Group #19135753 — subgroups

Subgroups — #19135753

Order 5504.

246 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 71 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	#14582907	C₂	1	2	yes	maximal
2	#14582804	C₂	1	1	yes	maximal, characteristic
3	#14582668	C₂	1	1	yes	maximal, characteristic
4	#14582658	C₂	1	2	yes	maximal
5	C₄₃×#544	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
7	C₂×#10621877	C₂²	1	2	yes	—
8	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
9	#13063248	—	2	2	no	—
10	#13063248	—	2	2	no	—
11	C₄₃⋊#95	—	2	2	no	—
12	C₄⋊Q₈×C₄₃	—	2	2	no	—
13	#125×C₄₃	—	2	2	no	—
14	C₂²⋊Q₈×C₄₃	—	2	2	no	—
15	#117×C₄₃	C₂²	1	2	yes	—
16	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₄₃	—	2	2	no	—
18	C₂²×C₄×C₄₃	D₄	1	2	yes	—
19	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
20	C₂²×Dic₄₃	—	2	1	no	—
21	C₂²×Dic₄₃	—	2	1	no	—
22	C₂×Dic₈₆	—	2	2	no	—
23	C₂×Dic₈₆	—	2	2	no	—
24	C₂×Dic₈₆	—	2	1	no	—
25	C₂×Dic₈₆	Q₈	1	2	yes	complemented
26	C₄⋊C₄×C₄₃	—	2	2	no	—
27	C₄⋊C₄×C₄₃	—	2	4	no	—
28	C₄⋊C₄×C₄₃	—	2	2	no	—
29	C₄⋊C₄×C₄₃	D₄	1	2	yes	—
30	C₄⋊C₄×C₄₃	D₄	1	2	yes	—
31	C₂²⋊C₄×C₄₃	—	2	2	no	—
32	C₄²×C₄₃	—	2	2	no	—
33	C₄×Dic₄₃	—	2	2	no	—
34	#10621877	—	2	2	no	—
35	#10621877	—	2	2	no	—
36	C₂×C₄₃⋊C₈	—	2	2	no	—
37	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
38	Q₈×C₄₃	—	8	2	no	—
39	C₂×C₄×C₄₃	—	2	2	no	—
40	C₂×C₄×C₄₃	—	2	2	no	—
41	C₂×C₄×C₄₃	—	2	2	no	—
42	C₂×C₄×C₄₃	—	4	2	no	—
43	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
44	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
45	C₂×C₄×C₄₃	#41	1	2	yes	—
46	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
47	C₂×Dic₄₃	—	2	2	no	—
48	C₂×Dic₄₃	—	2	2	no	—
49	C₂×Dic₄₃	—	4	1	no	—
50	C₂×Dic₄₃	—	4	1	no	—
51	C₂×Dic₄₃	—	4	1	no	—
52	C₂×Dic₄₃	—	4	1	no	—
53	Dic₈₆	—	2	4	no	—
54	Dic₈₆	—	4	2	no	—
55	C₄₃⋊C₈	—	4	2	no	—
56	C₂²×C₄₃	—	2	1	no	—
57	C₂²×C₄₃	—	2	1	no	—
58	C₂²×C₄₃	#120	1	1	yes	characteristic
59	C₂²×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
60	C₂²×C₄₃	#124	1	1	yes	characteristic
61	C₄×C₄₃	—	4	2	no	—
62	C₄×C₄₃	—	4	2	no	—
63	C₄×C₄₃	—	4	2	no	—
64	C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
65	C₄×C₄₃	#124	1	2	yes	—
66	Dic₄₃	—	4	2	no	—
67	Dic₄₃	—	4	2	no	—
68	#2028	—	43	1	no	maximal, Sylow
69	C₂×C₄₃	—	2	1	no	—
70	C₂×C₄₃	—	2	1	no	—
71	C₂×C₄₃	#393	1	1	yes	characteristic
72	C₂×C₄₃	#455	1	1	yes	characteristic
73	C₂×C₄₃	#456	1	1	yes	characteristic
74	#544	D₄₃	1	1	yes	characteristic
75	#419	—	43	2	no	—
76	#391	—	43	1	no	—
77	#343	—	43	1	no	—
78	#339	—	43	2	no	—
79	C₄₃	#2028	1	1	yes	characteristic, complemented, Sylow
80	C₂²×Q₈	—	43	1	no	—
81	C₂×M₁₆	—	43	2	no	—
82	C₄⋊Q₈	—	2	2	no	—
83	#125	—	2	2	no	—
84	C₂²⋊Q₈	—	2	2	no	—
85	#117	C₂×D₄₃	1	2	yes	—
86	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
87	C₂×C₄²	—	43	1	no	—
88	#103	—	86	2	no	—
89	#103	—	86	2	no	—
90	#95	—	86	2	no	—
91	C₂×Q₈	—	2	2	no	—
92	C₂×Q₈	—	43	2	no	—
93	C₂×Q₈	—	86	1	no	—
94	C₂×Q₈	—	86	2	no	—
95	C₂×Q₈	—	86	2	no	—
96	C₂²×C₄	—	86	1	no	—
97	C₂²×C₄	—	86	1	no	—
98	C₂²×C₄	C₂²⋊D₄₃	1	2	yes	—
99	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
100	M₁₆	—	86	2	no	—
101	M₁₆	—	86	2	no	—
102	C₂×C₈	—	86	2	no	—
103	C₄⋊C₄	—	2	2	no	—
104	C₄⋊C₄	—	2	4	no	—
105	C₄⋊C₄	—	2	2	no	—
106	C₄⋊C₄	C₂²⋊D₄₃	1	2	yes	—
107	C₄⋊C₄	C₂²⋊D₄₃	1	2	yes	—
108	C₂²⋊C₄	—	2	2	no	—
109	C₄²	—	2	2	no	—
110	C₄²	—	86	2	no	—
111	C₂³	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
112	Q₈	—	8	2	no	—
113	Q₈	—	86	4	no	—
114	Q₈	—	172	2	no	—
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	2	no	—
118	C₂×C₄	—	4	2	no	—
119	C₂×C₄	—	86	2	no	—
120	C₂×C₄	—	86	2	no	—
121	C₂×C₄	—	172	1	no	—
122	C₂×C₄	—	172	1	no	—
123	C₂×C₄	—	172	1	no	—
124	C₂×C₄	—	172	1	no	—
125	C₂×C₄	Q₈×D₄₃	1	1	yes	characteristic
126	C₂×C₄	#10621902	1	2	yes	—
127	C₂×C₄	#10621902	1	1	yes	characteristic
128	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
129	C₈	—	172	2	no	—
130	C₂²	—	2	1	no	—
131	C₂²	—	2	1	no	—
132	C₂²	#13063294	1	1	yes	characteristic
133	C₂²	#13063301	1	1	yes	characteristic
134	C₂²	#13063314	1	1	yes	characteristic
135	C₄	—	4	2	no	—
136	C₄	—	4	2	no	—
137	C₄	—	4	2	no	—
138	C₄	—	172	2	no	—
139	C₄	—	172	2	no	—
140	C₄	#13063301	1	2	yes	—
141	C₄	#13063314	1	2	yes	—
142	C₂	—	2	1	no	—
143	C₂	—	2	1	no	—
144	C₂	#14582810	1	1	yes	characteristic
145	C₂	#14583077	1	1	yes	characteristic
146	C₂	#14583082	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582907

