Group #20256536 — subgroups

Subgroups — #20256536

Order 6016.

360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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	#15689940	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689928	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689566	C₂	1	3	yes	maximal, complemented
4	#15689561	C₂	1	3	yes	maximal, complemented
5	#15689555	C₂	1	3	yes	maximal, complemented
6	C₂×#13093969	C₂	1	3	yes	maximal, complemented
7	C₄₇×#504	C₂	1	1	yes	maximal, characteristic, complemented
8	#13094071	—	2	1	no	—
9	#13094070	—	2	1	no	—
10	#13094057	—	2	3	no	—
11	#13094052	—	2	3	no	—
12	#13094046	C₂²	1	3	yes	—
13	#13094046	C₂²	1	3	yes	complemented
14	C₂×Dic₁₈₈	C₂²	1	3	yes	complemented
15	C₂×D₃₇₆	C₂²	1	3	yes	—
16	Dic₃₇₆	C₂²	1	3	yes	complemented
17	#13093969	C₂²	1	3	yes	complemented
18	#13093969	C₂²	1	6	yes	complemented
19	#13093969	C₂²	1	1	yes	characteristic, complemented
20	D₇₅₂	C₂²	1	3	yes	complemented
21	#131×C₄₇	C₂²	1	1	yes	characteristic
22	M₃₂×C₄₇	C₂²	1	3	yes	complemented
23	C₂×C₁₆×C₄₇	C₂²	1	3	yes	complemented
24	#41×C₄₇	D₄	1	1	yes	characteristic
25	#10625354	—	4	1	no	—
26	Q₈×D₄₇	—	4	1	no	—
27	#10625352	—	4	3	no	—
28	D₄×D₄₇	—	4	3	no	—
29	#10625350	—	2	3	no	—
30	#10625350	—	2	3	no	—
31	C₂×D₁₈₈	—	2	3	no	—
32	C₂×Dic₉₄	—	2	3	no	—
33	M₁₆×C₄₇	D₄	1	3	yes	—
34	C₂×C₈×C₄₇	C₂³	1	3	yes	—
35	Dic₁₈₈	—	2	3	no	—
36	Dic₁₈₈	C₂³	1	3	yes	—
37	Dic₁₈₈	C₂³	1	1	yes	characteristic
38	D₃₇₆	—	2	3	no	—
39	D₃₇₆	C₂³	1	1	yes	characteristic
40	D₃₇₆	C₂³	1	3	yes	—
41	#10625325	—	2	3	no	—
42	#10625325	—	2	3	no	—
43	C₁₆×C₄₇	C₂³	1	1	yes	characteristic
44	C₁₆×C₄₇	C₂³	1	3	yes	—
45	C₂²×D₄₇	—	4	3	no	—
46	Q₈×C₄₇	D₈	1	1	yes	characteristic
47	D₄×C₄₇	D₈	1	3	yes	—
48	C₂×C₄×C₄₇	C₂×D₄	1	3	yes	—
49	C₂²⋊D₄₇	—	4	3	no	—
50	C₂²⋊D₄₇	—	4	3	no	—
51	C₂×Dic₄₇	—	4	3	no	—
52	D₁₈₈	—	2	1	no	—
53	D₁₈₈	—	2	3	no	—
54	D₁₈₈	—	4	3	no	—
55	C₄×D₄₇	—	4	3	no	—
56	C₄×D₄₇	—	4	3	no	—
57	Dic₉₄	—	2	1	no	—
58	Dic₉₄	—	2	3	no	—
59	Dic₉₄	—	4	3	no	—
60	C₈×C₄₇	C₂×D₄	1	3	yes	—
61	C₈×C₄₇	C₂⁴	1	1	yes	characteristic
62	C₂²×C₄₇	C₂×D₈	1	3	yes	—
63	C₂×D₄₇	—	4	1	no	—
64	C₂×D₄₇	—	4	3	no	—
