Group #19143387 — subgroups

Subgroups — C₂×#14583010 #19143387

Order 5504.

608 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 197 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×D₃₄₄	C₂	1	1	yes	maximal, characteristic
2	C₂×#13063287	C₂	1	2	yes	maximal, complemented
3	#14583010	C₂	1	8	yes	maximal, direct product factor
4	C₂×#13063245	C₂	1	2	yes	maximal, complemented
5	C₂×#13063235	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#106×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×D₁₇₂	C₂²	1	2	yes	—
8	C₂²×C₄×D₄₃	—	2	2	no	—
9	C₂×D₃₄₄	C₄	1	8	yes	complemented
10	C₂×D₃₄₄	C₂²	1	4	yes	—
11	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
12	#13063287	—	2	4	no	—
13	#13063287	C₂²	1	8	yes	complemented
14	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
15	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
16	#13063245	C₂²	1	8	yes	complemented
17	#13063235	C₂²	1	4	yes	complemented
18	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
20	#106×C₄₃	C₂²	1	4	yes	complemented
21	C₂³×D₄₃	—	2	2	no	—
22	C₂²×C₄×C₄₃	—	2	2	no	—
23	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
24	C₂²×Dic₄₃	D₄	1	2	yes	—
25	C₂×D₁₇₂	—	2	2	no	—
26	C₂×D₁₇₂	—	2	4	no	—
27	C₂×D₁₇₂	C₂×C₄	1	8	yes	complemented
28	C₂×D₁₇₂	C₂³	1	4	yes	—
29	C₂×C₄×D₄₃	—	2	8	no	—
30	C₂×C₄×D₄₃	—	4	8	no	—
31	C₂×C₈×C₄₃	C₂×C₄	1	4	yes	complemented
32	C₂×C₈×C₄₃	C₂³	1	2	yes	—
33	C₄⋊C₄×C₄₃	—	2	2	no	—
34	C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
35	(C₂×D₄₃)⋊C₄	—	2	8	no	—
36	C₄×Dic₄₃	D₄	1	2	yes	—
37	C₄×Dic₄₃	C₂³	1	2	yes	—
38	C₂×C₄₃⋊C₈	—	2	2	no	—
39	C₂×C₄₃⋊C₈	C₂³	1	2	yes	—
40	D₃₄₄	C₂×C₄	1	16	yes	complemented
41	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
42	C₂²×D₄₃	—	2	8	no	—
43	C₂²×D₄₃	—	2	4	no	—
44	C₂²×D₄₃	—	4	4	no	—
45	C₂²×D₄₃	—	4	4	no	—
46	C₂×C₄×C₄₃	—	2	4	no	—
47	C₂×C₄×C₄₃	—	4	4	no	—
48	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
49	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₄₃	#41	1	2	yes	—
51	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
52	C₂×Dic₄₃	—	2	4	no	—
53	C₂×Dic₄₃	C₂×D₄	1	4	yes	—
54	D₁₇₂	—	2	8	no	—
55	D₁₇₂	—	2	4	no	—
56	D₁₇₂	C₂²×C₄	1	8	yes	complemented
57	C₄×D₄₃	—	4	16	no	—
58	C₈×C₄₃	C₂²×C₄	1	4	yes	complemented
59	C₄₃⋊C₈	—	2	2	no	—
60	C₂²×C₄₃	C₄×D₄	1	2	yes	—
61	C₂²×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
62	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
63	C₂×D₄₃	—	2	8	no	—
64	C₂×D₄₃	—	4	4	no	—
65	C₂×D₄₃	—	4	4	no	—
66	C₂×D₄₃	—	4	16	no	—
67	C₄×C₄₃	—	4	4	no	—
68	C₄×C₄₃	C₄×D₄	1	2	yes	—
69	C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
70	C₄×C₄₃	C₂×#41	1	1	yes	characteristic
71	Dic₄₃	—	2	4	no	—
72	C₂×#442	—	43	1	no	maximal, Sylow
73	C₂×C₄₃	#442	1	4	yes	complemented
74	C₂×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
75	C₂×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
76	D₄₃	—	4	8	no	—
77	C₂²×D₈	—	43	1	no	—
78	C₂×C₄×D₄	—	43	2	no	—
79	#442	—	43	8	no	—
80	C₂×#106	D₄₃	1	1	yes	characteristic, complemented
81	C₂×#102	—	43	2	no	—
82	C₂×#97	—	43	1	no	—
83	C₄₃	C₂×#442	1	1	yes	characteristic, complemented, Sylow
84	C₂²×D₄	—	43	2	no	—
85	C₂³×C₄	—	86	2	no	—
86	C₂×D₈	—	43	4	no	—
87	C₂×D₈	—	43	8	no	—
88	C₂²×C₈	—	43	1	no	—
89	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
90	C₄×D₄	—	43	8	no	—
91	C₄×D₄	—	86	4	no	—
92	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
93	C₂×C₂²⋊C₄	—	86	2	no	—
94	C₂×C₄²	—	43	1	no	—
95	#106	C₂×D₄₃	1	4	yes	complemented
96	#102	—	43	8	no	—
97	#97	—	43	4	no	—
98	C₂⁴	—	86	2	no	—
99	C₂×D₄	—	43	8	no	—
100	C₂×D₄	—	43	4	no	—
101	C₂×D₄	—	86	2	no	—
102	C₂×D₄	—	86	4	no	—
103	C₂²×C₄	—	2	2	no	—
104	C₂²×C₄	—	43	2	no	—
105	C₂²×C₄	—	86	8	no	—
106	C₂²×C₄	—	172	8	no	—
107	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
108	D₈	—	43	16	no	—
109	C₂×C₈	—	43	2	no	—
110	C₂×C₈	—	86	2	no	—
111	C₂×C₈	C₄×D₄₃	1	4	yes	complemented
112	C₂×C₈	C₂²×D₄₃	1	2	yes	—
113	C₄⋊C₄	—	2	2	no	—
114	C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
115	C₂²⋊C₄	—	86	8	no	—
116	C₄²	—	43	2	no	—
117	C₄²	—	43	2	no	—
118	C₂³	—	86	8	no	—
119	C₂³	—	86	4	no	—
120	C₂³	—	172	4	no	—
121	C₂³	—	172	4	no	—
122	C₂³	D₄×D₄₃	1	1	yes	characteristic
123	D₄	—	43	8	no	—
124	D₄	—	86	8	no	—
125	D₄	—	86	4	no	—
126	C₂×C₄	—	2	4	no	—
127	C₂×C₄	—	4	4	no	—
128	C₂×C₄	—	43	4	no	—
129	C₂×C₄	—	86	4	no	—
130	C₂×C₄	—	172	16	no	—
131	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
132	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
133	C₂×C₄	#10621902	1	2	yes	—
134	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
135	C₈	—	86	2	no	—
136	C₈	C₂×C₄×D₄₃	1	4	yes	complemented
137	C₂²	—	86	8	no	—
138	C₂²	—	172	4	no	—
139	C₂²	—	172	4	no	—
140	C₂²	—	172	16	no	—
141	C₂²	#13063287	1	2	yes	—
142	C₂²	#13063352	1	4	yes	—
143	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
144	C₄	—	4	4	no	—
145	C₄	—	86	4	no	—
146	C₄	#13063287	1	2	yes	—
147	C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
148	C₄	C₂×#10621902	1	1	yes	characteristic
149	C₂	—	172	8	no	—
150	C₂	#14583010	1	4	yes	direct product factor
151	C₂	C₂×#13063287	1	1	yes	characteristic
152	C₂	C₂×#13063352	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×D₃₄₄

