Group #14561923 — subgroups

Subgroups — #14561923

Order 2432.

208 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 101 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	#11926595	C₂	1	1	yes	maximal, characteristic
2	C₄×#64515	C₂	1	1	yes	maximal, characteristic
3	C₄×C₈×D₁₉	C₂	1	1	yes	maximal, characteristic
4	#11926266	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926266	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926266	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#322	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#64515	C₄	1	2	yes	—
9	C₂×C₈×D₁₉	C₄	1	2	yes	—
10	C₄²×D₁₉	C₂²	1	1	yes	characteristic
11	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	(C₂×D₁₉)⋊C₈	C₄	1	2	yes	—
15	#10597272	C₄	1	2	yes	—
16	Dic₁₉⋊C₈	C₄	1	2	yes	—
17	C₈×Dic₁₉	C₄	1	2	yes	—
18	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
19	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
20	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
25	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
26	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
27	C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
29	C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
30	C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
32	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
33	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
34	#64515	—	2	4	no	—
35	C₈×D₁₉	—	2	4	no	—
36	C₂²×D₁₉	C₄²	1	1	yes	characteristic
37	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
40	C₂×Dic₁₉	C₄²	1	1	yes	characteristic
41	C₂×Dic₁₉	C₄²	1	1	yes	characteristic
42	C₂×Dic₁₉	C₄²	1	1	yes	characteristic
43	C₄×D₁₉	—	2	2	no	—
44	C₄×D₁₉	—	2	2	no	—
45	C₄×D₁₉	M₁₆	1	4	yes	—
46	C₈×C₁₉	—	2	2	no	—
47	C₈×C₁₉	—	2	2	no	—
48	C₈×C₁₉	—	2	2	no	—
49	C₁₉⋊C₈	—	2	2	no	—
50	C₁₉⋊C₈	—	2	2	no	—
51	C₁₉⋊C₈	M₁₆	1	4	yes	complemented
52	#1451	—	19	1	no	maximal, Sylow
53	C₂²×C₁₉	C₂×C₄²	1	1	yes	characteristic
54	C₂×D₁₉	—	2	1	no	—
55	C₂×D₁₉	—	2	1	no	—
56	C₂×D₁₉	#97	1	2	yes	—
57	C₄×C₁₉	C₂×M₁₆	1	2	yes	—
58	C₄×C₁₉	C₂×M₁₆	1	2	yes	—
59	C₄×C₁₉	#131	1	2	yes	—
60	Dic₁₉	—	2	1	no	—
61	Dic₁₉	—	2	1	no	—
62	Dic₁₉	#97	1	2	yes	—
63	#431	—	19	1	no	—
64	C₄×M₁₆	—	19	1	no	—
65	C₂×C₄×C₈	—	19	1	no	—
66	#322	—	19	1	no	—
67	#322	—	19	1	no	—
68	#322	—	19	1	no	—
69	#322	D₁₉	1	1	yes	characteristic, complemented
70	C₂×C₁₉	C₂×#97	1	1	yes	characteristic
71	C₂×C₁₉	C₄×M₁₆	1	1	yes	characteristic
72	C₂×C₁₉	#405	1	1	yes	characteristic
73	D₁₉	—	2	2	no	—
74	C₂×M₁₆	—	19	2	no	—
75	C₂²×C₈	—	19	2	no	—
76	C₂×C₄²	—	19	1	no	—
77	C₄⋊C₈	—	19	2	no	—
78	C₂²⋊C₈	—	19	2	no	—
79	#97	—	19	2	no	—
80	C₄×C₈	—	19	2	no	—
81	C₄×C₈	—	19	1	no	—
82	C₄×C₈	—	19	1	no	—
83	C₄×C₈	—	19	1	no	—
84	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
85	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
86	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
87	C₁₉	#1451	1	1	yes	characteristic, complemented, Sylow
88	C₂²×C₄	—	19	1	no	—
89	C₂²×C₄	—	19	1	no	—
90	C₂²×C₄	—	19	1	no	—
91	M₁₆	—	38	4	no	—
92	C₂×C₈	—	19	2	no	—
93	C₂×C₈	—	19	2	no	—
94	C₂×C₈	—	19	2	no	—
95	C₂×C₈	—	38	4	no	—
96	C₂×C₈	C₄×D₁₉	1	2	yes	—
97	C₂×C₈	C₄×D₁₉	1	2	yes	—
98	C₂×C₈	C₄×D₁₉	1	2	yes	—
99	C₄²	—	19	1	no	—
100	C₄²	—	19	1	no	—
101	C₄²	—	19	1	no	—
102	C₄²	C₂²×D₁₉	1	1	yes	characteristic
103	C₂³	—	19	1	no	—
104	C₂×C₄	—	19	1	no	—
105	C₂×C₄	—	19	4	no	—
106	C₂×C₄	—	19	1	no	—
107	C₂×C₄	—	19	1	no	—
108	C₂×C₄	—	38	2	no	—
109	C₂×C₄	—	38	2	no	—
110	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
111	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
112	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
113	C₈	—	2	2	no	—
114	C₈	—	2	2	no	—
115	C₈	—	2	2	no	—
116	C₈	—	19	4	no	—
117	C₈	—	38	2	no	—
118	C₈	—	38	2	no	—
119	C₂²	—	19	2	no	—
120	C₂²	—	38	1	no	—
121	C₂²	—	38	1	no	—
122	C₂²	C₄²×D₁₉	1	1	yes	characteristic
123	C₄	—	19	2	no	—
124	C₄	—	38	1	no	—
125	C₄	—	38	1	no	—
126	C₄	#10597347	1	2	yes	—
127	C₄	M₁₆×D₁₉	1	2	yes	—
128	C₄	M₁₆×D₁₉	1	2	yes	—
129	C₂	—	38	2	no	—
130	C₂	#97×D₁₉	1	1	yes	characteristic
131	C₂	#11926496	1	1	yes	characteristic
132	C₂	#11926498	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926595

