Group #20244540 — subgroups

Subgroups — #20244540

Order 6016.

258 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 83 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×#13094016	C₂	1	1	yes	maximal, characteristic
2	C₂×#13093949	C₂	1	2	yes	maximal
3	#15689029	C₂	1	1	yes	maximal, characteristic
4	#15688886	C₂	1	2	yes	maximal
5	C₄₇×#336	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic
7	#13094016	—	2	4	no	—
8	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
10	C₂×Dic₄₇⋊C₄	—	2	2	no	—
11	#13093949	—	2	4	no	—
12	C₄₇⋊#95	—	2	2	no	—
13	C₂²×C₈×C₄₇	C₂²	1	2	yes	—
14	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₄₇	D₄	1	2	yes	—
16	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
17	C₂²×Dic₄₇	—	2	1	no	—
18	C₂²×Dic₄₇	—	2	2	no	—
19	C₂²×Dic₄₇	—	2	1	no	—
20	C₂×Dic₉₄	—	2	2	no	—
21	C₂×Dic₉₄	—	2	2	no	—
22	C₂×Dic₉₄	—	2	1	no	—
23	C₂×Dic₉₄	Q₈	1	2	yes	—
24	C₂×C₈×C₄₇	—	2	2	no	—
25	C₂×C₈×C₄₇	—	2	2	no	—
26	C₂×C₈×C₄₇	—	2	2	no	—
27	C₄²×C₄₇	—	2	2	no	—
28	C₄⋊Dic₄₇	—	2	2	no	—
29	C₄⋊Dic₄₇	—	2	2	no	—
30	C₄⋊Dic₄₇	D₄	1	4	yes	—
31	Dic₄₇⋊C₄	—	2	8	no	—
32	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₄₇	—	2	2	no	—
34	C₂×C₄×C₄₇	—	2	2	no	—
35	C₂×C₄×C₄₇	—	2	2	no	—
36	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
37	C₂×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
38	C₂×C₄×C₄₇	#41	1	2	yes	—
39	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
40	C₂×Dic₄₇	—	2	4	no	—
41	C₂×Dic₄₇	—	2	2	no	—
42	C₂×Dic₄₇	—	4	1	no	—
43	C₂×Dic₄₇	—	4	1	no	—
44	C₂×Dic₄₇	—	4	2	no	—
45	C₂×Dic₄₇	—	4	2	no	—
46	C₂×Dic₄₇	—	4	1	no	—
47	C₂×Dic₄₇	—	4	2	no	—
48	Dic₉₄	—	2	4	no	—
49	Dic₉₄	—	4	2	no	—
50	C₈×C₄₇	—	4	2	no	—
51	C₂²×C₄₇	#120	1	1	yes	characteristic
52	C₂²×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
53	C₂²×C₄₇	#124	1	1	yes	characteristic
54	C₂²×C₄₇	#135	1	2	yes	—
55	C₂²×C₄₇	#137	1	2	yes	—
56	C₄×C₄₇	—	4	2	no	—
57	C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
58	C₄×C₄₇	#124	1	2	yes	—
59	Dic₄₇	—	4	2	no	—
60	Dic₄₇	—	4	4	no	—
61	Dic₄₇	—	8	1	no	—
62	#2026	—	47	1	no	maximal, Sylow
63	C₂×C₄₇	#393	1	1	yes	characteristic
64	C₂×C₄₇	#452	1	2	yes	—
65	C₂×C₄₇	#479	1	2	yes	—
66	C₂×C₄₇	#488	1	1	yes	characteristic
67	C₂×C₄₇	#491	1	1	yes	characteristic
68	C₂×#125	—	47	1	no	—
69	C₂×#103	—	47	2	no	—
70	#391	—	47	1	no	—
71	#340	—	47	2	no	—
72	#336	D₄₇	1	1	yes	characteristic
73	C₄₇	#2026	1	1	yes	characteristic, complemented, Sylow
74	C₂²×Q₈	—	47	1	no	—
75	C₂²×C₈	C₂×D₄₇	1	2	yes	—
76	#125	—	94	4	no	—
77	C₂×C₄⋊C₄	—	47	2	no	—
78	C₂×C₄⋊C₄	—	47	1	no	—
79	C₂×C₄⋊C₄	—	94	2	no	—
80	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
81	#103	—	94	4	no	—
82	#95	—	94	2	no	—
83	C₂×Q₈	—	47	2	no	—
84	C₂×Q₈	—	94	1	no	—
85	C₂×Q₈	—	94	2	no	—
86	C₂×Q₈	—	94	2	no	—
87	C₂²×C₄	—	94	1	no	—
88	C₂²×C₄	—	94	2	no	—
89	C₂²×C₄	—	94	1	no	—
90	C₂²×C₄	D₁₈₈	1	2	yes	—
91	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
92	C₂×C₈	—	2	2	no	—
93	C₂×C₈	—	2	2	no	—
94	C₂×C₈	—	2	2	no	—
95	C₄⋊C₄	—	47	4	no	—
96	C₄⋊C₄	—	94	8	no	—
97	C₄⋊C₄	—	94	2	no	—
98	C₄⋊C₄	—	94	2	no	—
99	C₄²	—	2	2	no	—
100	C₂³	C₂×D₁₈₈	1	1	yes	characteristic
101	Q₈	—	94	4	no	—
102	Q₈	—	188	2	no	—
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	2	2	no	—
106	C₂×C₄	—	94	4	no	—
107	C₂×C₄	—	94	2	no	—
108	C₂×C₄	—	188	1	no	—
109	C₂×C₄	—	188	2	no	—
110	C₂×C₄	—	188	1	no	—
111	C₂×C₄	—	188	1	no	—
112	C₂×C₄	—	188	2	no	—
113	C₂×C₄	—	188	2	no	—
114	C₂×C₄	#10625350	1	2	yes	—
115	C₂×C₄	D₄×D₄₇	1	2	yes	—
116	C₂×C₄	#10625352	1	1	yes	characteristic
117	C₂×C₄	Q₈×D₄₇	1	1	yes	characteristic
118	C₈	—	4	2	no	—
119	C₂²	#13093994	1	1	yes	characteristic
120	C₂²	#13094004	1	1	yes	characteristic
121	C₂²	#13094012	1	1	yes	characteristic
122	C₂²	#13094046	1	2	yes	—
123	C₂²	#13094057	1	2	yes	—
124	C₄	—	4	2	no	—
125	C₄	—	376	1	no	—
126	C₄	—	188	4	no	—
127	C₄	—	188	2	no	—
128	C₄	#13094002	1	2	yes	—
129	C₄	#13094010	1	2	yes	—
130	C₂	#15689036	1	1	yes	characteristic
131	C₂	#15689287	1	2	yes	—
132	C₂	#15689431	1	2	yes	—
133	C₂	#15689478	1	1	yes	characteristic
134	C₂	#15689492	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13094016

