Group #14563684 — subgroups

Subgroups — #14563684

Order 2432.

252 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 81 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	C₂×#10597353	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597279	C₂	1	2	yes	maximal, complemented
3	#11926526	C₂	1	2	yes	maximal
4	C₁₉⋊#338	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#338	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#64541	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
8	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×#64520	C₂²	1	2	yes	—
10	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
11	#10597353	—	2	4	no	—
12	C₂×#64515	C₄	1	2	yes	—
13	C₂×C₈×D₁₉	C₄	1	2	yes	—
14	#10597281	—	2	2	no	—
15	#10597280	—	2	2	no	—
16	#10597279	—	2	4	no	—
17	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
18	C₂×C₂²⋊D₁₉	Q₈	1	2	yes	—
19	#64541	—	2	2	no	—
20	#64541	—	2	2	no	—
21	C₂×D₇₆	D₄	1	1	yes	characteristic
22	C₂×C₄×D₁₉	C₂×C₄	1	2	yes	—
23	C₂×Dic₃₈	D₄	1	1	yes	characteristic
24	M₁₆×C₁₉	—	2	2	no	—
25	M₁₆×C₁₉	—	2	2	no	—
26	M₁₆×C₁₉	—	2	2	no	—
27	C₂×C₈×C₁₉	—	2	2	no	—
28	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
29	#64520	—	2	2	no	—
30	#64520	—	2	2	no	—
31	C₂×C₁₉⋊C₈	—	2	2	no	—
32	C₂×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
33	C₂×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
34	C₂×C₁₉⋊C₈	D₄	1	4	yes	—
35	#64515	—	2	4	no	—
36	C₈×D₁₉	—	2	4	no	—
37	C₂³×C₁₉	C₂×Q₈	1	1	yes	characteristic
38	C₂²×D₁₉	C₄⋊C₄	1	2	yes	—
39	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
41	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₁₉	#41	1	2	yes	—
43	C₂²⋊D₁₉	—	2	4	no	—
44	C₂×Dic₁₉	C₄⋊C₄	1	2	yes	—
45	D₇₆	—	2	2	no	—
46	C₄×D₁₉	—	2	2	no	—
47	C₄×D₁₉	—	2	2	no	—
48	Dic₃₈	—	2	2	no	—
49	C₈×C₁₉	—	2	2	no	—
50	C₈×C₁₉	—	4	2	no	—
51	C₁₉⋊C₈	—	4	2	no	—
52	C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
53	C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
54	#1813	—	19	1	no	maximal, Sylow
55	C₂²×C₁₉	—	4	1	no	—
56	C₂²×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
57	C₂²×C₁₉	C₂²⋊Q₈	1	2	yes	—
58	C₂×D₁₉	—	2	2	no	—
59	C₂×D₁₉	—	4	2	no	—
60	C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
61	C₄×C₁₉	#117	1	1	yes	characteristic
62	C₄×C₁₉	#121	1	2	yes	—
63	Dic₁₉	—	2	2	no	—
64	C₂×#131	—	19	1	no	—
65	C₂×#108	—	19	2	no	—
66	#413	—	19	2	no	—
67	#338	—	19	1	no	—
68	#338	D₁₉	1	1	yes	characteristic, complemented
69	C₂×C₁₉	—	2	1	no	—
70	C₂×C₁₉	—	2	2	no	—
71	C₂×C₁₉	#380	1	1	yes	characteristic
72	D₁₉	—	4	2	no	—
73	C₂×#41	—	19	1	no	—
74	#131	—	38	4	no	—
75	C₂×M₁₆	—	19	2	no	—
76	C₂×M₁₆	—	19	2	no	—
77	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
78	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
79	C₂²×C₈	—	19	1	no	—
80	C₂²×C₈	—	19	2	no	—
81	#108	—	38	4	no	—
82	#101	—	38	2	no	—
83	#100	—	38	2	no	—
84	C₁₉	#1813	1	1	yes	characteristic, complemented, Sylow
85	#41	—	38	2	no	—
86	#41	—	38	2	no	—
87	C₂×Q₈	—	19	1	no	—
88	C₂×D₄	—	19	2	no	—
89	C₂×D₄	—	19	1	no	—
90	C₂²×C₄	—	19	2	no	—
91	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
92	M₁₆	—	2	2	no	—
93	M₁₆	—	2	2	no	—
94	M₁₆	—	2	2	no	—
95	M₁₆	—	38	4	no	—
96	M₁₆	—	38	2	no	—
97	M₁₆	—	38	2	no	—
98	C₂×C₈	—	2	2	no	—
99	C₂×C₈	—	19	1	no	—
100	C₂×C₈	—	19	1	no	—
101	C₂×C₈	—	19	4	no	—
102	C₂×C₈	—	38	4	no	—
103	C₂×C₈	—	38	2	no	—
104	C₂×C₈	C₄×D₁₉	1	2	yes	—
105	C₂³	—	19	2	no	—
106	C₂³	Q₈×D₁₉	1	1	yes	characteristic
107	Q₈	—	38	2	no	—
108	D₄	—	38	4	no	—
109	D₄	—	38	2	no	—
110	C₂×C₄	—	19	2	no	—
111	C₂×C₄	—	38	2	no	—
112	C₂×C₄	—	38	2	no	—
113	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
114	C₂×C₄	#64541	1	2	yes	—
115	C₂×C₄	D₄×D₁₉	1	2	yes	—
116	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
117	C₈	—	2	2	no	—
118	C₈	—	4	2	no	—
119	C₈	—	19	2	no	—
120	C₈	—	19	2	no	—
121	C₈	—	76	2	no	—
122	C₂²	—	4	1	no	—
123	C₂²	—	38	2	no	—
124	C₂²	—	76	2	no	—
125	C₂²	C₄⋊C₄×D₁₉	1	1	yes	characteristic
126	C₂²	#10597342	1	2	yes	—
127	C₄	—	38	2	no	—
128	C₄	#10597318	1	1	yes	characteristic
129	C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
130	C₄	#10597330	1	2	yes	—
131	C₂	—	2	1	no	—
132	C₂	—	2	2	no	—
133	C₂	—	76	2	no	—
134	C₂	#11926403	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597353