C₂

yes

maximal, characteristic

C₄×#64515

C₂

yes

maximal, characteristic

C₄×C₈×D₁₉

C₂

yes

maximal, characteristic

#11926266

C₂

yes

maximal, characteristic, complemented

#11926266

C₂

yes

maximal, characteristic, complemented

#11926266

C₂

yes

maximal, characteristic, complemented

C₁₉×#322

C₂

yes

maximal, characteristic, complemented

C₂×#64515

C₄

yes

—

C₂×C₈×D₁₉

C₄

yes

—

C₄²×D₁₉

C₂²

yes

characteristic

C₄×C₈×C₁₉

C₂²

yes

characteristic

C₄×C₈×C₁₉

C₂²

yes

characteristic

C₄×C₈×C₁₉

C₂²

yes

characteristic

(C₂×D₁₉)⋊C₈

C₄

yes

—

#10597272

C₄

yes

—

Dic₁₉⋊C₈

C₄

yes

—

C₈×Dic₁₉

C₄

yes

—

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×C₄×D₁₉

C₂×C₄

yes

characteristic

C₂×C₄×D₁₉

C₂×C₄

yes

characteristic

C₂×C₄×D₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

C₂³

yes

characteristic

C₄×Dic₁₉

C₂×C₄

yes

characteristic

C₄×Dic₁₉

C₂×C₄

yes

characteristic

C₄×Dic₁₉

C₂×C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

#64515

—

C₈×D₁₉

—

C₂²×D₁₉

C₄²

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×Dic₁₉

C₄²

yes

characteristic

C₂×Dic₁₉

C₄²

yes

characteristic

C₂×Dic₁₉

C₄²

yes

characteristic

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

M₁₆

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

M₁₆

yes

complemented

#1451

—

maximal, Sylow

C₂²×C₁₉

C₂×C₄²

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

#97

yes

—

C₄×C₁₉

C₂×M₁₆

yes

—

C₄×C₁₉

C₂×M₁₆

yes

—

C₄×C₁₉

#131

yes

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

#97

yes

—

#431

—

C₄×M₁₆

—

C₂×C₄×C₈

—

—

—

—

D₁₉

yes

characteristic, complemented

C₂×C₁₉

C₂×#97

yes

characteristic

C₂×C₁₉

C₄×M₁₆

yes

characteristic

C₂×C₁₉

#405

yes

characteristic

D₁₉

—

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₄×C₈

C₂×D₁₉

yes

characteristic

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#1451

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₁₉

yes

—

C₂×C₈

C₄×D₁₉

yes

—

C₂×C₈

C₄×D₁₉

yes

—

C₄²

—

100

C₄²

—

101

C₄²

—

102

C₄²

C₂²×D₁₉

yes

characteristic

103

C₂³

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

111

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

112

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

113

C₈

—

114

C₈

—

115

C₈

—

116

C₈

—

117

C₈

—

118

C₈

—

119

C₂²

—

120

C₂²

—

121

C₂²

—

122

C₂²

C₄²×D₁₉

yes

characteristic

123

C₄

—

124

C₄

—

125

C₄

—

126

C₄

#10597347

yes

—

127

C₄

M₁₆×D₁₉

yes

—

128

C₄

M₁₆×D₁₉

yes

—

129

C₂

—

130

C₂

#97×D₁₉

yes

characteristic

131

C₂

#11926496

yes

characteristic

132

C₂

#11926498

yes

characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₁₉
commutator, socle	C₂²×C₁₉	C₂×C₄²
Fitting	C₁₉×#322	C₂
prime radical	C₂²×D₁₉	C₄²
cosocle	C₄²×C₁₉	C₂³
hypercenter	#322	D₁₉
hypocenter	C₁₉	#1451
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄² ◁ #322

subgroup

G/H

center, Frattini

C₄²

C₂²×D₁₉

commutator, socle

C₂²×C₁₉

C₂×C₄²

Fitting

C₁₉×#322

C₂

prime radical

C₂²×D₁₉

C₄²

cosocle

C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₄² ◁ #322

N	H ≅ G/N	type
4. #11926266	C₂	semidirect
5. #11926266	C₂	semidirect
6. #11926266	C₂	semidirect
7. C₁₉×#322	C₂	semidirect
51. C₁₉⋊C₈	M₁₆	semidirect
69. #322	D₁₉	semidirect
87. C₁₉	#1451	semidirect

H ≅ G/N

type

4. #11926266

C₂

semidirect

5. #11926266

C₂

semidirect

6. #11926266

C₂

semidirect

7. C₁₉×#322

C₂

semidirect

51. C₁₉⋊C₈

M₁₆

semidirect

69. #322

D₁₉

semidirect

87. C₁₉

#1451

semidirect

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

subgroup	index
#11926595	2
C₄×#64515	2
C₄×C₈×D₁₉	2
#11926266	2
C₁₉×#322	2
#1451	19

subgroup

index

C₄×C₈×D₁₉

C₁₉×#322

Subgroups — #14561923

Conjugacy classes of subgroups

Complements

Maximal subgroups