Group #24985987 — subgroups

Subgroups — #24985987

Order 11008.

610 conjugacy classes of subgroups; only the 207 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 207 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×#14582950	C₂	1	3	yes	maximal
2	C₄₃⋊#1273	C₂	1	3	yes	maximal, complemented
3	C₄₃×#1273	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄²×D₄₃	C₂²	1	1	yes	characteristic
5	#14582950	—	2	12	no	—
6	C₂×Dic₄₃⋊C₈	C₄	1	6	yes	—
7	C₂×(C₂×D₄₃)⋊C₈	C₄	1	6	yes	—
8	C₂×C₄×C₄₃⋊C₈	C₂²	1	3	yes	—
9	C₂×C₄×C₈×C₄₃	C₂²	1	3	yes	—
10	C₂²×C₄×D₄₃	C₂×C₄	1	3	yes	—
11	C₂²×C₄₃⋊C₈	C₂×C₄	1	6	yes	—
12	C₂×C₄×Dic₄₃	C₂×C₄	1	3	yes	—
13	C₄²×D₄₃	D₄	1	6	yes	—
14	C₄²×D₄₃	Q₈	1	2	yes	—
15	Dic₄₃⋊C₈	—	2	12	no	—
16	(C₂×D₄₃)⋊C₈	—	2	12	no	—
17	C₄×C₄₃⋊C₈	—	2	6	no	—
18	C₂²×C₈×C₄₃	C₂×C₄	1	6	yes	—
19	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
20	C₄×C₈×C₄₃	—	2	6	no	—
21	C₂³×D₄₃	C₄²	1	1	yes	characteristic
22	C₂²×C₄×C₄₃	C₂²×C₄	1	3	yes	—
23	C₂²×Dic₄₃	C₄²	1	3	yes	—
24	C₂×C₄×D₄₃	—	2	6	no	—
25	C₂×C₄×D₄₃	—	2	6	no	—
26	C₂×C₄×D₄₃	C₂²⋊C₄	1	6	yes	—
27	C₂×C₄×D₄₃	C₄⋊C₄	1	6	yes	—
28	C₂×C₈×C₄₃	—	2	6	no	—
29	C₂×C₈×C₄₃	—	2	6	no	—
30	C₂×C₈×C₄₃	—	2	6	no	—
31	C₄²×C₄₃	C₂×D₄	1	3	yes	—
32	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
33	C₄×Dic₄₃	C₂²⋊C₄	1	6	yes	—
34	C₄×Dic₄₃	C₄⋊C₄	1	6	yes	—
35	C₂×C₄₃⋊C₈	—	2	6	no	—
36	C₂×C₄₃⋊C₈	—	2	6	no	—
37	C₂×C₄₃⋊C₈	—	2	6	no	—
38	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
39	C₂²×D₄₃	—	2	3	no	—
40	C₂²×D₄₃	—	2	3	no	—
41	C₂²×D₄₃	#95	1	2	yes	—
42	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	3	yes	—
43	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	3	yes	—
44	C₂×C₄×C₄₃	#131	1	6	yes	—
45	C₂×C₄×C₄₃	#131	1	6	yes	—
46	C₂×Dic₄₃	—	2	3	no	—
47	C₂×Dic₄₃	—	2	3	no	—
48	C₂×Dic₄₃	#95	1	6	yes	—
49	C₄×D₄₃	—	2	12	no	—
50	C₄×D₄₃	—	2	12	no	—
51	C₈×C₄₃	—	4	6	no	—
52	C₄₃⋊C₈	—	4	6	no	—
53	#7851	—	43	1	no	maximal, Sylow
54	C₂²×C₄₃	C₂×#95	1	1	yes	characteristic
55	C₂²×C₄₃	#405	1	3	yes	—
56	C₂²×C₄₃	#405	1	3	yes	—
57	C₂×D₄₃	—	2	6	no	—
