Group #16815482 — subgroups

Subgroups — C₂₉×#1768 #16815482

Order 3712.

260 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 168 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×C₂₉×C₄⋊C₈	C₂	1	2	yes	maximal
2	C₂×C₂₉×#97	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₈×C₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#376	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#336	C₂	1	2	yes	maximal
6	C₂²×C₈×C₂₉	C₂²	1	2	yes	—
7	C₂²×C₈×C₂₉	C₂²	1	2	yes	—
8	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
9	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
10	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
11	C₂₉×C₄⋊C₈	C₄	1	8	yes	complemented
12	C₂₉×#97	—	2	2	no	—
13	C₄×C₈×C₂₉	—	2	2	no	—
14	C₂₉×#95	C₄	1	4	yes	—
15	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
16	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
17	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
18	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
19	C₂×C₈×C₂₉	—	2	2	no	—
20	C₂×C₈×C₂₉	—	2	2	no	—
21	C₂×C₈×C₂₉	—	2	2	no	—
22	C₂×C₈×C₂₉	—	2	2	no	—
23	C₂×C₈×C₂₉	C₂×C₄	1	4	yes	—
24	C₂×C₈×C₂₉	C₂×C₄	1	4	yes	—
25	C₄²×C₂₉	—	2	2	no	—
26	C₄²×C₂₉	C₂×C₄	1	4	yes	—
27	C₄²×C₂₉	D₄	1	2	yes	—
28	C₄²×C₂₉	Q₈	1	2	yes	—
29	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₂₉	—	2	4	no	—
31	C₂×C₄×C₂₉	—	2	4	no	—
32	C₂×C₄×C₂₉	—	2	2	no	—
33	C₂×C₄×C₂₉	—	2	4	no	—
34	C₂×C₄×C₂₉	C₄²	1	4	yes	—
35	C₂×C₄×C₂₉	C₄⋊C₄	1	4	yes	—
36	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
37	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₄×C₂₉	#41	1	2	yes	—
40	C₈×C₂₉	—	2	4	no	—
41	C₈×C₂₉	—	2	4	no	—
42	#1768	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
44	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
45	C₂²×C₂₉	#117	1	1	yes	characteristic
46	C₂²×C₂₉	#131	1	4	yes	—
47	C₄×C₂₉	—	2	4	no	—
48	C₄×C₂₉	—	2	4	no	—
49	C₄×C₂₉	—	4	2	no	—
