Group #19134406 — subgroups

Subgroups — #19134406

Order 5504.

320 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 113 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	C₄×#10621898	C₂	1	1	yes	maximal, characteristic
2	C₂×#13063253	C₂	1	2	yes	maximal
3	C₄×#10621877	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582659	C₂	1	2	yes	maximal, complemented
5	C₄₃×#376	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10621898	C₂²	1	1	yes	characteristic
7	C₂×#10621877	C₂²	1	2	yes	—
8	C₄×Dic₈₆	C₄	1	2	yes	complemented
9	C₄×D₁₇₂	C₄	1	2	yes	complemented
10	C₄×C₂²⋊D₄₃	—	2	2	no	—
11	#13063284	C₂²	1	1	yes	characteristic
12	#13063282	—	2	1	no	—
13	C₄²×D₄₃	—	2	1	no	—
14	#13063253	C₄	1	8	yes	complemented
15	#13063236	—	2	1	no	—
16	C₄×C₄₃⋊C₈	—	2	1	no	—
17	C₂×C₄²×C₄₃	C₂²	1	2	yes	—
18	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
19	#95×C₄₃	—	2	2	no	—
20	C₂²×C₄×C₄₃	—	2	2	no	—
21	C₂²×C₄×C₄₃	D₄	1	2	yes	—
22	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
23	C₂×C₂²⋊D₄₃	—	2	1	no	—
24	#10621898	—	2	2	no	—
25	#10621898	C₂×C₄	1	4	yes	—
26	C₂×D₁₇₂	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄×D₄₃	—	2	1	no	—
28	C₂×C₄×D₄₃	—	2	2	no	—
29	C₂×Dic₈₆	C₂×C₄	1	1	yes	characteristic
30	C₄²×C₄₃	—	2	2	no	—
31	C₄²×C₄₃	C₂×C₄	1	2	yes	—
32	C₄²×C₄₃	C₂×C₄	1	4	yes	complemented
33	C₄²×C₄₃	D₄	1	1	yes	characteristic
34	C₄²×C₄₃	D₄	1	1	yes	characteristic
35	C₂²⋊Dic₄₃	—	2	1	no	—
36	(C₂×D₄₃)⋊C₄	—	2	2	no	—
37	C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
38	Dic₄₃⋊C₄	—	2	2	no	—
39	C₄×Dic₄₃	—	2	2	no	—
40	C₄×Dic₄₃	—	2	1	no	—
41	#10621877	—	2	2	no	—
42	#10621877	C₂×C₄	1	4	yes	complemented
43	C₂×C₄₃⋊C₈	—	2	2	no	—
44	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
45	C₂²×D₄₃	—	2	1	no	—
46	C₂×C₄×C₄₃	—	2	4	no	—
47	C₂×C₄×C₄₃	—	4	2	no	—
48	C₂×C₄×C₄₃	—	4	4	no	—
49	C₂×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
50	C₂×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
51	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
52	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
53	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
54	C₂×C₄×C₄₃	#41	1	2	yes	—
55	C₂²⋊D₄₃	—	2	4	no	—
56	C₂×Dic₄₃	—	2	1	no	—
57	C₂×Dic₄₃	—	2	2	no	—
58	D₁₇₂	—	2	1	no	—
59	D₁₇₂	C₄²	1	2	yes	—
60	C₄×D₄₃	—	2	4	no	—
61	C₄×D₄₃	—	4	4	no	—
62	Dic₈₆	—	2	1	no	—
63	Dic₈₆	C₄²	1	2	yes	—
64	C₄₃⋊C₈	—	2	4	no	—
65	C₂²×C₄₃	—	2	2	no	—
66	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
67	C₂²×C₄₃	C₄×D₄	1	2	yes	—
68	C₂×D₄₃	—	2	2	no	—
69	C₂×D₄₃	—	4	2	no	—
70	C₄×C₄₃	—	2	2	no	—
71	C₄×C₄₃	—	2	2	no	—
72	C₄×C₄₃	—	4	4	no	—
73	C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
