Group #20253834 — subgroups

Subgroups — #20253834

Order 6016.

564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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×#13094046	C₂	1	4	yes	maximal, complemented
2	#15689673	C₂	1	2	yes	maximal, complemented
3	#15689517	C₂	1	4	yes	maximal, complemented
4	#15689512	C₂	1	4	yes	maximal, complemented
5	C₂×#97×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10625350	C₂²	1	4	yes	—
7	#13094046	—	2	16	no	—
8	C₂×Dic₁₈₈	C₂²	1	4	yes	—
9	C₂×#10625325	C₂²	1	8	yes	—
10	C₂×D₃₇₆	C₂²	1	4	yes	—
11	#13094024	C₂²	1	2	yes	—
12	#13094021	C₂²	1	2	yes	—
13	#13094012	C₂²	1	4	yes	—
14	#13093998	—	2	4	no	—
15	C₄×D₁₈₈	—	2	4	no	—
16	C₂²×C₈×C₄₇	C₂²	1	2	yes	—
17	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
18	#97×C₄₇	C₂²	1	4	yes	—
19	C₂²×C₄×C₄₇	D₄	1	2	yes	—
20	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
21	C₂×C₂²⋊D₄₇	—	2	4	no	—
22	#10625350	—	2	16	no	—
23	C₂×D₁₈₈	—	2	4	no	—
24	C₂×D₁₈₈	C₂³	1	4	yes	—
25	C₂×C₄×D₄₇	—	2	4	no	—
26	C₂×Dic₉₄	C₂³	1	4	yes	—
27	C₂×C₈×C₄₇	D₄	1	8	yes	complemented
28	C₂×C₈×C₄₇	C₂³	1	4	yes	—
29	C₄²×C₄₇	D₄	1	2	yes	—
30	C₄²×C₄₇	C₂³	1	2	yes	—
31	(C₂×D₄₇)⋊C₄	—	2	8	no	—
32	C₄⋊Dic₄₇	—	2	4	no	—
33	Dic₁₈₈	—	2	8	no	—
34	D₃₇₆	—	2	8	no	—
35	#10625325	—	2	16	no	—
36	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
37	C₂²×D₄₇	—	2	4	no	—
38	C₂×C₄×C₄₇	—	4	2	no	—
39	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
40	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
41	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
43	C₂²⋊D₄₇	—	4	8	no	—
44	C₂×Dic₄₇	—	2	4	no	—
45	D₁₈₈	—	2	8	no	—
46	D₁₈₈	—	4	8	no	—
47	C₄×D₄₇	—	4	8	no	—
48	Dic₉₄	—	2	8	no	—
49	C₈×C₄₇	C₂×D₄	1	8	yes	—
50	C₂²×C₄₇	—	2	2	no	—
51	C₂²×C₄₇	#127	1	2	yes	—
52	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
53	C₂×D₄₇	—	4	4	no	—
54	C₂×D₄₇	—	4	8	no	—
55	C₄×C₄₇	—	2	4	no	—
56	C₄×C₄₇	#127	1	2	yes	—
57	C₄×C₄₇	C₂²×D₄	1	2	yes	—
