Group #18069319 — subgroups

Subgroups — #18069319

Order 4864.

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

normal subgroups only

This group has 230 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	#14561715	C₂	1	2	yes	maximal
2	C₁₉×#1960	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×C₁₉×#97	C₂²	1	1	yes	characteristic
7	C₁₉×#382	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×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₁₉×#103	—	4	2	no	—
17	C₁₉×#103	—	4	2	no	—
18	C₁₉×#97	—	4	1	no	—
19	C₁₉×#95	—	4	1	no	—
20	#10597269	—	4	2	no	—
21	#10597269	—	4	2	no	—
22	C₂×C₁₉⋊C₁₆	—	2	4	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	C₄²×C₁₉	—	2	1	no	—
39	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
40	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
41	C₁₉⋊C₁₆	—	4	4	no	—
42	#7117	—	19	1	no	maximal, Sylow
43	C₂³×C₁₉	#100	1	1	yes	characteristic
44	Q₈×C₁₉	—	4	4	no	—
45	Q₈×C₁₉	—	8	2	no	—
46	C₂×C₄×C₁₉	—	2	1	no	—
47	C₂×C₄×C₁₉	—	2	1	no	—
48	C₂×C₄×C₁₉	—	4	2	no	—
49	C₂×C₄×C₁₉	—	4	2	no	—
50	C₂×C₄×C₁₉	—	8	1	no	—
51	C₂×C₄×C₁₉	—	8	1	no	—
52	C₂×C₄×C₁₉	—	8	2	no	—
53	C₂×C₄×C₁₉	—	8	1	no	—
54	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
55	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
56	C₂×C₄×C₁₉	#102	1	2	yes	—
57	C₂×C₄×C₁₉	#104	1	2	yes	—
58	C₈×C₁₉	—	2	2	no	—
59	C₈×C₁₉	—	2	2	no	—
60	#1960	D₁₉	1	1	yes	characteristic
61	#1375	—	19	2	no	—
62	C₂²×C₁₉	—	2	2	no	—
63	C₂²×C₁₉	#323	1	1	yes	characteristic
64	C₂²×C₁₉	#329	1	1	yes	characteristic
65	C₂²×C₁₉	#331	1	1	yes	characteristic
66	C₄×C₁₉	—	4	1	no	—
67	C₄×C₁₉	—	4	1	no	—
68	C₄×C₁₉	—	8	2	no	—
69	C₄×C₁₉	—	16	1	no	—
70	C₄×C₁₉	D₄⋊C₈	1	2	yes	—
71	C₄×C₁₉	#327	1	2	yes	—
72	C₂×C₄⋊Q₈	Dic₁₉	1	1	yes	characteristic
73	C₂×M₃₂	—	38	2	no	—
74	C₂×#103	—	2	2	no	—
75	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
76	#382	Dic₁₉	1	1	yes	characteristic
77	C₂×C₁₉	—	2	1	no	—
78	C₂×C₁₉	—	2	1	no	—
79	C₂×C₁₉	#1270	1	1	yes	characteristic
80	C₂×C₁₉	#1356	1	2	yes	—
81	C₂²×Q₈	—	2	1	no	—
82	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
83	C₄⋊Q₈	—	2	1	no	—
84	C₄⋊Q₈	—	4	1	no	—
85	C₄⋊Q₈	C₁₉⋊C₈	1	2	yes	—
86	C₂×C₄⋊C₄	—	2	1	no	—
87	C₂×C₄⋊C₄	—	4	1	no	—
88	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
89	M₃₂	—	76	2	no	—
90	M₃₂	—	76	2	no	—
91	C₂×C₁₆	—	38	4	no	—
92	#103	—	4	2	no	—
93	#103	—	4	2	no	—
94	#97	—	4	1	no	—
95	#95	—	4	1	no	—
96	C₁₉	#7117	1	1	yes	characteristic, complemented, Sylow
97	C₂×Q₈	—	2	2	no	—
98	C₂×Q₈	—	4	1	no	—
99	C₂×Q₈	—	4	2	no	—
100	C₂×Q₈	—	4	2	no	—
101	C₂²×C₄	—	2	1	no	—
102	C₂²×C₄	—	4	1	no	—
103	C₂²×C₄	—	4	1	no	—
104	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
105	C₂×C₈	—	2	2	no	—
106	C₂×C₈	—	2	2	no	—
107	C₂×C₈	#64525	1	2	yes	—
108	C₂×C₈	#64526	1	2	yes	—
109	C₄⋊C₄	—	4	2	no	—
110	C₄⋊C₄	—	4	2	no	—
111	C₄⋊C₄	—	4	2	no	—
112	C₄²	—	2	1	no	—
113	C₄²	C₂×C₁₉⋊C₈	1	1	yes	characteristic
114	C₄²	#64520	1	1	yes	characteristic
115	C₁₆	—	76	4	no	—
116	C₂³	#10597290	1	1	yes	characteristic
117	Q₈	—	4	4	no	—
118	Q₈	—	8	2	no	—
119	C₂×C₄	—	2	1	no	—
120	C₂×C₄	—	2	1	no	—
121	C₂×C₄	—	4	2	no	—
122	C₂×C₄	—	4	2	no	—
123	C₂×C₄	—	8	1	no	—
124	C₂×C₄	—	8	1	no	—
125	C₂×C₄	—	8	2	no	—
126	C₂×C₄	—	8	1	no	—
127	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
128	C₂×C₄	#10597289	1	2	yes	—
129	C₂×C₄	#10597291	1	1	yes	characteristic
130	C₂×C₄	#10597294	1	2	yes	—
131	C₈	—	2	2	no	—
132	C₈	—	2	2	no	—
133	C₂²	—	2	2	no	—
134	C₂²	#11926268	1	1	yes	characteristic
135	C₂²	#11926284	1	1	yes	characteristic
136	C₂²	#11926288	1	1	yes	characteristic
137	C₄	—	4	1	no	—
138	C₄	—	4	1	no	—
139	C₄	—	8	2	no	—
140	C₄	—	16	1	no	—
141	C₄	D₄⋊(C₁₉⋊C₈)	1	2	yes	—
142	C₄	#11926278	1	2	yes	—
143	C₂	—	2	1	no	—
144	C₂	—	2	1	no	—
145	C₂	#14561456	1	1	yes	characteristic
146	C₂	#14561670	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14561715

