Group #18072984 — subgroups

Subgroups — #18072984

Order 4864.

354 conjugacy classes of subgroups; only the 195 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 195 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	#14561918	C₂	1	2	yes	maximal
2	#14561466	C₂	1	2	yes	maximal
3	#14561464	C₂	1	2	yes	maximal
4	C₁₉×#1726	C₂	1	1	yes	maximal, characteristic
5	#11926597	C₂²	1	4	yes	—
6	#11926265	C₄	1	4	yes	complemented
7	C₈×C₁₉⋊C₈	C₄	1	4	yes	complemented
8	C₂×C₁₉×#97	C₄	1	2	yes	—
9	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₈×C₁₉	C₄	1	2	yes	—
11	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#376	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
14	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
17	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
18	C₁₉×#97	—	2	2	no	—
19	C₁₉×#97	C₈	1	8	yes	complemented
20	C₄×C₈×C₁₉	—	2	4	no	—
21	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
22	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
23	C₁₉×#95	—	2	2	no	—
24	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
25	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
26	C₄×C₁₉⋊C₈	C₂×C₄	1	8	yes	—
27	C₂²×C₄×C₁₉	—	2	2	no	—
28	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
29	C₂²×C₄×C₁₉	#41	1	2	yes	—
30	C₂×C₈×C₁₉	—	2	2	no	—
31	C₂×C₈×C₁₉	—	2	2	no	—
32	C₂×C₈×C₁₉	C₄²	1	2	yes	—
33	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
34	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
35	C₂×C₈×C₁₉	C₂×C₈	1	4	yes	—
36	C₂×C₈×C₁₉	C₂×C₈	1	4	yes	—
37	C₂×C₈×C₁₉	M₁₆	1	4	yes	—
38	C₄²×C₁₉	—	2	2	no	—
39	C₄²×C₁₉	C₂×C₈	1	4	yes	—
40	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
41	C₄²×C₁₉	#41	1	2	yes	—
42	C₂×C₁₉⋊C₈	—	2	8	no	—
43	#8138	—	19	1	no	maximal, Sylow
44	C₂³×C₁₉	#117	1	1	yes	characteristic
45	C₂×C₄×C₁₉	—	2	4	no	—
46	C₂×C₄×C₁₉	—	4	2	no	—
47	C₂×C₄×C₁₉	—	4	4	no	—
48	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
49	C₂×C₄×C₁₉	#117	1	4	yes	—
50	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
51	C₂×C₄×C₁₉	C₂²×C₈	1	2	yes	—
52	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
53	C₈×C₁₉	—	2	4	no	—
54	C₈×C₁₉	C₄×C₈	1	4	yes	—
55	C₈×C₁₉	#97	1	2	yes	—
56	C₈×C₁₉	#97	1	2	yes	—
57	C₁₉⋊C₈	—	4	8	no	—
58	#1726	D₁₉	1	1	yes	characteristic
59	#1450	—	19	2	no	—
60	#1275	—	19	2	no	—
61	#1274	—	19	2	no	—
62	C₂²×C₁₉	—	2	2	no	—
63	C₂²×C₁₉	#376	1	1	yes	characteristic
