Group #25005635 — subgroups

Subgroups — #25005635

Order 11008.

260 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 131 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	#19136392	C₂	1	2	yes	maximal
2	#19132877	C₂	1	1	yes	maximal, characteristic
3	#19132514	C₂	1	2	yes	maximal, complemented
4	C₈×C₄₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#1311	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582950	C₄	1	2	yes	—
7	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
8	Dic₄₃⋊C₁₆	C₄	1	4	yes	—
9	(C₂×D₄₃)⋊C₁₆	C₄	1	4	yes	—
10	C₄×C₄₃⋊C₁₆	C₂²	1	2	yes	—
11	#14582621	C₄	1	2	yes	—
12	C₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
13	C₄×C₁₆×C₄₃	C₂²	1	2	yes	—
14	C₈²×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×C₈×D₄₃	C₂×C₄	1	2	yes	—
16	C₄²×D₄₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄₃⋊C₁₆	C₂×C₄	1	4	yes	—
18	Dic₄₃⋊C₈	C₈	1	4	yes	—
19	(C₂×D₄₃)⋊C₈	C₈	1	4	yes	—
20	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
21	C₄×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
22	C₈×Dic₄₃	C₂×C₄	1	2	yes	—
23	C₂×C₁₆×C₄₃	C₂×C₄	1	4	yes	—
24	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
25	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
26	C₂×C₄×D₄₃	C₄²	1	1	yes	characteristic
27	C₂×C₄×D₄₃	C₂×C₈	1	2	yes	—
28	C₂×C₈×C₄₃	C₂×C₈	1	4	yes	—
29	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
30	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
31	C₄×Dic₄₃	C₄²	1	1	yes	characteristic
32	C₄×Dic₄₃	C₂×C₈	1	2	yes	—
33	C₂×C₄₃⋊C₈	C₄²	1	2	yes	—
34	C₂×C₄₃⋊C₈	C₂×C₈	1	4	yes	—
35	C₈×D₄₃	—	2	4	no	—
36	C₁₆×C₄₃	—	2	4	no	—
37	C₄₃⋊C₁₆	—	2	4	no	—
38	C₂²×D₄₃	C₄×C₈	1	1	yes	characteristic
39	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
40	C₂×C₄×C₄₃	C₂²×C₈	1	2	yes	—
41	C₂×Dic₄₃	C₄×C₈	1	2	yes	—
42	C₂×Dic₄₃	C₄×C₈	1	1	yes	characteristic
43	C₄×D₄₃	—	2	2	no	—
44	C₄×D₄₃	—	2	4	no	—
45	C₈×C₄₃	—	2	4	no	—
46	C₈×C₄₃	#131	1	4	yes	—
47	C₄₃⋊C₈	—	2	2	no	—
