Group #20244806 — subgroups

Subgroups — #20244806

Order 6016.

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

normal subgroups only

This group has 222 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	C₂×#13093948	C₂	1	2	yes	maximal
2	#15688989	C₂	1	1	yes	maximal, characteristic
3	#15688885	C₂	1	2	yes	maximal
4	#15688878	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#391	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₇⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
8	#13093948	—	2	4	no	—
9	C₄₇⋊#95	—	2	2	no	—
10	C₂²×Q₈×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
12	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
13	#95×C₄₇	—	2	2	no	—
14	C₂×Q₈×C₄₇	—	2	1	no	—
15	C₂×Q₈×C₄₇	—	2	2	no	—
16	C₂×Q₈×C₄₇	—	2	2	no	—
17	C₂×Q₈×C₄₇	D₄	1	2	yes	—
18	C₂²×C₄×C₄₇	—	2	1	no	—
19	C₂²×C₄×C₄₇	—	2	1	no	—
20	C₂²×C₄×C₄₇	D₄	1	2	yes	—
21	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
22	C₂²×Dic₄₇	—	2	2	no	—
23	C₄⋊C₄×C₄₇	—	2	2	no	—
24	C₄²×C₄₇	—	2	2	no	—
25	C₄⋊Dic₄₇	—	2	2	no	—
26	C₄⋊Dic₄₇	—	2	2	no	—
27	C₂×C₄₇⋊C₈	—	2	2	no	—
28	C₂×C₄₇⋊C₈	—	2	2	no	—
29	C₂×C₄₇⋊C₈	—	2	2	no	—
30	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
31	Q₈×C₄₇	—	2	4	no	—
32	Q₈×C₄₇	—	4	2	no	—
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	—	2	2	no	—
37	C₂×C₄×C₄₇	—	4	1	no	—
38	C₂×C₄×C₄₇	—	4	1	no	—
39	C₂×C₄×C₄₇	—	4	1	no	—
40	C₂×C₄×C₄₇	—	4	2	no	—
41	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
43	C₂×C₄×C₄₇	#41	1	2	yes	—
44	C₂×C₄×C₄₇	#41	1	2	yes	—
45	C₂×Dic₄₇	—	4	2	no	—
46	C₂×Dic₄₇	—	4	2	no	—
47	C₂×Dic₄₇	—	4	2	no	—
48	C₄₇⋊C₈	—	4	2	no	—
49	C₂²×C₄₇	#121	1	1	yes	characteristic
50	C₂²×C₄₇	#123	1	1	yes	characteristic
51	C₂²×C₄₇	#124	1	1	yes	characteristic
52	C₂²×C₄₇	#135	1	2	yes	—
53	C₂²×C₄₇	#137	1	2	yes	—
54	C₄×C₄₇	—	4	2	no	—
55	C₄×C₄₇	—	4	2	no	—
56	C₄×C₄₇	—	8	1	no	—
57	C₄×C₄₇	#123	1	2	yes	—
58	C₄×C₄₇	#126	1	2	yes	—
59	Dic₄₇	—	8	2	no	—
60	#2074	—	47	1	no	maximal, Sylow
61	C₂×C₄₇	#397	1	1	yes	characteristic
62	C₂×C₄₇	#464	1	2	yes	—
63	C₂×C₄₇	#485	1	2	yes	—
64	C₂×C₄₇	#488	1	1	yes	characteristic
65	C₂×C₄₇	#491	1	1	yes	characteristic
66	C₂×#103	—	47	2	no	—
67	#391	D₄₇	1	1	yes	characteristic
68	#382	—	47	1	no	—
69	#340	—	47	2	no	—
70	#336	—	47	1	no	—
71	C₄₇	#2074	1	1	yes	characteristic, complemented, Sylow
72	C₂²×Q₈	C₂×D₄₇	1	1	yes	characteristic
73	C₂²×C₈	—	47	2	no	—
74	C₂×C₄⋊C₄	—	47	2	no	—
75	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
76	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
77	#103	—	94	4	no	—
78	#95	—	2	2	no	—
79	#95	—	94	2	no	—
80	C₂×Q₈	—	2	1	no	—
81	C₂×Q₈	—	2	2	no	—
82	C₂×Q₈	—	2	2	no	—
83	C₂×Q₈	D₁₈₈	1	2	yes	—
84	C₂²×C₄	—	2	1	no	—
85	C₂²×C₄	—	2	1	no	—
86	C₂²×C₄	—	94	2	no	—
87	C₂²×C₄	C₂²⋊D₄₇	1	2	yes	—
88	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
89	C₂×C₈	—	94	2	no	—
90	C₂×C₈	—	94	2	no	—
91	C₂×C₈	—	94	2	no	—
92	C₄⋊C₄	—	2	2	no	—
93	C₄⋊C₄	—	94	2	no	—
94	C₄⋊C₄	—	94	2	no	—
95	C₄²	—	2	2	no	—
96	C₂³	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
97	Q₈	—	2	4	no	—
98	Q₈	—	4	2	no	—
99	C₂×C₄	—	2	2	no	—
100	C₂×C₄	—	2	2	no	—
101	C₂×C₄	—	2	2	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	4	1	no	—
104	C₂×C₄	—	4	1	no	—
105	C₂×C₄	—	4	1	no	—
106	C₂×C₄	—	4	2	no	—
107	C₂×C₄	—	188	2	no	—
108	C₂×C₄	—	188	2	no	—
109	C₂×C₄	—	188	2	no	—
110	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
111	C₂×C₄	#10625350	1	1	yes	characteristic
112	C₂×C₄	#10625352	1	2	yes	—
113	C₂×C₄	#10625352	1	2	yes	—
114	C₈	—	188	2	no	—
115	C₂²	#13093998	1	1	yes	characteristic
116	C₂²	#13094005	1	1	yes	characteristic
117	C₂²	#13094011	1	1	yes	characteristic
118	C₂²	#13094044	1	2	yes	—
119	C₂²	#13094055	1	2	yes	—
120	C₄	—	4	2	no	—
121	C₄	—	4	2	no	—
122	C₄	—	8	1	no	—
123	C₄	—	376	2	no	—
124	C₄	#13094008	1	2	yes	—
125	C₄	#13094017	1	2	yes	—
126	C₂	#15689048	1	1	yes	characteristic
127	C₂	#15689345	1	2	yes	—
128	C₂	#15689461	1	2	yes	—
129	C₂	#15689477	1	1	yes	characteristic
130	C₂	#15689491	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093948

