Group #20243497 — subgroups

Subgroups — #20243497

Order 6016.

272 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 81 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	#15689598	C₂	1	1	yes	maximal, characteristic
2	C₂×#13093941	C₂	1	1	yes	maximal, characteristic
3	#15688895	C₂	1	2	yes	maximal, complemented
4	#15688894	C₂	1	2	yes	maximal, complemented
5	C₂×#100×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#10625329	C₂²	1	2	yes	—
7	D₄×Dic₄₇	—	2	2	no	—
8	D₄×Dic₄₇	—	2	2	no	—
9	#13093983	C₂²	1	1	yes	characteristic
10	#13093983	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊Dic₄₇	C₄	1	4	yes	—
12	#13093941	—	2	2	no	—
13	C₂²×D₄×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×M₁₆×C₄₇	C₂²	1	2	yes	—
15	#100×C₄₇	—	2	2	no	—
16	C₂⁴×C₄₇	C₂×C₄	1	2	yes	—
17	C₂×D₄×C₄₇	—	2	2	no	—
18	C₂×D₄×C₄₇	—	2	2	no	—
19	C₂×D₄×C₄₇	D₄	1	2	yes	—
20	C₂×D₄×C₄₇	D₄	1	2	yes	—
21	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
22	C₂²×Dic₄₇	—	2	4	no	—
23	M₁₆×C₄₇	—	2	2	no	—
24	M₁₆×C₄₇	—	2	2	no	—
25	C₂×C₈×C₄₇	—	2	2	no	—
26	C₂²⋊Dic₄₇	—	2	4	no	—
27	C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
28	C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
29	C₄⋊Dic₄₇	—	2	1	no	—
30	C₄⋊Dic₄₇	—	2	1	no	—
31	C₄×Dic₄₇	—	2	1	no	—
32	C₄×Dic₄₇	—	2	1	no	—
33	#10625329	—	2	2	no	—
34	#10625329	—	2	2	no	—
35	C₂×C₄₇⋊C₈	—	2	2	no	—
36	C₂³×C₄₇	—	2	2	no	—
37	C₂³×C₄₇	—	2	2	no	—
38	C₂³×C₄₇	—	8	2	no	—
39	C₂³×C₄₇	C₂²⋊C₄	1	4	yes	—
40	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
41	D₄×C₄₇	—	2	4	no	—
42	D₄×C₄₇	—	2	4	no	—
43	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₄₇	#41	1	2	yes	—
46	C₂×C₄×C₄₇	#41	1	2	yes	—
47	C₂×Dic₄₇	—	2	2	no	—
48	C₂×Dic₄₇	—	2	2	no	—
49	C₂×Dic₄₇	—	8	4	no	—
50	C₈×C₄₇	—	4	2	no	—
51	C₄₇⋊C₈	—	4	2	no	—
52	C₂²×C₄₇	—	2	4	no	—
53	C₂²×C₄₇	—	4	1	no	—
54	C₂²×C₄₇	—	4	4	no	—
55	C₂²×C₄₇	—	8	2	no	—
56	C₂²×C₄₇	—	8	2	no	—
57	C₂²×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
58	C₂²×C₄₇	#117	1	1	yes	characteristic
59	C₂²×C₄₇	#117	1	1	yes	characteristic
60	C₄×C₄₇	#123	1	2	yes	—
61	C₄×C₄₇	#123	1	2	yes	—
62	Dic₄₇	—	4	2	no	—
63	Dic₄₇	—	4	2	no	—
64	#1829	—	47	1	no	maximal, Sylow
65	C₂×C₄₇	—	2	1	no	—
66	C₂×C₄₇	—	2	1	no	—
67	C₂×C₄₇	—	2	1	no	—
68	C₂×C₄₇	—	4	4	no	—
69	C₂×C₄₇	#381	1	1	yes	characteristic
70	#518	—	47	1	no	—
71	C₂×#100	—	47	1	no	—
72	C₂×#100	D₄₇	1	1	yes	characteristic
73	#344	—	47	2	no	—
74	#344	—	47	2	no	—
75	C₄₇	#1829	1	1	yes	characteristic, complemented, Sylow
76	C₂²×D₄	C₂×D₄₇	1	1	yes	characteristic
77	C₂×M₁₆	—	47	2	no	—
78	C₂×M₁₆	C₂×D₄₇	1	2	yes	—
79	C₄×D₄	—	94	2	no	—
80	C₄×D₄	—	94	2	no	—
81	#117	—	47	1	no	—
82	#117	—	47	1	no	—
83	C₂×C₂²⋊C₄	—	47	4	no	—
84	#100	—	2	2	no	—
85	#100	—	94	2	no	—
86	C₂⁴	C₄×D₄₇	1	2	yes	—
87	C₂×D₄	—	2	2	no	—
88	C₂×D₄	—	2	2	no	—
89	C₂×D₄	D₁₈₈	1	2	yes	—
90	C₂×D₄	C₂²⋊D₄₇	1	2	yes	—
91	C₂²×C₄	—	94	4	no	—
92	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
93	M₁₆	—	2	2	no	—
94	M₁₆	—	2	2	no	—
95	M₁₆	—	94	2	no	—
96	M₁₆	—	94	2	no	—
97	C₂×C₈	—	2	2	no	—
98	C₂×C₈	—	94	2	no	—
99	C₄⋊C₄	—	94	1	no	—
100	C₄⋊C₄	—	94	1	no	—
101	C₂²⋊C₄	—	47	2	no	—
102	C₂²⋊C₄	—	47	2	no	—
103	C₂²⋊C₄	—	94	4	no	—
104	C₄²	—	94	1	no	—
105	C₄²	—	94	1	no	—
106	C₂³	—	2	2	no	—
107	C₂³	—	2	2	no	—
108	C₂³	—	8	2	no	—
109	C₂³	(C₂×D₄₇)⋊C₄	1	4	yes	—
110	C₂³	C₂×C₄×D₄₇	1	1	yes	characteristic
111	D₄	—	2	4	no	—
112	D₄	—	2	4	no	—
113	C₂×C₄	—	94	2	no	—
114	C₂×C₄	—	94	2	no	—
115	C₂×C₄	—	376	4	no	—
116	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
117	C₂×C₄	#10625352	1	2	yes	—
118	C₂×C₄	#10625352	1	2	yes	—
119	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
120	C₈	—	4	2	no	—
121	C₈	—	188	2	no	—
122	C₂²	—	2	4	no	—
123	C₂²	—	4	1	no	—
124	C₂²	—	4	4	no	—
125	C₂²	—	8	2	no	—
126	C₂²	—	8	2	no	—
127	C₂²	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
128	C₂²	#13093980	1	1	yes	characteristic
129	C₂²	#13093980	1	1	yes	characteristic
130	C₄	—	188	2	no	—
131	C₄	—	188	2	no	—
132	C₄	#13094005	1	2	yes	—
133	C₄	#13094008	1	2	yes	—
134	C₂	—	2	1	no	—
135	C₂	—	2	1	no	—
136	C₂	—	2	1	no	—
137	C₂	—	4	4	no	—
138	C₂	#15688984	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689598