74	C₄×C₄₃	#117	1	1	yes	characteristic
75	C₄×C₄₃	C₄×D₄	1	2	yes	—
76	Dic₄₃	—	2	2	no	—
77	Dic₄₃	—	4	2	no	—
78	#1759	—	43	1	no	maximal, Sylow
79	C₂×C₄₃	—	2	2	no	—
80	C₂×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₄₃	#421	1	2	yes	—
82	D₄₃	—	4	2	no	—
83	C₄×#41	—	43	1	no	—
84	C₂×#104	—	43	2	no	—
85	C₄×M₁₆	—	43	1	no	—
86	#376	D₄₃	1	1	yes	characteristic, complemented
87	#339	—	43	2	no	—
88	C₄₃	#1759	1	1	yes	characteristic, complemented, Sylow
89	C₂×#41	—	43	1	no	—
90	C₂×M₁₆	—	43	2	no	—
91	C₄×Q₈	—	43	2	no	—
92	C₄×D₄	—	43	2	no	—
93	C₄×D₄	—	86	2	no	—
94	#117	—	43	1	no	—
95	#117	—	86	1	no	—
96	C₂×C₄²	—	86	1	no	—
97	C₂×C₄²	C₂×D₄₃	1	2	yes	—
98	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
99	#104	—	43	8	no	—
100	#97	—	86	1	no	—
101	C₄×C₈	—	86	1	no	—
102	#95	—	2	2	no	—
103	#41	—	43	4	no	—
104	#41	—	86	2	no	—
105	C₂×Q₈	—	43	1	no	—
106	C₂×D₄	—	43	1	no	—
107	C₂×D₄	—	86	1	no	—
108	C₂²×C₄	—	2	2	no	—
109	C₂²×C₄	—	86	1	no	—
110	C₂²×C₄	—	86	2	no	—
111	C₂²×C₄	C₂²⋊D₄₃	1	2	yes	—
112	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
113	M₁₆	—	43	4	no	—
114	M₁₆	—	86	2	no	—
115	C₂×C₈	—	86	2	no	—
116	C₄⋊C₄	—	43	2	no	—
117	C₄⋊C₄	—	86	2	no	—
118	C₂²⋊C₄	—	86	1	no	—
119	C₂²⋊C₄	—	86	2	no	—
120	C₄²	—	2	2	no	—
121	C₄²	—	86	2	no	—
122	C₄²	—	86	1	no	—
123	C₄²	C₄×D₄₃	1	2	yes	—
124	C₄²	C₄×D₄₃	1	4	yes	complemented
125	C₄²	D₁₇₂	1	1	yes	characteristic
126	C₄²	D₁₇₂	1	1	yes	characteristic
127	C₂³	—	86	1	no	—
128	C₂³	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
129	Q₈	—	43	2	no	—
130	Q₈	—	86	1	no	—
131	D₄	—	43	2	no	—
132	D₄	—	86	4	no	—
133	D₄	—	86	1	no	—
134	C₂×C₄	—	2	4	no	—
135	C₂×C₄	—	4	2	no	—
136	C₂×C₄	—	4	4	no	—
137	C₂×C₄	—	86	1	no	—
138	C₂×C₄	—	86	4	no	—
139	C₂×C₄	—	86	2	no	—
140	C₂×C₄	—	172	4	no	—
141	C₂×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
142	C₂×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
143	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
144	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
145	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
146	C₂×C₄	#10621898	1	2	yes	—
147	C₈	—	86	4	no	—
148	C₂²	—	2	2	no	—
149	C₂²	—	86	2	no	—
150	C₂²	—	172	2	no	—
151	C₂²	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
152	C₂²	C₄×C₂²⋊D₄₃	1	2	yes	—
153	C₄	—	2	2	no	—
154	C₄	—	2	2	no	—
155	C₄	—	4	4	no	—
156	C₄	—	86	2	no	—
157	C₄	—	172	2	no	—
158	C₄	C₄²×D₄₃	1	1	yes	characteristic
159	C₄	#13063282	1	1	yes	characteristic
160	C₄	C₄×D₁₇₂	1	2	yes	—
161	C₂	—	2	2	no	—
162	C₂	—	172	2	no	—
163	C₂	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
164	C₂	#14582917	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#10621898

