Group #16819656 — subgroups

Subgroups — #16819656

Order 3712.

248 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 141 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×#11745166	C₂	1	2	yes	maximal
2	C₂×#11745165	C₂	1	2	yes	maximal
3	#14271029	C₂	1	2	yes	maximal
4	C₂×C₄×C₈×C₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
6	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
7	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₂₉	C₂²	1	4	yes	—
9	C₄×C₈×C₂₉	C₄	1	4	yes	complemented
10	#11745179	—	2	4	no	—
11	#11745166	—	2	4	no	—
12	#11745165	—	2	4	no	—
13	C₂²×C₄×C₂₉	D₄	1	2	yes	—
14	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
15	C₂²×Dic₂₉	—	2	4	no	—
16	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
18	C₂×C₈×C₂₉	D₄	1	2	yes	—
19	C₂×C₈×C₂₉	D₄	1	2	yes	—
20	C₂×C₈×C₂₉	Q₈	1	2	yes	—
21	C₂×C₈×C₂₉	Q₈	1	2	yes	—
22	C₄²×C₂₉	C₂×C₄	1	2	yes	—
23	C₄²×C₂₉	Q₈	1	2	yes	—
24	C₄⋊Dic₂₉	—	2	4	no	—
25	C₄⋊Dic₂₉	—	2	4	no	—
26	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
27	C₂×C₄×C₂₉	—	2	4	no	—
28	C₂×C₄×C₂₉	C₄⋊C₄	1	4	yes	—
29	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
33	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
34	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
35	C₂×Dic₂₉	—	4	4	no	—
36	C₂×Dic₂₉	—	4	8	no	—
37	C₈×C₂₉	C₄⋊C₄	1	4	yes	—
38	C₈×C₂₉	C₄⋊C₄	1	4	yes	—
39	#1846	—	29	1	no	maximal, Sylow
40	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
41	C₂²×C₂₉	#127	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	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
47	C₄×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
48	C₄×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
49	Dic₂₉	—	8	4	no	—
50	C₂×#107	—	29	2	no	—
51	C₂×#106	—	29	2	no	—
52	C₂×C₄×C₈	D₂₉	1	1	yes	characteristic
53	#382	—	29	2	no	—
54	C₂×C₂₉	#384	1	1	yes	characteristic
55	C₂×C₂₉	#427	1	2	yes	—
56	C₂×C₂₉	#495	1	2	yes	—
57	C₂×C₂₉	#499	1	2	yes	—
58	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
59	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
60	C₂×C₄⋊C₄	—	29	4	no	—
61	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
62	#107	—	58	4	no	—
63	#106	—	58	4	no	—
64	C₄×C₈	Dic₂₉	1	4	yes	complemented
65	#95	—	58	4	no	—
66	C₂₉	#1846	1	1	yes	characteristic, complemented, Sylow
67	C₂²×C₄	—	58	4	no	—
68	C₂²×C₄	D₁₁₆	1	2	yes	—
69	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
70	C₂×C₈	Dic₅₈	1	2	yes	—
71	C₂×C₈	Dic₅₈	1	2	yes	—
72	C₂×C₈	D₁₁₆	1	2	yes	—
73	C₂×C₈	D₁₁₆	1	2	yes	—
74	C₂×C₈	C₂×Dic₂₉	1	2	yes	—
75	C₂×C₈	C₂×Dic₂₉	1	2	yes	—
76	C₄⋊C₄	—	58	4	no	—
77	C₄⋊C₄	—	58	4	no	—
78	C₄²	Dic₅₈	1	2	yes	—
79	C₄²	C₂×Dic₂₉	1	2	yes	—
80	C₂³	C₂×D₁₁₆	1	1	yes	characteristic
81	C₂×C₄	—	2	4	no	—
82	C₂×C₄	—	116	4	no	—
83	C₂×C₄	—	116	8	no	—
84	C₂×C₄	C₄⋊Dic₂₉	1	4	yes	—
85	C₂×C₄	C₂×Dic₅₈	1	1	yes	characteristic
86	C₂×C₄	C₂×Dic₅₈	1	1	yes	characteristic
87	C₂×C₄	C₂×Dic₅₈	1	1	yes	characteristic
88	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
89	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
90	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
91	C₈	C₄⋊Dic₂₉	1	4	yes	—
92	C₈	C₄⋊Dic₂₉	1	4	yes	—
93	C₂²	#11745231	1	1	yes	characteristic
94	C₂²	#11745236	1	1	yes	characteristic
95	C₂²	#11745266	1	4	yes	—
96	C₂²	C₂×C₄⋊Dic₂₉	1	1	yes	characteristic
97	C₄	—	2	4	no	—
98	C₄	—	232	4	no	—
99	C₄	#11745231	1	1	yes	characteristic
100	C₄	#11745231	1	1	yes	characteristic
101	C₄	C₂×C₄⋊Dic₂₉	1	1	yes	characteristic
102	C₄	C₂×C₄⋊Dic₂₉	1	1	yes	characteristic
103	C₂	#14271033	1	1	yes	characteristic
104	C₂	#14271201	1	2	yes	—
105	C₂	#14271547	1	2	yes	—
106	C₂	#14271565	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745166

