Group #24999363 — subgroups

Subgroups — #24999363

Order 11008.

478 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 89 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	#19145989	C₂	1	3	yes	maximal
2	#19135571	C₂	1	3	yes	maximal
3	C₄₃×#1309	C₂	1	1	yes	maximal, characteristic
4	#14583456	C₂²	1	3	yes	—
5	#14583185	—	2	6	no	—
6	#14583157	—	2	6	no	—
7	#14583110	—	2	6	no	—
8	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
9	#14582660	—	2	6	no	—
10	C₄₃×#423	C₂²	1	3	yes	—
11	C₂×Dic₁₇₂	—	2	6	no	—
12	#13063325	D₄	1	6	yes	—
13	#13063317	—	2	3	no	—
14	#13063304	—	2	6	no	—
15	C₄×Dic₈₆	—	2	6	no	—
16	#13063284	—	2	3	no	—
17	C₂×C₄×Dic₄₃	—	2	3	no	—
18	#13063257	—	2	6	no	—
19	#13063250	—	2	12	no	—
20	C₂×M₁₆×C₄₃	D₄	1	6	yes	—
21	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
22	C₄⋊C₈×C₄₃	—	2	6	no	—
23	C₂²×C₄×C₄₃	C₂×D₄	1	3	yes	—
24	C₂²×Dic₄₃	—	4	1	no	—
25	C₂×Dic₈₆	—	2	6	no	—
26	M₁₆×C₄₃	—	4	6	no	—
27	C₂×C₈×C₄₃	—	2	6	no	—
28	C₄²×C₄₃	C₂×D₄	1	3	yes	—
29	C₄²×C₄₃	#41	1	1	yes	characteristic
30	C₂²⋊Dic₄₃	—	4	3	no	—
31	C₄⋊Dic₄₃	—	2	6	no	—
32	C₄⋊Dic₄₃	—	2	6	no	—
33	Dic₄₃⋊C₄	—	4	6	no	—
34	C₄×Dic₄₃	—	2	6	no	—
35	C₄×Dic₄₃	—	4	3	no	—
36	C₄×Dic₄₃	—	4	3	no	—
37	Dic₁₇₂	—	8	6	no	—
38	C₂³×C₄₃	#127	1	1	yes	characteristic
39	C₂×C₄×C₄₃	—	2	3	no	—
40	C₂×C₄×C₄₃	—	2	3	no	—
41	C₂×C₄×C₄₃	#120	1	3	yes	—
42	C₂×C₄×C₄₃	#121	1	3	yes	—
43	C₂×Dic₄₃	—	4	6	no	—
44	C₂×Dic₄₃	—	4	6	no	—
45	Dic₈₆	—	4	6	no	—
46	Dic₈₆	—	4	6	no	—
47	C₈×C₄₃	—	4	6	no	—
48	#10303	—	43	1	no	maximal, Sylow
49	C₂²×C₄₃	—	2	3	no	—
50	C₂²×C₄₃	#392	1	1	yes	characteristic
51	C₄×C₄₃	—	2	3	no	—
52	C₄×C₄₃	#455	1	3	yes	—
53	C₄×C₄₃	#456	1	3	yes	—
54	Dic₄₃	—	4	4	no	—
55	Dic₄₃	—	8	6	no	—
56	#3255	—	43	3	no	—
57	#1994	—	43	3	no	—
58	#1309	D₄₃	1	1	yes	characteristic
59	C₂×C₄₃	—	4	1	no	—
60	C₂×C₄₃	#2007	1	3	yes	—
61	#533	—	43	3	no	—
62	#475	—	86	6	no	—
63	#470	—	86	6	no	—
64	#462	—	86	6	no	—
65	#423	C₂×D₄₃	1	3	yes	—
66	C₄³	—	43	1	no	—
67	#339	—	86	6	no	—
68	C₄₃	#10303	1	1	yes	characteristic, complemented, Sylow
69	C₂×Q₁₆	—	86	6	no	—
70	C₂×M₁₆	D₁₇₂	1	6	yes	—
71	C₄⋊Q₈	—	43	6	no	—
72	#125	—	86	3	no	—
73	C₂²⋊Q₈	—	86	6	no	—
74	C₄×Q₈	—	86	6	no	—
75	#117	—	86	3	no	—
76	C₂×C₄²	—	86	3	no	—
77	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
78	#106	—	86	6	no	—
79	C₄⋊C₈	—	2	6	no	—
80	#103	—	86	12	no	—
81	C₂×Q₈	—	86	6	no	—
82	C₂²×C₄	—	172	1	no	—
83	C₂²×C₄	C₂×D₁₇₂	1	3	yes	—
84	Q₁₆	—	344	6	no	—
85	M₁₆	—	4	6	no	—
86	C₂×C₈	—	2	6	no	—
87	C₄⋊C₄	—	86	6	no	—
88	C₄⋊C₄	—	86	6	no	—
89	C₄⋊C₄	—	172	6	no	—
90	C₂²⋊C₄	—	172	3	no	—
91	C₄²	—	86	6	no	—
92	C₄²	—	172	3	no	—
93	C₄²	—	172	3	no	—
94	C₄²	D₄×D₄₃	1	3	yes	—
95	C₄²	#10621902	1	1	yes	characteristic
96	C₂³	#13063322	1	1	yes	characteristic
97	Q₈	—	172	6	no	—
98	Q₈	—	172	6	no	—
99	C₂×C₄	—	2	3	no	—
100	C₂×C₄	—	2	3	no	—
101	C₂×C₄	—	172	6	no	—
102	C₂×C₄	—	172	6	no	—
103	C₂×C₄	#13063295	1	3	yes	—
104	C₂×C₄	#13063300	1	3	yes	—
105	C₈	—	4	6	no	—
106	C₂²	—	2	3	no	—
107	C₂²	#14582809	1	1	yes	characteristic
108	C₄	—	2	3	no	—
109	C₄	—	344	6	no	—
110	C₄	—	172	4	no	—
111	C₄	#14583079	1	3	yes	—
112	C₄	#14583084	1	3	yes	—
113	C₂	—	4	1	no	—
114	C₂	#19135644	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19145989