C₂

yes

maximal

#14582804

C₂

yes

maximal, characteristic

#14582668

C₂

yes

maximal, characteristic

#14582658

C₂

yes

maximal

C₄₃×#544

C₂

yes

maximal, characteristic

C₂²×Dic₈₆

C₂²

yes

characteristic

C₂×#10621877

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

#13063248

—

#13063248

—

C₄₃⋊#95

—

C₄⋊Q₈×C₄₃

—

#125×C₄₃

—

C₂²⋊Q₈×C₄₃

—

#117×C₄₃

C₂²

yes

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

Q₈

yes

complemented

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

D₄

yes

—

C₄⋊C₄×C₄₃

D₄

yes

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄×Dic₄₃

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#120

yes

characteristic

C₂²×C₄₃

C₂²⋊Q₈

yes

characteristic

C₂²×C₄₃

#124

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂²⋊Q₈

yes

—

C₄×C₄₃

#124

yes

—

Dic₄₃

—

Dic₄₃

—

#2028

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

yes

—

—

—

—

C₄₃

#2028

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂×M₁₆

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

#117

C₂×D₄₃

yes

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

characteristic

C₂×C₄²

—

#103

—

#103

—

#95

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

100

M₁₆

—

101

M₁₆

—

102

C₂×C₈

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

C₂²⋊D₄₃

yes

—

107

C₄⋊C₄

C₂²⋊D₄₃

yes

—

108

C₂²⋊C₄

—

109

C₄²

—

110

C₄²

—

111

C₂³

C₂×C₂²⋊D₄₃

yes

characteristic

112

Q₈

—

113

Q₈

—

114

Q₈

—

172

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

172

—

122

C₂×C₄

—

172

—

123

C₂×C₄

—

172

—

124

C₂×C₄

—

172

—

125

C₂×C₄

Q₈×D₄₃

yes

characteristic

126

C₂×C₄

#10621902

yes

—

127

C₂×C₄

#10621902

yes

characteristic

128

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

129

C₈

—

172

—

130

C₂²

—

131

C₂²

—

132

C₂²

#13063294

yes

characteristic

133

C₂²

#13063301

yes

characteristic

134

C₂²

#13063314

yes

characteristic

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

172

—

139

C₄

—

172

—

140

C₄

#13063301

yes

—

141

C₄

#13063314

yes

—

142

C₂

—

143

C₂

—

144

C₂

#14582810

yes

characteristic

145

C₂

#14583077

yes

characteristic

146

C₂

#14583082

yes

characteristic

	subgroup	G/H
center	C₂²	#13063294
commutator	C₂²×C₄×C₄₃	C₂³
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#544	C₂
socle	C₂²×C₄₃	#120
hypercenter	#544	D₄₃
hypocenter	C₄₃	#2028
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #544

subgroup

G/H

center

C₂²

#13063294

commutator

C₂²×C₄×C₄₃

C₂³

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#544

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #544

N	H ≅ G/N	type
25. C₂×Dic₈₆	Q₈	semidirect
79. C₄₃	#2028	semidirect

H ≅ G/N

type

25. C₂×Dic₈₆

Q₈

semidirect

79. C₄₃

#2028

semidirect

Subgroups — #19135753

Conjugacy classes of subgroups

Complements