Group #24987029 — subgroups

Subgroups — #24987029

Order 11008.

414 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 187 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	1	yes	maximal, characteristic
2	C₄×#13063236	C₂	1	1	yes	maximal, characteristic
3	C₄₃⋊#1273	C₂	1	4	yes	maximal
4	C₄₃×#1744	C₂	1	1	yes	maximal, characteristic
5	C₂×#13063236	C₄	1	4	yes	—
6	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
8	#14582654	C₄	1	4	yes	—
9	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
10	C₄³×C₄₃	C₂²	1	1	yes	characteristic
11	C₄₃×#336	C₄	1	4	yes	—
12	C₂²×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
13	C₂²×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
14	#13063236	—	2	8	no	—
15	C₄×C₄₃⋊C₈	—	2	4	no	—
16	C₄×C₄₃⋊C₈	—	2	4	no	—
17	C₂²×C₈×C₄₃	C₂×C₄	1	4	yes	—
18	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
19	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
20	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
21	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
22	C₄×C₈×C₄₃	—	2	4	no	—
23	C₂²×C₄×C₄₃	C₄²	1	4	yes	—
24	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
25	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
26	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₈×C₄₃	—	2	4	no	—
28	C₂×C₈×C₄₃	—	2	8	no	—
29	C₄²×C₄₃	—	2	4	no	—
30	C₄²×C₄₃	—	2	4	no	—
31	C₄²×C₄₃	—	2	4	no	—
32	C₄²×C₄₃	#41	1	4	yes	—
33	C₂×C₄₃⋊C₈	—	2	4	no	—
34	C₂×C₄₃⋊C₈	—	2	4	no	—
35	C₂×C₄₃⋊C₈	—	2	4	no	—
36	C₂×C₄₃⋊C₈	—	2	8	no	—
37	C₂×C₄₃⋊C₈	M₁₆	1	8	yes	—
38	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
39	C₂×C₄×C₄₃	—	2	4	no	—
40	C₂×C₄×C₄₃	—	2	4	no	—
41	C₂×C₄×C₄₃	—	2	4	no	—
42	C₂×C₄×C₄₃	#117	1	2	yes	—
43	C₂×C₄×C₄₃	#117	1	2	yes	—
44	C₂×C₄×C₄₃	#117	1	2	yes	—
45	C₂×C₄×C₄₃	C₂×M₁₆	1	4	yes	—
46	C₂×C₄×C₄₃	#131	1	4	yes	—
47	C₂×C₄×C₄₃	#131	1	4	yes	—
48	C₈×C₄₃	—	4	4	no	—
49	C₄₃⋊C₈	—	2	8	no	—
50	C₄₃⋊C₈	—	4	4	no	—
51	#8134	—	43	1	no	maximal, Sylow
52	C₂²×C₄₃	#376	1	1	yes	characteristic
53	C₂²×C₄₃	C₄×M₁₆	1	2	yes	—
54	C₂²×C₄₃	#405	1	2	yes	—
55	C₂²×C₄₃	#405	1	2	yes	—
56	C₄×C₄₃	—	4	4	no	—
57	C₄×C₄₃	#432	1	4	yes	—
58	C₄×C₄₃	#433	1	4	yes	—
59	C₄×C₄₃	#433	1	4	yes	—
60	#1744	—	43	1	no	—
61	#1744	D₄₃	1	1	yes	characteristic
62	C₄×#97	—	43	1	no	—
63	#1273	—	43	4	no	—
64	C₂×C₄₃	#1453	1	4	yes	—
65	C₂×C₄₃	#1745	1	1	yes	characteristic
66	C₂×C₄₃	#1746	1	1	yes	characteristic
67	C₂×C₄₃	#1746	1	1	yes	characteristic
68	C₂×#97	—	43	4	no	—
69	C₂×C₄×C₈	—	43	2	no	—
70	C₂×C₄×C₈	—	43	2	no	—
71	C₂×C₄×C₈	C₂×D₄₃	1	2	yes	—
72	C₄³	C₂×D₄₃	1	1	yes	characteristic
73	#336	—	43	4	no	—
74	#336	Dic₄₃	1	4	yes	—
75	C₄₃	#8134	1	1	yes	characteristic, complemented, Sylow
76	C₂²×C₈	—	43	4	no	—
77	C₂²×C₈	—	43	4	no	—
78	C₂²×C₈	C₂×Dic₄₃	1	4	yes	—
79	C₂×C₄²	C₄×D₄₃	1	2	yes	—
80	C₂×C₄²	C₄×D₄₃	1	2	yes	—
81	C₂×C₄²	C₂×Dic₄₃	1	2	yes	—
82	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
83	#97	—	86	8	no	—
84	C₄×C₈	—	2	4	no	—
85	C₄×C₈	—	86	4	no	—
86	C₄×C₈	—	86	4	no	—
87	C₂²×C₄	C₄×Dic₄₃	1	4	yes	—
88	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
89	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
90	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
91	C₂×C₈	—	2	4	no	—
92	C₂×C₈	—	2	8	no	—
93	C₂×C₈	—	43	8	no	—
94	C₂×C₈	—	86	4	no	—
95	C₂×C₈	—	86	4	no	—
96	C₂×C₈	—	86	4	no	—
97	C₂×C₈	—	86	8	no	—
98	C₄²	—	2	4	no	—
99	C₄²	—	2	4	no	—
100	C₄²	—	2	4	no	—
101	C₄²	#10621898	1	4	yes	—
102	C₂³	C₂×C₄×Dic₄₃	1	1	yes	characteristic
103	C₂×C₄	—	2	4	no	—
104	C₂×C₄	—	2	4	no	—
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	#13063282	1	2	yes	—
107	C₂×C₄	#13063282	1	2	yes	—
108	C₂×C₄	#13063284	1	2	yes	—
109	C₂×C₄	M₁₆×D₄₃	1	4	yes	—
110	C₂×C₄	#13063331	1	4	yes	—
111	C₂×C₄	#13063332	1	4	yes	—
112	C₈	—	4	4	no	—
113	C₈	—	86	8	no	—
114	C₈	—	172	4	no	—
115	C₂²	#14582745	1	1	yes	characteristic
116	C₂²	M₁₆×Dic₄₃	1	2	yes	—
117	C₂²	#14582854	1	2	yes	—
118	C₂²	#14582855	1	2	yes	—
119	C₄	—	4	4	no	—
120	C₄	#14582954	1	4	yes	—
121	C₄	#14582958	1	4	yes	—
122	C₄	#14582960	1	4	yes	—
123	C₂	#19132890	1	4	yes	—
124	C₂	#19134343	1	1	yes	characteristic
125	C₂	#19134346	1	1	yes	characteristic
126	C₂	#19134347	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19134341