C₂

yes

maximal, characteristic

C₂×#13093949

C₂

yes

maximal

#15689029

C₂

yes

maximal, characteristic

#15688886

C₂

yes

maximal

C₄₇×#336

C₂

yes

maximal, characteristic

C₂²×Dic₉₄

C₂²

yes

characteristic

#13094016

—

C₂×C₄⋊Dic₄₇

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

—

#13093949

—

C₄₇⋊#95

—

C₂²×C₈×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

Q₈

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄²×C₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

D₄

yes

—

Dic₄₇⋊C₄

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₇

#41

yes

—

C₂×C₄×C₄₇

#41

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₂²×C₄₇

#120

yes

characteristic

C₂²×C₄₇

C₂²⋊Q₈

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

—

C₂²×C₄₇

#137

yes

—

C₄×C₄₇

—

C₄×C₄₇

C₂²⋊Q₈

yes

—

C₄×C₄₇

#124

yes

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₄₇

#479

yes

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

—

—

—

D₄₇

yes

characteristic

C₄₇

#2026

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×C₈

C₂×D₄₇

yes

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₄₇

yes

characteristic

#103

—

#95

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₁₈₈

yes

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

100

C₂³

C₂×D₁₈₈

yes

characteristic

101

Q₈

—

102

Q₈

—

188

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

188

—

109

C₂×C₄

—

188

—

110

C₂×C₄

—

188

—

111

C₂×C₄

—

188

—

112

C₂×C₄

—

188

—

113

C₂×C₄

—

188

—

114

C₂×C₄

#10625350

yes

—

115

C₂×C₄

D₄×D₄₇

yes

—

116

C₂×C₄

#10625352

yes

characteristic

117

C₂×C₄

Q₈×D₄₇

yes

characteristic

118

C₈

—

119

C₂²

#13093994

yes

characteristic

120

C₂²

#13094004

yes

characteristic

121

C₂²

#13094012

yes

characteristic

122

C₂²

#13094046

yes

—

123

C₂²

#13094057

yes

—

124

C₄

—

125

C₄

—

376

—

126

C₄

—

188

—

127

C₄

—

188

—

128

C₄

#13094002

yes

—

129

C₄

#13094010

yes

—

130

C₂

#15689036

yes

characteristic

131

C₂

#15689287

yes

—

132

C₂

#15689431

yes

—

133

C₂

#15689478

yes

characteristic

134

C₂

#15689492

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₁₈₈
commutator	C₂²×C₄×C₄₇	C₂³
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×#336	C₂
socle	C₂³×C₄₇	C₂×D₄
hypercenter	#336	D₄₇
hypocenter	C₄₇	#2026
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

subgroup

G/H

center

C₂³

C₂×D₁₈₈

commutator

C₂²×C₄×C₄₇

C₂³

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₄₇×#336

C₂

socle

C₂³×C₄₇

C₂×D₄

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

N	H ≅ G/N	type
73. C₄₇	#2026	semidirect

H ≅ G/N

type

73. C₄₇

#2026

semidirect

Subgroups — #20244540

Conjugacy classes of subgroups

Complements