Group #20267943 — subgroups

Subgroups — #20267943

Order 6592.

188 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 45 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×D₄×D₁₀₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#13110094	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#13110093	C₂	1	1	yes	maximal, characteristic, complemented
4	#15693001	C₂	1	1	yes	maximal, characteristic, complemented
5	#15692941	C₂	1	1	yes	maximal, characteristic, complemented
6	(C₂×D₁₀₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	#102×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₁₀₃	—	2	1	no	—
9	C₂×Dic₂₀₆	C₂²	1	1	yes	characteristic, complemented
10	C₂×D₄₁₂	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊D₁₀₃	—	2	1	no	—
12	D₄×D₁₀₃	—	2	2	no	—
13	D₄×D₁₀₃	—	2	2	no	—
14	C₂×C₄×D₁₀₃	C₂²	1	1	yes	characteristic
15	#13110094	—	2	2	no	—
16	#13110093	—	2	2	no	—
17	C₂×C₁₀₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
18	C₄⋊Dic₁₀₃	—	2	1	no	—
19	(C₂×D₁₀₃)⋊C₄	—	2	1	no	—
20	C₂×D₄×C₁₀₃	C₂²	1	1	yes	characteristic
21	C₂×C₈×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
22	C₄⋊C₄×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
23	C₂³×C₁₀₃	—	2	1	no	—
24	C₂²×D₁₀₃	—	2	4	no	—
25	C₂²×D₁₀₃	—	2	1	no	—
26	C₂²×D₁₀₃	—	4	2	no	—
27	C₂²×D₁₀₃	—	4	2	no	—
28	C₂²×D₁₀₃	D₄	1	1	yes	characteristic
29	D₄×C₁₀₃	—	2	1	no	—
30	D₄×C₁₀₃	D₄	1	2	yes	—
31	C₂×C₄×C₁₀₃	—	2	1	no	—
32	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
33	C₂²⋊D₁₀₃	—	2	4	no	—
34	C₂×Dic₁₀₃	—	2	1	no	—
35	C₂×Dic₁₀₃	D₄	1	1	yes	characteristic
36	D₄₁₂	—	2	1	no	—
37	D₄₁₂	D₄	1	2	yes	—
38	C₄×D₁₀₃	—	2	1	no	—
39	C₄×D₁₀₃	—	2	1	no	—
40	Dic₂₀₆	—	2	1	no	—
41	Dic₂₀₆	—	2	1	no	—
42	C₈×C₁₀₃	—	2	1	no	—
43	C₁₀₃⋊C₈	—	2	1	no	—
44	C₂²×C₁₀₃	—	2	2	no	—
45	C₂²×C₁₀₃	—	4	1	no	—
46	C₂²×C₁₀₃	—	4	1	no	—
47	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
48	C₂×D₁₀₃	—	2	1	no	—
49	C₂×D₁₀₃	—	2	1	no	—
50	C₂×D₁₀₃	—	2	2	no	—
51	C₂×D₁₀₃	—	4	8	no	—
52	C₂×D₁₀₃	—	4	1	no	—
53	C₂×D₁₀₃	—	4	1	no	—
54	C₂×D₁₀₃	SD₁₆	1	2	yes	complemented
55	C₄×C₁₀₃	—	4	1	no	—
56	C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
