Group #19145033 — subgroups

Subgroups — C₂×#14583291 #19145033

Order 5504.

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	C₂²×#10621885	C₂	1	2	yes	maximal, complemented
2	C₂²×#10621884	C₂	1	2	yes	maximal
3	C₂×#13063313	C₂	1	1	yes	maximal, characteristic
4	#14583291	C₂	1	8	yes	maximal, direct product factor
5	C₂×#13063236	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄⋊Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
8	C₂²×D₁₇₂	C₂²	1	1	yes	characteristic
9	C₂×#10621885	—	2	8	no	—
10	C₂×#10621885	C₂²	1	8	yes	complemented
11	C₂×#10621884	—	2	8	no	—
12	C₂×#10621884	C₂²	1	8	yes	—
13	C₂²×C₄₃⋊C₈	C₂²	1	2	yes	—
14	#13063313	—	2	2	no	—
15	#13063313	C₂²	1	4	yes	—
16	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
17	#13063236	C₂²	1	4	yes	complemented
18	C₂²×Q₈×C₄₃	C₂²	1	2	yes	—
19	C₄⋊Q₈×C₄₃	—	2	2	no	—
20	C₄⋊Q₈×C₄₃	C₂²	1	4	yes	complemented
21	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
22	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
23	C₂³×D₄₃	—	2	1	no	—
24	C₂×Q₈×C₄₃	—	2	2	no	—
25	C₂×Q₈×C₄₃	—	2	4	no	—
26	C₂×Q₈×C₄₃	—	2	4	no	—
27	C₂×Q₈×C₄₃	C₂³	1	4	yes	—
28	C₂²×C₄×C₄₃	—	2	2	no	—
29	C₂²×C₄×C₄₃	D₄	1	2	yes	—
30	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
31	C₂²×Dic₄₃	—	2	1	no	—
32	C₂×D₁₇₂	—	2	1	no	—
33	C₂×D₁₇₂	—	2	4	no	—
34	C₂×D₁₇₂	C₂³	1	2	yes	—
35	C₂×Dic₈₆	—	2	4	no	—
36	C₂×Dic₈₆	—	2	1	no	—
37	C₂×Dic₈₆	C₂³	1	2	yes	—
38	C₄⋊C₄×C₄₃	—	2	8	no	—
39	C₄²×C₄₃	D₄	1	2	yes	—
40	C₄²×C₄₃	C₂³	1	2	yes	—
41	#10621885	—	2	16	no	—
42	#10621884	—	2	16	no	—
43	(C₂×D₄₃)⋊C₄	—	2	8	no	—
44	C₂×C₄₃⋊C₈	D₄	1	8	yes	—
45	C₂×C₄₃⋊C₈	C₂³	1	4	yes	—
46	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
47	C₂²×D₄₃	—	2	2	no	—
48	C₂²×D₄₃	—	4	2	no	—
49	C₂²×D₄₃	—	4	4	no	—
50	Q₈×C₄₃	—	2	4	no	—
51	Q₈×C₄₃	—	2	4	no	—
52	Q₈×C₄₃	—	4	4	no	—
53	C₂×C₄×C₄₃	—	2	4	no	—
54	C₂×C₄×C₄₃	—	2	4	no	—
55	C₂×C₄×C₄₃	—	4	4	no	—
56	C₂×C₄×C₄₃	C₂×D₄	1	4	yes	—
57	C₂×C₄×C₄₃	C₂×D₄	1	4	yes	—
58	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
59	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
60	C₂×Dic₄₃	—	2	2	no	—
61	C₂×Dic₄₃	—	4	2	no	—
62	D₁₇₂	—	2	4	no	—
63	D₁₇₂	—	4	2	no	—
64	Dic₈₆	—	2	4	no	—
65	Dic₈₆	—	4	2	no	—
66	C₄₃⋊C₈	C₂×D₄	1	8	yes	—
67	C₂²×C₄₃	#127	1	2	yes	—
68	C₂²×C₄₃	#137	1	4	yes	—
69	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
70	C₂×D₄₃	—	4	2	no	—
71	C₂×D₄₃	—	4	4	no	—
72	C₂×D₄₃	—	8	4	no	—
73	C₄×C₄₃	—	2	4	no	—
74	C₄×C₄₃	—	4	4	no	—
75	C₄×C₄₃	#127	1	2	yes	—
76	C₄×C₄₃	C₂²×D₄	1	2	yes	—
