Group #18072996 — subgroups

Subgroups — #18072996

Order 4864.

294 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 131 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	#14561927	C₂	1	1	yes	maximal, characteristic
2	#14561918	C₂	1	1	yes	maximal, characteristic
3	#14561466	C₂	1	2	yes	maximal
4	#14561464	C₂	1	2	yes	maximal
5	C₁₉×#1746	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	2	yes	—
7	#11926597	C₂²	1	2	yes	—
8	#11926266	C₄	1	4	yes	complemented
9	#11926265	C₄	1	2	yes	complemented
10	C₈×C₁₉⋊C₈	C₄	1	2	yes	complemented
11	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#376	C₂²	1	1	yes	characteristic
14	C₁₉×#336	C₄	1	4	yes	—
15	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
16	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
17	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
18	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
19	C₁₉×#97	—	2	2	no	—
20	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
23	C₁₉×#95	—	2	2	no	—
24	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
25	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
26	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
27	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
28	C₄×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
29	C₄×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
30	C₂²×C₄×C₁₉	—	2	2	no	—
31	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	#41	1	2	yes	—
33	C₂×C₈×C₁₉	—	2	4	no	—
34	C₂×C₈×C₁₉	—	2	2	no	—
35	C₂×C₈×C₁₉	—	2	4	no	—
36	C₂×C₈×C₁₉	C₄²	1	2	yes	—
37	C₂×C₈×C₁₉	C₄²	1	2	yes	—
38	C₄²×C₁₉	—	2	4	no	—
39	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
40	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
41	C₄²×C₁₉	#41	1	2	yes	—
42	C₂×C₁₉⋊C₈	—	2	4	no	—
43	C₂×C₁₉⋊C₈	—	2	4	no	—
44	#8141	—	19	1	no	maximal, Sylow
45	C₂³×C₁₉	#117	1	1	yes	characteristic
46	C₂×C₄×C₁₉	—	4	2	no	—
47	C₂×C₄×C₁₉	—	4	4	no	—
48	C₂×C₄×C₁₉	—	4	2	no	—
49	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
50	C₂×C₄×C₁₉	#117	1	2	yes	—
51	C₂×C₄×C₁₉	#117	1	2	yes	—
52	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
53	C₂×C₄×C₁₉	#131	1	4	yes	—
54	C₈×C₁₉	—	2	2	no	—
55	C₈×C₁₉	—	2	2	no	—
56	C₈×C₁₉	—	4	2	no	—
57	C₁₉⋊C₈	—	4	4	no	—
58	C₁₉⋊C₈	—	4	4	no	—
59	#1746	D₁₉	1	1	yes	characteristic
60	#1452	—	19	1	no	—
61	#1450	—	19	1	no	—
62	#1275	—	19	2	no	—
63	#1274	—	19	2	no	—
64	C₂²×C₁₉	—	2	2	no	—
65	C₂²×C₁₉	#376	1	1	yes	characteristic
66	C₂²×C₁₉	#433	1	2	yes	—
67	C₄×C₁₉	—	2	2	no	—
68	C₄×C₁₉	—	2	2	no	—
69	C₄×C₁₉	—	8	2	no	—
70	C₄×C₁₉	#405	1	2	yes	—
71	C₄×C₁₉	#433	1	2	yes	—
72	#431	—	19	2	no	—
73	#431	—	19	2	no	—
74	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
75	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
76	#376	C₂×D₁₉	1	1	yes	characteristic
77	#336	Dic₁₉	1	4	yes	—
78	#322	—	19	2	no	—
79	#322	—	19	4	no	—
80	C₈²	—	19	2	no	—
81	C₂×C₁₉	—	2	2	no	—
82	C₂×C₁₉	#1746	1	1	yes	characteristic
83	C₂×C₁₉	#1747	1	2	yes	—
84	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
85	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
86	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
87	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
88	C₄⋊C₈	—	38	2	no	—
89	C₄⋊C₈	—	38	2	no	—
90	C₂²⋊C₈	—	38	2	no	—
91	C₂²⋊C₈	—	38	2	no	—
92	#97	—	2	2	no	—
93	C₄×C₈	—	19	4	no	—
94	C₄×C₈	—	19	4	no	—
95	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
96	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
97	C₄×C₈	C₄×D₁₉	1	2	yes	—
98	#95	—	2	2	no	—
99	C₁₉	#8141	1	1	yes	characteristic, complemented, Sylow
100	C₂²×C₄	—	2	2	no	—
101	C₂²×C₄	#64541	1	2	yes	—
102	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
103	C₂×C₈	—	2	4	no	—
104	C₂×C₈	—	2	4	no	—
105	C₂×C₈	—	2	2	no	—
106	C₂×C₈	—	38	4	no	—
107	C₂×C₈	—	38	4	no	—
108	C₂×C₈	C₄×Dic₁₉	1	2	yes	—
109	C₂×C₈	C₄×Dic₁₉	1	2	yes	—
110	C₄²	—	2	4	no	—
111	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
112	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
113	C₄²	#64541	1	2	yes	—
114	C₂³	#10597372	1	1	yes	characteristic
115	C₂×C₄	—	4	2	no	—
116	C₂×C₄	—	4	4	no	—
117	C₂×C₄	—	4	2	no	—
118	C₂×C₄	#10597318	1	2	yes	—
119	C₂×C₄	#10597318	1	2	yes	—
120	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
121	C₂×C₄	#10597372	1	1	yes	characteristic
122	C₂×C₄	#10597394	1	4	yes	—
123	C₈	—	2	2	no	—
124	C₈	—	2	2	no	—
125	C₈	—	4	2	no	—
126	C₈	—	76	4	no	—
127	C₈	—	76	4	no	—
128	C₂²	—	2	2	no	—
129	C₂²	#11926390	1	1	yes	characteristic
130	C₂²	#11926605	1	2	yes	—
131	C₄	—	2	2	no	—
132	C₄	—	2	2	no	—
133	C₄	—	8	2	no	—
134	C₄	#11926500	1	2	yes	—
135	C₄	#11926605	1	2	yes	—
136	C₂	—	2	2	no	—
137	C₂	#14563387	1	1	yes	characteristic
138	C₂	#14563390	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14561927

