Group #24990369 — subgroups

Subgroups — #24990369

Order 11008.

422 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 203 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	#19134752	C₂	1	1	yes	maximal, characteristic
2	#19134722	C₂	1	4	yes	maximal
3	C₂×C₈×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#1844	C₂	1	1	yes	maximal, characteristic
5	C₂×#13063257	—	2	2	no	—
6	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
7	#14582769	C₂²	1	2	yes	—
8	#14582661	—	2	8	no	—
9	C₈×C₄₃⋊C₈	C₄	1	4	yes	complemented
10	C₂×#106×C₄₃	—	2	2	no	—
11	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
12	C₄₃×#384	C₂²	1	2	yes	—
13	C₂²×C₄₃⋊C₈	D₄	1	4	yes	—
14	C₂×C₄⋊Dic₄₃	—	2	4	no	—
15	C₂×C₄⋊Dic₄₃	—	2	2	no	—
16	#13063257	—	4	4	no	—
17	C₄×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
18	C₄×C₄₃⋊C₈	Q₈	1	4	yes	—
19	C₂²×C₈×C₄₃	D₄	1	2	yes	—
20	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
21	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
22	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
23	#106×C₄₃	—	4	4	no	—
24	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
25	C₄×C₈×C₄₃	Q₈	1	2	yes	—
26	C₂²×C₄×C₄₃	—	4	2	no	—
27	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
28	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
29	C₂²×Dic₄₃	—	4	2	no	—
30	C₂×C₈×C₄₃	C₄⋊C₄	1	4	yes	—
31	C₂×C₈×C₄₃	SD₁₆	1	4	yes	—
32	C₂×C₈×C₄₃	SD₁₆	1	4	yes	—
33	C₄⋊C₄×C₄₃	—	4	4	no	—
34	C₄⋊C₄×C₄₃	—	4	8	no	—
35	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
36	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
37	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
38	C₄⋊Dic₄₃	—	4	4	no	—
39	C₄⋊Dic₄₃	—	4	8	no	—
40	C₂×C₄₃⋊C₈	—	2	8	no	—
41	C₂×C₄₃⋊C₈	C₄⋊C₄	1	8	yes	—
42	C₂³×C₄₃	#127	1	1	yes	characteristic
43	C₂×C₄×C₄₃	—	8	2	no	—
44	C₂×C₄×C₄₃	—	8	4	no	—
45	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
46	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
47	C₂×C₄×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
48	C₂×C₄×C₄₃	C₄⋊Q₈	1	2	yes	—
49	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
50	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
51	C₂×C₄×C₄₃	#135	1	8	yes	—
52	C₂×Dic₄₃	—	8	2	no	—
53	C₂×Dic₄₃	—	8	4	no	—
54	C₈×C₄₃	#106	1	8	yes	—
55	C₄₃⋊C₈	—	2	8	no	—
56	#8815	—	43	1	no	maximal, Sylow
57	C₂²×C₄₃	#384	1	1	yes	characteristic
58	C₂²×C₄₃	#492	1	1	yes	characteristic
59	C₂²×C₄₃	#492	1	1	yes	characteristic
