊C₈	C₂	semidirect
3. C₂×(C₂×D₄₇)⋊C₈	C₂	direct (N × H)
4. C₂³×C₈×C₄₇	C₂	semidirect
12. C₂²×C₄₇⋊C₈	C₂²	semidirect
13. (C₂×D₄₇)⋊C₈	C₂²	direct (N × H)
16. C₂²×C₈×C₄₇	C₂²	semidirect
20. C₂³×D₄₇	C₈	semidirect
34. C₂×C₈×C₄₇	C₂³	semidirect
36. C₂×C₄₇⋊C₈	C₂³	semidirect
44. C₂²×D₄₇	C₂×C₈	semidirect
58. C₂²×C₄₇	C₂²⋊C₈	semidirect
66. C₂×D₄₇	C₂²×C₈	semidirect
72. C₂×C₄₇	C₂×C₂²⋊C₈	semidirect
79. C₂³×C₈	D₄₇	semidirect
81. C₄₇	C₂²×C₂²⋊C₈	semidirect
92. C₂²×C₈	C₂×D₄₇	semidirect
113. C₂×C₈	C₂²×D₄₇	semidirect
139. C₂²	(C₂×D₄₇)⋊C₈	direct (N × H)
149. C₂	C₂×(C₂×D₄₇)⋊C₈	direct (N × H)

H ≅ G/N

type

2. C₂³×C₄₇⋊C₈

C₂

semidirect

3. C₂×(C₂×D₄₇)⋊C₈

C₂

direct (N × H)

4. C₂³×C₈×C₄₇

C₂

semidirect

12. C₂²×C₄₇⋊C₈

C₂²

semidirect

13. (C₂×D₄₇)⋊C₈

C₂²

direct (N × H)

16. C₂²×C₈×C₄₇

C₂²

semidirect

20. C₂³×D₄₇

C₈

semidirect

34. C₂×C₈×C₄₇

C₂³

semidirect

36. C₂×C₄₇⋊C₈

C₂³

semidirect

44. C₂²×D₄₇

C₂×C₈

semidirect

58. C₂²×C₄₇

C₂²⋊C₈

semidirect

66. C₂×D₄₇

C₂²×C₈

semidirect

72. C₂×C₄₇

C₂×C₂²⋊C₈

semidirect

79. C₂³×C₈

D₄₇

semidirect

81. C₄₇

C₂²×C₂²⋊C₈

semidirect

92. C₂²×C₈

C₂×D₄₇

semidirect

113. C₂×C₈

C₂²×D₄₇

semidirect

139. C₂²

(C₂×D₄₇)⋊C₈

direct (N × H)

149. C₂

C₂×(C₂×D₄₇)⋊C₈

direct (N × H)

Subgroups — C₂²×(C₂×D₄₇)⋊C₈ #20251819

Conjugacy classes of subgroups

Complements

Subgroups — C22×(C2×D47)⋊C8 #20251819

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×(C₂×D₄₇)⋊C₈ #20251819