Group #20253817 — subgroups

Subgroups — #20253817

Order 6016.

572 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 145 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×#13094047	C₂	1	4	yes	maximal, complemented
2	#15689674	C₂	1	2	yes	maximal, complemented
3	#15689508	C₂	1	4	yes	maximal, complemented
4	#15689500	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689497	C₂	1	2	yes	maximal, complemented
6	C₄×C₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#494	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10625354	C₂²	1	4	yes	—
9	#13094047	—	2	16	no	—
10	C₂×#10625336	C₂²	1	8	yes	—
11	C₂×D₃₇₆	C₂²	1	4	yes	—
12	C₂×C₈×D₄₇	C₂²	1	2	yes	—
13	#13094021	C₂²	1	2	yes	—
14	#13094013	C₂²	1	4	yes	—
15	#13093999	—	2	4	no	—
16	#13093986	—	2	4	no	—
17	C₄²×D₄₇	C₂²	1	1	yes	characteristic
18	C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
19	C₈×Dic₄₇	C₂²	1	2	yes	—
20	C₂×Q₁₆×C₄₇	C₂²	1	4	yes	—
21	C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
22	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×Q₈×C₄₇	C₂³	1	4	yes	—
24	#10625354	—	2	16	no	—
25	C₂×D₁₈₈	—	2	4	no	—
26	C₂×D₁₈₈	—	2	4	no	—
27	C₂×D₁₈₈	C₂³	1	4	yes	—
28	C₂×C₄×D₄₇	—	2	4	no	—
29	C₂×C₄×D₄₇	D₄	1	2	yes	—
30	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
31	Q₁₆×C₄₇	—	2	8	no	—
32	C₂×C₈×C₄₇	C₂³	1	2	yes	—
33	C₄⋊C₄×C₄₇	—	2	4	no	—
34	C₄²×C₄₇	C₂³	1	1	yes	characteristic
35	#10625336	—	2	16	no	—
36	(C₂×D₄₇)⋊C₄	—	2	8	no	—
37	C₄×Dic₄₇	D₄	1	2	yes	—
38	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
39	C₂×C₄₇⋊C₈	C₂³	1	2	yes	—
40	D₃₇₆	—	2	8	no	—
41	C₈×D₄₇	D₄	1	8	yes	complemented
42	C₂²×D₄₇	—	2	4	no	—
43	C₂²×D₄₇	C₂×D₄	1	1	yes	characteristic
44	Q₈×C₄₇	—	2	8	no	—
45	C₂×C₄×C₄₇	—	2	4	no	—
46	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
47	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
48	C₂×Dic₄₇	C₂×D₄	1	2	yes	—
49	C₂×Dic₄₇	C₂×D₄	1	1	yes	characteristic
50	D₁₈₈	—	2	8	no	—
51	D₁₈₈	—	4	8	no	—
52	D₁₈₈	—	4	8	no	—
53	C₄×D₄₇	—	2	4	no	—
54	C₄×D₄₇	—	4	8	no	—
55	C₄×D₄₇	C₂×D₄	1	4	yes	—
56	C₈×C₄₇	C₂×D₄	1	4	yes	—
57	C₄₇⋊C₈	C₂×D₄	1	4	yes	—
58	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
59	C₂×D₄₇	—	2	2	no	—
60	C₂×D₄₇	—	4	4	no	—
