Group #18069603 — subgroups

Subgroups — #18069603

Order 4864.

180 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 59 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	#14565447	C₂	1	1	yes	maximal, characteristic
2	#14563784	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1453	C₂	1	1	yes	maximal, characteristic
4	#11926365	—	2	1	no	—
5	#11926326	—	2	1	no	—
6	#11926322	C₄	1	2	yes	complemented
7	#11926315	—	2	1	no	—
8	#11926304	—	2	1	no	—
9	C₁₉⋊#338	C₄	1	1	yes	characteristic
10	#11926301	C₄	1	1	yes	characteristic
11	C₁₉×#431	—	2	1	no	—
12	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#322	—	2	1	no	—
14	C₁₉×#322	C₄	1	1	yes	characteristic, complemented
15	C₈²×C₁₉	C₄	1	1	yes	characteristic, complemented
16	C₂×M₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
18	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
19	#10597372	—	2	1	no	—
20	C₂×#64520	—	2	1	no	—
21	C₁₉×C₄⋊C₈	—	2	2	no	—
22	C₁₉×C₂²⋊C₈	—	2	2	no	—
23	C₁₉×#97	C₂×C₄	1	1	yes	characteristic
24	C₁₉×#97	Q₈	1	1	yes	characteristic
25	C₄×C₈×C₁₉	—	2	1	no	—
26	C₄×C₈×C₁₉	—	2	1	no	—
27	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
29	#10597269	—	2	2	no	—
30	C₂²×C₄×C₁₉	—	2	1	no	—
31	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
32	M₁₆×C₁₉	—	4	1	no	—
33	M₁₆×C₁₉	—	4	1	no	—
34	C₂×C₈×C₁₉	—	2	2	no	—
35	C₂×C₈×C₁₉	—	2	2	no	—
36	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
37	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
38	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
40	C₄²×C₁₉	—	2	1	no	—
41	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
42	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
43	C₂²⋊Dic₁₉	—	4	1	no	—
44	C₄⋊Dic₁₉	—	4	1	no	—
45	C₄×Dic₁₉	—	4	1	no	—
46	#64520	—	4	1	no	—
47	#64520	—	4	1	no	—
48	C₂×C₁₉⋊C₈	—	4	1	no	—
49	C₁₉⋊C₁₆	—	4	2	no	—
50	#7226	—	19	1	no	maximal, Sylow
51	C₂³×C₁₉	#104	1	1	yes	characteristic
52	C₂×C₄×C₁₉	—	2	1	no	—
53	C₂×C₄×C₁₉	—	2	1	no	—
54	C₂×C₄×C₁₉	—	2	1	no	—
55	C₂×C₄×C₁₉	—	2	1	no	—
56	C₂×C₄×C₁₉	—	4	2	no	—
57	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
58	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
59	C₂×Dic₁₉	—	8	1	no	—
60	C₈×C₁₉	—	2	1	no	—
61	C₈×C₁₉	—	2	1	no	—
62	C₈×C₁₉	—	2	1	no	—
63	C₈×C₁₉	—	2	1	no	—
64	C₈×C₁₉	—	4	2	no	—
65	C₈×C₁₉	—	4	2	no	—
66	C₁₉⋊C₈	—	8	1	no	—
67	#2165	—	19	1	no	—
68	#1841	—	19	1	no	—
69	#1453	D₁₉	1	1	yes	characteristic
70	C₂²×C₁₉	—	2	1	no	—
71	C₂²×C₁₉	—	4	1	no	—
72	C₂²×C₁₉	#339	1	1	yes	characteristic
73	C₄×C₁₉	—	2	2	no	—
74	C₄×C₁₉	—	2	1	no	—