60	C₂²×C₄₃	#495	1	4	yes	—
61	C₄×C₄₃	—	16	2	no	—
62	C₄×C₄₃	C₂×#106	1	2	yes	—
63	C₄×C₄₃	#427	1	4	yes	—
64	C₄×C₄₃	#498	1	2	yes	—
65	C₄×C₄₃	#499	1	4	yes	—
66	Dic₄₃	—	16	2	no	—
67	#1844	—	43	1	no	—
68	#1844	D₄₃	1	1	yes	characteristic
69	#1834	—	43	4	no	—
70	C₂×C₈²	—	43	1	no	—
71	C₂×C₄₃	#1708	1	2	yes	—
72	C₂×C₄₃	#1708	1	2	yes	—
73	C₂×C₄₃	#1844	1	1	yes	characteristic
74	C₂×C₄₃	#1846	1	2	yes	—
75	C₂×#106	—	2	2	no	—
76	C₂×#106	—	86	2	no	—
77	C₂×C₄×C₈	—	43	2	no	—
78	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
79	#384	—	43	2	no	—
80	#384	C₂×D₄₃	1	2	yes	—
81	#340	—	86	8	no	—
82	C₈²	—	43	4	no	—
83	C₄₃	#8815	1	1	yes	characteristic, complemented, Sylow
84	C₂²×C₈	—	43	4	no	—
85	C₂²×C₈	C₂²⋊D₄₃	1	2	yes	—
86	C₂×C₄⋊C₄	—	2	4	no	—
87	C₂×C₄⋊C₄	—	2	2	no	—
88	C₂×C₄⋊C₄	—	86	4	no	—
89	C₂×C₄⋊C₄	—	86	2	no	—
90	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
91	#106	—	4	4	no	—
92	#106	—	172	4	no	—
93	C₄×C₈	—	43	4	no	—
94	C₄×C₈	—	43	4	no	—
95	C₄×C₈	Dic₈₆	1	2	yes	—
96	C₄×C₈	C₄×D₄₃	1	2	yes	—
97	C₂²×C₄	—	4	2	no	—
98	C₂²×C₄	—	172	2	no	—
99	C₂²×C₄	D₄×D₄₃	1	2	yes	—
100	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
101	C₂×C₈	—	43	8	no	—
102	C₂×C₈	—	86	8	no	—
103	C₂×C₈	Dic₄₃⋊C₄	1	4	yes	—
104	C₂×C₈	#10621883	1	4	yes	—
105	C₂×C₈	#10621884	1	4	yes	—
106	C₄⋊C₄	—	4	4	no	—
107	C₄⋊C₄	—	4	8	no	—
108	C₄⋊C₄	—	172	4	no	—
109	C₄⋊C₄	—	172	8	no	—
110	C₄²	C₂×Dic₈₆	1	1	yes	characteristic
111	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
112	C₄²	Q₈×D₄₃	1	2	yes	—
113	C₂³	#13063321	1	1	yes	characteristic
114	C₂×C₄	—	8	2	no	—
115	C₂×C₄	—	8	4	no	—
116	C₂×C₄	—	344	2	no	—
117	C₂×C₄	—	344	4	no	—
118	C₂×C₄	C₄⋊C₄×D₄₃	1	2	yes	—
119	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
120	C₂×C₄	#13063323	1	1	yes	characteristic
121	C₂×C₄	#13063324	1	2	yes	—
122	C₂×C₄	C₂×#10621884	1	2	yes	—
123	C₂×C₄	C₂×#10621883	1	2	yes	—
124	C₂×C₄	#13063346	1	8	yes	—
125	C₈	—	86	8	no	—
126	C₈	#13063256	1	8	yes	—
127	C₂²	#14582768	1	1	yes	characteristic
128	C₂²	#14583271	1	1	yes	characteristic
129	C₂²	#14583273	1	1	yes	characteristic
130	C₂²	#14583280	1	4	yes	—
131	C₄	—	16	2	no	—
132	C₄	—	688	2	no	—
133	C₄	C₂×#13063256	1	2	yes	—
134	C₄	#14582934	1	4	yes	—
135	C₄	#14583295	1	2	yes	—
136	C₄	#14583299	1	4	yes	—
137	C₂	#19134194	1	2	yes	—
138	C₂	#19134197	1	2	yes	—
139	C₂	#19134751	1	1	yes	characteristic
140	C₂	#19134756	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19134752

