Group #24983708 — subgroups

Subgroups — #24983708

Order 11008.

184 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 83 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	C₄₃×#2150	C₂	1	1	yes	maximal, characteristic
3	#14582956	—	2	2	no	—
4	#14582652	—	2	2	no	—
5	#14582650	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	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	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	C₂×C₄₃⋊C₈	—	4	4	no	—
31	C₁₆×C₄₃	—	4	2	no	—
32	C₂³×C₄₃	#106	1	1	yes	characteristic
33	C₂×C₄×C₄₃	—	2	1	no	—
34	C₂×C₄×C₄₃	—	2	1	no	—
35	C₂×C₄×C₄₃	—	4	2	no	—
36	C₂×C₄×C₄₃	#95	1	1	yes	characteristic
37	C₂×C₄×C₄₃	#102	1	2	yes	—
38	C₂×C₄×C₄₃	#103	1	2	yes	—
39	C₂×C₄×C₄₃	#107	1	1	yes	characteristic
40	C₈×C₄₃	—	2	2	no	—
41	C₈×C₄₃	—	2	1	no	—
42	C₈×C₄₃	#100	1	1	yes	characteristic
43	C₈×C₄₃	#101	1	1	yes	characteristic
44	C₄₃⋊C₈	—	8	4	no	—
45	#7246	—	43	1	no	maximal, Sylow
46	C₂²×C₄₃	—	2	1	no	—
47	C₂²×C₄₃	—	2	2	no	—
48	C₂²×C₄₃	#340	1	1	yes	characteristic
49	C₄×C₄₃	—	2	1	no	—
50	C₄×C₄₃	—	2	2	no	—
51	C₄×C₄₃	—	2	2	no	—
52	C₄×C₄₃	#338	1	1	yes	characteristic
53	C₄×C₄₃	#343	1	1	yes	characteristic
54	#2150	D₄₃	1	1	yes	characteristic
55	#1568	—	43	2	no	—
56	C₂×C₄₃	—	4	1	no	—
57	C₂×C₄₃	#1292	1	1	yes	characteristic
58	C₂×C₄₃	#1389	1	2	yes	—
59	C₂×M₃₂	Dic₄₃	1	2	yes	—
60	#432	—	86	2	no	—
61	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
62	C₄⋊C₁₆	—	2	2	no	—
63	#335	—	86	2	no	—
64	#334	—	43	4	no	—
65	C₄₃	#7246	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₈	Dic₈₆	1	1	yes	characteristic
67	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
68	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
69	M₃₂	—	4	2	no	—
70	C₂×C₁₆	—	2	2	no	—
71	C₄⋊C₈	—	86	4	no	—
72	C₂²⋊C₈	—	172	2	no	—
73	#97	—	172	2	no	—
74	C₄×C₈	C₄×D₄₃	1	2	yes	—
75	C₄×C₈	C₂²⋊D₄₃	1	2	yes	—
76	C₂²×C₄	#10621873	1	2	yes	—
77	C₂²×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
78	C₂×C₈	—	2	1	no	—
79	C₂×C₈	—	2	1	no	—
80	C₂×C₈	—	4	1	no	—
81	C₂×C₈	—	172	4	no	—
82	C₂×C₈	C₄×Dic₄₃	1	1	yes	characteristic
83	C₂×C₈	Dic₄₃⋊C₄	1	2	yes	—
84	C₂×C₈	C₂²⋊Dic₄₃	1	1	yes	characteristic
85	C₄²	D₃₄₄	1	1	yes	characteristic
86	C₄²	Dic₁₇₂	1	1	yes	characteristic
87	C₄²	(C₂×D₄₃)⋊C₄	1	2	yes	—
88	C₁₆	—	4	2	no	—
89	C₂³	#13063257	1	1	yes	characteristic
90	C₂×C₄	—	2	1	no	—
91	C₂×C₄	—	2	1	no	—
92	C₂×C₄	—	4	2	no	—
93	C₂×C₄	C₄₃⋊#95	1	1	yes	characteristic
94	C₂×C₄	#13063247	1	2	yes	—
95	C₂×C₄	#13063250	1	2	yes	—
96	C₂×C₄	#13063259	1	1	yes	characteristic
97	C₈	—	2	2	no	—
98	C₈	—	2	1	no	—
99	C₈	—	344	4	no	—
100	C₈	#13063242	1	1	yes	characteristic
101	C₈	#13063244	1	1	yes	characteristic
102	C₂²	—	2	2	no	—
103	C₂²	—	2	1	no	—
104	C₂²	#14582662	1	1	yes	characteristic
105	C₄	—	2	2	no	—
106	C₄	—	2	2	no	—
107	C₄	—	2	1	no	—
108	C₄	C₄₃⋊#338	1	1	yes	characteristic
109	C₄	#14582668	1	1	yes	characteristic
110	C₂	—	4	1	no	—
111	C₂	#19132470	1	1	yes	characteristic
112	C₂	#19132710	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19133358

C₂

yes

maximal

C₄₃×#2150

C₂

yes

maximal, characteristic

#14582956

—

#14582652

—

#14582650

C₄

yes

—

C₂×M₃₂×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

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

C₂×C₄₃⋊C₈

—

C₁₆×C₄₃

—

C₂³×C₄₃

#106

yes

characteristic

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

—

#7246

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#340

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

D₄₃

yes

characteristic

#1568

—

C₂×C₄₃

—

C₂×C₄₃

#1292

yes

characteristic

C₂×C₄₃

#1389

yes

—

C₂×M₃₂

Dic₄₃

yes

—

#432

—

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

C₄⋊C₁₆

—

#335

—

#334

—

C₄₃

#7246

yes

characteristic, complemented, Sylow

C₂²×C₈

Dic₈₆

yes

characteristic

C₂²×C₈

C₂×Dic₄₃

yes

characteristic

C₂×C₄²

D₁₇₂

yes

characteristic

M₃₂

—

C₂×C₁₆

—

C₄⋊C₈

—

C₂²⋊C₈

—

172

—

#97

—

172

—

C₄×C₈

C₄×D₄₃

yes

—

C₄×C₈

C₂²⋊D₄₃

yes

—

C₂²×C₄

#10621873

yes

—

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

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

C₄₃⋊#95

yes

characteristic

C₂×C₄

#13063247

yes

—

C₂×C₄

#13063250

yes

—

C₂×C₄

#13063259

yes

characteristic

C₈

—

C₈

—

C₈

—

344

—

100

C₈

#13063242

yes

characteristic

101

C₈

#13063244

yes

characteristic

102

C₂²

—

103

C₂²

—

104

C₂²

#14582662

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

C₄₃⋊#338

yes

characteristic

109

C₄

#14582668

yes

characteristic

110

C₂

—

111

C₂

#19132470

yes

characteristic

112

C₂

#19132710

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	#7246
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
65. C₄₃	#7246	semidirect

H ≅ G/N

type

65. C₄₃

#7246

semidirect

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

subgroup	index
#19133358	2
C₄₃×#2150	2
#7246	43

subgroup

index

#19133358

C₄₃×#2150

#7246

Subgroups — #24983708

Conjugacy classes of subgroups

Complements

Maximal subgroups