Group #16819626 — subgroups

Subgroups — #16819626

Order 3712.

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

normal subgroups only

This group has 224 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	#14271033	C₂	1	1	yes	maximal, characteristic
2	#14271029	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	C₂₉×#97	C₄	1	4	yes	complemented
11	#11745179	—	2	2	no	—
12	C₂²×C₄×C₂₉	D₄	1	2	yes	—
13	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
14	C₂²×Dic₂₉	—	2	2	no	—
15	C₂²×Dic₂₉	—	2	2	no	—
16	C₂×C₈×C₂₉	—	2	2	no	—
17	C₂×C₈×C₂₉	—	2	2	no	—
18	C₂×C₈×C₂₉	C₂×C₄	1	4	yes	—
19	C₄²×C₂₉	C₂×C₄	1	2	yes	—
20	C₄²×C₂₉	Q₈	1	2	yes	—
21	C₄⋊Dic₂₉	—	2	4	no	—
22	C₄⋊Dic₂₉	—	2	4	no	—
23	C₄⋊Dic₂₉	—	4	4	no	—
24	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
25	C₂×C₄×C₂₉	—	2	2	no	—
26	C₂×C₄×C₂₉	—	2	2	no	—
27	C₂×C₄×C₂₉	C₄⋊C₄	1	4	yes	—
28	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
30	C₂×C₄×C₂₉	#41	1	2	yes	—
31	C₂×C₄×C₂₉	#41	1	2	yes	—
32	C₂×Dic₂₉	—	4	2	no	—
33	C₂×Dic₂₉	—	4	2	no	—
34	C₂×Dic₂₉	—	4	4	no	—
35	C₂×Dic₂₉	—	4	2	no	—
36	C₂×Dic₂₉	—	4	2	no	—
37	C₈×C₂₉	—	2	4	no	—
38	#1836	—	29	1	no	maximal, Sylow
39	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
40	C₂²×C₂₉	#124	1	1	yes	characteristic
41	C₂²×C₂₉	#124	1	1	yes	characteristic
42	C₂²×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
43	C₂²×C₂₉	#137	1	2	yes	—
44	C₄×C₂₉	—	2	4	no	—
45	C₄×C₂₉	#117	1	2	yes	—
46	C₄×C₂₉	#125	1	2	yes	—
47	Dic₂₉	—	8	2	no	—
48	Dic₂₉	—	8	2	no	—
49	C₂×#97	D₂₉	1	1	yes	characteristic
50	#384	—	29	1	no	—
51	#382	—	29	1	no	—
52	#340	—	29	4	no	—
53	C₂×C₂₉	#382	1	1	yes	characteristic
54	C₂×C₂₉	#428	1	2	yes	—
55	C₂×C₂₉	#489	1	2	yes	—
56	C₂×C₂₉	#490	1	1	yes	characteristic
57	C₂×C₂₉	#491	1	1	yes	characteristic
58	C₂²×C₈	C₂×D₂₉	1	2	yes	—
59	C₂×C₄⋊C₄	—	29	2	no	—
60	C₂×C₄⋊C₄	—	29	2	no	—
61	C₂×C₄⋊C₄	—	58	2	no	—
62	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
63	#97	Dic₂₉	1	4	yes	complemented
64	#95	—	58	2	no	—
65	C₂₉	#1836	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₄	—	58	2	no	—
67	C₂²×C₄	—	58	2	no	—
68	C₂²×C₄	D₁₁₆	1	2	yes	—
69	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
70	C₂×C₈	—	2	2	no	—
71	C₂×C₈	—	2	2	no	—
72	C₂×C₈	C₂×Dic₂₉	1	4	yes	—
73	C₄⋊C₄	—	58	4	no	—
74	C₄⋊C₄	—	58	4	no	—
75	C₄⋊C₄	—	116	4	no	—
76	C₄²	Dic₅₈	1	2	yes	—
77	C₄²	C₂×Dic₂₉	1	2	yes	—
78	C₂³	C₂×D₁₁₆	1	1	yes	characteristic
79	C₂×C₄	—	2	2	no	—
80	C₂×C₄	—	2	2	no	—
81	C₂×C₄	—	116	2	no	—
82	C₂×C₄	—	116	2	no	—
83	C₂×C₄	—	116	4	no	—
84	C₂×C₄	—	116	2	no	—
85	C₂×C₄	—	116	2	no	—
86	C₂×C₄	C₄⋊Dic₂₉	1	4	yes	—
87	C₂×C₄	C₂×Dic₅₈	1	1	yes	characteristic
88	C₂×C₄	#90805	1	2	yes	—
89	C₂×C₄	#90805	1	2	yes	—
90	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
91	C₈	—	2	4	no	—
92	C₂²	#11745237	1	1	yes	characteristic
93	C₂²	#11745237	1	1	yes	characteristic
94	C₂²	#11745270	1	2	yes	—
95	C₂²	#11745271	1	2	yes	—
96	C₂²	C₂×C₄⋊Dic₂₉	1	1	yes	characteristic
97	C₄	—	2	4	no	—
98	C₄	—	232	2	no	—
99	C₄	—	232	2	no	—
100	C₄	#11745232	1	2	yes	—
101	C₄	#11745288	1	2	yes	—
102	C₂	#14271029	1	1	yes	characteristic
103	C₂	#14271205	1	2	yes	—
104	C₂	#14271523	1	2	yes	—
105	C₂	#14271528	1	1	yes	characteristic
106	C₂	#14271532	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271033

