Group #24983123 — subgroups

Subgroups — C₄₃⋊#7014 #24983123

Order 11008.

338 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 159 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	#19134341	C₂	1	2	yes	maximal
2	C₄₃×#1744	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄₃⋊C₈	C₄	1	4	yes	—
4	#14582654	—	2	2	no	—
5	#14582654	—	2	2	no	—
6	C₂×C₄×C₈×C₄₃	C₄	1	2	yes	—
7	C₄³×C₄₃	C₂²	1	1	yes	characteristic
8	C₄₃×#336	—	2	2	no	—
9	C₂²×C₄₃⋊C₈	—	2	4	no	—
10	C₄×C₄₃⋊C₈	—	2	4	no	—
11	C₄×C₄₃⋊C₈	C₈	1	8	yes	complemented
12	C₂²×C₈×C₄₃	—	2	2	no	—
13	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
14	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
16	C₂×C₄²×C₄₃	D₄	1	2	yes	—
17	C₂×C₄²×C₄₃	Q₈	1	1	yes	characteristic
18	C₄×C₈×C₄₃	—	2	2	no	—
19	C₄×C₈×C₄₃	C₈	1	4	yes	complemented
20	C₂²×C₄×C₄₃	C₄²	1	1	yes	characteristic
21	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
22	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₂²×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
24	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
25	C₂×C₈×C₄₃	—	2	4	no	—
26	C₂×C₈×C₄₃	—	4	4	no	—
27	C₄²×C₄₃	—	4	1	no	—
28	C₄²×C₄₃	—	4	2	no	—
29	C₄²×C₄₃	—	4	1	no	—
30	C₄²×C₄₃	C₂×C₈	1	4	yes	—
31	C₄²×C₄₃	C₂×C₈	1	2	yes	—
32	C₄²×C₄₃	M₁₆	1	4	yes	—
33	C₄²×C₄₃	M₁₆	1	2	yes	—
34	C₂×C₄₃⋊C₈	—	2	8	no	—
35	C₂×C₄₃⋊C₈	—	4	4	no	—
36	C₂×C₄₃⋊C₈	—	4	4	no	—
37	C₂³×C₄₃	#95	1	1	yes	characteristic
38	C₂×C₄×C₄₃	—	2	2	no	—
39	C₂×C₄×C₄₃	—	2	2	no	—
40	C₂×C₄×C₄₃	—	2	2	no	—
41	C₂×C₄×C₄₃	—	2	2	no	—
42	C₂×C₄×C₄₃	—	2	1	no	—
43	C₂×C₄×C₄₃	—	2	2	no	—
44	C₂×C₄×C₄₃	—	2	1	no	—
45	C₂×C₄×C₄₃	C₄×C₈	1	2	yes	—
46	C₂×C₄×C₄₃	C₄×C₈	1	1	yes	characteristic
47	C₂×C₄×C₄₃	#97	1	2	yes	—
48	C₂×C₄×C₄₃	#97	1	1	yes	characteristic
49	C₂×C₄×C₄₃	C₂²⋊C₈	1	4	yes	—
50	C₂×C₄×C₄₃	C₂²⋊C₈	1	2	yes	—
51	C₂×C₄×C₄₃	C₄⋊C₈	1	4	yes	—
52	C₂×C₄×C₄₃	C₄⋊C₈	1	2	yes	—
53	C₈×C₄₃	—	4	4	no	—
54	C₄₃⋊C₈	—	4	8	no	—
55	#7014	—	43	1	no	maximal, Sylow
56	C₂²×C₄₃	#336	1	2	yes	—
57	C₂²×C₄₃	#336	1	1	yes	characteristic
58	C₂²×C₄₃	H(3,ℤ/4)	1	2	yes	—
59	C₂²×C₄₃	H(3,ℤ/4)	1	1	yes	characteristic
60	C₂²×C₄₃	#338	1	1	yes	characteristic
61	C₄×C₄₃	—	2	4	no	—
62	C₄×C₄₃	—	2	2	no	—
63	C₄×C₄₃	—	2	4	no	—
64	C₄×C₄₃	—	2	2	no	—
65	C₄×C₄₃	C₈²	1	1	yes	characteristic
66	C₄×C₄₃	#322	1	1	yes	characteristic
67	C₄×C₄₃	#322	1	2	yes	—
68	#1744	—	43	2	no	—
69	#1744	D₄₃	1	1	yes	characteristic
70	C₂×C₄₃	#1273	1	1	yes	characteristic
71	C₂×C₄₃	#1274	1	2	yes	—
72	C₂×C₄₃	#1274	1	1	yes	characteristic
73	C₂×C₄₃	#1275	1	2	yes	—
74	C₂×C₄₃	#1275	1	1	yes	characteristic
75	C₂×C₄×C₈	—	43	4	no	—
76	C₂×C₄×C₈	Dic₄₃	1	2	yes	—
77	C₄³	C₂×D₄₃	1	1	yes	characteristic
78	#336	—	2	2	no	—
79	#336	—	86	2	no	—
80	#336	—	86	2	no	—
81	C₄₃	#7014	1	1	yes	characteristic, complemented, Sylow
82	C₂²×C₈	—	2	2	no	—
83	C₂²×C₈	—	86	4	no	—
84	C₂×C₄²	Dic₈₆	1	1	yes	characteristic
85	C₂×C₄²	C₄×D₄₃	1	2	yes	—
86	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
87	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
88	C₂×C₄²	C₂²⋊D₄₃	1	2	yes	—
89	C₄×C₈	—	2	2	no	—
90	C₄×C₈	—	43	8	no	—
91	C₄×C₈	—	86	4	no	—
92	C₄×C₈	C₄₃⋊C₈	1	4	yes	complemented
93	C₂²×C₄	C₄×Dic₄₃	1	1	yes	characteristic
94	C₂²×C₄	Dic₄₃⋊C₄	1	2	yes	—
95	C₂²×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
96	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
97	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
98	C₂×C₈	—	2	4	no	—
99	C₂×C₈	—	4	4	no	—
100	C₂×C₈	—	86	8	no	—
101	C₂×C₈	—	172	4	no	—
102	C₂×C₈	—	172	4	no	—
103	C₄²	—	4	1	no	—
104	C₄²	—	4	1	no	—
105	C₄²	—	4	2	no	—
106	C₄²	C₈×D₄₃	1	4	yes	—
107	C₄²	#10621872	1	4	yes	—
108	C₄²	C₂×C₄₃⋊C₈	1	2	yes	—
109	C₄²	#10621877	1	2	yes	—
110	C₂³	C₄₃⋊#95	1	1	yes	characteristic
111	C₂×C₄	—	2	2	no	—
112	C₂×C₄	—	2	2	no	—
113	C₂×C₄	—	2	2	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	C₈×Dic₄₃	1	2	yes	—
119	C₂×C₄	C₄×C₄₃⋊C₈	1	1	yes	characteristic
120	C₂×C₄	#13063235	1	2	yes	—
121	C₂×C₄	#13063236	1	1	yes	characteristic
122	C₂×C₄	(C₂×D₄₃)⋊C₈	1	4	yes	—
123	C₂×C₄	C₂²⋊(C₄₃⋊C₈)	1	2	yes	—
124	C₂×C₄	Dic₄₃⋊C₈	1	4	yes	—
125	C₂×C₄	C₄⋊(C₄₃⋊C₈)	1	2	yes	—
126	C₈	—	4	4	no	—
127	C₈	—	172	8	no	—
128	C₂²	#14582653	1	2	yes	—
129	C₂²	#14582654	1	1	yes	characteristic
130	C₂²	#14582655	1	2	yes	—
131	C₂²	#14582656	1	1	yes	characteristic
132	C₂²	C₄₃⋊#338	1	1	yes	characteristic
133	C₄	—	2	4	no	—
134	C₄	—	2	2	no	—
135	C₄	—	2	4	no	—
136	C₄	—	2	2	no	—
137	C₄	C₈×C₄₃⋊C₈	1	1	yes	characteristic
138	C₄	#14582620	1	1	yes	characteristic
139	C₄	#14582621	1	2	yes	—
140	C₂	C₄₃⋊#1273	1	1	yes	characteristic
141	C₂	#19132423	1	2	yes	—
142	C₂	#19132424	1	1	yes	characteristic
143	C₂	#19132425	1	2	yes	—
144	C₂	#19132426	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19134341