58	C₂×D₄₃	—	4	1	no	—
59	C₂×D₄₃	—	4	3	no	—
60	C₄×C₄₃	#408	1	6	yes	—
61	C₄×C₄₃	#424	1	6	yes	—
62	Dic₄₃	—	2	6	no	—
63	C₂×#431	—	43	3	no	—
64	#1273	—	43	3	no	—
65	#1273	D₄₃	1	1	yes	characteristic, complemented
66	C₂×C₄₃	#1454	1	1	yes	characteristic
67	C₂×C₄₃	#1454	1	3	yes	—
68	C₂×C₄₃	#1729	1	3	yes	—
69	D₄₃	—	4	2	no	—
70	C₂²×C₄²	—	43	1	no	—
71	#431	—	86	12	no	—
72	C₂×C₄⋊C₈	—	43	6	no	—
73	C₂×C₂²⋊C₈	—	43	6	no	—
74	C₂×C₄×C₈	—	43	3	no	—
75	C₂×C₄×C₈	C₂×D₄₃	1	3	yes	—
76	C₄₃	#7851	1	1	yes	characteristic, complemented, Sylow
77	C₂³×C₄	—	43	3	no	—
78	C₂²×C₈	—	43	6	no	—
79	C₂²×C₈	C₄×D₄₃	1	6	yes	—
80	C₂×C₄²	—	43	3	no	—
81	C₂×C₄²	—	43	6	no	—
82	C₂×C₄²	—	43	2	no	—
83	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
84	C₄⋊C₈	—	86	12	no	—
85	C₂²⋊C₈	—	86	12	no	—
86	C₄×C₈	—	2	6	no	—
87	C₄×C₈	—	86	6	no	—
88	C₂⁴	—	43	1	no	—
89	C₂²×C₄	—	43	3	no	—
90	C₂²×C₄	—	43	6	no	—
91	C₂²×C₄	—	43	6	no	—
92	C₂²×C₄	—	86	6	no	—
93	C₂²×C₄	—	86	6	no	—
94	C₂²×C₄	C₂×C₄×D₄₃	1	3	yes	—
95	C₂×C₈	—	2	6	no	—
96	C₂×C₈	—	2	6	no	—
97	C₂×C₈	—	2	6	no	—
98	C₂×C₈	—	86	6	no	—
99	C₂×C₈	—	86	6	no	—
100	C₂×C₈	—	86	6	no	—
101	C₄²	—	43	6	no	—
102	C₄²	—	43	6	no	—
103	C₄²	D₄×D₄₃	1	3	yes	—
104	C₄²	Q₈×D₄₃	1	1	yes	characteristic
105	C₂³	—	43	2	no	—
106	C₂³	—	86	3	no	—
107	C₂³	—	86	3	no	—
108	C₂³	C₄²×D₄₃	1	1	yes	characteristic
109	C₂×C₄	—	43	6	no	—
110	C₂×C₄	—	86	3	no	—
111	C₂×C₄	—	86	3	no	—
112	C₂×C₄	—	86	12	no	—
113	C₂×C₄	—	86	12	no	—
114	C₂×C₄	C₂²⋊C₄×D₄₃	1	3	yes	—
115	C₂×C₄	C₄⋊C₄×D₄₃	1	3	yes	—
116	C₂×C₄	#13063331	1	6	yes	—
117	C₂×C₄	#13063333	1	6	yes	—
118	C₈	—	4	6	no	—
119	C₈	—	172	6	no	—
120	C₂²	—	86	6	no	—
121	C₂²	—	172	1	no	—
122	C₂²	—	172	3	no	—
123	C₂²	#95×D₄₃	1	1	yes	characteristic
124	C₂²	#14582853	1	3	yes	—
125	C₂²	#14582856	1	3	yes	—
126	C₄	—	86	6	no	—
127	C₄	#14582864	1	6	yes	—
128	C₄	#14582924	1	6	yes	—
129	C₂	—	172	2	no	—
130	C₂	#19132894	1	1	yes	characteristic
131	C₂	#19132896	1	3	yes	—
132	C₂	#19134290	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14582950

