Group #24983329 — subgroups

Subgroups — #24983329

Order 11008.

142 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 57 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	#19134213	C₂	1	1	yes	maximal, characteristic
2	#19132665	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1370	C₂	1	1	yes	maximal, characteristic
4	#14583304	—	2	1	no	—
5	#14583304	C₄	1	2	yes	—
6	#14583279	—	2	1	no	—
7	C₄⋊(C₄₃⋊C₁₆)	—	2	1	no	—
8	C₄₃×C₄⋊C₁₆	—	2	1	no	—
9	C₈²×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×Dic₁₇₂	—	4	1	no	—
11	C₂×Dic₁₇₂	—	4	1	no	—
12	#13063325	—	2	2	no	—
13	C₂×C₄₃⋊C₁₆	—	4	1	no	—
14	#13063259	—	4	1	no	—
15	#13063259	—	4	1	no	—
16	#13063259	—	4	2	no	—
17	C₂×C₁₆×C₄₃	—	4	1	no	—
18	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
19	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
20	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
21	C₂×Dic₈₆	—	4	2	no	—
22	C₂×C₈×C₄₃	—	2	1	no	—
23	C₂×C₈×C₄₃	D₈	1	1	yes	characteristic
24	C₂×C₈×C₄₃	D₈	1	1	yes	characteristic
25	C₂×C₈×C₄₃	SD₁₆	1	1	yes	characteristic
26	C₂×C₈×C₄₃	SD₁₆	1	1	yes	characteristic
27	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₄⋊Dic₄₃	—	4	2	no	—
29	C₄⋊Dic₄₃	—	4	2	no	—
30	Dic₁₇₂	—	8	2	no	—
31	Dic₁₇₂	—	8	1	no	—
32	Dic₁₇₂	—	8	1	no	—
33	C₁₆×C₄₃	—	8	1	no	—
34	C₄₃⋊C₁₆	—	8	1	no	—
35	C₂×C₄×C₄₃	#100	1	1	yes	characteristic
36	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
37	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
38	C₂×Dic₄₃	—	8	2	no	—
39	Dic₈₆	—	8	2	no	—
40	Dic₈₆	—	8	2	no	—
41	C₈×C₄₃	—	2	2	no	—
42	C₈×C₄₃	—	2	1	no	—
43	C₈×C₄₃	—	2	1	no	—
44	C₈×C₄₃	D₁₆	1	1	yes	characteristic
45	C₈×C₄₃	SD₃₂	1	1	yes	characteristic
46	C₈×C₄₃	SD₃₂	1	1	yes	characteristic
47	C₈×C₄₃	Q₃₂	1	1	yes	characteristic
48	#7097	—	43	1	no	maximal, Sylow
49	C₂²×C₄₃	#331	1	1	yes	characteristic
50	C₄×C₄₃	—	2	1	no	—
51	C₄×C₄₃	#357	1	1	yes	characteristic
52	C₄×C₄₃	#358	1	1	yes	characteristic
53	C₄×C₄₃	#361	1	1	yes	characteristic
54	C₄×C₄₃	#362	1	1	yes	characteristic
55	Dic₄₃	—	16	2	no	—
56	#1713	—	43	1	no	—
57	#1370	—	43	1	no	—
58	#1370	D₄₃	1	1	yes	characteristic
59	C₂×C₄₃	#1358	1	1	yes	characteristic
60	C₂×C₄₃	#1361	1	1	yes	characteristic
61	C₂×C₄₃	#1362	1	1	yes	characteristic
62	#500	—	43	2	no	—
63	#500	—	86	1	no	—
64	#494	—	86	1	no	—
65	C₄⋊C₁₆	—	2	1	no	—
66	C₄⋊C₁₆	—	86	1	no	—
67	C₈²	C₂×D₄₃	1	1	yes	characteristic
68	C₄₃	#7097	1	1	yes	characteristic, complemented, Sylow
69	C₂×Q₁₆	—	172	1	no	—
70	C₂×Q₁₆	—	172	1	no	—
71	C₄⋊Q₈	—	86	2	no	—
72	C₂×C₁₆	—	4	1	no	—
73	C₂×C₁₆	—	172	1	no	—
74	#107	—	172	1	no	—
75	#107	—	172	1	no	—
76	#107	—	172	2	no	—
77	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
78	C₄×C₈	D₁₇₂	1	1	yes	characteristic
79	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
80	C₂×Q₈	—	172	2	no	—
81	Q₁₆	—	344	2	no	—
82	Q₁₆	—	344	1	no	—
83	Q₁₆	—	344	1	no	—
84	C₂×C₈	—	2	1	no	—
85	C₂×C₈	#10621873	1	1	yes	characteristic
86	C₂×C₈	D₃₄₄	1	1	yes	characteristic
87	C₂×C₈	#10621882	1	1	yes	characteristic
88	C₂×C₈	#10621884	1	1	yes	characteristic
89	C₄⋊C₄	—	172	2	no	—
90	C₄⋊C₄	—	172	2	no	—
91	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
92	C₁₆	—	8	1	no	—
93	C₁₆	—	344	1	no	—
94	Q₈	—	344	2	no	—
95	Q₈	—	344	2	no	—
96	C₂×C₄	—	344	2	no	—
97	C₂×C₄	#13063241	1	1	yes	characteristic
98	C₂×C₄	#13063245	1	1	yes	characteristic
99	C₂×C₄	#13063247	1	1	yes	characteristic
100	C₈	—	2	2	no	—
101	C₈	—	2	1	no	—
102	C₈	—	2	1	no	—
103	C₈	D₆₈₈	1	1	yes	characteristic
104	C₈	#13063269	1	1	yes	characteristic
105	C₈	#13063270	1	1	yes	characteristic
106	C₈	#13063271	1	1	yes	characteristic
107	C₂²	#14582642	1	1	yes	characteristic
108	C₄	—	2	1	no	—
109	C₄	—	688	2	no	—
110	C₄	#14582701	1	1	yes	characteristic
111	C₄	#14582702	1	1	yes	characteristic
112	C₄	#14582713	1	1	yes	characteristic
113	C₄	#14582714	1	1	yes	characteristic
114	C₂	#19132633	1	1	yes	characteristic
115	C₂	#19132642	1	1	yes	characteristic
116	C₂	#19132643	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19134213

