Group #24983326 — subgroups

Subgroups — #24983326

Order 11008.

136 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 53 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	#19134192	C₂	1	1	yes	maximal, characteristic
2	#19132665	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1367	C₂	1	1	yes	maximal, characteristic
4	#14583304	C₄	1	1	yes	characteristic
5	#14583297	—	2	1	no	—
6	#14583279	C₄	1	1	yes	characteristic
7	#14583250	—	2	1	no	—
8	C₄⋊(C₄₃⋊C₁₆)	—	2	1	no	—
9	C₄₃×C₄⋊C₁₆	—	2	1	no	—
10	C₈²×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₇₂	—	4	1	no	—
12	#13063325	—	2	1	no	—
13	#13063325	—	2	1	no	—
14	C₂×C₄₃⋊C₁₆	—	4	1	no	—
15	#13063259	—	4	1	no	—
16	#13063257	—	4	1	no	—
17	#13063257	—	4	1	no	—
18	#13063250	—	4	1	no	—
19	#13063250	—	4	1	no	—
20	C₂×C₁₆×C₄₃	—	4	1	no	—
21	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
22	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
23	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
24	C₂×Dic₈₆	—	4	1	no	—
25	C₂×Dic₈₆	—	4	1	no	—
26	C₂×C₈×C₄₃	—	2	1	no	—
27	C₂×C₈×C₄₃	D₈	1	1	yes	characteristic
28	C₂×C₈×C₄₃	D₈	1	1	yes	characteristic
29	C₂×C₈×C₄₃	SD₁₆	1	1	yes	characteristic
30	C₂×C₈×C₄₃	SD₁₆	1	1	yes	characteristic
31	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
32	C₄⋊Dic₄₃	—	4	1	no	—
33	C₄⋊Dic₄₃	—	4	1	no	—
34	C₄⋊Dic₄₃	—	4	1	no	—
35	C₄⋊Dic₄₃	—	4	1	no	—
36	Dic₁₇₂	—	8	2	no	—
37	C₁₆×C₄₃	—	8	1	no	—
38	C₄₃⋊C₁₆	—	8	1	no	—
39	C₂×C₄×C₄₃	#100	1	1	yes	characteristic
40	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
41	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
42	C₂×Dic₄₃	—	8	1	no	—
43	C₂×Dic₄₃	—	8	1	no	—
44	Dic₈₆	—	8	2	no	—
45	Dic₈₆	—	8	1	no	—
46	Dic₈₆	—	8	1	no	—
47	C₈×C₄₃	—	2	2	no	—
48	C₈×C₄₃	—	2	1	no	—
49	C₈×C₄₃	—	2	1	no	—
50	C₈×C₄₃	—	2	1	no	—
51	C₈×C₄₃	SD₃₂	1	1	yes	characteristic
52	C₈×C₄₃	Q₃₂	1	1	yes	characteristic
53	#7095	—	43	1	no	maximal, Sylow
54	C₂²×C₄₃	#331	1	1	yes	characteristic
55	C₄×C₄₃	—	2	1	no	—
56	C₄×C₄₃	#358	1	1	yes	characteristic
57	C₄×C₄₃	#359	1	1	yes	characteristic
58	C₄×C₄₃	#360	1	1	yes	characteristic
59	C₄×C₄₃	#362	1	1	yes	characteristic
60	Dic₄₃	—	16	1	no	—
61	Dic₄₃	—	16	1	no	—
62	#1707	—	43	1	no	—
63	#1370	—	43	1	no	—
64	#1367	D₄₃	1	1	yes	characteristic
65	C₂×C₄₃	#1359	1	1	yes	characteristic
66	C₂×C₄₃	#1360	1	1	yes	characteristic
67	C₂×C₄₃	#1362	1	1	yes	characteristic
68	#500	—	43	1	no	—
69	#498	—	86	1	no	—
70	#494	—	43	1	no	—
71	#487	—	86	1	no	—
72	C₄⋊C₁₆	—	2	1	no	—
73	C₄⋊C₁₆	—	86	1	no	—
74	C₈²	C₂×D₄₃	1	1	yes	characteristic
75	C₄₃	#7095	1	1	yes	characteristic, complemented, Sylow
76	C₂×Q₁₆	—	172	1	no	—
77	C₄⋊Q₈	—	86	1	no	—
78	C₄⋊Q₈	—	86	1	no	—
79	C₂×C₁₆	—	4	1	no	—
80	C₂×C₁₆	—	172	1	no	—
81	#107	—	172	1	no	—
82	#106	—	172	1	no	—
83	#106	—	172	1	no	—
84	#103	—	172	1	no	—
85	#103	—	172	1	no	—
86	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
87	C₄×C₈	D₁₇₂	1	1	yes	characteristic
88	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
89	C₂×Q₈	—	172	1	no	—
90	C₂×Q₈	—	172	1	no	—
91	Q₁₆	—	344	2	no	—
92	C₂×C₈	—	2	1	no	—
93	C₂×C₈	#10621873	1	1	yes	characteristic
94	C₂×C₈	D₃₄₄	1	1	yes	characteristic
95	C₂×C₈	#10621882	1	1	yes	characteristic
96	C₂×C₈	#10621884	1	1	yes	characteristic
97	C₄⋊C₄	—	172	1	no	—
98	C₄⋊C₄	—	172	1	no	—
99	C₄⋊C₄	—	172	1	no	—
100	C₄⋊C₄	—	172	1	no	—
101	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
102	C₁₆	—	8	1	no	—
103	C₁₆	—	344	1	no	—
104	Q₈	—	344	2	no	—
105	Q₈	—	344	1	no	—
106	Q₈	—	344	1	no	—
107	C₂×C₄	—	344	1	no	—
108	C₂×C₄	—	344	1	no	—
109	C₂×C₄	#13063241	1	1	yes	characteristic
110	C₂×C₄	#13063245	1	1	yes	characteristic
111	C₂×C₄	#13063247	1	1	yes	characteristic
112	C₈	—	2	2	no	—
113	C₈	—	2	1	no	—
114	C₈	—	2	1	no	—
115	C₈	—	2	1	no	—
116	C₈	#13063270	1	1	yes	characteristic
117	C₈	Dic₃₄₄	1	1	yes	characteristic
118	C₂²	#14582642	1	1	yes	characteristic
119	C₄	—	2	1	no	—
120	C₄	—	688	1	no	—
121	C₄	—	688	1	no	—
122	C₄	#14582704	1	1	yes	characteristic
123	C₄	#14582705	1	1	yes	characteristic
124	C₄	#14582708	1	1	yes	characteristic
125	C₄	#14582716	1	1	yes	characteristic
126	C₂	#19132635	1	1	yes	characteristic
127	C₂	#19132637	1	1	yes	characteristic
128	C₂	#19132645	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19134192