77	Dic₄₃	—	4	2	no	—
78	C₂×#497	—	43	1	no	maximal, Sylow
79	C₂×C₄₃	#497	1	4	yes	complemented
80	C₂×C₄₃	C₂×#127	1	1	yes	characteristic
81	C₂×C₄₃	C₂×#137	1	2	yes	—
82	D₄₃	—	8	2	no	—
83	C₂²×Q₁₆	—	43	2	no	—
84	C₂²×SD₁₆	—	43	2	no	—
85	C₂×C₄⋊Q₈	D₄₃	1	1	yes	characteristic, complemented
86	C₂×#124	—	43	1	no	—
87	#497	—	43	8	no	—
88	C₂×#97	—	43	1	no	—
89	C₄₃	C₂×#497	1	1	yes	characteristic, complemented, Sylow
90	C₂²×Q₈	—	43	1	no	—
91	C₂²×Q₈	C₂×D₄₃	1	2	yes	—
92	C₂²×D₄	—	43	1	no	—
93	C₂×Q₁₆	—	43	8	no	—
94	C₂×Q₁₆	—	86	8	no	—
95	C₂×SD₁₆	—	43	8	no	—
96	C₂×SD₁₆	—	86	8	no	—
97	C₂²×C₈	—	43	2	no	—
98	C₄⋊Q₈	—	2	2	no	—
99	C₄⋊Q₈	C₂×D₄₃	1	4	yes	complemented
100	#124	—	43	4	no	—
101	#124	—	86	2	no	—
102	C₂×C₄⋊C₄	—	2	2	no	—
103	C₂×C₂²⋊C₄	—	86	2	no	—
104	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
105	#97	—	43	4	no	—
106	C₂⁴	—	86	1	no	—
107	C₂×Q₈	—	2	2	no	—
108	C₂×Q₈	—	2	4	no	—
109	C₂×Q₈	—	2	4	no	—
110	C₂×Q₈	—	43	2	no	—
111	C₂×Q₈	—	86	1	no	—
112	C₂×Q₈	—	86	4	no	—
113	C₂×Q₈	C₂²×D₄₃	1	4	yes	—
114	C₂×D₄	—	43	2	no	—
115	C₂×D₄	—	86	4	no	—
116	C₂×D₄	—	86	1	no	—
117	C₂²×C₄	—	2	2	no	—
118	C₂²×C₄	—	86	1	no	—
119	C₂²×C₄	C₂²⋊D₄₃	1	2	yes	—
120	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
121	Q₁₆	—	86	16	no	—
122	SD₁₆	—	86	16	no	—
123	C₂×C₈	—	43	8	no	—
124	C₂×C₈	—	43	4	no	—
125	C₄⋊C₄	—	2	8	no	—
126	C₂²⋊C₄	—	86	8	no	—
127	C₄²	C₂²⋊D₄₃	1	2	yes	—
128	C₄²	C₂²×D₄₃	1	2	yes	—
129	C₂³	—	86	2	no	—
130	C₂³	—	172	2	no	—
131	C₂³	—	172	4	no	—
132	C₂³	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
133	Q₈	—	2	4	no	—
134	Q₈	—	2	4	no	—
135	Q₈	—	4	4	no	—
136	Q₈	—	86	4	no	—
137	Q₈	—	172	2	no	—
138	D₄	—	86	4	no	—
139	D₄	—	172	2	no	—
140	C₂×C₄	—	2	4	no	—
141	C₂×C₄	—	2	4	no	—
142	C₂×C₄	—	4	4	no	—
143	C₂×C₄	—	86	2	no	—
144	C₂×C₄	—	172	2	no	—
145	C₂×C₄	D₄×D₄₃	1	4	yes	—
146	C₂×C₄	C₂×C₂²⋊D₄₃	1	4	yes	—
147	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
148	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
149	C₈	—	43	8	no	—
150	C₂²	—	344	4	no	—
151	C₂²	—	172	4	no	—
152	C₂²	—	172	2	no	—
153	C₂²	#13063321	1	2	yes	—
154	C₂²	#13063356	1	4	yes	—
155	C₂²	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
156	C₄	—	2	4	no	—
157	C₄	—	4	4	no	—
158	C₄	—	172	2	no	—
159	C₄	#13063321	1	2	yes	—
160	C₄	C₂×D₄×D₄₃	1	2	yes	—
161	C₂	—	344	2	no	—
162	C₂	#14583291	1	4	yes	direct product factor
163	C₂	C₂×#13063321	1	1	yes	characteristic
164	C₂	C₂×#13063356	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#10621885

