Group #18069295 — subgroups

Subgroups — #18069295

Order 4864.

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

normal subgroups only

This group has 242 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	#14561717	C₂	1	2	yes	maximal
2	C₁₉×#1956	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597269	—	2	2	no	—
4	C₂×C₁₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
5	C₂×C₁₉×#103	—	2	2	no	—
6	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₁₉×#384	C₄	1	1	yes	characteristic
8	C₂²×Q₈×C₁₉	—	2	1	no	—
9	C₂²×C₈×C₁₉	D₄	1	2	yes	—
10	C₁₉×C₄⋊Q₈	—	2	1	no	—
11	C₁₉×C₄⋊Q₈	—	4	1	no	—
12	C₁₉×C₄⋊Q₈	C₈	1	2	yes	—
13	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
14	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
15	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
16	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₁₉×#103	—	4	2	no	—
18	C₁₉×#103	—	4	2	no	—
19	C₄×C₈×C₁₉	—	4	1	no	—
20	#10597269	—	2	4	no	—
21	#10597269	—	4	2	no	—
22	C₂×C₁₉⋊C₁₆	—	4	2	no	—
23	C₂×Q₈×C₁₉	—	2	2	no	—
24	C₂×Q₈×C₁₉	—	4	1	no	—
25	C₂×Q₈×C₁₉	—	4	2	no	—
26	C₂×Q₈×C₁₉	—	4	2	no	—
27	C₂²×C₄×C₁₉	—	2	1	no	—
28	C₂²×C₄×C₁₉	—	4	1	no	—
29	C₂²×C₄×C₁₉	—	4	1	no	—
30	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₈×C₁₉	—	2	2	no	—
32	C₂×C₈×C₁₉	—	2	2	no	—
33	C₂×C₈×C₁₉	D₈	1	2	yes	—
34	C₂×C₈×C₁₉	SD₁₆	1	2	yes	—
35	C₄⋊C₄×C₁₉	—	4	2	no	—
36	C₄⋊C₄×C₁₉	—	4	2	no	—
37	C₄⋊C₄×C₁₉	—	4	2	no	—
38	C₄⋊C₄×C₁₉	—	8	2	no	—
39	C₄²×C₁₉	—	2	1	no	—
40	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
41	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
42	C₁₉⋊C₁₆	—	4	4	no	—
43	#7108	—	19	1	no	maximal, Sylow
44	C₂³×C₁₉	#100	1	1	yes	characteristic
45	Q₈×C₁₉	—	4	4	no	—
46	Q₈×C₁₉	—	8	2	no	—
47	C₂×C₄×C₁₉	—	2	2	no	—
48	C₂×C₄×C₁₉	—	2	2	no	—
49	C₂×C₄×C₁₉	—	2	1	no	—
50	C₂×C₄×C₁₉	—	2	1	no	—
51	C₂×C₄×C₁₉	—	4	2	no	—
52	C₂×C₄×C₁₉	—	8	1	no	—
53	C₂×C₄×C₁₉	—	8	1	no	—
54	C₂×C₄×C₁₉	—	8	2	no	—
55	C₂×C₄×C₁₉	—	8	1	no	—
56	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
57	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
58	C₂×C₄×C₁₉	#102	1	2	yes	—
59	C₂×C₄×C₁₉	#104	1	2	yes	—
60	C₈×C₁₉	—	2	2	no	—
61	C₈×C₁₉	—	2	2	no	—
62	#1956	D₁₉	1	1	yes	characteristic
63	#1376	—	19	2	no	—
64	C₂²×C₁₉	—	2	1	no	—
65	C₂²×C₁₉	—	2	1	no	—
66	C₂²×C₁₉	#323	1	1	yes	characteristic
67	C₂²×C₁₉	#329	1	1	yes	characteristic
68	C₂²×C₁₉	#331	1	1	yes	characteristic
69	C₄×C₁₉	—	2	2	no	—
70	C₄×C₁₉	—	2	2	no	—
71	C₄×C₁₉	—	8	2	no	—
72	C₄×C₁₉	—	16	1	no	—
73	C₄×C₁₉	D₄⋊C₈	1	2	yes	—
74	C₄×C₁₉	#327	1	2	yes	—
75	C₂×C₄⋊Q₈	Dic₁₉	1	1	yes	characteristic
76	C₂×M₃₂	—	38	2	no	—
77	C₂×#103	—	2	2	no	—
78	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
79	#384	Dic₁₉	1	1	yes	characteristic
80	C₂×C₁₉	—	2	1	no	—
81	C₂×C₁₉	—	2	1	no	—
82	C₂×C₁₉	#1270	1	1	yes	characteristic
83	C₂×C₁₉	#1358	1	1	yes	characteristic
84	C₂×C₁₉	#1359	1	1	yes	characteristic
85	C₂²×Q₈	—	2	1	no	—
86	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
87	C₄⋊Q₈	—	2	1	no	—
88	C₄⋊Q₈	—	4	1	no	—
89	C₄⋊Q₈	C₁₉⋊C₈	1	2	yes	—
90	C₂×C₄⋊C₄	—	2	1	no	—
91	C₂×C₄⋊C₄	—	4	1	no	—
92	C₂×C₄⋊C₄	—	4	1	no	—
93	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
94	M₃₂	—	38	4	no	—
95	M₃₂	—	76	2	no	—
96	C₂×C₁₆	—	76	2	no	—
97	#103	—	4	2	no	—
98	#103	—	4	2	no	—
99	C₄×C₈	—	4	1	no	—
100	C₁₉	#7108	1	1	yes	characteristic, complemented, Sylow
101	C₂×Q₈	—	2	2	no	—
102	C₂×Q₈	—	4	1	no	—
103	C₂×Q₈	—	4	2	no	—
104	C₂×Q₈	—	4	2	no	—
105	C₂²×C₄	—	2	1	no	—
106	C₂²×C₄	—	4	1	no	—
107	C₂²×C₄	—	4	1	no	—
108	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
109	C₂×C₈	—	2	2	no	—
110	C₂×C₈	—	2	2	no	—
111	C₂×C₈	#64525	1	2	yes	—
112	C₂×C₈	#64526	1	2	yes	—
113	C₄⋊C₄	—	4	2	no	—
114	C₄⋊C₄	—	4	2	no	—
115	C₄⋊C₄	—	4	2	no	—
116	C₄⋊C₄	—	8	2	no	—
117	C₄²	—	2	1	no	—
118	C₄²	C₂×C₁₉⋊C₈	1	1	yes	characteristic
119	C₄²	#64520	1	1	yes	characteristic
120	C₁₆	—	76	4	no	—
121	C₂³	#10597290	1	1	yes	characteristic
122	Q₈	—	4	4	no	—
123	Q₈	—	8	2	no	—
124	C₂×C₄	—	2	2	no	—
125	C₂×C₄	—	2	2	no	—
126	C₂×C₄	—	2	1	no	—
127	C₂×C₄	—	2	1	no	—
128	C₂×C₄	—	4	2	no	—
129	C₂×C₄	—	8	1	no	—
130	C₂×C₄	—	8	1	no	—
131	C₂×C₄	—	8	2	no	—
132	C₂×C₄	—	8	1	no	—
133	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
134	C₂×C₄	#10597289	1	2	yes	—
135	C₂×C₄	#10597291	1	1	yes	characteristic
136	C₂×C₄	#10597294	1	2	yes	—
137	C₈	—	2	2	no	—
138	C₈	—	2	2	no	—
139	C₂²	—	2	1	no	—
140	C₂²	—	2	1	no	—
141	C₂²	#11926268	1	1	yes	characteristic
142	C₂²	#11926284	1	1	yes	characteristic
143	C₂²	#11926288	1	1	yes	characteristic
144	C₄	—	2	2	no	—
145	C₄	—	2	2	no	—
146	C₄	—	8	2	no	—
147	C₄	—	16	1	no	—
148	C₄	D₄⋊(C₁₉⋊C₈)	1	2	yes	—
149	C₄	#11926278	1	2	yes	—
150	C₂	—	2	1	no	—
151	C₂	—	2	1	no	—
152	C₂	#14561456	1	1	yes	characteristic
153	C₂	#14561674	1	1	yes	characteristic
154	C₂	#14561676	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561717