C₂

yes

maximal, characteristic

#19132665

C₂

yes

maximal, characteristic

C₄₃×#1370

C₂

yes

maximal, characteristic

#14583304

—

#14583304

C₄

yes

—

#14583279

—

C₄⋊(C₄₃⋊C₁₆)

—

C₄₃×C₄⋊C₁₆

—

C₈²×C₄₃

C₂²

yes

characteristic

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

#13063325

—

C₂×C₄₃⋊C₁₆

—

#13063259

—

#13063259

—

#13063259

—

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

D₈

yes

characteristic

C₂×C₈×C₄₃

D₈

yes

characteristic

C₂×C₈×C₄₃

SD₁₆

yes

characteristic

C₂×C₈×C₄₃

SD₁₆

yes

characteristic

C₄²×C₄₃

C₂²⋊C₄

yes

characteristic

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₁₇₂

—

Dic₁₇₂

—

Dic₁₇₂

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

D₁₆

yes

characteristic

C₈×C₄₃

SD₃₂

yes

characteristic

C₈×C₄₃

SD₃₂

yes

characteristic

C₈×C₄₃

Q₃₂

yes

—

C₂²×C₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

#1713

—

#1370

—

#1370

D₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

—

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₈²

C₂×D₄₃

yes

characteristic

C₄₃

#7097

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

172

—

C₂×Q₁₆

—

172

—

C₄⋊Q₈

—

C₂×C₁₆

—

C₂×C₁₆

—

172

—

#107

—

172

—

#107

—

172

—

#107

—

172

—

C₄×C₈

C₄×D₄₃

yes

characteristic

C₄×C₈

D₁₇₂

yes

characteristic

C₄×C₈

C₂²⋊D₄₃

yes

characteristic

C₂×Q₈

—

172

—

Q₁₆

—

344

—

Q₁₆

—

344

—

Q₁₆

—

344

—

C₂×C₈

—

C₂×C₈

#10621873

yes

characteristic

C₂×C₈

D₃₄₄

yes

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

172

—

C₄⋊C₄

—

172

—

C₄²

(C₂×D₄₃)⋊C₄

yes

characteristic

C₁₆

—

C₁₆

—

344

—

Q₈

—

344

—

Q₈

—

344

—

C₂×C₄

—

344

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

100

C₈

—

101

C₈

—

102

C₈

—

103

C₈

D₆₈₈

yes

characteristic

104

C₈

#13063269

yes

characteristic

105

C₈

#13063270

yes

characteristic

106

C₈

#13063271

yes

characteristic

107

C₂²

#14582642

yes

characteristic

108

C₄

—

109

C₄

—

688

—

110

C₄

#14582701

yes

characteristic

111

C₄

#14582702

yes

characteristic

112

C₄

#14582713

yes

characteristic

113

C₄

#14582714

yes

characteristic

114

C₂

#19132633

yes

characteristic

115

C₂

#19132642

yes

characteristic

116

C₂

#19132643

yes

characteristic

	subgroup	G/H
center	C₂²	#14582642
commutator	C₄×C₈×C₄₃	C₂×C₄
Frattini	C₈²	C₂×D₄₃
Fitting	C₄₃×#1370	C₂
socle, prime radical	C₂²×C₄₃	#331
cosocle	C₈²×C₄₃	C₂²
hypercenter	#1370	D₄₃
hypocenter	C₄₃	#7097
LCS	G ▷ C₄×C₈×C₄₃ ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1370

subgroup

G/H

center

C₂²

#14582642

commutator

C₄×C₈×C₄₃

C₂×C₄

Frattini

C₈²

C₂×D₄₃

Fitting

C₄₃×#1370

C₂

socle, prime radical

C₂²×C₄₃

#331

cosocle

C₈²×C₄₃

C₂²

D₄₃

C₄₃

G ▷ C₄×C₈×C₄₃ ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1370

N	H ≅ G/N	type
68. C₄₃	#7097	semidirect

H ≅ G/N

type

68. C₄₃

#7097

semidirect

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

subgroup	index
#19134213	2
#19132665	2
C₄₃×#1370	2
#7097	43

subgroup

index

#19134213

#19132665

C₄₃×#1370

#7097

Subgroups — #24983329

Conjugacy classes of subgroups

Complements

Maximal subgroups