Group #20243113 — subgroups

Subgroups — #20243113

Order 6016.

372 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 137 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	C₂²×#10625324	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆×D₄₇	C₂	1	2	yes	maximal
3	#15688888	C₂	1	1	yes	maximal, characteristic, complemented
4	#15688887	C₂	1	2	yes	maximal, complemented
5	C₄₇×#341	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic
7	C₂×#10625329	C₂²	1	2	yes	—
8	C₂×#10625324	—	2	2	no	—
9	C₂×#10625324	—	2	4	no	—
10	C₂×#10625324	C₄	1	4	yes	—
11	M₁₆×D₄₇	—	2	4	no	—
12	M₁₆×D₄₇	C₄	1	8	yes	—
13	C₂²×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₈×D₄₇	—	2	2	no	—
15	C₂×M₁₆×C₄₇	C₂²	1	2	yes	—
16	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂³×D₄₇	Q₈	1	1	yes	characteristic
18	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
19	C₂²×Dic₄₇	Q₈	1	1	yes	characteristic
20	C₂×C₄×D₄₇	C₂×C₄	1	4	yes	—
21	C₂×C₄×D₄₇	C₂×C₄	1	2	yes	—
22	C₂×C₄×D₄₇	D₄	1	2	yes	—
23	C₂×C₄×D₄₇	D₄	1	4	yes	—
24	M₁₆×C₄₇	—	2	2	no	—
25	M₁₆×C₄₇	C₂×C₄	1	4	yes	—
26	C₂×C₈×C₄₇	—	2	2	no	—
27	C₂×C₈×C₄₇	—	2	2	no	—
28	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
29	#10625329	—	2	2	no	—
30	#10625329	C₂×C₄	1	4	yes	—
31	C₂×C₄₇⋊C₈	—	2	2	no	—
32	C₂×C₄₇⋊C₈	—	2	2	no	—
33	C₂×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
34	#10625324	—	2	8	no	—
35	#10625324	—	2	8	no	—
36	C₈×D₄₇	—	2	8	no	—
37	C₂³×C₄₇	C₂×Q₈	1	1	yes	characteristic
38	C₂²×D₄₇	—	4	2	no	—
39	C₂²×D₄₇	C₄⋊C₄	1	2	yes	—
40	C₂²×D₄₇	C₄⋊C₄	1	4	yes	—
41	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
43	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
44	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
45	C₂×Dic₄₇	C₄⋊C₄	1	4	yes	—
46	C₂×Dic₄₇	C₄⋊C₄	1	2	yes	—
47	C₄×D₄₇	C₄²	1	4	yes	—
48	C₄×D₄₇	C₂²⋊C₄	1	4	yes	—
49	C₄×D₄₇	C₂²⋊C₄	1	4	yes	—
50	C₄×D₄₇	C₂²⋊C₄	1	4	yes	—
51	C₈×C₄₇	—	2	4	no	—
52	C₈×C₄₇	—	2	2	no	—
53	C₄₇⋊C₈	—	2	4	no	—
54	C₄₇⋊C₈	—	2	2	no	—
55	C₂²×C₄₇	—	2	2	no	—
56	C₂²×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
57	C₂²×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
58	C₂×D₄₇	—	2	4	no	—
59	C₂×D₄₇	—	4	4	no	—
60	C₂×D₄₇	#95	1	4	yes	—
61	C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
62	C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
63	C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
64	Dic₄₇	#95	1	4	yes	—
65	#1738	—	47	1	no	maximal, Sylow
66	C₂×C₄₇	—	2	2	no	—
67	C₂×C₄₇	C₂×#95	1	1	yes	characteristic
68	C₂×C₄₇	#430	1	2	yes	—
69	D₄₇	—	2	4	no	—
70	C₂²×M₁₆	—	47	1	no	—
71	C₂²×M₁₆	—	47	2	no	—
72	#341	—	47	2	no	—
73	#341	—	47	1	no	—
74	#341	D₄₇	1	1	yes	characteristic, complemented
75	C₄₇	#1738	1	1	yes	characteristic, complemented, Sylow
76	C₂³×C₄	—	47	1	no	—
77	C₂×M₁₆	—	47	4	no	—
78	C₂×M₁₆	—	47	2	no	—
79	C₂×M₁₆	—	47	8	no	—
80	C₂×M₁₆	—	94	4	no	—
81	C₂×M₁₆	—	94	2	no	—
82	C₂×M₁₆	—	94	4	no	—
83	C₂×M₁₆	C₂×D₄₇	1	2	yes	—
84	C₂²×C₈	—	47	1	no	—
85	C₂²×C₈	—	94	2	no	—
86	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
87	C₂⁴	—	47	1	no	—
88	C₂²×C₄	—	47	1	no	—
89	C₂²×C₄	—	47	4	no	—
90	C₂²×C₄	—	47	2	no	—
91	C₂²×C₄	—	47	4	no	—
92	C₂²×C₄	—	47	2	no	—
93	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
94	M₁₆	—	2	2	no	—
95	M₁₆	—	47	4	no	—
96	M₁₆	—	94	8	no	—
97	M₁₆	—	94	8	no	—
98	M₁₆	—	94	2	no	—
99	M₁₆	C₄×D₄₇	1	4	yes	—
100	C₂×C₈	—	2	2	no	—
101	C₂×C₈	—	2	2	no	—
102	C₂×C₈	—	47	2	no	—
103	C₂×C₈	—	94	8	no	—
104	C₂×C₈	—	94	2	no	—
105	C₂×C₈	—	94	2	no	—
106	C₂×C₈	C₄×D₄₇	1	2	yes	—
107	C₂³	—	47	2	no	—
108	C₂³	—	47	4	no	—
109	C₂³	—	188	2	no	—
110	C₂³	Q₈×D₄₇	1	1	yes	characteristic
111	C₂×C₄	—	47	4	no	—
112	C₂×C₄	—	47	2	no	—
113	C₂×C₄	—	47	4	no	—
114	C₂×C₄	—	47	4	no	—
115	C₂×C₄	—	47	4	no	—
116	C₂×C₄	—	47	4	no	—
117	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
118	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
119	C₂×C₄	D₄×D₄₇	1	2	yes	—
120	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
121	C₈	—	2	2	no	—
122	C₈	—	2	4	no	—
123	C₈	—	94	2	no	—
124	C₈	—	94	4	no	—
125	C₂²	—	2	2	no	—
126	C₂²	—	47	4	no	—
127	C₂²	—	94	4	no	—
128	C₂²	—	188	4	no	—
129	C₂²	C₄⋊C₄×D₄₇	1	2	yes	—
130	C₂²	C₄⋊C₄×D₄₇	1	1	yes	characteristic
131	C₄	—	47	4	no	—
132	C₄	C₄²×D₄₇	1	1	yes	characteristic
133	C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
134	C₄	C₂²⋊C₄×D₄₇	1	2	yes	—
135	C₂	—	2	2	no	—
136	C₂	—	94	4	no	—
137	C₂	#95×D₄₇	1	1	yes	characteristic
138	C₂	#15689170	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#10625324

