Group #16818206 — subgroups

Subgroups — #16818206

Order 3712.

332 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 85 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	#14271220	C₂	1	2	yes	maximal, complemented
2	#14270907	C₂	1	4	yes	maximal, complemented
3	C₂×C₂₉×#127	C₂	1	1	yes	maximal, characteristic
4	C₂²×D₄×C₂₉	—	2	2	no	—
5	C₂²×D₄×C₂₉	C₄	1	2	yes	—
6	C₂₉×#127	—	2	2	no	—
7	C₂₉×#127	C₄	1	2	yes	—
8	C₂₉×#127	C₂²	1	2	yes	—
9	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
10	C₂²⋊#6597	—	2	2	no	—
11	C₄⋊#6597	C₂²	1	4	yes	complemented
12	#11745151	—	2	2	no	—
13	C₂⁴×C₂₉	—	2	2	no	—
14	C₂×D₄×C₂₉	—	2	2	no	—
15	C₂×D₄×C₂₉	—	2	4	no	—
16	C₂×D₄×C₂₉	—	2	4	no	—
17	C₂×D₄×C₂₉	—	4	4	no	—
18	C₂×D₄×C₂₉	—	4	8	no	—
19	C₂×D₄×C₂₉	C₂×C₄	1	4	yes	—
20	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₄×C₂₉	D₄	1	2	yes	—
22	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
23	C₄²×C₂₉	D₄	1	2	yes	—
24	C₄²×C₂₉	C₂³	1	1	yes	characteristic
25	C₂×#6597	—	2	4	no	—
26	C₂³×C₂₉	—	2	4	no	—
27	C₂³×C₂₉	—	4	8	no	—
28	C₂³×C₂₉	—	4	4	no	—
29	C₂³×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
30	D₄×C₂₉	—	4	4	no	—
31	D₄×C₂₉	—	4	4	no	—
32	D₄×C₂₉	—	4	8	no	—
33	D₄×C₂₉	—	4	8	no	—
34	C₂×C₄×C₂₉	—	2	2	no	—
35	C₂×C₄×C₂₉	—	2	4	no	—
36	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
37	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
38	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
40	#6597	—	4	4	no	—
41	#1555	—	29	1	no	maximal, Sylow
42	C₂²×C₂₉	—	2	2	no	—
43	C₂²×C₂₉	—	4	4	no	—
44	C₂²×C₂₉	—	4	8	no	—
45	C₂²×C₂₉	—	8	8	no	—
46	C₂²×C₂₉	#100	1	2	yes	—
47	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
48	C₄×C₂₉	—	2	1	no	—
49	C₄×C₂₉	—	2	1	no	—
50	C₄×C₂₉	—	2	2	no	—
51	C₄×C₂₉	AGL(1,ℤ/8)	1	4	yes	—
52	C₂×#127	D₂₉	1	1	yes	characteristic
53	#432	—	29	2	no	—
54	#331	—	29	4	no	—
55	C₂×C₂₉	—	2	2	no	—
56	C₂×C₂₉	—	8	4	no	—
57	C₂×C₂₉	C₂×#100	1	1	yes	characteristic
58	C₂×C₂₉	#418	1	2	yes	—
59	C₂²×D₄	—	2	2	no	—
60	C₂²×D₄	Dic₂₉	1	2	yes	—
61	#127	—	2	2	no	—
62	#127	Dic₂₉	1	2	yes	—
63	#127	C₂×D₂₉	1	2	yes	—
64	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
65	C₄⋊C₈	—	29	4	no	—
66	C₂²⋊C₈	—	58	2	no	—
67	#97	—	58	2	no	—
68	C₂₉	#1555	1	1	yes	characteristic, complemented, Sylow
69	C₂⁴	—	2	2	no	—
70	C₂×D₄	—	2	2	no	—
71	C₂×D₄	—	2	4	no	—
72	C₂×D₄	—	2	4	no	—
73	C₂×D₄	—	4	4	no	—
74	C₂×D₄	—	4	8	no	—
75	C₂×D₄	C₂×Dic₂₉	1	4	yes	—
76	C₂²×C₄	C₂×Dic₂₉	1	1	yes	characteristic
77	C₂²×C₄	C₂²⋊D₂₉	1	2	yes	—
78	C₂×C₈	—	58	4	no	—
79	C₄²	C₂×Dic₂₉	1	1	yes	characteristic
80	C₄²	C₂²⋊D₂₉	1	2	yes	—
81	C₄²	C₂²×D₂₉	1	1	yes	characteristic
82	C₂³	—	2	4	no	—
83	C₂³	—	4	8	no	—
84	C₂³	—	4	4	no	—
85	C₂³	C₂²⋊Dic₂₉	1	1	yes	characteristic
86	D₄	—	4	4	no	—
87	D₄	—	4	4	no	—
88	D₄	—	4	8	no	—
89	D₄	—	4	8	no	—
90	C₂×C₄	—	2	2	no	—
91	C₂×C₄	—	2	4	no	—
92	C₂×C₄	C₂²⋊Dic₂₉	1	2	yes	—
93	C₂×C₄	C₂²⋊Dic₂₉	1	1	yes	characteristic
94	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
95	C₂×C₄	C₂×C₂²⋊D₂₉	1	2	yes	—
96	C₈	—	116	4	no	—
97	C₂²	—	2	2	no	—
98	C₂²	—	4	4	no	—
99	C₂²	—	4	8	no	—
100	C₂²	—	8	8	no	—
101	C₂²	#11745181	1	2	yes	—
102	C₂²	C₂×C₂²⋊Dic₂₉	1	1	yes	characteristic
103	C₄	—	2	1	no	—
104	C₄	—	2	1	no	—
105	C₄	—	2	2	no	—
106	C₄	#11745294	1	4	yes	—
107	C₂	—	2	2	no	—
108	C₂	—	8	4	no	—
109	C₂	C₂×#11745181	1	1	yes	characteristic
110	C₂	#14271168	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14271220