48	C₄₃⋊C₈	—	2	4	no	—
49	#11412	—	43	1	no	maximal, Sylow
50	C₂²×C₄₃	C₂×C₄×C₈	1	1	yes	characteristic
51	C₂×D₄₃	—	2	2	no	—
52	C₂×D₄₃	—	2	1	no	—
53	C₄×C₄₃	#405	1	2	yes	—
54	C₄×C₄₃	#504	1	4	yes	—
55	Dic₄₃	—	2	2	no	—
56	Dic₄₃	—	2	1	no	—
57	#2162	—	43	2	no	—
58	#1450	—	43	1	no	—
59	#1312	—	43	2	no	—
60	#1311	D₄₃	1	1	yes	characteristic, complemented
61	C₈×C₁₆	—	43	1	no	—
62	C₂×C₄₃	#1450	1	1	yes	characteristic
63	C₂×C₄₃	#2108	1	2	yes	—
64	D₄₃	—	4	1	no	—
65	#431	—	43	2	no	—
66	C₂×C₄×C₈	—	43	1	no	—
67	C₄⋊C₁₆	—	43	4	no	—
68	C₂²⋊C₁₆	—	43	4	no	—
69	C₄×C₁₆	—	43	2	no	—
70	C₄×C₁₆	C₂×D₄₃	1	2	yes	—
71	#322	—	43	2	no	—
72	C₈²	—	43	1	no	—
73	C₈²	C₂×D₄₃	1	1	yes	characteristic
74	C₄₃	#11412	1	1	yes	characteristic, complemented, Sylow
75	C₂²×C₈	—	43	2	no	—
76	C₂×C₄²	—	43	1	no	—
77	C₂×C₁₆	—	43	4	no	—
78	C₂×C₁₆	C₄×D₄₃	1	4	yes	—
79	C₄⋊C₈	—	43	4	no	—
80	C₂²⋊C₈	—	43	4	no	—
81	C₄×C₈	—	43	2	no	—
82	C₄×C₈	—	43	2	no	—
83	C₄×C₈	—	43	1	no	—
84	C₄×C₈	C₄×D₄₃	1	2	yes	—
85	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
86	C₂²×C₄	—	43	1	no	—
87	C₂²×C₄	—	43	2	no	—
88	C₂×C₈	—	43	2	no	—
89	C₂×C₈	—	43	4	no	—
90	C₂×C₈	—	86	4	no	—
91	C₂×C₈	C₈×D₄₃	1	4	yes	—
92	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
93	C₄²	—	43	1	no	—
94	C₄²	—	43	2	no	—
95	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
96	C₁₆	—	2	4	no	—
97	C₁₆	—	86	4	no	—
98	C₂³	—	43	1	no	—
99	C₂×C₄	—	43	2	no	—
100	C₂×C₄	—	43	1	no	—
101	C₂×C₄	—	86	4	no	—
102	C₂×C₄	—	86	2	no	—
103	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
104	C₂×C₄	C₂×C₈×D₄₃	1	2	yes	—
105	C₈	—	2	4	no	—
106	C₈	—	86	4	no	—
107	C₈	—	86	2	no	—
108	C₈	#13063331	1	4	yes	—
109	C₂²	—	86	2	no	—
110	C₂²	—	86	1	no	—
111	C₂²	C₄×C₈×D₄₃	1	1	yes	characteristic
112	C₄	—	86	2	no	—
113	C₄	—	86	1	no	—
114	C₄	#14582853	1	2	yes	—
115	C₄	#14583317	1	4	yes	—
116	C₂	—	172	1	no	—
117	C₂	#19132877	1	1	yes	characteristic
118	C₂	#19136193	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19136392