61	C₂×D₄₇	—	4	8	no	—
62	C₂×D₄₇	#127	1	2	yes	—
63	C₄×C₄₇	—	4	4	no	—
64	C₄×C₄₇	#135	1	4	yes	complemented
65	C₄×C₄₇	C₂²×D₄	1	2	yes	—
66	Dic₄₇	—	2	2	no	—
67	Dic₄₇	#127	1	2	yes	—
68	#3147	—	47	1	no	maximal, Sylow
69	C₂×C₄₇	C₂×#127	1	1	yes	characteristic
70	C₂×C₄₇	C₂×#135	1	2	yes	—
71	D₄₇	—	2	2	no	—
72	D₄₇	—	8	4	no	—
73	C₂×#135	—	47	4	no	—
74	#532	—	47	2	no	—
75	#495	—	47	4	no	—
76	#494	D₄₇	1	1	yes	characteristic, complemented
77	#493	—	47	1	no	—
78	#492	—	47	2	no	—
79	C₂×C₄×C₈	—	47	1	no	—
80	C₄₇	#3147	1	1	yes	characteristic, complemented, Sylow
81	C₂×#41	—	47	4	no	—
82	#135	—	94	16	no	—
83	C₂×Q₁₆	C₂×D₄₇	1	4	yes	—
84	C₂×SD₁₆	—	47	8	no	—
85	C₂×D₈	—	47	4	no	—
86	C₂²×C₈	—	47	2	no	—
87	C₄⋊Q₈	C₂×D₄₇	1	2	yes	—
88	#127	—	47	2	no	—
89	#124	—	47	4	no	—
90	#121	—	94	4	no	—
91	C₄×D₄	—	94	4	no	—
92	C₂×C₄²	—	47	1	no	—
93	C₄×C₈	—	47	2	no	—
94	C₄×C₈	—	47	1	no	—
95	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
96	#41	—	94	16	no	—
97	C₂×Q₈	C₂²×D₄₇	1	4	yes	—
98	C₂×D₄	—	47	4	no	—
99	C₂×D₄	—	94	4	no	—
100	C₂×D₄	—	94	4	no	—
101	C₂²×C₄	—	47	1	no	—
102	C₂²×C₄	—	47	2	no	—
103	C₂²×C₄	—	94	4	no	—
104	Q₁₆	—	2	8	no	—
105	SD₁₆	—	94	16	no	—
106	D₈	—	94	8	no	—
107	C₂×C₈	—	47	2	no	—
108	C₂×C₈	—	47	8	no	—
109	C₂×C₈	C₂²×D₄₇	1	2	yes	—
110	C₄⋊C₄	—	2	4	no	—
111	C₂²⋊C₄	—	94	8	no	—
112	C₄²	—	47	2	no	—
113	C₄²	—	47	1	no	—
114	C₄²	C₂²×D₄₇	1	1	yes	characteristic
115	C₂³	—	47	1	no	—
116	C₂³	—	94	4	no	—
117	Q₈	—	2	8	no	—
118	D₄	—	94	8	no	—
119	D₄	—	188	8	no	—
120	D₄	—	188	8	no	—
121	C₂×C₄	—	2	4	no	—
122	C₂×C₄	—	47	1	no	—
123	C₂×C₄	—	47	4	no	—
124	C₂×C₄	—	47	2	no	—
125	C₂×C₄	—	94	4	no	—
126	C₂×C₄	—	188	8	no	—
127	C₂×C₄	D₄×D₄₇	1	2	yes	—
128	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
129	C₈	—	47	4	no	—
130	C₈	D₄×D₄₇	1	4	yes	—
131	C₂²	—	47	2	no	—
132	C₂²	—	94	2	no	—
133	C₂²	—	188	8	no	—
134	C₂²	—	188	4	no	—
135	C₂²	C₂×D₄×D₄₇	1	1	yes	characteristic
136	C₄	—	4	4	no	—
137	C₄	—	47	2	no	—
138	C₄	—	94	2	no	—
139	C₄	#13094047	1	4	yes	complemented
140	C₄	C₂×D₄×D₄₇	1	2	yes	—
141	C₂	—	94	2	no	—
142	C₂	—	376	4	no	—
143	C₂	#127×D₄₇	1	1	yes	characteristic
144	C₂	C₂×#13094047	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13094047

