Group #24987042 — subgroups

Subgroups — #24987042

Order 11008.

354 conjugacy classes of subgroups; only the 195 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 195 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	#19132878	C₂	1	2	yes	maximal
2	#19132426	C₂	1	2	yes	maximal
3	#19132424	C₂	1	2	yes	maximal
4	C₄₃×#1726	C₂	1	1	yes	maximal, characteristic
5	#14582952	C₂²	1	4	yes	—
6	#14582620	C₄	1	4	yes	complemented
7	C₈×C₄₃⋊C₈	C₄	1	4	yes	complemented
8	C₂×#97×C₄₃	C₄	1	2	yes	—
9	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₈×C₄₃	C₄	1	2	yes	—
11	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
12	C₄₃×#376	C₂²	1	1	yes	characteristic
13	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
14	C₂²⋊(C₄₃⋊C₈)	—	2	4	no	—
15	C₄×C₄₃⋊C₈	C₂×C₄	1	8	yes	—
16	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
17	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
20	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
21	#97×C₄₃	—	2	2	no	—
22	#97×C₄₃	C₈	1	8	yes	complemented
23	C₄×C₈×C₄₃	—	2	4	no	—
24	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
25	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
26	#95×C₄₃	—	2	2	no	—
27	C₂²×C₄×C₄₃	—	2	2	no	—
28	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
29	C₂²×C₄×C₄₃	#41	1	2	yes	—
30	C₂×C₈×C₄₃	—	2	2	no	—
31	C₂×C₈×C₄₃	—	2	2	no	—
32	C₂×C₈×C₄₃	C₄²	1	2	yes	—
33	C₂×C₈×C₄₃	C₄²	1	1	yes	characteristic
34	C₂×C₈×C₄₃	C₄²	1	1	yes	characteristic
35	C₂×C₈×C₄₃	C₂×C₈	1	4	yes	—
36	C₂×C₈×C₄₃	C₂×C₈	1	4	yes	—
37	C₂×C₈×C₄₃	M₁₆	1	4	yes	—
38	C₄²×C₄₃	—	2	2	no	—
39	C₄²×C₄₃	C₂×C₈	1	4	yes	—
40	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
41	C₄²×C₄₃	#41	1	2	yes	—
42	C₂×C₄₃⋊C₈	—	2	8	no	—
43	C₂³×C₄₃	#117	1	1	yes	characteristic
44	C₂×C₄×C₄₃	—	2	4	no	—
45	C₂×C₄×C₄₃	—	4	2	no	—
46	C₂×C₄×C₄₃	—	4	4	no	—
47	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
48	C₂×C₄×C₄₃	#117	1	4	yes	—
49	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
50	C₂×C₄×C₄₃	C₂²×C₈	1	2	yes	—
51	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
52	C₈×C₄₃	—	2	4	no	—
53	C₈×C₄₃	C₄×C₈	1	4	yes	—
54	C₈×C₄₃	#97	1	2	yes	—
55	C₈×C₄₃	#97	1	2	yes	—
56	C₄₃⋊C₈	—	4	8	no	—
57	#8138	—	43	1	no	maximal, Sylow
58	C₂²×C₄₃	—	2	2	no	—
59	C₂²×C₄₃	#376	1	1	yes	characteristic
60	C₂²×C₄₃	#431	1	2	yes	—
61	C₄×C₄₃	—	2	4	no	—
62	C₄×C₄₃	—	4	4	no	—
