Group #14563115 — subgroups

Subgroups — #14563115

Order 2432.

198 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 55 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	#11926921	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926740	C₂	1	2	yes	maximal, complemented
3	#11926623	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926287	C₂	1	2	yes	maximal, complemented
5	C₁₉×#334	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₅₂	—	2	2	no	—
7	C₂×D₁₅₂	—	2	1	no	—
8	C₂×D₁₅₂	—	2	1	no	—
9	C₂×#64515	—	2	1	no	—
10	#10597320	C₂²	1	2	yes	—
11	C₄×D₇₆	C₂²	1	1	yes	characteristic
12	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
13	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	#10597278	—	2	2	no	—
15	(C₂×D₁₉)⋊C₈	—	2	1	no	—
16	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×D₇₆	—	2	2	no	—
18	C₂×D₇₆	—	2	2	no	—
19	C₂×D₇₆	—	2	2	no	—
20	C₂×D₇₆	D₄	1	1	yes	characteristic
21	C₂×C₄×D₁₉	—	2	1	no	—
22	C₂×C₈×C₁₉	—	2	2	no	—
23	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
25	C₄²×C₁₉	C₂³	1	1	yes	characteristic
26	(C₂×D₁₉)⋊C₄	—	2	1	no	—
27	C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
28	C₂×C₁₉⋊C₈	—	2	1	no	—
29	D₁₅₂	—	4	2	no	—
30	D₁₅₂	—	4	4	no	—
31	D₁₅₂	—	4	2	no	—
32	#64515	—	4	2	no	—
33	C₂²×D₁₉	—	2	1	no	—
34	C₂²×D₁₉	—	4	2	no	—
35	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
38	C₂×Dic₁₉	—	2	1	no	—
39	D₇₆	—	2	2	no	—
40	D₇₆	—	4	2	no	—
41	D₇₆	—	4	2	no	—
42	D₇₆	—	4	2	no	—
43	D₇₆	—	4	2	no	—
44	D₇₆	—	8	2	no	—
45	C₄×D₁₉	—	4	1	no	—
46	C₄×D₁₉	—	4	1	no	—
47	C₈×C₁₉	—	2	1	no	—
48	C₈×C₁₉	—	4	2	no	—
49	C₈×C₁₉	D₈	1	2	yes	complemented
50	C₁₉⋊C₈	—	4	1	no	—
51	#1687	—	19	1	no	maximal, Sylow
52	C₂²×C₁₉	#121	1	1	yes	characteristic
53	C₂×D₁₉	—	4	1	no	—
54	C₂×D₁₉	—	4	1	no	—
55	C₂×D₁₉	—	4	1	no	—
56	C₂×D₁₉	—	8	2	no	—
57	C₂×D₁₉	—	8	2	no	—
58	C₂×D₁₉	—	8	2	no	—
59	C₄×C₁₉	—	2	1	no	—
60	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
61	C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
62	C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
63	Dic₁₉	—	4	1	no	—
64	#493	—	19	1	no	—
65	#459	—	19	2	no	—
66	#436	—	19	1	no	—
67	#334	D₁₉	1	1	yes	characteristic, complemented
68	#331	—	19	2	no	—
69	C₂×C₁₉	#459	1	1	yes	characteristic
70	C₂×C₁₉	#469	1	1	yes	characteristic
71	C₂×C₁₉	#472	1	1	yes	characteristic
72	D₁₉	—	8	1	no	—
73	D₁₉	—	16	2	no	—
74	C₂×D₈	—	38	2	no	—
75	C₂×D₈	—	38	1	no	—
76	C₂×D₈	—	38	1	no	—
77	C₂×M₁₆	—	38	1	no	—
78	#127	—	19	2	no	—
79	C₄×D₄	—	19	1	no	—
80	C₄⋊C₈	—	19	1	no	—
81	C₄⋊C₈	C₂×D₁₉	1	2	yes	—
82	#102	—	38	2	no	—
83	C₂²⋊C₈	—	38	1	no	—
84	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
85	C₁₉	#1687	1	1	yes	characteristic, complemented, Sylow
86	C₂×D₄	—	19	1	no	—
87	C₂×D₄	—	38	2	no	—
88	C₂×D₄	—	38	2	no	—
89	C₂×D₄	—	38	2	no	—
90	C₂²×C₄	—	38	1	no	—
91	D₈	—	76	2	no	—
92	D₈	—	76	4	no	—
93	D₈	—	76	2	no	—
94	M₁₆	—	76	2	no	—
95	C₂×C₈	—	2	2	no	—
96	C₂×C₈	—	38	1	no	—
97	C₂×C₈	D₇₆	1	1	yes	characteristic
98	C₂×C₈	D₇₆	1	1	yes	characteristic
99	C₄⋊C₄	—	19	1	no	—
100	C₂²⋊C₄	—	38	1	no	—
101	C₄²	C₂²×D₁₉	1	1	yes	characteristic
102	C₂³	—	38	1	no	—
103	C₂³	—	76	2	no	—
104	D₄	—	38	2	no	—
105	D₄	—	76	2	no	—
106	D₄	—	76	2	no	—
107	D₄	—	76	2	no	—
108	D₄	—	76	2	no	—
109	D₄	—	152	2	no	—
110	C₂×C₄	—	38	1	no	—
111	C₂×C₄	—	76	1	no	—
112	C₂×C₄	—	76	1	no	—
113	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
114	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
115	C₂×C₄	#64545	1	1	yes	characteristic
116	C₈	—	2	1	no	—
117	C₈	—	4	2	no	—
118	C₈	—	76	1	no	—
119	C₈	D₁₅₂	1	2	yes	complemented
120	C₂²	—	76	1	no	—
121	C₂²	—	76	1	no	—
122	C₂²	—	76	1	no	—
123	C₂²	—	152	2	no	—
124	C₂²	—	152	2	no	—
125	C₂²	—	152	2	no	—
126	C₂²	#10597341	1	1	yes	characteristic
127	C₄	—	2	1	no	—
128	C₄	—	76	1	no	—
129	C₄	C₂×D₁₅₂	1	1	yes	characteristic
130	C₄	#10597354	1	1	yes	characteristic
131	C₄	#10597360	1	2	yes	—
132	C₂	—	304	2	no	—
133	C₂	—	152	1	no	—
134	C₂	#11926740	1	1	yes	characteristic
135	C₂	#11926798	1	1	yes	characteristic
136	C₂	#11926815	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926921