58	Dic₄₇	—	4	4	no	—
59	#3150	—	47	1	no	maximal, Sylow
60	C₂×C₄₇	—	2	2	no	—
61	C₂×C₄₇	C₂×#127	1	1	yes	characteristic
62	C₂×C₄₇	#575	1	2	yes	—
63	D₄₇	—	8	4	no	—
64	C₂×#135	—	47	4	no	—
65	#532	—	47	2	no	—
66	#497	—	47	4	no	—
67	#496	—	47	4	no	—
68	C₂×#97	D₄₇	1	1	yes	characteristic, complemented
69	C₄₇	#3150	1	1	yes	characteristic, complemented, Sylow
70	C₂×#41	—	47	4	no	—
71	#135	—	94	16	no	—
72	C₂×Q₁₆	—	47	4	no	—
73	C₂×SD₁₆	—	47	8	no	—
74	C₂×D₈	—	47	4	no	—
75	C₂²×C₈	C₂×D₄₇	1	2	yes	—
76	C₄⋊Q₈	—	47	2	no	—
77	#127	—	47	2	no	—
78	#124	—	47	4	no	—
79	#121	—	94	4	no	—
80	C₄×D₄	—	94	4	no	—
81	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
82	#97	C₂×D₄₇	1	4	yes	—
83	#41	—	94	16	no	—
84	C₂×Q₈	—	47	4	no	—
85	C₂×D₄	—	47	4	no	—
86	C₂×D₄	—	94	4	no	—
87	C₂×D₄	—	94	4	no	—
88	C₂²×C₄	—	94	4	no	—
89	C₂²×C₄	D₁₈₈	1	2	yes	—
90	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
91	Q₁₆	—	94	8	no	—
92	SD₁₆	—	94	16	no	—
93	D₈	—	94	8	no	—
94	C₂×C₈	D₁₈₈	1	8	yes	complemented
95	C₂×C₈	C₂²×D₄₇	1	4	yes	—
96	C₄⋊C₄	—	94	4	no	—
97	C₂²⋊C₄	—	94	8	no	—
98	C₄²	D₁₈₈	1	2	yes	—
99	C₄²	C₂²×D₄₇	1	2	yes	—
100	C₂³	—	94	4	no	—
101	C₂³	C₂×D₁₈₈	1	1	yes	characteristic
102	Q₈	—	94	8	no	—
103	D₄	—	94	8	no	—
104	D₄	—	188	8	no	—
105	D₄	—	188	8	no	—
106	C₂×C₄	—	4	2	no	—
107	C₂×C₄	—	94	4	no	—
108	C₂×C₄	—	188	8	no	—
109	C₂×C₄	C₂×D₁₈₈	1	4	yes	—
110	C₂×C₄	C₂×D₁₈₈	1	4	yes	—
111	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
112	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
113	C₈	C₂×D₁₈₈	1	8	yes	—
114	C₂²	—	2	2	no	—
115	C₂²	—	188	4	no	—
116	C₂²	—	188	8	no	—
117	C₂²	#13094021	1	2	yes	—
118	C₂²	C₂²×D₁₈₈	1	1	yes	characteristic
119	C₄	—	2	4	no	—
120	C₄	—	188	4	no	—
121	C₄	#13094021	1	2	yes	—
122	C₄	C₂²×D₁₈₈	1	2	yes	—
123	C₂	—	2	2	no	—
124	C₂	—	376	4	no	—
125	C₂	C₂×#13094021	1	1	yes	characteristic
126	C₂	#15689923	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13094046

