Group #18069935 — subgroups

Subgroups — #18069935

Order 4864.

184 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 39 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	#14564611	C₂	1	1	yes	maximal, characteristic
2	#14561586	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1327	C₂	1	1	yes	maximal, characteristic
4	#11927101	C₄	1	1	yes	characteristic
5	C₄²×Dic₁₉	C₄	1	1	yes	characteristic
6	#11926326	—	2	1	no	—
7	#11926305	—	2	1	no	—
8	#11926305	—	2	1	no	—
9	C₁₉×#423	C₂²	1	1	yes	characteristic
10	C₁₉×#349	—	2	1	no	—
11	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
12	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
13	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
14	#10597372	—	2	1	no	—
15	#10597370	—	4	1	no	—
16	C₂×C₄×Dic₁₉	—	2	1	no	—
17	C₂×C₄×Dic₁₉	—	4	1	no	—
18	#10597316	C₈	1	2	yes	—
19	#10597315	—	2	1	no	—
20	C₄×Dic₃₈	—	4	1	no	—
21	C₁₉×M₃₂	—	4	1	no	—
22	C₁₉×C₄⋊C₈	—	4	1	no	—
23	#10597269	—	4	1	no	—
24	C₂²×C₄×C₁₉	—	2	1	no	—
25	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₂²×Dic₁₉	—	4	1	no	—
27	C₂×Dic₃₈	—	4	1	no	—
28	M₁₆×C₁₉	—	4	1	no	—
29	M₁₆×C₁₉	—	4	1	no	—
30	C₂×C₈×C₁₉	—	2	1	no	—
31	C₂×C₈×C₁₉	—	2	1	no	—
32	C₄²×C₁₉	—	2	1	no	—
33	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
34	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
35	C₂²⋊Dic₁₉	—	4	1	no	—
36	C₄⋊Dic₁₉	—	2	2	no	—
37	C₄⋊Dic₁₉	—	4	1	no	—
38	Dic₁₉⋊C₄	—	4	2	no	—
39	C₄×Dic₁₉	—	2	2	no	—
40	C₄×Dic₁₉	—	4	1	no	—
41	C₄×Dic₁₉	—	4	4	no	—
42	C₄×Dic₁₉	—	4	1	no	—
43	C₁₆×C₁₉	—	8	1	no	—
44	C₁₉⋊C₁₆	—	8	1	no	—
45	#7361	—	19	1	no	maximal, Sylow
46	C₂³×C₁₉	#100	1	1	yes	characteristic
47	C₂×C₄×C₁₉	—	2	1	no	—
48	C₂×C₄×C₁₉	—	2	1	no	—
49	C₂×C₄×C₁₉	—	2	1	no	—
50	C₂×C₄×C₁₉	—	2	1	no	—
51	C₂×C₄×C₁₉	—	4	2	no	—
52	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
53	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
54	C₂×Dic₁₉	—	4	2	no	—
55	C₂×Dic₁₉	—	4	4	no	—
56	C₂×Dic₁₉	—	4	2	no	—
57	Dic₃₈	—	8	2	no	—
58	C₈×C₁₉	—	4	1	no	—
59	C₈×C₁₉	—	4	1	no	—
60	#1994	—	19	1	no	—
61	#1327	—	19	1	no	—
62	#1327	D₁₉	1	1	yes	characteristic
63	C₂²×C₁₉	—	2	1	no	—
64	C₂²×C₁₉	—	4	1	no	—
65	C₂²×C₁₉	#323	1	1	yes	characteristic
66	C₄×C₁₉	—	2	2	no	—
67	C₄×C₁₉	—	2	1	no	—
68	C₄×C₁₉	—	4	1	no	—
69	C₄×C₁₉	#354	1	1	yes	characteristic
70	C₄×C₁₉	#356	1	1	yes	characteristic
71	Dic₁₉	—	4	4	no	—
72	Dic₁₉	—	8	2	no	—
73	#533	—	19	1	no	—
74	#423	C₂×D₁₉	1	1	yes	characteristic
75	C₄³	—	19	1	no	—
76	#349	—	2	1	no	—
77	#349	—	38	1	no	—
78	#339	—	38	1	no	—
79	#339	—	38	1	no	—
80	C₂×C₁₉	—	2	1	no	—
81	C₂×C₁₉	—	4	1	no	—
82	C₂×C₁₉	#1319	1	1	yes	characteristic
83	C₂×M₁₆	D₇₆	1	1	yes	characteristic
84	C₂×M₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
85	C₄⋊Q₈	—	38	1	no	—
86	#125	—	19	2	no	—
87	C₂²⋊Q₈	—	76	1	no	—
88	C₄×Q₈	—	76	1	no	—
89	#117	—	38	1	no	—
90	C₂×C₄²	—	38	1	no	—
91	C₂×C₄²	—	76	1	no	—
92	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
93	M₃₂	—	4	1	no	—
94	M₃₂	—	76	1	no	—
95	C₄⋊C₈	—	4	1	no	—
96	C₁₉	#7361	1	1	yes	characteristic, complemented, Sylow
97	C₂×Q₈	—	76	1	no	—
98	C₂²×C₄	—	2	1	no	—
99	C₂²×C₄	—	76	1	no	—
100	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
101	M₁₆	—	4	1	no	—
102	M₁₆	—	4	1	no	—
103	C₂×C₈	—	2	1	no	—
104	C₂×C₈	—	2	1	no	—
105	C₄⋊C₄	—	38	2	no	—
106	C₄⋊C₄	—	76	2	no	—
107	C₄⋊C₄	—	76	1	no	—
108	C₂²⋊C₄	—	76	1	no	—
109	C₄²	—	2	1	no	—
110	C₄²	—	38	2	no	—
111	C₄²	—	76	1	no	—
112	C₄²	—	76	4	no	—
113	C₄²	—	76	1	no	—
114	C₄²	C₈×D₁₉	1	1	yes	characteristic
115	C₄²	#64515	1	1	yes	characteristic
116	C₁₆	—	8	1	no	—
117	C₁₆	—	152	1	no	—
118	C₂³	#10597280	1	1	yes	characteristic
119	Q₈	—	152	2	no	—
120	C₂×C₄	—	2	1	no	—
121	C₂×C₄	—	2	1	no	—
122	C₂×C₄	—	2	1	no	—
123	C₂×C₄	—	2	1	no	—
124	C₂×C₄	—	4	2	no	—
125	C₂×C₄	—	76	2	no	—
126	C₂×C₄	—	76	4	no	—
127	C₂×C₄	—	76	2	no	—
128	C₂×C₄	#10597263	1	1	yes	characteristic
129	C₂×C₄	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
130	C₈	—	4	1	no	—
131	C₈	—	4	1	no	—
132	C₂²	—	2	1	no	—
133	C₂²	—	4	1	no	—
134	C₂²	#11926267	1	1	yes	characteristic
135	C₄	—	2	2	no	—
136	C₄	—	2	1	no	—
137	C₄	—	4	1	no	—
138	C₄	—	76	4	no	—
139	C₄	—	152	2	no	—
140	C₄	#11926338	1	1	yes	characteristic
141	C₄	#11926342	1	1	yes	characteristic
142	C₂	—	2	1	no	—
143	C₂	—	4	1	no	—
144	C₂	#14561568	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564611

