Group #20243282 — subgroups

Subgroups — C₄×#13093957 #20243282

Order 6016.

280 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 145 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×#13093957	C₂	1	2	yes	maximal
2	C₂×C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
4	#15688885	C₂	1	2	yes	maximal
5	C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
7	C₂²×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
9	C₂×C₄×Dic₄₇	—	2	1	no	—
10	#13093957	C₄	1	8	yes	direct product factor
11	C₄×C₄₇⋊C₈	C₄	1	4	yes	complemented
12	C₄₇⋊#95	—	2	1	no	—
13	C₂×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
14	C₂×C₄²×C₄₇	—	2	1	no	—
15	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
16	#95×C₄₇	—	2	1	no	—
17	C₂²×C₄×C₄₇	—	2	2	no	—
18	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
19	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
20	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
21	C₂²×Dic₄₇	—	2	2	no	—
22	C₄⋊C₄×C₄₇	—	2	2	no	—
23	C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
24	C₄²×C₄₇	—	4	2	no	—
25	C₄²×C₄₇	C₂×C₄	1	2	yes	—
26	C₄²×C₄₇	Q₈	1	2	yes	—
27	C₄⋊Dic₄₇	—	2	2	no	—
28	C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
29	C₄×Dic₄₇	—	4	2	no	—
30	C₂×C₄₇⋊C₈	—	2	2	no	—
31	C₂×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
32	C₂×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
33	C₂×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
34	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₄₇	—	2	2	no	—
36	C₂×C₄×C₄₇	—	2	4	no	—
37	C₂×C₄×C₄₇	—	4	2	no	—
38	C₂×C₄×C₄₇	—	4	2	no	—
39	C₂×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
40	C₂×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
41	C₂×C₄×C₄₇	D₈	1	2	yes	—
42	C₂×C₄×C₄₇	Q₁₆	1	2	yes	—
43	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
45	C₂×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
46	C₂×C₄×C₄₇	#41	1	2	yes	—
47	C₂×Dic₄₇	—	2	4	no	—
48	C₂×Dic₄₇	—	4	2	no	—
49	C₂×Dic₄₇	—	4	2	no	—
50	C₄₇⋊C₈	—	2	2	no	—
51	C₄₇⋊C₈	C₄²	1	4	yes	complemented
52	C₂²×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₂²×C₄₇	C₄×D₄	1	2	yes	—
54	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
55	C₂²×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
56	C₂²×C₄₇	#135	1	2	yes	—
57	C₄×C₄₇	—	2	2	no	—
58	C₄×C₄₇	—	4	4	no	—
59	C₄×C₄₇	#107	1	4	yes	complemented
60	C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
61	C₄×C₄₇	#117	1	1	yes	characteristic
62	C₄×C₄₇	C₄×Q₈	1	2	yes	—
