Group #18070113 — subgroups

Subgroups — #18070113

Order 4864.

146 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 41 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	#14565738	C₂	1	1	yes	maximal, characteristic
2	#14561739	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1400	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	#11926372	C₄	1	1	yes	characteristic
8	#11926346	—	2	1	no	—
9	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
10	C₁₉×M₆₄	—	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	C₁₉×M₃₂	—	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	#7424	—	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	#2218	—	19	1	no	—
56	#1400	D₁₉	1	1	yes	characteristic, complemented
57	#1385	—	19	1	no	—
58	C₂²×C₁₉	—	2	1	no	—
59	C₂²×C₁₉	—	4	1	no	—
60	C₂²×C₁₉	#357	1	1	yes	characteristic
61	C₂×D₁₉	—	16	1	no	—
62	C₂×D₁₉	—	16	1	no	—
63	C₂×D₁₉	—	16	1	no	—
64	C₄×C₁₉	—	2	1	no	—
65	C₄×C₁₉	#327	1	1	yes	characteristic
66	C₄×C₁₉	#360	1	1	yes	characteristic
67	Dic₁₉	—	16	1	no	—
68	C₂×D₁₆	—	19	1	no	—
69	C₂×M₃₂	C₂×D₁₉	1	1	yes	characteristic
70	#466	—	38	1	no	—
71	C₂×#108	—	38	1	no	—
72	M₆₄	—	2	1	no	—
73	#367	—	19	1	no	—
74	#357	—	38	1	no	—
75	C₂×C₁₉	—	2	1	no	—
76	C₂×C₁₉	—	4	1	no	—
77	C₂×C₁₉	#1347	1	1	yes	characteristic
78	D₁₉	—	32	1	no	—
79	C₂×D₈	—	38	1	no	—
80	C₂×M₁₆	—	76	1	no	—
81	C₂²×C₈	D₇₆	1	1	yes	characteristic
82	#121	—	76	1	no	—
83	D₁₆	—	76	1	no	—
84	M₃₂	—	4	1	no	—
85	C₂×C₁₆	C₄×D₁₉	1	1	yes	characteristic
86	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
87	#108	—	38	2	no	—
88	#108	—	76	1	no	—
89	#107	—	38	1	no	—
90	#102	—	76	1	no	—
91	C₃₂	—	4	1	no	—
92	C₁₉	#7424	1	1	yes	characteristic, complemented, Sylow
93	C₂×D₄	—	76	1	no	—
94	C₂×D₄	—	152	1	no	—
95	C₂²×C₄	D₁₅₂	1	1	yes	characteristic
96	D₈	—	76	1	no	—
97	D₈	—	76	1	no	—
98	M₁₆	—	76	2	no	—
99	M₁₆	—	152	1	no	—
100	C₂×C₈	—	2	1	no	—
101	C₂×C₈	—	2	1	no	—
102	C₂×C₈	—	152	1	no	—
103	C₂×C₈	#64516	1	1	yes	characteristic
104	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
105	C₄⋊C₄	—	76	1	no	—
106	C₂²⋊C₄	—	152	1	no	—
107	C₁₆	—	2	1	no	—
108	C₁₆	—	2	1	no	—
109	C₂³	—	152	1	no	—
110	C₂³	#10597257	1	1	yes	characteristic
111	D₄	—	304	2	no	—
112	D₄	—	152	1	no	—
113	D₄	—	152	1	no	—
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	152	1	no	—
117	C₂×C₄	D₃₀₄	1	1	yes	characteristic
118	C₂×C₄	#10597278	1	1	yes	characteristic
119	C₈	—	2	1	no	—
120	C₈	—	152	2	no	—
121	C₈	#10597263	1	1	yes	characteristic
122	C₈	#10597282	1	1	yes	characteristic
123	C₂²	—	2	1	no	—
124	C₂²	—	4	1	no	—
125	C₂²	—	304	1	no	—
126	C₂²	—	304	1	no	—
127	C₂²	—	304	1	no	—
128	C₂²	#11926346	1	1	yes	characteristic
129	C₄	—	2	1	no	—
130	C₄	—	304	1	no	—
131	C₄	#11926279	1	1	yes	characteristic
132	C₄	#11926355	1	1	yes	characteristic
133	C₂	—	2	1	no	—
134	C₂	—	4	1	no	—
135	C₂	—	608	1	no	—
136	C₂	#14561645	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565738