C₂

yes

maximal, complemented

C₂²×#10621884

C₂

yes

maximal

C₂×#13063313

C₂

yes

maximal, characteristic

#14583291

C₂

yes

maximal, direct product factor

C₂×#13063236

C₂

yes

maximal, characteristic, complemented

C₂×C₄⋊Q₈×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂²×Dic₈₆

C₂²

yes

characteristic

C₂²×D₁₇₂

C₂²

yes

characteristic

C₂×#10621885

—

C₂×#10621885

C₂²

yes

complemented

C₂×#10621884

—

C₂×#10621884

C₂²

yes

—

C₂²×C₄₃⋊C₈

C₂²

yes

—

#13063313

—

#13063313

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

—

#13063236

C₂²

yes

complemented

C₂²×Q₈×C₄₃

C₂²

yes

—

C₄⋊Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

C₂²

yes

complemented

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂³×D₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

C₂³

yes

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

C₂³

yes

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

D₄

yes

—

C₄²×C₄₃

C₂³

yes

—

#10621885

—

#10621884

—

(C₂×D₄₃)⋊C₄

—

C₂×C₄₃⋊C₈

D₄

yes

—

C₂×C₄₃⋊C₈

C₂³

yes

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

Dic₈₆

—

Dic₈₆

—

C₄₃⋊C₈

C₂×D₄

yes

—

C₂²×C₄₃

#127

yes

—

C₂²×C₄₃

#137

yes

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#127

yes

—

C₄×C₄₃

C₂²×D₄

yes

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

D₄₃

—

C₂²×Q₁₆

—

C₂²×SD₁₆

—

C₂×C₄⋊Q₈

D₄₃

yes

characteristic, complemented

C₂×#124

—

#497

—

C₂×#97

—

C₄₃

C₂×#497

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×Q₈

C₂×D₄₃

yes

—

C₂²×D₄

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×SD₁₆

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₄₃

yes

complemented

100

#124

—

101

#124

—

102

C₂×C₄⋊C₄

—

103

C₂×C₂²⋊C₄

—

104

C₂×C₄²

C₂×D₄₃

yes

characteristic

105

#97

—

106

C₂⁴

—

107

C₂×Q₈

—

108

C₂×Q₈

—

109

C₂×Q₈

—

110

C₂×Q₈

—

111

C₂×Q₈

—

112

C₂×Q₈

—

113

C₂×Q₈

C₂²×D₄₃

yes

—

114

C₂×D₄

—

115

C₂×D₄

—

116

C₂×D₄

—

117

C₂²×C₄

—

118

C₂²×C₄

—

119

C₂²×C₄

C₂²⋊D₄₃

yes

—

120

C₂²×C₄

C₂²×D₄₃

yes

characteristic

121

Q₁₆

—

122

SD₁₆

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₄⋊C₄

—

126

C₂²⋊C₄

—

127

C₄²

C₂²⋊D₄₃

yes

—

128

C₄²

C₂²×D₄₃

yes

—

129

C₂³

—

130

C₂³

—

172

—

131

C₂³

—

172

—

132

C₂³

C₂×C₂²⋊D₄₃

yes

characteristic

133

Q₈

—

134

Q₈

—

135

Q₈

—

136

Q₈

—

137

Q₈

—

172

—

138

D₄

—

139

D₄

—

172

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

172

—

145

C₂×C₄

D₄×D₄₃

yes

—

146

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

147

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

148

C₂×C₄

C₂³×D₄₃

yes

characteristic

149

C₈

—

150

C₂²

—

344

—

151

C₂²

—

172

—

152

C₂²

—

172

—

153

C₂²

#13063321

yes

—

154

C₂²

#13063356

yes

—

155

C₂²

C₂²×C₂²⋊D₄₃

yes

characteristic

156

C₄

—

157

C₄

—

158

C₄

—

172

—

159

C₄

#13063321

yes

—

160

C₄

C₂×D₄×D₄₃

yes

—

161

C₂

—

344

—

162

C₂

#14583291

yes

direct product factor

163

C₂

C₂×#13063321

yes

characteristic

164

C₂

C₂×#13063356

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₂×C₄⋊Q₈×C₄₃	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	C₂×C₄⋊Q₈	D₄₃
hypocenter	C₄₃	C₂×#497
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊Q₈

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₄₃

commutator

C₂×C₄×C₄₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₂×C₄⋊Q₈×C₄₃

C₂

socle

C₂³×C₄₃

C₂×D₄

hypercenter

C₂×C₄⋊Q₈

D₄₃

hypocenter

C₄₃

C₂×#497

LCS

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
1. C₂²×#10621885	C₂	semidirect
4. #14583291	C₂	direct (N × H)
5. C₂×#13063236	C₂	semidirect
6. C₂×C₄⋊Q₈×C₄₃	C₂	semidirect
10. C₂×#10621885	C₂²	semidirect
17. #13063236	C₂²	semidirect
20. C₄⋊Q₈×C₄₃	C₂²	semidirect
79. C₂×C₄₃	#497	semidirect
85. C₂×C₄⋊Q₈	D₄₃	semidirect
89. C₄₃	C₂×#497	semidirect
99. C₄⋊Q₈	C₂×D₄₃	semidirect
162. C₂	#14583291	direct (N × H)

H ≅ G/N

type

1. C₂²×#10621885

C₂

semidirect

4. #14583291

C₂

direct (N × H)

5. C₂×#13063236

C₂

semidirect

6. C₂×C₄⋊Q₈×C₄₃

C₂

semidirect

10. C₂×#10621885

C₂²

semidirect

17. #13063236

C₂²

semidirect

20. C₄⋊Q₈×C₄₃

C₂²

semidirect

79. C₂×C₄₃

#497

semidirect

85. C₂×C₄⋊Q₈

D₄₃

semidirect

89. C₄₃

C₂×#497

semidirect

99. C₄⋊Q₈

C₂×D₄₃

semidirect

162. C₂

#14583291

direct (N × H)

Subgroups — C₂×#14583291 #19145033

Conjugacy classes of subgroups

Complements

Subgroups — C2×#14583291 #19145033

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14583291 #19145033