75	C₄×C₁₉	—	4	1	no	—
76	C₄×C₁₉	H(3,ℤ/4)	1	1	yes	characteristic
77	C₄×C₁₉	#344	1	1	yes	characteristic
78	Dic₁₉	—	16	1	no	—
79	#431	—	2	1	no	—
80	C₄×M₁₆	C₂×D₁₉	1	1	yes	characteristic
81	#364	—	38	1	no	—
82	#349	—	38	1	no	—
83	#347	—	19	2	no	—
84	#344	—	38	1	no	—
85	#339	—	38	1	no	—
86	#338	—	19	1	no	—
87	H(3,ℤ/4)	—	19	1	no	—
88	#322	—	2	1	no	—
89	#322	Dic₁₉	1	1	yes	characteristic, complemented
90	C₈²	Dic₁₉	1	1	yes	characteristic, complemented
91	C₂×C₁₉	—	2	1	no	—
92	C₂×C₁₉	—	4	1	no	—
93	C₂×C₁₉	#1288	1	1	yes	characteristic
94	C₂×M₁₆	—	38	1	no	—
95	C₂×M₁₆	C₄×D₁₉	1	1	yes	characteristic
96	C₂×M₁₆	D₇₆	1	1	yes	characteristic
97	#117	—	38	1	no	—
98	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
99	M₃₂	—	38	2	no	—
100	C₄⋊C₈	—	2	2	no	—
101	C₂²⋊C₈	—	2	2	no	—
102	#97	Dic₃₈	1	1	yes	characteristic
103	#97	C₄×D₁₉	1	1	yes	characteristic
104	C₄×C₈	—	2	1	no	—
105	C₄×C₈	—	2	1	no	—
106	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
107	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
108	C₁₉	#7226	1	1	yes	characteristic, complemented, Sylow
109	C₂²×C₄	—	2	1	no	—
110	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
111	M₁₆	—	4	1	no	—
112	M₁₆	—	4	1	no	—
113	M₁₆	—	76	1	no	—
114	M₁₆	—	76	1	no	—
115	C₂×C₈	—	2	2	no	—
116	C₂×C₈	—	2	2	no	—
117	C₂×C₈	—	76	1	no	—
118	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
119	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
120	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
121	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
122	C₄⋊C₄	—	76	1	no	—
123	C₂²⋊C₄	—	76	1	no	—
124	C₄²	—	2	1	no	—
125	C₄²	—	76	1	no	—
126	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
127	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
128	C₁₆	—	76	2	no	—
129	C₂³	#10597262	1	1	yes	characteristic
130	C₂×C₄	—	2	1	no	—
131	C₂×C₄	—	2	1	no	—
132	C₂×C₄	—	2	1	no	—
133	C₂×C₄	—	2	1	no	—
134	C₂×C₄	—	4	2	no	—
135	C₂×C₄	—	152	1	no	—
136	C₂×C₄	#10597262	1	1	yes	characteristic
137	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
138	C₈	—	2	1	no	—
139	C₈	—	2	1	no	—
140	C₈	—	2	1	no	—
141	C₈	—	2	1	no	—
142	C₈	—	4	2	no	—
143	C₈	—	4	2	no	—
144	C₈	—	152	1	no	—
145	C₂²	—	2	1	no	—
146	C₂²	—	4	1	no	—
147	C₂²	#11926304	1	1	yes	characteristic
148	C₄	—	2	2	no	—
149	C₄	—	2	1	no	—
150	C₄	—	4	1	no	—
151	C₄	—	304	1	no	—
152	C₄	#11926301	1	1	yes	characteristic
153	C₄	#11926315	1	1	yes	characteristic
154	C₂	—	2	1	no	—
155	C₂	—	4	1	no	—
156	C₂	#14561500	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565447