63	C₄×C₄₃	C₂×C₄×C₈	1	1	yes	characteristic
64	C₄×C₄₃	C₂×#97	1	1	yes	characteristic
65	C₄×C₄₃	#431	1	2	yes	—
66	#1726	D₄₃	1	1	yes	characteristic
67	#1450	—	43	2	no	—
68	#1275	—	43	2	no	—
69	#1274	—	43	2	no	—
70	C₂×C₄₃	—	2	2	no	—
71	C₂×C₄₃	#1744	1	1	yes	characteristic
72	C₂×C₄₃	#1747	1	2	yes	—
73	#431	—	43	4	no	—
74	C₂×#97	Dic₄₃	1	2	yes	—
75	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
76	C₂×C₄×C₈	Dic₄₃	1	2	yes	—
77	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
78	#376	C₂×D₄₃	1	1	yes	characteristic
79	#322	—	43	4	no	—
80	C₈²	—	43	4	no	—
81	C₄₃	#8138	1	1	yes	characteristic, complemented, Sylow
82	C₂²×C₈	C₂×Dic₄₃	1	2	yes	—
83	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
84	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
85	C₂×C₄²	C₂×Dic₄₃	1	2	yes	—
86	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
87	C₄⋊C₈	—	86	4	no	—
88	C₂²⋊C₈	—	86	4	no	—
89	#97	—	2	2	no	—
90	#97	C₄₃⋊C₈	1	8	yes	complemented
91	C₄×C₈	—	2	4	no	—
92	C₄×C₈	—	43	8	no	—
93	C₄×C₈	C₄×D₄₃	1	2	yes	—
94	C₄×C₈	C₄×D₄₃	1	2	yes	—
95	#95	—	2	2	no	—
96	C₂²×C₄	—	2	2	no	—
97	C₂²×C₄	#10621898	1	2	yes	—
98	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
99	C₂×C₈	—	2	2	no	—
100	C₂×C₈	—	2	2	no	—
101	C₂×C₈	—	86	8	no	—
102	C₂×C₈	C₂×C₄₃⋊C₈	1	4	yes	—
103	C₂×C₈	C₂×C₄₃⋊C₈	1	4	yes	—
104	C₂×C₈	#10621877	1	4	yes	—
105	C₂×C₈	C₄×Dic₄₃	1	2	yes	—
106	C₂×C₈	C₄×Dic₄₃	1	1	yes	characteristic
107	C₂×C₈	C₄×Dic₄₃	1	1	yes	characteristic
108	C₄²	—	2	2	no	—
109	C₄²	C₂×C₄₃⋊C₈	1	4	yes	—
110	C₄²	C₂×C₄×D₄₃	1	2	yes	—
111	C₄²	#10621898	1	2	yes	—
112	C₂³	#13063284	1	1	yes	characteristic
113	C₂×C₄	—	2	4	no	—
114	C₂×C₄	—	4	2	no	—
115	C₂×C₄	—	4	4	no	—
116	C₂×C₄	C₂×C₄×Dic₄₃	1	1	yes	characteristic
117	C₂×C₄	#13063282	1	4	yes	—
118	C₂×C₄	#13063284	1	1	yes	characteristic
119	C₂×C₄	C₂²×C₄₃⋊C₈	1	2	yes	—
120	C₂×C₄	C₂×#10621877	1	2	yes	—
121	C₈	—	2	4	no	—
122	C₈	—	172	8	no	—
123	C₈	C₄×C₄₃⋊C₈	1	4	yes	—
124	C₈	#13063236	1	2	yes	—
125	C₈	#13063236	1	2	yes	—
126	C₂²	—	2	2	no	—
127	C₂²	#14582745	1	1	yes	characteristic
128	C₂²	#14582952	1	2	yes	—
129	C₄	—	2	4	no	—
130	C₄	—	4	4	no	—
131	C₄	C₂×C₄×C₄₃⋊C₈	1	1	yes	characteristic
132	C₄	C₂×#13063236	1	1	yes	characteristic
133	C₄	#14582952	1	2	yes	—
134	C₂	—	2	2	no	—
135	C₂	#19134341	1	1	yes	characteristic
136	C₂	#19134350	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19132878

