Group #14564892 — subgroups

Subgroups — #14564892

Order 2432.

296 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 67 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	C₂²×D₁₅₂	C₂	1	1	yes	maximal, characteristic
2	#11926570	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926550	C₂	1	2	yes	maximal, complemented
4	C₂×#10597280	C₂	1	2	yes	maximal, complemented
5	C₁₉×#341	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₇₆	C₂²	1	2	yes	—
7	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
8	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	#10597372	C₂²	1	1	yes	characteristic
10	C₂×#64520	C₂²	1	1	yes	characteristic
11	C₂×D₁₅₂	—	2	4	no	—
12	C₂×D₁₅₂	—	2	2	no	—
13	#10597280	—	2	4	no	—
14	#10597278	—	2	4	no	—
15	Dic₁₉⋊C₈	—	2	2	no	—
16	C₂³×D₁₉	—	2	2	no	—
17	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
18	C₂×D₇₆	—	2	2	no	—
19	C₂×D₇₆	—	2	2	no	—
20	C₂×D₇₆	—	2	2	no	—
21	C₂×D₇₆	—	2	2	no	—
22	C₂×D₇₆	—	2	2	no	—
23	C₂×D₇₆	D₄	1	4	yes	—
24	M₁₆×C₁₉	—	2	2	no	—
25	M₁₆×C₁₉	—	2	2	no	—
26	C₂×C₈×C₁₉	—	2	2	no	—
27	C₂×C₈×C₁₉	—	2	2	no	—
28	C₂×C₈×C₁₉	D₄	1	2	yes	—
29	C₂²⋊Dic₁₉	—	2	1	no	—
30	C₄⋊Dic₁₉	D₄	1	2	yes	—
31	C₄×Dic₁₉	—	2	1	no	—
32	#64520	—	2	2	no	—
33	C₂×C₁₉⋊C₈	—	2	1	no	—
34	D₁₅₂	—	2	8	no	—
35	C₂³×C₁₉	#41	1	1	yes	characteristic
36	C₂²×D₁₉	—	2	4	no	—
37	C₂²×D₁₉	—	4	2	no	—
38	C₂²×D₁₉	—	4	2	no	—
39	C₂²×D₁₉	—	8	4	no	—
40	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
42	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₁₉	#41	1	2	yes	—
44	C₂×Dic₁₉	—	2	2	no	—
45	D₇₆	—	2	4	no	—
46	D₇₆	—	2	4	no	—
47	D₇₆	—	4	2	no	—
48	D₇₆	—	4	2	no	—
49	C₈×C₁₉	—	2	2	no	—
50	C₈×C₁₉	—	4	2	no	—
51	C₁₉⋊C₈	—	4	1	no	—
52	#2045	—	19	1	no	maximal, Sylow
53	C₂²×C₁₉	—	2	2	no	—
54	C₂²×C₁₉	#121	1	1	yes	characteristic
55	C₂²×C₁₉	#123	1	2	yes	—
56	C₂×D₁₉	—	4	4	no	—
57	C₂×D₁₉	—	8	4	no	—
58	C₂×D₁₉	—	8	4	no	—
59	C₂×D₁₉	—	8	4	no	—
60	C₄×C₁₉	#120	1	1	yes	characteristic
61	C₄×C₁₉	#121	1	2	yes	—
62	C₄×C₁₉	#124	1	1	yes	characteristic
63	Dic₁₉	—	4	2	no	—
64	C₂²×D₈	—	19	1	no	—
65	#424	—	19	1	no	—
66	#418	—	19	2	no	—
67	C₂×#100	—	19	2	no	—
68	#341	D₁₉	1	1	yes	characteristic, complemented
69	C₂×C₁₉	—	2	2	no	—
70	C₂×C₁₉	#394	1	1	yes	characteristic
71	C₂×C₁₉	#472	1	2	yes	—
72	D₁₉	—	8	4	no	—
73	C₂²×D₄	—	19	2	no	—
74	C₂×D₈	—	38	4	no	—
75	C₂×D₈	—	38	2	no	—
76	C₂×M₁₆	—	19	1	no	—
77	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
78	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
79	#117	—	19	1	no	—
80	C₄⋊C₈	—	38	2	no	—
81	#102	—	38	4	no	—
82	#100	—	38	4	no	—
83	C₁₉	#2045	1	1	yes	characteristic, complemented, Sylow
84	C₂⁴	—	38	2	no	—
85	C₂×D₄	—	19	4	no	—
86	C₂×D₄	—	38	2	no	—
87	C₂×D₄	—	38	2	no	—
88	C₂×D₄	—	38	2	no	—
89	C₂×D₄	—	38	2	no	—
90	C₂×D₄	—	38	2	no	—
91	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
92	D₈	—	38	8	no	—
93	M₁₆	—	2	2	no	—
94	M₁₆	—	2	2	no	—
95	M₁₆	—	38	2	no	—
96	C₂×C₈	—	2	2	no	—
97	C₂×C₈	—	2	2	no	—
98	C₂×C₈	—	38	1	no	—
99	C₂×C₈	D₇₆	1	2	yes	—
100	C₄⋊C₄	—	19	2	no	—
101	C₂²⋊C₄	—	38	1	no	—
102	C₄²	—	38	1	no	—
103	C₂³	—	38	4	no	—
104	C₂³	—	76	2	no	—
105	C₂³	—	76	2	no	—
106	C₂³	—	152	4	no	—
107	C₂³	#64545	1	1	yes	characteristic
108	D₄	—	38	4	no	—
109	D₄	—	38	4	no	—
110	D₄	—	76	2	no	—
111	D₄	—	76	2	no	—
112	C₂×C₄	—	38	2	no	—
113	C₂×C₄	C₂×D₇₆	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	—	76	1	no	—
120	C₂²	—	2	2	no	—
121	C₂²	—	76	4	no	—
122	C₂²	—	152	4	no	—
123	C₂²	—	152	4	no	—
124	C₂²	—	152	4	no	—
125	C₂²	#10597340	1	2	yes	—
126	C₂²	#10597341	1	1	yes	characteristic
127	C₄	—	76	2	no	—
128	C₄	#10597321	1	1	yes	characteristic
129	C₄	#10597328	1	1	yes	characteristic
130	C₄	#10597330	1	2	yes	—
131	C₂	—	2	2	no	—
132	C₂	—	152	4	no	—
133	C₂	#11926462	1	1	yes	characteristic
134	C₂	#11926815	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×D₁₅₂