C₂

yes

maximal, characteristic

C₂×#10597279

C₂

yes

maximal, complemented

#11926526

C₂

yes

maximal

C₁₉⋊#338

C₂

yes

maximal, characteristic, complemented

C₁₉×#338

C₂

yes

maximal, characteristic, complemented

C₂×#64541

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

—

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

—

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

#10597353

—

C₂×#64515

C₄

yes

—

C₂×C₈×D₁₉

C₄

yes

—

#10597281

—

#10597280

—

#10597279

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

Q₈

yes

—

#64541

—

#64541

—

C₂×D₇₆

D₄

yes

characteristic

C₂×C₄×D₁₉

C₂×C₄

yes

—

C₂×Dic₃₈

D₄

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂×C₁₉⋊C₈

D₄

yes

—

#64515

—

C₈×D₁₉

—

C₂³×C₁₉

C₂×Q₈

yes

characteristic

C₂²×D₁₉

C₄⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

C₄⋊C₄

yes

—

D₇₆

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

C₂²⋊C₄

yes

—

C₁₉⋊C₈

C₂²⋊C₄

yes

—

#1813

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₉

C₂²⋊Q₈

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

C₂×C₂²⋊C₄

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

Dic₁₉

—

—

—

—

—

D₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#380

yes

characteristic

D₁₉

—

C₂×#41

—

#131

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

—

C₂×M₁₆

C₂×D₁₉

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

#108

—

#101

—

#100

—

C₁₉

#1813

yes

characteristic, complemented, Sylow

#41

—

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

C₄×D₁₉

yes

—

105

C₂³

—

106

C₂³

Q₈×D₁₉

yes

characteristic

107

Q₈

—

108

D₄

—

109

D₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

114

C₂×C₄

#64541

yes

—

115

C₂×C₄

D₄×D₁₉

yes

—

116

C₂×C₄

D₄×D₁₉

yes

characteristic

117

C₈

—

118

C₈

—

119

C₈

—

120

C₈

—

121

C₈

—

122

C₂²

—

123

C₂²

—

124

C₂²

—

125

C₂²

C₄⋊C₄×D₁₉

yes

characteristic

126

C₂²

#10597342

yes

—

127

C₄

—

128

C₄

#10597318

yes

characteristic

129

C₄

C₂²⋊C₄×D₁₉

yes

characteristic

130

C₄

#10597330

yes

—

131

C₂

—

132

C₂

—

133

C₂

—

134

C₂

#11926403

yes

characteristic

	subgroup	G/H
center	C₄	#10597318
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#338	C₂
socle	C₂×C₁₉	#380
prime radical	C₂×#64541	C₂²
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#338	D₁₉
hypocenter	C₁₉	#1813
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #338

subgroup

G/H

center

C₄

#10597318

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#338

C₂

C₂×C₁₉

C₂²

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #338

N	H ≅ G/N	type
2. C₂×#10597279	C₂	semidirect
4. C₁₉⋊#338	C₂	semidirect
5. C₁₉×#338	C₂	semidirect
68. #338	D₁₉	semidirect
84. C₁₉	#1813	semidirect

H ≅ G/N

type

2. C₂×#10597279

C₂

semidirect

4. C₁₉⋊#338

C₂

semidirect

5. C₁₉×#338

C₂

semidirect

68. #338

D₁₉

semidirect

84. C₁₉

#1813

semidirect

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

subgroup	index
C₂×#10597353	2
C₂×#10597279	2
#11926526	2
C₁₉⋊#338	2
C₁₉×#338	2
#1813	19

subgroup

index

C₂×#10597353

C₂×#10597279

#11926526

C₁₉⋊#338

C₁₉×#338

#1813

Subgroups — #14563684

Conjugacy classes of subgroups

Complements

Maximal subgroups