C₂

yes

maximal, characteristic

#14271029

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

—

C₂₉×#97

C₄

yes

complemented

#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

C₂×C₄

yes

—

C₄²×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

Q₈

yes

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₂³×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₄⋊C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

#41

yes

—

C₂×C₄×C₂₉

#41

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₈×C₂₉

—

#1836

—

maximal, Sylow

C₂²×C₂₉

C₂×C₄⋊C₄

yes

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₂²×C₂₉

yes

—

C₂²×C₂₉

#137

yes

—

C₄×C₂₉

—

C₄×C₂₉

#117

yes

—

C₄×C₂₉

#125

yes

—

Dic₂₉

—

Dic₂₉

—

C₂×#97

D₂₉

yes

—

—

—

C₂×C₂₉

#382

yes

characteristic

C₂×C₂₉

#428

yes

—

C₂×C₂₉

#489

yes

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂²×C₈

C₂×D₂₉

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

#97

Dic₂₉

yes

complemented

#95

—

C₂₉

#1836

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₁₁₆

yes

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×Dic₂₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

116

—

C₄²

Dic₅₈

yes

—

C₄²

C₂×Dic₂₉

yes

—

C₂³

C₂×D₁₁₆

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

116

—

C₂×C₄

—

116

—

C₂×C₄

—

116

—

C₂×C₄

—

116

—

C₂×C₄

—

116

—

C₂×C₄

C₄⋊Dic₂₉

yes

—

C₂×C₄

C₂×Dic₅₈

yes

characteristic

C₂×C₄

#90805

yes

—

C₂×C₄

#90805

yes

—

C₂×C₄

C₂²×Dic₂₉

yes

characteristic

C₈

—

C₂²

yes

C₂²

yes

C₂²

yes

—

C₂²

#11745271

yes

—

C₂²

C₂×C₄⋊Dic₂₉

yes

characteristic

C₄

—

C₄

—

232

—

C₄

—

232

—

100

C₄

#11745232

yes

—

101

C₄

#11745288

yes

—

102

C₂

#14271029

yes

characteristic

103

C₂

#14271205

yes

—

104

C₂

#14271523

yes

—

105

C₂

#14271528

yes

characteristic

106

C₂

#14271532

yes

characteristic

	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	#1836
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

#1836

LCS

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

N	H ≅ G/N	type
10. C₂₉×#97	C₄	semidirect
63. #97	Dic₂₉	semidirect
65. C₂₉	#1836	semidirect

H ≅ G/N

type

10. C₂₉×#97

C₄

semidirect

63. #97

Dic₂₉

semidirect

65. C₂₉

#1836

semidirect

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

subgroup	index
#14271033	2
#14271029	2
#14270926	2
C₂×C₂₉×#97	2
#1836	29

subgroup

index

C₂×C₂₉×#97

Subgroups — #16819626

Conjugacy classes of subgroups

Complements

Maximal subgroups