Group #14569364 — subgroups

Subgroups — #14569364

Order 2432.

816 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 816 conjugacy classes of subgroups — too many to draw. Only its 181 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×#10597370	C₂	1	3	yes	maximal, complemented
2	#11926463	C₂	1	2	yes	maximal, complemented
3	#11926458	C₂	1	6	yes	maximal, complemented
4	#11926404	C₂	1	3	yes	maximal, complemented
5	C₂²×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#41×C₁₉	—	2	12	no	—
7	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×D₄×C₁₉	C₂²	1	3	yes	—
9	C₂³×C₄×C₁₉	C₂²	1	3	yes	—
10	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊Dic₁₉	C₂²	1	6	yes	—
12	C₂×C₂²⋊Dic₁₉	C₂²	1	6	yes	—
13	C₂×C₄⋊Dic₁₉	C₂²	1	3	yes	—
14	#10597370	—	2	12	no	—
15	C₂×Dic₁₉⋊C₄	C₂²	1	6	yes	—
16	C₁₉⋊#95	C₂²	1	6	yes	—
17	C₂⁴×C₁₉	C₂³	1	3	yes	—
18	#41×C₁₉	—	2	32	no	—
19	C₂×Q₈×C₁₉	—	2	6	no	—
20	C₂×D₄×C₁₉	—	2	12	no	—
21	C₂×D₄×C₁₉	—	2	6	no	—
22	C₂²×C₄×C₁₉	—	2	12	no	—
23	C₂²×C₄×C₁₉	D₄	1	12	yes	—
24	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
25	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂²×Dic₁₉	C₂³	1	2	yes	—
27	C₂²×Dic₁₉	C₂³	1	6	yes	—
28	C₂×Dic₃₈	—	2	6	no	—
29	C₂²⋊Dic₁₉	—	2	12	no	—
30	C₂²⋊Dic₁₉	—	4	6	no	—
31	C₄⋊Dic₁₉	—	2	6	no	—
32	Dic₁₉⋊C₄	—	2	12	no	—
33	C₂³×C₁₉	—	2	6	no	—
34	C₂³×C₁₉	—	2	3	no	—
35	C₂³×C₁₉	—	2	6	no	—
36	C₂³×C₁₉	—	2	3	no	—
37	C₂³×C₁₉	C₂×D₄	1	6	yes	—
38	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
39	Q₈×C₁₉	—	2	8	no	—
40	D₄×C₁₉	—	2	24	no	—
41	C₂×C₄×C₁₉	—	2	6	no	—
42	C₂×C₄×C₁₉	—	2	24	no	—
43	C₂×C₄×C₁₉	C₂×D₄	1	6	yes	—
44	C₂×C₄×C₁₉	C₂×D₄	1	6	yes	—
45	C₂×Dic₁₉	—	2	6	no	—
46	C₂×Dic₁₉	—	2	6	no	—
47	C₂×Dic₁₉	—	2	6	no	—
48	C₂×Dic₁₉	—	2	6	no	—
49	Dic₃₈	—	4	4	no	—
50	#2616	—	19	1	no	maximal, Sylow
51	C₂²×C₁₉	—	2	6	no	—
52	C₂²×C₁₉	—	2	6	no	—
53	C₂²×C₁₉	—	2	6	no	—
54	C₂²×C₁₉	—	4	6	no	—
55	C₂²×C₁₉	—	4	6	no	—
56	C₂²×C₁₉	C₂²×D₄	1	3	yes	—
57	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
58	C₂²×C₁₉	2₋¹⁺⁴	1	3	yes	—
59	C₄×C₁₉	—	2	6	no	—
60	C₄×C₁₉	#120	1	4	yes	—
61	Dic₁₉	—	4	2	no	—
62	Dic₁₉	—	4	6	no	—
63	C₂²×#41	D₁₉	1	1	yes	characteristic
64	C₂×C₂²⋊Q₈	—	19	3	no	—
65	#395	—	19	2	no	—
66	#394	—	19	6	no	—
67	#380	—	19	3	no	—
68	C₂×C₁₉	—	4	6	no	—
69	C₂×C₁₉	C₂×#120	1	1	yes	characteristic
70	C₂×C₁₉	#536	1	3	yes	—
71	C₂×C₁₉	#537	1	3	yes	—
72	C₂×#41	—	2	12	no	—
73	C₂²×Q₈	—	19	1	no	—
74	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
75	C₂²×D₄	C₂×D₁₉	1	3	yes	—
76	C₂³×C₄	C₂×D₁₉	1	3	yes	—
77	C₂²⋊Q₈	—	38	12	no	—
78	C₂×C₄⋊C₄	—	19	3	no	—
79	C₂×C₄⋊C₄	—	19	6	no	—
80	C₂×C₂²⋊C₄	—	19	6	no	—
81	C₂×C₂²⋊C₄	—	19	6	no	—
82	#95	—	19	6	no	—
83	C₁₉	#2616	1	1	yes	characteristic, complemented, Sylow
84	C₂⁴	C₂²×D₁₉	1	3	yes	—
85	#41	—	2	32	no	—
86	C₂×Q₈	—	2	6	no	—
87	C₂×Q₈	—	38	6	no	—
88	C₂×D₄	—	2	12	no	—
89	C₂×D₄	—	2	6	no	—
90	C₂²×C₄	—	2	12	no	—
91	C₂²×C₄	—	19	6	no	—
92	C₂²×C₄	—	19	2	no	—
93	C₂²×C₄	C₂²⋊D₁₉	1	12	yes	—
94	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
95	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
96	C₄⋊C₄	—	38	12	no	—
97	C₄⋊C₄	—	38	6	no	—
98	C₂²⋊C₄	—	38	12	no	—
99	C₂²⋊C₄	—	76	6	no	—
100	C₂³	—	2	3	no	—
101	C₂³	—	2	6	no	—
102	C₂³	—	2	3	no	—
103	C₂³	—	2	6	no	—
104	C₂³	C₂×C₂²⋊D₁₉	1	6	yes	—
105	C₂³	C₂³×D₁₉	1	1	yes	characteristic
106	Q₈	—	2	8	no	—
107	Q₈	—	76	4	no	—
108	D₄	—	2	24	no	—
109	C₂×C₄	—	2	6	no	—
110	C₂×C₄	—	2	24	no	—
111	C₂×C₄	—	38	6	no	—
112	C₂×C₄	—	38	6	no	—
113	C₂×C₄	—	38	6	no	—
114	C₂×C₄	—	38	6	no	—
115	C₂×C₄	C₂×C₂²⋊D₁₉	1	6	yes	—
116	C₂×C₄	C₂×C₂²⋊D₁₉	1	6	yes	—
117	C₂²	—	2	6	no	—
118	C₂²	—	2	6	no	—
119	C₂²	—	2	6	no	—
120	C₂²	—	4	6	no	—
121	C₂²	—	4	6	no	—
122	C₂²	#10597435	1	1	yes	characteristic
123	C₂²	#10597436	1	3	yes	—
124	C₂²	C₂²×C₂²⋊D₁₉	1	3	yes	—
125	C₄	—	2	6	no	—
126	C₄	—	76	6	no	—
127	C₄	—	76	2	no	—
128	C₄	#10597399	1	4	yes	—
129	C₂	—	4	6	no	—
130	C₂	C₂×#10597399	1	1	yes	characteristic
131	C₂	#11927115	1	3	yes	—
132	C₂	#11927122	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597370

