Group #16820457 — subgroups

Subgroups — #16820457

Order 3712.

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

normal subgroups only

This group has 252 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	#14271029	C₂	1	1	yes	maximal, characteristic
3	#14270926	C₂	1	4	yes	maximal
4	C₂×C₄×C₈×C₂₉	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	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₂₉	C₂²	1	2	yes	—
9	C₂×#90779	—	2	2	no	—
10	#11745232	—	2	2	no	—
11	#11745232	C₄	1	4	yes	complemented
12	C₄×C₈×C₂₉	—	2	2	no	—
13	#11745179	—	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	C₂×C₄	1	4	yes	—
26	#90779	—	2	8	no	—
27	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₂₉	—	2	4	no	—
29	C₂×C₄×C₂₉	C₂²⋊C₄	1	4	yes	—
30	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₂₉	C₂×Q₈	1	2	yes	—
33	C₂×C₄×C₂₉	#41	1	2	yes	—
34	C₂×Dic₂₉	—	2	4	no	—
35	C₂×Dic₂₉	—	4	4	no	—
36	C₂×Dic₂₉	—	4	2	no	—
37	C₂×Dic₂₉	—	4	4	no	—
38	C₈×C₂₉	—	2	4	no	—
39	#1991	—	29	1	no	maximal, Sylow
40	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
41	C₂²×C₂₉	#124	1	1	yes	characteristic
42	C₂²×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
43	C₂²×C₂₉	#135	1	4	yes	—
44	C₄×C₂₉	—	2	4	no	—
45	C₄×C₂₉	C₄×Q₈	1	2	yes	—
46	C₄×C₂₉	C₂²⋊Q₈	1	2	yes	—
47	Dic₂₉	—	4	4	no	—
48	Dic₂₉	—	8	2	no	—
49	C₂×#125	—	29	1	no	—
50	C₂×C₄×C₈	D₂₉	1	1	yes	characteristic
51	#382	—	29	1	no	—
52	#340	—	29	4	no	—
53	C₂×C₂₉	#391	1	1	yes	characteristic
54	C₂×C₂₉	#416	1	2	yes	—
55	C₂×C₂₉	#488	1	2	yes	—
56	C₂×C₂₉	#499	1	2	yes	—
57	C₂²×C₈	C₂×D₂₉	1	2	yes	—
58	#125	—	29	4	no	—
59	#125	—	58	2	no	—
60	C₂×C₄⋊C₄	—	29	2	no	—
61	C₂×C₄⋊C₄	—	29	2	no	—
62	C₂×C₄⋊C₄	—	58	2	no	—
63	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
64	C₄×C₈	—	2	2	no	—
65	#95	—	58	2	no	—
66	C₂₉	#1991	1	1	yes	characteristic, complemented, Sylow
67	C₂²×C₄	—	58	2	no	—
68	C₂²×C₄	—	58	2	no	—
69	C₂²×C₄	D₁₁₆	1	2	yes	—
70	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
71	C₂×C₈	—	2	2	no	—
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	Dic₅₈	1	4	yes	—
74	C₄⋊C₄	—	29	4	no	—
75	C₄⋊C₄	—	58	8	no	—
76	C₄⋊C₄	—	58	2	no	—
77	C₄⋊C₄	—	58	4	no	—
78	C₄²	C₄×D₂₉	1	2	yes	—
79	C₄²	C₂²⋊D₂₉	1	2	yes	—
80	C₂³	C₂×D₁₁₆	1	1	yes	characteristic
81	C₂×C₄	—	2	4	no	—
82	C₂×C₄	—	58	4	no	—
83	C₂×C₄	—	116	4	no	—
84	C₂×C₄	—	116	2	no	—
85	C₂×C₄	—	116	4	no	—
86	C₂×C₄	#90781	1	4	yes	—
87	C₂×C₄	C₂×Dic₅₈	1	2	yes	—
88	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
89	C₂×C₄	#90805	1	2	yes	—
90	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
91	C₈	—	2	4	no	—
92	C₂²	#11745231	1	1	yes	characteristic
93	C₂²	#11745237	1	1	yes	characteristic
94	C₂²	#11745266	1	4	yes	—
95	C₂²	C₂×#90781	1	1	yes	characteristic
96	C₄	—	2	4	no	—
97	C₄	—	116	4	no	—
98	C₄	—	232	2	no	—
99	C₄	C₄×Dic₅₈	1	2	yes	—
100	C₄	#11745286	1	2	yes	—
101	C₂	#14271069	1	1	yes	characteristic
102	C₂	#14271160	1	2	yes	—
103	C₂	#14271518	1	2	yes	—
104	C₂	#14271565	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745232

