Group #19136307 — subgroups

Subgroups — #19136307

Order 5504.

232 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 93 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×#13063265	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13063259	C₂	1	1	yes	maximal, characteristic, complemented
3	#14582703	C₂	1	2	yes	maximal, complemented
4	#14582700	C₂	1	2	yes	maximal, complemented
5	C₂×#135×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Dic₄₃	—	2	1	no	—
7	#13063265	—	2	2	no	—
8	C₂×C₄₃⋊C₁₆	C₂²	1	2	yes	—
9	#13063259	—	2	1	no	—
10	#13063259	C₂²	1	2	yes	—
11	C₂×#41×C₄₃	—	2	1	no	—
12	#135×C₄₃	—	2	2	no	—
13	#135×C₄₃	C₄	1	4	yes	complemented
14	C₂×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×SD₁₆×C₄₃	—	2	1	no	—
16	C₂×D₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
18	#41×C₄₃	—	2	4	no	—
19	#41×C₄₃	—	4	2	no	—
20	C₂×Q₈×C₄₃	—	2	1	no	—
21	C₂×D₄×C₄₃	—	2	1	no	—
22	C₂×D₄×C₄₃	—	4	1	no	—
23	C₂²×C₄×C₄₃	—	4	1	no	—
24	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
25	C₂²×Dic₄₃	—	4	1	no	—
26	Q₁₆×C₄₃	—	2	1	no	—
27	Q₁₆×C₄₃	C₂×C₄	1	2	yes	complemented
28	SD₁₆×C₄₃	—	2	4	no	—
29	D₈×C₄₃	—	2	1	no	—
30	D₈×C₄₃	C₂×C₄	1	2	yes	complemented
31	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
32	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
33	C₂×C₈×C₄₃	D₄	1	2	yes	—
34	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
35	C₄⋊Dic₄₃	—	2	2	no	—
36	C₄⋊Dic₄₃	—	4	1	no	—
37	C₄₃⋊C₁₆	—	2	2	no	—
38	C₂³×C₄₃	—	4	1	no	—
39	C₂³×C₄₃	D₈	1	1	yes	characteristic
40	Q₈×C₄₃	—	2	2	no	—
41	Q₈×C₄₃	—	4	1	no	—
42	D₄×C₄₃	—	2	2	no	—
43	D₄×C₄₃	—	4	4	no	—
44	D₄×C₄₃	—	4	1	no	—
45	C₂×C₄×C₄₃	—	4	1	no	—
46	C₂×C₄×C₄₃	—	4	4	no	—
47	C₂×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
48	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
49	C₂×C₄×C₄₃	SD₁₆	1	2	yes	—
50	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
51	C₂×Dic₄₃	—	4	2	no	—
52	C₂×Dic₄₃	—	8	2	no	—
53	C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
54	C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
55	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄₃	—	2	1	no	—
57	C₂²×C₄₃	—	2	1	no	—
58	C₂²×C₄₃	—	4	2	no	—
59	C₂²×C₄₃	—	8	1	no	—
60	C₂²×C₄₃	—	8	1	no	—
61	C₂²×C₄₃	#102	1	2	yes	—
62	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
63	C₄×C₄₃	—	4	2	no	—
64	C₄×C₄₃	#102	1	2	yes	—
65	C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
66	C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
