Group #20302752 — subgroups

Subgroups — C₂₉×#7852 #20302752

Order 7424.

802 conjugacy classes of subgroups; only the 334 normal subgroups are shown.

normal subgroups only

This group has 802 conjugacy classes of subgroups — too many to draw. Only its 334 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×C₄×M₁₆×C₂₉	C₂	1	3	yes	maximal
2	C₂₉×#1273	C₂	1	4	yes	maximal, complemented
3	C₂²×M₁₆×C₂₉	C₄	1	6	yes	—
4	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
5	C₄×M₁₆×C₂₉	—	2	12	no	—
6	C₂×C₂₉×#97	C₄	1	6	yes	—
7	C₂×C₄×C₈×C₂₉	C₂²	1	6	yes	—
8	C₂³×C₄×C₂₉	C₂×C₄	1	3	yes	—
9	C₂×M₁₆×C₂₉	—	2	12	no	—
10	C₂×M₁₆×C₂₉	—	2	24	no	—
11	C₂²×C₈×C₂₉	C₂×C₄	1	12	yes	—
12	C₂×C₄²×C₂₉	C₂×C₄	1	3	yes	—
13	C₂×C₄²×C₂₉	D₄	1	6	yes	—
14	C₂×C₄²×C₂₉	Q₈	1	2	yes	—
15	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
16	C₂₉×#97	—	2	12	no	—
17	C₄×C₈×C₂₉	—	2	12	no	—
18	C₂⁴×C₂₉	C₄²	1	1	yes	characteristic
19	C₂²×C₄×C₂₉	—	2	12	no	—
20	C₂²×C₄×C₂₉	C₄²	1	3	yes	—
21	C₂²×C₄×C₂₉	C₂²⋊C₄	1	6	yes	—
22	C₂²×C₄×C₂₉	C₄⋊C₄	1	6	yes	—
23	C₂²×C₄×C₂₉	C₂²×C₄	1	3	yes	—
24	M₁₆×C₂₉	—	2	48	no	—
25	C₂×C₈×C₂₉	—	2	12	no	—
26	C₂×C₈×C₂₉	—	2	12	no	—
27	C₂×C₈×C₂₉	M₁₆	1	24	yes	complemented
28	C₄²×C₂₉	C₂²⋊C₄	1	6	yes	—
29	C₄²×C₂₉	C₄⋊C₄	1	6	yes	—
30	C₄²×C₂₉	C₂×D₄	1	3	yes	—
31	C₄²×C₂₉	C₂×Q₈	1	1	yes	characteristic
32	#7852	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂³×C₂₉	—	2	6	no	—
34	C₂³×C₂₉	#95	1	2	yes	—
35	C₂³×C₂₉	C₂×C₄²	1	1	yes	characteristic
36	C₂×C₄×C₂₉	—	2	6	no	—
37	C₂×C₄×C₂₉	—	2	12	no	—
38	C₂×C₄×C₂₉	—	2	12	no	—
39	C₂×C₄×C₂₉	#95	1	6	yes	—
40	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	3	yes	—
41	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	3	yes	—
42	C₂×C₄×C₂₉	C₂×M₁₆	1	12	yes	—
43	C₈×C₂₉	—	2	24	no	—
44	C₂×C₄×M₁₆	C₂×C₂₉	1	3	yes	—
45	#1273	C₂×C₂₉	1	4	yes	complemented
46	C₂²×C₂₉	—	2	6	no	—