C₂

yes

maximal

C₄₃×#1744

C₂

yes

maximal, characteristic

C₂×C₄×C₄₃⋊C₈

C₄

yes

—

#14582654

—

#14582654

—

C₂×C₄×C₈×C₄₃

C₄

yes

—

C₄³×C₄₃

C₂²

yes

characteristic

C₄₃×#336

—

C₂²×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

C₈

yes

complemented

C₂²×C₈×C₄₃

—

C₂×C₄²×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

Q₈

yes

characteristic

C₄×C₈×C₄₃

—

C₄×C₈×C₄₃

C₈

yes

complemented

C₂²×C₄×C₄₃

C₄²

yes

characteristic

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₃

C₄⋊C₄

yes

—

C₂²×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×C₈

yes

—

C₄²×C₄₃

C₂×C₈

yes

—

C₄²×C₄₃

M₁₆

yes

—

C₄²×C₄₃

M₁₆

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#95

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄×C₈

yes

—

C₂×C₄×C₄₃

C₄×C₈

yes

characteristic

C₂×C₄×C₄₃

#97

yes

—

C₂×C₄×C₄₃

#97

yes

characteristic

C₂×C₄×C₄₃

C₂²⋊C₈

yes

—

C₂×C₄×C₄₃

C₂²⋊C₈

yes

—

C₂×C₄×C₄₃

C₄⋊C₈

yes

—

C₂×C₄×C₄₃

C₄⋊C₈

yes

—

C₈×C₄₃

—

C₄₃⋊C₈

—

#7014

—

maximal, Sylow

C₂²×C₄₃

#336

yes

—

C₂²×C₄₃

#336

yes

characteristic

C₂²×C₄₃

H(3,ℤ/4)