65	C₂×D₄₇	—	16	3	no	—
66	C₄×C₄₇	C₂×D₈	1	3	yes	—
67	C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
68	Dic₄₇	—	4	3	no	—
69	Dic₄₇	—	4	1	no	—
70	#3416	—	47	1	no	maximal, Sylow
71	C₂×C₄₇	—	2	3	no	—
72	C₂×C₄₇	C₂²×D₈	1	1	yes	characteristic
73	D₄₇	—	8	1	no	—
74	D₄₇	—	8	3	no	—
75	#578	—	47	1	no	—
76	#576	—	47	1	no	—
77	#510	—	47	3	no	—
78	#509	—	47	3	no	—
79	#508	—	47	3	no	—
80	C₂×SD₃₂	—	47	3	no	—
81	#504	D₄₇	1	1	yes	characteristic, complemented
82	C₄₇	#3416	1	1	yes	characteristic, complemented, Sylow
83	2₋¹⁺⁴	—	94	1	no	—
84	H(5,𝔽₂)	—	94	1	no	—
85	#137	—	94	3	no	—
86	AGL(1,ℤ/8)	—	94	3	no	—
87	#135	—	47	3	no	—
88	#135	—	47	3	no	—
89	C₂×Q₁₆	—	47	3	no	—
90	C₂×D₈	—	47	3	no	—
91	#131	C₂×D₄₇	1	1	yes	characteristic
92	Q₃₂	—	47	3	no	—
93	SD₃₂	—	47	3	no	—
94	SD₃₂	—	47	6	no	—
95	SD₃₂	—	47	1	no	—
96	D₁₆	—	47	3	no	—
97	M₃₂	C₂×D₄₇	1	3	yes	complemented
98	C₂×C₁₆	C₂×D₄₇	1	3	yes	complemented
99	#41	—	94	3	no	—
100	#41	—	94	3	no	—
101	#41	—	188	1	no	—
102	#41	—	188	3	no	—
103	#41	D₁₈₈	1	1	yes	characteristic
104	C₂×Q₈	—	94	3	no	—
105	C₂×Q₈	—	188	1	no	—
106	C₂×D₄	—	94	3	no	—
107	C₂×D₄	—	188	3	no	—
108	Q₁₆	—	47	3	no	—
109	Q₁₆	—	47	1	no	—
110	Q₁₆	—	94	3	no	—
111	SD₁₆	—	94	3	no	—
112	SD₁₆	—	94	3	no	—
113	D₈	—	47	1	no	—
114	D₈	—	47	3	no	—
115	D₈	—	94	3	no	—
116	M₁₆	D₁₈₈	1	3	yes	—
117	C₂×C₈	C₂²×D₄₇	1	3	yes	—
118	C₁₆	C₂²×D₄₇	1	1	yes	characteristic
119	C₁₆	C₂²×D₄₇	1	3	yes	—
120	C₂³	—	188	3	no	—
121	Q₈	—	94	1	no	—
122	Q₈	—	94	3	no	—
123	Q₈	—	188	3	no	—
124	Q₈	D₃₇₆	1	1	yes	characteristic
125	D₄	—	94	3	no	—
126	D₄	—	94	1	no	—
127	D₄	—	188	3	no	—
128	D₄	—	188	3	no	—
129	D₄	—	188	3	no	—
130	D₄	D₃₇₆	1	3	yes	—
131	C₂×C₄	—	188	3	no	—
132	C₂×C₄	—	188	3	no	—
133	C₂×C₄	—	188	3	no	—
134	C₂×C₄	C₂×D₁₈₈	1	3	yes	—
135	C₈	C₂×D₁₈₈	1	3	yes	—
136	C₈	C₂³×D₄₇	1	1	yes	characteristic
137	C₂²	—	188	1	no	—
138	C₂²	—	188	3	no	—
139	C₂²	—	752	3	no	—
140	C₂²	C₂×D₃₇₆	1	3	yes	—
141	C₄	—	188	1	no	—
142	C₄	—	188	3	no	—
143	C₄	C₂×D₃₇₆	1	3	yes	—
144	C₄	C₂²×D₁₈₈	1	1	yes	characteristic
145	C₂	—	2	3	no	—
146	C₂	—	376	3	no	—
147	C₂	—	376	1	no	—
148	C₂	C₂²×D₃₇₆	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689940