67	Dic₄₃	—	8	2	no	—
68	#2139	—	43	1	no	maximal, Sylow
69	C₂×C₄₃	—	2	2	no	—
70	C₂×C₄₃	—	8	2	no	—
71	C₂×C₄₃	C₂×#102	1	1	yes	characteristic
72	C₂×C₄₃	#509	1	1	yes	characteristic
73	C₂×C₄₃	#510	1	1	yes	characteristic
74	C₂×#135	D₄₃	1	1	yes	characteristic
75	C₂×M₃₂	—	43	1	no	—
76	C₂×#107	—	43	1	no	—
77	#358	—	43	2	no	—
78	#357	—	43	2	no	—
79	C₄₃	#2139	1	1	yes	characteristic, complemented, Sylow
80	C₂×#41	—	2	1	no	—
81	#135	—	2	2	no	—
82	#135	Dic₄₃	1	4	yes	complemented
83	C₂×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
84	C₂×SD₁₆	—	2	1	no	—
85	C₂×D₈	C₂×D₄₃	1	1	yes	characteristic
86	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
87	C₂×C₄⋊C₄	—	86	1	no	—
88	M₃₂	—	86	2	no	—
89	C₂×C₁₆	—	43	2	no	—
90	#107	—	43	2	no	—
91	#107	—	86	1	no	—
92	#41	—	2	4	no	—
93	#41	—	4	2	no	—
94	C₂×Q₈	—	2	1	no	—
95	C₂×D₄	—	2	1	no	—
96	C₂×D₄	—	4	1	no	—
97	C₂²×C₄	—	4	1	no	—
98	C₂²×C₄	—	172	1	no	—
99	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
100	Q₁₆	—	2	1	no	—
101	Q₁₆	C₂×Dic₄₃	1	2	yes	complemented
102	SD₁₆	—	2	4	no	—
103	D₈	—	2	1	no	—
104	D₈	C₂×Dic₄₃	1	2	yes	complemented
105	C₂×C₈	C₂×Dic₄₃	1	2	yes	—
106	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
107	C₂×C₈	C₂²⋊D₄₃	1	2	yes	—
108	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
109	C₄⋊C₄	—	86	2	no	—
110	C₄⋊C₄	—	172	1	no	—
111	C₁₆	—	86	2	no	—
112	C₂³	—	4	1	no	—
113	C₂³	#10621882	1	1	yes	characteristic
114	Q₈	—	2	2	no	—
115	Q₈	—	4	1	no	—
116	D₄	—	2	2	no	—
117	D₄	—	4	4	no	—
118	D₄	—	4	1	no	—
119	C₂×C₄	—	4	1	no	—
120	C₂×C₄	—	4	4	no	—
121	C₂×C₄	—	344	2	no	—
122	C₂×C₄	—	172	2	no	—
123	C₂×C₄	#10621882	1	1	yes	characteristic
124	C₂×C₄	#10621883	1	2	yes	—
125	C₂×C₄	C₂²⋊Dic₄₃	1	2	yes	—
126	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
127	C₈	C₂²⋊Dic₄₃	1	2	yes	—
128	C₈	C₂²×Dic₄₃	1	1	yes	characteristic
129	C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
130	C₂²	—	2	1	no	—
131	C₂²	—	2	1	no	—
132	C₂²	—	4	2	no	—
133	C₂²	—	8	1	no	—
134	C₂²	—	8	1	no	—
135	C₂²	#13063246	1	2	yes	—
136	C₂²	C₂×#10621882	1	1	yes	characteristic
137	C₄	—	4	2	no	—
138	C₄	—	344	2	no	—
139	C₄	#13063246	1	2	yes	—
140	C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
141	C₄	C₂×#10621883	1	1	yes	characteristic
142	C₂	—	2	2	no	—
143	C₂	—	8	2	no	—
144	C₂	C₂×#13063246	1	1	yes	characteristic
145	C₂	#14583334	1	1	yes	characteristic
146	C₂	#14583339	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063265