57	C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
58	Dic₁₀₃	—	2	1	no	—
59	Dic₁₀₃	—	4	1	no	—
60	C₂×C₁₀₃	—	4	2	no	—
61	C₂×C₁₀₃	#120	1	1	yes	characteristic
62	C₂×C₁₀₃	C₂×SD₁₆	1	1	yes	characteristic
63	C₂×C₁₀₃	AGL(1,ℤ/8)	1	1	yes	characteristic
64	D₁₀₃	—	2	2	no	—
65	D₁₀₃	—	4	2	no	—
66	C₁₀₃	#450	1	1	yes	characteristic, complemented, Sylow
67	#450	—	103	1	no	maximal, Sylow
68	C₂²×D₄	—	103	1	no	—
69	C₂×SD₁₆	—	103	1	no	—
70	C₂×SD₁₆	—	103	1	no	—
71	C₂²⋊Q₈	—	103	1	no	—
72	#102	—	103	1	no	—
73	#102	D₁₀₃	1	1	yes	characteristic, complemented
74	C₂²⋊C₈	—	103	1	no	—
75	C₂⁴	—	206	1	no	—
76	C₂×Q₈	—	103	1	no	—
77	C₂×D₄	—	103	1	no	—
78	C₂×D₄	—	206	1	no	—
79	C₂×D₄	—	206	2	no	—
80	C₂×D₄	—	206	2	no	—
81	C₂×D₄	C₂×D₁₀₃	1	1	yes	characteristic
82	C₂²×C₄	—	103	1	no	—
83	SD₁₆	—	206	2	no	—
84	SD₁₆	—	206	2	no	—
85	C₂×C₈	—	103	1	no	—
86	C₂×C₈	C₂×D₁₀₃	1	1	yes	characteristic, complemented
87	C₄⋊C₄	—	206	1	no	—
88	C₄⋊C₄	C₂×D₁₀₃	1	1	yes	characteristic, complemented
89	C₂²⋊C₄	—	206	1	no	—
90	C₂³	—	2	1	no	—
91	C₂³	—	103	1	no	—
92	C₂³	—	412	2	no	—
93	C₂³	—	412	2	no	—
94	C₂³	—	206	4	no	—
95	C₂³	—	206	1	no	—
96	Q₈	—	206	1	no	—
97	Q₈	—	206	1	no	—
98	D₄	—	2	1	no	—
99	D₄	—	103	2	no	—
100	D₄	—	206	4	no	—
101	D₄	—	206	1	no	—
102	D₄	D₄₁₂	1	2	yes	—
103	C₂×C₄	—	2	1	no	—
104	C₂×C₄	—	103	1	no	—
105	C₂×C₄	—	206	1	no	—
106	C₂×C₄	—	206	1	no	—
107	C₂×C₄	—	206	1	no	—
108	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
109	C₈	—	2	1	no	—
110	C₈	—	206	1	no	—
111	C₂²	—	2	2	no	—
112	C₂²	—	4	1	no	—
113	C₂²	—	4	1	no	—
114	C₂²	—	103	2	no	—
115	C₂²	—	412	8	no	—
116	C₂²	—	412	1	no	—
117	C₂²	—	412	1	no	—
118	C₂²	—	206	2	no	—
119	C₂²	—	206	1	no	—
120	C₂²	—	206	1	no	—
121	C₂²	D₄×D₁₀₃	1	1	yes	characteristic
122	C₄	—	4	1	no	—
123	C₄	—	412	1	no	—
124	C₄	—	206	1	no	—
125	C₄	D₄×D₁₀₃	1	1	yes	characteristic
126	C₄	C₂×D₄₁₂	1	1	yes	characteristic
127	C₂	—	4	2	no	—
128	C₂	—	412	2	no	—
129	C₂	—	206	2	no	—
130	C₂	#15692991	1	1	yes	characteristic
131	C₂	SD₁₆×D₁₀₃	1	1	yes	characteristic
132	C₂	#15693045	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₄×D₁₀₃