C₂

yes

maximal, characteristic

C₂×#13063287

C₂

yes

maximal, complemented

#14583010

C₂

yes

maximal, direct product factor

C₂×#13063245

C₂

yes

maximal, complemented

C₂×#13063235

C₂

yes

maximal, characteristic, complemented

C₂×#106×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₇₂

C₂²

yes

—

C₂²×C₄×D₄₃

—

C₂×D₃₄₄

C₄

yes

complemented

C₂×D₃₄₄

C₂²

yes

—

C₂²×C₄₃⋊C₈

C₂²

yes

characteristic

#13063287

—

#13063287

C₂²

yes

complemented

C₂×(C₂×D₄₃)⋊C₄

—

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

#13063245

C₂²

yes

complemented

#13063235

C₂²

yes

complemented

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

#106×C₄₃

C₂²

yes

complemented

C₂³×D₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

D₄

yes

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

C₂×C₄

yes

complemented

C₂×D₁₇₂

C₂³

yes

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₈×C₄₃

C₂×C₄

yes

complemented

C₂×C₈×C₄₃

C₂³

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

C₂³

yes

—

(C₂×D₄₃)⋊C₄

—

C₄×Dic₄₃

D₄

yes

—

C₄×Dic₄₃

C₂³

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₂³

yes

—

D₃₄₄

C₂×C₄

yes

complemented

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂×D₄

yes

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

C₂²×C₄

yes

complemented

C₄×D₄₃

—

C₈×C₄₃

C₂²×C₄

yes

complemented

C₄₃⋊C₈

—

C₂²×C₄₃

C₄×D₄

yes

—

C₂²×C₄₃

AGL(1,ℤ/8)

yes

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₄×D₄

yes

—

C₄×C₄₃

C₂³×C₄

yes

characteristic

C₄×C₄₃

C₂×#41

yes

characteristic

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

C₂×C₄×D₄

yes

characteristic

C₂×C₄₃

C₂×AGL(1,ℤ/8)

