Group #16820461 — subgroups

Subgroups — #16820461

Order 3712.

260 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 109 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	C₂×#11745232	C₂	1	1	yes	maximal, characteristic
2	#14271033	C₂	1	1	yes	maximal, characteristic
3	#14270926	C₂	1	4	yes	maximal
4	C₂×C₂₉×#97	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₈×C₂₉	C₂²	1	2	yes	—
6	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₂₉	—	2	2	no	—
8	C₂×C₄⋊Dic₂₉	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₂₉	C₂²	1	2	yes	—
10	C₂×#90779	—	2	2	no	—
11	#11745232	—	2	2	no	—
12	#11745232	C₄	1	4	yes	complemented
13	C₂₉×#97	—	2	2	no	—
14	C₂²×C₄×C₂₉	D₄	1	2	yes	—
15	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
16	C₂²×Dic₂₉	—	2	2	no	—
17	C₂²×Dic₂₉	—	2	2	no	—
18	C₂×C₈×C₂₉	—	2	2	no	—
19	C₂×C₈×C₂₉	—	2	2	no	—
20	C₂×C₈×C₂₉	Q₈	1	4	yes	—
21	C₄²×C₂₉	C₂×C₄	1	2	yes	—
22	C₄²×C₂₉	D₄	1	2	yes	—
23	C₄⋊Dic₂₉	—	2	2	no	—
24	C₄⋊Dic₂₉	—	2	4	no	—
25	C₄⋊Dic₂₉	—	4	4	no	—
26	C₄⋊Dic₂₉	C₂×C₄	1	4	yes	—
27	#90779	—	2	8	no	—
28	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₂₉	—	2	2	no	—
30	C₂×C₄×C₂₉	—	2	2	no	—
31	C₂×C₄×C₂₉	C₂²⋊C₄	1	4	yes	—
32	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₂₉	C₂×Q₈	1	2	yes	—
35	C₂×C₄×C₂₉	#41	1	2	yes	—
36	C₂×Dic₂₉	—	2	4	no	—
37	C₂×Dic₂₉	—	4	2	no	—
38	C₂×Dic₂₉	—	4	2	no	—
39	C₂×Dic₂₉	—	4	2	no	—
40	C₂×Dic₂₉	—	4	4	no	—
41	C₈×C₂₉	—	2	4	no	—
42	#1992	—	29	1	no	maximal, Sylow
43	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
44	C₂²×C₂₉	#124	1	1	yes	characteristic
45	C₂²×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
46	C₂²×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
47	C₂²×C₂₉	#137	1	2	yes	—
48	C₄×C₂₉	—	2	4	no	—
49	C₄×C₂₉	C₄×Q₈	1	2	yes	—
50	C₄×C₂₉	C₂²⋊Q₈	1	2	yes	—
51	Dic₂₉	—	4	4	no	—
52	Dic₂₉	—	8	2	no	—
53	C₂×#125	—	29	1	no	—
54	C₂×#97	D₂₉	1	1	yes	characteristic
55	#384	—	29	1	no	—
56	#340	—	29	4	no	—
57	C₂×C₂₉	#391	1	1	yes	characteristic
58	C₂×C₂₉	#417	1	2	yes	—
59	C₂×C₂₉	#490	1	1	yes	characteristic
60	C₂×C₂₉	#491	1	1	yes	characteristic
61	C₂×C₂₉	#501	1	2	yes	—
62	C₂²×C₈	C₂×D₂₉	1	2	yes	—
63	#125	—	29	4	no	—
64	#125	—	58	2	no	—
65	C₂×C₄⋊C₄	—	29	2	no	—
66	C₂×C₄⋊C₄	—	29	2	no	—
67	C₂×C₄⋊C₄	—	58	2	no	—
68	C₂×C₄⋊C₄	—	58	2	no	—
69	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
70	#97	—	2	2	no	—
71	C₂₉	#1992	1	1	yes	characteristic, complemented, Sylow
72	C₂²×C₄	—	58	2	no	—
73	C₂²×C₄	—	58	2	no	—
74	C₂²×C₄	D₁₁₆	1	2	yes	—
75	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
76	C₂×C₈	—	2	2	no	—
77	C₂×C₈	—	2	2	no	—
78	C₂×C₈	Dic₅₈	1	4	yes	—
79	C₄⋊C₄	—	29	4	no	—
80	C₄⋊C₄	—	58	8	no	—
81	C₄⋊C₄	—	58	2	no	—
82	C₄⋊C₄	—	58	4	no	—
83	C₄⋊C₄	—	116	4	no	—
84	C₄²	C₄×D₂₉	1	2	yes	—
85	C₄²	C₂²⋊D₂₉	1	2	yes	—
86	C₂³	C₂×D₁₁₆	1	1	yes	characteristic
87	C₂×C₄	—	2	2	no	—
88	C₂×C₄	—	2	2	no	—
89	C₂×C₄	—	58	4	no	—
90	C₂×C₄	—	116	2	no	—
91	C₂×C₄	—	116	2	no	—
92	C₂×C₄	—	116	2	no	—
93	C₂×C₄	—	116	4	no	—
94	C₂×C₄	#90781	1	4	yes	—
95	C₂×C₄	C₂×Dic₅₈	1	2	yes	—
96	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
97	C₂×C₄	#90805	1	2	yes	—
98	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
99	C₈	—	2	4	no	—
100	C₂²	#11745231	1	1	yes	characteristic
101	C₂²	#11745237	1	1	yes	characteristic
102	C₂²	#11745270	1	2	yes	—
103	C₂²	#11745271	1	2	yes	—
104	C₂²	C₂×#90781	1	1	yes	characteristic
105	C₄	—	2	4	no	—
106	C₄	—	116	4	no	—
107	C₄	—	232	2	no	—
108	C₄	C₄×Dic₅₈	1	2	yes	—
109	C₄	#11745286	1	2	yes	—
110	C₂	#14271069	1	1	yes	characteristic
111	C₂	#14271165	1	2	yes	—
112	C₂	#14271528	1	1	yes	characteristic
113	C₂	#14271532	1	1	yes	characteristic
114	C₂	#14271572	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745232