C₂

yes

maximal, characteristic

C₂×M₁₆×D₄₇

C₂

yes

maximal

#15688888

C₂

yes

maximal, characteristic, complemented

#15688887

C₂

yes

maximal, complemented

C₄₇×#341

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₄₇

C₂²

yes

characteristic

C₂×#10625329

C₂²

yes

—

C₂×#10625324

—

C₂×#10625324

—

C₂×#10625324

C₄

yes

—

M₁₆×D₄₇

—

M₁₆×D₄₇

C₄

yes

—

C₂²×C₄₇⋊C₈

C₂²

yes

characteristic

C₂×C₈×D₄₇

—

C₂×M₁₆×C₄₇

C₂²

yes

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂³×D₄₇

Q₈

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

Q₈

yes

characteristic

C₂×C₄×D₄₇

C₂×C₄

yes

—

C₂×C₄×D₄₇

C₂×C₄

yes

—

C₂×C₄×D₄₇

D₄

yes

—

C₂×C₄×D₄₇

D₄

yes

—

M₁₆×C₄₇

—

M₁₆×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

#10625329

—

#10625329

C₂×C₄

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

C₂×C₄

yes

—

#10625324

—

#10625324

—

C₈×D₄₇

—

C₂³×C₄₇

C₂×Q₈

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

C₄⋊C₄

yes

—

C₂²×D₄₇

C₄⋊C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

C₄⋊C₄

yes

—

C₂×Dic₄₇

C₄⋊C₄

yes

—

C₄×D₄₇

C₄²

yes

—

C₄×D₄₇

C₂²⋊C₄

yes

—

C₄×D₄₇

C₂²⋊C₄

yes

—

C₄×D₄₇

C₂²⋊C₄

yes

—

C₈×C₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×C₄⋊C₄

yes

—

C₂²×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

#95

yes

—

C₄×C₄₇

C₂×C₄²

yes

characteristic

C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₄₇

C₂×C₂²⋊C₄

yes

—

Dic₄₇

#95

yes

—

#1738

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

C₂×#95

yes

characteristic

C₂×C₄₇

#430

yes

—

D₄₇

—

C₂²×M₁₆

—

C₂²×M₁₆

—

#341

—

#341

—

#341

D₄₇

yes

characteristic, complemented

C₄₇

#1738

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₇

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×D₄₇

yes

characteristic

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

C₄×D₄₇

yes

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

C₄×D₄₇

yes

—

107

C₂³

—

108

C₂³

—

109

C₂³

—

188

—

110

C₂³

Q₈×D₄₇

yes

characteristic

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

118

C₂×C₄

C₂×C₄×D₄₇

yes

—

119

C₂×C₄

D₄×D₄₇

yes

—

120

C₂×C₄

D₄×D₄₇

yes

characteristic

121

C₈

—

122

C₈

—

123

C₈

—

124

C₈

—

125

C₂²

—

126

C₂²

—

127

C₂²

—

128

C₂²

—

188

—

129

C₂²

C₄⋊C₄×D₄₇

yes

—

130

C₂²

C₄⋊C₄×D₄₇

yes

characteristic

131

C₄

—

132

C₄

C₄²×D₄₇

yes

characteristic

133

C₄

C₂²⋊C₄×D₄₇

yes

characteristic

134

C₄

C₂²⋊C₄×D₄₇

yes

—

135

C₂

—

136

C₂

—

137

C₂

#95×D₄₇

yes

characteristic

138

C₂

#15689170

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₄₇
commutator	C₄×C₄₇	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×#341	C₂
socle	C₂²×C₄₇	C₂×C₄⋊C₄
hypercenter	#341	D₄₇
hypocenter	C₄₇	#1738
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂×C₄

D₄×D₄₇

commutator

C₄×C₄₇

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₄₇×#341

C₂

socle

C₂²×C₄₇

C₂×C₄⋊C₄

D₄₇

C₄₇

G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
3. #15688888	C₂	semidirect
4. #15688887	C₂	semidirect
5. C₄₇×#341	C₂	semidirect
74. #341	D₄₇	semidirect
75. C₄₇	#1738	semidirect

H ≅ G/N

type

3. #15688888

C₂

semidirect

4. #15688887

C₂

semidirect

5. C₄₇×#341

C₂

semidirect

74. #341

D₄₇

semidirect

75. C₄₇

#1738

semidirect

Subgroups — #20243113

Conjugacy classes of subgroups

Complements