Group #20245939 — subgroups

Subgroups — C₄×#13094018 #20245939

Order 6016.

516 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 205 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×#13094018	C₂	1	1	yes	maximal, characteristic
2	#15689014	C₂	1	3	yes	maximal
3	#15689007	C₂	1	3	yes	maximal, complemented
4	#15688991	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×Dic₄₇⋊C₄	C₂	1	3	yes	maximal, complemented
6	C₄×(C₂×D₄₇)⋊C₄	C₂	1	3	yes	maximal
7	C₄³×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic
9	#13094018	C₄	1	8	yes	direct product factor
10	C₂×Dic₄₇⋊C₄	C₂²	1	3	yes	—
11	C₂×Dic₄₇⋊C₄	C₂²	1	3	yes	—
12	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	3	yes	—
13	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	3	yes	—
14	C₂×C₄×Dic₄₇	C₂²	1	3	yes	—
15	C₄₇⋊#95	C₂²	1	3	yes	—
16	C₄₇⋊#95	C₂²	1	3	yes	—
17	C₄₇⋊#95	C₂²	1	3	yes	—
18	C₄₇⋊#95	C₂²	1	3	yes	—
19	C₂×C₄²×C₄₇	C₂²	1	3	yes	—
20	C₂×C₄²×C₄₇	C₂²	1	3	yes	—
21	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
22	C₂³×D₄₇	C₂³	1	1	yes	characteristic
23	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
24	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
25	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
26	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
27	C₂²×Dic₄₇	C₂³	1	3	yes	—
28	C₂²×Dic₄₇	C₂³	1	3	yes	—
29	C₂×C₄×D₄₇	—	2	6	no	—
30	C₄²×C₄₇	—	2	6	no	—
31	C₄²×C₄₇	—	2	6	no	—
32	C₄²×C₄₇	C₂×C₄	1	4	yes	complemented
33	(C₂×D₄₇)⋊C₄	—	2	6	no	—
34	(C₂×D₄₇)⋊C₄	C₂×C₄	1	12	yes	—
35	Dic₄₇⋊C₄	—	2	6	no	—
36	Dic₄₇⋊C₄	C₂×C₄	1	12	yes	complemented
37	C₄×Dic₄₇	—	2	6	no	—
38	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
39	C₂²×D₄₇	—	2	3	no	—
40	C₂²×D₄₇	—	2	3	no	—
41	C₂²×D₄₇	C₂²×C₄	1	2	yes	—
42	C₂×C₄×C₄₇	—	2	3	no	—
43	C₂×C₄×C₄₇	—	2	3	no	—
44	C₂×C₄×C₄₇	—	2	3	no	—
45	C₂×C₄×C₄₇	—	2	3	no	—
46	C₂×C₄×C₄₇	C₂²×C₄	1	6	yes	—
47	C₂×C₄×C₄₇	#41	1	6	yes	—
48	C₂×C₄×C₄₇	#41	1	6	yes	—
49	C₂×Dic₄₇	—	2	3	no	—
50	C₂×Dic₄₇	—	2	3	no	—
51	C₂×Dic₄₇	—	2	3	no	—
52	C₂×Dic₄₇	—	2	3	no	—
53	C₂×Dic₄₇	—	2	3	no	—
54	C₂×Dic₄₇	—	2	3	no	—
55	C₂×Dic₄₇	C₂²×C₄	1	6	yes	—
56	C₄×D₄₇	—	4	4	no	—
57	C₂²×C₄₇	C₂³×C₄	1	1	yes	characteristic
58	C₂²×C₄₇	C₂×#41	1	3	yes	—
59	C₂²×C₄₇	C₂×#41	1	3	yes	—
60	C₂×D₄₇	—	2	6	no	—
61	C₂×D₄₇	—	4	1	no	—
62	C₂×D₄₇	—	4	3	no	—
63	C₄×C₄₇	—	2	6	no	—