C₂

yes

maximal, complemented

#11926463

C₂

yes

maximal, complemented

#11926458

C₂

yes

maximal, complemented

#11926404

C₂

yes

maximal, complemented

C₂²×#41×C₁₉

C₂

yes

maximal, characteristic

C₂×#41×C₁₉

—

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂²×D₄×C₁₉

C₂²

yes

—

C₂³×C₄×C₁₉

C₂²

yes

—

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

#10597370

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂⁴×C₁₉

C₂³

yes

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×Dic₃₈

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

#2616

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×D₄

yes

—

C₂²×C₁₉

H(5,𝔽₂)

yes

characteristic

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₄×C₁₉

—

C₄×C₁₉

#120

yes

—

Dic₁₉

—

Dic₁₉

—

C₂²×#41

D₁₉

yes

characteristic

C₂×C₂²⋊Q₈

—

#395

—

#394

—

#380

—

C₂×C₁₉

—

C₂×C₁₉

C₂×#120

yes

characteristic

C₂×C₁₉

#536

yes

—

C₂×C₁₉

#537

yes

—

C₂×#41

—

C₂²×Q₈

—

C₂²×Q₈

C₂×D₁₉

yes

characteristic

C₂²×D₄

C₂×D₁₉

yes

—

C₂³×C₄

C₂×D₁₉

yes

—

C₂²⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

#95

—

C₁₉

#2616

yes

characteristic, complemented, Sylow

C₂⁴

C₂²×D₁₉

yes

—

#41

—

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

100

C₂³

—

101

C₂³

—

102

C₂³

—

103

C₂³

—

104

C₂³

C₂×C₂²⋊D₁₉

yes

—

105

C₂³

C₂³×D₁₉

yes

characteristic

106

Q₈

—

107

Q₈

—

108

D₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

116

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

—

122

C₂²

#10597435

yes

characteristic

123

C₂²

#10597436

yes

—

124

C₂²

C₂²×C₂²⋊D₁₉

yes

—

125

C₄

—

126

C₄

—

127

C₄

—

128

C₄

#10597399

yes

—

129

C₂

—

130

C₂

C₂×#10597399

yes

characteristic

131

C₂

#11927115

yes

—

132

C₂

#11927122

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting, prime radical	C₂²×#41×C₁₉	C₂
hypercenter	C₂²×#41	D₁₉
hypocenter	C₁₉	#2616
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×#41

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting, prime radical

C₂²×#41×C₁₉

C₂

hypercenter

C₂²×#41

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂²×#41

N	H ≅ G/N	type
1. C₂×#10597370	C₂	semidirect
2. #11926463	C₂	semidirect
3. #11926458	C₂	semidirect
4. #11926404	C₂	semidirect
83. C₁₉	#2616	semidirect

H ≅ G/N

type

1. C₂×#10597370

C₂

semidirect

2. #11926463

C₂

semidirect

3. #11926458

C₂

semidirect

4. #11926404

C₂

semidirect

83. C₁₉

#2616

semidirect

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

subgroup	index
C₂×#10597370	2
#11926463	2
#11926458	2
#11926404	2
C₂²×#41×C₁₉	2
#2616	19

subgroup

index

C₂²×#41×C₁₉

Subgroups — #14569364

Conjugacy classes of subgroups

Complements

Maximal subgroups