Group #24983997 — subgroups

Subgroups — #24983997

Order 11008.

124 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 49 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	#19136353	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊(C₄₃⋊C₃₂)	C₂	1	1	yes	maximal, characteristic
3	C₄₃×C₂²⋊C₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂×#13063265	C₄	1	1	yes	characteristic
5	#14582854	C₄	1	1	yes	characteristic
6	C₂×C₄₃⋊C₃₂	—	2	1	no	—
7	Dic₄₃⋊C₁₆	—	2	1	no	—
8	Dic₄₃⋊C₁₆	—	2	1	no	—
9	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×C₃₂×C₄₃	—	2	1	no	—
11	C₂×#10621877	C₈	1	1	yes	characteristic
12	#13063284	C₈	1	1	yes	characteristic
13	#13063265	—	4	1	no	—
14	C₂×C₄₃⋊C₁₆	—	2	1	no	—
15	#13063235	—	2	1	no	—
16	C₈×Dic₄₃	—	2	1	no	—
17	C₄₃⋊C₃₂	—	4	1	no	—
18	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₁₆×C₄₃	—	4	1	no	—
20	C₂×C₁₆×C₄₃	D₄	1	1	yes	characteristic
21	C₂×C₁₆×C₄₃	D₄	1	1	yes	characteristic
22	C₃₂×C₄₃	—	4	1	no	—
23	C₂²×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
24	C₂×C₈×C₄₃	—	2	1	no	—
25	C₂×C₈×C₄₃	—	2	1	no	—
26	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₈×C₄₃	M₁₆	1	1	yes	characteristic
28	C₂²⋊Dic₄₃	—	2	1	no	—
29	C₄⋊Dic₄₃	C₁₆	1	1	yes	characteristic
30	C₄⋊Dic₄₃	C₁₆	1	1	yes	characteristic
31	C₄×Dic₄₃	—	2	1	no	—
32	#10621877	—	4	1	no	—
33	C₂×C₄₃⋊C₈	—	2	1	no	—
34	C₁₆×C₄₃	—	2	1	no	—
35	C₁₆×C₄₃	—	2	1	no	—
36	C₄₃⋊C₁₆	—	4	1	no	—
37	C₂³×C₄₃	M₃₂	1	1	yes	characteristic
38	C₂×C₄×C₄₃	—	2	1	no	—
39	C₂×C₄×C₄₃	—	2	1	no	—
40	C₂×C₄×C₄₃	C₂²⋊C₈	1	1	yes	characteristic
41	C₂×C₄×C₄₃	C₂×C₁₆	1	1	yes	characteristic
42	C₂×Dic₄₃	—	2	1	no	—
43	C₂×Dic₄₃	—	2	1	no	—
44	C₈×C₄₃	—	2	1	no	—
45	C₈×C₄₃	#99	1	1	yes	characteristic
46	C₈×C₄₃	#101	1	1	yes	characteristic
47	C₄₃⋊C₈	—	4	1	no	—
48	#7363	—	43	1	no	maximal, Sylow
49	C₂²×C₄₃	—	2	1	no	—
50	C₂²×C₄₃	—	2	1	no	—
51	C₂²×C₄₃	—	2	1	no	—
52	C₂²×C₄₃	C₂²⋊C₁₆	1	1	yes	characteristic
53	C₄×C₄₃	—	2	1	no	—
54	C₄×C₄₃	#324	1	1	yes	characteristic
55	C₄×C₄₃	#349	1	1	yes	characteristic
