Group #24987050 — subgroups

Subgroups — #24987050

Order 11008.

330 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 147 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	#19132887	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	#14582621	C₄	1	8	yes	complemented
7	C₂×#97×C₄₃	C₄	1	2	yes	—
8	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₈×C₄₃	C₄	1	2	yes	—
10	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₄₃×#376	C₂²	1	1	yes	characteristic
12	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
13	C₂²⋊(C₄₃⋊C₈)	—	2	4	no	—
14	C₄×C₄₃⋊C₈	C₂×C₄	1	8	yes	—
15	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
18	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
19	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
20	#97×C₄₃	—	2	4	no	—
21	#97×C₄₃	—	2	2	no	—
22	C₄×C₈×C₄₃	—	2	4	no	—
23	C₄×C₈×C₄₃	C₂×C₄	1	4	yes	—
24	#95×C₄₃	—	2	2	no	—
25	C₂²×C₄×C₄₃	—	2	2	no	—
26	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
27	C₂²×C₄×C₄₃	#41	1	2	yes	—
28	C₂×C₈×C₄₃	—	2	2	no	—
29	C₂×C₈×C₄₃	—	2	2	no	—
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	2	yes	—
34	C₂×C₈×C₄₃	M₁₆	1	4	yes	—
35	C₄²×C₄₃	—	2	2	no	—
36	C₄²×C₄₃	M₁₆	1	4	yes	—
37	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
38	C₄²×C₄₃	#41	1	2	yes	—
39	C₂×C₄₃⋊C₈	—	2	8	no	—
40	C₂³×C₄₃	#117	1	1	yes	characteristic
41	C₂×C₄×C₄₃	—	2	4	no	—
42	C₂×C₄×C₄₃	—	4	2	no	—
43	C₂×C₄×C₄₃	—	4	4	no	—
44	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
45	C₂×C₄×C₄₃	#117	1	4	yes	—
46	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
47	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
48	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
49	C₈×C₄₃	—	2	2	no	—
50	C₈×C₄₃	—	2	2	no	—
51	C₈×C₄₃	—	2	4	no	—
52	C₄₃⋊C₈	—	4	8	no	—
53	#8140	—	43	1	no	maximal, Sylow
54	C₂²×C₄₃	—	2	2	no	—
55	C₂²×C₄₃	#376	1	1	yes	characteristic
56	C₂²×C₄₃	#432	1	2	yes	—
57	C₄×C₄₃	—	2	4	no	—
58	C₄×C₄₃	—	4	4	no	—
59	C₄×C₄₃	C₄×M₁₆	1	1	yes	characteristic
60	C₄×C₄₃	C₄×M₁₆	1	1	yes	characteristic
61	C₄×C₄₃	#432	1	2	yes	—
62	#1726	D₄₃	1	1	yes	characteristic
63	#1452	—	43	2	no	—
64	#1275	—	43	2	no	—
65	#1274	—	43	2	no	—
66	C₂×C₄₃	—	2	2	no	—
67	C₂×C₄₃	#1745	1	1	yes	characteristic
68	C₂×C₄₃	#1747	1	2	yes	—
69	#431	—	43	4	no	—
70	C₂×#97	Dic₄₃	1	2	yes	—
71	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
72	C₂×C₄×C₈	Dic₄₃	1	2	yes	—
73	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
74	#376	C₂×D₄₃	1	1	yes	characteristic
75	#322	—	43	8	no	—
76	C₄₃	#8140	1	1	yes	characteristic, complemented, Sylow
77	C₂²×C₈	C₂×Dic₄₃	1	2	yes	—
78	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
79	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
80	C₂×C₄²	C₂×Dic₄₃	1	2	yes	—
81	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
82	C₄⋊C₈	—	86	4	no	—
83	C₂²⋊C₈	—	86	4	no	—
84	#97	—	2	4	no	—
85	#97	—	2	2	no	—
86	C₄×C₈	—	2	4	no	—
87	C₄×C₈	—	43	8	no	—
88	C₄×C₈	C₄×D₄₃	1	4	yes	—
89	#95	—	2	2	no	—
90	C₂²×C₄	—	2	2	no	—
91	C₂²×C₄	#10621898	1	2	yes	—
92	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
93	C₂×C₈	—	2	2	no	—
94	C₂×C₈	—	2	2	no	—
95	C₂×C₈	—	2	2	no	—
96	C₂×C₈	—	2	2	no	—
97	C₂×C₈	—	86	8	no	—
98	C₂×C₈	#10621877	1	4	yes	—
99	C₂×C₈	C₄×Dic₄₃	1	2	yes	—
100	C₂×C₈	C₄×Dic₄₃	1	2	yes	—
101	C₄²	—	2	2	no	—
102	C₄²	#10621877	1	4	yes	—
103	C₄²	C₂×C₄×D₄₃	1	2	yes	—
104	C₄²	#10621898	1	2	yes	—
105	C₂³	#13063284	1	1	yes	characteristic
106	C₂×C₄	—	2	4	no	—
107	C₂×C₄	—	4	2	no	—
108	C₂×C₄	—	4	4	no	—
109	C₂×C₄	C₂×C₄×Dic₄₃	1	1	yes	characteristic
110	C₂×C₄	#13063282	1	4	yes	—
111	C₂×C₄	#13063284	1	1	yes	characteristic
112	C₂×C₄	C₂×#10621877	1	2	yes	—
113	C₂×C₄	C₂×#10621877	1	2	yes	—
114	C₈	—	2	2	no	—
115	C₈	—	2	2	no	—
116	C₈	—	2	4	no	—
117	C₈	—	172	8	no	—
118	C₂²	—	2	2	no	—
119	C₂²	#14582745	1	1	yes	characteristic
120	C₂²	#14582956	1	2	yes	—
121	C₄	—	2	4	no	—
122	C₄	—	4	4	no	—
123	C₄	C₄×#10621877	1	1	yes	characteristic
124	C₄	C₄×#10621877	1	1	yes	characteristic
125	C₄	#14582956	1	2	yes	—
126	C₂	—	2	2	no	—
127	C₂	#19134344	1	1	yes	characteristic
128	C₂	#19134350	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19132887

