Group #20243047 — subgroups

Subgroups — #20243047

Order 6016.

186 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 57 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	#15689519	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689503	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689473	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689469	C₂	1	1	yes	maximal, characteristic
5	#15689469	C₂	1	1	yes	maximal, characteristic
6	#15688845	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#486	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₁₈₈	—	2	2	no	—
9	#13094024	C₂²	1	1	yes	characteristic
10	#13094024	C₂²	1	1	yes	characteristic
11	#13093955	—	2	2	no	—
12	#13093948	—	2	2	no	—
13	#13093945	—	2	2	no	—
14	#13093945	—	2	2	no	—
15	C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
16	C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
17	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
18	#127×C₄₇	C₂²	1	1	yes	characteristic
19	#102×C₄₇	—	2	2	no	—
20	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×Q₈×C₄₇	—	2	1	no	—
22	C₂×D₄×C₄₇	—	2	1	no	—
23	C₂×D₄×C₄₇	—	2	1	no	—
24	C₂×D₄×C₄₇	—	2	1	no	—
25	C₂×Dic₉₄	—	2	1	no	—
26	C₂×Dic₉₄	—	2	1	no	—
27	C₂×C₈×C₄₇	D₄	1	2	yes	—
28	C₄⋊C₄×C₄₇	—	2	1	no	—
29	C₄⋊C₄×C₄₇	—	2	1	no	—
30	C₄²×C₄₇	C₂³	1	1	yes	characteristic
31	C₄⋊Dic₄₇	—	2	1	no	—
32	C₄⋊Dic₄₇	—	2	1	no	—
33	C₄⋊Dic₄₇	—	2	1	no	—
34	C₄⋊Dic₄₇	—	2	1	no	—
35	C₂×C₄₇⋊C₈	D₄	1	2	yes	—
36	C₂×C₄₇⋊C₈	D₄	1	2	yes	—
37	Dic₁₈₈	—	4	4	no	—
38	C₂³×C₄₇	—	4	1	no	—
39	Q₈×C₄₇	—	4	2	no	—
40	D₄×C₄₇	—	4	2	no	—
41	D₄×C₄₇	—	4	2	no	—
42	D₄×C₄₇	—	4	2	no	—
43	C₂×C₄×C₄₇	—	4	1	no	—
44	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
47	C₂×Dic₄₇	—	4	1	no	—
48	C₂×Dic₄₇	—	4	1	no	—
49	Dic₉₄	—	4	2	no	—
50	Dic₉₄	—	4	2	no	—
51	C₈×C₄₇	—	2	2	no	—
52	C₄₇⋊C₈	—	2	2	no	—
53	C₄₇⋊C₈	—	2	2	no	—
54	C₂²×C₄₇	—	8	1	no	—
55	C₂²×C₄₇	—	8	1	no	—
56	C₂²×C₄₇	—	8	1	no	—
57	C₂²×C₄₇	#127	1	1	yes	characteristic
58	C₄×C₄₇	—	8	1	no	—
59	C₄×C₄₇	#135	1	2	yes	—
60	C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
61	C₄×C₄₇	#137	1	2	yes	—
62	Dic₄₇	—	8	1	no	—
63	Dic₄₇	—	8	1	no	—
64	#1720	—	47	1	no	maximal, Sylow
65	C₂×C₄₇	—	16	1	no	—
66	C₂×C₄₇	#495	1	1	yes	characteristic
67	C₂×C₄₇	#496	1	1	yes	characteristic
68	C₂×C₄₇	#497	1	1	yes	characteristic
69	#498	—	47	1	no	—
70	#494	—	47	1	no	—
71	#487	—	47	1	no	—
72	#486	—	47	1	no	—
73	#486	—	47	1	no	—
74	#486	D₄₇	1	1	yes	characteristic
75	#322	—	47	1	no	—
76	C₄₇	#1720	1	1	yes	characteristic, complemented, Sylow
77	C₂×Q₁₆	—	94	2	no	—
78	C₄⋊Q₈	—	47	1	no	—
79	C₄⋊Q₈	—	47	1	no	—
80	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
81	#127	C₂×D₄₇	1	1	yes	characteristic
82	#106	—	94	2	no	—
83	#103	—	94	2	no	—
84	#102	—	2	2	no	—
85	#102	—	94	2	no	—
86	#102	—	94	2	no	—
87	C₄×C₈	—	47	1	no	—
88	C₄×C₈	—	47	1	no	—
89	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
90	C₂×Q₈	—	2	1	no	—
91	C₂×Q₈	—	94	1	no	—
92	C₂×Q₈	—	94	1	no	—
93	C₂×D₄	—	2	1	no	—
94	C₂×D₄	—	2	1	no	—
95	C₂×D₄	—	2	1	no	—
96	Q₁₆	—	188	4	no	—
97	C₂×C₈	—	47	2	no	—
98	C₂×C₈	—	47	2	no	—
99	C₂×C₈	C₂²⋊D₄₇	1	2	yes	—
100	C₄⋊C₄	—	2	1	no	—
101	C₄⋊C₄	—	2	1	no	—
102	C₄⋊C₄	—	94	1	no	—
103	C₄⋊C₄	—	94	1	no	—
104	C₄⋊C₄	—	94	1	no	—
105	C₄⋊C₄	—	94	1	no	—
106	C₄²	C₂²×D₄₇	1	1	yes	characteristic
107	C₂³	—	4	1	no	—
108	Q₈	—	4	2	no	—
109	Q₈	—	188	2	no	—
110	Q₈	—	188	2	no	—
111	D₄	—	4	2	no	—
112	D₄	—	4	2	no	—
113	D₄	—	4	2	no	—
114	C₂×C₄	—	4	1	no	—
115	C₂×C₄	—	188	1	no	—
116	C₂×C₄	—	188	1	no	—
117	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
118	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
119	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
120	C₈	—	2	2	no	—
121	C₈	—	94	2	no	—
122	C₈	—	94	2	no	—
123	C₂²	—	8	1	no	—
124	C₂²	—	8	1	no	—
125	C₂²	—	8	1	no	—
126	C₂²	#13094020	1	1	yes	characteristic
127	C₄	—	8	1	no	—
128	C₄	—	376	1	no	—
129	C₄	—	376	1	no	—
130	C₄	#13094043	1	2	yes	—
131	C₄	#13094049	1	2	yes	—
132	C₄	#13094053	1	2	yes	—
133	C₂	—	16	1	no	—
134	C₂	#15689506	1	1	yes	characteristic
135	C₂	#15689513	1	1	yes	characteristic
136	C₂	#15689514	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689519

