Group #24983262 — subgroups

Subgroups — #24983262

Order 11008.

132 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 55 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	#19133493	C₂	1	1	yes	maximal, characteristic
2	#19132665	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1312	C₂	1	1	yes	maximal, characteristic
4	#14583029	—	2	1	no	—
5	C₄×Dic₁₇₂	C₄	1	1	yes	characteristic
6	C₄⋊(C₄₃⋊C₁₆)	—	2	1	no	—
7	#14582652	C₄	1	1	yes	characteristic
8	#14582631	—	2	1	no	—
9	C₄×C₁₆×C₄₃	—	2	1	no	—
10	C₈²×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₇₂	C₈	1	1	yes	characteristic
12	C₄×Dic₈₆	—	2	1	no	—
13	C₂×C₄₃⋊C₁₆	—	4	1	no	—
14	#13063259	C₈	1	1	yes	characteristic
15	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
16	Dic₄₃⋊C₈	—	4	1	no	—
17	#13063250	—	2	1	no	—
18	#13063235	—	4	1	no	—
19	C₂×C₁₆×C₄₃	—	2	2	no	—
20	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
21	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
22	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
23	C₂×Dic₈₆	—	2	1	no	—
24	C₂×C₈×C₄₃	—	2	1	no	—
25	C₂×C₈×C₄₃	C₂×C₈	1	1	yes	characteristic
26	C₂×C₈×C₄₃	M₁₆	1	1	yes	characteristic
27	C₂×C₈×C₄₃	D₈	1	1	yes	characteristic
28	C₂×C₈×C₄₃	SD₁₆	1	1	yes	characteristic
29	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₄⋊Dic₄₃	—	2	1	no	—
31	Dic₄₃⋊C₄	—	4	1	no	—
32	C₄×Dic₄₃	—	4	1	no	—
33	C₂×C₄₃⋊C₈	—	4	1	no	—
34	Dic₁₇₂	—	4	1	no	—
35	C₁₆×C₄₃	—	4	2	no	—
36	C₄₃⋊C₁₆	—	8	1	no	—
37	C₂×C₄×C₄₃	C₂²⋊C₈	1	1	yes	characteristic
38	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
39	C₂×C₄×C₄₃	#104	1	1	yes	characteristic
40	C₂×Dic₄₃	—	4	1	no	—
41	C₂×Dic₄₃	—	4	1	no	—
42	Dic₈₆	—	4	1	no	—
43	Dic₈₆	—	4	1	no	—
44	C₈×C₄₃	—	2	2	no	—
45	C₈×C₄₃	—	2	1	no	—
46	C₈×C₄₃	—	2	1	no	—
47	C₈×C₄₃	—	2	1	no	—
48	C₈×C₄₃	SD₃₂	1	1	yes	characteristic
49	C₈×C₄₃	Q₃₂	1	1	yes	characteristic
50	C₄₃⋊C₈	—	8	1	no	—
51	#7073	—	43	1	no	maximal, Sylow
52	C₂²×C₄₃	D₄⋊C₈	1	1	yes	characteristic
53	C₄×C₄₃	—	2	1	no	—
54	C₄×C₄₃	#349	1	1	yes	characteristic
55	C₄×C₄₃	#350	1	1	yes	characteristic
56	C₄×C₄₃	#358	1	1	yes	characteristic
57	C₄×C₄₃	#359	1	1	yes	characteristic
58	Dic₄₃	—	8	1	no	—
59	Dic₄₃	—	8	1	no	—
60	#1591	—	43	1	no	—
61	#1370	—	43	1	no	—
62	#1312	D₄₃	1	1	yes	characteristic
63	C₂×C₄₃	#1330	1	1	yes	characteristic
64	C₂×C₄₃	#1332	1	1	yes	characteristic
65	C₂×C₄₃	#1336	1	1	yes	characteristic
66	#446	—	86	1	no	—
67	C₄×Q₁₆	—	43	1	no	—
68	C₄⋊C₁₆	—	86	1	no	—
69	C₄×C₁₆	—	2	1	no	—
70	#335	—	43	1	no	—
71	Q₈⋊C₈	—	86	1	no	—
72	C₈²	C₂×D₄₃	1	1	yes	characteristic
73	C₄₃	#7073	1	1	yes	characteristic, complemented, Sylow
74	C₂×Q₁₆	—	43	1	no	—
75	C₄×Q₈	—	86	1	no	—
76	C₂×C₁₆	—	2	2	no	—
77	C₂×C₁₆	—	172	1	no	—
78	#107	—	43	1	no	—
79	C₄⋊C₈	—	86	1	no	—
80	C₄⋊C₈	—	172	1	no	—
81	#103	—	86	1	no	—
82	#97	—	172	1	no	—
83	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
84	C₄×C₈	D₁₇₂	1	1	yes	characteristic
85	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
86	C₂×Q₈	—	86	1	no	—
87	Q₁₆	—	172	1	no	—
88	C₂×C₈	—	2	1	no	—
89	C₂×C₈	—	172	1	no	—
90	C₂×C₈	C₈×D₄₃	1	1	yes	characteristic
91	C₂×C₈	#10621872	1	1	yes	characteristic
92	C₂×C₈	#10621873	1	1	yes	characteristic
93	C₂×C₈	D₃₄₄	1	1	yes	characteristic
94	C₄⋊C₄	—	86	1	no	—
95	C₄⋊C₄	—	172	1	no	—
96	C₄²	—	172	1	no	—
97	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
98	C₁₆	—	4	2	no	—
99	C₁₆	—	344	1	no	—
100	Q₈	—	172	1	no	—
101	Q₈	—	172	1	no	—
102	C₂×C₄	—	172	1	no	—
103	C₂×C₄	—	172	1	no	—
104	C₂×C₄	(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
105	C₂×C₄	#13063247	1	1	yes	characteristic
106	C₂×C₄	#13063253	1	1	yes	characteristic
107	C₈	—	2	2	no	—
108	C₈	—	2	1	no	—
109	C₈	—	2	1	no	—
110	C₈	—	2	1	no	—
111	C₈	—	344	1	no	—
112	C₈	#13063270	1	1	yes	characteristic
113	C₈	Dic₃₄₄	1	1	yes	characteristic
114	C₂²	#14582628	1	1	yes	characteristic
115	C₄	—	2	1	no	—
116	C₄	—	344	1	no	—
117	C₄	—	344	1	no	—
118	C₄	#14582680	1	1	yes	characteristic
119	C₄	#14582684	1	1	yes	characteristic
120	C₄	#14582704	1	1	yes	characteristic
121	C₄	#14582707	1	1	yes	characteristic
122	C₂	#19132554	1	1	yes	characteristic
123	C₂	#19132560	1	1	yes	characteristic
124	C₂	#19132572	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19133493