C₂

yes

maximal, characteristic, complemented

#11926740

C₂

yes

maximal, complemented

#11926623

C₂

yes

maximal, characteristic, complemented

#11926287

C₂

yes

maximal, complemented

C₁₉×#334

C₂

yes

maximal, characteristic, complemented

C₂×D₁₅₂

—

C₂×D₁₅₂

—

C₂×D₁₅₂

—

C₂×#64515

—

#10597320

C₂²

yes

—

C₄×D₇₆

C₂²

yes

characteristic

C₁₉×C₄⋊C₈

C₂²

yes

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597278

—

(C₂×D₁₉)⋊C₈

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

D₄

yes

characteristic

C₂×C₄×D₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

D₄

yes

characteristic

C₂×C₁₉⋊C₈

—

D₁₅₂

—

D₁₅₂

—

D₁₅₂

—

#64515

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

C₄×D₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

D₈

yes

complemented

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×D₈

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

Dic₁₉

—

—

—

—

D₁₉

yes

characteristic, complemented

#331

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

D₁₉

—

D₁₉

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

C₂×M₁₆

—

#127

—

C₄×D₄

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₁₉

yes

—

#102

—

C₂²⋊C₈

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#1687

yes

characteristic, complemented, Sylow

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

D₈

—

D₈

—

D₈

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₇₆

yes

characteristic

C₂×C₈

D₇₆

yes

characteristic

C₄⋊C₄

—

100

C₂²⋊C₄

—

101

C₄²

C₂²×D₁₉

yes

characteristic

102

C₂³

—

103

C₂³

—

104

D₄

—

105

D₄

—

106

D₄

—

107

D₄

—

108

D₄

—

109

D₄

—

152

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

C₂×D₇₆

yes

characteristic

114

C₂×C₄

D₄×D₁₉

yes

characteristic

115

C₂×C₄

#64545

yes

characteristic

116

C₈

—

117

C₈

—

118

C₈

—

119

C₈

D₁₅₂

yes

complemented

120

C₂²

—

121

C₂²

—

122

C₂²

—

123

C₂²

—

152

—

124

C₂²

—

152

—

125

C₂²

—

152

—

126

C₂²

#10597341

yes

characteristic

127

C₄

—

128

C₄

—

129

C₄

C₂×D₁₅₂

yes

characteristic

130

C₄

#10597354

yes

characteristic

131

C₄

#10597360

yes

—

132

C₂

—

304

—

133

C₂

—

152

—

134

C₂

#11926740

yes

characteristic

135

C₂

#11926798

yes

characteristic

136

C₂

#11926815

yes

characteristic

	subgroup	G/H
center	C₂²	#10597341
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#334	C₂
socle	C₂²×C₁₉	#121
hypercenter	#334	D₁₉
hypocenter	C₁₉	#1687
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #334

subgroup

G/H

center

C₂²

#10597341

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#334

C₂

C₂²×C₁₉

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #334

N	H ≅ G/N	type
1. #11926921	C₂	semidirect
2. #11926740	C₂	semidirect
3. #11926623	C₂	semidirect
4. #11926287	C₂	semidirect
5. C₁₉×#334	C₂	semidirect
49. C₈×C₁₉	D₈	semidirect
67. #334	D₁₉	semidirect
85. C₁₉	#1687	semidirect
119. C₈	D₁₅₂	semidirect

H ≅ G/N

type

1. #11926921

C₂

semidirect

2. #11926740

C₂

semidirect

3. #11926623

C₂

semidirect

4. #11926287

C₂

semidirect

5. C₁₉×#334

C₂

semidirect

49. C₈×C₁₉

D₈

semidirect

67. #334

D₁₉

semidirect

85. C₁₉

#1687

semidirect

119. C₈

D₁₅₂

semidirect

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

subgroup	index
#11926921	2
#11926740	2
#11926623	2
#11926287	2
C₁₉×#334	2
#1687	19

subgroup

index

C₁₉×#334

Subgroups — #14563115

Conjugacy classes of subgroups

Complements

Maximal subgroups