Group #19134489 — subgroups

Subgroups — C₄×#13063258 #19134489

Order 5504.

280 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 145 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×#13063258	C₂	1	2	yes	maximal
2	C₂×C₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₄⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic
4	#14582661	C₂	1	2	yes	maximal
5	C₄×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
7	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
9	C₂×C₄×Dic₄₃	—	2	1	no	—
10	#13063258	C₄	1	8	yes	direct product factor
11	C₄×C₄₃⋊C₈	C₄	1	4	yes	complemented
12	C₄₃⋊#95	—	2	1	no	—
13	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
14	C₂×C₄²×C₄₃	—	2	1	no	—
15	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
16	#95×C₄₃	—	2	1	no	—
17	C₂²×C₄×C₄₃	—	2	2	no	—
18	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
19	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
20	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
21	C₂²×Dic₄₃	—	2	2	no	—
22	C₄⋊C₄×C₄₃	—	2	2	no	—
23	C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
24	C₄²×C₄₃	—	4	2	no	—
25	C₄²×C₄₃	C₂×C₄	1	2	yes	—
26	C₄²×C₄₃	Q₈	1	2	yes	—
27	C₄⋊Dic₄₃	—	2	2	no	—
28	C₄⋊Dic₄₃	C₂×C₄	1	4	yes	—
29	C₄×Dic₄₃	—	4	2	no	—
30	C₂×C₄₃⋊C₈	—	2	2	no	—
31	C₂×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
32	C₂×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
33	C₂×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
34	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₄₃	—	2	2	no	—
36	C₂×C₄×C₄₃	—	2	4	no	—
37	C₂×C₄×C₄₃	—	4	2	no	—
38	C₂×C₄×C₄₃	—	4	2	no	—
39	C₂×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
40	C₂×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
41	C₂×C₄×C₄₃	D₈	1	2	yes	—
42	C₂×C₄×C₄₃	Q₁₆	1	2	yes	—
43	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
45	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
46	C₂×C₄×C₄₃	#41	1	2	yes	—
47	C₂×Dic₄₃	—	2	4	no	—
48	C₂×Dic₄₃	—	4	2	no	—
49	C₂×Dic₄₃	—	4	2	no	—
50	C₄₃⋊C₈	—	2	2	no	—
51	C₄₃⋊C₈	C₄²	1	4	yes	complemented
52	C₂²×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₂²×C₄₃	C₄×D₄	1	2	yes	—
54	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
55	C₂²×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
56	C₂²×C₄₃	#135	1	2	yes	—
57	C₄×C₄₃	—	2	2	no	—
58	C₄×C₄₃	—	4	4	no	—
59	C₄×C₄₃	#107	1	4	yes	complemented
60	C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
61	C₄×C₄₃	#117	1	1	yes	characteristic
62	C₄×C₄₃	C₄×Q₈	1	2	yes	—