56	Dic₄₃	—	4	1	no	—
57	Dic₄₃	—	4	1	no	—
58	#2151	—	43	1	no	—
59	C₂²⋊C₃₂	—	43	1	no	—
60	C₂²⋊C₃₂	D₄₃	1	1	yes	characteristic
61	C₂×C₄₃	—	4	1	no	—
62	C₂×C₄₃	#1322	1	1	yes	characteristic
63	C₂×C₄₃	#1401	1	1	yes	characteristic
64	C₂×C₄₃	#1401	1	1	yes	characteristic
65	C₂×M₃₂	—	43	1	no	—
66	C₂²×C₁₆	C₂×D₄₃	1	1	yes	characteristic
67	#405	—	43	1	no	—
68	C₂×C₃₂	—	2	1	no	—
69	C₂×C₃₂	—	86	1	no	—
70	C₄⋊C₁₆	—	86	1	no	—
71	C₄⋊C₁₆	—	86	1	no	—
72	C₄₃	#7363	1	1	yes	characteristic, complemented, Sylow
73	C₂×M₁₆	—	43	1	no	—
74	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
75	#117	—	43	1	no	—
76	M₃₂	—	172	1	no	—
77	C₂×C₁₆	—	4	1	no	—
78	C₂×C₁₆	—	86	1	no	—
79	C₂×C₁₆	D₁₇₂	1	1	yes	characteristic
80	C₂×C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
81	#97	—	86	1	no	—
82	C₄×C₈	—	86	1	no	—
83	C₃₂	—	4	1	no	—
84	C₃₂	—	172	1	no	—
85	C₂²×C₄	C₈×D₄₃	1	1	yes	characteristic
86	M₁₆	—	172	1	no	—
87	C₂×C₈	—	2	1	no	—
88	C₂×C₈	—	2	1	no	—
89	C₂×C₈	—	86	1	no	—
90	C₂×C₈	#10621872	1	1	yes	characteristic
91	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
92	C₄⋊C₄	—	43	1	no	—
93	C₄⋊C₄	—	43	1	no	—
94	C₂²⋊C₄	—	86	1	no	—
95	C₄²	—	86	1	no	—
96	C₁₆	—	2	1	no	—
97	C₁₆	—	2	1	no	—
98	C₁₆	—	172	1	no	—
99	C₂³	#13063264	1	1	yes	characteristic
100	C₂×C₄	—	2	1	no	—
101	C₂×C₄	—	2	1	no	—
102	C₂×C₄	—	86	1	no	—
103	C₂×C₄	—	86	1	no	—
104	C₂×C₄	(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
105	C₂×C₄	C₁₆×D₄₃	1	1	yes	characteristic
106	C₈	—	2	1	no	—
107	C₈	—	172	1	no	—
108	C₈	#13063239	1	1	yes	characteristic
109	C₈	#13063243	1	1	yes	characteristic
110	C₂²	—	2	1	no	—
111	C₂²	—	2	1	no	—
112	C₂²	—	2	1	no	—
113	C₂²	(C₂×D₄₃)⋊C₁₆	1	1	yes	characteristic
114	C₄	—	2	1	no	—
115	C₄	—	172	1	no	—
116	C₄	—	172	1	no	—
117	C₄	#14582624	1	1	yes	characteristic
118	C₄	#14582680	1	1	yes	characteristic
119	C₂	—	4	1	no	—
120	C₂	#19132534	1	1	yes	characteristic
121	C₂	#19132736	1	1	yes	characteristic
122	C₂	#19132738	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19136353