C₂

yes

maximal, characteristic

#11926570

C₂

yes

maximal, characteristic, complemented

#11926550

C₂

yes

maximal, complemented

C₂×#10597280

C₂

yes

maximal, complemented

C₁₉×#341

C₂

yes

maximal, characteristic, complemented

C₂²×D₇₆

C₂²

yes

—

C₂×M₁₆×C₁₉

C₂²

yes

—

C₂²×C₈×C₁₉

C₂²

yes

characteristic

#10597372

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

characteristic

C₂×D₁₅₂

—

C₂×D₁₅₂

—

#10597280

—

#10597278

—

Dic₁₉⋊C₈

—

C₂³×D₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

D₄

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

—

C₄×Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

D₁₅₂

—

C₂³×C₁₉

#41

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2045

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

#121

yes

characteristic

C₂²×C₁₉

#123

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

#120

yes

characteristic

C₄×C₁₉

#121

yes

—

C₄×C₁₉

#124

yes

characteristic

Dic₁₉

—

C₂²×D₈

—

—

—

—

D₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

#394

yes

characteristic

C₂×C₁₉

#472

yes

—

D₁₉

—

C₂²×D₄

—

C₂×D₈

—

C₂×D₈

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

#117

—

C₄⋊C₈

—

#102

—

#100

—

C₁₉

#2045

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

D₈

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₇₆

yes

—

100

C₄⋊C₄

—

101

C₂²⋊C₄

—

102

C₄²

—

103

C₂³

—

104

C₂³

—

105

C₂³

—

106

C₂³

—

152

—

107

C₂³

#64545

yes

characteristic

108

D₄

—

109

D₄

—

110

D₄

—

111

D₄

—

112

C₂×C₄

—

113

C₂×C₄

C₂×D₇₆

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

C₂²

—

121

C₂²

—

122

C₂²

—

152

—

123

C₂²

—

152

—

124

C₂²

—

152

—

125

C₂²

#10597340

yes

—

126

C₂²

#10597341

yes

characteristic

127

C₄

—

128

C₄

#10597321

yes

characteristic

129

C₄

#10597328

yes

characteristic

130

C₄

#10597330

yes

—

131

C₂

—

132

C₂

—

152

—

133

C₂

#11926462

yes

characteristic

134

C₂

#11926815

yes

—

	subgroup	G/H
center	C₂²	#10597341
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#341	C₂
socle	C₂²×C₁₉	#121
prime radical	C₂²×D₁₅₂	C₂
hypercenter	#341	D₁₉
hypocenter	C₁₉	#2045
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂²

#10597341

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#341

C₂

socle

C₂²×C₁₉

#121

prime radical

C₂²×D₁₅₂

C₂

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
2. #11926570	C₂	semidirect
3. #11926550	C₂	semidirect
4. C₂×#10597280	C₂	semidirect
5. C₁₉×#341	C₂	semidirect
68. #341	D₁₉	semidirect
83. C₁₉	#2045	semidirect

H ≅ G/N

type

2. #11926570

C₂

semidirect

3. #11926550

C₂

semidirect

4. C₂×#10597280

C₂

semidirect

5. C₁₉×#341

C₂

semidirect

68. #341

D₁₉

semidirect

83. C₁₉

#2045

semidirect

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

subgroup	index
C₂²×D₁₅₂	2
#11926570	2
#11926550	2
C₂×#10597280	2
C₁₉×#341	2
#2045	19

subgroup

index

C₂²×D₁₅₂

C₁₉×#341

Subgroups — #14564892

Conjugacy classes of subgroups

Complements

Maximal subgroups