47	C₂²×C₂₉	—	4	4	no	—
48	C₂²×C₂₉	C₂×#95	1	1	yes	characteristic
49	C₂²×C₂₉	C₄×M₁₆	1	6	yes	—
50	C₄×C₂₉	—	2	6	no	—
51	C₄×C₂₉	#407	1	6	yes	—
52	C₄×C₂₉	#423	1	6	yes	—
53	C₂²×M₁₆	C₄×C₂₉	1	6	yes	—
54	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
55	C₄×M₁₆	—	2	12	no	—
56	C₂×#97	C₄×C₂₉	1	6	yes	—
57	C₂×C₄×C₈	C₂²×C₂₉	1	6	yes	—
58	C₂×C₂₉	—	4	2	no	—
59	C₂×C₂₉	#1455	1	4	yes	—
60	C₂×C₂₉	#1728	1	3	yes	—
61	C₂³×C₄	C₂×C₄×C₂₉	1	3	yes	—
62	C₂×M₁₆	—	2	12	no	—
63	C₂×M₁₆	—	2	24	no	—
64	C₂²×C₈	C₂×C₄×C₂₉	1	12	yes	—
65	C₂×C₄²	C₂×C₄×C₂₉	1	3	yes	—
66	C₂×C₄²	D₄×C₂₉	1	6	yes	—
67	C₂×C₄²	Q₈×C₂₉	1	2	yes	—
68	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
69	#97	—	2	12	no	—
70	C₄×C₈	—	2	12	no	—
71	C₂₉	#7852	1	1	yes	characteristic, direct product factor, Sylow
72	C₂⁴	C₄²×C₂₉	1	1	yes	characteristic
73	C₂²×C₄	—	2	12	no	—
74	C₂²×C₄	C₄²×C₂₉	1	3	yes	—
75	C₂²×C₄	C₂²⋊C₄×C₂₉	1	6	yes	—
76	C₂²×C₄	C₄⋊C₄×C₂₉	1	6	yes	—
77	C₂²×C₄	C₂²×C₄×C₂₉	1	3	yes	—
78	M₁₆	—	2	48	no	—
79	C₂×C₈	—	2	12	no	—
80	C₂×C₈	—	2	12	no	—
81	C₂×C₈	M₁₆×C₂₉	1	24	yes	complemented
82	C₄²	C₂²⋊C₄×C₂₉	1	6	yes	—
83	C₄²	C₄⋊C₄×C₂₉	1	6	yes	—
84	C₄²	C₂×D₄×C₂₉	1	3	yes	—
85	C₄²	C₂×Q₈×C₂₉	1	1	yes	characteristic
86	C₂³	—	2	6	no	—
87	C₂³	C₂₉×#95	1	2	yes	—
88	C₂³	C₂×C₄²×C₂₉	1	1	yes	characteristic
89	C₂×C₄	—	2	6	no	—
90	C₂×C₄	—	2	12	no	—
91	C₂×C₄	—	2	12	no	—
92	C₂×C₄	C₂₉×#95	1	6	yes	—
93	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	3	yes	—
94	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	3	yes	—
95	C₂×C₄	C₂×M₁₆×C₂₉	1	12	yes	—
96	C₈	—	2	24	no	—
97	C₂²	—	2	6	no	—
98	C₂²	—	4	4	no	—
99	C₂²	C₂×C₂₉×#95	1	1	yes	characteristic
100	C₂²	C₄×M₁₆×C₂₉	1	6	yes	—
101	C₄	—	2	6	no	—
102	C₄	C₂₉×#407	1	6	yes	—
103	C₄	C₂₉×#423	1	6	yes	—
104	C₂	—	4	2	no	—
105	C₂	C₂₉×#1455	1	4	yes	—
106	C₂	C₂₉×#1728	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×M₁₆×C₂₉