C₂

yes

maximal, characteristic

#14561739

C₂

yes

maximal, characteristic, complemented

C₁₉×#1400

C₂

yes

maximal, characteristic, complemented

C₂×D₃₀₄

C₄

yes

—

—

C₄

yes

characteristic

#11926346

—

C₂×C₁₉×M₃₂

C₂²

yes

characteristic

C₁₉×M₆₄

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

#10597376

—

C₂×#64520

—

C₂×D₁₅₂

—

C₁₉×M₃₂

—

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

—

#7424

—

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

—

#2218

—

#1400

D₁₉

yes

characteristic, complemented

#1385

—

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

—

C₂×M₃₂

C₂×D₁₉

yes

characteristic

#466

—

C₂×#108

—

M₆₄

—

#367

—

#357

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1347

yes

characteristic

D₁₉

—

C₂×D₈

—

C₂×M₁₆

—

C₂²×C₈

D₇₆

yes

characteristic

#121

—

D₁₆

—

M₃₂

—

C₂×C₁₆

C₄×D₁₉

yes

characteristic

C₂×C₁₆

C₂²⋊D₁₉

yes

—

—

—

—

C₃₂

—

C₁₉

#7424

yes

characteristic, complemented, Sylow

C₂×D₄

—

C₂×D₄

—

152

—

C₂²×C₄

D₁₅₂

yes

characteristic

D₈

—

D₈

—

M₁₆

—

M₁₆

—

152

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

152

—

103

C₂×C₈

#64516

yes

characteristic

104

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

105

C₄⋊C₄

—

106

C₂²⋊C₄

—

152

—

107

C₁₆

—

108

C₁₆

—

109

C₂³

—

152

—

110

C₂³

#10597257

yes

characteristic

111

D₄

—

304

—

112

D₄

—

152

—

113

D₄

—

152

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

152

—

117

C₂×C₄

D₃₀₄

yes

characteristic

118

C₂×C₄

#10597278

yes

characteristic

119

C₈

—

120

C₈

—

152

—

121

C₈

#10597263

yes

characteristic

122

C₈

#10597282

yes

characteristic

123

C₂²

—

124

C₂²

—

125

C₂²

—

304

—

126

C₂²

—

304

—

127

C₂²

—

304

—

128

C₂²

#11926346

yes

characteristic

129

C₄

—

130

C₄

—

304

—

131

C₄

#11926279

yes

characteristic

132

C₄

#11926355

yes

characteristic

133

C₂

—

134

C₂

—

135

C₂

—

608

—

136

C₂

#14561645

yes

characteristic

	subgroup	G/H
center	C₂	#14561645
commutator	C₂×C₁₆×C₁₉	C₂×C₄
Frattini	C₂×M₃₂	C₂×D₁₉
Fitting	C₁₉×#1400	C₂
socle	C₂×C₁₉	#1347
prime radical	#14565738	C₂
cosocle	C₂×C₁₉×M₃₂	C₂²
hypercenter	#1400	D₁₉
hypocenter	C₁₉	#7424
LCS	G ▷ C₂×C₁₆×C₁₉ ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂ ◁ #1400

subgroup

G/H

center

C₂

#14561645

commutator

C₂×C₁₆×C₁₉

C₂×C₄

Frattini

C₂×M₃₂

C₂×D₁₉

Fitting

C₁₉×#1400

C₂

C₂×C₁₉

C₂

C₂×C₁₉×M₃₂

C₂²

D₁₉

C₁₉

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

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂ ◁ #1400

N	H ≅ G/N	type
2. #14561739	C₂	semidirect
3. C₁₉×#1400	C₂	semidirect
56. #1400	D₁₉	semidirect
92. C₁₉	#7424	semidirect

H ≅ G/N

type

2. #14561739

C₂

semidirect

3. C₁₉×#1400

C₂

semidirect

56. #1400

D₁₉

semidirect

92. C₁₉

#7424

semidirect

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

subgroup	index
#14565738	2
#14561739	2
C₁₉×#1400	2
#7424	19

subgroup

index

#14565738

#14561739

C₁₉×#1400

#7424

Subgroups — #18070113

Conjugacy classes of subgroups

Complements

Maximal subgroups