C₂

yes

maximal, characteristic, complemented

C₂×#13063259

C₂

yes

maximal, characteristic, complemented

#14582703

C₂

yes

maximal, complemented

#14582700

C₂

yes

maximal, complemented

C₂×#135×C₄₃

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₄₃

—

#13063265

—

C₂×C₄₃⋊C₁₆

C₂²

yes

—

#13063259

—

#13063259

C₂²

yes

—

C₂×#41×C₄₃

—

#135×C₄₃

—

#135×C₄₃

C₄

yes

complemented

C₂×Q₁₆×C₄₃

C₂²

yes

characteristic

C₂×SD₁₆×C₄₃

—

C₂×D₈×C₄₃

C₂²

yes

characteristic

C₂²×C₈×C₄₃

C₂²

yes

characteristic

#41×C₄₃

—

#41×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×Dic₄₃

—

Q₁₆×C₄₃

—

Q₁₆×C₄₃

C₂×C₄

yes

complemented

SD₁₆×C₄₃

—

D₈×C₄₃

—

D₈×C₄₃

C₂×C₄

yes

complemented

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

—

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

—

C₂³×C₄₃

D₈

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂×C₄×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

SD₁₆

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

C₂²⋊C₄

yes

—

C₈×C₄₃

C₂²×C₄

yes

characteristic

C₈×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#102

yes

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

#102

yes

—

C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₄₃

C₂×SD₁₆

yes

characteristic

Dic₄₃

—

#2139

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

yes

characteristic

C₂×M₃₂

—

C₂×#107

—

#358

—

#357

—

C₄₃

#2139

yes

characteristic, complemented, Sylow

C₂×#41

—

#135

—

#135

Dic₄₃

yes

complemented

C₂×Q₁₆

C₂×D₄₃

yes

characteristic

C₂×SD₁₆

—

C₂×D₈

C₂×D₄₃

yes

characteristic

C₂²×C₈

C₂×D₄₃

yes

characteristic

C₂×C₄⋊C₄

—

M₃₂

—

C₂×C₁₆

—

—

—

—

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

172

—

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

100

Q₁₆

—

101

Q₁₆

C₂×Dic₄₃

yes

complemented

102

SD₁₆

—

103

D₈

—

104

D₈

C₂×Dic₄₃

yes

complemented

105

C₂×C₈

C₂×Dic₄₃

yes

—

106

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

107

C₂×C₈

C₂²⋊D₄₃

yes

—

108

C₂×C₈

C₂²×D₄₃

yes

characteristic

109

C₄⋊C₄

—

110

C₄⋊C₄

—

172

—

111

C₁₆

—

112

C₂³

—

113

C₂³

#10621882

yes

characteristic

114

Q₈

—

115

Q₈

—

116

D₄

—

117

D₄

—

118

D₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

344

—

122

C₂×C₄

—

172

—

123

C₂×C₄

#10621882

yes

characteristic

124

C₂×C₄

#10621883

yes

—

125

C₂×C₄

C₂²⋊Dic₄₃

yes

—

126

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

127

C₈

C₂²⋊Dic₄₃

yes

—

128

C₈

C₂²×Dic₄₃

yes

characteristic

129

C₈

C₂×C₂²⋊D₄₃

yes

characteristic

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

—

134

C₂²

—

135

C₂²

#13063246

yes

—

136

C₂²

C₂×#10621882

yes

characteristic

137

C₄

—

138

C₄

—

344

—

139

C₄

#13063246

yes

—

140

C₄

C₂×C₂²⋊Dic₄₃

yes

characteristic

141

C₄

C₂×#10621883

yes

characteristic

142

C₂

—

143

C₂

—

144

C₂

C₂×#13063246

yes

characteristic

145

C₂

#14583334

yes

characteristic

146

C₂

#14583339

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#10621882
commutator	C₈×C₄₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₂×#135×C₄₃	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	C₂×#135	D₄₃
hypocenter	C₄₃	#2139
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#135

subgroup

G/H

center

C₂²

C₂×#10621882

commutator

C₈×C₄₃

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₂×#135×C₄₃

C₂

socle

C₂²×C₄₃

C₂×D₈

D₄₃

C₄₃

G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#135

N	H ≅ G/N	type
1. C₂×#13063265	C₂	semidirect
2. C₂×#13063259	C₂	semidirect
3. #14582703	C₂	semidirect
4. #14582700	C₂	semidirect
13. #135×C₄₃	C₄	semidirect
27. Q₁₆×C₄₃	C₂×C₄	semidirect
30. D₈×C₄₃	C₂×C₄	semidirect
79. C₄₃	#2139	semidirect
82. #135	Dic₄₃	semidirect
101. Q₁₆	C₂×Dic₄₃	semidirect
104. D₈	C₂×Dic₄₃	semidirect

H ≅ G/N

type

1. C₂×#13063265

C₂

semidirect

2. C₂×#13063259

C₂

semidirect

3. #14582703

C₂

semidirect

4. #14582700

C₂

semidirect

13. #135×C₄₃

C₄

semidirect

27. Q₁₆×C₄₃

C₂×C₄

semidirect

30. D₈×C₄₃

C₂×C₄

semidirect

79. C₄₃

#2139

semidirect

82. #135

Dic₄₃

semidirect

101. Q₁₆

C₂×Dic₄₃

semidirect

104. D₈

C₂×Dic₄₃

semidirect

Subgroups — #19136307

Conjugacy classes of subgroups

Complements