Group #18069945 — subgroups

Subgroups — #18069945

Order 4864.

158 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 43 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	#14563765	C₂	1	1	yes	maximal, characteristic
2	#14561579	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1324	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₁₉⋊C₈	C₄	1	1	yes	characteristic
5	#11926410	C₄	1	1	yes	characteristic
6	#11926306	—	2	1	no	—
7	#11926306	—	2	1	no	—
8	#11926270	—	2	1	no	—
9	C₁₉×#382	C₂²	1	1	yes	characteristic
10	C₁₉×#324	—	2	1	no	—
11	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
12	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
13	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄⋊Dic₁₉	—	2	1	no	—
15	C₂²×C₁₉⋊C₈	—	2	1	no	—
16	C₁₉×C₂²⋊C₈	—	4	1	no	—
17	C₁₉×#95	—	4	1	no	—
18	C₁₉⋊#95	—	4	1	no	—
19	C₂²⋊(C₁₉⋊C₈)	—	4	1	no	—
20	C₄×C₁₉⋊C₈	—	2	1	no	—
21	C₄×C₁₉⋊C₈	C₈	1	2	yes	complemented
22	C₂²×C₄×C₁₉	—	2	1	no	—
23	C₂²×C₄×C₁₉	—	2	1	no	—
24	C₂²×C₄×C₁₉	—	2	1	no	—
25	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₂²×Dic₁₉	—	4	1	no	—
27	C₂×C₈×C₁₉	—	8	1	no	—
28	C₄⋊C₄×C₁₉	—	4	1	no	—
29	C₄⋊C₄×C₁₉	—	4	1	no	—
30	C₄²×C₁₉	—	2	1	no	—
31	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
32	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
33	C₄⋊Dic₁₉	—	4	2	no	—
34	C₂×C₁₉⋊C₈	—	2	2	no	—
35	C₂×C₁₉⋊C₈	—	4	1	no	—
36	C₂×C₁₉⋊C₈	—	4	1	no	—
37	C₂×C₁₉⋊C₈	—	8	1	no	—
38	#7366	—	19	1	no	maximal, Sylow
39	C₂³×C₁₉	#99	1	1	yes	characteristic
40	C₂×C₄×C₁₉	—	2	1	no	—
41	C₂×C₄×C₁₉	—	2	1	no	—
42	C₂×C₄×C₁₉	—	2	1	no	—
43	C₂×C₄×C₁₉	—	2	1	no	—
44	C₂×C₄×C₁₉	—	4	1	no	—
45	C₂×C₄×C₁₉	—	4	1	no	—
46	C₂×C₄×C₁₉	—	4	1	no	—
47	C₂×C₄×C₁₉	—	4	1	no	—
48	C₂×C₄×C₁₉	—	8	1	no	—
49	C₂×C₄×C₁₉	—	8	1	no	—
50	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
51	C₂×C₄×C₁₉	#101	1	1	yes	characteristic
52	C₂×Dic₁₉	—	8	1	no	—
53	C₂×Dic₁₉	—	8	1	no	—
54	C₂×Dic₁₉	—	8	1	no	—
55	C₈×C₁₉	—	16	1	no	—
56	C₁₉⋊C₈	—	4	2	no	—
57	C₁₉⋊C₈	—	16	1	no	—
58	#1835	—	19	1	no	—
59	#1324	—	19	1	no	—
60	#1324	D₁₉	1	1	yes	characteristic
61	C₂²×C₁₉	—	2	1	no	—
62	C₂²×C₁₉	—	2	1	no	—
63	C₂²×C₁₉	#324	1	1	yes	characteristic
64	C₂²×C₁₉	#354	1	1	yes	characteristic
65	C₂²×C₁₉	#355	1	1	yes	characteristic
66	C₄×C₁₉	—	2	1	no	—
67	C₄×C₁₉	—	2	1	no	—
68	C₄×C₁₉	—	4	1	no	—
69	C₄×C₁₉	—	4	1	no	—
70	C₄×C₁₉	—	8	1	no	—
71	C₄×C₁₉	—	8	1	no	—
72	Dic₁₉	—	16	1	no	—
73	C₂×C₄×C₈	—	19	1	no	—
74	#382	—	19	1	no	—
75	#382	C₂×D₁₉	1	1	yes	characteristic
76	#340	—	38	1	no	—
77	#340	—	38	1	no	—
78	#324	—	2	1	no	—
79	#324	—	38	1	no	—
80	C₂×C₁₉	—	2	1	no	—
81	C₂×C₁₉	—	2	1	no	—
82	C₂×C₁₉	#1324	1	1	yes	characteristic
83	C₂×C₁₉	#1414	1	1	yes	characteristic
84	C₂×C₁₉	#1414	1	1	yes	characteristic
85	C₂²×C₈	—	38	1	no	—
86	C₂×C₄⋊C₄	—	38	1	no	—
87	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
88	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
89	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
90	C₂²⋊C₈	—	4	1	no	—
91	C₂²⋊C₈	—	76	1	no	—
92	C₄×C₈	—	19	2	no	—
93	C₄×C₈	—	38	1	no	—
94	#95	—	4	1	no	—
95	#95	—	76	1	no	—
96	C₁₉	#7366	1	1	yes	characteristic, complemented, Sylow
97	C₂²×C₄	—	2	1	no	—
98	C₂²×C₄	—	2	1	no	—
99	C₂²×C₄	—	2	1	no	—
100	C₂²×C₄	—	76	1	no	—
101	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
102	C₂×C₈	—	8	1	no	—
103	C₂×C₈	—	38	2	no	—
104	C₂×C₈	—	76	1	no	—
105	C₂×C₈	—	76	1	no	—
106	C₂×C₈	—	152	1	no	—
107	C₄⋊C₄	—	4	1	no	—
108	C₄⋊C₄	—	4	1	no	—
109	C₄⋊C₄	—	76	2	no	—
110	C₄²	—	2	1	no	—
111	C₄²	C₈×D₁₉	1	1	yes	characteristic
112	C₄²	#64515	1	1	yes	characteristic
113	C₂³	#10597263	1	1	yes	characteristic
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	2	1	no	—
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	—	4	1	no	—
119	C₂×C₄	—	4	1	no	—
120	C₂×C₄	—	4	1	no	—
121	C₂×C₄	—	4	1	no	—
122	C₂×C₄	—	8	1	no	—
123	C₂×C₄	—	8	1	no	—
124	C₂×C₄	—	152	1	no	—
125	C₂×C₄	—	152	1	no	—
126	C₂×C₄	—	152	1	no	—
127	C₂×C₄	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
128	C₂×C₄	#10597281	1	1	yes	characteristic
129	C₈	—	16	1	no	—
130	C₈	—	304	1	no	—
131	C₈	—	76	2	no	—
132	C₂²	—	2	1	no	—
133	C₂²	—	2	1	no	—
134	C₂²	#11926269	1	1	yes	characteristic
135	C₂²	#11926338	1	1	yes	characteristic
136	C₂²	#11926340	1	1	yes	characteristic
137	C₄	—	2	1	no	—
138	C₄	—	2	1	no	—
139	C₄	—	4	1	no	—
140	C₄	—	4	1	no	—
141	C₄	—	8	1	no	—
142	C₄	—	8	1	no	—
143	C₄	—	304	1	no	—
144	C₂	—	2	1	no	—
145	C₂	—	2	1	no	—
146	C₂	#14561578	1	1	yes	characteristic
147	C₂	#14561809	1	1	yes	characteristic
148	C₂	#14561811	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563765

