Group #18070357 — subgroups

Subgroups — #18070357

Order 4864.

162 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 25 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	#14562692	C₂	1	1	yes	maximal, characteristic
2	#14561672	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1408	C₂	1	1	yes	maximal, characteristic
4	#11927280	C₄	1	1	yes	characteristic, complemented
5	#11926741	—	2	1	no	—
6	#11926365	—	2	1	no	—
7	#11926288	C₄	1	1	yes	characteristic, complemented
8	#11926276	—	2	1	no	—
9	C₁₉×#493	C₂²	1	1	yes	characteristic
10	C₁₉×#353	—	2	1	no	—
11	C₂×D₈×C₁₉	—	4	1	no	—
12	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
13	C₁₉×#127	D₄	1	1	yes	characteristic
14	#10597382	—	4	1	no	—
15	#10597381	—	4	1	no	—
16	D₄×Dic₁₉	—	4	1	no	—
17	C₂×#64526	—	4	1	no	—
18	C₄×Dic₃₈	—	2	1	no	—
19	C₁₉×#99	—	4	1	no	—
20	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
21	#10597289	—	4	1	no	—
22	#10597269	—	4	1	no	—
23	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
24	C₂×D₄×C₁₉	—	2	1	no	—
25	C₂×D₄×C₁₉	—	2	1	no	—
26	C₂×D₄×C₁₉	—	4	1	no	—
27	C₂×D₄×C₁₉	—	4	1	no	—
28	C₂²×Dic₁₉	—	4	1	no	—
29	C₂×Dic₃₈	—	2	1	no	—
30	D₈×C₁₉	—	8	1	no	—
31	D₈×C₁₉	—	8	1	no	—
32	C₂×C₈×C₁₉	—	2	1	no	—
33	C₂²⋊C₄×C₁₉	—	8	1	no	—
34	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₂²⋊Dic₁₉	—	4	2	no	—
36	C₂²⋊Dic₁₉	—	4	1	no	—
37	#64526	—	8	2	no	—
38	C₄⋊Dic₁₉	—	2	1	no	—
39	Dic₁₉⋊C₄	—	4	1	no	—
40	C₄×Dic₁₉	—	4	1	no	—
41	C₂×C₁₉⋊C₈	—	4	1	no	—
42	C₁₉⋊C₁₆	—	8	1	no	—
43	#7516	—	19	1	no	maximal, Sylow
44	C₂³×C₁₉	—	4	1	no	—
45	C₂³×C₁₉	—	4	1	no	—
46	D₄×C₁₉	—	8	1	no	—
47	D₄×C₁₉	—	8	1	no	—
48	D₄×C₁₉	—	8	1	no	—
49	D₄×C₁₉	—	8	1	no	—
50	D₄×C₁₉	—	8	1	no	—
51	D₄×C₁₉	—	8	1	no	—
52	C₂×C₄×C₁₉	—	2	1	no	—
53	C₂×C₄×C₁₉	—	16	1	no	—
54	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
55	C₂×Dic₁₉	—	4	1	no	—
56	C₂×Dic₁₉	—	4	1	no	—
57	C₂×Dic₁₉	—	16	1	no	—
58	Dic₃₈	—	4	1	no	—
59	Dic₃₈	—	4	1	no	—
60	C₈×C₁₉	—	2	1	no	—
61	C₈×C₁₉	—	2	1	no	—
62	C₁₉⋊C₈	—	8	1	no	—
63	#1620	—	19	1	no	—
64	#1408	D₁₉	1	1	yes	characteristic
65	#1357	—	19	1	no	—
66	C₂²×C₁₉	—	8	2	no	—
67	C₂²×C₁₉	—	8	1	no	—