C₂

yes

maximal

#19132877

C₂

yes

maximal, characteristic

#19132514

C₂

yes

maximal, complemented

C₈×C₄₃⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₄₃×#1311

C₂

yes

maximal, characteristic, complemented

#14582950

C₄

yes

—

C₄×C₈×D₄₃

C₂²

yes

characteristic

Dic₄₃⋊C₁₆

C₄

yes

—

(C₂×D₄₃)⋊C₁₆

C₄

yes

—

C₄×C₄₃⋊C₁₆

C₂²

yes

—

#14582621

C₄

yes

—

C₈×C₄₃⋊C₈

C₂²

yes

characteristic

C₄×C₁₆×C₄₃

C₂²

yes

—

C₈²×C₄₃

C₂²

yes

characteristic

C₂×C₈×D₄₃

C₂×C₄

yes

—

C₄²×D₄₃

C₂×C₄

yes

characteristic

C₂×C₄₃⋊C₁₆

C₂×C₄

yes

—

Dic₄₃⋊C₈

C₈

yes

—

(C₂×D₄₃)⋊C₈

C₈

yes

—

C₄×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₄×C₄₃⋊C₈

C₂×C₄

yes

—

C₈×Dic₄₃

C₂×C₄

yes

—

C₂×C₁₆×C₄₃

C₂×C₄

yes

—

C₄×C₈×C₄₃

C₂×C₄

yes

—

C₄×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₄×D₄₃

C₄²

yes

characteristic

C₂×C₄×D₄₃

C₂×C₈

yes

—

C₂×C₈×C₄₃

C₂×C₈

yes

—

C₂×C₈×C₄₃

C₂²×C₄

yes

—

C₄²×C₄₃

C₂²×C₄

yes

characteristic

C₄×Dic₄₃

C₄²

yes

characteristic

C₄×Dic₄₃

C₂×C₈

yes

—

C₂×C₄₃⋊C₈

C₄²

yes

—

C₂×C₄₃⋊C₈

C₂×C₈

yes

—

C₈×D₄₃

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂²×D₄₃

C₄×C₈

yes

characteristic

C₂×C₄×C₄₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₈

yes

—

C₂×Dic₄₃

C₄×C₈

yes

—

C₂×Dic₄₃

C₄×C₈

yes

characteristic

C₄×D₄₃

—

C₄×D₄₃

—

C₈×C₄₃

—

C₈×C₄₃

#131

yes

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

#11412

—

maximal, Sylow

C₂²×C₄₃

C₂×C₄×C₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

#405

yes

—

C₄×C₄₃

#504

yes

—

Dic₄₃

—

Dic₄₃

—

—

—

—

D₄₃

yes

characteristic, complemented

C₈×C₁₆

—

C₂×C₄₃

#1450

yes

characteristic

C₂×C₄₃

#2108

yes

—

D₄₃

—

#431

—

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

C₄×C₁₆

—

C₄×C₁₆

C₂×D₄₃

yes

—

#322

—

C₈²

—

C₈²

C₂×D₄₃

yes

characteristic

C₄₃

#11412

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

C₄×D₄₃

yes

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₄×D₄₃

yes

—

C₄×C₈

C₂²×D₄₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₈×D₄₃

yes

—

C₂×C₈

C₂×C₄×D₄₃

yes

—

C₄²

—

C₄²

—

C₄²

C₂×C₄×D₄₃

yes

characteristic

C₁₆

—

C₁₆

—

C₂³

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

C₄²×D₄₃

yes

characteristic

104

C₂×C₄

C₂×C₈×D₄₃

yes

—

105

C₈

—

106

C₈

—

107

C₈

—

108

C₈

#13063331

yes

—

109

C₂²

—

110

C₂²

—

111

C₂²

C₄×C₈×D₄₃

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

#14582853

yes

—

115

C₄

#14583317

yes

—

116

C₂

—

172

—

117

C₂

#19132877

yes

characteristic

118

C₂

#19136193

yes

—

	subgroup	G/H
center, Frattini	C₄×C₈	C₂²×D₄₃
commutator, socle	C₂²×C₄₃	C₂×C₄×C₈
Fitting	C₄₃×#1311	C₂
prime radical	C₂²×D₄₃	C₄×C₈
cosocle	C₄×C₈×C₄₃	C₂³
hypercenter	#1311	D₄₃
hypocenter	C₄₃	#11412
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄×C₈ ◁ #1311

subgroup

G/H

center, Frattini

C₄×C₈

C₂²×D₄₃

commutator, socle

C₂²×C₄₃

C₂×C₄×C₈

Fitting

C₄₃×#1311

C₂

prime radical

C₂²×D₄₃

C₄×C₈

cosocle

C₄×C₈×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₄₃

C₁ ◁ C₄×C₈ ◁ #1311

N	H ≅ G/N	type
3. #19132514	C₂	semidirect
4. C₈×C₄₃⋊C₁₆	C₂	semidirect
5. C₄₃×#1311	C₂	semidirect
60. #1311	D₄₃	semidirect
74. C₄₃	#11412	semidirect

H ≅ G/N

type

3. #19132514

C₂

semidirect

4. C₈×C₄₃⋊C₁₆

C₂

semidirect

5. C₄₃×#1311

C₂

semidirect

60. #1311

D₄₃

semidirect

74. C₄₃

#11412

semidirect

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

subgroup	index
#19136392	2
#19132877	2
#19132514	2
C₈×C₄₃⋊C₁₆	2
C₄₃×#1311	2
#11412	43

subgroup

index

#19136392

#19132877

#19132514

C₈×C₄₃⋊C₁₆

C₄₃×#1311

#11412

Subgroups — #25005635

Conjugacy classes of subgroups

Complements

Maximal subgroups