C₂

yes

maximal

C₂×#11745165

C₂

yes

maximal

#14271029

C₂

yes

maximal

C₂×C₄×C₈×C₂₉

C₂

yes

maximal, characteristic

C₂²×C₈×C₂₉

C₂²

yes

characteristic

C₂²×C₈×C₂₉

C₂²

yes

characteristic

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₂₉

C₂²

yes

—

C₄×C₈×C₂₉

C₄

yes

—

—

—

C₂²×C₄×C₂₉

D₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₂×C₈×C₂₉

D₄

yes

—

C₂×C₈×C₂₉

D₄

yes

—

C₂×C₈×C₂₉

Q₈

yes

—

C₂×C₈×C₂₉

Q₈

yes

—

C₄²×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

Q₈

yes

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₂³×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₄⋊C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₈×C₂₉

C₄⋊C₄

yes

—

C₈×C₂₉

C₄⋊C₄

yes

—

#1846

—

maximal, Sylow

C₂²×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₉

#127

yes

characteristic

C₂²×C₂₉

C₄⋊Q₈

yes

characteristic

C₂²×C₂₉

#135

yes

—

C₄×C₂₉

—

C₄×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₂₉

C₄⋊Q₈

yes

characteristic

C₄×C₂₉

C₄⋊Q₈

yes

characteristic

Dic₂₉

—

C₂×#107

—

C₂×#106

—

C₂×C₄×C₈

D₂₉

yes

characteristic

#382

—

C₂×C₂₉

#384

yes

characteristic

C₂×C₂₉

#427

yes

—

C₂×C₂₉

#495

yes

—

C₂×C₂₉

#499

yes

—

C₂²×C₈

C₂×D₂₉

yes

characteristic

C₂²×C₈

C₂×D₂₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

#107

—

#106

—

C₄×C₈

Dic₂₉

yes

complemented

#95

—

C₂₉

#1846

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

D₁₁₆

yes

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

C₂×C₈

Dic₅₈

yes

—

C₂×C₈

Dic₅₈

yes

—

C₂×C₈

D₁₁₆

yes

—

C₂×C₈

D₁₁₆

yes

—

C₂×C₈

C₂×Dic₂₉

yes

—

C₂×C₈

C₂×Dic₂₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

Dic₅₈

yes

—

C₄²

C₂×Dic₂₉

yes

—

C₂³

C₂×D₁₁₆

yes

characteristic

C₂×C₄

—

C₂×C₄

—

116

—

C₂×C₄

—

116

—

C₂×C₄

C₄⋊Dic₂₉

yes

—

C₂×C₄

C₂×Dic₅₈

yes

characteristic

C₂×C₄

C₂×Dic₅₈

yes

characteristic

C₂×C₄

C₂×Dic₅₈

yes

characteristic

C₂×C₄

C₂×D₁₁₆

yes

characteristic

C₂×C₄

C₂×D₁₁₆

yes

characteristic

C₂×C₄

C₂²×Dic₂₉

yes

characteristic

C₈

C₄⋊Dic₂₉

yes

—

C₈

C₄⋊Dic₂₉

yes

—

C₂²

yes

C₂²

yes

C₂²

yes

—

C₂²

C₂×C₄⋊Dic₂₉

yes

characteristic

C₄

—

C₄

—

232

—

C₄

#11745231

yes

characteristic

100

C₄

#11745231

yes

characteristic

101

C₄

C₂×C₄⋊Dic₂₉

yes

characteristic

102

C₄

C₂×C₄⋊Dic₂₉

yes

characteristic

103

C₂

#14271033

yes

characteristic

104

C₂

#14271201

yes

—

105

C₂

#14271547

yes

—

106

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	#1846
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

#1846

LCS

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
9. C₄×C₈×C₂₉	C₄	semidirect
64. C₄×C₈	Dic₂₉	semidirect
66. C₂₉	#1846	semidirect

H ≅ G/N

type

9. C₄×C₈×C₂₉

C₄

semidirect

64. C₄×C₈

Dic₂₉

semidirect

66. C₂₉

#1846

semidirect

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

subgroup	index
C₂×#11745166	2
C₂×#11745165	2
#14271029	2
C₂×C₄×C₈×C₂₉	2
#1846	29

subgroup

index

C₂×C₄×C₈×C₂₉

Subgroups — #16819656

Conjugacy classes of subgroups

Complements

Maximal subgroups