Group #24983696 — subgroups

Subgroups — #24983696

Order 11008.

206 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 103 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	#19133354	C₂	1	2	yes	maximal
2	C₂×C₄₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	#14582923	—	2	2	no	—
4	#14582652	—	2	2	no	—
5	#14582652	C₄	1	4	yes	—
6	C₂²×C₁₆×C₄₃	C₄	1	2	yes	—
7	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
8	C₄₃×C₄⋊C₁₆	—	2	2	no	—
9	C₂×#10621877	—	4	2	no	—
10	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
11	C₄⋊(C₄₃⋊C₈)	—	4	2	no	—
12	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₈×C₄₃	Q₈	1	1	yes	characteristic
14	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
15	C₂×C₁₆×C₄₃	—	2	2	no	—
16	C₂×C₁₆×C₄₃	—	4	2	no	—
17	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
18	C₄×C₈×C₄₃	D₄	1	2	yes	—
19	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
20	C₂²×C₄×C₄₃	D₈	1	1	yes	characteristic
21	C₂²×C₄×C₄₃	Q₁₆	1	1	yes	characteristic
22	C₂×C₈×C₄₃	—	2	1	no	—
23	C₂×C₈×C₄₃	—	2	1	no	—
24	C₂×C₈×C₄₃	—	4	1	no	—
25	C₂×C₈×C₄₃	C₄²	1	1	yes	characteristic
26	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₈×C₄₃	C₄⋊C₄	1	2	yes	—
28	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
29	C₄²×C₄₃	SD₁₆	1	2	yes	—
30	#10621877	—	8	2	no	—
31	#10621877	—	8	2	no	—
32	C₂×C₄₃⋊C₈	—	4	4	no	—
33	C₁₆×C₄₃	—	4	2	no	—
34	C₂³×C₄₃	#107	1	1	yes	characteristic
35	C₂×C₄×C₄₃	—	2	1	no	—
36	C₂×C₄×C₄₃	—	2	1	no	—
37	C₂×C₄×C₄₃	—	4	1	no	—
38	C₂×C₄×C₄₃	#95	1	1	yes	characteristic
39	C₂×C₄×C₄₃	#102	1	2	yes	—
40	C₂×C₄×C₄₃	#103	1	2	yes	—
41	C₂×C₄×C₄₃	#106	1	1	yes	characteristic
42	C₂×C₄×C₄₃	D₁₆	1	1	yes	characteristic
43	C₂×C₄×C₄₃	SD₃₂	1	2	yes	—
44	C₂×C₄×C₄₃	Q₃₂	1	1	yes	characteristic
45	C₈×C₄₃	—	2	2	no	—
46	C₈×C₄₃	—	2	1	no	—
47	C₈×C₄₃	#100	1	1	yes	characteristic
48	C₈×C₄₃	#101	1	1	yes	characteristic
49	C₄₃⋊C₈	—	8	4	no	—
50	#7241	—	43	1	no	maximal, Sylow
51	C₂²×C₄₃	—	2	1	no	—
52	C₂²×C₄₃	—	2	1	no	—
53	C₂²×C₄₃	#340	1	1	yes	characteristic
54	C₂²×C₄₃	#366	1	1	yes	characteristic
55	C₂²×C₄₃	#367	1	1	yes	characteristic
56	C₄×C₄₃	—	2	1	no	—
57	C₄×C₄₃	—	2	2	no	—
58	C₄×C₄₃	#338	1	1	yes	characteristic
59	C₄×C₄₃	#343	1	1	yes	characteristic
60	C₄×C₄₃	#357	1	2	yes	—
61	C₄×C₄₃	#358	1	2	yes	—