C₂

yes

maximal, complemented

#15689673

C₂

yes

maximal, complemented

#15689517

C₂

yes

maximal, complemented

#15689512

C₂

yes

maximal, complemented

C₂×#97×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂×#10625350

C₂²

yes

—

#13094046

—

C₂×Dic₁₈₈

C₂²

yes

—

C₂×#10625325

C₂²

yes

—

C₂×D₃₇₆

C₂²

yes

—

#13094024

C₂²

yes

—

#13094021

C₂²

yes

—

#13094012

C₂²

yes

—

#13093998

—

C₄×D₁₈₈

—

C₂²×C₈×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

#97×C₄₇

C₂²

yes

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂×C₂²⋊D₄₇

—

#10625350

—

C₂×D₁₈₈

—

C₂×D₁₈₈

C₂³

yes

—

C₂×C₄×D₄₇

—

C₂×Dic₉₄

C₂³

yes

—

C₂×C₈×C₄₇

D₄

yes

complemented

C₂×C₈×C₄₇

C₂³

yes

—

C₄²×C₄₇

D₄

yes

—

C₄²×C₄₇

C₂³

yes

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

Dic₁₈₈

—

D₃₇₆

—

#10625325

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

C₂²×D₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂⁴

yes

characteristic

C₂²⋊D₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

C₄×D₄₇

—

Dic₉₄

—

C₈×C₄₇

C₂×D₄

yes

—

C₂²×C₄₇

—

C₂²×C₄₇

#127

yes

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#127

yes

—

C₄×C₄₇

C₂²×D₄

yes

—

Dic₄₇

—

#3150

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

C₂×#127

yes

characteristic

C₂×C₄₇

#575

yes

—

D₄₇

—

—

—

—

—

C₂×#97

D₄₇

yes

characteristic, complemented

C₄₇

#3150

yes

characteristic, complemented, Sylow

C₂×#41

—

#135

—

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×D₈

—

C₂²×C₈

C₂×D₄₇

yes

—

C₄⋊Q₈

—

#127

—

#124

—

#121

—

C₄×D₄

—

C₂×C₄²

C₂×D₄₇

yes

characteristic

#97

C₂×D₄₇

yes

—

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

D₁₈₈

yes

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

Q₁₆

—

SD₁₆

—

D₈

—

C₂×C₈

D₁₈₈

yes

complemented

C₂×C₈

C₂²×D₄₇

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

D₁₈₈

yes

—

C₄²

C₂²×D₄₇

yes

—

100

C₂³

—

101

C₂³

C₂×D₁₈₈

yes

characteristic

102

Q₈

—

103

D₄

—

104

D₄

—

188

—

105

D₄

—

188

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

188

—

109

C₂×C₄

C₂×D₁₈₈

yes

—

110

C₂×C₄

C₂×D₁₈₈

yes

—

111

C₂×C₄

C₂×D₁₈₈

yes

characteristic

112

C₂×C₄

C₂³×D₄₇

yes

characteristic

113

C₈

C₂×D₁₈₈

yes

—

114

C₂²

—

115

C₂²

—

188

—

116

C₂²

—

188

—

117

C₂²

#13094021

yes

—

118

C₂²

C₂²×D₁₈₈

yes

characteristic

119

C₄

—

120

C₄

—

188

—

121

C₄

#13094021

yes

—

122

C₄

C₂²×D₁₈₈

yes

—

123

C₂

—

124

C₂

—

376

—

125

C₂

C₂×#13094021

yes

characteristic

126

C₂

#15689923

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₂×#97×C₄₇	C₂
socle	C₂²×C₄₇	C₂²×D₄
hypercenter	C₂×#97	D₄₇
hypocenter	C₄₇	#3150
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

subgroup

G/H

center

C₂×C₄

C₂×D₁₈₈

commutator

C₂×C₄×C₄₇

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₇

Fitting

C₂×#97×C₄₇

C₂

socle

C₂²×C₄₇

C₂²×D₄

hypercenter

C₂×#97

D₄₇

hypocenter

C₄₇

#3150

LCS

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

N	H ≅ G/N	type
1. C₂×#13094046	C₂	semidirect
2. #15689673	C₂	semidirect
3. #15689517	C₂	semidirect
4. #15689512	C₂	semidirect
5. C₂×#97×C₄₇	C₂	semidirect
27. C₂×C₈×C₄₇	D₄	semidirect
68. C₂×#97	D₄₇	semidirect
69. C₄₇	#3150	semidirect
94. C₂×C₈	D₁₈₈	semidirect

H ≅ G/N

type

1. C₂×#13094046

C₂

semidirect

2. #15689673

C₂

semidirect

3. #15689517

C₂

semidirect

4. #15689512

C₂

semidirect

5. C₂×#97×C₄₇

C₂

semidirect

27. C₂×C₈×C₄₇

D₄

semidirect

68. C₂×#97

D₄₇

semidirect

69. C₄₇

#3150

semidirect

94. C₂×C₈

D₁₈₈

semidirect

Subgroups — #20253834

Conjugacy classes of subgroups

Complements