Group #18070101 — subgroups

Subgroups — #18070101

Order 4864.

150 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 45 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	#14561729	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×C₂²⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₃₀₄	C₄	1	1	yes	characteristic
5	#11926780	—	2	1	no	—
6	C₂×#10597276	—	2	1	no	—
7	#11926370	C₄	1	1	yes	characteristic
8	#11926346	—	2	1	no	—
9	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×C₃₂	—	2	1	no	—
11	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
12	#10597376	—	4	1	no	—
13	C₂×#64520	—	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	#10597278	—	4	1	no	—
19	#10597276	—	2	2	no	—
20	#10597276	—	4	1	no	—
21	#10597275	—	2	1	no	—
22	D₃₀₄	—	4	1	no	—
23	C₁₉×C₃₂	—	4	1	no	—
24	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
25	C₂×C₂²⋊D₁₉	—	8	1	no	—
26	C₂×D₇₆	—	4	1	no	—
27	C₂×C₈×C₁₉	—	2	1	no	—
28	C₂×C₈×C₁₉	—	2	1	no	—
29	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
31	(C₂×D₁₉)⋊C₄	—	8	1	no	—
32	C₄⋊Dic₁₉	—	4	1	no	—
33	#64520	—	4	2	no	—
34	#64520	—	8	1	no	—
35	C₂×C₁₉⋊C₈	—	8	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	#7420	—	19	1	no	maximal, Sylow
41	C₂³×C₁₉	SD₃₂	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	#102	1	1	yes	characteristic
46	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
47	C₂²⋊D₁₉	—	16	2	no	—
48	C₂×Dic₁₉	—	8	1	no	—
49	D₇₆	—	8	1	no	—
50	D₇₆	—	8	1	no	—
51	C₈×C₁₉	—	2	1	no	—
52	C₈×C₁₉	#99	1	1	yes	characteristic
53	C₈×C₁₉	#104	1	1	yes	characteristic
54	C₁₉⋊C₈	—	8	2	no	—
55	#2215	—	19	1	no	—
56	C₂²⋊C₃₂	D₁₉	1	1	yes	characteristic, complemented
57	#1381	—	19	1	no	—
58	C₂²×C₁₉	—	2	1	no	—
59	C₂²×C₁₉	—	2	1	no	—
60	C₂²×C₁₉	—	2	1	no	—
61	C₂²×C₁₉	#357	1	1	yes	characteristic
62	C₂×D₁₉	—	16	1	no	—
63	C₂×D₁₉	—	16	1	no	—
64	C₂×D₁₉	—	16	1	no	—
65	C₄×C₁₉	—	2	1	no	—
66	C₄×C₁₉	#327	1	1	yes	characteristic
67	C₄×C₁₉	#360	1	1	yes	characteristic
68	Dic₁₉	—	16	1	no	—
69	C₂×D₁₆	—	19	1	no	—
70	C₂²×C₁₆	C₂×D₁₉	1	1	yes	characteristic
71	#466	—	38	1	no	—
72	C₂×#108	—	38	1	no	—
73	C₂×C₃₂	—	2	1	no	—
74	#366	—	19	1	no	—
75	#357	—	38	1	no	—
76	C₂×C₁₉	—	4	1	no	—
77	C₂×C₁₉	#1347	1	1	yes	characteristic
78	C₂×C₁₉	#1417	1	1	yes	characteristic
79	C₂×C₁₉	#1419	1	1	yes	characteristic
80	D₁₉	—	32	1	no	—
81	C₂×D₈	—	38	1	no	—
82	C₂×M₁₆	—	76	1	no	—
83	C₂²×C₈	D₇₆	1	1	yes	characteristic
84	#121	—	76	1	no	—
85	D₁₆	—	76	1	no	—
86	C₂×C₁₆	—	4	1	no	—
87	C₂×C₁₆	C₄×D₁₉	1	1	yes	characteristic
88	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
89	#108	—	38	2	no	—
90	#108	—	76	1	no	—
91	#107	—	38	1	no	—
92	#102	—	76	1	no	—
93	C₃₂	—	4	1	no	—
94	C₁₉	#7420	1	1	yes	characteristic, complemented, Sylow
95	C₂×D₄	—	76	1	no	—
96	C₂×D₄	—	152	1	no	—
97	C₂²×C₄	D₁₅₂	1	1	yes	characteristic
98	D₈	—	76	1	no	—
99	D₈	—	76	1	no	—
100	M₁₆	—	76	2	no	—
101	M₁₆	—	152	1	no	—
102	C₂×C₈	—	2	1	no	—
103	C₂×C₈	—	2	1	no	—
104	C₂×C₈	—	152	1	no	—
105	C₂×C₈	#64516	1	1	yes	characteristic
106	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
107	C₄⋊C₄	—	76	1	no	—
108	C₂²⋊C₄	—	152	1	no	—
109	C₁₆	—	2	1	no	—
110	C₁₆	—	2	1	no	—
111	C₂³	—	152	1	no	—
112	C₂³	#10597257	1	1	yes	characteristic
113	D₄	—	304	2	no	—
114	D₄	—	152	1	no	—
115	D₄	—	152	1	no	—
116	C₂×C₄	—	2	1	no	—
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	—	152	1	no	—
119	C₂×C₄	D₃₀₄	1	1	yes	characteristic
120	C₂×C₄	#10597278	1	1	yes	characteristic
121	C₈	—	2	1	no	—
122	C₈	—	152	2	no	—
123	C₈	#10597263	1	1	yes	characteristic
124	C₈	#10597282	1	1	yes	characteristic
125	C₂²	—	2	1	no	—
126	C₂²	—	2	1	no	—
127	C₂²	—	2	1	no	—
128	C₂²	—	304	1	no	—
129	C₂²	—	304	1	no	—
130	C₂²	—	304	1	no	—
131	C₂²	#11926346	1	1	yes	characteristic
132	C₄	—	2	1	no	—
133	C₄	—	304	1	no	—
134	C₄	#11926279	1	1	yes	characteristic
135	C₄	#11926355	1	1	yes	characteristic
136	C₂	—	4	1	no	—
137	C₂	—	608	1	no	—
138	C₂	#14561645	1	1	yes	characteristic
139	C₂	#14561820	1	1	yes	characteristic
140	C₂	#14561826	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565721

