Group #20252322 — subgroups

Subgroups — #20252322

Order 6016.

364 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 197 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	#15689680	C₂	1	1	yes	maximal, characteristic
2	#15689253	C₂	1	4	yes	maximal, complemented
3	C₈×Dic₉₄	C₂	1	4	yes	maximal, complemented
4	#15689149	C₂	1	2	yes	maximal
5	#15689147	C₂	1	1	yes	maximal, characteristic
6	#15689078	C₂	1	2	yes	maximal
7	C₂×C₄×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
8	C₂×#10625329	C₂²	1	2	yes	—
9	#13094024	C₄	1	2	yes	—
10	#13094016	C₄	1	2	yes	—
11	#13094003	C₄	1	4	yes	—
12	C₄×Dic₉₄	C₂²	1	4	yes	—
13	#13093983	C₂²	1	2	yes	—
14	C₄⋊(C₄₇⋊C₈)	C₂²	1	4	yes	—
15	Dic₄₇⋊C₈	C₂²	1	8	yes	—
16	#13093934	C₂²	1	4	yes	—
17	C₈×Dic₄₇	C₂²	1	4	yes	—
18	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
20	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
21	C₄×C₈×C₄₇	C₂²	1	2	yes	—
22	C₄×C₈×C₄₇	C₂²	1	2	yes	—
23	C₂²×C₄×C₄₇	C₂×C₄	1	2	yes	—
24	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
25	C₂×Dic₉₄	C₂×C₄	1	4	yes	—
26	C₂×C₈×C₄₇	—	2	2	no	—
27	C₂×C₈×C₄₇	Q₈	1	4	yes	complemented
28	C₂×C₈×C₄₇	C₂³	1	2	yes	—
29	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
30	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
31	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
32	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
33	C₄²×C₄₇	C₂³	1	2	yes	—
34	C₂²⋊Dic₄₇	C₂×C₄	1	4	yes	—
35	C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
36	C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
37	Dic₄₇⋊C₄	C₂×C₄	1	8	yes	—
38	C₄×Dic₄₇	C₂³	1	4	yes	—
39	#10625329	—	2	4	no	—
40	C₂×C₄₇⋊C₈	C₂³	1	4	yes	—
41	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₄×C₄₇	—	2	4	no	—
43	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
44	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
46	C₂×C₄×C₄₇	C₂×Q₈	1	2	yes	—
47	C₂×C₄×C₄₇	#41	1	2	yes	—
48	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
49	C₂×Dic₄₇	C₂²×C₄	1	8	yes	—
50	Dic₉₄	—	2	8	no	—
51	C₈×C₄₇	—	2	2	no	—
52	C₈×C₄₇	C₂×Q₈	1	2	yes	—
53	C₈×C₄₇	C₂×Q₈	1	2	yes	—
54	C₄₇⋊C₈	—	2	4	no	—
55	C₂²×C₄₇	—	2	2	no	—
56	C₂²×C₄₇	C₄×Q₈	1	2	yes	—
57	C₂²×C₄₇	C₂³×C₄	1	1	yes	characteristic
58	C₄×C₄₇	—	2	2	no	—
59	C₄×C₄₇	C₄×Q₈	1	2	yes	—
60	C₄×C₄₇	#131	1	4	yes	—
61	C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