63	Dic₄₃	—	4	4	no	—
64	C₄×#107	—	43	1	no	maximal, Sylow
65	C₂×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
66	C₂×C₄₃	C₂×#107	1	1	yes	characteristic
67	C₂×C₄₃	#427	1	1	yes	characteristic
68	C₂×C₄₃	C₄×D₈	1	2	yes	—
69	C₂×C₄₃	C₄×Q₁₆	1	2	yes	—
70	C₂×#107	—	43	2	no	—
71	C₂×C₄×C₈	—	43	1	no	—
72	C₄×C₄⋊C₄	—	43	1	no	—
73	C₄×C₄⋊C₄	D₄₃	1	1	yes	characteristic
74	#340	—	43	2	no	—
75	C₄₃	C₄×#107	1	1	yes	characteristic, complemented, Sylow
76	C₂²×C₈	—	43	1	no	—
77	C₂²×C₈	—	43	1	no	—
78	C₂×C₄⋊C₄	—	43	2	no	—
79	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
80	C₂×C₄²	—	2	1	no	—
81	C₂×C₄²	—	86	1	no	—
82	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
83	#107	—	43	8	no	—
84	C₄×C₈	—	43	4	no	—
85	#95	—	2	1	no	—
86	#95	—	86	1	no	—
87	C₂²×C₄	—	2	2	no	—
88	C₂²×C₄	—	86	2	no	—
89	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
90	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
91	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
92	C₂×C₈	—	43	2	no	—
93	C₂×C₈	—	43	4	no	—
94	C₂×C₈	—	43	2	no	—
95	C₂×C₈	—	86	2	no	—
96	C₄⋊C₄	—	2	2	no	—
97	C₄⋊C₄	—	43	4	no	—
98	C₄⋊C₄	—	86	2	no	—
99	C₄⋊C₄	C₄×D₄₃	1	4	yes	—
100	C₄²	—	4	2	no	—
101	C₄²	—	172	2	no	—
102	C₄²	Dic₈₆	1	2	yes	—
103	C₄²	C₄×D₄₃	1	2	yes	—
104	C₂³	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
105	C₂×C₄	—	2	2	no	—
106	C₂×C₄	—	2	4	no	—
107	C₂×C₄	—	4	2	no	—
108	C₂×C₄	—	4	2	no	—
109	C₂×C₄	—	86	4	no	—
110	C₂×C₄	—	172	2	no	—
111	C₂×C₄	—	172	2	no	—
112	C₂×C₄	Dic₄₃⋊C₄	1	2	yes	—
113	C₂×C₄	Dic₄₃⋊C₄	1	2	yes	—
114	C₂×C₄	#10621882	1	2	yes	—
115	C₂×C₄	#10621885	1	2	yes	—
116	C₂×C₄	C₂×Dic₈₆	1	1	yes	characteristic
117	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
118	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
119	C₂×C₄	#10621898	1	2	yes	—
120	C₈	—	43	4	no	—
121	C₈	—	86	2	no	—
122	C₂²	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
123	C₂²	C₄×C₂²⋊D₄₃	1	2	yes	—
124	C₂²	C₂×#10621882	1	1	yes	characteristic
125	C₂²	C₂×#10621885	1	1	yes	characteristic
126	C₂²	#13063345	1	2	yes	—
127	C₄	—	2	2	no	—
128	C₄	—	4	4	no	—
129	C₄	—	172	4	no	—
130	C₄	#13063258	1	4	yes	direct product factor
131	C₄	C₄²×D₄₃	1	1	yes	characteristic
132	C₄	#13063282	1	1	yes	characteristic
133	C₄	C₄×Dic₈₆	1	2	yes	—
134	C₂	C₄×Dic₄₃⋊C₄	1	1	yes	characteristic
135	C₂	C₂×#13063258	1	1	yes	characteristic
136	C₂	#14582935	1	1	yes	characteristic
137	C₂	C₄×#10621882	1	2	yes	—
138	C₂	C₄×#10621885	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063258