C₂

yes

maximal

C₁₉×#1960

C₂

yes

maximal, characteristic

C₂×#10597269

—

C₂×C₁₉×C₄⋊Q₈

C₄

yes

characteristic

C₂×C₁₉×#103

—

C₂×C₁₉×#97

C₂²

yes

characteristic

C₁₉×#382

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×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₁₉×#103

—

C₁₉×#103

—

C₁₉×#97

—

C₁₉×#95

—

#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

—

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

C₂²⋊C₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#104

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

#1960

D₁₉

yes

characteristic

#1375

—

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×#97

C₂×D₁₉

yes

characteristic

#382

Dic₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1270

yes

characteristic

C₂×C₁₉

#1356

yes

—

C₂²×Q₈

—

C₂²×C₈

C₂²⋊D₁₉

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₁₉⋊C₈

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

—

—

—

—

C₁₉

#7117

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

100

C₂×Q₈

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

#64525

yes

—

108

C₂×C₈

#64526

yes

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄²

—

113

C₄²

C₂×C₁₉⋊C₈

yes

characteristic

114

C₄²

#64520

yes

characteristic

115

C₁₆

—

116

C₂³

#10597290

yes

characteristic

117

Q₈

—

118

Q₈

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

128

C₂×C₄

#10597289

yes

—

129

C₂×C₄

#10597291

yes

characteristic

130

C₂×C₄

#10597294

yes

—

131

C₈

—

132

C₈

—

133

C₂²

—

134

C₂²

#11926268

yes

characteristic

135

C₂²

#11926284

yes

characteristic

136

C₂²

#11926288

yes

characteristic

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

D₄⋊(C₁₉⋊C₈)

yes

—

142

C₄

#11926278

yes

—

143

C₂

—

144

C₂

—

145

C₂

#14561456

yes

characteristic

146

C₂

#14561670

yes

—

	subgroup	G/H
center	C₂²	#11926284
commutator	C₄²×C₁₉	C₂×C₈
Frattini	C₂×#97	C₂×D₁₉
Fitting	C₁₉×#1960	C₂
socle	C₂²×C₁₉	#329
prime radical	C₂³×C₁₉	#100
cosocle	C₂×C₁₉×#97	C₂²
hypercenter	#1960	D₁₉
hypocenter	C₁₉	#7117
LCS	G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#97 ◁ #1960

subgroup

G/H

center

C₂²

#11926284

commutator

C₄²×C₁₉

C₂×C₈

Frattini

C₂×#97

C₂×D₁₉

Fitting

C₁₉×#1960

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₁₉×#97

C₂²

D₁₉

C₁₉

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

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#97 ◁ #1960

N	H ≅ G/N	type
96. C₁₉	#7117	semidirect

H ≅ G/N

type

96. C₁₉

#7117

semidirect

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

subgroup	index
#14561715	2
C₁₉×#1960	2
#7117	19

subgroup

index

#14561715

C₁₉×#1960

#7117

Subgroups — #18069319

Conjugacy classes of subgroups

Complements

Maximal subgroups