64	C₄×C₄₇	—	2	6	no	—
65	C₄×C₄₇	#126	1	4	yes	complemented
66	Dic₄₇	—	2	6	no	—
67	Dic₄₇	—	4	1	no	—
68	Dic₄₇	—	4	3	no	—
69	C₄×#126	—	47	1	no	maximal, Sylow
70	C₂×C₄₇	C₄×#41	1	3	yes	—
71	C₂×C₄₇	C₂×#126	1	1	yes	characteristic
72	C₂×C₄₇	#529	1	3	yes	—
73	D₄₇	—	4	2	no	—
74	C₂×#126	—	47	1	no	—
75	#388	—	47	3	no	—
76	#387	—	47	3	no	—
77	#383	—	47	1	no	—
78	C₄×C₄⋊C₄	—	47	3	no	—
79	C₄×C₂²⋊C₄	—	47	3	no	—
80	C₄³	D₄₇	1	1	yes	characteristic, complemented
81	C₄₇	C₄×#126	1	1	yes	characteristic, complemented, Sylow
82	C₂³×C₄	—	47	1	no	—
83	#126	—	47	8	no	—
84	C₂×C₄⋊C₄	—	47	3	no	—
85	C₂×C₄⋊C₄	—	47	3	no	—
86	C₂×C₂²⋊C₄	—	47	3	no	—
87	C₂×C₂²⋊C₄	—	47	3	no	—
88	C₂×C₄²	—	47	3	no	—
89	C₂×C₄²	C₂×D₄₇	1	3	yes	—
90	C₂×C₄²	C₂×D₄₇	1	3	yes	—
91	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
92	#95	—	47	3	no	—
93	#95	—	47	3	no	—
94	#95	—	47	3	no	—
95	#95	—	47	3	no	—
96	C₂⁴	—	47	1	no	—
97	C₂²×C₄	—	47	3	no	—
98	C₂²×C₄	—	47	1	no	—
99	C₂²×C₄	—	47	3	no	—
100	C₂²×C₄	—	94	6	no	—
101	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
102	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
103	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
104	C₄⋊C₄	—	47	12	no	—
105	C₄⋊C₄	—	94	6	no	—
106	C₂²⋊C₄	—	47	12	no	—
107	C₂²⋊C₄	—	94	6	no	—
108	C₄²	—	2	6	no	—
109	C₄²	—	2	6	no	—
110	C₄²	—	94	6	no	—
111	C₄²	C₄×D₄₇	1	4	yes	complemented
112	C₂³	—	47	2	no	—
113	C₂³	—	94	3	no	—
114	C₂³	—	94	3	no	—
115	C₂³	C₂³×D₄₇	1	1	yes	characteristic
116	C₂×C₄	—	2	3	no	—
117	C₂×C₄	—	2	3	no	—
118	C₂×C₄	—	2	3	no	—
119	C₂×C₄	—	2	3	no	—
120	C₂×C₄	—	47	6	no	—
121	C₂×C₄	—	94	3	no	—
122	C₂×C₄	—	94	3	no	—
123	C₂×C₄	—	94	3	no	—
124	C₂×C₄	—	94	3	no	—
125	C₂×C₄	—	94	3	no	—
126	C₂×C₄	—	94	3	no	—
127	C₂×C₄	—	188	4	no	—
128	C₂×C₄	C₂×C₄×D₄₇	1	6	yes	—
129	C₂×C₄	#10625350	1	6	yes	—
130	C₂×C₄	#10625350	1	6	yes	—
131	C₂²	—	94	6	no	—
132	C₂²	—	188	1	no	—
133	C₂²	—	188	3	no	—
134	C₂²	C₂²×C₄×D₄₇	1	1	yes	characteristic
135	C₂²	C₂×#10625350	1	3	yes	—
136	C₂²	C₂×#10625350	1	3	yes	—
137	C₄	—	2	6	no	—
138	C₄	—	2	6	no	—
139	C₄	—	94	6	no	—
140	C₄	—	188	1	no	—
141	C₄	—	188	3	no	—
142	C₄	#13094018	1	4	yes	direct product factor
143	C₂	—	188	2	no	—
144	C₂	C₄×#10625350	1	3	yes	—
145	C₂	C₂×#13094018	1	1	yes	characteristic
146	C₂	#15689657	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13094018