C₂

yes

maximal, characteristic

#14271033

C₂

yes

maximal, characteristic

#14270926

C₂

yes

maximal

C₂×C₂₉×#97

C₂

yes

maximal, characteristic

C₂²×C₈×C₂₉

C₂²

yes

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₂₉

—

C₂×C₄⋊Dic₂₉

C₂²

yes

—

C₂×C₄⋊Dic₂₉

C₂²

yes

—

C₂×#90779

—

#11745232

—

#11745232

C₄

yes

complemented

C₂₉×#97

—

C₂²×C₄×C₂₉

D₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

—

C₂²×Dic₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

Q₈

yes

—

C₄²×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

D₄

yes

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

C₂×C₄

yes

—

#90779

—

C₂³×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²⋊C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

—

C₂×C₄×C₂₉

#41

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₈×C₂₉

—

#1992

—

maximal, Sylow

C₂²×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₂₉

#124

yes

characteristic

C₂²×C₂₉

C₄⋊Q₈

yes

characteristic

C₂²×C₂₉

AGL(1,ℤ/8)

yes

—

C₂²×C₂₉

#137

yes

—

C₄×C₂₉

—

C₄×C₂₉

C₄×Q₈

yes

—

C₄×C₂₉

C₂²⋊Q₈

yes

—

Dic₂₉

—

Dic₂₉

—

C₂×#125

—

C₂×#97

D₂₉

yes

characteristic

#384

—

#340

—

C₂×C₂₉

#391

yes

characteristic

C₂×C₂₉

#417

yes

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

—

C₂²×C₈

C₂×D₂₉

yes

—

#125

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

#97

—

C₂₉

#1992

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₁₁₆

yes

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₅₈

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

116

—

C₄²

C₄×D₂₉

yes

—

C₄²

C₂²⋊D₂₉

yes

—

C₂³

C₂×D₁₁₆

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

116

—

C₂×C₄

—

116

—

C₂×C₄

—

116

—

C₂×C₄

—

116

—

C₂×C₄

#90781

yes

—

C₂×C₄

C₂×Dic₅₈

yes

—

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

C₂×C₄

#90805

yes

—

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

C₈

—

100

C₂²

#11745231

yes

characteristic

101

C₂²

#11745237

yes

characteristic

102

C₂²

#11745270

yes

—

103

C₂²

#11745271

yes

—

104

C₂²

C₂×#90781

yes

characteristic

105

C₄

—

106

C₄

—

116

—

107

C₄

—

232

—

108

C₄

C₄×Dic₅₈

yes

—

109

C₄

#11745286

yes

—

110

C₂

#14271069

yes

characteristic

111

C₂

#14271165

yes

—

112

C₂

#14271528

yes

characteristic

113

C₂

#14271532

yes

characteristic

114

C₂

#14271572

yes

—

	subgroup	G/H
center	C₂³	C₂×D₁₁₆
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂×C₂₉×#97	C₂
socle, prime radical	C₂³×C₂₉	C₂×D₄
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	C₂×#97	D₂₉
hypocenter	C₂₉	#1992
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

subgroup

G/H

center

C₂³

C₂×D₁₁₆

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂×C₂₉×#97

C₂

socle, prime radical

C₂³×C₂₉

C₂×D₄

cosocle

C₂²×C₄×C₂₉

C₂³

hypercenter

C₂×#97

D₂₉

hypocenter

C₂₉

#1992

LCS

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

N	H ≅ G/N	type
12. #11745232	C₄	semidirect
71. C₂₉	#1992	semidirect

H ≅ G/N

type

12. #11745232

C₄

semidirect

71. C₂₉

#1992

semidirect

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

subgroup	index
C₂×#11745232	2
#14271033	2
#14270926	2
C₂×C₂₉×#97	2
#1992	29

subgroup

index

C₂×C₂₉×#97

Subgroups — #16820461

Conjugacy classes of subgroups

Complements

Maximal subgroups