C₂

yes

maximal

C₂₉×#1273

C₂

yes

maximal, complemented

C₂²×M₁₆×C₂₉

C₄

yes

—

C₂²×C₄²×C₂₉

C₂²

yes

characteristic

C₄×M₁₆×C₂₉

—

C₂×C₂₉×#97

C₄

yes

—

C₂×C₄×C₈×C₂₉

C₂²

yes

—

C₂³×C₄×C₂₉

C₂×C₄

yes

—

C₂×M₁₆×C₂₉

—

C₂×M₁₆×C₂₉

—

C₂²×C₈×C₂₉

C₂×C₄

yes

—

C₂×C₄²×C₂₉

C₂×C₄

yes

—

C₂×C₄²×C₂₉

D₄

yes

—

C₂×C₄²×C₂₉

Q₈

yes

—

C₂×C₄²×C₂₉

C₂³

yes

characteristic

C₂₉×#97

—

C₄×C₈×C₂₉

—

C₂⁴×C₂₉

C₄²

yes

characteristic

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

C₄²

yes

—

C₂²×C₄×C₂₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₂₉

C₄⋊C₄

yes

—

C₂²×C₄×C₂₉

C₂²×C₄

yes

—

M₁₆×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

M₁₆

yes

complemented

C₄²×C₂₉

C₂²⋊C₄

yes

—

C₄²×C₂₉

C₄⋊C₄

yes

—

C₄²×C₂₉

C₂×D₄

yes

—

C₄²×C₂₉

C₂×Q₈

yes

characteristic

#7852

C₂₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₂₉

—

C₂³×C₂₉

#95

yes

—

C₂³×C₂₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

#95

yes

—

C₂×C₄×C₂₉

C₂×C₂²⋊C₄

yes

—

C₂×C₄×C₂₉

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₂₉

C₂×M₁₆

yes

—

C₈×C₂₉

—

C₂×C₄×M₁₆

C₂×C₂₉

yes

—

#1273

C₂×C₂₉

yes

complemented

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

C₂×#95

yes

characteristic

C₂²×C₂₉

C₄×M₁₆

yes

—

C₄×C₂₉

—

C₄×C₂₉

#407

yes

—

C₄×C₂₉

#423

yes

—

C₂²×M₁₆

C₄×C₂₉

yes

—

C₂²×C₄²

C₂²×C₂₉

yes

characteristic

C₄×M₁₆

—

C₂×#97

C₄×C₂₉

yes

—

C₂×C₄×C₈

C₂²×C₂₉

yes

—

C₂×C₂₉

—

C₂×C₂₉

#1455

yes

—

C₂×C₂₉

#1728

yes

—

C₂³×C₄

C₂×C₄×C₂₉

yes

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂×C₄×C₂₉

yes

—

C₂×C₄²

C₂×C₄×C₂₉

yes

—

C₂×C₄²

D₄×C₂₉

yes

—

C₂×C₄²

Q₈×C₂₉

yes

—

C₂×C₄²

C₂³×C₂₉

yes

characteristic

#97

—

C₄×C₈

—

C₂₉

#7852

yes

characteristic, direct product factor, Sylow

C₂⁴

C₄²×C₂₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₄²×C₂₉

yes

—

C₂²×C₄

C₂²⋊C₄×C₂₉

yes

—

C₂²×C₄

C₄⋊C₄×C₂₉

yes

—

C₂²×C₄

C₂²×C₄×C₂₉

yes

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

M₁₆×C₂₉

yes

complemented

C₄²

C₂²⋊C₄×C₂₉

yes

—

C₄²

C₄⋊C₄×C₂₉

yes

—

C₄²

C₂×D₄×C₂₉

yes

—

C₄²

C₂×Q₈×C₂₉

yes

characteristic

C₂³

—

C₂³

C₂₉×#95

yes

—

C₂³

C₂×C₄²×C₂₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂₉×#95

yes

—

C₂×C₄

C₂×C₂²⋊C₄×C₂₉

yes

—

C₂×C₄

C₂×C₄⋊C₄×C₂₉

yes

—

C₂×C₄

C₂×M₁₆×C₂₉

yes

—

C₈

—

C₂²

—

C₂²

—

C₂²

C₂×C₂₉×#95

yes

characteristic

100

C₂²

C₄×M₁₆×C₂₉

yes

—

101

C₄

—

102

C₄

C₂₉×#407

yes

—

103

C₄

C₂₉×#423

yes

—

104

C₂

—

105

C₂

C₂₉×#1455

yes

—

106

C₂

C₂₉×#1728

yes

—

	subgroup	G/H
center	C₂×C₄²×C₂₉	C₂³
commutator	C₂³	C₂×C₄²×C₂₉
Frattini, cosocle	C₂×C₄²	C₂³×C₂₉
socle	C₂³×C₂₉	C₂×C₄²
prime radical	C₂⁴×C₂₉	C₄²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₂₉ ◁ G

subgroup

G/H

center

C₂×C₄²×C₂₉

C₂³

commutator

C₂³

C₂×C₄²×C₂₉

Frattini, cosocle

C₂×C₄²

C₂³×C₂₉

socle

C₂³×C₂₉

C₂×C₄²

prime radical

C₂⁴×C₂₉

C₄²

LCS

G ▷ C₂³ ▷ C₁

UCS

C₁ ◁ C₂×C₄²×C₂₉ ◁ G

N	H ≅ G/N	type
2. C₂₉×#1273	C₂	semidirect
27. C₂×C₈×C₂₉	M₁₆	semidirect
32. #7852	C₂₉	direct (N × H)
45. #1273	C₂×C₂₉	semidirect
71. C₂₉	#7852	direct (N × H)
81. C₂×C₈	M₁₆×C₂₉	semidirect

H ≅ G/N

type

2. C₂₉×#1273

C₂

semidirect

27. C₂×C₈×C₂₉

M₁₆

semidirect

32. #7852

C₂₉

direct (N × H)

45. #1273

C₂×C₂₉

semidirect

71. C₂₉

#7852

direct (N × H)

81. C₂×C₈

M₁₆×C₂₉

semidirect

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

subgroup	index
C₂×C₄×M₁₆×C₂₉	2
C₂₉×#1273	2
#7852	29

subgroup

index

C₂×C₄×M₁₆×C₂₉

C₂₉×#1273

#7852

Subgroups — C₂₉×#7852 #20302752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C29×#7852 #20302752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#7852 #20302752