Group #19134013 — subgroups

Subgroups — #19134013

Order 5504.

160 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 55 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	#14583247	C₂	1	1	yes	maximal, characteristic
2	#14583099	C₂	1	1	yes	maximal, characteristic
3	Q₈×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582649	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582648	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582642	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10621884	—	2	1	no	—
9	#13063322	C₂²	1	1	yes	characteristic
10	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
11	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
12	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
13	#13063245	—	2	1	no	—
14	#13063245	—	2	1	no	—
15	#13063245	—	2	1	no	—
16	C₄×C₄₃⋊C₈	—	2	1	no	—
17	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
18	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
20	#107×C₄₃	—	2	1	no	—
21	C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
22	#103×C₄₃	—	2	1	no	—
23	C₂×Q₈×C₄₃	—	2	1	no	—
24	C₂×Q₈×C₄₃	D₄	1	1	yes	characteristic
25	C₂×D₁₇₂	—	2	1	no	—
26	C₂×D₁₇₂	—	2	1	no	—
27	C₂×D₁₇₂	—	2	1	no	—
28	C₂×C₈×C₄₃	—	2	1	no	—
29	C₄⋊C₄×C₄₃	—	2	1	no	—
30	C₄⋊C₄×C₄₃	—	2	1	no	—
31	C₄⋊C₄×C₄₃	—	2	1	no	—
32	C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
33	C₄²×C₄₃	—	2	1	no	—
34	C₄²×C₄₃	C₂³	1	1	yes	characteristic
35	#10621884	—	4	2	no	—
36	C₂×C₄₃⋊C₈	—	2	1	no	—
37	C₂×C₄₃⋊C₈	—	2	1	no	—
38	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
39	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
40	C₂²×D₄₃	—	4	1	no	—
41	Q₈×C₄₃	—	2	1	no	—
42	Q₈×C₄₃	—	8	1	no	—
43	Q₈×C₄₃	SD₁₆	1	2	yes	—
44	C₂×C₄×C₄₃	—	2	1	no	—
45	C₂×C₄×C₄₃	—	2	1	no	—
46	C₂×C₄×C₄₃	—	4	1	no	—
47	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
50	D₁₇₂	—	4	1	no	—
51	D₁₇₂	—	4	1	no	—
52	D₁₇₂	—	4	1	no	—
53	D₁₇₂	—	4	1	no	—
54	D₁₇₂	—	8	1	no	—
55	C₈×C₄₃	—	4	1	no	—
56	C₄₃⋊C₈	—	2	1	no	—
57	C₄₃⋊C₈	—	2	1	no	—
58	C₄₃⋊C₈	—	4	1	no	—
59	C₄₃⋊C₈	—	4	1	no	—
60	C₂²×C₄₃	#121	1	1	yes	characteristic
61	C₂×D₄₃	—	8	1	no	—
62	C₂×D₄₃	—	8	1	no	—
63	C₂×D₄₃	—	8	1	no	—
64	C₄×C₄₃	—	2	2	no	—
65	C₄×C₄₃	—	2	1	no	—
66	C₄×C₄₃	—	4	1	no	—
67	C₄×C₄₃	—	8	1	no	—
68	C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
69	C₄×C₄₃	#135	1	1	yes	characteristic
70	C₄×C₄₃	#135	1	1	yes	characteristic
71	C₄×C₄₃	#137	1	1	yes	characteristic
72	#1678	—	43	1	no	maximal, Sylow
73	C₂×C₄₃	#464	1	1	yes	characteristic
74	C₂×C₄₃	#465	1	1	yes	characteristic
75	C₂×C₄₃	#472	1	1	yes	characteristic
76	D₄₃	—	16	1	no	—
77	#486	—	43	1	no	—
78	#477	D₄₃	1	1	yes	characteristic, complemented
79	#460	—	43	1	no	—
80	C₈×Q₈	—	43	1	no	—
81	#334	—	43	1	no	—
82	#333	—	43	1	no	—
83	#331	—	43	1	no	—
84	C₄₃	#1678	1	1	yes	characteristic, complemented, Sylow
85	C₂×SD₁₆	—	86	1	no	—
86	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
87	#127	—	43	1	no	—
88	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
89	#107	—	2	1	no	—
90	C₄⋊C₈	—	43	1	no	—
91	C₄⋊C₈	—	43	1	no	—
92	C₄⋊C₈	—	86	1	no	—
93	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
94	#103	—	2	1	no	—
95	#102	—	86	1	no	—
96	#102	—	86	1	no	—
97	#102	—	86	1	no	—
98	C₄×C₈	—	43	1	no	—
99	C₄×C₈	—	86	1	no	—
100	C₂×Q₈	—	2	1	no	—
101	C₂×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
102	C₂×D₄	—	86	1	no	—
103	C₂×D₄	—	86	1	no	—
104	C₂×D₄	—	86	1	no	—
105	SD₁₆	—	172	2	no	—
106	C₂×C₈	—	2	1	no	—
107	C₂×C₈	—	43	1	no	—
108	C₂×C₈	—	43	1	no	—
109	C₂×C₈	—	86	1	no	—
110	C₂×C₈	—	86	1	no	—
111	C₄⋊C₄	—	2	1	no	—
112	C₄⋊C₄	—	2	1	no	—
113	C₄⋊C₄	—	2	1	no	—
114	C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
115	C₄²	—	2	1	no	—
116	C₄²	C₂²×D₄₃	1	1	yes	characteristic
117	C₂³	—	172	1	no	—
118	Q₈	—	2	1	no	—
119	Q₈	—	8	1	no	—
120	Q₈	#10621884	1	2	yes	—
121	D₄	—	344	1	no	—
122	D₄	—	172	1	no	—
123	D₄	—	172	1	no	—
124	D₄	—	172	1	no	—
125	D₄	—	172	1	no	—
126	C₂×C₄	—	2	1	no	—
127	C₂×C₄	—	2	1	no	—
128	C₂×C₄	—	4	1	no	—
129	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
130	C₂×C₄	#10621900	1	1	yes	characteristic
131	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
132	C₈	—	4	1	no	—
133	C₈	—	86	1	no	—
134	C₈	—	86	1	no	—
135	C₈	—	172	1	no	—
136	C₈	—	172	1	no	—
137	C₂²	—	344	1	no	—
138	C₂²	—	344	1	no	—
139	C₂²	—	344	1	no	—
140	C₂²	#13063297	1	1	yes	characteristic
141	C₄	—	2	2	no	—
142	C₄	—	2	1	no	—
143	C₄	—	4	1	no	—
144	C₄	—	8	1	no	—
145	C₄	C₂×#10621884	1	1	yes	characteristic
146	C₄	#13063345	1	1	yes	characteristic
147	C₄	#13063348	1	1	yes	characteristic
148	C₄	#13063357	1	1	yes	characteristic
149	C₂	—	688	1	no	—
150	C₂	#14583123	1	1	yes	characteristic
151	C₂	#14583130	1	1	yes	characteristic
152	C₂	#14583167	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583247