C₂

yes

maximal, characteristic

C₄×#13063236

C₂

yes

maximal, characteristic

C₄₃⋊#1273

C₂

yes

maximal

C₄₃×#1744

C₂

yes

maximal, characteristic

C₂×#13063236

C₄

yes

—

C₂×C₄×C₄₃⋊C₈

C₂²

yes

—

C₂×C₄×C₄₃⋊C₈

C₂²

yes

—

#14582654

C₄

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

—

C₄³×C₄₃

C₂²

yes

characteristic

C₄₃×#336

C₄

yes

—

C₂²×C₄₃⋊C₈

C₂×C₄

yes

—

C₂²×C₄₃⋊C₈

C₂×C₄

yes

—

#13063236

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

—

C₂²×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄×C₈×C₄₃

—

C₂²×C₄×C₄₃

C₄²

yes

—

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

#41

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

M₁₆

yes

—

C₂³×C₄₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#117

yes

—

C₂×C₄×C₄₃

#117

yes

—

C₂×C₄×C₄₃

#117

yes

—

C₂×C₄×C₄₃

C₂×M₁₆

yes

—

C₂×C₄×C₄₃

#131

yes

—

C₂×C₄×C₄₃

#131

yes

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

—

C₂²×C₄₃

yes

C₂²×C₄₃

C₄×M₁₆

yes

—

C₂²×C₄₃

#405

yes

—

C₂²×C₄₃

#405

yes

—

C₄×C₄₃

—

C₄×C₄₃

#432

yes

—

C₄×C₄₃

#433

yes

—

C₄×C₄₃

#433

yes

—

#1744

—

#1744

D₄₃

yes

characteristic

C₄×#97

—

#1273

—

C₂×C₄₃

#1453

yes

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₄₃

yes

—

C₄³

C₂×D₄₃

yes

characteristic

#336

—

#336

Dic₄₃

yes

—

C₄₃

#8134

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×Dic₄₃

yes

—

C₂×C₄²

C₄×D₄₃

yes

—

C₂×C₄²

C₄×D₄₃

yes

—

C₂×C₄²

C₂×Dic₄₃

yes

—

C₂×C₄²

C₂²×D₄₃

yes

characteristic

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

C₄×Dic₄₃

yes

—

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

C₂²×C₄

C₂²×Dic₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

100

C₄²

—

101

C₄²

#10621898

yes

—

102

C₂³

C₂×C₄×Dic₄₃

yes

characteristic

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

#13063282

yes

—

107

C₂×C₄

#13063282

yes

—

108

C₂×C₄

#13063284

yes

—

109

C₂×C₄

M₁₆×D₄₃

yes

—

110

C₂×C₄

#13063331

yes

—

111

C₂×C₄

#13063332

yes

—

112

C₈

—

113

C₈

—

114

C₈

—

172

—

115

C₂²

#14582745

yes

characteristic

116

C₂²

M₁₆×Dic₄₃

yes

—

117

C₂²

#14582854

yes

—

118

C₂²

#14582855

yes

—

119

C₄

—

120

C₄

#14582954

yes

—

121

C₄

#14582958

yes

—

122

C₄

#14582960

yes

—

123

C₂

#19132890

yes

—

124

C₂

#19134343

yes

characteristic

125

C₂

#19134346

yes

characteristic

126

C₂

#19134347

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₄₃
commutator, socle, prime radical	C₂³×C₄₃	C₂×C₄²
Fitting	C₄₃×#1744	C₂
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1744	D₄₃
hypocenter	C₄₃	#8134
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄² ◁ #1744

subgroup

G/H

center, Frattini

C₂×C₄²

C₂²×D₄₃

commutator, socle, prime radical

C₂³×C₄₃

C₂×C₄²

Fitting

C₄₃×#1744

C₂

cosocle

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂×C₄² ◁ #1744

N	H ≅ G/N	type
75. C₄₃	#8134	semidirect

H ≅ G/N

type

75. C₄₃

#8134

semidirect

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

subgroup	index
#19134341	2
C₄×#13063236	2
C₄₃⋊#1273	2
C₄₃×#1744	2
#8134	43

subgroup

index

#19134341

C₄×#13063236

C₄₃⋊#1273

C₄₃×#1744

#8134

Subgroups — #24987029

Conjugacy classes of subgroups

Complements

Maximal subgroups