Group #20302168 — subgroups

Subgroups — C₂₉×#7268 #20302168

Order 7424.

238 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 118 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×#364	C₂	1	2	yes	maximal
2	C₂₉×#1844	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₉×M₃₂	—	2	2	no	—
4	C₂×C₂₉×#106	—	2	2	no	—
5	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
6	C₂₉×#384	C₄	1	2	yes	—
7	C₂₉×#364	—	2	2	no	—
8	C₂₉×#364	C₄	1	4	yes	complemented
9	C₂²×C₈×C₂₉	D₄	1	2	yes	—
10	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
11	C₂×C₄⋊C₄×C₂₉	—	4	2	no	—
12	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
13	C₂₉×M₃₂	—	2	4	no	—
14	C₂₉×M₃₂	—	4	2	no	—
15	C₂×C₁₆×C₂₉	—	4	2	no	—
16	C₂₉×#106	—	4	2	no	—
17	C₂₉×#106	—	4	2	no	—
18	C₄×C₈×C₂₉	C₂×C₄	1	2	yes	—
19	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
20	C₄×C₈×C₂₉	Q₈	1	1	yes	characteristic
21	C₂²×C₄×C₂₉	—	2	1	no	—
22	C₂²×C₄×C₂₉	—	4	2	no	—
23	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×C₈×C₂₉	C₂²⋊C₄	1	2	yes	—
25	C₂×C₈×C₂₉	C₄⋊C₄	1	2	yes	—
26	C₂×C₈×C₂₉	D₈	1	2	yes	—
27	C₂×C₈×C₂₉	SD₁₆	1	2	yes	—
28	C₂×C₈×C₂₉	SD₁₆	1	2	yes	—
29	C₂×C₈×C₂₉	Q₁₆	1	2	yes	—
30	C₄⋊C₄×C₂₉	—	4	4	no	—
31	C₄⋊C₄×C₂₉	—	8	4	no	—
32	C₄²×C₂₉	—	2	1	no	—
33	C₄²×C₂₉	C₄²	1	1	yes	characteristic
34	C₄²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
35	C₁₆×C₂₉	—	4	4	no	—
36	#7268	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂³×C₂₉	#100	1	1	yes	characteristic
38	C₂×C₄×C₂₉	—	2	4	no	—
39	C₂×C₄×C₂₉	—	2	1	no	—
40	C₂×C₄×C₂₉	—	2	1	no	—
41	C₂×C₄×C₂₉	—	8	4	no	—
42	C₂×C₄×C₂₉	—	8	2	no	—
43	C₂×C₄×C₂₉	#95	1	1	yes	characteristic
44	C₂×C₄×C₂₉	#101	1	1	yes	characteristic
45	C₂×C₄×C₂₉	#102	1	2	yes	—
46	C₂×C₄×C₂₉	#103	1	2	yes	—
47	C₈×C₂₉	#102	1	2	yes	—
48	C₈×C₂₉	#103	1	2	yes	—
49	C₈×C₂₉	#106	1	2	yes	—
50	C₈×C₂₉	#107	1	2	yes	—
51	C₂×#364	C₂×C₂₉	1	2	yes	—
52	#1844	C₂×C₂₉	1	1	yes	characteristic
53	C₂²×C₂₉	—	2	2	no	—
54	C₂²×C₂₉	#331	1	1	yes	characteristic
55	C₂²×C₂₉	#333	1	1	yes	characteristic
56	C₂²×C₂₉	#343	1	1	yes	characteristic
57	C₄×C₂₉	—	2	2	no	—
58	C₄×C₂₉	—	2	2	no	—
59	C₄×C₂₉	—	16	2	no	—
60	C₄×C₂₉	#332	1	2	yes	—
61	C₄×C₂₉	#340	1	2	yes	—
62	C₂×M₃₂	—	2	2	no	—
63	C₂×#106	—	2	2	no	—
64	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
65	#384	C₄×C₂₉	1	2	yes	—
66	#364	—	2	2	no	—
67	#364	C₄×C₂₉	1	4	yes	complemented
68	C₂×C₂₉	—	2	1	no	—
69	C₂×C₂₉	—	2	1	no	—
70	C₂×C₂₉	#1296	1	1	yes	characteristic
71	C₂×C₂₉	#1359	1	2	yes	—
72	C₂²×C₈	D₄×C₂₉	1	2	yes	—
73	C₂×C₄⋊C₄	—	2	2	no	—
74	C₂×C₄⋊C₄	—	4	2	no	—
75	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
76	M₃₂	—	2	4	no	—
77	M₃₂	—	4	2	no	—
78	C₂×C₁₆	—	4	2	no	—
79	#106	—	4	2	no	—
80	#106	—	4	2	no	—
81	C₄×C₈	C₂×C₄×C₂₉	1	2	yes	—
82	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
83	C₄×C₈	Q₈×C₂₉	1	1	yes	characteristic
84	C₂₉	#7268	1	1	yes	characteristic, direct product factor, Sylow
85	C₂²×C₄	—	2	1	no	—
86	C₂²×C₄	—	4	2	no	—
87	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
88	C₂×C₈	C₂²⋊C₄×C₂₉	1	2	yes	—
89	C₂×C₈	C₄⋊C₄×C₂₉	1	2	yes	—
90	C₂×C₈	D₈×C₂₉	1	2	yes	—
91	C₂×C₈	SD₁₆×C₂₉	1	2	yes	—
92	C₂×C₈	SD₁₆×C₂₉	1	2	yes	—
93	C₂×C₈	Q₁₆×C₂₉	1	2	yes	—
94	C₄⋊C₄	—	4	4	no	—
95	C₄⋊C₄	—	8	4	no	—
96	C₄²	—	2	1	no	—
97	C₄²	C₄²×C₂₉	1	1	yes	characteristic
98	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
99	C₁₆	—	4	4	no	—
100	C₂³	C₂₉×#100	1	1	yes	characteristic
101	C₂×C₄	—	2	4	no	—
102	C₂×C₄	—	2	1	no	—
103	C₂×C₄	—	2	1	no	—
104	C₂×C₄	—	8	4	no	—
105	C₂×C₄	—	8	2	no	—
106	C₂×C₄	C₂₉×#95	1	1	yes	characteristic
107	C₂×C₄	C₂₉×#101	1	1	yes	characteristic
108	C₂×C₄	C₂₉×#102	1	2	yes	—
109	C₂×C₄	C₂₉×#103	1	2	yes	—
110	C₈	C₂₉×#102	1	2	yes	—
111	C₈	C₂₉×#103	1	2	yes	—
112	C₈	C₂₉×#106	1	2	yes	—
113	C₈	C₂₉×#107	1	2	yes	—
114	C₂²	—	2	2	no	—
115	C₂²	C₂₉×#331	1	1	yes	characteristic
116	C₂²	C₂₉×#333	1	1	yes	characteristic
117	C₂²	C₂₉×#343	1	1	yes	characteristic
118	C₄	—	2	2	no	—
119	C₄	—	2	2	no	—
120	C₄	—	16	2	no	—
121	C₄	C₂₉×#332	1	2	yes	—
122	C₄	C₂₉×#340	1	2	yes	—
123	C₂	—	2	1	no	—
124	C₂	—	2	1	no	—
125	C₂	C₂₉×#1296	1	1	yes	characteristic
126	C₂	C₂₉×#1359	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₂₉×#364

