Group #20241653 — subgroups

Subgroups — #20241653

Order 6016.

608 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 229 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×C₄⋊Dic₄₇	C₂	1	3	yes	maximal
2	C₂×C₄₇⋊#95	C₂	1	3	yes	maximal
3	C₂×#95×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂³×Dic₄₇	C₂²	1	3	yes	—
5	C₂³×Dic₄₇	C₂²	1	1	yes	characteristic
6	C₂×C₄⋊Dic₄₇	—	2	6	no	—
7	C₂×C₄⋊Dic₄₇	—	2	12	no	—
8	C₄₇⋊#95	—	2	6	no	—
9	C₂³×C₄×C₄₇	C₂²	1	3	yes	—
10	#95×C₄₇	C₄	1	4	yes	complemented
11	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
12	C₂²×C₄×C₄₇	—	2	6	no	—
13	C₂²×C₄×C₄₇	—	2	6	no	—
14	C₂²×C₄×C₄₇	C₂×C₄	1	6	yes	—
15	C₂²×C₄×C₄₇	D₄	1	6	yes	—
16	C₂²×C₄×C₄₇	Q₈	1	6	yes	—
17	C₂²×Dic₄₇	—	2	3	no	—
18	C₂²×Dic₄₇	—	2	3	no	—
19	C₂²×Dic₄₇	—	2	6	no	—
20	C₂²×Dic₄₇	—	2	6	no	—
21	C₂²×Dic₄₇	—	2	3	no	—
22	C₂²×Dic₄₇	—	2	3	no	—
23	C₂²×Dic₄₇	D₄	1	6	yes	—
24	C₂²×Dic₄₇	Q₈	1	2	yes	—
25	C₄⋊Dic₄₇	—	2	24	no	—
26	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
27	C₂³×C₄₇	C₂×D₄	1	3	yes	—
28	C₂³×C₄₇	C₂×D₄	1	3	yes	—
29	C₂³×C₄₇	C₂×Q₈	1	3	yes	—
30	C₂³×C₄₇	C₂×Q₈	1	1	yes	characteristic
31	C₂³×C₄₇	#41	1	3	yes	—
32	C₂³×C₄₇	#41	1	1	yes	characteristic
33	C₂×C₄×C₄₇	—	2	12	no	—
34	C₂×C₄×C₄₇	—	2	6	no	—
35	C₂×C₄×C₄₇	—	2	12	no	—
36	C₂×C₄×C₄₇	—	2	6	no	—
37	C₂×C₄×C₄₇	C₄⋊C₄	1	12	yes	complemented
38	C₂×Dic₄₇	—	2	12	no	—
39	C₂×Dic₄₇	—	2	6	no	—
40	C₂×Dic₄₇	—	2	6	no	—
41	C₂×Dic₄₇	—	4	3	no	—
42	C₂×Dic₄₇	—	4	6	no	—
43	C₂×Dic₄₇	—	4	3	no	—
44	C₂×Dic₄₇	—	4	3	no	—
45	C₂×Dic₄₇	—	4	1	no	—
46	C₂²×C₄₇	C₂×C₄⋊C₄	1	3	yes	—
47	C₂²×C₄₇	C₄×D₄	1	3	yes	—
48	C₂²×C₄₇	C₄×Q₈	1	1	yes	characteristic
49	C₂²×C₄₇	#120	1	3	yes	—
50	C₂²×C₄₇	#121	1	3	yes	—
51	C₂²×C₄₇	C₂²⋊Q₈	1	6	yes	—
52	C₂²×C₄₇	C₂²⋊Q₈	1	3	yes	—
53	C₂²×C₄₇	#123	1	3	yes	—
54	C₂²×C₄₇	#125	1	3	yes	—
55	C₂²×C₄₇	#127	1	1	yes	characteristic
56	C₂²×C₄₇	C₄⋊Q₈	1	3	yes	—
57	C₂²×C₄₇	C₄⋊Q₈	1	3	yes	—
58	C₄×C₄₇	—	2	12	no	—
59	Dic₄₇	—	4	6	no	—
60	Dic₄₇	—	4	2	no	—
61	#1444	—	47	1	no	maximal, Sylow
62	C₂×C₄₇	#384	1	1	yes	characteristic
63	C₂×C₄₇	#385	1	3	yes	—
64	C₂×C₄₇	#389	1	3	yes	—