64	C₂²×C₁₉	#431	1	2	yes	—
65	C₄×C₁₉	—	2	4	no	—
66	C₄×C₁₉	—	4	4	no	—
67	C₄×C₁₉	C₂×C₄×C₈	1	1	yes	characteristic
68	C₄×C₁₉	C₂×#97	1	1	yes	characteristic
69	C₄×C₁₉	#431	1	2	yes	—
70	#431	—	19	4	no	—
71	C₂×#97	Dic₁₉	1	2	yes	—
72	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
73	C₂×C₄×C₈	Dic₁₉	1	2	yes	—
74	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
75	#376	C₂×D₁₉	1	1	yes	characteristic
76	#322	—	19	4	no	—
77	C₈²	—	19	4	no	—
78	C₂×C₁₉	—	2	2	no	—
79	C₂×C₁₉	#1744	1	1	yes	characteristic
80	C₂×C₁₉	#1747	1	2	yes	—
81	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
82	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
83	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
84	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
85	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
86	C₄⋊C₈	—	38	4	no	—
87	C₂²⋊C₈	—	38	4	no	—
88	#97	—	2	2	no	—
89	#97	C₁₉⋊C₈	1	8	yes	complemented
90	C₄×C₈	—	2	4	no	—
91	C₄×C₈	—	19	8	no	—
92	C₄×C₈	C₄×D₁₉	1	2	yes	—
93	C₄×C₈	C₄×D₁₉	1	2	yes	—
94	#95	—	2	2	no	—
95	C₁₉	#8138	1	1	yes	characteristic, complemented, Sylow
96	C₂²×C₄	—	2	2	no	—
97	C₂²×C₄	#64541	1	2	yes	—
98	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
99	C₂×C₈	—	2	2	no	—
100	C₂×C₈	—	2	2	no	—
101	C₂×C₈	—	38	8	no	—
102	C₂×C₈	C₂×C₁₉⋊C₈	1	4	yes	—
103	C₂×C₈	C₂×C₁₉⋊C₈	1	4	yes	—
104	C₂×C₈	#64520	1	4	yes	—
105	C₂×C₈	C₄×Dic₁₉	1	2	yes	—
106	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
107	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
108	C₄²	—	2	2	no	—
109	C₄²	C₂×C₁₉⋊C₈	1	4	yes	—
110	C₄²	C₂×C₄×D₁₉	1	2	yes	—
111	C₄²	#64541	1	2	yes	—
112	C₂³	#10597372	1	1	yes	characteristic
113	C₂×C₄	—	2	4	no	—
114	C₂×C₄	—	4	2	no	—
115	C₂×C₄	—	4	4	no	—
116	C₂×C₄	#10597318	1	4	yes	—
117	C₂×C₄	C₂²×C₁₉⋊C₈	1	2	yes	—
118	C₂×C₄	C₂×#64520	1	2	yes	—
119	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
120	C₂×C₄	#10597372	1	1	yes	characteristic
121	C₈	—	2	4	no	—
122	C₈	—	76	8	no	—
123	C₈	C₄×C₁₉⋊C₈	1	4	yes	—
124	C₈	#10597260	1	2	yes	—
125	C₈	#10597260	1	2	yes	—
126	C₂²	—	2	2	no	—
127	C₂²	#11926390	1	1	yes	characteristic
128	C₂²	#11926597	1	2	yes	—
129	C₄	—	2	4	no	—
130	C₄	—	4	4	no	—
131	C₄	C₂×C₄×C₁₉⋊C₈	1	1	yes	characteristic
132	C₄	C₂×#10597260	1	1	yes	characteristic
133	C₄	#11926597	1	2	yes	—
134	C₂	—	2	2	no	—
135	C₂	#14563381	1	1	yes	characteristic
136	C₂	#14563390	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14561918

