Group #18070105 — subgroups

Subgroups — #18070105

Order 4864.

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

normal subgroups only

This group has 150 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	#14561775	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1384	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₃₀₄	C₄	1	1	yes	characteristic, complemented
5	#11926780	—	2	1	no	—
6	#11926378	—	2	1	no	—
7	#11926372	C₄	1	1	yes	characteristic, complemented
8	#11926346	—	2	1	no	—
9	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
10	C₁₉×#427	—	2	1	no	—
11	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
12	C₁₉×#117	—	4	1	no	—
13	#10597376	—	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	C₁₉×#107	—	4	1	no	—
19	C₁₉×#106	—	2	2	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	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	C₄⋊C₄×C₁₉	—	4	2	no	—
32	C₂²⋊C₄×C₁₉	—	8	1	no	—
33	C₄²×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	#7422	—	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	#102	1	1	yes	characteristic
47	C₂×C₄×C₁₉	SD₃₂	1	1	yes	characteristic
48	C₂²⋊D₁₉	—	16	2	no	—
49	C₂×Dic₁₉	—	8	1	no	—
50	D₇₆	—	8	1	no	—
51	D₇₆	—	8	1	no	—
52	C₈×C₁₉	—	2	1	no	—
53	C₈×C₁₉	#99	1	1	yes	characteristic
54	C₈×C₁₉	#104	1	1	yes	characteristic
55	#2218	—	19	1	no	—
56	#1400	—	19	1	no	—
57	#1384	D₁₉	1	1	yes	characteristic, complemented
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	—	16	2	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	C₂×M₃₂	C₂×D₁₉	1	1	yes	characteristic
71	#466	—	38	1	no	—
72	#427	—	2	1	no	—
73	M₆₄	—	38	1	no	—
74	#367	—	19	1	no	—
75	#357	—	38	1	no	—
76	C₂×C₁₉	—	2	1	no	—
77	C₂×C₁₉	—	4	1	no	—
78	C₂×C₁₉	#1347	1	1	yes	characteristic
79	D₁₉	—	32	1	no	—
80	C₂×D₈	—	38	1	no	—
81	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
82	#121	—	76	1	no	—
83	#117	—	4	1	no	—
84	D₁₆	—	76	1	no	—
85	M₃₂	—	4	1	no	—
86	C₂×C₁₆	C₄×D₁₉	1	1	yes	characteristic
87	C₂×C₁₆	D₇₆	1	1	yes	characteristic
88	#107	—	4	1	no	—
89	#107	—	38	1	no	—
90	#106	—	2	2	no	—
91	#102	—	76	1	no	—
92	C₃₂	—	76	1	no	—
93	C₁₉	#7422	1	1	yes	characteristic, complemented, Sylow
94	C₂×D₄	—	76	1	no	—
95	C₂×D₄	—	152	1	no	—
96	C₂²×C₄	#64525	1	1	yes	characteristic
97	D₈	—	76	1	no	—
98	D₈	—	76	1	no	—
99	C₂×C₈	—	2	1	no	—
100	C₂×C₈	—	2	1	no	—
101	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
102	C₂×C₈	#64527	1	1	yes	characteristic
103	C₄⋊C₄	—	4	2	no	—
104	C₄⋊C₄	—	76	1	no	—
105	C₂²⋊C₄	—	8	1	no	—
106	C₂²⋊C₄	—	152	1	no	—
107	C₄²	—	8	1	no	—
108	C₁₆	—	2	1	no	—
109	C₁₆	—	2	1	no	—
110	C₂³	—	152	1	no	—
111	C₂³	#10597283	1	1	yes	characteristic
112	D₄	—	304	2	no	—
113	D₄	—	152	1	no	—
114	D₄	—	152	1	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	2	1	no	—
117	C₂×C₄	—	8	2	no	—
118	C₂×C₄	—	152	1	no	—
119	C₂×C₄	#10597266	1	1	yes	characteristic
120	C₂×C₄	#10597285	1	1	yes	characteristic
121	C₈	—	2	1	no	—
122	C₈	#10597262	1	1	yes	characteristic
123	C₈	#10597263	1	1	yes	characteristic
124	C₂²	—	2	1	no	—
125	C₂²	—	4	1	no	—
126	C₂²	—	304	1	no	—
127	C₂²	—	304	1	no	—
128	C₂²	—	304	1	no	—
129	C₂²	#11926344	1	1	yes	characteristic
130	C₄	—	2	1	no	—
131	C₄	—	16	2	no	—
132	C₄	—	304	1	no	—
133	C₄	#11926277	1	1	yes	characteristic
134	C₄	#11926353	1	1	yes	characteristic
135	C₂	—	2	1	no	—
136	C₂	—	4	1	no	—
137	C₂	—	608	1	no	—
138	C₂	#14561643	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565738