C₂

yes

maximal, characteristic

#14561729

C₂

yes

maximal, characteristic, complemented

C₁₉×C₂²⋊C₃₂

C₂

yes

maximal, characteristic, complemented

C₂×D₃₀₄

C₄

yes

—

—

C₄

yes

characteristic

#11926346

—

C₂²×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×C₃₂

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

#10597376

—

C₂×#64520

—

C₂×D₁₅₂

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

—

—

—

—

D₃₀₄

—

C₁₉×C₃₂

—

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

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

D₁₅₂

—

D₁₅₂

—

C₁₆×C₁₉

—

C₁₆×C₁₉

—

#7420

—

maximal, Sylow

C₂³×C₁₉

SD₃₂

yes

characteristic

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#102

yes

characteristic

C₂×C₄×C₁₉

D₁₆

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

C₈×C₁₉

—

C₈×C₁₉

yes

C₈×C₁₉

yes

C₁₉⋊C₈

—

#2215

—

C₂²⋊C₃₂

D₁₉

yes

characteristic, complemented

#1381

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#357

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

C₂×D₁₆

—

C₂²×C₁₆

C₂×D₁₉

yes

characteristic

#466

—

C₂×#108

—

C₂×C₃₂

—

#366

—

#357

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

D₁₉

—

C₂×D₈

—

C₂×M₁₆

—

C₂²×C₈

D₇₆

yes

characteristic

#121

—

D₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₄×D₁₉

yes

characteristic

C₂×C₁₆

C₂²⋊D₁₉

yes

—

—

—

—

C₃₂

—

C₁₉

#7420

yes

characteristic, complemented, Sylow

C₂×D₄

—

C₂×D₄

—

152

—

C₂²×C₄

D₁₅₂

yes

characteristic

D₈

—

D₈

—

100

M₁₆

—

101

M₁₆

—

152

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

152

—

105

C₂×C₈

#64516

yes

characteristic

106

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

107

C₄⋊C₄

—

108

C₂²⋊C₄

—

152

—

109

C₁₆

—

110

C₁₆

—

111

C₂³

—

152

—

112

C₂³

#10597257

yes

characteristic

113

D₄

—

304

—

114

D₄

—

152

—

115

D₄

—

152

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

152

—

119

C₂×C₄

D₃₀₄

yes

characteristic

120

C₂×C₄

#10597278

yes

characteristic

121

C₈

—

122

C₈

—

152

—

123

C₈

#10597263

yes

characteristic

124

C₈

#10597282

yes

characteristic

125

C₂²

—

126

C₂²

—

127

C₂²

—

128

C₂²

—

304

—

129

C₂²

—

304

—

130

C₂²

—

304

—

131

C₂²

#11926346

yes

characteristic

132

C₄

—

133

C₄

—

304

—

134

C₄

#11926279

yes

characteristic

135

C₄

#11926355

yes

characteristic

136

C₂

—

137

C₂

—

608

—

138

C₂

#14561645

yes

characteristic

139

C₂

#14561820

yes

characteristic

140

C₂

#14561826

yes

characteristic

	subgroup	G/H
center	C₂²	#11926346
commutator	C₂×C₁₆×C₁₉	C₂×C₄
Frattini	C₂²×C₁₆	C₂×D₁₉
Fitting	C₁₉×C₂²⋊C₃₂	C₂
socle	C₂²×C₁₉	#357
prime radical	#14565721	C₂
cosocle	C₂²×C₁₆×C₁₉	C₂²
hypercenter	C₂²⋊C₃₂	D₁₉
hypocenter	C₁₉	#7420
LCS	G ▷ C₂×C₁₆×C₁₉ ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ C₂²⋊C₃₂

subgroup

G/H

center

C₂²

#11926346

commutator

C₂×C₁₆×C₁₉

C₂×C₄

Frattini

C₂²×C₁₆

C₂×D₁₉

Fitting

C₁₉×C₂²⋊C₃₂

C₂

C₂²×C₁₉

C₂

C₂²×C₁₆×C₁₉

C₂²

hypercenter

C₂²⋊C₃₂

D₁₉

hypocenter

C₁₉

#7420

LCS

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

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ C₂²⋊C₃₂

N	H ≅ G/N	type
2. #14561729	C₂	semidirect
3. C₁₉×C₂²⋊C₃₂	C₂	semidirect
56. C₂²⋊C₃₂	D₁₉	semidirect
94. C₁₉	#7420	semidirect

H ≅ G/N

type

2. #14561729

C₂

semidirect

3. C₁₉×C₂²⋊C₃₂

C₂

semidirect

56. C₂²⋊C₃₂

D₁₉

semidirect

94. C₁₉

#7420

semidirect

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

subgroup	index
#14565721	2
#14561729	2
C₁₉×C₂²⋊C₃₂	2
#7420	19

subgroup

index

#14565721

#14561729

C₁₉×C₂²⋊C₃₂

#7420

Subgroups — #18070101

Conjugacy classes of subgroups

Complements

Maximal subgroups