C₂

yes

maximal, characteristic

#14561586

C₂

yes

maximal, characteristic

C₁₉×#1327

C₂

yes

maximal, characteristic

#11927101

C₄

yes

characteristic

C₄²×Dic₁₉

C₄

yes

—

—

—

C₁₉×#423

C₂²

yes

characteristic

C₁₉×#349

—

C₂×M₁₆×C₁₉

D₄

yes

characteristic

C₂×M₁₆×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

#10597372

—

#10597370

—

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

—

#10597316

C₈

yes

—

#10597315

—

C₄×Dic₃₈

—

C₁₉×M₃₂

—

C₁₉×C₄⋊C₈

—

#10597269

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₈

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

#99

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

#1994

—

#1327

—

#1327

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#323

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

#533

—

#423

C₂×D₁₉

yes

characteristic

C₄³

—

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1319

yes

characteristic

C₂×M₁₆

D₇₆

yes

characteristic

C₂×M₁₆

C₂²⋊D₁₉

yes

characteristic

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₄×D₁₉

yes

characteristic

M₃₂

—

M₃₂

—

C₄⋊C₈

—

C₁₉

#7361

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

101

M₁₆

—

102

M₁₆

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₂²⋊C₄

—

109

C₄²

—

110

C₄²

—

111

C₄²

—

112

C₄²

—

113

C₄²

—

114

C₄²

C₈×D₁₉

yes

characteristic

115

C₄²

#64515

yes

characteristic

116

C₁₆

—

117

C₁₆

—

152

—

118

C₂³

#10597280

yes

characteristic

119

Q₈

—

152

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

#10597263

yes

characteristic

129

C₂×C₄

(C₂×D₁₉)⋊C₈

yes

characteristic

130

C₈

—

131

C₈

—

132

C₂²

—

133

C₂²

—

134

C₂²

#11926267

yes

characteristic

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

152

—

140

C₄

#11926338

yes

characteristic

141

C₄

#11926342

yes

characteristic

142

C₂

—

143

C₂

—

144

C₂

#14561568

yes

characteristic

	subgroup	G/H
center	C₄	#11926338
commutator	C₄²×C₁₉	C₂×C₈
Frattini	#423	C₂×D₁₉
Fitting	C₁₉×#1327	C₂
socle	C₂×C₁₉	#1319
prime radical	C₂³×C₁₉	#100
cosocle	C₁₉×#423	C₂²
hypercenter	#1327	D₁₉
hypocenter	C₁₉	#7361
LCS	G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #423 ◁ #1327

subgroup

G/H

center

C₄

#11926338

commutator

C₄²×C₁₉

C₂×C₈

Frattini

#423

C₂×D₁₉

Fitting

C₁₉×#1327

C₂

C₂×C₁₉

C₂³×C₁₉

C₁₉×#423

C₂²

D₁₉

C₁₉

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

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #423 ◁ #1327

N	H ≅ G/N	type
96. C₁₉	#7361	semidirect

H ≅ G/N

type

96. C₁₉

#7361

semidirect

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

subgroup	index
#14564611	2
#14561586	2
C₁₉×#1327	2
#7361	19

subgroup

index

#14564611

#14561586

C₁₉×#1327

#7361

Subgroups — #18069935

Conjugacy classes of subgroups

Complements

Maximal subgroups