yes

—

D₄₃

—

C₂²×D₈

—

C₂×C₄×D₄

—

#442

—

C₂×#106

D₄₃

yes

characteristic, complemented

C₂×#102

—

C₂×#97

—

C₄₃

C₂×#442

yes

characteristic, complemented, Sylow

C₂²×D₄

—

C₂³×C₄

—

C₂×D₈

—

C₂×D₈

—

C₂²×C₈

—

C₂²×C₈

C₂×D₄₃

yes

characteristic

C₄×D₄

—

C₄×D₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

#106

C₂×D₄₃

yes

complemented

#102

—

#97

—

C₂⁴

—

C₂×D₄

—

100

C₂×D₄

—

101

C₂×D₄

—

102

C₂×D₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

172

—

107

C₂²×C₄

C₂²×D₄₃

yes

characteristic

108

D₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

C₄×D₄₃

yes

complemented

112

C₂×C₈

C₂²×D₄₃

yes

—

113

C₄⋊C₄

—

114

C₄⋊C₄

C₂²×D₄₃

yes

—

115

C₂²⋊C₄

—

116

C₄²

—

117

C₄²

—

118

C₂³

—

119

C₂³

—

120

C₂³

—

172

—

121

C₂³

—

172

—

122

C₂³

D₄×D₄₃

yes

characteristic

123

D₄

—

124

D₄

—

125

D₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

172

—

131

C₂×C₄

C₂×C₄×D₄₃

yes

—

132

C₂×C₄

D₄×D₄₃

yes

characteristic

133

C₂×C₄

#10621902

yes

—

134

C₂×C₄

C₂³×D₄₃

yes

characteristic

135

C₈

—

136

C₈

C₂×C₄×D₄₃

yes

complemented

137

C₂²

—

138

C₂²

—

172

—

139

C₂²

—

172

—

140

C₂²

—

172

—

141

C₂²

#13063287

yes

—

142

C₂²

#13063352

yes

—

143

C₂²

C₂×D₄×D₄₃

yes

characteristic

144

C₄

—

145

C₄

—

146

C₄

#13063287

yes

—

147

C₄

C₂²×C₄×D₄₃

yes

characteristic

148

C₄

C₂×#10621902

yes

characteristic

149

C₂

—

172

—

150

C₂

#14583010

yes

direct product factor

151

C₂

C₂×#13063287

yes

characteristic

152

C₂

C₂×#13063352

yes

—

	subgroup	G/H
center	C₂³	D₄×D₄₃
commutator	C₄×C₄₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₂×#106×C₄₃	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	C₂×#106	D₄₃
hypocenter	C₄₃	C₂×#442
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#106

subgroup

G/H

center

C₂³

D₄×D₄₃

commutator

C₄×C₄₃

C₂³×C₄

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₂×#106×C₄₃

C₂

socle

C₂³×C₄₃

C₂×D₄

D₄₃

C₄₃

G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#106

N	H ≅ G/N	type
2. C₂×#13063287	C₂	semidirect
3. #14583010	C₂	direct (N × H)
4. C₂×#13063245	C₂	semidirect
5. C₂×#13063235	C₂	semidirect
6. C₂×#106×C₄₃	C₂	semidirect
9. C₂×D₃₄₄	C₄	semidirect
13. #13063287	C₂²	semidirect
16. #13063245	C₂²	semidirect
17. #13063235	C₂²	semidirect
20. #106×C₄₃	C₂²	semidirect
27. C₂×D₁₇₂	C₂×C₄	semidirect
31. C₂×C₈×C₄₃	C₂×C₄	semidirect
40. D₃₄₄	C₂×C₄	semidirect
56. D₁₇₂	C₂²×C₄	semidirect
58. C₈×C₄₃	C₂²×C₄	semidirect
73. C₂×C₄₃	#442	semidirect
80. C₂×#106	D₄₃	semidirect
83. C₄₃	C₂×#442	semidirect
95. #106	C₂×D₄₃	semidirect
111. C₂×C₈	C₄×D₄₃	semidirect
136. C₈	C₂×C₄×D₄₃	semidirect
150. C₂	#14583010	direct (N × H)

H ≅ G/N

type

2. C₂×#13063287

C₂

semidirect

3. #14583010

C₂

direct (N × H)

4. C₂×#13063245

C₂

semidirect

5. C₂×#13063235

C₂

semidirect

6. C₂×#106×C₄₃

C₂

semidirect

9. C₂×D₃₄₄

C₄

semidirect

13. #13063287

C₂²

semidirect

16. #13063245

C₂²

semidirect

17. #13063235

C₂²

semidirect

20. #106×C₄₃

C₂²

semidirect

27. C₂×D₁₇₂

C₂×C₄

semidirect

31. C₂×C₈×C₄₃

C₂×C₄

semidirect

40. D₃₄₄

C₂×C₄

semidirect

56. D₁₇₂

C₂²×C₄

semidirect

58. C₈×C₄₃

C₂²×C₄

semidirect

73. C₂×C₄₃

#442

semidirect

80. C₂×#106

D₄₃

semidirect

83. C₄₃

C₂×#442

semidirect

95. #106

C₂×D₄₃

semidirect

111. C₂×C₈

C₄×D₄₃

semidirect

136. C₈

C₂×C₄×D₄₃

semidirect

150. C₂

#14583010

direct (N × H)

Subgroups — C₂×#14583010 #19143387

Conjugacy classes of subgroups

Complements

Subgroups — C2×#14583010 #19143387

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14583010 #19143387