Group #19133247 — subgroups

Subgroups — C₂×#14582647 #19133247

Order 5504.

256 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 117 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×#13063325	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	#14582647	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄⋊C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₈₆	C₄	1	2	yes	—
6	C₂²×C₄₃⋊C₈	—	2	1	no	—
7	#13063325	—	2	1	no	—
8	#13063325	—	2	1	no	—
9	#13063325	C₄	1	2	yes	—
10	#13063325	C₂²	1	2	yes	—
11	C₂×C₄⋊Dic₄₃	—	2	1	no	—
12	C₂×C₄⋊Dic₄₃	—	2	1	no	—
13	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
14	C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
15	C₂²×C₈×C₄₃	—	2	1	no	—
16	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
17	C₄⋊C₈×C₄₃	—	2	1	no	—
18	C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
19	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
21	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
22	C₂²×Dic₄₃	—	2	2	no	—
23	C₂×Dic₈₆	—	2	2	no	—
24	C₂×Dic₈₆	—	4	4	no	—
25	C₂×Dic₈₆	C₂×C₄	1	4	yes	—
26	C₂×C₈×C₄₃	—	2	2	no	—
27	C₂×C₈×C₄₃	—	4	2	no	—
28	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
29	C₄²×C₄₃	D₄	1	1	yes	characteristic
30	C₄²×C₄₃	D₄	1	1	yes	characteristic
31	C₄²×C₄₃	C₂³	1	1	yes	characteristic
32	C₄⋊Dic₄₃	—	2	2	no	—
33	C₄⋊Dic₄₃	—	2	2	no	—
34	C₄⋊Dic₄₃	—	2	2	no	—
35	C₄⋊Dic₄₃	—	2	2	no	—
36	C₂×C₄₃⋊C₈	—	2	2	no	—
37	C₂×C₄₃⋊C₈	—	4	2	no	—
38	C₂³×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
39	C₂×C₄×C₄₃	—	2	2	no	—
40	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
41	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
42	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
43	C₂×C₄×C₄₃	SD₁₆	1	2	yes	—
44	C₂×C₄×C₄₃	SD₁₆	1	2	yes	—
45	C₂×C₄×C₄₃	Q₁₆	1	2	yes	—
46	C₂×C₄×C₄₃	Q₁₆	1	2	yes	—
47	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
48	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
50	C₂×Dic₄₃	—	2	4	no	—
51	C₂×Dic₄₃	—	4	4	no	—
52	Dic₈₆	—	4	4	no	—
53	Dic₈₆	—	4	4	no	—
54	C₈×C₄₃	—	4	2	no	—
55	C₄₃⋊C₈	—	4	2	no	—
56	C₂²×C₄₃	#100	1	2	yes	—
57	C₂²×C₄₃	#103	1	2	yes	—
58	C₂²×C₄₃	#103	1	2	yes	—
59	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
60	C₄×C₄₃	—	2	1	no	—
61	C₄×C₄₃	—	2	1	no	—
62	C₄×C₄₃	#103	1	2	yes	—
63	C₄×C₄₃	#103	1	2	yes	—
64	C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
65	C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
66	C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
67	C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
68	Dic₄₃	—	4	4	no	—
69	C₂×#333	—	43	1	no	maximal, Sylow
70	C₂×C₄₃	#333	1	4	yes	complemented
71	C₂×C₄₃	C₂×#100	1	1	yes	characteristic
72	C₂×C₄₃	C₂×#103	1	1	yes	characteristic
73	C₂×C₄₃	C₂×#103	1	1	yes	characteristic
74	C₂×C₄⋊Q₈	—	43	1	no	—
75	C₂×C₄⋊C₈	—	43	1	no	—
76	C₂×C₄⋊C₈	D₄₃	1	1	yes	characteristic
77	#333	—	43	4	no	—
78	C₄₃	C₂×#333	1	1	yes	characteristic, complemented, Sylow
79	C₂²×Q₈	—	43	2	no	—
80	C₂²×C₈	—	2	1	no	—
81	C₂²×C₈	—	86	1	no	—
82	C₄⋊Q₈	—	43	2	no	—
83	C₄⋊Q₈	—	43	2	no	—
84	C₄⋊Q₈	—	86	1	no	—
85	C₄⋊Q₈	—	86	1	no	—
86	C₂×C₄⋊C₄	—	86	1	no	—
87	C₂×C₄⋊C₄	—	86	1	no	—
88	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
89	C₄⋊C₈	—	2	1	no	—
90	C₄⋊C₈	—	43	2	no	—
91	C₄⋊C₈	—	86	1	no	—
92	C₄⋊C₈	C₂×D₄₃	1	2	yes	—
93	C₂×Q₈	—	43	4	no	—
94	C₂×Q₈	—	86	2	no	—
95	C₂×Q₈	—	172	4	no	—
96	C₂²×C₄	—	86	2	no	—
97	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
98	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
99	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
100	C₂×C₈	—	2	2	no	—
101	C₂×C₈	—	4	2	no	—
102	C₂×C₈	—	86	2	no	—
103	C₂×C₈	—	172	2	no	—
104	C₄⋊C₄	—	86	2	no	—
105	C₄⋊C₄	—	86	2	no	—
106	C₄⋊C₄	—	86	2	no	—
107	C₄⋊C₄	—	86	2	no	—
108	C₄²	C₄×D₄₃	1	1	yes	characteristic
109	C₄²	D₁₇₂	1	1	yes	characteristic
110	C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
111	C₄²	C₂²×D₄₃	1	1	yes	characteristic
112	C₂³	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
113	Q₈	—	172	4	no	—
114	Q₈	—	172	4	no	—
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	—	86	4	no	—
117	C₂×C₄	—	172	4	no	—
118	C₂×C₄	#10621873	1	2	yes	—
119	C₂×C₄	Dic₁₇₂	1	2	yes	—
120	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
121	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
122	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
123	C₂×C₄	#10621883	1	2	yes	—
124	C₂×C₄	#10621885	1	2	yes	—
125	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
126	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
127	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
128	C₈	—	4	2	no	—
129	C₈	—	172	2	no	—
130	C₂²	#13063241	1	2	yes	—
131	C₂²	#13063248	1	2	yes	—
132	C₂²	#13063250	1	2	yes	—
133	C₂²	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
134	C₄	—	2	1	no	—
135	C₄	—	2	1	no	—
136	C₄	—	172	4	no	—
137	C₄	#13063248	1	2	yes	—
138	C₄	#13063250	1	2	yes	—
139	C₄	C₂×#10621883	1	1	yes	characteristic
140	C₄	C₂×#10621873	1	1	yes	characteristic
141	C₄	C₂×#10621885	1	1	yes	characteristic
142	C₄	C₂×Dic₁₇₂	1	1	yes	characteristic
143	C₂	#14582647	1	4	yes	direct product factor
144	C₂	C₂×#13063241	1	1	yes	characteristic
145	C₂	C₂×#13063248	1	1	yes	characteristic
146	C₂	C₂×#13063250	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063325