C₂

yes

maximal

#19132426

C₂

yes

maximal

#19132424

C₂

yes

maximal

C₄₃×#1726

C₂

yes

maximal, characteristic

#14582952

C₂²

yes

—

#14582620

C₄

yes

complemented

C₈×C₄₃⋊C₈

C₄

yes

complemented

C₂×#97×C₄₃

C₄

yes

—

C₂×#97×C₄₃

C₂²

yes

characteristic

C₂×C₄×C₈×C₄₃

C₄

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄₃×#376

C₂²

yes

characteristic

C₄⋊(C₄₃⋊C₈)

—

C₂²⋊(C₄₃⋊C₈)

—

C₄×C₄₃⋊C₈

C₂×C₄

yes

—

C₂²×C₈×C₄₃

C₂×C₄

yes

—

C₂²×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

#97×C₄₃

—

#97×C₄₃

C₈

yes

complemented

C₄×C₈×C₄₃

—

C₄×C₈×C₄₃

C₂×C₄

yes

—

C₄×C₈×C₄₃

C₂×C₄

yes

—

#95×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

#41

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₄²

yes

—

C₂×C₈×C₄₃

C₄²

yes

characteristic

C₂×C₈×C₄₃

C₄²

yes

characteristic

C₂×C₈×C₄₃

C₂×C₈

yes

—

C₂×C₈×C₄₃

C₂×C₈

yes

—

C₂×C₈×C₄₃

M₁₆

yes

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×C₈

yes

—

C₄²×C₄₃

C₂²×C₄

yes

—

C₄²×C₄₃

#41

yes

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#117

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₄₃

#117

yes

—

C₂×C₄×C₄₃

#117

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₈

yes

—

C₂×C₄×C₄₃

C₂×M₁₆

yes

—

C₈×C₄₃

—

C₈×C₄₃

C₄×C₈

yes

—

C₈×C₄₃

#97

yes

—

C₈×C₄₃

#97

yes

—

C₄₃⋊C₈

—

#8138

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

#376

yes

characteristic

C₂²×C₄₃

#431

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×C₄×C₈

yes

characteristic

C₄×C₄₃

C₂×#97

yes

characteristic

C₄×C₄₃

#431

yes

—

#1726

D₄₃

yes

—

—

—

C₂×C₄₃

—

C₂×C₄₃

#1744

yes

characteristic

C₂×C₄₃

#1747

yes

—

#431

—

C₂×#97

Dic₄₃

yes

—

C₂×#97

C₂×D₄₃

yes

characteristic

C₂×C₄×C₈

Dic₄₃

yes

—

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

#376

C₂×D₄₃

yes

characteristic

#322

—

C₈²

—

C₄₃

#8138

yes

characteristic, complemented, Sylow

C₂²×C₈

C₂×Dic₄₃

yes

—

C₂²×C₈

C₂×Dic₄₃

yes

characteristic

C₂²×C₈

C₂×Dic₄₃

yes

characteristic

C₂×C₄²

C₂×Dic₄₃

yes

—

C₂×C₄²

C₂²×D₄₃

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

C₄₃⋊C₈

yes

complemented

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₄×D₄₃

yes

—

C₄×C₈

C₄×D₄₃

yes

—

#95

—

C₂²×C₄

—

C₂²×C₄

#10621898

yes

—

C₂²×C₄

C₂²×Dic₄₃

yes

characteristic

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

C₂×C₄₃⋊C₈

yes

—

103

C₂×C₈

C₂×C₄₃⋊C₈

yes

—

104

C₂×C₈

#10621877

yes

—

105

C₂×C₈

C₄×Dic₄₃

yes

—

106

C₂×C₈

C₄×Dic₄₃

yes

characteristic

107

C₂×C₈

C₄×Dic₄₃

yes

characteristic

108

C₄²

—

109

C₄²

C₂×C₄₃⋊C₈

yes

—

110

C₄²

C₂×C₄×D₄₃

yes

—

111

C₄²

#10621898

yes

—

112

C₂³

#13063284

yes

characteristic

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

C₂×C₄×Dic₄₃

yes

characteristic

117

C₂×C₄

#13063282

yes

—

118

C₂×C₄

#13063284

yes

characteristic

119

C₂×C₄

C₂²×C₄₃⋊C₈

yes

—

120

C₂×C₄

C₂×#10621877

yes

—

121

C₈

—

122

C₈

—

172

—

123

C₈

C₄×C₄₃⋊C₈

yes

—

124

C₈

#13063236

yes

—

125

C₈

#13063236

yes

—

126

C₂²

—

127

C₂²

#14582745

yes

characteristic

128

C₂²

#14582952

yes

—

129

C₄

—

130

C₄

—

131

C₄

C₂×C₄×C₄₃⋊C₈

yes

characteristic

132

C₄

C₂×#13063236

yes

characteristic

133

C₄

#14582952

yes

—

134

C₂

—

135

C₂

#19134341

yes

characteristic

136

C₂

#19134350

yes

—

	subgroup	G/H
center	C₂×C₈	C₄×Dic₄₃
commutator	C₄×C₄₃	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1726	C₂
socle	C₂²×C₄₃	#376
prime radical	C₂³×C₄₃	#117
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1726	D₄₃
hypocenter	C₄₃	#8138
LCS	G ▷ C₄×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ #1726

subgroup

G/H

center

C₂×C₈

C₄×Dic₄₃

commutator

C₄×C₄₃

C₂×C₄×C₈

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1726

C₂

C₂²×C₄₃

C₂³×C₄₃

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₄×C₄₃ ▷ C₄₃

C₁ ◁ C₂×C₈ ◁ #1726

N	H ≅ G/N	type
6. #14582620	C₄	semidirect
7. C₈×C₄₃⋊C₈	C₄	semidirect
22. #97×C₄₃	C₈	semidirect
81. C₄₃	#8138	semidirect
90. #97	C₄₃⋊C₈	semidirect

H ≅ G/N

type

6. #14582620

C₄

semidirect

7. C₈×C₄₃⋊C₈

C₄

semidirect

22. #97×C₄₃

C₈

semidirect

81. C₄₃

#8138

semidirect

90. #97

C₄₃⋊C₈

semidirect

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

subgroup	index
#19132878	2
#19132426	2
#19132424	2
C₄₃×#1726	2
#8138	43

subgroup

index

C₄₃×#1726

Subgroups — #24987042

Conjugacy classes of subgroups

Complements

Maximal subgroups