Group #24983706 — subgroups

Subgroups — #24983706

Order 11008.

200 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 91 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	C₄₃×#2150	C₂	1	1	yes	maximal, characteristic
3	#14582923	—	2	2	no	—
4	#14582652	—	2	2	no	—
5	#14582652	C₄	1	4	yes	—
6	C₂×M₃₂×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	M₃₂×C₄₃	—	4	2	no	—
16	C₂×C₁₆×C₄₃	—	2	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	SD₁₆	1	2	yes	—
21	C₂×C₈×C₄₃	—	2	1	no	—
22	C₂×C₈×C₄₃	—	2	1	no	—
23	C₂×C₈×C₄₃	—	4	1	no	—
24	C₂×C₈×C₄₃	C₄²	1	1	yes	characteristic
25	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₈×C₄₃	C₄⋊C₄	1	2	yes	—
27	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
28	C₄²×C₄₃	D₈	1	1	yes	characteristic
29	C₄²×C₄₃	Q₁₆	1	1	yes	characteristic
30	#10621877	—	8	4	no	—
31	C₂×C₄₃⋊C₈	—	4	4	no	—
32	C₁₆×C₄₃	—	4	2	no	—
33	C₂³×C₄₃	#106	1	1	yes	characteristic
34	C₂×C₄×C₄₃	—	2	1	no	—
35	C₂×C₄×C₄₃	—	2	1	no	—
36	C₂×C₄×C₄₃	—	2	2	no	—
37	C₂×C₄×C₄₃	—	2	2	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	#107	1	1	yes	characteristic
42	C₈×C₄₃	—	2	2	no	—
43	C₈×C₄₃	—	2	1	no	—
44	C₈×C₄₃	#100	1	1	yes	characteristic
45	C₈×C₄₃	#101	1	1	yes	characteristic
46	C₄₃⋊C₈	—	8	4	no	—
47	#7245	—	43	1	no	maximal, Sylow
48	C₂²×C₄₃	—	2	1	no	—
49	C₂²×C₄₃	—	2	2	no	—
50	C₂²×C₄₃	#340	1	1	yes	characteristic
51	C₄×C₄₃	—	2	1	no	—
52	C₄×C₄₃	—	2	2	no	—
53	C₄×C₄₃	#338	1	1	yes	characteristic
54	C₄×C₄₃	#343	1	1	yes	characteristic
55	C₄×C₄₃	#361	1	2	yes	—
56	C₄×C₄₃	#362	1	2	yes	—
57	#2150	D₄₃	1	1	yes	characteristic
58	#1567	—	43	2	no	—
59	C₂×C₄₃	—	4	1	no	—
60	C₂×C₄₃	#1292	1	1	yes	characteristic
61	C₂×C₄₃	#1387	1	2	yes	—
62	C₂×M₃₂	Dic₄₃	1	2	yes	—
63	#423	—	86	2	no	—
64	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
65	C₄⋊C₁₆	—	2	2	no	—
66	#335	—	43	4	no	—
67	#335	—	86	2	no	—
68	C₄₃	#7245	1	1	yes	characteristic, complemented, Sylow
69	C₂×M₁₆	—	172	2	no	—
70	C₂²×C₈	Dic₈₆	1	1	yes	characteristic
71	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
72	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
73	M₃₂	—	4	2	no	—
74	C₂×C₁₆	—	2	2	no	—
75	C₄⋊C₈	—	86	4	no	—
76	C₄⋊C₈	—	172	2	no	—
77	C₄×C₈	C₄×D₄₃	1	2	yes	—
78	C₄×C₈	C₂²⋊D₄₃	1	2	yes	—
79	C₂²×C₄	#10621873	1	2	yes	—
80	C₂²×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
81	M₁₆	—	344	4	no	—
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	D₃₄₄	1	1	yes	characteristic
90	C₄²	Dic₁₇₂	1	1	yes	characteristic
91	C₄²	(C₂×D₄₃)⋊C₄	1	2	yes	—
92	C₁₆	—	4	2	no	—
93	C₂³	#13063257	1	1	yes	characteristic
94	C₂×C₄	—	2	1	no	—
95	C₂×C₄	—	2	1	no	—
96	C₂×C₄	—	2	2	no	—
97	C₂×C₄	—	2	2	no	—
98	C₂×C₄	C₄₃⋊#95	1	1	yes	characteristic
99	C₂×C₄	#13063247	1	2	yes	—
100	C₂×C₄	#13063250	1	2	yes	—
101	C₂×C₄	#13063259	1	1	yes	characteristic
102	C₈	—	2	2	no	—
103	C₈	—	2	1	no	—
104	C₈	—	344	4	no	—
105	C₈	#13063242	1	1	yes	characteristic
106	C₈	#13063244	1	1	yes	characteristic
107	C₂²	—	2	2	no	—
108	C₂²	—	2	1	no	—
109	C₂²	#14582662	1	1	yes	characteristic
110	C₄	—	2	2	no	—
111	C₄	—	2	1	no	—
112	C₄	C₄₃⋊#338	1	1	yes	characteristic
113	C₄	#14582668	1	1	yes	characteristic
114	C₄	#14582713	1	2	yes	—
115	C₄	#14582716	1	2	yes	—
116	C₂	—	4	1	no	—
117	C₂	#19132470	1	1	yes	characteristic
118	C₂	#19132704	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19133354