C₂

yes

maximal

C₄₃⋊#1273

C₂

yes

maximal, complemented

C₄₃×#1273

C₂

yes

maximal, characteristic, complemented

C₂×C₄²×D₄₃

C₂²

yes

characteristic

#14582950

—

C₂×Dic₄₃⋊C₈

C₄

yes

—

C₂×(C₂×D₄₃)⋊C₈

C₄

yes

—

C₂×C₄×C₄₃⋊C₈

C₂²

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

—

C₂²×C₄×D₄₃

C₂×C₄

yes

—

C₂²×C₄₃⋊C₈

C₂×C₄

yes

—

C₂×C₄×Dic₄₃

C₂×C₄

yes

—

C₄²×D₄₃

D₄

yes

—

C₄²×D₄₃

Q₈

yes

—

Dic₄₃⋊C₈

—

(C₂×D₄₃)⋊C₈

—

C₄×C₄₃⋊C₈

—

C₂²×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄×C₈×C₄₃

—

C₂³×D₄₃

C₄²

yes

characteristic

C₂²×C₄×C₄₃

C₂²×C₄

yes

—

C₂²×Dic₄₃

C₄²

yes

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

C₂²⋊C₄

yes

—

C₂×C₄×D₄₃

C₄⋊C₄

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

C₂×D₄

yes

—

C₄²×C₄₃

C₂×Q₈

yes

characteristic

C₄×Dic₄₃

C₂²⋊C₄

yes

—

C₄×Dic₄₃

C₄⋊C₄

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂×C₄²

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

#95

yes

—

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

—

C₂×C₄×C₄₃

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₄₃

#131

yes

—

C₂×C₄×C₄₃

#131

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

#95

yes

—

C₄×D₄₃

—

C₄×D₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

#7851

—

maximal, Sylow

C₂²×C₄₃

C₂×#95

yes

characteristic

C₂²×C₄₃

#405

yes

—

C₂²×C₄₃

#405

yes

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

#408

yes

—

C₄×C₄₃

#424

yes

—

Dic₄₃

—

C₂×#431

—

#1273

—

#1273

D₄₃

yes

characteristic, complemented

C₂×C₄₃

#1454

yes

characteristic

C₂×C₄₃

#1454

yes

—

C₂×C₄₃

#1729

yes

—

D₄₃

—

C₂²×C₄²

—

#431

—

C₂×C₄⋊C₈

—

C₂×C₂²⋊C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₄₃

yes

—

C₄₃

#7851

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

C₄×D₄₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₄₃

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×C₄×D₄₃

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₄²

—

102

C₄²

—

103

C₄²

D₄×D₄₃

yes

—

104

C₄²

Q₈×D₄₃

yes

characteristic

105

C₂³

—

106

C₂³

—

107

C₂³

—

108

C₂³

C₄²×D₄₃

yes

characteristic

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

C₂²⋊C₄×D₄₃

yes

—

115

C₂×C₄

C₄⋊C₄×D₄₃

yes

—

116

C₂×C₄

#13063331

yes

—

117

C₂×C₄

#13063333

yes

—

118

C₈

—

119

C₈

—

172

—

120

C₂²

—

121

C₂²

—

172

—

122

C₂²

—

172

—

123

C₂²

#95×D₄₃

yes

characteristic

124

C₂²

#14582853

yes

—

125

C₂²

#14582856

yes

—

126

C₄

—

127

C₄

#14582864

yes

—

128

C₄

#14582924

yes

—

129

C₂

—

172

—

130

C₂

#19132894

yes

characteristic

131

C₂

#19132896

yes

—

132

C₂

#19134290

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₄₃
commutator, socle	C₂³×C₄₃	C₂×C₄²
Fitting	C₄₃×#1273	C₂
prime radical	C₂³×D₄₃	C₄²
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1273	D₄₃
hypocenter	C₄₃	#7851
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄² ◁ #1273

subgroup

G/H

center, Frattini

C₂×C₄²

C₂²×D₄₃

commutator, socle

C₂³×C₄₃

C₂×C₄²

Fitting

C₄₃×#1273

C₂

prime radical

C₂³×D₄₃

C₄²

cosocle

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂×C₄² ◁ #1273

N	H ≅ G/N	type
2. C₄₃⋊#1273	C₂	semidirect
3. C₄₃×#1273	C₂	semidirect
65. #1273	D₄₃	semidirect
76. C₄₃	#7851	semidirect

H ≅ G/N

type

2. C₄₃⋊#1273

C₂

semidirect

3. C₄₃×#1273

C₂

semidirect

65. #1273

D₄₃

semidirect

76. C₄₃

#7851

semidirect

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

subgroup	index
C₂×#14582950	2
C₄₃⋊#1273	2
C₄₃×#1273	2
#7851	43

subgroup

index

C₂×#14582950

C₄₃⋊#1273

C₄₃×#1273

#7851

Subgroups — #24985987

Conjugacy classes of subgroups

Complements

Maximal subgroups