C₂

yes

maximal, characteristic

#19134722

C₂

yes

maximal

C₂×C₈×C₄₃⋊C₈

C₂

yes

maximal, characteristic

C₄₃×#1844

C₂

yes

maximal, characteristic

C₂×#13063257

—

C₂×C₄×C₄₃⋊C₈

C₂²

yes

—

#14582769

C₂²

yes

—

#14582661

—

C₈×C₄₃⋊C₈

C₄

yes

complemented

C₂×#106×C₄₃

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄₃×#384

C₂²

yes

—

C₂²×C₄₃⋊C₈

D₄

yes

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

#13063257

—

C₄×C₄₃⋊C₈

C₂×C₄

yes

—

C₄×C₄₃⋊C₈

Q₈

yes

—

C₂²×C₈×C₄₃

D₄

yes

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

#106×C₄₃

—

C₄×C₈×C₄₃

C₂×C₄

yes

—

C₄×C₈×C₄₃

Q₈

yes

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂×C₈×C₄₃

C₄⋊C₄

yes

—

C₂×C₈×C₄₃

SD₁₆

yes

—

C₂×C₈×C₄₃

SD₁₆

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

C₂²×C₄

yes

characteristic

C₄²×C₄₃

C₂×Q₈

yes

characteristic

C₄²×C₄₃

C₂×Q₈

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₄⋊C₄

yes

—

C₂³×C₄₃

#127

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₄₃

C₄⋊Q₈

yes

—

C₂×C₄×C₄₃

C₂×SD₁₆

yes

—

C₂×C₄×C₄₃

C₂×SD₁₆

yes

—

C₂×C₄×C₄₃

#135

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

#106

yes

—

C₄₃⋊C₈

—

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

—

C₄×C₄₃

—

C₄×C₄₃

C₂×#106

yes

—

C₄×C₄₃

#427

yes

—

C₄×C₄₃

#498

yes

—

C₄×C₄₃

#499

yes

—

Dic₄₃

—

#1844

—

#1844

D₄₃

yes

characteristic

#1834

—

C₂×C₈²

—

C₂×C₄₃

#1708

yes

—

C₂×C₄₃

#1708

yes

—

C₂×C₄₃

#1844

yes

characteristic

C₂×C₄₃

#1846

yes

—

C₂×#106

—

C₂×#106

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

#384

—

#384

C₂×D₄₃

yes

—

#340

—

C₈²

—

C₄₃

#8815

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂²⋊D₄₃

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂²×D₄₃

yes

characteristic

#106

—

#106

—

172

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

Dic₈₆

yes

—

C₄×C₈

C₄×D₄₃

yes

—

C₂²×C₄

—

C₂²×C₄

—

172

—

C₂²×C₄

D₄×D₄₃

yes

—

100

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

Dic₄₃⋊C₄

yes

—

104

C₂×C₈

#10621883

yes

—

105

C₂×C₈

#10621884

yes

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

172

—

109

C₄⋊C₄

—

172

—

110

C₄²

C₂×Dic₈₆

yes

characteristic

111

C₄²

C₂×C₄×D₄₃

yes

characteristic

112

C₄²

Q₈×D₄₃

yes

—

113

C₂³

#13063321

yes

characteristic

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

344

—

117

C₂×C₄

—

344

—

118

C₂×C₄

C₄⋊C₄×D₄₃

yes

—

119

C₂×C₄

C₂×Dic₄₃⋊C₄

yes

characteristic

120

C₂×C₄

#13063323

yes

characteristic

121

C₂×C₄

#13063324

yes

—

122

C₂×C₄

C₂×#10621884

yes

—

123

C₂×C₄

C₂×#10621883

yes

—

124

C₂×C₄

#13063346

yes

—

125

C₈

—

126

C₈

#13063256

yes

—

127

C₂²

#14582768

yes

characteristic

128

C₂²

#14583271

yes

characteristic

129

C₂²

#14583273

yes

characteristic

130

C₂²

#14583280

yes

—

131

C₄

—

132

C₄

—

688

—

133

C₄

C₂×#13063256

yes

—

134

C₄

#14582934

yes

—

135

C₄

#14583295

yes

—

136

C₄

#14583299

yes

—

137

C₂

#19134194

yes

—

138

C₂

#19134197

yes

—

139

C₂

#19134751

yes

characteristic

140

C₂

#19134756

yes

—

	subgroup	G/H
center	C₂³	#13063321
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1844	C₂
socle, prime radical	C₂³×C₄₃	#127
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1844	D₄₃
hypocenter	C₄₃	#8815
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1844

subgroup

G/H

center

C₂³

#13063321

commutator

C₄²×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1844

C₂

socle, prime radical

C₂³×C₄₃

#127

cosocle

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1844

N	H ≅ G/N	type
9. C₈×C₄₃⋊C₈	C₄	semidirect
83. C₄₃	#8815	semidirect

H ≅ G/N

type

9. C₈×C₄₃⋊C₈

C₄

semidirect

83. C₄₃

#8815

semidirect

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

subgroup	index
#19134752	2
#19134722	2
C₂×C₈×C₄₃⋊C₈	2
C₄₃×#1844	2
#8815	43

subgroup

index

#19134752

#19134722

C₂×C₈×C₄₃⋊C₈

C₄₃×#1844

#8815

Subgroups — #24990369

Conjugacy classes of subgroups

Complements

Maximal subgroups