C₂

yes

maximal, characteristic

#14563784

C₂

yes

maximal, characteristic

C₁₉×#1453

C₂

yes

maximal, characteristic

#11926365

—

#11926326

—

#11926322

C₄

yes

complemented

#11926315

—

#11926304

—

C₁₉⋊#338

C₄

yes

characteristic

#11926301

C₄

yes

characteristic

C₁₉×#431

—

C₄×M₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#322

—

C₁₉×#322

C₄

yes

characteristic, complemented

C₈²×C₁₉

C₄

yes

characteristic, complemented

C₂×M₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×M₁₆×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

#10597372

—

C₂×#64520

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

C₂×C₄

yes

characteristic

C₁₉×#97

Q₈

yes

characteristic

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

#10597269

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄²

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₄²×C₁₉

—

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

C₄⋊C₄

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₁₉⋊C₁₆

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2165

—

#1841

—

#1453

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#339

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

#431

—

C₄×M₁₆

C₂×D₁₉

yes

—

—

—

—

—

—

—

—

Dic₁₉

yes

characteristic, complemented

C₈²

Dic₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1288

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₄×D₁₉

yes

characteristic

C₂×M₁₆

D₇₆

yes

characteristic

#117

—

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

M₃₂

—

100

C₄⋊C₈

—

101

C₂²⋊C₈

—

102

#97

Dic₃₈

yes

characteristic

103

#97

C₄×D₁₉

yes

characteristic

104

C₄×C₈

—

105

C₄×C₈

—

106

C₄×C₈

C₂×Dic₁₉

yes

characteristic

107

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

108

C₁₉

#7226

yes

characteristic, complemented, Sylow

109

C₂²×C₄

—

110

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

111

M₁₆

—

112

M₁₆

—

113

M₁₆

—

114

M₁₆

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

C₄×Dic₁₉

yes

characteristic

119

C₂×C₈

Dic₁₉⋊C₄

yes

characteristic

120

C₂×C₈

C₄⋊Dic₁₉

yes

characteristic

121

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

122

C₄⋊C₄

—

123

C₂²⋊C₄

—

124

C₄²

—

125

C₄²

—

126

C₄²

Dic₁₉⋊C₄

yes

characteristic

127

C₄²

C₂²⋊Dic₁₉

yes

characteristic

128

C₁₆

—

129

C₂³

#10597262

yes

characteristic

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

152

—

136

C₂×C₄

#10597262

yes

characteristic

137

C₂×C₄

C₁₉⋊#95

yes

characteristic

138

C₈

—

139

C₈

—

140

C₈

—

141

C₈

—

142

C₈

—

143

C₈

—

144

C₈

—

152

—

145

C₂²

—

146

C₂²

—

147

C₂²

#11926304

yes

characteristic

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

—

304

—

152

C₄

#11926301

yes

characteristic

153

C₄

#11926315

yes

characteristic

154

C₂

—

155

C₂

—

156

C₂

#14561500

yes

characteristic

	subgroup	G/H
center	C₄	#11926301
commutator	C₂×C₈×C₁₉	C₄²
Frattini	C₄×M₁₆	C₂×D₁₉
Fitting	C₁₉×#1453	C₂
socle	C₂×C₁₉	#1288
prime radical	C₂³×C₁₉	#104
cosocle	C₄×M₁₆×C₁₉	C₂²
hypercenter	#1453	D₁₉
hypocenter	C₁₉	#7226
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #1453

subgroup

G/H

center

C₄

#11926301

commutator

C₂×C₈×C₁₉

C₄²

Frattini

C₄×M₁₆

C₂×D₁₉

Fitting

C₁₉×#1453

C₂

C₂×C₁₉

C₂³×C₁₉

C₄×M₁₆×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄ ◁ C₂×C₈ ◁ #1453

N	H ≅ G/N	type
6. #11926322	C₄	semidirect
14. C₁₉×#322	C₄	semidirect
15. C₈²×C₁₉	C₄	semidirect
89. #322	Dic₁₉	semidirect
90. C₈²	Dic₁₉	semidirect
108. C₁₉	#7226	semidirect

H ≅ G/N

type

6. #11926322

C₄

semidirect

14. C₁₉×#322

C₄

semidirect

15. C₈²×C₁₉

C₄

semidirect

89. #322

Dic₁₉

semidirect

90. C₈²

Dic₁₉

semidirect

108. C₁₉

#7226

semidirect

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

subgroup	index
#14565447	2
#14563784	2
C₁₉×#1453	2
#7226	19

subgroup

index

#14565447

#14563784

C₁₉×#1453

#7226

Subgroups — #18069603

Conjugacy classes of subgroups

Complements

Maximal subgroups