Group #18069920 — subgroups

Subgroups — #18069920

Order 4864.

204 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 47 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	#14561579	C₂	1	2	yes	maximal
2	C₁₉×#1960	C₂	1	1	yes	maximal, characteristic
3	#11926270	—	2	2	no	—
4	C₂×C₁₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
5	C₂×C₁₉×#103	—	2	2	no	—
6	C₂×C₁₉×#97	C₄	1	1	yes	characteristic
7	C₁₉×#382	C₂²	1	1	yes	characteristic
8	C₂²×Q₈×C₁₉	—	2	1	no	—
9	C₂²×C₈×C₁₉	—	2	1	no	—
10	C₁₉×C₄⋊Q₈	—	2	1	no	—
11	C₁₉×C₄⋊Q₈	—	4	1	no	—
12	C₁₉×C₄⋊Q₈	C₈	1	2	yes	complemented
13	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
14	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
15	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₁₉×#103	—	4	4	no	—
17	C₁₉×#97	—	4	1	no	—
18	C₁₉×#95	—	4	1	no	—
19	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
20	C₂×Q₈×C₁₉	—	2	2	no	—
21	C₂×Q₈×C₁₉	—	4	2	no	—
22	C₂×Q₈×C₁₉	—	4	2	no	—
23	C₂×Q₈×C₁₉	—	4	1	no	—
24	C₂²×C₄×C₁₉	—	2	1	no	—
25	C₂²×C₄×C₁₉	—	2	2	no	—
26	C₂²×C₄×C₁₉	—	4	1	no	—
27	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₈×C₁₉	—	2	2	no	—
29	C₂×C₈×C₁₉	—	4	1	no	—
30	C₂×C₈×C₁₉	—	4	1	no	—
31	C₄⋊C₄×C₁₉	—	4	2	no	—
32	C₄⋊C₄×C₁₉	—	4	2	no	—
33	C₄⋊C₄×C₁₉	—	4	2	no	—
34	C₄²×C₁₉	—	2	1	no	—
35	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
36	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
37	C₂×C₁₉⋊C₈	—	8	2	no	—
38	#7353	—	19	1	no	maximal, Sylow
39	C₂³×C₁₉	#99	1	1	yes	characteristic
40	Q₈×C₁₉	—	4	4	no	—
41	Q₈×C₁₉	—	8	2	no	—
42	C₂×C₄×C₁₉	—	2	1	no	—
43	C₂×C₄×C₁₉	—	2	1	no	—
44	C₂×C₄×C₁₉	—	2	1	no	—
45	C₂×C₄×C₁₉	—	2	1	no	—
46	C₂×C₄×C₁₉	—	4	2	no	—
47	C₂×C₄×C₁₉	—	4	2	no	—
48	C₂×C₄×C₁₉	—	4	2	no	—
49	C₂×C₄×C₁₉	—	8	1	no	—
50	C₂×C₄×C₁₉	—	8	1	no	—
51	C₂×C₄×C₁₉	—	8	2	no	—
52	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
53	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
54	C₈×C₁₉	—	4	2	no	—
55	C₁₉⋊C₈	—	16	2	no	—
56	#1960	D₁₉	1	1	yes	characteristic
57	#1324	—	19	2	no	—
58	C₂²×C₁₉	—	2	2	no	—
59	C₂²×C₁₉	#323	1	1	yes	characteristic
60	C₂²×C₁₉	#353	1	1	yes	characteristic
61	C₂²×C₁₉	#355	1	1	yes	characteristic
62	C₄×C₁₉	—	2	1	no	—
63	C₄×C₁₉	—	2	1	no	—
64	C₄×C₁₉	—	4	1	no	—
65	C₄×C₁₉	—	4	1	no	—
66	C₄×C₁₉	—	8	2	no	—
67	C₄×C₁₉	—	8	2	no	—
68	C₂×C₄⋊Q₈	Dic₁₉	1	1	yes	characteristic
69	C₂×#103	—	2	2	no	—
70	C₂×#97	Dic₁₉	1	1	yes	characteristic
71	#382	C₂×D₁₉	1	1	yes	characteristic
72	#324	—	38	2	no	—
73	C₂×C₁₉	—	2	1	no	—
74	C₂×C₁₉	—	2	1	no	—
75	C₂×C₁₉	#1318	1	1	yes	characteristic
76	C₂×C₁₉	#1407	1	2	yes	—
77	C₂²×Q₈	—	2	1	no	—
78	C₂²×C₈	—	2	1	no	—
79	C₄⋊Q₈	—	2	1	no	—
80	C₄⋊Q₈	—	4	1	no	—
81	C₄⋊Q₈	C₁₉⋊C₈	1	2	yes	complemented
82	C₂×C₄⋊C₄	—	4	1	no	—
83	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
84	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
85	#103	—	4	4	no	—
86	C₂²⋊C₈	—	76	2	no	—
87	#97	—	4	1	no	—
88	#95	—	4	1	no	—
89	C₁₉	#7353	1	1	yes	characteristic, complemented, Sylow
90	C₂×Q₈	—	2	2	no	—
91	C₂×Q₈	—	4	2	no	—
92	C₂×Q₈	—	4	2	no	—
93	C₂×Q₈	—	4	1	no	—
94	C₂²×C₄	—	2	1	no	—
95	C₂²×C₄	—	2	2	no	—
96	C₂²×C₄	—	4	1	no	—
97	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
98	C₂×C₈	—	2	2	no	—
99	C₂×C₈	—	4	1	no	—
100	C₂×C₈	—	4	1	no	—
101	C₂×C₈	—	152	2	no	—
102	C₄⋊C₄	—	4	2	no	—
103	C₄⋊C₄	—	4	2	no	—
104	C₄⋊C₄	—	4	2	no	—
105	C₄²	—	2	1	no	—
106	C₄²	C₂×C₁₉⋊C₈	1	1	yes	characteristic
107	C₄²	#64520	1	1	yes	characteristic
108	C₂³	#10597291	1	1	yes	characteristic
109	Q₈	—	4	4	no	—
110	Q₈	—	8	2	no	—
111	C₂×C₄	—	2	1	no	—
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	2	1	no	—
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	4	2	no	—
116	C₂×C₄	—	4	2	no	—
117	C₂×C₄	—	4	2	no	—
118	C₂×C₄	—	8	1	no	—
119	C₂×C₄	—	8	1	no	—
120	C₂×C₄	—	8	2	no	—
121	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
122	C₂×C₄	#10597290	1	1	yes	characteristic
123	C₈	—	4	2	no	—
124	C₈	—	304	2	no	—
125	C₂²	—	2	2	no	—
126	C₂²	#11926268	1	1	yes	characteristic
127	C₂²	#11926337	1	1	yes	characteristic
128	C₂²	#11926341	1	1	yes	characteristic
129	C₄	—	2	1	no	—
130	C₄	—	2	1	no	—
131	C₄	—	4	1	no	—
132	C₄	—	4	1	no	—
133	C₄	—	8	2	no	—
134	C₄	—	8	2	no	—
135	C₂	—	2	1	no	—
136	C₂	—	2	1	no	—
137	C₂	#14561567	1	1	yes	characteristic
138	C₂	#14561795	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14561579

