Group #18070093 — subgroups

Subgroups — #18070093

Order 4864.

162 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 49 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	#14565721	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊(C₁₉⋊C₃₂)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1380	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₃₀₄	C₄	1	1	yes	characteristic, complemented
5	#11926780	—	2	1	no	—
6	C₂×C₁₉⋊C₃₂	—	2	1	no	—
7	#11926370	C₄	1	1	yes	characteristic, complemented
8	#11926346	—	2	1	no	—
9	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#107	—	2	1	no	—
11	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
12	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
13	#10597376	—	4	1	no	—
14	C₂×D₁₅₂	—	2	1	no	—
15	C₂×C₁₆×C₁₉	—	4	1	no	—
16	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
18	C₁₉×#107	—	2	2	no	—
19	C₁₉×#107	—	4	1	no	—
20	#10597278	—	4	1	no	—
21	#10597275	—	2	1	no	—
22	D₃₀₄	—	4	1	no	—
23	C₁₉⋊C₃₂	—	4	1	no	—
24	C₂²×C₄×C₁₉	—	8	1	no	—
25	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
26	C₂×C₂²⋊D₁₉	—	8	1	no	—
27	C₂×D₇₆	—	4	1	no	—
28	C₂×C₈×C₁₉	—	2	1	no	—
29	C₂×C₈×C₁₉	—	2	1	no	—
30	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
32	C₄⋊C₄×C₁₉	—	4	2	no	—
33	C₄⋊C₄×C₁₉	—	8	1	no	—
34	(C₂×D₁₉)⋊C₄	—	8	1	no	—
35	C₄⋊Dic₁₉	—	4	1	no	—
36	D₁₅₂	—	4	1	no	—
37	D₁₅₂	—	4	1	no	—
38	C₁₆×C₁₉	—	2	1	no	—
39	C₁₆×C₁₉	—	2	1	no	—
40	#7418	—	19	1	no	maximal, Sylow
41	C₂³×C₁₉	D₁₆	1	1	yes	characteristic
42	C₂²×D₁₉	—	8	1	no	—
43	C₂×C₄×C₁₉	—	2	1	no	—
44	C₂×C₄×C₁₉	—	2	1	no	—
45	C₂×C₄×C₁₉	—	8	2	no	—
46	C₂×C₄×C₁₉	—	16	1	no	—
47	C₂×C₄×C₁₉	—	16	1	no	—
48	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
49	C₂×C₄×C₁₉	SD₃₂	1	1	yes	characteristic
50	C₂²⋊D₁₉	—	16	1	no	—
51	C₂²⋊D₁₉	—	16	1	no	—
52	C₂×Dic₁₉	—	8	1	no	—
53	D₇₆	—	8	1	no	—
54	D₇₆	—	8	1	no	—
55	C₈×C₁₉	—	2	1	no	—
56	C₈×C₁₉	#99	1	1	yes	characteristic
57	C₈×C₁₉	#104	1	1	yes	characteristic
58	#2215	—	19	1	no	—
59	C₂²⋊C₃₂	—	19	1	no	—
60	#1380	D₁₉	1	1	yes	characteristic, complemented
61	C₂²×C₁₉	—	2	1	no	—
62	C₂²×C₁₉	—	2	1	no	—
63	C₂²×C₁₉	#357	1	1	yes	characteristic
64	C₂²×C₁₉	D₃₂	1	1	yes	characteristic
65	C₂²×C₁₉	SD₆₄	1	1	yes	characteristic
66	C₂×D₁₉	—	16	1	no	—
67	C₂×D₁₉	—	16	1	no	—
68	C₂×D₁₉	—	16	1	no	—
69	C₄×C₁₉	—	2	1	no	—
70	C₄×C₁₉	—	16	2	no	—