50	C₄×C₂₉	C₄×D₄	1	2	yes	—
51	C₄×C₂₉	C₄×Q₈	1	2	yes	—
52	C₂×C₄⋊C₈	C₂×C₂₉	1	2	yes	—
53	C₂×#97	C₂×C₂₉	1	1	yes	characteristic
54	C₂×C₄×C₈	C₂×C₂₉	1	1	yes	characteristic
55	#376	C₂×C₂₉	1	1	yes	characteristic
56	#336	C₂×C₂₉	1	2	yes	—
57	C₂×C₂₉	C₄×C₄⋊C₄	1	1	yes	characteristic
58	C₂×C₂₉	#405	1	2	yes	—
59	C₂×C₂₉	#424	1	2	yes	—
60	C₂×C₂₉	#433	1	2	yes	—
61	C₂²×C₈	C₂²×C₂₉	1	2	yes	—
62	C₂²×C₈	C₂²×C₂₉	1	2	yes	—
63	C₂×C₄²	C₂²×C₂₉	1	1	yes	characteristic
64	C₂×C₄²	C₂²×C₂₉	1	1	yes	characteristic
65	C₂×C₄²	C₂²×C₂₉	1	1	yes	characteristic
66	C₄⋊C₈	C₄×C₂₉	1	8	yes	complemented
67	#97	—	2	2	no	—
68	C₄×C₈	—	2	2	no	—
69	#95	C₄×C₂₉	1	4	yes	—
70	C₂₉	#1768	1	1	yes	characteristic, direct product factor, Sylow
71	C₂²×C₄	C₂×C₄×C₂₉	1	2	yes	—
72	C₂²×C₄	C₂×C₄×C₂₉	1	2	yes	—
73	C₂²×C₄	C₂×C₄×C₂₉	1	2	yes	—
74	C₂²×C₄	C₂³×C₂₉	1	1	yes	characteristic
75	C₂×C₈	—	2	2	no	—
76	C₂×C₈	—	2	2	no	—
77	C₂×C₈	—	2	2	no	—
78	C₂×C₈	—	2	2	no	—
79	C₂×C₈	C₂×C₄×C₂₉	1	4	yes	—
80	C₂×C₈	C₂×C₄×C₂₉	1	4	yes	—
81	C₄²	—	2	2	no	—
82	C₄²	C₂×C₄×C₂₉	1	4	yes	—
83	C₄²	D₄×C₂₉	1	2	yes	—
84	C₄²	Q₈×C₂₉	1	2	yes	—
85	C₂³	C₂²×C₄×C₂₉	1	1	yes	characteristic
86	C₂×C₄	—	2	4	no	—
87	C₂×C₄	—	2	4	no	—
88	C₂×C₄	—	2	2	no	—
89	C₂×C₄	—	2	4	no	—
90	C₂×C₄	C₄²×C₂₉	1	4	yes	—
91	C₂×C₄	C₄⋊C₄×C₂₉	1	4	yes	—
92	C₂×C₄	C₂²×C₄×C₂₉	1	2	yes	—
93	C₂×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
94	C₂×C₄	C₂×Q₈×C₂₉	1	1	yes	characteristic
95	C₂×C₄	#41×C₂₉	1	2	yes	—
96	C₈	—	2	4	no	—
97	C₈	—	2	4	no	—
98	C₂²	C₂×C₄²×C₂₉	1	1	yes	characteristic
99	C₂²	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
100	C₂²	C₂₉×#117	1	1	yes	characteristic
101	C₂²	C₂₉×#131	1	4	yes	—
102	C₄	—	2	4	no	—
103	C₄	—	2	4	no	—
104	C₄	—	4	2	no	—
105	C₄	C₄×D₄×C₂₉	1	2	yes	—
106	C₄	C₄×Q₈×C₂₉	1	2	yes	—
107	C₂	C₄×C₄⋊C₄×C₂₉	1	1	yes	characteristic
108	C₂	C₂₉×#405	1	2	yes	—
109	C₂	C₂₉×#424	1	2	yes	—
110	C₂	C₂₉×#433	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₂₉×C₄⋊C₈