C₂

yes

maximal, characteristic, complemented

#15689928

C₂

yes

maximal, characteristic, complemented

#15689566

C₂

yes

maximal, complemented

#15689561

C₂

yes

maximal, complemented

#15689555

C₂

yes

maximal, complemented

C₂×#13093969

C₂

yes

maximal, complemented

C₄₇×#504

C₂

yes

maximal, characteristic, complemented

—

—

—

—

C₂²

yes

—

#13094046

C₂²

yes

complemented

C₂×Dic₁₈₈

C₂²

yes

complemented

C₂×D₃₇₆

C₂²

yes

—

Dic₃₇₆

C₂²

yes

complemented

#13093969

C₂²

yes

complemented

#13093969

C₂²

yes

complemented

#13093969

C₂²

yes

characteristic, complemented

D₇₅₂

C₂²

yes

complemented

#131×C₄₇

C₂²

yes

characteristic

M₃₂×C₄₇

C₂²

yes

complemented

C₂×C₁₆×C₄₇

C₂²

yes

complemented

#41×C₄₇

D₄

yes

characteristic

#10625354

—

Q₈×D₄₇

—

#10625352

—

D₄×D₄₇

—

#10625350

—

#10625350

—

C₂×D₁₈₈

—

C₂×Dic₉₄

—

M₁₆×C₄₇

D₄

yes

—

C₂×C₈×C₄₇

C₂³

yes

—

Dic₁₈₈

—

Dic₁₈₈

C₂³

yes

—

Dic₁₈₈

C₂³

yes

characteristic

D₃₇₆

—

D₃₇₆

C₂³

yes

characteristic

D₃₇₆

C₂³

yes

—

#10625325

—

#10625325

—

C₁₆×C₄₇

C₂³

yes

characteristic

C₁₆×C₄₇

C₂³

yes

—

C₂²×D₄₇

—

Q₈×C₄₇

D₈

yes

characteristic

D₄×C₄₇

D₈

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂²⋊D₄₇

—

C₂²⋊D₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

C₄×D₄₇

—

C₄×D₄₇

—

Dic₉₄

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

C₂×D₄

yes

—

C₈×C₄₇

C₂⁴

yes

characteristic

C₂²×C₄₇

C₂×D₈

yes

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

C₂×D₈

yes

—

C₄×C₄₇

C₂²×D₄

yes

characteristic

Dic₄₇

—

Dic₄₇

—

#3416

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

C₂²×D₈

yes

characteristic

D₄₇

—

D₄₇

—

—

—

—

—

—

C₂×SD₃₂

—

#504

D₄₇

yes

characteristic, complemented

C₄₇

#3416

yes

characteristic, complemented, Sylow

2₋¹⁺⁴

—

—

—

—

—

—

C₂×Q₁₆

—

C₂×D₈

—

#131

C₂×D₄₇

yes

characteristic

Q₃₂

—

SD₃₂

—

SD₃₂

—

SD₃₂

—

D₁₆

—

M₃₂

C₂×D₄₇

yes

complemented

C₂×C₁₆

C₂×D₄₇

yes

complemented

#41

—

100

#41

—

101

#41

—

188

—

102

#41

—

188

—

103

#41

D₁₈₈

yes

characteristic

104

C₂×Q₈

—

105

C₂×Q₈

—

188

—

106

C₂×D₄

—

107

C₂×D₄

—

188

—

108

Q₁₆

—

109

Q₁₆

—

110

Q₁₆

—

111

SD₁₆

—

112

SD₁₆

—

113

D₈

—

114

D₈

—

115

D₈

—

116

M₁₆

D₁₈₈

yes

—

117

C₂×C₈

C₂²×D₄₇

yes

—

118

C₁₆

C₂²×D₄₇

yes

characteristic