C₂

yes

maximal, characteristic

#14561579

C₂

yes

maximal, characteristic

C₁₉×#1324

C₂

yes

maximal, characteristic

C₂×C₄×C₁₉⋊C₈

C₄

yes

characteristic

#11926410

C₄

yes

—

—

—

C₁₉×#382

C₂²

yes

characteristic

C₁₉×#324

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#95

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

C₈

yes

complemented

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₈

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

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

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

#101

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1835

—

#1324

—

#1324

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

C₂×C₄×C₈

—

#382

—

#382

C₂×D₁₉

yes

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

D₇₆

yes

characteristic

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

C₂×C₄²

C₄×D₁₉

yes

characteristic

C₂²⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

#95

—

#95

—

C₁₉

#7366

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

152

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄²

—

111

C₄²

C₈×D₁₉

yes

characteristic

112

C₄²

#64515

yes

characteristic

113

C₂³

#10597263

yes

characteristic

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

152

—

125

C₂×C₄

—

152

—

126

C₂×C₄

—

152

—

127

C₂×C₄

(C₂×D₁₉)⋊C₈

yes

characteristic

128

C₂×C₄

#10597281

yes

characteristic

129

C₈

—

130

C₈

—

304

—

131

C₈

—

132

C₂²

—

133

C₂²

—

134

C₂²

#11926269

yes

characteristic

135

C₂²

#11926338

yes

characteristic

136

C₂²

#11926340

yes

characteristic

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

—

304

—

144

C₂

—

145

C₂

—

146

C₂

#14561578

yes

characteristic

147

C₂

#14561809

yes

characteristic

148

C₂

#14561811

yes

characteristic

	subgroup	G/H
center	C₂²	#11926338
commutator	C₄²×C₁₉	C₂×C₈
Frattini	#382	C₂×D₁₉
Fitting	C₁₉×#1324	C₂
socle	C₂²×C₁₉	#354
prime radical	C₂³×C₁₉	#99
cosocle	C₁₉×#382	C₂²
hypercenter	#1324	D₁₉
hypocenter	C₁₉	#7366
LCS	G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ #382 ◁ #1324

subgroup

G/H

center

C₂²

#11926338

commutator

C₄²×C₁₉

C₂×C₈

Frattini

#382

C₂×D₁₉

Fitting

C₁₉×#1324

C₂

C₂²×C₁₉

C₂³×C₁₉

C₁₉×#382

C₂²

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ #382 ◁ #1324

N	H ≅ G/N	type
21. C₄×C₁₉⋊C₈	C₈	semidirect
96. C₁₉	#7366	semidirect

H ≅ G/N

type

21. C₄×C₁₉⋊C₈

C₈

semidirect

96. C₁₉

#7366

semidirect

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

subgroup	index
#14563765	2
#14561579	2
C₁₉×#1324	2
#7366	19

subgroup

index

#14563765

#14561579

C₁₉×#1324

#7366

Subgroups — #18069945

Conjugacy classes of subgroups

Complements

Maximal subgroups