C₂

yes

maximal, characteristic

#14561918

C₂

yes

maximal, characteristic

#14561466

C₂

yes

maximal

#14561464

C₂

yes

maximal

C₁₉×#1746

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

#11926597

C₂²

yes

—

#11926266

C₄

yes

complemented

#11926265

C₄

yes

complemented

C₈×C₁₉⋊C₈

C₄

yes

complemented

C₂×C₁₉×#97

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#376

C₂²

yes

characteristic

C₁₉×#336

C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×#97

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

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

—

C₂×C₈×C₁₉

C₄²

yes

—

C₂×C₈×C₁₉

C₄²

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₂×C₁₉⋊C₈

—

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

—

C₂×C₄×C₁₉

#117

yes

characteristic

C₂×C₄×C₁₉

#131

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1746

D₁₉

yes

—

—

—

—

C₂²×C₁₉

—

C₂²×C₁₉

#376

yes

characteristic

C₂²×C₁₉

#433

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#405

yes

—

C₄×C₁₉

#433

yes

—

#431

—

#431

—

C₂×#97

C₂×D₁₉

yes

characteristic

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

#376

C₂×D₁₉

yes

characteristic

#336

Dic₁₉

yes

—

#322

—

#322

—

C₈²

—

C₂×C₁₉

—

C₂×C₁₉

#1746

yes

characteristic

C₂×C₁₉

#1747

yes

—

C₂²×C₈

C₂×Dic₁₉

yes

—

C₂²×C₈

C₂×Dic₁₉

yes

—

C₂×C₄²

C₂×Dic₁₉

yes

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₄×D₁₉

yes

characteristic

C₄×C₈

C₄×D₁₉

yes

characteristic

C₄×C₈

C₄×D₁₉

yes

—

#95

—

C₁₉

#8141

yes

characteristic, complemented, Sylow

100

C₂²×C₄

—

101

C₂²×C₄

#64541

yes

—

102

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

C₄×Dic₁₉

yes

—

109

C₂×C₈

C₄×Dic₁₉

yes

—

110

C₄²

—

111

C₄²

C₂×C₄×D₁₉

yes

characteristic

112

C₄²

C₂×C₄×D₁₉

yes

characteristic

113

C₄²

#64541

yes

—

114

C₂³

#10597372

yes

characteristic

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

#10597318

yes

—

119

C₂×C₄

#10597318

yes

—

120

C₂×C₄

C₂×C₄×Dic₁₉

yes

characteristic

121

C₂×C₄

#10597372

yes

characteristic

122

C₂×C₄

#10597394

yes

—

123

C₈

—

124

C₈

—

125

C₈

—

126

C₈

—

127

C₈

—

128

C₂²

—

129

C₂²

#11926390

yes

characteristic

130

C₂²

#11926605

yes

—

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

#11926500

yes

—

135

C₄

#11926605

yes

—

136

C₂

—

137

C₂

#14563387

yes

characteristic

138

C₂

#14563390

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₄×Dic₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1746	C₂
socle	C₂²×C₁₉	#376
prime radical	C₂³×C₁₉	#117
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1746	D₁₉
hypocenter	C₁₉	#8141
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ #1746

subgroup

G/H

center

C₂×C₄

C₂×C₄×Dic₁₉

commutator

C₂×C₄×C₁₉

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1746

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₁₉

C₁ ◁ C₂×C₄ ◁ #1746

N	H ≅ G/N	type
8. #11926266	C₄	semidirect
9. #11926265	C₄	semidirect
10. C₈×C₁₉⋊C₈	C₄	semidirect
99. C₁₉	#8141	semidirect

H ≅ G/N

type

8. #11926266

C₄

semidirect

9. #11926265

C₄

semidirect

10. C₈×C₁₉⋊C₈

C₄

semidirect

99. C₁₉

#8141

semidirect

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

subgroup	index
#14561927	2
#14561918	2
#14561466	2
#14561464	2
C₁₉×#1746	2
#8141	19

subgroup

index

C₁₉×#1746

Subgroups — #18072996

Conjugacy classes of subgroups

Complements

Maximal subgroups