68	C₂²×C₁₉	—	8	1	no	—
69	C₂²×C₁₉	—	16	1	no	—
70	C₂²×C₁₉	AΣL(1,𝔽₁₆)	1	1	yes	characteristic
71	C₄×C₁₉	—	2	1	no	—
72	C₄×C₁₉	—	2	1	no	—
73	C₄×C₁₉	—	2	1	no	—
74	C₄×C₁₉	—	32	1	no	—
75	Dic₁₉	—	8	1	no	—
76	Dic₁₉	—	8	1	no	—
77	#559	—	19	1	no	—
78	#493	C₂×D₁₉	1	1	yes	characteristic
79	#460	—	38	1	no	—
80	#364	—	38	1	no	—
81	#353	—	2	1	no	—
82	#331	—	19	1	no	—
83	Q₈⋊C₈	—	38	1	no	—
84	C₂×C₁₉	—	2	1	no	—
85	C₂×C₁₉	—	16	1	no	—
86	C₂×C₁₉	—	16	1	no	—
87	C₂×C₁₉	#1402	1	1	yes	characteristic
88	C₂×SD₁₆	—	76	1	no	—
89	C₂×D₈	—	4	1	no	—
90	#127	C₄×D₁₉	1	1	yes	characteristic
91	#127	C₂²⋊D₁₉	1	1	yes	characteristic
92	#124	—	76	1	no	—
93	#123	—	76	1	no	—
94	C₄×Q₈	—	38	1	no	—
95	C₄×D₄	—	76	1	no	—
96	M₃₂	—	76	1	no	—
97	C₄⋊C₈	—	38	1	no	—
98	#102	—	76	1	no	—
99	#99	—	4	1	no	—
100	C₄×C₈	D₇₆	1	1	yes	characteristic
101	C₁₉	#7516	1	1	yes	characteristic, complemented, Sylow
102	C₂×Q₈	—	38	1	no	—
103	C₂×D₄	—	2	1	no	—
104	C₂×D₄	—	2	1	no	—
105	C₂×D₄	—	4	1	no	—
106	C₂×D₄	—	4	1	no	—
107	C₂²×C₄	—	76	1	no	—
108	SD₁₆	—	152	2	no	—
109	D₈	—	8	1	no	—
110	D₈	—	8	1	no	—
111	C₂×C₈	—	2	1	no	—
112	C₂×C₈	—	76	1	no	—
113	C₄⋊C₄	—	38	1	no	—
114	C₄⋊C₄	—	76	1	no	—
115	C₂²⋊C₄	—	8	1	no	—
116	C₂²⋊C₄	—	76	2	no	—
117	C₂²⋊C₄	—	76	1	no	—
118	C₄²	—	76	1	no	—
119	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
120	C₁₆	—	152	1	no	—
121	C₂³	—	4	1	no	—
122	C₂³	—	4	1	no	—
123	Q₈	—	76	1	no	—
124	Q₈	—	76	1	no	—
125	D₄	—	8	1	no	—
126	D₄	—	8	1	no	—
127	D₄	—	8	1	no	—
128	D₄	—	8	1	no	—
129	D₄	—	8	1	no	—
130	D₄	—	8	1	no	—
131	C₂×C₄	—	2	1	no	—
132	C₂×C₄	—	16	1	no	—
133	C₂×C₄	—	304	1	no	—
134	C₂×C₄	—	76	1	no	—
135	C₂×C₄	—	76	1	no	—
136	C₂×C₄	#10597263	1	1	yes	characteristic
137	C₈	—	2	1	no	—
138	C₈	—	2	1	no	—
139	C₈	—	152	1	no	—
140	C₂²	—	8	2	no	—
141	C₂²	—	8	1	no	—
142	C₂²	—	8	1	no	—
143	C₂²	—	16	1	no	—
144	C₂²	#11926330	1	1	yes	characteristic
145	C₄	—	2	1	no	—
146	C₄	—	2	1	no	—
147	C₄	—	2	1	no	—
148	C₄	—	32	1	no	—
149	C₄	—	152	1	no	—
150	C₄	—	152	1	no	—
151	C₂	—	2	1	no	—
152	C₂	—	16	1	no	—
153	C₂	—	16	1	no	—
154	C₂	#14561779	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14562692

