Group #14564475 — subgroups

Subgroups — #14564475

Order 2432.

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

normal subgroups only

This group has 396 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	C₂×#10597320	C₂	1	1	yes	maximal, characteristic
2	#11926568	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10597280	C₂	1	4	yes	maximal, complemented
4	C₄×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₇₆	C₄	1	4	yes	—
6	C₂²×D₇₆	C₂²	1	2	yes	—
7	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
8	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×#64520	C₂²	1	2	yes	—
10	#10597320	—	2	2	no	—
11	#10597320	—	2	1	no	—
12	#10597320	—	2	1	no	—
13	C₁₉×#97	—	2	1	no	—
14	C₄×C₈×C₁₉	—	2	1	no	—
15	#10597280	—	2	8	no	—
16	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
17	C₂³×D₁₉	C₂×C₄	1	4	yes	—
18	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
19	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
20	C₂×D₇₆	—	2	4	no	—
21	C₂×D₇₆	—	2	4	no	—
22	C₂×D₇₆	—	2	4	no	—
23	C₂×D₇₆	—	2	2	no	—
24	C₂×D₇₆	—	2	2	no	—
25	C₂×D₇₆	—	2	4	no	—
26	C₂×D₇₆	—	4	8	no	—
27	M₁₆×C₁₉	—	2	2	no	—
28	M₁₆×C₁₉	D₄	1	4	yes	complemented
29	C₂×C₈×C₁₉	—	2	2	no	—
30	C₄²×C₁₉	D₄	1	2	yes	—
31	C₄²×C₁₉	D₄	1	1	yes	characteristic
32	C₄²×C₁₉	D₄	1	1	yes	characteristic
33	#64520	—	2	4	no	—
34	C₂×C₁₉⋊C₈	—	2	2	no	—
35	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
36	C₂²×D₁₉	—	2	4	no	—
37	C₂²×D₁₉	—	2	8	no	—
38	C₂²×D₁₉	—	4	8	no	—
39	C₂×C₄×C₁₉	—	2	4	no	—
40	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
41	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
42	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
43	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₁₉	#41	1	2	yes	—
46	D₇₆	—	4	8	no	—
47	D₇₆	—	4	8	no	—
48	D₇₆	—	4	4	no	—
49	D₇₆	—	4	2	no	—
50	D₇₆	—	4	2	no	—
51	C₈×C₁₉	—	2	4	no	—
52	C₁₉⋊C₈	—	4	2	no	—
53	#1965	—	19	1	no	maximal, Sylow
54	C₂²×C₁₉	—	2	2	no	—
55	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
56	C₂²×C₁₉	C₄×D₄	1	2	yes	—
57	C₂×D₁₉	—	4	4	no	—
58	C₂×D₁₉	—	4	8	no	—
59	C₂×D₁₉	—	8	8	no	—
60	C₄×C₁₉	—	2	2	no	—
61	C₄×C₁₉	#100	1	4	yes	complemented
62	C₄×C₁₉	#121	1	2	yes	—
63	C₄×C₁₉	#124	1	1	yes	characteristic
64	C₄×C₁₉	#127	1	1	yes	characteristic
65	C₂×#127	—	19	1	no	—
66	#423	—	19	1	no	—
67	C₂×#100	—	19	4	no	—
68	C₄×M₁₆	D₁₉	1	1	yes	characteristic, complemented
69	C₂×C₁₉	—	2	2	no	—
70	C₂×C₁₉	#390	1	1	yes	characteristic
71	C₂×C₁₉	C₂×#100	1	2	yes	—
72	D₁₉	—	8	4	no	—
73	C₂²×D₄	—	19	4	no	—
74	C₂²×D₄	—	19	2	no	—
75	C₂×M₁₆	—	19	2	no	—
76	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
77	#127	—	38	2	no	—
78	#127	—	38	1	no	—
79	#127	—	38	1	no	—
80	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
81	C₄⋊C₈	—	38	2	no	—
82	#100	—	38	8	no	—
83	#97	—	2	1	no	—
84	C₄×C₈	—	2	1	no	—
85	C₁₉	#1965	1	1	yes	characteristic, complemented, Sylow
86	C₂⁴	—	19	4	no	—
87	C₂×D₄	—	38	4	no	—
88	C₂×D₄	—	38	4	no	—
89	C₂×D₄	—	38	4	no	—
90	C₂×D₄	—	38	2	no	—
91	C₂×D₄	—	38	4	no	—
92	C₂×D₄	—	38	2	no	—
93	C₂×D₄	—	76	8	no	—
94	C₂²×C₄	C₄×D₁₉	1	2	yes	—
95	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
96	M₁₆	—	2	2	no	—
97	M₁₆	—	38	4	no	—
98	M₁₆	D₇₆	1	4	yes	complemented
99	C₂×C₈	—	2	2	no	—
100	C₂×C₈	—	38	2	no	—
101	C₄²	D₇₆	1	2	yes	—
102	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
103	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
104	C₂³	—	38	4	no	—
105	C₂³	—	38	8	no	—
106	C₂³	—	76	8	no	—
107	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
108	D₄	—	76	8	no	—
109	D₄	—	76	4	no	—
110	D₄	—	76	8	no	—
111	D₄	—	76	2	no	—
112	D₄	—	76	2	no	—
113	C₂×C₄	—	2	4	no	—
114	C₂×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
115	C₂×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
116	C₂×C₄	C₂×D₇₆	1	2	yes	—
117	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
118	C₂×C₄	#64541	1	2	yes	—
119	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
120	C₈	—	2	4	no	—
121	C₈	—	76	2	no	—
122	C₂²	—	2	2	no	—
123	C₂²	—	76	4	no	—
124	C₂²	—	76	8	no	—
125	C₂²	—	152	8	no	—
126	C₂²	C₄×D₇₆	1	2	yes	—
127	C₂²	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
128	C₄	—	2	2	no	—
129	C₄	#10597280	1	4	yes	complemented
130	C₄	#10597320	1	1	yes	characteristic
131	C₄	#10597321	1	1	yes	characteristic
132	C₄	#10597376	1	2	yes	—
133	C₂	—	2	2	no	—
134	C₂	—	152	4	no	—
135	C₂	#11926446	1	1	yes	characteristic
136	C₂	C₂×#10597280	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597320