C₂

yes

maximal

#14561466

C₂

yes

maximal

#14561464

C₂

yes

maximal

C₁₉×#1726

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

#11926265

C₄

yes

complemented

C₈×C₁₉⋊C₈

C₄

yes

complemented

C₂×C₁₉×#97

C₄

yes

—

C₂×C₁₉×#97

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₉

C₄

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#376

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×#97

—

C₁₉×#97

C₈

yes

complemented

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄²

yes

—

C₂×C₈×C₁₉

C₄²

yes

characteristic

C₂×C₈×C₁₉

C₄²

yes

characteristic

C₂×C₈×C₁₉

C₂×C₈

yes

—

C₂×C₈×C₁₉

C₂×C₈

yes

—

C₂×C₈×C₁₉

M₁₆

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₈

yes

—

C₄²×C₁₉

C₂²×C₄

yes

—

C₄²×C₁₉

#41

yes

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

#117

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₈

yes

—

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₈×C₁₉

—

C₈×C₁₉

C₄×C₈

yes

—

C₈×C₁₉

#97

yes

—

C₈×C₁₉

#97

yes

—

C₁₉⋊C₈

—

#1726

D₁₉

yes

—

—

—

C₂²×C₁₉

—

C₂²×C₁₉

#376

yes

characteristic

C₂²×C₁₉

#431

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×C₄×C₈

yes

characteristic

C₄×C₁₉

C₂×#97

yes

characteristic

C₄×C₁₉

#431

yes

—

#431

—

C₂×#97

Dic₁₉

yes

—

C₂×#97

C₂×D₁₉

yes

characteristic

C₂×C₄×C₈

Dic₁₉

yes

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

#376

C₂×D₁₉

yes

characteristic

#322

—

C₈²

—

C₂×C₁₉

—

C₂×C₁₉

#1744

yes

characteristic

C₂×C₁₉

#1747

yes

—

C₂²×C₈

C₂×Dic₁₉

yes

—

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

C₂×C₄²

C₂×Dic₁₉

yes

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

C₁₉⋊C₈

yes

complemented

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₄×D₁₉

yes

—

C₄×C₈

C₄×D₁₉

yes

—

#95

—

C₁₉

#8138

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

#64541

yes

—

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

C₂×C₁₉⋊C₈

yes

—

103

C₂×C₈

C₂×C₁₉⋊C₈

yes

—

104

C₂×C₈

#64520

yes

—

105

C₂×C₈

C₄×Dic₁₉

yes

—

106

C₂×C₈

C₄×Dic₁₉

yes

characteristic

107

C₂×C₈

C₄×Dic₁₉

yes

characteristic

108

C₄²

—

109

C₄²

C₂×C₁₉⋊C₈

yes

—

110

C₄²

C₂×C₄×D₁₉

yes

—

111

C₄²

#64541

yes

—

112

C₂³

#10597372

yes

characteristic

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

#10597318

yes

—

117

C₂×C₄

C₂²×C₁₉⋊C₈

yes

—

118

C₂×C₄

C₂×#64520

yes

—

119

C₂×C₄

C₂×C₄×Dic₁₉

yes

characteristic

120

C₂×C₄

#10597372

yes

characteristic

121

C₈

—

122

C₈

—

123

C₈

C₄×C₁₉⋊C₈

yes

—

124

C₈

#10597260

yes

—

125

C₈

#10597260

yes

—

126

C₂²

—

127

C₂²

#11926390

yes

characteristic

128

C₂²

#11926597

yes

—

129

C₄

—

130

C₄

—

131

C₄

C₂×C₄×C₁₉⋊C₈

yes

characteristic

132

C₄

C₂×#10597260

yes

characteristic

133

C₄

#11926597

yes

—

134

C₂

—

135

C₂

#14563381

yes

characteristic

136

C₂

#14563390

yes

—

	subgroup	G/H
center	C₂×C₈	C₄×Dic₁₉
commutator	C₄×C₁₉	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1726	C₂
socle	C₂²×C₁₉	#376
prime radical	C₂³×C₁₉	#117
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1726	D₁₉
hypocenter	C₁₉	#8138
LCS	G ▷ C₄×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₈ ◁ #1726

subgroup

G/H

center

C₂×C₈

C₄×Dic₁₉

commutator

C₄×C₁₉

C₂×C₄×C₈

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1726

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄×C₁₉ ▷ C₁₉

C₁ ◁ C₂×C₈ ◁ #1726

N	H ≅ G/N	type
6. #11926265	C₄	semidirect
7. C₈×C₁₉⋊C₈	C₄	semidirect
19. C₁₉×#97	C₈	semidirect
89. #97	C₁₉⋊C₈	semidirect
95. C₁₉	#8138	semidirect

H ≅ G/N

type

6. #11926265

C₄

semidirect

7. C₈×C₁₉⋊C₈

C₄

semidirect

19. C₁₉×#97

C₈

semidirect

89. #97

C₁₉⋊C₈

semidirect

95. C₁₉

#8138

semidirect

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

subgroup	index
#14561918	2
#14561466	2
#14561464	2
C₁₉×#1726	2
#8138	19

subgroup

index

C₁₉×#1726

Subgroups — #18072984

Conjugacy classes of subgroups

Complements

Maximal subgroups