62	C₄×C₄₇	C₂×#41	1	1	yes	characteristic
63	Dic₄₇	—	2	8	no	—
64	#2960	—	47	1	no	maximal, Sylow
65	C₂×C₄₇	—	2	2	no	—
66	C₂×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
67	C₂×C₄₇	C₂×#131	1	2	yes	—
68	#533	—	47	1	no	—
69	#446	—	47	4	no	—
70	C₈×Q₈	—	47	4	no	—
71	#424	—	47	2	no	—
72	#423	—	47	1	no	—
73	#405	—	47	2	no	—
74	C₂×C₄×C₈	D₄₇	1	1	yes	characteristic
75	C₄₇	#2960	1	1	yes	characteristic, complemented, Sylow
76	C₂×M₁₆	—	47	2	no	—
77	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
78	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
79	C₄⋊Q₈	—	47	2	no	—
80	#125	—	47	2	no	—
81	C₂²⋊Q₈	—	47	4	no	—
82	C₄×Q₈	—	47	4	no	—
83	#117	—	47	2	no	—
84	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
85	C₄⋊C₈	—	47	8	no	—
86	C₄⋊C₈	—	47	4	no	—
87	#97	—	47	4	no	—
88	C₄×C₈	—	47	4	no	—
89	C₄×C₈	C₂×D₄₇	1	2	yes	—
90	C₄×C₈	C₂×D₄₇	1	2	yes	—
91	C₂×Q₈	—	47	4	no	—
92	C₂²×C₄	C₄×D₄₇	1	2	yes	—
93	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
94	M₁₆	—	94	4	no	—
95	C₂×C₈	—	2	2	no	—
96	C₂×C₈	—	47	4	no	—
97	C₂×C₈	Dic₉₄	1	4	yes	complemented
98	C₂×C₈	C₂²×D₄₇	1	2	yes	—
99	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
100	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
101	C₄⋊C₄	—	47	8	no	—
102	C₄⋊C₄	—	47	4	no	—
103	C₄⋊C₄	—	47	4	no	—
104	C₂²⋊C₄	—	47	4	no	—
105	C₄²	—	47	4	no	—
106	C₄²	C₄×D₄₇	1	1	yes	characteristic
107	C₄²	C₄×D₄₇	1	1	yes	characteristic
108	C₄²	C₂²×D₄₇	1	2	yes	—
109	C₂³	C₂×C₄×D₄₇	1	1	yes	characteristic
110	Q₈	—	94	8	no	—
111	C₂×C₄	—	2	4	no	—
112	C₂×C₄	—	47	8	no	—
113	C₂×C₄	C₂×Dic₉₄	1	2	yes	—
114	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
115	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
116	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
117	C₂×C₄	#10625350	1	2	yes	—
118	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
119	C₈	—	2	2	no	—
120	C₈	—	94	4	no	—
121	C₈	C₂×Dic₉₄	1	2	yes	—
122	C₈	C₂×Dic₉₄	1	2	yes	—
123	C₂²	—	2	2	no	—
124	C₂²	C₄×Dic₉₄	1	2	yes	—
125	C₂²	C₂²×C₄×D₄₇	1	1	yes	characteristic
126	C₄	—	2	2	no	—
127	C₄	—	94	8	no	—
128	C₄	C₄×Dic₉₄	1	2	yes	—
129	C₄	#13094030	1	4	yes	—
130	C₄	C₂²×Dic₉₄	1	1	yes	characteristic
131	C₄	C₂×#10625350	1	1	yes	characteristic
132	C₂	—	2	2	no	—
133	C₂	C₂×C₄×Dic₉₄	1	1	yes	characteristic
134	C₂	C₂×#13094030	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#15689680