C₂

yes

maximal

C₄₃×#2150

C₂

yes

maximal, characteristic

#14582923

—

#14582652

—

#14582652

C₄

yes

—

C₂×M₃₂×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

M₃₂×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

SD₁₆

yes

—

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

D₈

yes

characteristic

C₄²×C₄₃

Q₁₆

yes

characteristic

#10621877

—

C₂×C₄₃⋊C₈

—

C₁₆×C₄₃

—

C₂³×C₄₃

#106

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

#107

yes

characteristic

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

yes

C₈×C₄₃

yes

C₄₃⋊C₈

—

#7245

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#340

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

—

C₄×C₄₃

#362

yes

—

#2150

D₄₃

yes

characteristic

#1567

—

C₂×C₄₃

—

C₂×C₄₃

#1292

yes

characteristic

C₂×C₄₃

#1387

yes

—

C₂×M₃₂

Dic₄₃

yes

—

#423

—

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

C₄⋊C₁₆

—

#335

—

#335

—

C₄₃

#7245

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

172

—

C₂²×C₈

Dic₈₆

yes

characteristic

C₂²×C₈

C₂×Dic₄₃

yes

characteristic

C₂×C₄²

D₁₇₂

yes

characteristic

M₃₂

—

C₂×C₁₆

—

C₄⋊C₈

—

C₄⋊C₈

—

172

—

C₄×C₈

C₄×D₄₃

yes

—

C₄×C₈

C₂²⋊D₄₃

yes

—

C₂²×C₄

#10621873

yes

—

C₂²×C₄

C₄⋊Dic₄₃

yes

characteristic

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

D₃₄₄

yes

characteristic

C₄²

Dic₁₇₂

yes

characteristic

C₄²

(C₂×D₄₃)⋊C₄

yes

—

C₁₆

—

C₂³

#13063257

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄₃⋊#95

yes

characteristic

C₂×C₄

#13063247

yes

—

100

C₂×C₄

#13063250

yes

—

101

C₂×C₄

#13063259

yes

characteristic

102

C₈

—

103

C₈

—

104

C₈

—

344

—

105

C₈

#13063242

yes

characteristic

106

C₈

#13063244

yes

characteristic

107

C₂²

—

108

C₂²

—

109

C₂²

#14582662

yes

characteristic

110

C₄

—

111

C₄

—

112

C₄

C₄₃⋊#338

yes

characteristic

113

C₄

#14582668

yes

characteristic

114

C₄

#14582713

yes

—

115

C₄

#14582716

yes

—

116

C₂

—

117

C₂

#19132470

yes

characteristic

118

C₂

#19132704

yes

—

	subgroup	G/H
center	C₂²	#14582662
commutator	C₂×C₈×C₄₃	C₄²
Frattini	C₂×C₄×C₈	C₂×D₄₃
Fitting	C₄₃×#2150	C₂
socle	C₂²×C₄₃	#340
prime radical	C₂³×C₄₃	#106
cosocle	C₂×C₄×C₈×C₄₃	C₂²
hypercenter	#2150	D₄₃
hypocenter	C₄₃	#7245
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #2150

subgroup

G/H

center

C₂²

#14582662

commutator

C₂×C₈×C₄₃

C₄²

Frattini

C₂×C₄×C₈

C₂×D₄₃

Fitting

C₄₃×#2150

C₂

C₂²×C₄₃

C₂³×C₄₃

C₂×C₄×C₈×C₄₃

C₂²

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #2150

N	H ≅ G/N	type
68. C₄₃	#7245	semidirect

H ≅ G/N

type

68. C₄₃

#7245

semidirect

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

subgroup	index
#19133354	2
C₄₃×#2150	2
#7245	43

subgroup

index

#19133354

C₄₃×#2150

#7245

Subgroups — #24983706

Conjugacy classes of subgroups

Complements

Maximal subgroups