C₂

yes

maximal, characteristic

C₂×#13110094

C₂

yes

maximal, characteristic, complemented

C₂×#13110093

C₂

yes

maximal, characteristic, complemented

#15693001

C₂

yes

maximal, characteristic, complemented

#15692941

C₂

yes

maximal, characteristic, complemented

(C₂×D₁₀₃)⋊C₈

C₂

yes

maximal, characteristic, complemented

#102×C₁₀₃

C₂

yes

maximal, characteristic, complemented

C₂³×D₁₀₃

—

C₂×Dic₂₀₆

C₂²

yes

characteristic, complemented

C₂×D₄₁₂

C₂²

yes

characteristic

C₂×C₂²⋊D₁₀₃

—

D₄×D₁₀₃

—

D₄×D₁₀₃

—

C₂×C₄×D₁₀₃

C₂²

yes

characteristic

#13110094

—

#13110093

—

C₂×C₁₀₃⋊C₈

C₂²

yes

characteristic, complemented

C₄⋊Dic₁₀₃

—

(C₂×D₁₀₃)⋊C₄

—

C₂×D₄×C₁₀₃

C₂²

yes

characteristic

C₂×C₈×C₁₀₃

C₂²

yes

characteristic, complemented

C₄⋊C₄×C₁₀₃

C₂²

yes

characteristic, complemented

C₂³×C₁₀₃

—

C₂²×D₁₀₃

—

C₂²×D₁₀₃

—

C₂²×D₁₀₃

—

C₂²×D₁₀₃

—

C₂²×D₁₀₃

D₄

yes

characteristic

D₄×C₁₀₃

—

D₄×C₁₀₃

D₄

yes

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

C₂³

yes

characteristic

C₂²⋊D₁₀₃

—

C₂×Dic₁₀₃

—

C₂×Dic₁₀₃

D₄

yes

characteristic

D₄₁₂

—

D₄₁₂

D₄

yes

—

C₄×D₁₀₃

—

C₄×D₁₀₃

—

Dic₂₀₆

—

Dic₂₀₆

—

C₈×C₁₀₃

—

C₁₀₃⋊C₈

—

C₂²×C₁₀₃

—

C₂²×C₁₀₃

—

C₂²×C₁₀₃

—

C₂²×C₁₀₃

C₂×D₄

yes

characteristic

C₂×D₁₀₃

—

C₂×D₁₀₃

—

C₂×D₁₀₃

—

C₂×D₁₀₃

—

C₂×D₁₀₃

—

C₂×D₁₀₃

—

C₂×D₁₀₃

SD₁₆

yes

complemented

C₄×C₁₀₃

—

C₄×C₁₀₃

C₂×D₄

yes

characteristic

C₄×C₁₀₃

C₂×D₄

yes

characteristic

Dic₁₀₃

—

Dic₁₀₃

—

C₂×C₁₀₃

—

C₂×C₁₀₃

#120

yes

characteristic

C₂×C₁₀₃

C₂×SD₁₆

yes

characteristic

C₂×C₁₀₃

AGL(1,ℤ/8)