C₂

yes

maximal, characteristic

C₂×#13093941

C₂

yes

maximal, characteristic

#15688895

C₂

yes

maximal, complemented

#15688894

C₂

yes

maximal, complemented

C₂×#100×C₄₇

C₂

yes

maximal, characteristic

C₂×#10625329

C₂²

yes

—

D₄×Dic₄₇

—

D₄×Dic₄₇

—

#13093983

C₂²

yes

characteristic

#13093983

C₂²

yes

characteristic

C₂×C₂²⋊Dic₄₇

C₄

yes

—

#13093941

—

C₂²×D₄×C₄₇

C₂²

yes

characteristic

C₂×M₁₆×C₄₇

C₂²

yes

—

#100×C₄₇

—

C₂⁴×C₄₇

C₂×C₄

yes

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

D₄

yes

—

C₂×D₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

C₂×C₄

yes

—

C₂²⋊Dic₄₇

C₂×C₄

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂²⋊C₄

yes

—

C₂³×C₄₇

C₂²×C₄

yes

characteristic

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×C₂²⋊C₄

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₄×C₄₇

yes

—

C₄×C₄₇

#123

yes

—

Dic₄₇

—

Dic₄₇

—

#1829

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

yes

—

—

D₄₇

yes

characteristic

#344

—

#344

—

C₄₇

#1829

yes

characteristic, complemented, Sylow

C₂²×D₄

C₂×D₄₇

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₇

yes

—

C₄×D₄

—

C₄×D₄

—

#117

—

#117

—

C₂×C₂²⋊C₄

—

#100

—

#100

—

C₂⁴

C₄×D₄₇

yes

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

D₁₈₈

yes

—

C₂×D₄

C₂²⋊D₄₇

yes

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₂²⋊C₄

—

102

C₂²⋊C₄

—

103

C₂²⋊C₄

—

104

C₄²

—

105

C₄²

—

106

C₂³

—

107

C₂³

—

108

C₂³

—

109

C₂³

(C₂×D₄₇)⋊C₄

yes

—

110

C₂³

C₂×C₄×D₄₇

yes

characteristic

111

D₄

—

112

D₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

376

—

116

C₂×C₄

C₂×D₁₈₈

yes

characteristic

117

C₂×C₄

#10625352

yes

—

118

C₂×C₄

#10625352

yes

—

119

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

120

C₈

—

121

C₈

—

188

—

122

C₂²

—

123

C₂²

—

124

C₂²

—

125

C₂²

—

126

C₂²

—

127

C₂²

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

128

C₂²

#13093980

yes

characteristic

129

C₂²

#13093980

yes

characteristic

130

C₄

—

188

—

131

C₄

—

188

—

132

C₄

#13094005

yes

—

133

C₄

#13094008

yes

—

134

C₂

—

135

C₂

—

136

C₂

—

137

C₂

—

138

C₂

#15688984

yes

characteristic

	subgroup	G/H
center	C₂	#15688984
commutator	C₂³×C₄₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₂×#100×C₄₇	C₂
socle	C₂×C₄₇	#381
hypercenter	C₂×#100	D₄₇
hypocenter	C₄₇	#1829
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#100

subgroup

G/H

center

C₂

#15688984

commutator

C₂³×C₄₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₂×#100×C₄₇

C₂

C₂×C₄₇

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#100

N	H ≅ G/N	type
3. #15688895	C₂	semidirect
4. #15688894	C₂	semidirect
75. C₄₇	#1829	semidirect

H ≅ G/N

type

3. #15688895

C₂

semidirect

4. #15688894

C₂

semidirect

75. C₄₇

#1829

semidirect

Subgroups — #20243497

Conjugacy classes of subgroups

Complements