yes

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₈²

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

—

#1744

—

#1744

D₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

#1274

yes

characteristic

C₂×C₄₃

#1275

yes

—

C₂×C₄₃

#1275

yes

characteristic

C₂×C₄×C₈

—

C₂×C₄×C₈

Dic₄₃

yes

—

C₄³

C₂×D₄₃

yes

—

—

—

C₄₃

#7014

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

Dic₈₆

yes

characteristic

C₂×C₄²

C₄×D₄₃

yes

—

C₂×C₄²

D₁₇₂

yes

characteristic

C₂×C₄²

C₂×Dic₄₃

yes

characteristic

C₂×C₄²

C₂²⋊D₄₃

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₄₃⋊C₈

yes

complemented

C₂²×C₄

C₄×Dic₄₃

yes

characteristic

C₂²×C₄

Dic₄₃⋊C₄

yes

—

C₂²×C₄

C₄⋊Dic₄₃

yes

characteristic

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

—

C₂²×C₄

C₂²⋊Dic₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

172

—

102

C₂×C₈

—

172

—

103

C₄²

—

104

C₄²

—

105

C₄²

—

106

C₄²

C₈×D₄₃

yes

—

107

C₄²

#10621872

yes

—

108

C₄²

C₂×C₄₃⋊C₈

yes

—

109

C₄²

#10621877

yes

—

110

C₂³

C₄₃⋊#95

yes

characteristic

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

C₈×Dic₄₃

yes

—

119

C₂×C₄

C₄×C₄₃⋊C₈

yes

characteristic

120

C₂×C₄

#13063235

yes

—

121

C₂×C₄

#13063236

yes

characteristic

122

C₂×C₄

(C₂×D₄₃)⋊C₈

yes

—

123

C₂×C₄

C₂²⋊(C₄₃⋊C₈)

yes

—

124

C₂×C₄

Dic₄₃⋊C₈

yes

—

125

C₂×C₄

C₄⋊(C₄₃⋊C₈)

yes

—

126

C₈

—

127

C₈

—

172

—

128

C₂²

#14582653

yes

—

129

C₂²

#14582654

yes

characteristic

130

C₂²

#14582655

yes

—

131

C₂²

#14582656

yes

characteristic

132

C₂²

C₄₃⋊#338

yes

characteristic

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

C₈×C₄₃⋊C₈

yes

characteristic

138

C₄

#14582620

yes

characteristic

139

C₄

#14582621

yes

—

140

C₂

C₄₃⋊#1273

yes

characteristic

141

C₂

#19132423

yes

—

142

C₂

#19132424

yes

characteristic

143

C₂

#19132425

yes

—

144

C₂

#19132426

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₄×Dic₄₃
commutator	C₄×C₄₃	C₈²
Frattini	C₄³	C₂×D₄₃
Fitting	C₄₃×#1744	C₂
socle, prime radical	C₂³×C₄₃	#95
cosocle	C₄³×C₄₃	C₂²
hypercenter	#1744	D₄₃
hypocenter	C₄₃	#7014
LCS	G ▷ C₄×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1744

subgroup

G/H

center

C₂²×C₄

C₄×Dic₄₃

commutator

C₄×C₄₃

C₈²

Frattini

C₄³

C₂×D₄₃

Fitting

C₄₃×#1744

C₂

socle, prime radical

C₂³×C₄₃

#95

cosocle

C₄³×C₄₃

C₂²

D₄₃

C₄₃

G ▷ C₄×C₄₃ ▷ C₄₃

C₁ ◁ C₂²×C₄ ◁ #1744

N	H ≅ G/N	type
11. C₄×C₄₃⋊C₈	C₈	semidirect
19. C₄×C₈×C₄₃	C₈	semidirect
81. C₄₃	#7014	semidirect
92. C₄×C₈	C₄₃⋊C₈	semidirect

H ≅ G/N

type

11. C₄×C₄₃⋊C₈

C₈

semidirect

19. C₄×C₈×C₄₃

C₈

semidirect

81. C₄₃

#7014

semidirect

92. C₄×C₈

C₄₃⋊C₈

semidirect

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

subgroup	index
#19134341	2
C₄₃×#1744	2
#7014	43

subgroup

index

#19134341

C₄₃×#1744

#7014

Subgroups — C₄₃⋊#7014 #24983123

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C43⋊#7014 #24983123

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃⋊#7014 #24983123