C₂

yes

maximal, characteristic

#14561672

C₂

yes

maximal, characteristic

C₁₉×#1408

C₂

yes

maximal, characteristic

#11927280

C₄

yes

characteristic, complemented

#11926741

—

#11926365

—

#11926288

C₄

yes

characteristic, complemented

#11926276

—

C₁₉×#493

C₂²

yes

characteristic

C₁₉×#353

—

C₂×D₈×C₁₉

—

C₁₉×#127

C₂×C₄

yes

characteristic

C₁₉×#127

D₄

yes

characteristic

#10597382

—

#10597381

—

D₄×Dic₁₉

—

C₂×#64526

—

C₄×Dic₃₈

—

C₁₉×#99

—

C₄×C₈×C₁₉

D₄

yes

characteristic

#10597289

—

#10597269

—

C₄⋊(C₁₉⋊C₈)

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

#64526

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₁₉⋊C₁₆

—

#7516

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#99

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1620

—

#1408

D₁₉

yes

characteristic

#1357

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

AΣL(1,𝔽₁₆)

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

#559

—

#493

C₂×D₁₉

yes

—

—

—

—

Q₈⋊C₈

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1402

yes

characteristic

C₂×SD₁₆

—

C₂×D₈

—

#127

C₄×D₁₉

yes

characteristic

#127

C₂²⋊D₁₉

yes

characteristic

#124

—

#123

—

C₄×Q₈

—

C₄×D₄

—

M₃₂

—

C₄⋊C₈

—

#102

—

#99

—

100

C₄×C₈

D₇₆

yes

characteristic

101

C₁₉

#7516

yes

characteristic, complemented, Sylow

102

C₂×Q₈

—

103

C₂×D₄

—

104

C₂×D₄

—

105

C₂×D₄

—

106

C₂×D₄

—

107

C₂²×C₄

—

108

SD₁₆

—

152

—

109

D₈

—

110

D₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₂²⋊C₄

—

116

C₂²⋊C₄

—

117

C₂²⋊C₄

—

118

C₄²

—

119

C₄²

(C₂×D₁₉)⋊C₄

yes

characteristic

120

C₁₆

—

152

—

121

C₂³

—

122

C₂³

—

123

Q₈

—

124

Q₈

—

125

D₄

—

126

D₄

—

127

D₄

—

128

D₄

—

129

D₄

—

130

D₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

304

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

#10597263

yes

characteristic

137

C₈

—

138

C₈

—

139

C₈

—

152

—

140

C₂²

—

141

C₂²

—

142

C₂²

—

143

C₂²

—

144

C₂²

#11926330

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

—

152

—

150

C₄

—

152

—

151

C₂

—

152

C₂

—

153

C₂

—

154

C₂

#14561779

yes

characteristic

	subgroup	G/H
center	C₂	#14561779
commutator	C₁₉×#127	C₂×C₄
Frattini	#493	C₂×D₁₉
Fitting	C₁₉×#1408	C₂
socle	C₂×C₁₉	#1402
prime radical, cosocle	C₁₉×#493	C₂²
hypercenter	#1408	D₁₉
hypocenter	C₁₉	#7516
LCS	G ▷ C₁₉×#127 ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #493 ◁ #1408

subgroup

G/H

center

C₂

#14561779

commutator

C₁₉×#127

C₂×C₄

Frattini

#493

C₂×D₁₉

Fitting

C₁₉×#1408

C₂

socle

C₂×C₁₉

#1402

prime radical, cosocle

C₁₉×#493

C₂²

D₁₉

C₁₉

G ▷ C₁₉×#127 ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #493 ◁ #1408

N	H ≅ G/N	type
4. #11927280	C₄	semidirect
7. #11926288	C₄	semidirect
101. C₁₉	#7516	semidirect

H ≅ G/N

type

4. #11927280

C₄

semidirect

7. #11926288

C₄

semidirect

101. C₁₉

#7516

semidirect

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

subgroup	index
#14562692	2
#14561672	2
C₁₉×#1408	2
#7516	19

subgroup

index

#14562692

#14561672

C₁₉×#1408

#7516

Subgroups — #18070357

Conjugacy classes of subgroups

Complements

Maximal subgroups