C₂

yes

maximal, characteristic

C₂²⋊(C₄₃⋊C₃₂)

C₂

yes

maximal, characteristic

C₄₃×C₂²⋊C₃₂

C₂

yes

maximal, characteristic

C₂×#13063265

C₄

yes

characteristic

#14582854

C₄

yes

characteristic

C₂×C₄₃⋊C₃₂

—

Dic₄₃⋊C₁₆

—

Dic₄₃⋊C₁₆

—

C₂²×C₁₆×C₄₃

C₂²

yes

characteristic

C₂×C₃₂×C₄₃

—

C₂×#10621877

C₈

yes

characteristic

#13063284

C₈

yes

characteristic

#13063265

—

C₂×C₄₃⋊C₁₆

—

#13063235

—

C₈×Dic₄₃

—

C₄₃⋊C₃₂

—

C₂²×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

D₄

yes

characteristic

C₂×C₁₆×C₄₃

D₄

yes

characteristic

C₃₂×C₄₃

—

C₂²×C₄×C₄₃

C₂×C₈

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₃

M₁₆

yes

characteristic

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

C₁₆

yes

characteristic

C₄⋊Dic₄₃

C₁₆

yes

characteristic

C₄×Dic₄₃

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₁₆×C₄₃

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

M₃₂

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₄₃

C₂×C₁₆

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

—

C₈×C₄₃

yes

C₈×C₄₃

yes

C₄₃⋊C₈

—

#7363

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂²⋊C₁₆

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

#2151

—

C₂²⋊C₃₂

—

C₂²⋊C₃₂

D₄₃

yes

characteristic

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×M₃₂

—

C₂²×C₁₆

C₂×D₄₃

yes

characteristic

#405

—

C₂×C₃₂

—

C₂×C₃₂

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₄₃

#7363

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

C₄×D₄₃

yes

characteristic

#117

—

M₃₂

—

172

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

D₁₇₂

yes

characteristic

C₂×C₁₆

C₂²⋊D₄₃

yes

characteristic

#97

—

C₄×C₈

—

C₃₂

—

C₃₂

—

172

—

C₂²×C₄

C₈×D₄₃

yes

characteristic

M₁₆

—

172

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

#10621872

yes

characteristic

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₁₆

—

C₁₆

—

C₁₆

—

172

—

C₂³

#13063264

yes

characteristic

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

(C₂×D₄₃)⋊C₈

yes

characteristic

105

C₂×C₄

C₁₆×D₄₃

yes

characteristic

106

C₈

—

107

C₈

—

172

—

108

C₈

#13063239

yes

characteristic

109

C₈

#13063243

yes

characteristic

110

C₂²

—

111

C₂²

—

112

C₂²

—

113

C₂²

(C₂×D₄₃)⋊C₁₆

yes

characteristic

114

C₄

—

115

C₄

—

172

—

116

C₄

—

172

—

117

C₄

#14582624

yes

characteristic

118

C₄

#14582680

yes

characteristic

119

C₂

—

120

C₂

#19132534

yes

characteristic

121

C₂

#19132736

yes

characteristic

122

C₂

#19132738

yes

characteristic

	subgroup	G/H
center	C₂×C₈	(C₂×D₄₃)⋊C₄
commutator	C₂×C₄×C₄₃	C₂×C₁₆
Frattini	C₂²×C₁₆	C₂×D₄₃
Fitting	C₄₃×C₂²⋊C₃₂	C₂
socle	C₂²×C₄₃	C₂²⋊C₁₆
prime radical	C₂³×C₄₃	M₃₂
cosocle	C₂²×C₁₆×C₄₃	C₂²
hypercenter	C₂²⋊C₃₂	D₄₃
hypocenter	C₄₃	#7363
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₁₆ ◁ C₂²⋊C₃₂

subgroup

G/H

center

C₂×C₈

(C₂×D₄₃)⋊C₄

commutator

C₂×C₄×C₄₃

C₂×C₁₆

Frattini

C₂²×C₁₆

C₂×D₄₃

Fitting

C₄₃×C₂²⋊C₃₂

C₂

socle

C₂²×C₄₃

C₂²⋊C₁₆

prime radical

C₂³×C₄₃

M₃₂

cosocle

C₂²×C₁₆×C₄₃

C₂²

hypercenter

C₂²⋊C₃₂

D₄₃

hypocenter

C₄₃

#7363

LCS

G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₈ ◁ C₂²×C₁₆ ◁ C₂²⋊C₃₂

N	H ≅ G/N	type
72. C₄₃	#7363	semidirect

H ≅ G/N

type

72. C₄₃

#7363

semidirect

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

subgroup	index
#19136353	2
C₂²⋊(C₄₃⋊C₃₂)	2
C₄₃×C₂²⋊C₃₂	2
#7363	43

subgroup

index

#19136353

C₂²⋊(C₄₃⋊C₃₂)

C₄₃×C₂²⋊C₃₂

#7363

Subgroups — #24983997

Conjugacy classes of subgroups

Complements

Maximal subgroups