C₂

yes

maximal, characteristic

#15689253

C₂

yes

maximal, complemented

C₈×Dic₉₄

C₂

yes

maximal, complemented

#15689149

C₂

yes

maximal

#15689147

C₂

yes

maximal, characteristic

#15689078

C₂

yes

maximal

C₂×C₄×C₈×C₄₇

C₂

yes

maximal, characteristic

C₂×#10625329

C₂²

yes

—

#13094024

C₄

yes

—

#13094016

C₄

yes

—

#13094003

C₄

yes

—

C₄×Dic₉₄

C₂²

yes

—

#13093983

C₂²

yes

—

C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

Dic₄₇⋊C₈

C₂²

yes

—

#13093934

C₂²

yes

—

C₈×Dic₄₇

C₂²

yes

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₄×C₈×C₄₇

C₂²

yes

—

C₄×C₈×C₄₇

C₂²

yes

—

C₂²×C₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂×Dic₉₄

C₂×C₄

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

Q₈

yes

complemented

C₂×C₈×C₄₇

C₂³

yes

—

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄²×C₄₇

C₂×C₄

yes

characteristic

C₄²×C₄₇

C₂×C₄

yes

characteristic

C₄²×C₄₇

C₂³

yes

—

C₂²⋊Dic₄₇

C₂×C₄

yes

—

C₄⋊Dic₄₇

C₂×C₄

yes

—

C₄⋊Dic₄₇

C₂×C₄

yes

—

Dic₄₇⋊C₄

C₂×C₄

yes

—

C₄×Dic₄₇

C₂³

yes

—

#10625329

—

C₂×C₄₇⋊C₈

C₂³

yes

—

C₂³×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×C₄×C₄₇

C₂⁴

yes

characteristic

C₂×Dic₄₇

C₂²×C₄

yes

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

C₂×Q₈

yes

—

C₈×C₄₇

C₂×Q₈

yes

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

C₄×Q₈

yes

—

C₂²×C₄₇

C₂³×C₄

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

C₄×Q₈

yes

—

C₄×C₄₇

#131

yes

—

C₄×C₄₇

C₂²×Q₈

yes

characteristic

C₄×C₄₇

C₂×#41

yes

characteristic

Dic₄₇

—

#2960

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

C₂×C₄×Q₈

yes

characteristic

C₂×C₄₇

C₂×#131

yes

—

#533

—

#446

—

C₈×Q₈

—

#424

—

#423

—

#405

—

C₂×C₄×C₈

D₄₇

yes

characteristic

C₄₇

#2960

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

C₂×D₄₇

yes

characteristic

C₂²×C₈

C₂×D₄₇

yes

characteristic

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

C₂×D₄₇

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

#97

—

C₄×C₈

—

C₄×C₈

C₂×D₄₇

yes

—

C₄×C₈

C₂×D₄₇

yes

—

C₂×Q₈

—

C₂²×C₄

C₄×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₉₄

yes

complemented

C₂×C₈

C₂²×D₄₇

yes

—

C₂×C₈

C₂²×D₄₇

yes

characteristic

100

C₂×C₈

C₂²×D₄₇

yes

characteristic

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₂²⋊C₄

—

105

C₄²

—

106

C₄²

C₄×D₄₇

yes

characteristic

107

C₄²

C₄×D₄₇

yes

characteristic

108

C₄²

C₂²×D₄₇

yes

—

109

C₂³

C₂×C₄×D₄₇

yes

characteristic

110

Q₈

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

C₂×Dic₉₄

yes

—

114

C₂×C₄

C₂×C₄×D₄₇

yes

—

115

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

116

C₂×C₄

C₂×C₄×D₄₇

yes

—

117

C₂×C₄

#10625350

yes

—

118

C₂×C₄

C₂³×D₄₇

yes

characteristic

119

C₈

—

120

C₈

—

121

C₈

C₂×Dic₉₄

yes

—

122

C₈

C₂×Dic₉₄

yes

—

123

C₂²

—

124

C₂²

C₄×Dic₉₄

yes

—

125

C₂²

C₂²×C₄×D₄₇

yes

characteristic

126

C₄

—

127

C₄

—

128

C₄

C₄×Dic₉₄

yes

—

129

C₄

#13094030

yes

—

130

C₄

C₂²×Dic₉₄

yes

characteristic

131

C₄

C₂×#10625350

yes

characteristic

132

C₂

—

133

C₂

C₂×C₄×Dic₉₄

yes

characteristic

134

C₂

C₂×#13094030

yes

—

	subgroup	G/H
center	C₂×C₈	C₂²×D₄₇
commutator, socle	C₂²×C₄₇	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₂×C₄×C₈×C₄₇	C₂
hypercenter	C₂×C₄×C₈	D₄₇
hypocenter	C₄₇	#2960
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂×C₈

C₂²×D₄₇

commutator, socle

C₂²×C₄₇

C₂³×C₄

Frattini

C₂×C₄

C₂³×D₄₇

Fitting

C₂×C₄×C₈×C₄₇

C₂

hypercenter

C₂×C₄×C₈

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₄₇

C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈

N	H ≅ G/N	type
2. #15689253	C₂	semidirect
3. C₈×Dic₉₄	C₂	semidirect
27. C₂×C₈×C₄₇	Q₈	semidirect
75. C₄₇	#2960	semidirect
97. C₂×C₈	Dic₉₄	semidirect

H ≅ G/N

type

2. #15689253

C₂

semidirect

3. C₈×Dic₉₄

C₂

semidirect

27. C₂×C₈×C₄₇

Q₈

semidirect

75. C₄₇

#2960

semidirect

97. C₂×C₈

Dic₉₄

semidirect

Subgroups — #20252322

Conjugacy classes of subgroups

Complements