65	C₂×C₄₇	#392	1	1	yes	characteristic
66	C₂×C₄₇	#395	1	3	yes	—
67	C₂×C₄₇	#398	1	3	yes	—
68	C₂×C₄₇	#399	1	1	yes	characteristic
69	C₂²×C₄⋊C₄	—	47	3	no	—
70	C₂×#95	—	47	3	no	—
71	C₂×#95	D₄₇	1	1	yes	characteristic
72	C₄₇	#1444	1	1	yes	characteristic, complemented, Sylow
73	C₂³×C₄	—	47	3	no	—
74	C₂³×C₄	—	47	1	no	—
75	C₂³×C₄	C₂×D₄₇	1	3	yes	—
76	C₂×C₄⋊C₄	—	94	12	no	—
77	C₂×C₄⋊C₄	—	94	6	no	—
78	#95	—	94	6	no	—
79	#95	Dic₄₇	1	4	yes	complemented
80	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
81	C₂²×C₄	—	2	6	no	—
82	C₂²×C₄	—	2	6	no	—
83	C₂²×C₄	—	47	6	no	—
84	C₂²×C₄	—	47	2	no	—
85	C₂²×C₄	—	94	3	no	—
86	C₂²×C₄	—	94	3	no	—
87	C₂²×C₄	—	94	6	no	—
88	C₂²×C₄	—	94	6	no	—
89	C₂²×C₄	—	94	3	no	—
90	C₂²×C₄	—	94	3	no	—
91	C₂²×C₄	Dic₉₄	1	6	yes	—
92	C₂²×C₄	D₁₈₈	1	6	yes	—
93	C₂²×C₄	C₂×Dic₄₇	1	6	yes	—
94	C₄⋊C₄	—	94	24	no	—
95	C₂³	C₂×Dic₉₄	1	3	yes	—
96	C₂³	C₂×D₁₈₈	1	3	yes	—
97	C₂³	D₄×D₄₇	1	3	yes	—
98	C₂³	#10625352	1	3	yes	—
99	C₂³	Q₈×D₄₇	1	1	yes	characteristic
100	C₂³	#10625354	1	1	yes	characteristic
101	C₂³	C₂²×Dic₄₇	1	1	yes	characteristic
102	C₂×C₄	—	2	12	no	—
103	C₂×C₄	—	2	6	no	—
104	C₂×C₄	—	2	12	no	—
105	C₂×C₄	—	2	6	no	—
106	C₂×C₄	—	94	12	no	—
107	C₂×C₄	—	94	6	no	—
108	C₂×C₄	—	94	6	no	—
109	C₂×C₄	—	188	3	no	—
110	C₂×C₄	—	188	6	no	—
111	C₂×C₄	—	188	3	no	—
112	C₂×C₄	—	188	3	no	—
113	C₂×C₄	—	188	1	no	—
114	C₂×C₄	C₄⋊Dic₄₇	1	12	yes	complemented
115	C₂²	C₂×C₄⋊Dic₄₇	1	3	yes	—
116	C₂²	D₄×Dic₄₇	1	3	yes	—
117	C₂²	Q₈×Dic₄₇	1	1	yes	characteristic
118	C₂²	#13093994	1	3	yes	—
119	C₂²	#13093999	1	3	yes	—
120	C₂²	#13094001	1	6	yes	—
121	C₂²	#13094004	1	3	yes	—
122	C₂²	#13094008	1	3	yes	—
123	C₂²	#13094015	1	3	yes	—
124	C₂²	#13094021	1	1	yes	characteristic
125	C₂²	#13094023	1	3	yes	—
126	C₂²	#13094024	1	3	yes	—
127	C₄	—	2	12	no	—
128	C₄	—	188	6	no	—
129	C₄	—	188	2	no	—
130	C₂	#15688993	1	1	yes	characteristic
131	C₂	#15688998	1	3	yes	—
132	C₂	#15689022	1	3	yes	—
133	C₂	#15689033	1	1	yes	characteristic
134	C₂	#15689044	1	3	yes	—
135	C₂	#15689055	1	3	yes	—
136	C₂	#15689060	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₄⋊Dic₄₇