C₂

yes

maximal, characteristic

#15689014

C₂

yes

maximal

#15689007

C₂

yes

maximal, complemented

#15688991

C₂

yes

maximal, characteristic, complemented

C₄×Dic₄₇⋊C₄

C₂

yes

maximal, complemented

C₄×(C₂×D₄₇)⋊C₄

C₂

yes

maximal

C₄³×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₄₇

C₂²

yes

characteristic

#13094018

C₄

yes

direct product factor

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₇)⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₇)⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂³×D₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂×C₄×D₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

C₂×C₄

yes

complemented

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

C₂×C₄

yes

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

C₂×C₄

yes

complemented

C₄×Dic₄₇

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂²×C₄

yes

—

C₄×D₄₇

—

C₂²×C₄₇

C₂³×C₄

yes

characteristic

C₂²×C₄₇

C₂×#41

yes

—

C₂²×C₄₇

C₂×#41

yes

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#126

yes

complemented

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

C₄×#126

—

maximal, Sylow

C₂×C₄₇

C₄×#41

yes

—

C₂×C₄₇

C₂×#126

yes

characteristic

C₂×C₄₇

#529

yes

—

D₄₇

—

—

—

—

—

C₄×C₄⋊C₄

—

C₄×C₂²⋊C₄

—

C₄³

D₄₇

yes

characteristic, complemented

C₄₇

C₄×#126

yes

characteristic, complemented, Sylow

C₂³×C₄

—

#126

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₇

yes

—

C₂×C₄²

C₂×D₄₇

yes

—

C₂×C₄²

C₂×D₄₇

yes

—

—

—

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

C₂²×D₄₇

yes

—

102

C₂²×C₄

C₂²×D₄₇

yes

—

103

C₂²×C₄

C₂²×D₄₇

yes

characteristic

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₂²⋊C₄

—

107

C₂²⋊C₄

—

108

C₄²

—

109

C₄²

—

110

C₄²

—

111

C₄²

C₄×D₄₇

yes

complemented

112

C₂³

—

113

C₂³

—

114

C₂³

—

115

C₂³

C₂³×D₄₇

yes

characteristic

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

188

—

128

C₂×C₄

C₂×C₄×D₄₇

yes

—

129

C₂×C₄

#10625350

yes

—

130

C₂×C₄

#10625350

yes

—

131

C₂²

—

132

C₂²

—

188

—

133

C₂²

—

188

—

134

C₂²

C₂²×C₄×D₄₇

yes

characteristic

135

C₂²

C₂×#10625350

yes

—

136

C₂²

C₂×#10625350

yes

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

—

188

—

141

C₄

—

188

—

142

C₄

#13094018

yes

direct product factor

143

C₂

—

188

—

144

C₂

C₄×#10625350

yes

—

145

C₂

C₂×#13094018

yes

characteristic

146

C₂

#15689657

yes

—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂³×C₄
Frattini	C₂³	C₂³×D₄₇
Fitting	C₄³×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁴
hypercenter	C₄³	D₄₇
hypocenter	C₄₇	C₄×#126
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³

subgroup

G/H

center

C₂²×C₄

C₂²×D₄₇

commutator

C₂²×C₄₇

C₂³×C₄

Frattini

C₂³

C₂³×D₄₇

Fitting

C₄³×C₄₇

C₂

socle

C₂³×C₄₇

C₂⁴

hypercenter

C₄³

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₄₇

C₁ ◁ C₂²×C₄ ◁ C₄³

N	H ≅ G/N	type
3. #15689007	C₂	semidirect
4. #15688991	C₂	semidirect
5. C₄×Dic₄₇⋊C₄	C₂	semidirect
7. C₄³×C₄₇	C₂	semidirect
9. #13094018	C₄	direct (N × H)
32. C₄²×C₄₇	C₂×C₄	semidirect
36. Dic₄₇⋊C₄	C₂×C₄	semidirect
65. C₄×C₄₇	#126	semidirect
80. C₄³	D₄₇	semidirect
81. C₄₇	C₄×#126	semidirect
111. C₄²	C₄×D₄₇	semidirect
142. C₄	#13094018	direct (N × H)

H ≅ G/N

type

3. #15689007

C₂

semidirect

4. #15688991

C₂

semidirect

5. C₄×Dic₄₇⋊C₄

C₂

semidirect

7. C₄³×C₄₇

C₂

semidirect

9. #13094018

C₄

direct (N × H)

32. C₄²×C₄₇

C₂×C₄

semidirect

36. Dic₄₇⋊C₄

C₂×C₄

semidirect

65. C₄×C₄₇

#126

semidirect

80. C₄³

D₄₇

semidirect

81. C₄₇

C₄×#126

semidirect

111. C₄²

C₄×D₄₇

semidirect

142. C₄

#13094018

direct (N × H)

Subgroups — C₄×#13094018 #20245939

Conjugacy classes of subgroups

Complements

Subgroups — C4×#13094018 #20245939

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#13094018 #20245939