C₂

yes

maximal

#19132426

C₂

yes

maximal

#19132424

C₂

yes

maximal

C₄₃×#1726

C₂

yes

maximal, characteristic

#14582952

C₂²

yes

—

#14582621

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

characteristic

C₂²×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

#97×C₄₃

—

#97×C₄₃

—

C₄×C₈×C₄₃

—

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

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₄²

yes

—

C₂×C₈×C₄₃

C₄²

yes

—

C₂×C₈×C₄₃

M₁₆

yes

—

C₄²×C₄₃

—

C₄²×C₄₃

M₁₆

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

C₂×M₁₆

yes

—

C₂×C₄×C₄₃

C₂×M₁₆

yes

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

#8140

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

#376

yes

characteristic

C₂²×C₄₃

#432

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₄×M₁₆

yes

characteristic

C₄×C₄₃

C₄×M₁₆

yes

characteristic

C₄×C₄₃

#432

yes

—

#1726

D₄₃

yes

—

—

—

C₂×C₄₃

—

C₂×C₄₃

#1745

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

—

C₄₃

#8140

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

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₄×D₄₃

yes

—

#95

—

C₂²×C₄

—

C₂²×C₄

#10621898

yes

—

C₂²×C₄

C₂²×Dic₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

#10621877

yes

—

C₂×C₈

C₄×Dic₄₃

yes

—

100

C₂×C₈

C₄×Dic₄₃

yes

—

101

C₄²

—

102

C₄²

#10621877

yes

—

103

C₄²

C₂×C₄×D₄₃

yes

—

104

C₄²

#10621898

yes

—

105

C₂³

#13063284

yes

characteristic

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

C₂×C₄×Dic₄₃

yes

characteristic

110

C₂×C₄

#13063282

yes

—

111

C₂×C₄

#13063284

yes

characteristic

112

C₂×C₄

C₂×#10621877

yes

—

113

C₂×C₄

C₂×#10621877

yes

—

114

C₈

—

115

C₈

—

116

C₈

—

117

C₈

—

172

—

118

C₂²

—

119

C₂²

#14582745

yes

characteristic

120

C₂²

#14582956

yes

—

121

C₄

—

122

C₄

—

123

C₄

C₄×#10621877

yes

characteristic

124

C₄

C₄×#10621877

yes

characteristic

125

C₄

#14582956

yes

—

126

C₂

—

127

C₂

#19134344

yes

characteristic

128

C₂

#19134350

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₄×Dic₄₃
commutator	C₂×C₄×C₄₃	C₂×C₄²
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	#8140
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ #1726

subgroup

G/H

center

C₂×C₄

C₂×C₄×Dic₄₃

commutator

C₂×C₄×C₄₃

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1726

C₂

C₂²×C₄₃

C₂³×C₄₃

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₄₃

C₁ ◁ C₂×C₄ ◁ #1726

N	H ≅ G/N	type
6. #14582621	C₄	semidirect
76. C₄₃	#8140	semidirect

H ≅ G/N

type

6. #14582621

C₄

semidirect

76. C₄₃

#8140

semidirect

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

subgroup	index
#19132887	2
#19132426	2
#19132424	2
C₄₃×#1726	2
#8140	43

subgroup

index

C₄₃×#1726

Subgroups — #24987050

Conjugacy classes of subgroups

Complements

Maximal subgroups