Group #24983698 — subgroups

Subgroups — #24983698

Order 11008.

190 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 87 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	#19133358	C₂	1	2	yes	maximal
2	C₂×C₄₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	#14582956	—	2	2	no	—
4	#14582652	—	2	2	no	—
5	#14582650	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	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
10	C₂²⋊(C₄₃⋊C₈)	—	4	2	no	—
11	#13063236	—	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	C₂×C₄₃⋊C₈	—	4	4	no	—
31	C₁₆×C₄₃	—	4	2	no	—
32	C₂³×C₄₃	#107	1	1	yes	characteristic
33	C₂×C₄×C₄₃	—	2	2	no	—
34	C₂×C₄×C₄₃	—	2	1	no	—
35	C₂×C₄×C₄₃	—	2	1	no	—
36	C₂×C₄×C₄₃	—	4	1	no	—
37	C₂×C₄×C₄₃	#95	1	1	yes	characteristic
38	C₂×C₄×C₄₃	#102	1	2	yes	—
39	C₂×C₄×C₄₃	#103	1	2	yes	—
40	C₂×C₄×C₄₃	#106	1	1	yes	characteristic
41	C₈×C₄₃	—	2	2	no	—
42	C₈×C₄₃	—	2	1	no	—
43	C₈×C₄₃	#100	1	1	yes	characteristic
44	C₈×C₄₃	#101	1	1	yes	characteristic
45	C₄₃⋊C₈	—	8	4	no	—
46	#7242	—	43	1	no	maximal, Sylow
47	C₂²×C₄₃	—	2	1	no	—
48	C₂²×C₄₃	—	2	1	no	—
49	C₂²×C₄₃	#340	1	1	yes	characteristic
50	C₂²×C₄₃	#368	1	2	yes	—
51	C₄×C₄₃	—	2	1	no	—
52	C₄×C₄₃	—	2	2	no	—
53	C₄×C₄₃	—	2	2	no	—
54	C₄×C₄₃	#338	1	1	yes	characteristic
55	C₄×C₄₃	#343	1	1	yes	characteristic
56	C₂×C₄⋊C₁₆	D₄₃	1	1	yes	characteristic
57	#1568	—	43	2	no	—
58	C₂×C₄₃	—	2	2	no	—
59	C₂×C₄₃	#1292	1	1	yes	characteristic
60	C₂×C₄₃	#1381	1	1	yes	characteristic
61	C₂×C₄₃	#1384	1	1	yes	characteristic
62	C₂²×C₁₆	Dic₄₃	1	2	yes	—
63	#432	—	86	2	no	—
64	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
65	C₄⋊C₁₆	—	2	2	no	—
66	#335	—	86	2	no	—
67	#334	—	43	4	no	—
68	C₄₃	#7242	1	1	yes	characteristic, complemented, Sylow
69	C₂²×C₈	Dic₈₆	1	1	yes	characteristic
70	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
71	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
72	C₂×C₁₆	—	2	2	no	—
73	C₂×C₁₆	—	4	2	no	—
74	C₄⋊C₈	—	86	4	no	—
75	C₂²⋊C₈	—	172	2	no	—
76	#97	—	172	2	no	—
77	C₄×C₈	C₄×D₄₃	1	2	yes	—
78	C₄×C₈	C₂²⋊D₄₃	1	2	yes	—
79	C₂²×C₄	D₃₄₄	1	1	yes	characteristic
80	C₂²×C₄	Dic₁₇₂	1	1	yes	characteristic
81	C₂²×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
82	C₂×C₈	—	2	1	no	—
83	C₂×C₈	—	2	1	no	—
84	C₂×C₈	—	4	1	no	—
85	C₂×C₈	—	172	4	no	—
86	C₂×C₈	C₄×Dic₄₃	1	1	yes	characteristic
87	C₂×C₈	Dic₄₃⋊C₄	1	2	yes	—
88	C₂×C₈	C₂²⋊Dic₄₃	1	1	yes	characteristic
89	C₄²	#10621873	1	2	yes	—
90	C₄²	(C₂×D₄₃)⋊C₄	1	2	yes	—
91	C₁₆	—	4	2	no	—
92	C₂³	#13063259	1	1	yes	characteristic
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	2	1	no	—
95	C₂×C₄	—	2	1	no	—
96	C₂×C₄	—	4	1	no	—
97	C₂×C₄	C₄₃⋊#95	1	1	yes	characteristic
98	C₂×C₄	#13063247	1	2	yes	—
99	C₂×C₄	#13063250	1	2	yes	—
100	C₂×C₄	#13063257	1	1	yes	characteristic
101	C₈	—	2	2	no	—
102	C₈	—	2	1	no	—
103	C₈	—	344	4	no	—
104	C₈	#13063242	1	1	yes	characteristic
105	C₈	#13063244	1	1	yes	characteristic
106	C₂²	—	2	1	no	—
107	C₂²	—	2	1	no	—
108	C₂²	#14582662	1	1	yes	characteristic
109	C₂²	#14582729	1	2	yes	—
110	C₄	—	2	2	no	—
111	C₄	—	2	2	no	—
112	C₄	—	2	1	no	—
113	C₄	C₄₃⋊#338	1	1	yes	characteristic
114	C₄	#14582668	1	1	yes	characteristic
115	C₂	—	2	2	no	—
116	C₂	#19132470	1	1	yes	characteristic
117	C₂	#19132689	1	1	yes	characteristic
118	C₂	#19132697	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19133358