62	C₂×C₄⋊C₁₆	D₄₃	1	1	yes	characteristic
63	#1567	—	43	2	no	—
64	C₂×C₄₃	—	2	1	no	—
65	C₂×C₄₃	—	2	1	no	—
66	C₂×C₄₃	#1292	1	1	yes	characteristic
67	C₂×C₄₃	#1380	1	1	yes	characteristic
68	C₂×C₄₃	#1385	1	1	yes	characteristic
69	C₂²×C₁₆	Dic₄₃	1	2	yes	—
70	#423	—	86	2	no	—
71	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
72	C₄⋊C₁₆	—	2	2	no	—
73	#335	—	43	4	no	—
74	#335	—	86	2	no	—
75	C₄₃	#7241	1	1	yes	characteristic, complemented, Sylow
76	C₂×M₁₆	—	172	2	no	—
77	C₂²×C₈	Dic₈₆	1	1	yes	characteristic
78	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
79	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
80	C₂×C₁₆	—	2	2	no	—
81	C₂×C₁₆	—	4	2	no	—
82	C₄⋊C₈	—	86	4	no	—
83	C₄⋊C₈	—	172	2	no	—
84	C₄×C₈	C₄×D₄₃	1	2	yes	—
85	C₄×C₈	C₂²⋊D₄₃	1	2	yes	—
86	C₂²×C₄	D₃₄₄	1	1	yes	characteristic
87	C₂²×C₄	Dic₁₇₂	1	1	yes	characteristic
88	C₂²×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
89	M₁₆	—	344	2	no	—
90	M₁₆	—	344	2	no	—
91	C₂×C₈	—	2	1	no	—
92	C₂×C₈	—	2	1	no	—
93	C₂×C₈	—	4	1	no	—
94	C₂×C₈	—	172	4	no	—
95	C₂×C₈	C₄×Dic₄₃	1	1	yes	characteristic
96	C₂×C₈	Dic₄₃⋊C₄	1	2	yes	—
97	C₂×C₈	C₂²⋊Dic₄₃	1	1	yes	characteristic
98	C₄²	#10621873	1	2	yes	—
99	C₄²	(C₂×D₄₃)⋊C₄	1	2	yes	—
100	C₁₆	—	4	2	no	—
101	C₂³	#13063259	1	1	yes	characteristic
102	C₂×C₄	—	2	1	no	—
103	C₂×C₄	—	2	1	no	—
104	C₂×C₄	—	4	1	no	—
105	C₂×C₄	C₄₃⋊#95	1	1	yes	characteristic
106	C₂×C₄	#13063247	1	2	yes	—
107	C₂×C₄	#13063250	1	2	yes	—
108	C₂×C₄	#13063257	1	1	yes	characteristic
109	C₂×C₄	D₆₈₈	1	1	yes	characteristic
110	C₂×C₄	#13063270	1	2	yes	—
111	C₂×C₄	Dic₃₄₄	1	1	yes	characteristic
112	C₈	—	2	2	no	—
113	C₈	—	2	1	no	—
114	C₈	—	344	4	no	—
115	C₈	#13063242	1	1	yes	characteristic
116	C₈	#13063244	1	1	yes	characteristic
117	C₂²	—	2	1	no	—
118	C₂²	—	2	1	no	—
119	C₂²	#14582662	1	1	yes	characteristic
120	C₂²	#14582725	1	1	yes	characteristic
121	C₂²	#14582727	1	1	yes	characteristic
122	C₄	—	2	2	no	—
123	C₄	—	2	1	no	—
124	C₄	C₄₃⋊#338	1	1	yes	characteristic
125	C₄	#14582668	1	1	yes	characteristic
126	C₄	#14582701	1	2	yes	—
127	C₄	#14582704	1	2	yes	—
128	C₂	—	2	1	no	—
129	C₂	—	2	1	no	—
130	C₂	#19132470	1	1	yes	characteristic
131	C₂	#19132687	1	1	yes	characteristic
132	C₂	#19132699	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19133354