yes

characteristic

D₁₀₃

—

D₁₀₃

—

C₁₀₃

#450

yes

characteristic, complemented, Sylow

#450

—

103

maximal, Sylow

C₂²×D₄

—

103

—

C₂×SD₁₆

—

103

—

C₂×SD₁₆

—

103

—

C₂²⋊Q₈

—

103

—

#102

—

103

—

#102

D₁₀₃

yes

characteristic, complemented

C₂²⋊C₈

—

103

—

C₂⁴

—

206

—

C₂×Q₈

—

103

—

C₂×D₄

—

103

—

C₂×D₄

—

206

—

C₂×D₄

—

206

—

C₂×D₄

—

206

—

C₂×D₄

C₂×D₁₀₃

yes

characteristic

C₂²×C₄

—

103

—

SD₁₆

—

206

—

SD₁₆

—

206

—

C₂×C₈

—

103

—

C₂×C₈

C₂×D₁₀₃

yes

characteristic, complemented

C₄⋊C₄

—

206

—

C₄⋊C₄

C₂×D₁₀₃

yes

characteristic, complemented

C₂²⋊C₄

—

206

—

C₂³

—

C₂³

—

103

—

C₂³

—

412

—

C₂³

—

412

—

C₂³

—

206

—

C₂³

—

206

—

Q₈

—

206

—

Q₈

—

206

—

D₄

—

D₄

—

103

—

100

D₄

—

206

—

101

D₄

—

206

—

102

D₄

D₄₁₂

yes

—

103

C₂×C₄

—

104

C₂×C₄

—

103

—

105

C₂×C₄

—

206

—

106

C₂×C₄

—

206

—

107

C₂×C₄

—

206

—

108

C₂×C₄

C₂²×D₁₀₃

yes

characteristic

109

C₈

—

110

C₈

—

206

—

111

C₂²

—

112

C₂²

—

113

C₂²

—

114

C₂²

—

103

—

115

C₂²

—

412

—

116

C₂²

—

412

—

117

C₂²

—

412

—

118

C₂²

—

206

—

119

C₂²

—

206

—

120

C₂²

—

206

—

121

C₂²

D₄×D₁₀₃

yes

characteristic

122

C₄

—

123

C₄

—

412

—

124

C₄

—

206

—

125

C₄

D₄×D₁₀₃

yes

characteristic

126

C₄

C₂×D₄₁₂

yes

characteristic

127

C₂

—

128

C₂

—

412

—

129

C₂

—

206

—

130

C₂

#15692991

yes

characteristic

131

C₂

SD₁₆×D₁₀₃

yes

characteristic

132

C₂

#15693045

yes

characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₀₃
commutator	C₂×C₄×C₁₀₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₃
Fitting	#102×C₁₀₃	C₂
socle	C₂²×C₁₀₃	C₂×D₄
hypercenter	#102	D₁₀₃
hypocenter	C₁₀₃	#450
LCS	G ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #102

subgroup

G/H

center

C₂²

D₄×D₁₀₃

commutator

C₂×C₄×C₁₀₃

C₂³

Frattini

C₂×C₄

C₂²×D₁₀₃

Fitting

#102×C₁₀₃

C₂

socle

C₂²×C₁₀₃

C₂×D₄

D₁₀₃

C₁₀₃

G ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ #102

N	H ≅ G/N	type
2. C₂×#13110094	C₂	semidirect
3. C₂×#13110093	C₂	semidirect
4. #15693001	C₂	semidirect
5. #15692941	C₂	semidirect
6. (C₂×D₁₀₃)⋊C₈	C₂	semidirect
7. #102×C₁₀₃	C₂	semidirect
9. C₂×Dic₂₀₆	C₂²	semidirect
17. C₂×C₁₀₃⋊C₈	C₂²	semidirect
21. C₂×C₈×C₁₀₃	C₂²	semidirect
22. C₄⋊C₄×C₁₀₃	C₂²	semidirect
54. C₂×D₁₀₃	SD₁₆	semidirect
66. C₁₀₃	#450	semidirect
73. #102	D₁₀₃	semidirect
86. C₂×C₈	C₂×D₁₀₃	semidirect
88. C₄⋊C₄	C₂×D₁₀₃	semidirect

H ≅ G/N

type

2. C₂×#13110094

C₂

semidirect

3. C₂×#13110093

C₂

semidirect

4. #15693001

C₂

semidirect

5. #15692941

C₂

semidirect

6. (C₂×D₁₀₃)⋊C₈

C₂

semidirect

7. #102×C₁₀₃

C₂

semidirect

9. C₂×Dic₂₀₆

C₂²

semidirect

17. C₂×C₁₀₃⋊C₈

C₂²

semidirect

21. C₂×C₈×C₁₀₃

C₂²

semidirect

22. C₄⋊C₄×C₁₀₃

C₂²

semidirect

54. C₂×D₁₀₃

SD₁₆

semidirect

66. C₁₀₃

#450

semidirect

73. #102

D₁₀₃

semidirect

86. C₂×C₈

C₂×D₁₀₃

semidirect

88. C₄⋊C₄

C₂×D₁₀₃

semidirect

Subgroups — #20267943

Conjugacy classes of subgroups

Complements