C₂

yes

maximal, characteristic

#19132665

C₂

yes

maximal, characteristic

C₄₃×#1312

C₂

yes

maximal, characteristic

#14583029

—

C₄×Dic₁₇₂

C₄

yes

characteristic

C₄⋊(C₄₃⋊C₁₆)

—

#14582652

C₄

yes

characteristic

#14582631

—

C₄×C₁₆×C₄₃

—

C₈²×C₄₃

C₂²

yes

characteristic

C₂×Dic₁₇₂

C₈

yes

characteristic

C₄×Dic₈₆

—

C₂×C₄₃⋊C₁₆

—

#13063259

C₈

yes

characteristic

C₄⋊(C₄₃⋊C₈)

—

Dic₄₃⋊C₈

—

#13063250

—

#13063235

—

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×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂×C₈

yes

characteristic

C₂×C₈×C₄₃

M₁₆

yes

characteristic

C₂×C₈×C₄₃

D₈

yes

characteristic

C₂×C₈×C₄₃

SD₁₆

yes

characteristic

C₄²×C₄₃

C₂²⋊C₄

yes

characteristic

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

Dic₁₇₂

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂×C₄×C₄₃

C₂²⋊C₈

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

SD₃₂

yes

characteristic

C₈×C₄₃

Q₃₂

yes

characteristic

C₄₃⋊C₈

—

#7073

—

maximal, Sylow

C₂²×C₄₃

D₄⋊C₈

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

#1591

—

#1370

—

#1312

D₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₄×Q₁₆

—

C₄⋊C₁₆

—

C₄×C₁₆

—

#335

—

Q₈⋊C₈

—

C₈²

C₂×D₄₃

yes

characteristic

C₄₃

#7073

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₄×Q₈

—

C₂×C₁₆

—

C₂×C₁₆

—

172

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

172

—

#103

—

#97

—

172

—

C₄×C₈

C₄×D₄₃

yes

characteristic

C₄×C₈

D₁₇₂

yes

characteristic

C₄×C₈

C₂²⋊D₄₃

yes

characteristic

C₂×Q₈

—

Q₁₆

—

172

—

C₂×C₈

—

C₂×C₈

—

172

—

C₂×C₈

C₈×D₄₃

yes

C₂×C₈

yes

C₂×C₈

yes

C₂×C₈

D₃₄₄

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₄²

—

172

—

C₄²

(C₂×D₄₃)⋊C₄

yes

characteristic

C₁₆

—

C₁₆

—

344

—

100

Q₈

—

172

—

101

Q₈

—

172

—

102

C₂×C₄

—

172

—

103

C₂×C₄

—

172

—

104

C₂×C₄

(C₂×D₄₃)⋊C₈

yes

characteristic

105

C₂×C₄

#13063247

yes

characteristic

106

C₂×C₄

#13063253

yes

characteristic

107

C₈

—

108

C₈

—

109

C₈

—

110

C₈

—

111

C₈

—

344

—

112

C₈

#13063270

yes

characteristic

113

C₈

Dic₃₄₄

yes

characteristic

114

C₂²

#14582628

yes

characteristic

115

C₄

—

116

C₄

—

344

—

117

C₄

—

344

—

118

C₄

#14582680

yes

characteristic

119

C₄

#14582684

yes

characteristic

120

C₄

#14582704

yes

characteristic

121

C₄

#14582707

yes

characteristic

122

C₂

#19132554

yes

characteristic

123

C₂

#19132560

yes

characteristic

124

C₂

#19132572

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#13063247
commutator	C₂×C₈×C₄₃	C₂×C₈
Frattini	C₈²	C₂×D₄₃
Fitting	C₄₃×#1312	C₂
socle, prime radical	C₂²×C₄₃	D₄⋊C₈
cosocle	C₈²×C₄₃	C₂²
hypercenter	#1312	D₄₃
hypocenter	C₄₃	#7073
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈² ◁ #1312

subgroup

G/H

center

C₂×C₄

#13063247

commutator

C₂×C₈×C₄₃

C₂×C₈

Frattini

C₈²

C₂×D₄₃

Fitting

C₄₃×#1312

C₂

socle, prime radical

C₂²×C₄₃

D₄⋊C₈

cosocle

C₈²×C₄₃

C₂²

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈² ◁ #1312

N	H ≅ G/N	type
73. C₄₃	#7073	semidirect

H ≅ G/N

type

73. C₄₃

#7073

semidirect

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

subgroup	index
#19133493	2
#19132665	2
C₄₃×#1312	2
#7073	43

subgroup

index

#19133493

#19132665

C₄₃×#1312

#7073

Subgroups — #24983262

Conjugacy classes of subgroups

Complements

Maximal subgroups