119

C₁₆

C₂²×D₄₇

yes

—

120

C₂³

—

188

—

121

Q₈

—

122

Q₈

—

123

Q₈

—

188

—

124

Q₈

D₃₇₆

yes

characteristic

125

D₄

—

126

D₄

—

127

D₄

—

188

—

128

D₄

—

188

—

129

D₄

—

188

—

130

D₄

D₃₇₆

yes

—

131

C₂×C₄

—

188

—

132

C₂×C₄

—

188

—

133

C₂×C₄

—

188

—

134

C₂×C₄

C₂×D₁₈₈

yes

—

135

C₈

C₂×D₁₈₈

yes

—

136

C₈

C₂³×D₄₇

yes

characteristic

137

C₂²

—

188

—

138

C₂²

—

188

—

139

C₂²

—

752

—

140

C₂²

C₂×D₃₇₆

yes

—

141

C₄

—

188

—

142

C₄

—

188

—

143

C₄

C₂×D₃₇₆

yes

—

144

C₄

C₂²×D₁₈₈

yes

characteristic

145

C₂

—

146

C₂

—

376

—

147

C₂

—

376

—

148

C₂

C₂²×D₃₇₆

yes

characteristic

	subgroup	G/H
center	C₂	C₂²×D₃₇₆
commutator	C₈×C₄₇	C₂⁴
Frattini	C₈	C₂³×D₄₇
Fitting	C₄₇×#504	C₂
socle	C₂×C₄₇	C₂²×D₈
hypercenter	#504	D₄₇
hypocenter	C₄₇	#3416
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ #41 ◁ #131 ◁ #504

subgroup

G/H

center

C₂

C₂²×D₃₇₆

commutator

C₈×C₄₇

C₂⁴

Frattini

C₈

C₂³×D₄₇

Fitting

C₄₇×#504

C₂

socle

C₂×C₄₇

C₂²×D₈

D₄₇

C₄₇

G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂ ◁ #41 ◁ #131 ◁ #504

N	H ≅ G/N	type
1. #15689940	C₂	semidirect
2. #15689928	C₂	semidirect
3. #15689566	C₂	semidirect
4. #15689561	C₂	semidirect
5. #15689555	C₂	semidirect
6. C₂×#13093969	C₂	semidirect
7. C₄₇×#504	C₂	semidirect
13. #13094046	C₂²	semidirect
14. C₂×Dic₁₈₈	C₂²	semidirect
16. Dic₃₇₆	C₂²	semidirect
17. #13093969	C₂²	semidirect
18. #13093969	C₂²	semidirect
19. #13093969	C₂²	semidirect
20. D₇₅₂	C₂²	semidirect
22. M₃₂×C₄₇	C₂²	semidirect
23. C₂×C₁₆×C₄₇	C₂²	semidirect
81. #504	D₄₇	semidirect
82. C₄₇	#3416	semidirect
97. M₃₂	C₂×D₄₇	semidirect
98. C₂×C₁₆	C₂×D₄₇	semidirect

H ≅ G/N

type

1. #15689940

C₂

semidirect

2. #15689928

C₂

semidirect

3. #15689566

C₂

semidirect

4. #15689561

C₂

semidirect

5. #15689555

C₂

semidirect

6. C₂×#13093969

C₂

semidirect

7. C₄₇×#504

C₂

semidirect

13. #13094046

C₂²

semidirect

14. C₂×Dic₁₈₈

C₂²

semidirect

16. Dic₃₇₆

C₂²

semidirect

17. #13093969

C₂²

semidirect

18. #13093969

C₂²

semidirect

19. #13093969

C₂²

semidirect

20. D₇₅₂

C₂²

semidirect

22. M₃₂×C₄₇

C₂²

semidirect

23. C₂×C₁₆×C₄₇

C₂²

semidirect

81. #504

D₄₇

semidirect

82. C₄₇

#3416

semidirect

97. M₃₂

C₂×D₄₇

semidirect

98. C₂×C₁₆

C₂×D₄₇

semidirect

Subgroups — #20256536

Conjugacy classes of subgroups

Complements