C₂

yes

maximal, characteristic

#14583099

C₂

yes

maximal, characteristic

Q₈×C₄₃⋊C₈

C₂

yes

maximal, characteristic, complemented

#14582649

C₂

yes

maximal, characteristic, complemented

#14582648

C₂

yes

maximal, characteristic, complemented

#14582642

C₂

yes

maximal, characteristic

C₄₃×#477

C₂

yes

maximal, characteristic, complemented

C₂×#10621884

—

#13063322

C₂²

yes

characteristic

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

—

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₄⋊Q₈×C₄₃

C₂²

yes

characteristic

C₄×Q₈×C₄₃

C₂²

yes

characteristic

#107×C₄₃

—

C₄⋊C₈×C₄₃

C₂²

yes

characteristic

#103×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

D₄

yes

characteristic

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

—

C₄²×C₄₃

C₂³

yes

characteristic

#10621884

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

D₄

yes

characteristic

C₂×C₄₃⋊C₈

D₄

yes

characteristic

C₂²×D₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

SD₁₆

yes

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

characteristic

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

#121

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×SD₁₆

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

#486

—

#477

D₄₃

yes

characteristic, complemented

#460

—

C₈×Q₈

—

#334

—

#333

—

#331

—

C₄₃

#1678

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

C₄⋊Q₈

C₂×D₄₃

yes

characteristic

#127

—

C₄×Q₈

C₂×D₄₃

yes

characteristic

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₃

yes

—

—

—

—

C₄×C₈

—

C₄×C₈

—

100

C₂×Q₈

—

101

C₂×Q₈

C₂²⋊D₄₃

yes

characteristic

102

C₂×D₄

—

103

C₂×D₄

—

104

C₂×D₄

—

105

SD₁₆

—

172

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄⋊C₄

C₂²⋊D₄₃

yes

characteristic

115

C₄²

—

116

C₄²

C₂²×D₄₃

yes

characteristic

117

C₂³

—

172

—

118

Q₈

—

119

Q₈

—

120

Q₈

#10621884

yes

—

121

D₄

—

344

—

122

D₄

—

172

—

123

D₄

—

172

—

124

D₄

—

172

—

125

D₄

—

172

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

D₄×D₄₃

yes

characteristic

130

C₂×C₄

#10621900

yes

characteristic

131

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

132

C₈

—

133

C₈

—

134

C₈

—

135

C₈

—

172

—

136

C₈

—

172

—

137

C₂²

—

344

—

138

C₂²

—

344

—

139

C₂²

—

344

—

140

C₂²

#13063297

yes

characteristic

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

C₂×#10621884

yes

characteristic

146

C₄

#13063345

yes

characteristic

147

C₄

#13063348

yes

characteristic

148

C₄

#13063357

yes

characteristic

149

C₂

—

688

—

150

C₂

#14583123

yes

characteristic

151

C₂

#14583130

yes

characteristic

152

C₂

#14583167

yes

characteristic

	subgroup	G/H
center	C₂²	#13063297
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#477	C₂
socle	C₂²×C₄₃	#121
hypercenter	#477	D₄₃
hypocenter	C₄₃	#1678
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #477

subgroup

G/H

center

C₂²

#13063297

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#477

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #477

N	H ≅ G/N	type
3. Q₈×C₄₃⋊C₈	C₂	semidirect
4. #14582649	C₂	semidirect
5. #14582648	C₂	semidirect
7. C₄₃×#477	C₂	semidirect
78. #477	D₄₃	semidirect
84. C₄₃	#1678	semidirect

H ≅ G/N

type

3. Q₈×C₄₃⋊C₈

C₂

semidirect

4. #14582649

C₂

semidirect

5. #14582648

C₂

semidirect

7. C₄₃×#477

C₂

semidirect

78. #477

D₄₃

semidirect

84. C₄₃

#1678

semidirect

Subgroups — #19134013

Conjugacy classes of subgroups

Complements