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₄₃⋊C₈)

C₂

yes

maximal, characteristic

#14582647

C₂

yes

maximal, direct product factor

C₂×C₄⋊C₈×C₄₃

C₂

yes

maximal, characteristic

C₂²×Dic₈₆

C₄

yes

—

C₂²×C₄₃⋊C₈

—

#13063325

—

#13063325

—

#13063325

C₄

yes

—

#13063325

C₂²

yes

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

C₂²×C₈×C₄₃

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

C₂×C₄

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

SD₁₆

yes

—

C₂×C₄×C₄₃

SD₁₆

yes

—

C₂×C₄×C₄₃

Q₁₆

yes

—

C₂×C₄×C₄₃

Q₁₆

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

#100

yes

—

C₂²×C₄₃

#103

yes

—

C₂²×C₄₃

#103

yes

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#103

yes

—

C₄×C₄₃

#103

yes

—

C₄×C₄₃

C₂×SD₁₆

yes

characteristic

C₄×C₄₃

C₂×SD₁₆

yes

characteristic

C₄×C₄₃

C₂×Q₁₆

yes

characteristic

C₄×C₄₃

C₂×Q₁₆

yes

characteristic

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄⋊Q₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

D₄₃

yes

characteristic

#333

—

C₄₃

C₂×#333

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×C₈

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₃

yes

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

172

—

C₂²×C₄

—

C₂²×C₄

C₄×D₄₃

yes

characteristic

C₂²×C₄

D₁₇₂

yes

characteristic

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

172

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄²

C₄×D₄₃

yes

characteristic

109

C₄²

D₁₇₂

yes

characteristic

110

C₄²

C₂²⋊D₄₃

yes

characteristic

111

C₄²

C₂²×D₄₃

yes

characteristic

112

C₂³

(C₂×D₄₃)⋊C₄

yes

characteristic

113

Q₈

—

172

—

114

Q₈

—

172

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

172

—

118

C₂×C₄

#10621873

yes

—

119

C₂×C₄

Dic₁₇₂

yes

—

120

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

121

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

122

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

123

C₂×C₄

#10621883

yes

—

124

C₂×C₄

#10621885

yes

—

125

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

126

C₂×C₄

C₂×D₁₇₂

yes

characteristic

127

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

128

C₈

—

129

C₈

—

172

—

130

C₂²

#13063241

yes

—

131

C₂²

#13063248

yes

—

132

C₂²

#13063250

yes

—

133

C₂²

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

134

C₄

—

135

C₄

—

136

C₄

—

172

—

137

C₄

#13063248

yes

—

138

C₄

#13063250

yes

—

139

C₄

C₂×#10621883

yes

characteristic

140

C₄

C₂×#10621873

yes

characteristic

141

C₄

C₂×#10621885

yes

characteristic

142

C₄

C₂×Dic₁₇₂

yes

characteristic

143

C₂

#14582647

yes

direct product factor

144

C₂

C₂×#13063241

yes

characteristic

145

C₂

C₂×#13063248

yes

characteristic

146

C₂

C₂×#13063250

yes

characteristic

	subgroup	G/H
center	C₂³	(C₂×D₄₃)⋊C₄
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₄²	C₂²×D₄₃
Fitting	C₂×C₄⋊C₈×C₄₃	C₂
socle	C₂³×C₄₃	C₂²⋊C₄
hypercenter	C₂×C₄⋊C₈	D₄₃
hypocenter	C₄₃	C₂×#333
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

subgroup

G/H

center

C₂³

(C₂×D₄₃)⋊C₄

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₄²

C₂²×D₄₃

Fitting

C₂×C₄⋊C₈×C₄₃

C₂

socle

C₂³×C₄₃

C₂²⋊C₄

hypercenter

C₂×C₄⋊C₈

D₄₃

hypocenter

C₄₃

C₂×#333

LCS

G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
3. #14582647	C₂	direct (N × H)
70. C₂×C₄₃	#333	semidirect
78. C₄₃	C₂×#333	semidirect
143. C₂	#14582647	direct (N × H)

H ≅ G/N

type

3. #14582647

C₂

direct (N × H)

70. C₂×C₄₃

#333

semidirect

78. C₄₃

C₂×#333

semidirect

143. C₂

#14582647

direct (N × H)

Subgroups — C₂×#14582647 #19133247

Conjugacy classes of subgroups

Complements

Subgroups — C2×#14582647 #19133247

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14582647 #19133247