C₂

yes

maximal, characteristic

#14561775

C₂

yes

maximal, characteristic, complemented

C₁₉×#1384

C₂

yes

maximal, characteristic, complemented

C₂×D₃₀₄

C₄

yes

characteristic, complemented

#11926780

—

#11926378

—

#11926372

C₄

yes

characteristic, complemented

#11926346

—

C₂×C₁₉×M₃₂

C₂²

yes

characteristic

C₁₉×#427

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₁₉×#117

—

#10597376

—

C₂×D₁₅₂

—

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₁₉×#107

—

C₁₉×#106

—

#10597278

—

#10597275

—

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

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

D₁₅₂

—

D₁₅₂

—

C₁₆×C₁₉

—

C₁₆×C₁₉

—

#7422

—

maximal, Sylow

C₂³×C₁₉

D₁₆

yes

characteristic

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#102

yes

characteristic

C₂×C₄×C₁₉

SD₃₂

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

C₈×C₁₉

—

C₈×C₁₉

yes

C₈×C₁₉

yes

—

—

D₁₉

yes

characteristic, complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#357

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

C₂×D₁₆

—

C₂×M₃₂

C₂×D₁₉

yes

characteristic

#466

—

#427

—

M₆₄

—

#367

—

#357

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1347

yes

characteristic

D₁₉

—

C₂×D₈

—

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

#121

—

#117

—

D₁₆

—

M₃₂

—

C₂×C₁₆

C₄×D₁₉

yes

characteristic

C₂×C₁₆

D₇₆

yes

—

—

—

—

C₃₂

—

C₁₉

#7422

yes

characteristic, complemented, Sylow

C₂×D₄

—

C₂×D₄

—

152

—

C₂²×C₄

#64525

yes

characteristic

D₈

—

D₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

102

C₂×C₈

#64527

yes

characteristic

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₂²⋊C₄

—

106

C₂²⋊C₄

—

152

—

107

C₄²

—

108

C₁₆

—

109

C₁₆

—

110

C₂³

—

152

—

111

C₂³

#10597283

yes

characteristic

112

D₄

—

304

—

113

D₄

—

152

—

114

D₄

—

152

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

152

—

119

C₂×C₄

#10597266

yes

characteristic

120

C₂×C₄

#10597285

yes

characteristic

121

C₈

—

122

C₈

#10597262

yes

characteristic

123

C₈

#10597263

yes

characteristic

124

C₂²

—

125

C₂²

—

126

C₂²

—

304

—

127

C₂²

—

304

—

128

C₂²

—

304

—

129

C₂²

#11926344

yes

characteristic

130

C₄

—

131

C₄

—

132

C₄

—

304

—

133

C₄

#11926277

yes

characteristic

134

C₄

#11926353

yes

characteristic

135

C₂

—

136

C₂

—

137

C₂

—

608

—

138

C₂

#14561643

yes

characteristic

	subgroup	G/H
center	C₂	#14561643
commutator	C₂×C₁₆×C₁₉	C₂×C₄
Frattini	C₂×M₃₂	C₂×D₁₉
Fitting	C₁₉×#1384	C₂
socle	C₂×C₁₉	#1347
prime radical	#14565738	C₂
cosocle	C₂×C₁₉×M₃₂	C₂²
hypercenter	#1384	D₁₉
hypocenter	C₁₉	#7422
LCS	G ▷ C₂×C₁₆×C₁₉ ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂ ◁ #1384

subgroup

G/H

center

C₂

#14561643

commutator

C₂×C₁₆×C₁₉

C₂×C₄

Frattini

C₂×M₃₂

C₂×D₁₉

Fitting

C₁₉×#1384

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 ◁ #1384

N	H ≅ G/N	type
2. #14561775	C₂	semidirect
3. C₁₉×#1384	C₂	semidirect
4. C₂×D₃₀₄	C₄	semidirect
7. #11926372	C₄	semidirect
57. #1384	D₁₉	semidirect
93. C₁₉	#7422	semidirect

H ≅ G/N

type

2. #14561775

C₂

semidirect

3. C₁₉×#1384

C₂

semidirect

4. C₂×D₃₀₄

C₄

semidirect

7. #11926372

C₄

semidirect

57. #1384

D₁₉

semidirect

93. C₁₉

#7422

semidirect

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

subgroup	index
#14565738	2
#14561775	2
C₁₉×#1384	2
#7422	19

subgroup

index

#14565738

#14561775

C₁₉×#1384

#7422

Subgroups — #18070105

Conjugacy classes of subgroups

Complements

Maximal subgroups