71	C₄×C₁₉	#327	1	1	yes	characteristic
72	C₄×C₁₉	#360	1	1	yes	characteristic
73	Dic₁₉	—	16	1	no	—
74	C₂×D₁₆	—	19	1	no	—
75	C₂²×C₁₆	C₂×D₁₉	1	1	yes	characteristic
76	#466	—	38	1	no	—
77	C₂×#107	—	2	1	no	—
78	C₂×C₃₂	—	38	1	no	—
79	#366	—	19	1	no	—
80	#357	—	38	1	no	—
81	C₂×C₁₉	—	2	1	no	—
82	C₂×C₁₉	—	2	1	no	—
83	C₂×C₁₉	#1347	1	1	yes	characteristic
84	C₂×C₁₉	#1415	1	1	yes	characteristic
85	C₂×C₁₉	#1418	1	1	yes	characteristic
86	D₁₉	—	32	1	no	—
87	C₂×D₈	—	38	1	no	—
88	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
89	#121	—	76	1	no	—
90	C₂×C₄⋊C₄	—	4	1	no	—
91	D₁₆	—	76	1	no	—
92	C₂×C₁₆	—	4	1	no	—
93	C₂×C₁₆	C₄×D₁₉	1	1	yes	characteristic
94	C₂×C₁₆	D₇₆	1	1	yes	characteristic
95	#107	—	2	2	no	—
96	#107	—	4	1	no	—
97	#107	—	38	1	no	—
98	#102	—	76	1	no	—
99	C₃₂	—	76	1	no	—
100	C₁₉	#7418	1	1	yes	characteristic, complemented, Sylow
101	C₂×D₄	—	76	1	no	—
102	C₂×D₄	—	152	1	no	—
103	C₂²×C₄	—	8	1	no	—
104	C₂²×C₄	#64525	1	1	yes	characteristic
105	D₈	—	76	1	no	—
106	D₈	—	76	1	no	—
107	C₂×C₈	—	2	1	no	—
108	C₂×C₈	—	2	1	no	—
109	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
110	C₂×C₈	#64527	1	1	yes	characteristic
111	C₄⋊C₄	—	4	2	no	—
112	C₄⋊C₄	—	8	1	no	—
113	C₄⋊C₄	—	76	1	no	—
114	C₂²⋊C₄	—	152	1	no	—
115	C₁₆	—	2	1	no	—
116	C₁₆	—	2	1	no	—
117	C₂³	—	152	1	no	—
118	C₂³	#10597283	1	1	yes	characteristic
119	D₄	—	304	1	no	—
120	D₄	—	304	1	no	—
121	D₄	—	152	1	no	—
122	D₄	—	152	1	no	—
123	C₂×C₄	—	2	1	no	—
124	C₂×C₄	—	2	1	no	—
125	C₂×C₄	—	8	2	no	—
126	C₂×C₄	—	16	1	no	—
127	C₂×C₄	—	16	1	no	—
128	C₂×C₄	—	152	1	no	—
129	C₂×C₄	#10597266	1	1	yes	characteristic
130	C₂×C₄	#10597285	1	1	yes	characteristic
131	C₈	—	2	1	no	—
132	C₈	#10597262	1	1	yes	characteristic
133	C₈	#10597263	1	1	yes	characteristic
134	C₂²	—	2	1	no	—
135	C₂²	—	2	1	no	—
136	C₂²	—	304	1	no	—
137	C₂²	—	304	1	no	—
138	C₂²	—	304	1	no	—
139	C₂²	#11926344	1	1	yes	characteristic
140	C₂²	#11926379	1	1	yes	characteristic
141	C₂²	#11926381	1	1	yes	characteristic
142	C₄	—	2	1	no	—
143	C₄	—	16	2	no	—
144	C₄	—	304	1	no	—
145	C₄	#11926277	1	1	yes	characteristic
146	C₄	#11926353	1	1	yes	characteristic
147	C₂	—	2	1	no	—
148	C₂	—	2	1	no	—
149	C₂	—	608	1	no	—
150	C₂	#14561643	1	1	yes	characteristic
151	C₂	#14561812	1	1	yes	characteristic
152	C₂	#14561821	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565721