C₂

yes

maximal, characteristic

#19132665

C₂

yes

maximal, characteristic

C₄₃×#1367

C₂

yes

maximal, characteristic

#14583304

C₄

yes

characteristic

#14583297

—

#14583279

C₄

yes

characteristic

#14583250

—

C₄⋊(C₄₃⋊C₁₆)

—

C₄₃×C₄⋊C₁₆

—

C₈²×C₄₃

C₂²

yes

characteristic

C₂×Dic₁₇₂

—

#13063325

—

#13063325

—

C₂×C₄₃⋊C₁₆

—

—

—

—

—

—

C₂×C₁₆×C₄₃

—

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

D₄

yes

characteristic

C₄×C₈×C₄₃

D₄

yes

characteristic

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₈

yes

characteristic

C₂×C₈×C₄₃

D₈

yes

characteristic

C₂×C₈×C₄₃

SD₁₆

yes

characteristic

C₂×C₈×C₄₃

SD₁₆

yes

characteristic

C₄²×C₄₃

C₂²⋊C₄

yes

characteristic

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₁₇₂

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

SD₃₂

yes

characteristic

C₈×C₄₃

Q₃₂

yes

—

C₂²×C₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

#1707

—

#1370

—

#1367

D₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

—

—

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₈²

C₂×D₄₃

yes

characteristic

C₄₃

#7095

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

172

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₂×C₁₆

—

C₂×C₁₆

—

172

—

#107

—

172

—

#106

—

172

—

#106

—

172

—

#103

—

172

—

#103

—

172

—

C₄×C₈

C₄×D₄₃

yes

characteristic

C₄×C₈

D₁₇₂

yes

characteristic

C₄×C₈

C₂²⋊D₄₃

yes

characteristic

C₂×Q₈

—

172

—

C₂×Q₈

—

172

—

Q₁₆

—

344

—

C₂×C₈

—

C₂×C₈

#10621873

yes

characteristic

C₂×C₈

D₃₄₄

yes

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

172

—

C₄⋊C₄

—

172

—

C₄⋊C₄

—

172

—

100

C₄⋊C₄

—

172

—

101

C₄²

(C₂×D₄₃)⋊C₄

yes

characteristic

102

C₁₆

—

103

C₁₆

—

344

—

104

Q₈

—

344

—

105

Q₈

—

344

—

106

Q₈

—

344

—

107

C₂×C₄

—

344

—

108

C₂×C₄

—

344

—

109

C₂×C₄

#13063241

yes

characteristic

110

C₂×C₄

#13063245

yes

characteristic

111

C₂×C₄

#13063247

yes

characteristic

112

C₈

—

113

C₈

—

114

C₈

—

115

C₈

—

116

C₈

#13063270

yes

characteristic

117

C₈

Dic₃₄₄

yes

characteristic

118

C₂²

#14582642

yes

characteristic

119

C₄

—

120

C₄

—

688

—

121

C₄

—

688

—

122

C₄

#14582704

yes

characteristic

123

C₄

#14582705

yes

characteristic

124

C₄

#14582708

yes

characteristic

125

C₄

#14582716

yes

characteristic

126

C₂

#19132635

yes

characteristic

127

C₂

#19132637

yes

characteristic

128

C₂

#19132645

yes

characteristic

	subgroup	G/H
center	C₂²	#14582642
commutator	C₄×C₈×C₄₃	C₂×C₄
Frattini	C₈²	C₂×D₄₃
Fitting	C₄₃×#1367	C₂
socle, prime radical	C₂²×C₄₃	#331
cosocle	C₈²×C₄₃	C₂²
hypercenter	#1367	D₄₃
hypocenter	C₄₃	#7095
LCS	G ▷ C₄×C₈×C₄₃ ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1367

subgroup

G/H

center

C₂²

#14582642

commutator

C₄×C₈×C₄₃

C₂×C₄

Frattini

C₈²

C₂×D₄₃

Fitting

C₄₃×#1367

C₂

socle, prime radical

C₂²×C₄₃

#331

cosocle

C₈²×C₄₃

C₂²

D₄₃

C₄₃

G ▷ C₄×C₈×C₄₃ ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1367

N	H ≅ G/N	type
75. C₄₃	#7095	semidirect

H ≅ G/N

type

75. C₄₃

#7095

semidirect

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

subgroup	index
#19134192	2
#19132665	2
C₄₃×#1367	2
#7095	43

subgroup

index

#19134192

#19132665

C₄₃×#1367

#7095

Subgroups — #24983326

Conjugacy classes of subgroups

Complements

Maximal subgroups