C₂

yes

maximal, complemented

#15689674

C₂

yes

maximal, complemented

#15689508

C₂

yes

maximal, complemented

#15689500

C₂

yes

maximal, characteristic, complemented

#15689497

C₂

yes

maximal, complemented

C₄×C₈×D₄₇

C₂

yes

maximal, characteristic, complemented

C₄₇×#494

C₂

yes

maximal, characteristic, complemented

C₂×#10625354

C₂²

yes

—

#13094047

—

C₂×#10625336

C₂²

yes

—

C₂×D₃₇₆

C₂²

yes

—

C₂×C₈×D₄₇

C₂²

yes

—

#13094021

C₂²

yes

—

#13094013

C₂²

yes

—

#13093999

—

#13093986

—

C₄²×D₄₇

C₂²

yes

characteristic

C₄×C₄₇⋊C₈

C₂²

yes

characteristic

C₈×Dic₄₇

C₂²

yes

—

C₂×Q₁₆×C₄₇

C₂²

yes

—

C₄⋊Q₈×C₄₇

C₂²

yes

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

C₂³

yes

—

#10625354

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

C₂³

yes

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

D₄

yes

—

C₂×C₄×D₄₇

C₂³

yes

characteristic

Q₁₆×C₄₇

—

C₂×C₈×C₄₇

C₂³

yes

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

C₂³

yes

characteristic

#10625336

—

(C₂×D₄₇)⋊C₄

—

C₄×Dic₄₇

D₄

yes

—

C₄×Dic₄₇

C₂³

yes

characteristic

C₂×C₄₇⋊C₈

C₂³

yes

—

D₃₇₆

—

C₈×D₄₇

D₄

yes

complemented

C₂²×D₄₇

—

C₂²×D₄₇

C₂×D₄

yes

characteristic

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂⁴

yes

characteristic

C₂×Dic₄₇

C₂×D₄

yes

—

C₂×Dic₄₇

C₂×D₄

yes

characteristic

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

C₄×D₄₇

—

C₄×D₄₇

—

C₄×D₄₇

C₂×D₄

yes

—

C₈×C₄₇

C₂×D₄

yes

—

C₄₇⋊C₈

C₂×D₄

yes

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

#127

yes

—

C₄×C₄₇

—

C₄×C₄₇

#135

yes

complemented

C₄×C₄₇

C₂²×D₄

yes

—

Dic₄₇

—

Dic₄₇

#127

yes

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

D₄₇

—

D₄₇

—

—

—

—

D₄₇

yes

characteristic, complemented

#493

—

#492

—

C₂×C₄×C₈

—

C₄₇

#3147

yes

characteristic, complemented, Sylow

C₂×#41

—

#135

—

C₂×Q₁₆

C₂×D₄₇

yes

—

C₂×SD₁₆

—

C₂×D₈

—

C₂²×C₈

—

C₄⋊Q₈

C₂×D₄₇

yes

—

#127

—

#124

—

#121

—

C₄×D₄

—

C₂×C₄²

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₄₇

yes

characteristic

#41

—

C₂×Q₈

C₂²×D₄₇

yes

—

C₂×D₄

—

C₂×D₄

—

100

C₂×D₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

Q₁₆

—

105

SD₁₆

—

106

D₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

C₂²×D₄₇

yes

—

110

C₄⋊C₄

—

111

C₂²⋊C₄

—

112

C₄²

—

113

C₄²

—

114

C₄²

C₂²×D₄₇

yes

characteristic

115

C₂³

—

116

C₂³

—

117

Q₈

—

118

D₄

—

119

D₄

—

188

—

120

D₄

—

188

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

188

—

127

C₂×C₄

D₄×D₄₇

yes

—

128

C₂×C₄

C₂³×D₄₇

yes

characteristic

129

C₈

—

130

C₈

D₄×D₄₇

yes

—

131

C₂²

—

132

C₂²

—

133

C₂²

—

188

—

134

C₂²

—

188

—

135

C₂²

C₂×D₄×D₄₇

yes

characteristic

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

#13094047

yes

complemented

140

C₄

C₂×D₄×D₄₇

yes

—

141

C₂

—

142

C₂

—

376

—

143

C₂

#127×D₄₇

yes

characteristic

144

C₂

C₂×#13094047

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₄₇×#494	C₂
socle	C₂²×C₄₇	C₂²×D₄
hypercenter	#494	D₄₇
hypocenter	C₄₇	#3147
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

subgroup

G/H

center

C₂²

C₂×D₄×D₄₇

commutator

C₂×C₄×C₄₇

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₇

Fitting

C₄₇×#494

C₂

socle

C₂²×C₄₇

C₂²×D₄

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #494

N	H ≅ G/N	type
1. C₂×#13094047	C₂	semidirect
2. #15689674	C₂	semidirect
3. #15689508	C₂	semidirect
4. #15689500	C₂	semidirect
5. #15689497	C₂	semidirect
6. C₄×C₈×D₄₇	C₂	semidirect
7. C₄₇×#494	C₂	semidirect
41. C₈×D₄₇	D₄	semidirect
64. C₄×C₄₇	#135	semidirect
76. #494	D₄₇	semidirect
80. C₄₇	#3147	semidirect
139. C₄	#13094047	semidirect

H ≅ G/N

type

1. C₂×#13094047

C₂

semidirect

2. #15689674

C₂

semidirect

3. #15689508

C₂

semidirect

4. #15689500

C₂

semidirect

5. #15689497

C₂

semidirect

6. C₄×C₈×D₄₇

C₂

semidirect

7. C₄₇×#494

C₂

semidirect

41. C₈×D₄₇

D₄

semidirect

64. C₄×C₄₇

#135

semidirect

76. #494

D₄₇

semidirect

80. C₄₇

#3147

semidirect

139. C₄

#13094047

semidirect

Subgroups — #20253817

Conjugacy classes of subgroups

Complements