C₂

yes

maximal, characteristic

C₂×#13063253

C₂

yes

maximal

C₄×#10621877

C₂

yes

maximal, characteristic, complemented

#14582659

C₂

yes

maximal, complemented

C₄₃×#376

C₂

yes

maximal, characteristic, complemented

C₂×#10621898

C₂²

yes

characteristic

C₂×#10621877

C₂²

yes

—

C₄×Dic₈₆

C₄

yes

complemented

C₄×D₁₇₂

C₄

yes

complemented

C₄×C₂²⋊D₄₃

—

#13063284

C₂²

yes

characteristic

#13063282

—

C₄²×D₄₃

—

#13063253

C₄

yes

complemented

#13063236

—

C₄×C₄₃⋊C₈

—

C₂×C₄²×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

#95×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂×C₂²⋊D₄₃

—

#10621898

—

#10621898

C₂×C₄

yes

—

C₂×D₁₇₂

C₂×C₄

yes

characteristic

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×Dic₈₆

C₂×C₄

yes

characteristic

C₄²×C₄₃

—

C₄²×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

C₂×C₄

yes

complemented

C₄²×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

C₂²⋊Dic₄₃

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

C₂×C₄

yes

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

#10621877

—

#10621877

C₂×C₄

yes

complemented

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

C₄²

yes

—

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

Dic₈₆

C₄²

yes

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₄₃

C₄×D₄

yes

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×C₄²

yes

characteristic

C₄×C₄₃

#117

yes

characteristic

C₄×C₄₃

C₄×D₄

yes

—

Dic₄₃

—

Dic₄₃

—

#1759

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₄×C₂²⋊C₄

yes

characteristic

C₂×C₄₃

#421

yes

—

D₄₃

—

C₄×#41

—

C₂×#104

—

C₄×M₁₆

—

#376

D₄₃

yes

characteristic, complemented

#339

—

C₄₃

#1759

yes

characteristic, complemented, Sylow

C₂×#41

—

C₂×M₁₆

—

C₄×Q₈

—

C₄×D₄

—

C₄×D₄

—

#117

—

#117

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₃

yes

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

#104

—

100

#97

—

101

C₄×C₈

—

102

#95

—

103

#41

—

104

#41

—

105

C₂×Q₈

—

106

C₂×D₄

—

107

C₂×D₄

—

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

C₂²⋊D₄₃

yes

—

112

C₂²×C₄

C₂²×D₄₃

yes

characteristic

113

M₁₆

—

114

M₁₆

—

115

C₂×C₈

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₂²⋊C₄

—

119

C₂²⋊C₄

—

120

C₄²

—

121

C₄²

—

122

C₄²

—

123

C₄²

C₄×D₄₃

yes

—

124

C₄²

C₄×D₄₃

yes

complemented

125

C₄²

D₁₇₂

yes

characteristic

126

C₄²

D₁₇₂

yes

characteristic

127

C₂³

—

128

C₂³

C₂×C₂²⋊D₄₃

yes

characteristic

129

Q₈

—

130

Q₈

—

131

D₄

—

132

D₄

—

133

D₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

172

—

141

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

—

142

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

—

143

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

144

C₂×C₄

C₂×C₄×D₄₃

yes

—

145

C₂×C₄

C₂×D₁₇₂

yes

characteristic

146

C₂×C₄

#10621898

yes

—

147

C₈

—

148

C₂²

—

149

C₂²

—

150

C₂²

—

172

—

151

C₂²

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

152

C₂²

C₄×C₂²⋊D₄₃

yes

—

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

—

157

C₄

—

172

—

158

C₄

C₄²×D₄₃

yes

characteristic

159

C₄

#13063282

yes

characteristic

160

C₄

C₄×D₁₇₂

yes

—

161

C₂

—

162

C₂

—

172

—

163

C₂

C₄×(C₂×D₄₃)⋊C₄

yes

characteristic

164

C₂

#14582917

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×D₁₇₂
commutator	C₄×C₄₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#376	C₂
socle	C₂²×C₄₃	C₂×C₂²⋊C₄
hypercenter	#376	D₄₃
hypocenter	C₄₃	#1759
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #376

subgroup

G/H

center

C₂×C₄

C₂×D₁₇₂

commutator

C₄×C₄₃

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#376

C₂

socle

C₂²×C₄₃

C₂×C₂²⋊C₄

D₄₃

C₄₃

G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #376

N	H ≅ G/N	type
3. C₄×#10621877	C₂	semidirect
4. #14582659	C₂	semidirect
5. C₄₃×#376	C₂	semidirect
8. C₄×Dic₈₆	C₄	semidirect
9. C₄×D₁₇₂	C₄	semidirect
14. #13063253	C₄	semidirect
32. C₄²×C₄₃	C₂×C₄	semidirect
42. #10621877	C₂×C₄	semidirect
86. #376	D₄₃	semidirect
88. C₄₃	#1759	semidirect
124. C₄²	C₄×D₄₃	semidirect

H ≅ G/N

type

3. C₄×#10621877

C₂

semidirect

4. #14582659

C₂

semidirect

5. C₄₃×#376

C₂

semidirect

8. C₄×Dic₈₆

C₄

semidirect

9. C₄×D₁₇₂

C₄

semidirect

14. #13063253

C₄

semidirect

32. C₄²×C₄₃

C₂×C₄

semidirect

42. #10621877

C₂×C₄

semidirect

86. #376

D₄₃

semidirect

88. C₄₃

#1759

semidirect

124. C₄²

C₄×D₄₃

semidirect

Subgroups — #19134406

Conjugacy classes of subgroups

Complements