Group #20245618 — subgroups

Subgroups — #20245618

Order 6016.

138 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 47 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	#15689524	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689506	C₂	1	1	yes	maximal, characteristic
3	#15688928	C₂	1	1	yes	maximal, characteristic, complemented
4	#15688926	C₂	1	1	yes	maximal, characteristic, complemented
5	#15688924	C₂	1	1	yes	maximal, characteristic
6	C₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#357	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₁₈₈	C₂²	1	1	yes	characteristic
9	C₂×#10625335	—	2	1	no	—
10	#13094015	—	2	1	no	—
11	#13094011	—	2	1	no	—
12	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
13	#13093958	C₂²	1	1	yes	characteristic
14	#13093955	—	2	1	no	—
15	C₈×Dic₄₇	C₂²	1	1	yes	characteristic
16	C₂×D₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
18	#107×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×D₄×C₄₇	—	2	1	no	—
20	C₂×Dic₉₄	—	2	1	no	—
21	D₈×C₄₇	—	2	1	no	—
22	D₈×C₄₇	—	2	1	no	—
23	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
24	C₄⋊C₄×C₄₇	—	2	1	no	—
25	C₂²⋊Dic₄₇	—	4	1	no	—
26	C₂²⋊Dic₄₇	—	4	1	no	—
27	#10625335	—	4	2	no	—
28	C₄⋊Dic₄₇	—	2	1	no	—
29	C₄⋊Dic₄₇	—	4	1	no	—
30	Dic₄₇⋊C₄	—	4	1	no	—
31	C₄×Dic₄₇	D₄	1	1	yes	characteristic
32	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
33	Dic₁₈₈	—	2	1	no	—
34	Dic₁₈₈	—	2	1	no	—
35	C₁₆×C₄₇	—	2	1	no	—
36	C₄₇⋊C₁₆	—	2	1	no	—
37	C₂³×C₄₇	—	4	1	no	—
38	D₄×C₄₇	—	4	1	no	—
39	D₄×C₄₇	—	4	1	no	—
40	C₂×C₄×C₄₇	—	4	1	no	—
41	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
42	C₂×Dic₄₇	—	4	1	no	—
43	C₂×Dic₄₇	—	4	1	no	—
44	C₂×Dic₄₇	D₈	1	1	yes	characteristic
45	C₂×Dic₄₇	D₈	1	1	yes	characteristic
46	Dic₉₄	—	4	1	no	—
47	Dic₉₄	—	4	1	no	—
48	C₈×C₄₇	#41	1	1	yes	characteristic
49	C₈×C₄₇	#41	1	1	yes	characteristic
50	C₄₇⋊C₈	SD₁₆	1	2	yes	—
51	C₂²×C₄₇	—	8	1	no	—
52	C₂²×C₄₇	—	8	1	no	—
53	C₂²×C₄₇	—	8	1	no	—
54	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
55	C₄×C₄₇	—	8	1	no	—
56	C₄×C₄₇	#124	1	1	yes	characteristic
57	C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
58	Dic₄₇	—	2	1	no	—
59	Dic₄₇	—	2	1	no	—
60	Dic₄₇	—	8	1	no	—
61	Dic₄₇	—	8	1	no	—
62	#2242	—	47	1	no	maximal, Sylow
63	C₂×C₄₇	—	16	1	no	—
64	C₂×C₄₇	#486	1	1	yes	characteristic
65	C₂×C₄₇	#508	1	1	yes	characteristic
66	C₂×C₄₇	#508	1	1	yes	characteristic
67	#499	—	47	1	no	—
68	#495	—	47	1	no	—
69	#358	—	47	1	no	—
70	#358	—	47	1	no	—
71	#357	—	47	1	no	—
72	#357	D₄₇	1	1	yes	characteristic
73	C₄×C₁₆	—	47	1	no	—
74	C₄₇	#2242	1	1	yes	characteristic, complemented, Sylow
75	C₂×Q₁₆	—	47	1	no	—
76	C₂×SD₁₆	—	94	1	no	—
77	C₂×D₈	C₂×D₄₇	1	1	yes	characteristic
78	#125	—	94	1	no	—
79	#124	—	94	1	no	—
80	C₂×C₁₆	—	47	1	no	—
81	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
82	#107	—	47	1	no	—
83	#107	C₂×D₄₇	1	1	yes	characteristic
84	#106	—	94	1	no	—
85	C₄×C₈	—	47	1	no	—
86	C₂×Q₈	—	94	1	no	—
87	C₂×D₄	—	2	1	no	—
88	Q₁₆	—	94	1	no	—
89	Q₁₆	—	94	1	no	—
90	SD₁₆	—	188	2	no	—
91	D₈	—	2	1	no	—
92	D₈	—	2	1	no	—
93	C₂×C₈	—	47	1	no	—
94	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
95	C₄⋊C₄	—	2	1	no	—
96	C₄⋊C₄	—	94	1	no	—
97	C₄⋊C₄	—	188	1	no	—
98	C₄⋊C₄	—	188	1	no	—
99	C₂²⋊C₄	—	188	1	no	—
100	C₂²⋊C₄	—	188	1	no	—
101	C₄²	—	47	1	no	—
102	C₁₆	—	2	1	no	—
103	C₁₆	—	94	1	no	—
104	C₂³	—	4	1	no	—
105	Q₈	—	188	1	no	—
106	Q₈	—	188	1	no	—
107	D₄	—	4	1	no	—
108	D₄	—	4	1	no	—
109	C₂×C₄	—	4	1	no	—
110	C₂×C₄	—	47	1	no	—
111	C₂×C₄	—	47	1	no	—
112	C₂×C₄	—	188	1	no	—
113	C₂×C₄	—	188	1	no	—
114	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
115	C₈	—	47	2	no	—
116	C₈	#10625350	1	1	yes	characteristic
117	C₈	#10625352	1	1	yes	characteristic
118	C₂²	—	8	1	no	—
119	C₂²	—	8	1	no	—
120	C₂²	—	8	1	no	—
121	C₂²	D₈×D₄₇	1	1	yes	characteristic
122	C₄	—	8	1	no	—
123	C₄	—	94	1	no	—
124	C₄	—	94	1	no	—
125	C₄	—	376	1	no	—
126	C₄	—	376	1	no	—
127	C₄	#13094010	1	1	yes	characteristic
128	C₄	SD₁₆×D₄₇	1	1	yes	characteristic
129	C₂	—	16	1	no	—
130	C₂	#15689468	1	1	yes	characteristic
131	C₂	#15689552	1	1	yes	characteristic
132	C₂	#15689554	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689524