C₂

yes

maximal

C₁₉×#1956

C₂

yes

maximal, characteristic

C₂×#10597269

—

C₂×C₁₉×C₄⋊Q₈

C₄

yes

characteristic

C₂×C₁₉×#103

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#384

C₄

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

C₈

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₁₉×#103

—

C₁₉×#103

—

C₄×C₈×C₁₉

—

#10597269

—

#10597269

—

C₂×C₁₉⋊C₁₆

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

—

C₂×C₈×C₁₉

SD₁₆

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₈

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₁₉⋊C₁₆

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#104

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

#1956

D₁₉

yes

characteristic

#1376

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

D₄⋊C₈

yes

—

C₄×C₁₉

#327

yes

—

C₂×C₄⋊Q₈

Dic₁₉

yes

characteristic

C₂×M₃₂

—

C₂×#103

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

#384

Dic₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

—

C₂²×C₈

C₂²⋊D₁₉

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₁₉⋊C₈

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

#103

—

#103

—

C₄×C₈

—

100

C₁₉

#7108

yes

characteristic, complemented, Sylow

101

C₂×Q₈

—

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂×Q₈

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

#64525

yes

—

112

C₂×C₈

#64526

yes

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄⋊C₄

—

117

C₄²

—

118

C₄²

C₂×C₁₉⋊C₈

yes

characteristic

119

C₄²

#64520

yes

characteristic

120

C₁₆

—

121

C₂³

#10597290

yes

characteristic

122

Q₈

—

123

Q₈

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

134

C₂×C₄

#10597289

yes

—

135

C₂×C₄

#10597291

yes

characteristic

136

C₂×C₄

#10597294

yes

—

137

C₈

—

138

C₈

—

139

C₂²

—

140

C₂²

—

141

C₂²

#11926268

yes

characteristic

142

C₂²

#11926284

yes

characteristic

143

C₂²

#11926288

yes

characteristic

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

D₄⋊(C₁₉⋊C₈)

yes

—

149

C₄

#11926278

yes

—

150

C₂

—

151

C₂

—

152

C₂

#14561456

yes

characteristic

153

C₂

#14561674

yes

characteristic

154

C₂

#14561676

yes

characteristic

	subgroup	G/H
center	C₂²	#11926288
commutator	C₄²×C₁₉	C₂×C₈
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₁₉×#1956	C₂
socle	C₂²×C₁₉	#331
prime radical	C₂³×C₁₉	#100
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	#1956	D₁₉
hypocenter	C₁₉	#7108
LCS	G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1956

subgroup

G/H

center

C₂²

#11926288

commutator

C₄²×C₁₉

C₂×C₈

Frattini

C₂×C₄×C₈

C₂×D₁₉

Fitting

C₁₉×#1956

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄×C₈×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1956

N	H ≅ G/N	type
100. C₁₉	#7108	semidirect

H ≅ G/N

type

100. C₁₉

#7108

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#14561717	2
C₁₉×#1956	2
#7108	19

subgroup

index

#14561717

C₁₉×#1956

#7108

Subgroups — #18069295

Conjugacy classes of subgroups

Complements

Maximal subgroups