C₂

yes

maximal

C₂×C₂₉×#97

C₂

yes

maximal, characteristic

C₂×C₄×C₈×C₂₉

C₂

yes

maximal, characteristic

C₂₉×#376

C₂

yes

maximal, characteristic

C₂₉×#336

C₂

yes

maximal

C₂²×C₈×C₂₉

C₂²

yes

—

C₂²×C₈×C₂₉

C₂²

yes

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂₉×C₄⋊C₈

C₄

yes

complemented

C₂₉×#97

—

C₄×C₈×C₂₉

—

C₂₉×#95

C₄

yes

—

C₂²×C₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

—

C₄²×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

D₄

yes

—

C₄²×C₂₉

Q₈

yes

—

C₂³×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₄²

yes

—

C₂×C₄×C₂₉

C₄⋊C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

#41

yes

—

C₈×C₂₉

—

C₈×C₂₉

—

#1768

C₂₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₂₉

C₂×C₄²

yes

characteristic

C₂²×C₂₉

C₂×C₄⋊C₄

yes

C₂²×C₂₉

yes

C₂²×C₂₉

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₄×D₄

yes

—

C₄×C₂₉

C₄×Q₈

yes

—

C₂×C₄⋊C₈

C₂×C₂₉

yes

—

C₂×#97

C₂×C₂₉

yes

characteristic

C₂×C₄×C₈

C₂×C₂₉

yes

characteristic

#376

C₂×C₂₉

yes

characteristic

#336

C₂×C₂₉

yes

—

C₂×C₂₉

C₄×C₄⋊C₄

yes

characteristic

C₂×C₂₉

#405

yes

—

C₂×C₂₉

#424

yes

—

C₂×C₂₉

#433

yes

—

C₂²×C₈

C₂²×C₂₉

yes

—

C₂²×C₈

C₂²×C₂₉

yes

—

C₂×C₄²

C₂²×C₂₉

yes

characteristic

C₂×C₄²

C₂²×C₂₉

yes

characteristic

C₂×C₄²

C₂²×C₂₉

yes

characteristic

C₄⋊C₈

C₄×C₂₉

yes

complemented

#97

—

C₄×C₈

—

#95

C₄×C₂₉

yes

—

C₂₉

#1768

yes

characteristic, direct product factor, Sylow

C₂²×C₄

C₂×C₄×C₂₉

yes

—

C₂²×C₄

C₂×C₄×C₂₉

yes

—

C₂²×C₄

C₂×C₄×C₂₉

yes

—

C₂²×C₄

C₂³×C₂₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×C₄×C₂₉

yes

—

C₂×C₈

C₂×C₄×C₂₉

yes

—

C₄²

—

C₄²

C₂×C₄×C₂₉

yes

—

C₄²

D₄×C₂₉

yes

—

C₄²

Q₈×C₂₉

yes

—

C₂³

C₂²×C₄×C₂₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄²×C₂₉

yes

—

C₂×C₄

C₄⋊C₄×C₂₉

yes

—

C₂×C₄

C₂²×C₄×C₂₉

yes

—

C₂×C₄

C₂×D₄×C₂₉

yes

characteristic

C₂×C₄

C₂×Q₈×C₂₉

yes

characteristic

C₂×C₄

#41×C₂₉

yes

—

C₈

—

C₈

—

C₂²

C₂×C₄²×C₂₉

yes

characteristic

C₂²

C₂×C₄⋊C₄×C₂₉

yes

characteristic

100

C₂²

C₂₉×#117

yes

characteristic

101

C₂²

C₂₉×#131

yes

—

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

C₄×D₄×C₂₉

yes

—

106

C₄

C₄×Q₈×C₂₉

yes

—

107

C₂

C₄×C₄⋊C₄×C₂₉

yes

characteristic

108

C₂

C₂₉×#405

yes

—

109

C₂

C₂₉×#424

yes

—

110

C₂

C₂₉×#433

yes

—

	subgroup	G/H
center	C₂²×C₄×C₂₉	C₂³
commutator	C₂²	C₂×C₄²×C₂₉
Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
socle, prime radical	C₂³×C₂₉	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₉ ◁ G

subgroup

G/H

center

C₂²×C₄×C₂₉

C₂³

commutator

C₂²

C₂×C₄²×C₂₉

Frattini, cosocle

C₂²×C₄

C₂³×C₂₉

socle, prime radical

C₂³×C₂₉

C₂²×C₄

LCS

G ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₄×C₂₉ ◁ G

N	H ≅ G/N	type
11. C₂₉×C₄⋊C₈	C₄	semidirect
42. #1768	C₂₉	direct (N × H)
66. C₄⋊C₈	C₄×C₂₉	semidirect
70. C₂₉	#1768	direct (N × H)

H ≅ G/N

type

11. C₂₉×C₄⋊C₈

C₄

semidirect

42. #1768

C₂₉

direct (N × H)

66. C₄⋊C₈

C₄×C₂₉

semidirect

70. C₂₉

#1768

direct (N × H)

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

subgroup	index
C₂×C₂₉×C₄⋊C₈	2
C₂×C₂₉×#97	2
C₂×C₄×C₈×C₂₉	2
C₂₉×#376	2
C₂₉×#336	2
#1768	29

subgroup

index

C₂×C₂₉×C₄⋊C₈

C₂×C₂₉×#97

C₂×C₄×C₈×C₂₉

C₂₉×#376

C₂₉×#336

#1768

Subgroups — C₂₉×#1768 #16815482

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C29×#1768 #16815482

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#1768 #16815482