C₂

yes

maximal

#19135571

C₂

yes

maximal

C₄₃×#1309

C₂

yes

maximal, characteristic

#14583456

C₂²

yes

—

#14583185

—

#14583157

—

#14583110

—

C₄²×Dic₄₃

C₂²

yes

characteristic

#14582660

—

C₄₃×#423

C₂²

yes

—

C₂×Dic₁₇₂

—

#13063325

D₄

yes

—

#13063317

—

#13063304

—

C₄×Dic₈₆

—

#13063284

—

C₂×C₄×Dic₄₃

—

#13063257

—

#13063250

—

C₂×M₁₆×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

C₂×D₄

yes

—

C₄²×C₄₃

#41

yes

characteristic

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

Dic₁₇₂

—

C₂³×C₄₃

#127

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#120

yes

—

C₂×C₄×C₄₃

#121

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

#10303

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

#392

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

#455

yes

—

C₄×C₄₃

#456

yes

—

Dic₄₃

—

Dic₄₃

—

#3255

—

#1994

—

#1309

D₄₃

yes

characteristic

C₂×C₄₃

—

C₂×C₄₃

#2007

yes

—

—

—

—

—

C₂×D₄₃

yes

—

C₄³

—

#339

—

C₄₃

#10303

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×M₁₆

D₁₇₂

yes

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₄₃

yes

characteristic

#106

—

C₄⋊C₈

—

#103

—

C₂×Q₈

—

C₂²×C₄

—

172

—

C₂²×C₄

C₂×D₁₇₂

yes

—

Q₁₆

—

344

—

M₁₆

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₂²⋊C₄

—

172

—

C₄²

—

C₄²

—

172

—

C₄²

—

172

—

C₄²

D₄×D₄₃

yes

—

C₄²

yes

C₂³

yes

Q₈

—

172

—

Q₈

—

172

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

172

—

102

C₂×C₄

—

172

—

103

C₂×C₄

#13063295

yes

—

104

C₂×C₄

#13063300

yes

—

105

C₈

—

106

C₂²

—

107

C₂²

#14582809

yes

characteristic

108

C₄

—

109

C₄

—

344

—

110

C₄

—

172

—

111

C₄

#14583079

yes

—

112

C₄

#14583084

yes

—

113

C₂

—

114

C₂

#19135644

yes

—

	subgroup	G/H
center	C₂²	#14582809
commutator, cosocle	C₂×C₄²×C₄₃	C₂³
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1309	C₂
socle	C₂²×C₄₃	#392
prime radical	C₂³×C₄₃	#127
hypercenter	#1309	D₄₃
hypocenter	C₄₃	#10303
LCS	G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1309

subgroup

G/H

center

C₂²

#14582809

commutator, cosocle

C₂×C₄²×C₄₃

C₂³

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1309

C₂

C₂²×C₄₃

C₂³×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1309

N	H ≅ G/N	type
68. C₄₃	#10303	semidirect

H ≅ G/N

type

68. C₄₃

#10303

semidirect

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

subgroup	index
#19145989	2
#19135571	2
C₄₃×#1309	2
#10303	43

subgroup

index

#19145989

#19135571

C₄₃×#1309

#10303

Subgroups — #24999363

Conjugacy classes of subgroups

Complements

Maximal subgroups