C₂

yes

maximal

C₂×C₄₇⋊#95

C₂

yes

maximal

C₂×#95×C₄₇

C₂

yes

maximal, characteristic

C₂³×Dic₄₇

C₂²

yes

—

C₂³×Dic₄₇

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₄₇⋊#95

—

C₂³×C₄×C₄₇

C₂²

yes

—

#95×C₄₇

C₄

yes

complemented

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

Q₈

yes

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

D₄

yes

—

C₂²×Dic₄₇

Q₈

yes

—

C₄⋊Dic₄₇

—

C₂³×C₄₇

C₂²×C₄

yes

characteristic

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

C₂×Q₈

yes

—

C₂³×C₄₇

C₂×Q₈

yes

characteristic

C₂³×C₄₇

#41

yes

—

C₂³×C₄₇

#41

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₄⋊C₄

yes

complemented

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂²×C₄₇

C₂×C₄⋊C₄

yes

—

C₂²×C₄₇

C₄×D₄

yes

—

C₂²×C₄₇

C₄×Q₈

yes

characteristic

C₂²×C₄₇

#120

yes

—

C₂²×C₄₇

#121

yes

—

C₂²×C₄₇

C₂²⋊Q₈

yes

—

C₂²×C₄₇

C₂²⋊Q₈

yes

—

C₂²×C₄₇

#123

yes

—

C₂²×C₄₇

#125

yes

—

C₂²×C₄₇

#127

yes

characteristic

C₂²×C₄₇

C₄⋊Q₈

yes

—

C₂²×C₄₇

C₄⋊Q₈

yes

—

C₄×C₄₇

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₄₇

#389

yes

—

C₂×C₄₇

#392

yes

characteristic

C₂×C₄₇

#395

yes

—

C₂×C₄₇

#398

yes

—

C₂×C₄₇

#399

yes

characteristic

C₂²×C₄⋊C₄

—

C₂×#95

—

C₂×#95

D₄₇

yes

characteristic

C₄₇

#1444

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

C₂×D₄₇

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

#95

—

#95

Dic₄₇

yes

complemented

C₂⁴

C₂²×D₄₇

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

Dic₉₄

yes

—

C₂²×C₄

D₁₈₈

yes

—

C₂²×C₄

C₂×Dic₄₇

yes

—

C₄⋊C₄

—

C₂³

C₂×Dic₉₄

yes

—

C₂³

C₂×D₁₈₈

yes

—

C₂³

D₄×D₄₇

yes

—

C₂³

#10625352

yes

—

C₂³

Q₈×D₄₇

yes

characteristic

100

C₂³

#10625354

yes

characteristic

101

C₂³

C₂²×Dic₄₇

yes

characteristic

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

188

—

110

C₂×C₄

—

188

—

111

C₂×C₄

—

188

—

112

C₂×C₄

—

188

—

113

C₂×C₄

—

188

—

114

C₂×C₄

C₄⋊Dic₄₇

yes

complemented

115

C₂²

C₂×C₄⋊Dic₄₇

yes

—

116

C₂²

D₄×Dic₄₇

yes

—

117

C₂²

Q₈×Dic₄₇

yes

characteristic

118

C₂²

#13093994

yes

—

119

C₂²

#13093999

yes

—

120

C₂²

#13094001

yes

—

121

C₂²

#13094004

yes

—

122

C₂²

#13094008

yes

—

123

C₂²

#13094015

yes

—

124

C₂²

#13094021

yes

characteristic

125

C₂²

#13094023

yes

—

126

C₂²

#13094024

yes

—

127

C₄

—

128

C₄

—

188

—

129

C₄

—

188

—

130

C₂

#15688993

yes

characteristic

131

C₂

#15688998

yes

—

132

C₂

#15689022

yes

—

133

C₂

#15689033

yes

characteristic

134

C₂

#15689044

yes

—

135

C₂

#15689055

yes

—

136

C₂

#15689060

yes

characteristic

	subgroup	G/H
center, Frattini	C₂⁴	C₂²×D₄₇
commutator	C₂³×C₄₇	C₂²×C₄
Fitting	C₂×#95×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂³
hypercenter	C₂×#95	D₄₇
hypocenter	C₄₇	#1444
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂×#95

subgroup

G/H

center, Frattini

C₂⁴

C₂²×D₄₇

commutator

C₂³×C₄₇

C₂²×C₄

Fitting

C₂×#95×C₄₇

C₂

socle

C₂⁴×C₄₇

C₂³

hypercenter

C₂×#95

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂⁴ ◁ C₂×#95

N	H ≅ G/N	type
10. #95×C₄₇	C₄	semidirect
37. C₂×C₄×C₄₇	C₄⋊C₄	semidirect
72. C₄₇	#1444	semidirect
79. #95	Dic₄₇	semidirect
114. C₂×C₄	C₄⋊Dic₄₇	semidirect

H ≅ G/N

type

10. #95×C₄₇

C₄

semidirect

37. C₂×C₄×C₄₇

C₄⋊C₄

semidirect

72. C₄₇

#1444

semidirect

79. #95

Dic₄₇

semidirect

114. C₂×C₄

C₄⋊Dic₄₇

semidirect

Subgroups — #20241653

Conjugacy classes of subgroups

Complements