C₂

yes

maximal

C₂×C₄₃×C₄⋊C₁₆

C₂

yes

maximal, characteristic

#14582956

—

#14582652

—

#14582650

C₄

yes

—

C₂²×C₁₆×C₄₃

C₄

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄₃×C₄⋊C₁₆

—

C₄⋊(C₄₃⋊C₈)

—

C₂²⋊(C₄₃⋊C₈)

—

#13063236

—

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

—

C₂×C₄₃⋊C₈

—

C₁₆×C₄₃

—

C₂³×C₄₃

#107

yes

characteristic

C₂×C₄×C₄₃

—

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

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

yes

C₈×C₄₃

yes

C₄₃⋊C₈

—

#7242

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#340

yes

characteristic

C₂²×C₄₃

#368

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₂×C₄⋊C₁₆

D₄₃

yes

characteristic

#1568

—

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂²×C₁₆

Dic₄₃

yes

—

#432

—

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

C₄⋊C₁₆

—

#335

—

#334

—

C₄₃

#7242

yes

characteristic, complemented, Sylow

C₂²×C₈

Dic₈₆

yes

characteristic

C₂²×C₈

C₂×Dic₄₃

yes

characteristic

C₂×C₄²

D₁₇₂

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₄⋊C₈

—

C₂²⋊C₈

—

172

—

#97

—

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

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

—

C₁₆

—

C₂³

#13063259

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄₃⋊#95

yes

characteristic

C₂×C₄

#13063247

yes

—

C₂×C₄

#13063250

yes

—

100

C₂×C₄

#13063257

yes

characteristic

101

C₈

—

102

C₈

—

103

C₈

—

344

—

104

C₈

#13063242

yes

characteristic

105

C₈

#13063244

yes

characteristic

106

C₂²

—

107

C₂²

—

108

C₂²

#14582662

yes

characteristic

109

C₂²

#14582729

yes

—

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

C₄₃⋊#338

yes

characteristic

114

C₄

#14582668

yes

characteristic

115

C₂

—

116

C₂

#19132470

yes

characteristic

117

C₂

#19132689

yes

characteristic

118

C₂

#19132697

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	#7242
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

#7242

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
68. C₄₃	#7242	semidirect

H ≅ G/N

type

68. C₄₃

#7242

semidirect

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

subgroup	index
#19133358	2
C₂×C₄₃×C₄⋊C₁₆	2
#7242	43

subgroup

index

#19133358

C₂×C₄₃×C₄⋊C₁₆

#7242

Subgroups — #24983698

Conjugacy classes of subgroups

Complements

Maximal subgroups