C₂

yes

maximal

C₂×C₄₃×C₄⋊C₁₆

C₂

yes

maximal, characteristic

#14582923

—

#14582652

—

#14582652

C₄

yes

—

C₂²×C₁₆×C₄₃

C₄

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄₃×C₄⋊C₁₆

—

C₂×#10621877

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

C₂²×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₄₃

Q₈

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

characteristic

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

—

C₄×C₈×C₄₃

C₂×C₄

yes

—

C₄×C₈×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₄₃

D₈

yes

characteristic

C₂²×C₄×C₄₃

Q₁₆

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₄²

yes

characteristic

C₂×C₈×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₃

C₄⋊C₄

yes

—

C₄²×C₄₃

C₂²⋊C₄

yes

—

C₄²×C₄₃

SD₁₆

yes

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₁₆×C₄₃

—

C₂³×C₄₃

#107

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#95

yes

characteristic

C₂×C₄×C₄₃

#102

yes

—

C₂×C₄×C₄₃

#103

yes

—

C₂×C₄×C₄₃

#106

yes

characteristic

C₂×C₄×C₄₃

D₁₆

yes

characteristic

C₂×C₄×C₄₃

SD₃₂

yes

—

C₂×C₄×C₄₃

Q₃₂

yes

characteristic

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

yes

C₈×C₄₃

yes

C₄₃⋊C₈

—

#7241

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

—

C₄×C₄₃

#358

yes

—

C₂×C₄⋊C₁₆

D₄₃

yes

characteristic

#1567

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂²×C₁₆

Dic₄₃

yes

—

#423

—

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

C₄⋊C₁₆

—

#335

—

#335

—

C₄₃

#7241

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

172

—

C₂²×C₈

Dic₈₆

yes

characteristic

C₂²×C₈

C₂×Dic₄₃

yes

characteristic

C₂×C₄²

D₁₇₂

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₄⋊C₈

—

C₄⋊C₈

—

172

—

C₄×C₈

C₄×D₄₃

yes

—

C₄×C₈

C₂²⋊D₄₃

yes

—

C₂²×C₄

D₃₄₄

yes

characteristic

C₂²×C₄

Dic₁₇₂

yes

characteristic

C₂²×C₄

C₄⋊Dic₄₃

yes

characteristic

M₁₆

—

344

—

M₁₆

—

344

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

172

—

C₂×C₈

C₄×Dic₄₃

yes

characteristic

C₂×C₈

Dic₄₃⋊C₄

yes

—

C₂×C₈

C₂²⋊Dic₄₃

yes

characteristic

C₄²

#10621873

yes

—

C₄²

(C₂×D₄₃)⋊C₄

yes

—

100

C₁₆

—

101

C₂³

#13063259

yes

characteristic

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

C₄₃⋊#95

yes

characteristic

106

C₂×C₄

#13063247

yes

—

107

C₂×C₄

#13063250

yes

—

108

C₂×C₄

#13063257

yes

characteristic

109

C₂×C₄

D₆₈₈

yes

characteristic

110

C₂×C₄

#13063270

yes

—

111

C₂×C₄

Dic₃₄₄

yes

characteristic

112

C₈

—

113

C₈

—

114

C₈

—

344

—

115

C₈

#13063242

yes

characteristic

116

C₈

#13063244

yes

characteristic

117

C₂²

—

118

C₂²

—

119

C₂²

#14582662

yes

characteristic

120

C₂²

#14582725

yes

characteristic

121

C₂²

#14582727

yes

characteristic

122

C₄

—

123

C₄

—

124

C₄

C₄₃⋊#338

yes

characteristic

125

C₄

#14582668

yes

characteristic

126

C₄

#14582701

yes

—

127

C₄

#14582704

yes

—

128

C₂

—

129

C₂

—

130

C₂

#19132470

yes

characteristic

131

C₂

#19132687

yes

characteristic

132

C₂

#19132699

yes

characteristic

	subgroup	G/H
center	C₂²	#14582662
commutator	C₂×C₈×C₄₃	C₄²
Frattini	C₂×C₄×C₈	C₂×D₄₃
Fitting	C₂×C₄₃×C₄⋊C₁₆	C₂
socle	C₂²×C₄₃	#340
prime radical	C₂³×C₄₃	#107
cosocle	C₂×C₄×C₈×C₄₃	C₂²
hypercenter	C₂×C₄⋊C₁₆	D₄₃
hypocenter	C₄₃	#7241
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄⋊C₁₆

subgroup

G/H

center

C₂²

#14582662

commutator

C₂×C₈×C₄₃

C₄²

Frattini

C₂×C₄×C₈

C₂×D₄₃

Fitting

C₂×C₄₃×C₄⋊C₁₆

C₂

C₂²×C₄₃

C₂³×C₄₃

C₂×C₄×C₈×C₄₃

C₂²

hypercenter

C₂×C₄⋊C₁₆

D₄₃

hypocenter

C₄₃

#7241

LCS

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄⋊C₁₆

N	H ≅ G/N	type
75. C₄₃	#7241	semidirect

H ≅ G/N

type

75. C₄₃

#7241

semidirect

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

subgroup	index
#19133354	2
C₂×C₄₃×C₄⋊C₁₆	2
#7241	43

subgroup

index

#19133354

C₂×C₄₃×C₄⋊C₁₆

#7241

Subgroups — #24983696

Conjugacy classes of subgroups

Complements

Maximal subgroups