C₂

yes

maximal, characteristic, complemented

#15689506

C₂

yes

maximal, characteristic

#15688928

C₂

yes

maximal, characteristic, complemented

#15688926

C₂

yes

maximal, characteristic, complemented

#15688924

C₂

yes

maximal, characteristic

C₁₆×Dic₄₇

C₂

yes

maximal, characteristic, complemented

C₄₇×#357

C₂

yes

maximal, characteristic

C₂×Dic₁₈₈

C₂²

yes

—

—

—

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

#13093958

C₂²

yes

characteristic

#13093955

—

C₈×Dic₄₇

C₂²

yes

characteristic

C₂×D₈×C₄₇

C₂²

yes

characteristic

C₂×C₁₆×C₄₇

C₂²

yes

characteristic

#107×C₄₇

C₂²

yes

characteristic

C₂×D₄×C₄₇

—

C₂×Dic₉₄

—

D₈×C₄₇

—

D₈×C₄₇

—

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄⋊C₄×C₄₇

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

#10625335

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

D₄

yes

characteristic

C₂×C₄₇⋊C₈

D₄

yes

characteristic

Dic₁₈₈

—

Dic₁₈₈

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

D₈

yes

characteristic

C₂×Dic₄₇

D₈

yes

characteristic

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

yes

C₈×C₄₇

yes

C₄₇⋊C₈

SD₁₆

yes

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

#124

yes

characteristic

C₄×C₄₇

C₂×SD₁₆

yes

characteristic

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

#2242

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

—

—

—

—

D₄₇

yes

characteristic

C₄×C₁₆

—

C₄₇

#2242

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×D₈

C₂×D₄₇

yes

characteristic

#125

—

#124

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₇

yes

characteristic

#107

—

#107

C₂×D₄₇

yes

characteristic

#106

—

C₄×C₈

—

C₂×Q₈

—

C₂×D₄

—

Q₁₆

—

Q₁₆

—

SD₁₆

—

188

—

D₈

—

D₈

—

C₂×C₈

—

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

188

—

C₄⋊C₄

—

188

—

C₂²⋊C₄

—

188

—

100

C₂²⋊C₄

—

188

—

101

C₄²

—

102

C₁₆

—

103

C₁₆

—

104

C₂³

—

105

Q₈

—

188

—

106

Q₈

—

188

—

107

D₄

—

108

D₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

188

—

113

C₂×C₄

—

188

—

114

C₂×C₄

D₄×D₄₇

yes

characteristic

115

C₈

—

116

C₈

#10625350

yes

characteristic

117

C₈

#10625352

yes

characteristic

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

D₈×D₄₇

yes

characteristic

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

—

376

—

126

C₄

—

376

—

127

C₄

#13094010

yes

characteristic

128

C₄

SD₁₆×D₄₇

yes

characteristic

129

C₂

—

130

C₂

#15689468

yes

characteristic

131

C₂

#15689552

yes

characteristic

132

C₂

#15689554

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₄₇
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#357	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	#357	D₄₇
hypocenter	C₄₇	#2242
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

subgroup

G/H

center

C₂²

D₈×D₄₇

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×#357

C₂

socle

C₂²×C₄₇

C₂×D₈

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

N	H ≅ G/N	type
1. #15689524	C₂	semidirect
3. #15688928	C₂	semidirect
4. #15688926	C₂	semidirect
6. C₁₆×Dic₄₇	C₂	semidirect
74. C₄₇	#2242	semidirect

H ≅ G/N

type

1. #15689524

C₂

semidirect

3. #15688928

C₂

semidirect

4. #15688926

C₂

semidirect

6. C₁₆×Dic₄₇

C₂

semidirect

74. C₄₇

#2242

semidirect

Subgroups — #20245618

Conjugacy classes of subgroups

Complements