C₂

yes

maximal

#15688989

C₂

yes

maximal, characteristic

#15688885

C₂

yes

maximal

#15688878

C₂

yes

maximal, characteristic

C₄₇×#391

C₂

yes

maximal, characteristic

C₂²×C₄₇⋊C₈

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

#13093948

—

C₄₇⋊#95

—

C₂²×Q₈×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₇

C₂²

yes

characteristic

C₂×C₄²×C₄₇

C₂²

yes

characteristic

#95×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

—

C₂²×C₄₇

#137

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#123

yes

—

C₄×C₄₇

#126

yes

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₄₇

#485

yes

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

D₄₇

yes

—

—

—

C₄₇

#2074

yes

characteristic, complemented, Sylow

C₂²×Q₈

C₂×D₄₇

yes

characteristic

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₇

yes

characteristic

C₂×C₄²

C₂×D₄₇

yes

—

—

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

D₁₈₈

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₂³

C₂×C₂²⋊D₄₇

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

188

—

108

C₂×C₄

—

188

—

109

C₂×C₄

—

188

—

110

C₂×C₄

C₂×D₁₈₈

yes

characteristic

111

C₂×C₄

#10625350

yes

characteristic

112

C₂×C₄

#10625352

yes

—

113

C₂×C₄

#10625352

yes

—

114

C₈

—

188

—

115

C₂²

#13093998

yes

characteristic

116

C₂²

#13094005

yes

characteristic

117

C₂²

#13094011

yes

characteristic

118

C₂²

#13094044

yes

—

119

C₂²

#13094055

yes

—

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

—

376

—

124

C₄

#13094008

yes

—

125

C₄

#13094017

yes

—

126

C₂

#15689048

yes

characteristic

127

C₂

#15689345

yes

—

128

C₂

#15689461

yes

—

129

C₂

#15689477

yes

characteristic

130

C₂

#15689491

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₄₇
commutator	C₂²×C₄×C₄₇	C₂³
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×#391	C₂
socle	C₂³×C₄₇	C₂×D₄
hypercenter	#391	D₄₇
hypocenter	C₄₇	#2074
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #391

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₄₇

commutator

C₂²×C₄×C₄₇

C₂³

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₄₇×#391

C₂

socle

C₂³×C₄₇

C₂×D₄

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #391

N	H ≅ G/N	type
71. C₄₇	#2074	semidirect

H ≅ G/N

type

71. C₄₇

#2074

semidirect

Subgroups — #20244806

Conjugacy classes of subgroups

Complements