Group #18069363 — subgroups

Subgroups — #18069363

Order 4864.

230 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 67 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	#14561468	C₂	1	2	yes	maximal
2	C₁₉×#1994	C₂	1	1	yes	maximal, characteristic
3	#11926597	—	2	2	no	—
4	C₁₉×#533	C₄	1	1	yes	characteristic
5	C₁₉×#423	C₄	1	1	yes	characteristic
6	C₄³×C₁₉	C₂²	1	1	yes	characteristic
7	C₁₉×#339	—	2	2	no	—
8	C₂×M₁₆×C₁₉	—	2	1	no	—
9	C₁₉×C₄⋊Q₈	—	2	1	no	—
10	C₁₉×#125	C₈	1	2	yes	complemented
11	C₁₉×C₂²⋊Q₈	—	4	1	no	—
12	C₄×Q₈×C₁₉	—	4	1	no	—
13	C₁₉×#117	—	2	1	no	—
14	C₂×C₄²×C₁₉	—	4	1	no	—
15	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₉	D₄	1	2	yes	—
17	C₁₉×C₄⋊C₈	—	4	1	no	—
18	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
19	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
20	C₄×C₁₉⋊C₈	—	4	2	no	—
21	C₂×Q₈×C₁₉	—	4	1	no	—
22	C₂²×C₄×C₁₉	—	2	1	no	—
23	C₂²×C₄×C₁₉	—	2	2	no	—
24	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
25	M₁₆×C₁₉	—	4	2	no	—
26	C₂×C₈×C₁₉	—	4	1	no	—
27	C₄⋊C₄×C₁₉	—	2	2	no	—
28	C₄⋊C₄×C₁₉	—	4	2	no	—
29	C₄⋊C₄×C₁₉	—	4	1	no	—
30	C₂²⋊C₄×C₁₉	—	4	1	no	—
31	C₄²×C₁₉	—	2	1	no	—
32	C₄²×C₁₉	—	2	2	no	—
33	C₄²×C₁₉	—	4	4	no	—
34	C₄²×C₁₉	—	4	1	no	—
35	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
36	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
37	C₄²×C₁₉	SD₁₆	1	2	yes	—
38	C₄²×C₁₉	Q₁₆	1	2	yes	—
39	C₂×C₁₉⋊C₈	—	4	4	no	—
40	#7134	—	19	1	no	maximal, Sylow
41	C₂³×C₁₉	#99	1	1	yes	characteristic
42	Q₈×C₁₉	—	8	2	no	—
43	C₂×C₄×C₁₉	—	2	1	no	—
44	C₂×C₄×C₁₉	—	2	2	no	—
45	C₂×C₄×C₁₉	—	2	1	no	—
46	C₂×C₄×C₁₉	—	2	2	no	—
47	C₂×C₄×C₁₉	—	4	4	no	—
48	C₂×C₄×C₁₉	—	4	2	no	—
49	C₂×C₄×C₁₉	—	4	2	no	—
50	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
51	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
52	C₂×C₄×C₁₉	#103	1	2	yes	—
53	C₂×C₄×C₁₉	#104	1	2	yes	—
54	C₈×C₁₉	—	8	1	no	—
55	C₁₉⋊C₈	—	8	4	no	—
56	#1994	D₁₉	1	1	yes	characteristic
57	#1276	—	19	2	no	—
58	C₂²×C₁₉	—	4	1	no	—
59	C₂²×C₁₉	#323	1	1	yes	characteristic
60	C₂²×C₁₉	#328	1	2	yes	—
61	C₄×C₁₉	—	2	4	no	—
62	C₄×C₁₉	—	2	2	no	—
63	C₄×C₁₉	—	4	1	no	—
64	C₄×C₁₉	—	4	2	no	—
65	C₄×C₁₉	—	8	2	no	—
66	C₄×C₁₉	Q₈⋊C₈	1	2	yes	—
67	C₄×C₁₉	#329	1	1	yes	characteristic
68	C₄×C₁₉	#333	1	1	yes	characteristic
69	#533	Dic₁₉	1	1	yes	characteristic
70	#431	—	38	2	no	—
71	#423	Dic₁₉	1	1	yes	characteristic
72	C₄³	C₂×D₁₉	1	1	yes	characteristic
73	#339	—	2	2	no	—
74	C₂×C₁₉	—	2	1	no	—
75	C₂×C₁₉	—	2	2	no	—
76	C₂×C₁₉	#1272	1	1	yes	characteristic
77	C₂×M₁₆	—	2	1	no	—
78	C₄⋊Q₈	—	2	1	no	—
79	#125	C₁₉⋊C₈	1	2	yes	complemented
80	C₂²⋊Q₈	—	4	1	no	—
81	C₄×Q₈	—	4	1	no	—
82	#117	—	2	1	no	—
83	C₂×C₄²	—	4	1	no	—
84	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
85	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
86	C₄⋊C₈	—	4	1	no	—
87	C₄⋊C₈	—	38	4	no	—
88	C₂²⋊C₈	—	76	2	no	—
89	C₄×C₈	—	76	2	no	—
90	C₁₉	#7134	1	1	yes	characteristic, complemented, Sylow
91	C₂×Q₈	—	4	1	no	—
92	C₂²×C₄	—	2	2	no	—
93	C₂²×C₄	—	2	1	no	—
94	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
95	M₁₆	—	4	2	no	—
96	C₂×C₈	—	4	1	no	—
97	C₂×C₈	—	76	4	no	—
98	C₄⋊C₄	—	2	2	no	—
99	C₄⋊C₄	—	4	2	no	—
100	C₄⋊C₄	—	4	1	no	—
101	C₂²⋊C₄	—	4	1	no	—
102	C₄²	—	2	1	no	—
103	C₄²	—	2	2	no	—
104	C₄²	—	4	4	no	—
105	C₄²	—	4	1	no	—
106	C₄²	C₂×C₁₉⋊C₈	1	1	yes	characteristic
107	C₄²	#64520	1	1	yes	characteristic
108	C₄²	#64527	1	2	yes	—
109	C₄²	#64528	1	2	yes	—
110	C₂³	#10597291	1	1	yes	characteristic
111	Q₈	—	8	2	no	—
112	C₂×C₄	—	2	2	no	—
113	C₂×C₄	—	2	1	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	4	4	no	—
117	C₂×C₄	—	4	2	no	—
118	C₂×C₄	—	4	2	no	—
119	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
120	C₂×C₄	#10597290	1	1	yes	characteristic
121	C₂×C₄	#10597292	1	2	yes	—
122	C₂×C₄	#10597294	1	2	yes	—
123	C₈	—	8	1	no	—
124	C₈	—	152	4	no	—
125	C₂²	—	4	1	no	—
126	C₂²	#11926268	1	1	yes	characteristic
127	C₂²	#11926281	1	2	yes	—
128	C₄	—	2	4	no	—
129	C₄	—	2	2	no	—
130	C₄	—	4	1	no	—
131	C₄	—	4	2	no	—
132	C₄	—	8	2	no	—
133	C₄	Q₈⋊(C₁₉⋊C₈)	1	2	yes	—
134	C₄	#11926284	1	1	yes	characteristic
135	C₄	#11926293	1	1	yes	characteristic
136	C₂	—	2	1	no	—
137	C₂	—	2	2	no	—
138	C₂	#14561461	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561468