C₂

yes

maximal

C₁₉×#1960

C₂

yes

maximal, characteristic

#11926270

—

C₂×C₁₉×C₄⋊Q₈

C₄

yes

characteristic

C₂×C₁₉×#103

—

C₂×C₁₉×#97

C₄

yes

characteristic

C₁₉×#382

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

C₈

yes

complemented

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₁₉×#103

—

C₁₉×#97

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₈

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

#100

yes

characteristic

C₈×C₁₉

—

C₁₉⋊C₈

—

#1960

D₁₉

yes

characteristic

#1324

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₂×C₄⋊Q₈

Dic₁₉

yes

characteristic

C₂×#103

—

C₂×#97

Dic₁₉

yes

characteristic

#382

C₂×D₁₉

yes

characteristic

#324

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1318

yes

characteristic

C₂×C₁₉

#1407

yes

—

C₂²×Q₈

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₁₉⋊C₈

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

#103

—

C₂²⋊C₈

—

#97

—

#95

—

C₁₉

#7353

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

152

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄²

—

106

C₄²

C₂×C₁₉⋊C₈

yes

characteristic

107

C₄²

#64520

yes

characteristic

108

C₂³

#10597291

yes

characteristic

109

Q₈

—

110

Q₈

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

122

C₂×C₄

#10597290

yes

characteristic

123

C₈

—

124

C₈

—

304

—

125

C₂²

—

126

C₂²

#11926268

yes

characteristic

127

C₂²

#11926337

yes

characteristic

128

C₂²

#11926341

yes

characteristic

129

C₄

—

130

C₄

—

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

135

C₂

—

136

C₂

—

137

C₂

#14561567

yes

characteristic

138

C₂

#14561795

yes

—

	subgroup	G/H
center	C₂²	#11926337
commutator	C₄²×C₁₉	C₂×C₈
Frattini	#382	C₂×D₁₉
Fitting	C₁₉×#1960	C₂
socle	C₂²×C₁₉	#353
prime radical	C₂³×C₁₉	#99
cosocle	C₁₉×#382	C₂²
hypercenter	#1960	D₁₉
hypocenter	C₁₉	#7353
LCS	G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ #382 ◁ #1960

subgroup

G/H

center

C₂²

#11926337

commutator

C₄²×C₁₉

C₂×C₈

Frattini

#382

C₂×D₁₉

Fitting

C₁₉×#1960

C₂

C₂²×C₁₉

C₂³×C₁₉

C₁₉×#382

C₂²

D₁₉

C₁₉

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

UCS

C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ #382 ◁ #1960

N	H ≅ G/N	type
12. C₁₉×C₄⋊Q₈	C₈	semidirect
81. C₄⋊Q₈	C₁₉⋊C₈	semidirect
89. C₁₉	#7353	semidirect

H ≅ G/N

type

12. C₁₉×C₄⋊Q₈

C₈

semidirect

81. C₄⋊Q₈

C₁₉⋊C₈

semidirect

89. C₁₉

#7353

semidirect

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

subgroup	index
#14561579	2
C₁₉×#1960	2
#7353	19

subgroup

index

#14561579

C₁₉×#1960

#7353

Subgroups — #18069920

Conjugacy classes of subgroups

Complements

Maximal subgroups