C₂

yes

maximal, complemented

#14270907

C₂

yes

maximal, complemented

C₂×C₂₉×#127

C₂

yes

maximal, characteristic

C₂²×D₄×C₂₉

—

C₂²×D₄×C₂₉

C₄

yes

—

C₂₉×#127

—

C₂₉×#127

C₄

yes

—

C₂₉×#127

C₂²

yes

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂²⋊#6597

—

C₄⋊#6597

C₂²

yes

complemented

#11745151

—

C₂⁴×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₉

D₄

yes

—

C₄²×C₂₉

C₂×C₄

yes

characteristic

C₄²×C₂₉

D₄

yes

—

C₄²×C₂₉

C₂³

yes

characteristic

C₂×#6597

—

C₂³×C₂₉

—

C₂³×C₂₉

—

C₂³×C₂₉

—

C₂³×C₂₉

C₂²⋊C₄

yes

characteristic

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²⋊C₄

yes

—

C₂×C₄×C₂₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

—

#6597

—

#1555

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

#100

yes

—

C₂²×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

AGL(1,ℤ/8)

yes

—

C₂×#127

D₂₉

yes

characteristic

#432

—

#331

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

C₂×#100

yes

characteristic

C₂×C₂₉

#418

yes

—

C₂²×D₄

—

C₂²×D₄

Dic₂₉

yes

—

#127

—

#127

Dic₂₉

yes

—

#127

C₂×D₂₉

yes

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₂₉

#1555

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

C₂×Dic₂₉

yes

—

C₂²×C₄

C₂×Dic₂₉

yes

characteristic

C₂²×C₄

C₂²⋊D₂₉

yes

—

C₂×C₈

—

C₄²

C₂×Dic₂₉

yes

characteristic

C₄²

C₂²⋊D₂₉

yes

—

C₄²

C₂²×D₂₉

yes

characteristic

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂²⋊Dic₂₉

yes

characteristic

D₄

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊Dic₂₉

yes

—

C₂×C₄

C₂²⋊Dic₂₉

yes

characteristic

C₂×C₄

C₂²×Dic₂₉

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₂₉

yes

—

C₈

—

116

—

C₂²

—

C₂²

—

C₂²

—

100

C₂²

—

101

C₂²

#11745181

yes

—

102

C₂²

C₂×C₂²⋊Dic₂₉

yes

characteristic

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

#11745294

yes

—

107

C₂

—

108

C₂

—

109

C₂

C₂×#11745181

yes

characteristic

110

C₂

#14271168

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊Dic₂₉
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₄²	C₂²×D₂₉
Fitting, prime radical	C₂×C₂₉×#127	C₂
socle	C₂²×C₂₉	C₂×C₂²⋊C₄
cosocle	C₄²×C₂₉	C₂³
hypercenter	C₂×#127	D₂₉
hypocenter	C₂₉	#1555
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#127

subgroup

G/H

center

C₂²

C₂×C₂²⋊Dic₂₉

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₄²

C₂²×D₂₉

Fitting, prime radical

C₂×C₂₉×#127

C₂

socle

C₂²×C₂₉

C₂×C₂²⋊C₄

cosocle

C₄²×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#127

N	H ≅ G/N	type
1. #14271220	C₂	semidirect
2. #14270907	C₂	semidirect
11. C₄⋊#6597	C₂²	semidirect
68. C₂₉	#1555	semidirect

H ≅ G/N

type

1. #14271220

C₂

semidirect

2. #14270907

C₂

semidirect

11. C₄⋊#6597

C₂²

semidirect

68. C₂₉

#1555

semidirect

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

subgroup	index
#14271220	2
#14270907	2
C₂×C₂₉×#127	2
#1555	29

subgroup

index

#14271220

#14270907

C₂×C₂₉×#127

#1555

Subgroups — #16818206

Conjugacy classes of subgroups

Complements

Maximal subgroups