C₂

yes

maximal, characteristic, complemented

#15689503

C₂

yes

maximal, characteristic, complemented

#15689473

C₂

yes

maximal, characteristic, complemented

#15689469

C₂

yes

maximal, characteristic

#15689469

C₂

yes

maximal, characteristic

#15688845

C₂

yes

maximal, characteristic, complemented

C₄₇×#486

C₂

yes

maximal, characteristic

C₂×Dic₁₈₈

—

#13094024

C₂²

yes

characteristic

#13094024

C₂²

yes

—

—

—

—

C₄×C₄₇⋊C₈

C₂²

yes

characteristic

C₄×C₄₇⋊C₈

C₂²

yes

characteristic

C₄⋊Q₈×C₄₇

C₂²

yes

characteristic

#127×C₄₇

C₂²

yes

characteristic

#102×C₄₇

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×C₈×C₄₇

D₄

yes

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₂×C₄₇⋊C₈

D₄

yes

—

C₂×C₄₇⋊C₈

D₄

yes

—

Dic₁₈₈

—

C₂³×C₄₇

—

Q₈×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#127

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

#135

yes

—

C₄×C₄₇

AGL(1,ℤ/8)

yes

—

C₄×C₄₇

#137

yes

—

Dic₄₇

—

Dic₄₇

—

#1720

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

—

—

—

—

D₄₇

yes

characteristic

#322

—

C₄₇

#1720

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₄₇

yes

characteristic

#127

C₂×D₄₇

yes

—

—

—

—

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

Q₁₆

—

188

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₄₇

yes

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄²

C₂²×D₄₇

yes

characteristic

107

C₂³

—

108

Q₈

—

109

Q₈

—

188

—

110

Q₈

—

188

—

111

D₄

—

112

D₄

—

113

D₄

—

114

C₂×C₄

—

115

C₂×C₄

—

188

—

116

C₂×C₄

—

188

—

117

C₂×C₄

D₄×D₄₇

yes

characteristic

118

C₂×C₄

D₄×D₄₇

yes

characteristic

119

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

120

C₈

—

121

C₈

—

122

C₈

—

123

C₂²

—

124

C₂²

—

125

C₂²

—

126

C₂²

#13094020

yes

characteristic

127

C₄

—

128

C₄

—

376

—

129

C₄

—

376

—

130

C₄

#13094043

yes

—

131

C₄

#13094049

yes

—

132

C₄

#13094053

yes

—

133

C₂

—

134

C₂

#15689506

yes

characteristic

135

C₂

#15689513

yes

characteristic

136

C₂

#15689514

yes

characteristic

	subgroup	G/H
center	C₂²	#13094020
commutator	C₄²×C₄₇	C₂³
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄₇×#486	C₂
socle	C₂²×C₄₇	#127
hypercenter	#486	D₄₇
hypocenter	C₄₇	#1720
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #486

subgroup

G/H

center

C₂²

#13094020

commutator

C₄²×C₄₇

C₂³

Frattini

C₄²

C₂²×D₄₇

Fitting

C₄₇×#486

C₂

C₂²×C₄₇

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #486

N	H ≅ G/N	type
1. #15689519	C₂	semidirect
2. #15689503	C₂	semidirect
3. #15689473	C₂	semidirect
6. #15688845	C₂	semidirect
76. C₄₇	#1720	semidirect

H ≅ G/N

type

1. #15689519

C₂

semidirect

2. #15689503

C₂

semidirect

3. #15689473

C₂

semidirect

6. #15688845

C₂

semidirect

76. C₄₇

#1720

semidirect

Subgroups — #20243047

Conjugacy classes of subgroups

Complements