C₂

yes

maximal, characteristic

C₂²⋊(C₁₉⋊C₃₂)

C₂

yes

maximal, characteristic, complemented

C₁₉×#1380

C₂

yes

maximal, characteristic, complemented

C₂×D₃₀₄

C₄

yes

characteristic, complemented

#11926780

—

C₂×C₁₉⋊C₃₂

—

#11926370

C₄

yes

characteristic, complemented

#11926346

—

C₂²×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×#107

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

—

#10597376

—

C₂×D₁₅₂

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₁₉×#107

—

C₁₉×#107

—

#10597278

—

#10597275

—

D₃₀₄

—

C₁₉⋊C₃₂

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₈

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂×D₇₆

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

D₁₅₂

—

D₁₅₂

—

C₁₆×C₁₉

—

C₁₆×C₁₉

—

#7418

—

maximal, Sylow

C₂³×C₁₉

D₁₆

yes

characteristic

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#102

yes

characteristic

C₂×C₄×C₁₉

SD₃₂

yes

characteristic

C₂²⋊D₁₉

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

C₈×C₁₉

—

C₈×C₁₉

yes

C₈×C₁₉

yes

—

C₂²⋊C₃₂

—

#1380

D₁₉

yes

characteristic, complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#357

yes

characteristic

C₂²×C₁₉

D₃₂

yes

characteristic

C₂²×C₁₉

SD₆₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

C₂×D₁₆

—

C₂²×C₁₆

C₂×D₁₉

yes

characteristic

#466

—

C₂×#107

—

C₂×C₃₂

—

#366

—

#357

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

D₁₉

—

C₂×D₈

—

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

#121

—

C₂×C₄⋊C₄

—

D₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₄×D₁₉

yes

characteristic

C₂×C₁₆

D₇₆

yes

—

—

—

—

C₃₂

—

100

C₁₉

#7418

yes

characteristic, complemented, Sylow

101

C₂×D₄

—

102

C₂×D₄

—

152

—

103

C₂²×C₄

—

104

C₂²×C₄

#64525

yes

characteristic

105

D₈

—

106

D₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

110

C₂×C₈

#64527

yes

characteristic

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₂²⋊C₄

—

152

—

115

C₁₆

—

116

C₁₆

—

117

C₂³

—

152

—

118

C₂³

#10597283

yes

characteristic

119

D₄

—

304

—

120

D₄

—

304

—

121

D₄

—

152

—

122

D₄

—

152

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

152

—

129

C₂×C₄

#10597266

yes

characteristic

130

C₂×C₄

#10597285

yes

characteristic

131

C₈

—

132

C₈

#10597262

yes

characteristic

133

C₈

#10597263

yes

characteristic

134

C₂²

—

135

C₂²

—

136

C₂²

—

304

—

137

C₂²

—

304

—

138

C₂²

—

304

—

139

C₂²

#11926344

yes

characteristic

140

C₂²

#11926379

yes

characteristic

141

C₂²

#11926381

yes

characteristic

142

C₄

—

143

C₄

—

144

C₄

—

304

—

145

C₄

#11926277

yes

characteristic

146

C₄

#11926353

yes

characteristic

147

C₂

—

148

C₂

—

149

C₂

—

608

—

150

C₂

#14561643

yes

characteristic

151

C₂

#14561812

yes

characteristic

152

C₂

#14561821

yes

characteristic

	subgroup	G/H
center	C₂²	#11926344
commutator	C₂×C₁₆×C₁₉	C₂×C₄
Frattini	C₂²×C₁₆	C₂×D₁₉
Fitting	C₁₉×#1380	C₂
socle	C₂²×C₁₉	#357
prime radical	#14565721	C₂
cosocle	C₂²×C₁₆×C₁₉	C₂²
hypercenter	#1380	D₁₉
hypocenter	C₁₉	#7418
LCS	G ▷ C₂×C₁₆×C₁₉ ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ #1380

subgroup

G/H

center

C₂²

#11926344

commutator

C₂×C₁₆×C₁₉

C₂×C₄

Frattini

C₂²×C₁₆

C₂×D₁₉

Fitting

C₁₉×#1380

C₂

C₂²×C₁₉

C₂

C₂²×C₁₆×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₁₆×C₁₉ ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ #1380

N	H ≅ G/N	type
2. C₂²⋊(C₁₉⋊C₃₂)	C₂	semidirect
3. C₁₉×#1380	C₂	semidirect
4. C₂×D₃₀₄	C₄	semidirect
7. #11926370	C₄	semidirect
60. #1380	D₁₉	semidirect
100. C₁₉	#7418	semidirect

H ≅ G/N

type

2. C₂²⋊(C₁₉⋊C₃₂)

C₂

semidirect

3. C₁₉×#1380

C₂

semidirect

4. C₂×D₃₀₄

C₄

semidirect

7. #11926370

C₄

semidirect

60. #1380

D₁₉

semidirect

100. C₁₉

#7418

semidirect

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

subgroup	index
#14565721	2
C₂²⋊(C₁₉⋊C₃₂)	2
C₁₉×#1380	2
#7418	19

subgroup

index

#14565721

C₂²⋊(C₁₉⋊C₃₂)

C₁₉×#1380

#7418

Subgroups — #18070093

Conjugacy classes of subgroups

Complements

Maximal subgroups