63	Dic₄₇	—	4	4	no	—
64	C₄×#107	—	47	1	no	maximal, Sylow
65	C₂×C₄₇	C₄×C₄⋊C₄	1	1	yes	characteristic
66	C₂×C₄₇	C₂×#107	1	1	yes	characteristic
67	C₂×C₄₇	#427	1	1	yes	characteristic
68	C₂×C₄₇	C₄×D₈	1	2	yes	—
69	C₂×C₄₇	C₄×Q₁₆	1	2	yes	—
70	C₂×#107	—	47	2	no	—
71	C₂×C₄×C₈	—	47	1	no	—
72	C₄×C₄⋊C₄	—	47	1	no	—
73	C₄×C₄⋊C₄	D₄₇	1	1	yes	characteristic
74	#340	—	47	2	no	—
75	C₄₇	C₄×#107	1	1	yes	characteristic, complemented, Sylow
76	C₂²×C₈	—	47	1	no	—
77	C₂²×C₈	—	47	1	no	—
78	C₂×C₄⋊C₄	—	47	2	no	—
79	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
80	C₂×C₄²	—	2	1	no	—
81	C₂×C₄²	—	94	1	no	—
82	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
83	#107	—	47	8	no	—
84	C₄×C₈	—	47	4	no	—
85	#95	—	2	1	no	—
86	#95	—	94	1	no	—
87	C₂²×C₄	—	2	2	no	—
88	C₂²×C₄	—	94	2	no	—
89	C₂²×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
90	C₂²×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
91	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
92	C₂×C₈	—	47	2	no	—
93	C₂×C₈	—	47	4	no	—
94	C₂×C₈	—	47	2	no	—
95	C₂×C₈	—	94	2	no	—
96	C₄⋊C₄	—	2	2	no	—
97	C₄⋊C₄	—	47	4	no	—
98	C₄⋊C₄	—	94	2	no	—
99	C₄⋊C₄	C₄×D₄₇	1	4	yes	—
100	C₄²	—	4	2	no	—
101	C₄²	—	188	2	no	—
102	C₄²	Dic₉₄	1	2	yes	—
103	C₄²	C₄×D₄₇	1	2	yes	—
104	C₂³	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
105	C₂×C₄	—	2	2	no	—
106	C₂×C₄	—	2	4	no	—
107	C₂×C₄	—	4	2	no	—
108	C₂×C₄	—	4	2	no	—
109	C₂×C₄	—	94	4	no	—
110	C₂×C₄	—	188	2	no	—
111	C₂×C₄	—	188	2	no	—
112	C₂×C₄	Dic₄₇⋊C₄	1	2	yes	—
113	C₂×C₄	Dic₄₇⋊C₄	1	2	yes	—
114	C₂×C₄	#10625334	1	2	yes	—
115	C₂×C₄	#10625337	1	2	yes	—
116	C₂×C₄	C₂×Dic₉₄	1	1	yes	characteristic
117	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
118	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
119	C₂×C₄	#10625350	1	2	yes	—
120	C₈	—	47	4	no	—
121	C₈	—	94	2	no	—
122	C₂²	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
123	C₂²	C₄×C₂²⋊D₄₇	1	2	yes	—
124	C₂²	C₂×#10625334	1	1	yes	characteristic
125	C₂²	C₂×#10625337	1	1	yes	characteristic
126	C₂²	#13094044	1	2	yes	—
127	C₄	—	2	2	no	—
128	C₄	—	4	4	no	—
129	C₄	—	188	4	no	—
130	C₄	#13093957	1	4	yes	direct product factor
131	C₄	C₄²×D₄₇	1	1	yes	characteristic
132	C₄	#13093981	1	1	yes	characteristic
133	C₄	C₄×Dic₉₄	1	2	yes	—
134	C₂	C₄×Dic₄₇⋊C₄	1	1	yes	characteristic
135	C₂	C₂×#13093957	1	1	yes	characteristic
136	C₂	#15689159	1	1	yes	characteristic
137	C₂	C₄×#10625334	1	2	yes	—
138	C₂	C₄×#10625337	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093957