C₂

yes

maximal, characteristic

#11926568

C₂

yes

maximal, characteristic, complemented

C₂×#10597280

C₂

yes

maximal, complemented

C₄×M₁₆×C₁₉

C₂

yes

maximal, characteristic, complemented

C₂²×D₇₆

C₄

yes

—

C₂²×D₇₆

C₂²

yes

—

C₂×M₁₆×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

—

#10597320

—

#10597320

—

#10597320

—

C₁₉×#97

—

C₄×C₈×C₁₉

—

#10597280

—

C₄⋊(C₁₉⋊C₈)

—

C₂³×D₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

M₁₆×C₁₉

—

M₁₆×C₁₉

D₄

yes

complemented

C₂×C₈×C₁₉

—

C₄²×C₁₉

D₄

yes

—

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

#64520

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1965

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

C₄×D₄

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#100

yes

complemented

C₄×C₁₉

#121

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

—

—

—

C₄×M₁₆

D₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

#390

yes

characteristic

C₂×C₁₉

C₂×#100

yes

—

D₁₉

—

C₂²×D₄

—

C₂²×D₄

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

—

#127

—

#127

—

#127

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

#100

—

#97

—

C₄×C₈

—

C₁₉

#1965

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

C₄×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

D₇₆

yes

complemented

C₂×C₈

—

100

C₂×C₈

—

101

C₄²

D₇₆

yes

—

102

C₄²

C₂²⋊D₁₉

yes

characteristic

103

C₄²

C₂²⋊D₁₉

yes

characteristic

104

C₂³

—

105

C₂³

—

106

C₂³

—

107

C₂³

C₂×C₄×D₁₉

yes

characteristic

108

D₄

—

109

D₄

—

110

D₄

—

111

D₄

—

112

D₄

—

113

C₂×C₄

—

114

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

—

115

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

—

116

C₂×C₄

C₂×D₇₆

yes

—

117

C₂×C₄

C₂×D₇₆

yes

characteristic

118

C₂×C₄

#64541

yes

—

119

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

120

C₈

—

121

C₈

—

122

C₂²

—

123

C₂²

—

124

C₂²

—

125

C₂²

—

152

—

126

C₂²

C₄×D₇₆

yes

—

127

C₂²

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

128

C₄

—

129

C₄

#10597280

yes

complemented

130

C₄

#10597320

yes

characteristic

131

C₄

#10597321

yes

characteristic

132

C₄

#10597376

yes

—

133

C₂

—

134

C₂

—

152

—

135

C₂

#11926446

yes

characteristic

136

C₂

C₂×#10597280

yes

—

	subgroup	G/H
center	C₂²	C₂×(C₂×D₁₉)⋊C₄
commutator	C₂³×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₄×M₁₆×C₁₉	C₂
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂×#10597320	C₂
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₄×M₁₆	D₁₉
hypocenter	C₁₉	#1965
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×M₁₆

subgroup

G/H

center

C₂²

C₂×(C₂×D₁₉)⋊C₄

commutator

C₂³×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₄×M₁₆×C₁₉

C₂

socle

C₂²×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂×#10597320

C₂

cosocle

C₂²×C₄×C₁₉

C₂³

hypercenter

C₄×M₁₆

D₁₉

hypocenter

C₁₉

#1965

LCS

G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×M₁₆

N	H ≅ G/N	type
2. #11926568	C₂	semidirect
3. C₂×#10597280	C₂	semidirect
4. C₄×M₁₆×C₁₉	C₂	semidirect
28. M₁₆×C₁₉	D₄	semidirect
61. C₄×C₁₉	#100	semidirect
68. C₄×M₁₆	D₁₉	semidirect
85. C₁₉	#1965	semidirect
98. M₁₆	D₇₆	semidirect
129. C₄	#10597280	semidirect

H ≅ G/N

type

2. #11926568

C₂

semidirect

3. C₂×#10597280

C₂

semidirect

4. C₄×M₁₆×C₁₉

C₂

semidirect

28. M₁₆×C₁₉

D₄

semidirect

61. C₄×C₁₉

#100

semidirect

68. C₄×M₁₆

D₁₉

semidirect

85. C₁₉

#1965

semidirect

98. M₁₆

D₇₆

semidirect

129. C₄

#10597280

semidirect

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

subgroup	index
C₂×#10597320	2
#11926568	2
C₂×#10597280	2
C₄×M₁₆×C₁₉	2
#1965	19

subgroup

index

C₄×M₁₆×C₁₉

Subgroups — #14564475

Conjugacy classes of subgroups

Complements

Maximal subgroups