C₂

yes

maximal

C₁₉×#1994

C₂

yes

maximal, characteristic

#11926597

—

C₁₉×#533

C₄

yes

characteristic

C₁₉×#423

C₄

yes

characteristic

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#339

—

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×#125

C₈

yes

complemented

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₁₉×#117

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₁₉×C₄⋊C₈

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₈

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₄²×C₁₉

SD₁₆

yes

—

C₄²×C₁₉

Q₁₆

yes

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#104

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1994

D₁₉

yes

characteristic

#1276

—

C₂²×C₁₉

—

C₂²×C₁₉

#323

yes

characteristic

C₂²×C₁₉

#328

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

Q₈⋊C₈

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

yes

characteristic

#431

—

#423

Dic₁₉

yes

characteristic

C₄³

C₂×D₁₉

yes

characteristic

#339

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1272

yes

characteristic

C₂×M₁₆

—

C₄⋊Q₈

—

#125

C₁₉⋊C₈

yes

complemented

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

C₂×C₄²

C₂²⋊D₁₉

yes

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₁₉

#7134

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₂²⋊C₄

—

102

C₄²

—

103

C₄²

—

104

C₄²

—

105

C₄²

—

106

C₄²

C₂×C₁₉⋊C₈

yes

characteristic

107

C₄²

#64520

yes

characteristic

108

C₄²

#64527

yes

—

109

C₄²

#64528

yes

—

110

C₂³

#10597291

yes

characteristic

111

Q₈

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

120

C₂×C₄

#10597290

yes

characteristic

121

C₂×C₄

#10597292

yes

—

122

C₂×C₄

#10597294

yes

—

123

C₈

—

124

C₈

—

152

—

125

C₂²

—

126

C₂²

#11926268

yes

characteristic

127

C₂²

#11926281

yes

—

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

—

132

C₄

—

133

C₄

Q₈⋊(C₁₉⋊C₈)

yes

—

134

C₄

#11926284

yes

characteristic

135

C₄

#11926293

yes

characteristic

136

C₂

—

137

C₂

—

138

C₂

#14561461

yes

characteristic

	subgroup	G/H
center	C₄	#11926293
commutator	C₄²×C₁₉	C₂×C₈
Frattini	C₄³	C₂×D₁₉
Fitting	C₁₉×#1994	C₂
socle	C₂×C₁₉	#1272
prime radical	C₂³×C₁₉	#99
cosocle	C₄³×C₁₉	C₂²
hypercenter	#1994	D₁₉
hypocenter	C₁₉	#7134
LCS	G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₄³ ◁ #1994

subgroup

G/H

center

C₄

#11926293

commutator

C₄²×C₁₉

C₂×C₈

Frattini

C₄³

C₂×D₁₉

Fitting

C₁₉×#1994

C₂

C₂×C₁₉

C₂³×C₁₉

C₄³×C₁₉

C₂²

D₁₉

C₁₉

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

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₄³ ◁ #1994

N	H ≅ G/N	type
10. C₁₉×#125	C₈	semidirect
79. #125	C₁₉⋊C₈	semidirect
90. C₁₉	#7134	semidirect

H ≅ G/N

type

10. C₁₉×#125

C₈

semidirect

79. #125

C₁₉⋊C₈

semidirect

90. C₁₉

#7134

semidirect

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

subgroup	index
#14561468	2
C₁₉×#1994	2
#7134	19

subgroup

index

#14561468

C₁₉×#1994

#7134

Subgroups — #18069363

Conjugacy classes of subgroups

Complements

Maximal subgroups