C₂

yes

maximal

C₂×C₄×C₄₃⋊C₈

C₂

yes

maximal, characteristic

C₄×C₄⋊Dic₄₃

C₂

yes

maximal, characteristic

#14582661

C₂

yes

maximal

C₄×C₄⋊C₄×C₄₃

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₈

C₂²

yes

characteristic

C₂²×C₄₃⋊C₈

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

—

#13063258

C₄

yes

direct product factor

C₄×C₄₃⋊C₈

C₄

yes

complemented

C₄₃⋊#95

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

#95×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

Q₈

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

C₂×C₄

yes

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄⋊C₄

yes

—

C₂×C₄×C₄₃

C₄⋊C₄

yes

—

C₂×C₄×C₄₃

D₈

yes

—

C₂×C₄×C₄₃

Q₁₆

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

C₄²

yes

complemented

C₂²×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₄₃

C₄×D₄

yes

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₂²×C₄₃

C₂×Q₁₆

yes

characteristic

C₂²×C₄₃

#135

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#107

yes

complemented

C₄×C₄₃

C₂×C₄²

yes

characteristic

C₄×C₄₃

#117

yes

characteristic

C₄×C₄₃

C₄×Q₈

yes

—

Dic₄₃

—

C₄×#107

—

maximal, Sylow

C₂×C₄₃

C₄×C₄⋊C₄

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

C₄×D₈

yes

—

C₂×C₄₃

C₄×Q₁₆

yes

—

C₂×#107

—

C₂×C₄×C₈

—

C₄×C₄⋊C₄

—

C₄×C₄⋊C₄

D₄₃

yes

characteristic

#340

—

C₄₃

C₄×#107

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

#107

—

C₄×C₈

—

#95

—

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₄×D₄₃

yes

—

100

C₄²

—

101

C₄²

—

172

—

102

C₄²

Dic₈₆

yes

—

103

C₄²

C₄×D₄₃

yes

—

104

C₂³

C₂×C₂²⋊D₄₃

yes

characteristic

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

172

—

111

C₂×C₄

—

172

—

112

C₂×C₄

Dic₄₃⋊C₄

yes

—

113

C₂×C₄

Dic₄₃⋊C₄

yes

—

114

C₂×C₄

#10621882

yes

—

115

C₂×C₄

#10621885

yes

—

116

C₂×C₄

C₂×Dic₈₆

yes

characteristic

117

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

118

C₂×C₄

C₂×C₄×D₄₃

yes

—

119

C₂×C₄

#10621898

yes

—

120

C₈

—

121

C₈

—

122

C₂²

C₂×Dic₄₃⋊C₄

yes

characteristic

123

C₂²

C₄×C₂²⋊D₄₃

yes

—

124

C₂²

C₂×#10621882

yes

characteristic

125

C₂²

C₂×#10621885

yes

characteristic

126

C₂²

#13063345

yes

—

127

C₄

—

128

C₄

—

129

C₄

—

172

—

130

C₄

#13063258

yes

direct product factor

131

C₄

C₄²×D₄₃

yes

characteristic

132

C₄

#13063282

yes

characteristic

133

C₄

C₄×Dic₈₆

yes

—

134

C₂

C₄×Dic₄₃⋊C₄

yes

characteristic

135

C₂

C₂×#13063258

yes

characteristic

136

C₂

#14582935

yes

characteristic

137

C₂

C₄×#10621882

yes

—

138

C₂

C₄×#10621885

yes

—

	subgroup	G/H
center	C₂²×C₄	C₂²⋊D₄₃
commutator	C₄×C₄₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄×C₄⋊C₄×C₄₃	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	C₄×C₄⋊C₄	D₄₃
hypocenter	C₄₃	C₄×#107
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₄×C₄⋊C₄

subgroup

G/H

center

C₂²×C₄

C₂²⋊D₄₃

commutator

C₄×C₄₃

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄×C₄⋊C₄×C₄₃

C₂

socle

C₂³×C₄₃

C₂×D₄

hypercenter

C₄×C₄⋊C₄

D₄₃

hypocenter

C₄₃

C₄×#107

LCS

G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₄×C₄⋊C₄

N	H ≅ G/N	type
10. #13063258	C₄	direct (N × H)
11. C₄×C₄₃⋊C₈	C₄	semidirect
51. C₄₃⋊C₈	C₄²	semidirect
59. C₄×C₄₃	#107	semidirect
75. C₄₃	C₄×#107	semidirect
130. C₄	#13063258	direct (N × H)

H ≅ G/N

type

10. #13063258

C₄

direct (N × H)

11. C₄×C₄₃⋊C₈

C₄

semidirect

51. C₄₃⋊C₈

C₄²

semidirect

59. C₄×C₄₃

#107

semidirect

75. C₄₃

C₄×#107

semidirect

130. C₄

#13063258

direct (N × H)

Subgroups — C₄×#13063258 #19134489

Conjugacy classes of subgroups

Complements

Subgroups — C4×#13063258 #19134489

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#13063258 #19134489