C₂

yes

maximal, characteristic

#14271029

C₂

yes

maximal, characteristic

#14270926

C₂

yes

maximal

C₂×C₄×C₈×C₂₉

C₂

yes

maximal, characteristic

C₂²×C₈×C₂₉

C₂²

yes

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₂₉

C₂²

yes

—

C₂×C₄⋊Dic₂₉

C₂²

yes

—

C₂×#90779

—

#11745232

—

#11745232

C₄

yes

complemented

C₄×C₈×C₂₉

—

#11745179

—

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

C₂×C₄

yes

—

#90779

—

C₂³×C₂₉

C₂×D₄

yes

characteristic

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

—

C₈×C₂₉

—

#1991

—

maximal, Sylow

C₂²×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₂₉

#124

yes

characteristic

C₂²×C₂₉

C₄⋊Q₈

yes

characteristic

C₂²×C₂₉

#135

yes

—

C₄×C₂₉

—

C₄×C₂₉

C₄×Q₈

yes

—

C₄×C₂₉

C₂²⋊Q₈

yes

—

Dic₂₉

—

Dic₂₉

—

C₂×#125

—

C₂×C₄×C₈

D₂₉

yes

characteristic

#382

—

#340

—

C₂×C₂₉

#391

yes

characteristic

C₂×C₂₉

#416

yes

—

C₂×C₂₉

#488

yes

—

C₂×C₂₉

#499

yes

—

C₂²×C₈

C₂×D₂₉

yes

—

#125

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

C₄×C₈

—

#95

—

C₂₉

#1991

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

—

C₄²

C₄×D₂₉

yes

—

C₄²

C₂²⋊D₂₉

yes

—

C₂³

C₂×D₁₁₆

yes

characteristic

C₂×C₄

—

C₂×C₄

—

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

—

C₂²

yes

C₂²

yes

C₂²

yes

—

C₂²

C₂×#90781

yes

characteristic

C₄

—

C₄

—

116

—

C₄

—

232

—

C₄

C₄×Dic₅₈

yes

—

100

C₄

#11745286

yes

—

101

C₂

#14271069

yes

characteristic

102

C₂

#14271160

yes

—

103

C₂

#14271518

yes

—

104

C₂

#14271565

yes

—

	subgroup	G/H
center	C₂³	C₂×D₁₁₆
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂×C₄×C₈×C₂₉	C₂
socle, prime radical	C₂³×C₂₉	C₂×D₄
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	C₂×C₄×C₈	D₂₉
hypocenter	C₂₉	#1991
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂³

C₂×D₁₁₆

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂×C₄×C₈×C₂₉

C₂

socle, prime radical

C₂³×C₂₉

C₂×D₄

cosocle

C₂²×C₄×C₂₉

C₂³

hypercenter

C₂×C₄×C₈

D₂₉

hypocenter

C₂₉

#1991

LCS

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
11. #11745232	C₄	semidirect
66. C₂₉	#1991	semidirect

H ≅ G/N

type

11. #11745232

C₄

semidirect

66. C₂₉

#1991

semidirect

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

subgroup	index
C₂×#11745232	2
#14271029	2
#14270926	2
C₂×C₄×C₈×C₂₉	2
#1991	29

subgroup

index

C₂×C₄×C₈×C₂₉

Subgroups — #16820457

Conjugacy classes of subgroups

Complements

Maximal subgroups