C₂

yes

maximal

C₂×C₄×C₄₇⋊C₈

C₂

yes

maximal, characteristic

C₄×C₄⋊Dic₄₇

C₂

yes

maximal, characteristic

#15688885

C₂

yes

maximal

C₄×C₄⋊C₄×C₄₇

C₂

yes

maximal, characteristic

C₂²×C₄₇⋊C₈

C₂²

yes

characteristic

C₂²×C₄₇⋊C₈

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

—

#13093957

C₄

yes

direct product factor

C₄×C₄₇⋊C₈

C₄

yes

complemented

C₄₇⋊#95

—

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

#95×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

C₂×C₄

yes

—

C₄²×C₄₇

—

C₄²×C₄₇

C₂×C₄

yes

—

C₄²×C₄₇

Q₈

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

C₂×C₄

yes

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

C₂×C₄

yes

—

C₂×C₄₇⋊C₈

C₂×C₄

yes

—

C₂×C₄₇⋊C₈

C₂×C₄

yes

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₄⋊C₄

yes

—

C₂×C₄×C₄₇

C₄⋊C₄

yes

—

C₂×C₄×C₄₇

D₈

yes

—

C₂×C₄×C₄₇

Q₁₆

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₄₇⋊C₈

—

C₄₇⋊C₈

C₄²

yes

complemented

C₂²×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₄₇

C₄×D₄

yes

—

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₂²×C₄₇

C₂×Q₁₆

yes

characteristic

C₂²×C₄₇

#135

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#107

yes

complemented

C₄×C₄₇

C₂×C₄²

yes

characteristic

C₄×C₄₇

#117

yes

characteristic

C₄×C₄₇

C₄×Q₈

yes

—

Dic₄₇

—

C₄×#107

—

maximal, Sylow

C₂×C₄₇

C₄×C₄⋊C₄

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

C₄×D₈

yes

—

C₂×C₄₇

C₄×Q₁₆

yes

—

C₂×#107

—

C₂×C₄×C₈

—

C₄×C₄⋊C₄

—

C₄×C₄⋊C₄

D₄₇

yes

characteristic

#340

—

C₄₇

C₄×#107

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₇

yes

characteristic

#107

—

C₄×C₈

—

#95

—

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₄₇

yes

characteristic

C₂²×C₄

C₂²⋊D₄₇

yes

characteristic

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₄×D₄₇

yes

—

100

C₄²

—

101

C₄²

—

188

—

102

C₄²

Dic₉₄

yes

—

103

C₄²

C₄×D₄₇

yes

—

104

C₂³

C₂×C₂²⋊D₄₇

yes

characteristic

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

188

—

111

C₂×C₄

—

188

—

112

C₂×C₄

Dic₄₇⋊C₄

yes

—

113

C₂×C₄

Dic₄₇⋊C₄

yes

—

114

C₂×C₄

#10625334

yes

—

115

C₂×C₄

#10625337

yes

—

116

C₂×C₄

C₂×Dic₉₄

yes

characteristic

117

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

118

C₂×C₄

C₂×C₄×D₄₇

yes

—

119

C₂×C₄

#10625350

yes

—

120

C₈

—

121

C₈

—

122

C₂²

C₂×Dic₄₇⋊C₄

yes

characteristic

123

C₂²

C₄×C₂²⋊D₄₇

yes

—

124

C₂²

C₂×#10625334

yes

characteristic

125

C₂²

C₂×#10625337

yes

characteristic

126

C₂²

#13094044

yes

—

127

C₄

—

128

C₄

—

129

C₄

—

188

—

130

C₄

#13093957

yes

direct product factor

131

C₄

C₄²×D₄₇

yes

characteristic

132

C₄

#13093981

yes

characteristic

133

C₄

C₄×Dic₉₄

yes

—

134

C₂

C₄×Dic₄₇⋊C₄

yes

characteristic

135

C₂

C₂×#13093957

yes

characteristic

136

C₂

#15689159

yes

characteristic

137

C₂

C₄×#10625334

yes

—

138

C₂

C₄×#10625337

yes

—

	subgroup	G/H
center	C₂²×C₄	C₂²⋊D₄₇
commutator	C₄×C₄₇	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄×C₄⋊C₄×C₄₇	C₂
socle	C₂³×C₄₇	C₂×D₄
hypercenter	C₄×C₄⋊C₄	D₄₇
hypocenter	C₄₇	C₄×#107
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₄×C₄⋊C₄

subgroup

G/H

center

C₂²×C₄

C₂²⋊D₄₇

commutator

C₄×C₄₇

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₄×C₄⋊C₄×C₄₇

C₂

socle

C₂³×C₄₇

C₂×D₄

hypercenter

C₄×C₄⋊C₄

D₄₇

hypocenter

C₄₇

C₄×#107

LCS

G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₄×C₄⋊C₄

N	H ≅ G/N	type
10. #13093957	C₄	direct (N × H)
11. C₄×C₄₇⋊C₈	C₄	semidirect
51. C₄₇⋊C₈	C₄²	semidirect
59. C₄×C₄₇	#107	semidirect
75. C₄₇	C₄×#107	semidirect
130. C₄	#13093957	direct (N × H)

H ≅ G/N

type

10. #13093957

C₄

direct (N × H)

11. C₄×C₄₇⋊C₈

C₄

semidirect

51. C₄₇⋊C₈

C₄²

semidirect

59. C₄×C₄₇

#107

semidirect

75. C₄₇

C₄×#107

semidirect

130. C₄

#13093957

direct (N × H)

Subgroups — C₄×#13093957 #20243282

Conjugacy classes of subgroups

Complements

Subgroups — C4×#13093957 #20243282

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#13093957 #20243282