C₂

yes

maximal

C₂₉×#1844

C₂

yes

maximal, characteristic

C₂×C₂₉×M₃₂

—

C₂×C₂₉×#106

—

C₂×C₄×C₈×C₂₉

C₂²

yes

characteristic

C₂₉×#384

C₄

yes

—

C₂₉×#364

—

C₂₉×#364

C₄

yes

complemented

C₂²×C₈×C₂₉

D₄

yes

—

C₂×C₄⋊C₄×C₂₉

—

C₂×C₄⋊C₄×C₂₉

—

C₂×C₄²×C₂₉

C₂×C₄

yes

characteristic

C₂₉×M₃₂

—

C₂₉×M₃₂

—

C₂×C₁₆×C₂₉

—

C₂₉×#106

—

C₂₉×#106

—

C₄×C₈×C₂₉

C₂×C₄

yes

—

C₄×C₈×C₂₉

D₄

yes

characteristic

C₄×C₈×C₂₉

Q₈

yes

characteristic

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₂₉

C₂²⋊C₄

yes

—

C₂×C₈×C₂₉

C₄⋊C₄

yes

—

C₂×C₈×C₂₉

D₈

yes

—

C₂×C₈×C₂₉

SD₁₆

yes

—

C₂×C₈×C₂₉

SD₁₆

yes

—

C₂×C₈×C₂₉

Q₁₆

yes

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄²×C₂₉

—

C₄²×C₂₉

C₄²

yes

characteristic

C₄²×C₂₉

C₄⋊C₄

yes

characteristic

C₁₆×C₂₉

—

#7268

C₂₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₂₉

#100

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

yes

C₂×C₄×C₂₉

yes

C₂×C₄×C₂₉

yes

—

C₂×C₄×C₂₉

#103

yes

—

C₈×C₂₉

#102

yes

—

C₈×C₂₉

#103

yes

—

C₈×C₂₉

#106

yes

—

C₈×C₂₉

#107

yes

—

C₂×#364

C₂×C₂₉

yes

—

#1844

C₂×C₂₉

yes

characteristic

C₂²×C₂₉

—

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

#332

yes

—

C₄×C₂₉

#340

yes

—

C₂×M₃₂

—

C₂×#106

—

C₂×C₄×C₈

C₂²×C₂₉

yes

characteristic

#384

C₄×C₂₉

yes

—

#364

—

#364

C₄×C₂₉

yes

complemented

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

#1296

yes

characteristic

C₂×C₂₉

#1359

yes

—

C₂²×C₈

D₄×C₂₉

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×C₄×C₂₉

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

#106

—

#106

—

C₄×C₈

C₂×C₄×C₂₉

yes

—

C₄×C₈

D₄×C₂₉

yes

characteristic

C₄×C₈

Q₈×C₂₉

yes

characteristic

C₂₉

#7268

yes

characteristic, direct product factor, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊C₄×C₂₉

yes

characteristic

C₂×C₈

C₂²⋊C₄×C₂₉

yes

—

C₂×C₈

C₄⋊C₄×C₂₉

yes

—

C₂×C₈

D₈×C₂₉

yes

—

C₂×C₈

SD₁₆×C₂₉

yes

—

C₂×C₈

SD₁₆×C₂₉

yes

—

C₂×C₈

Q₁₆×C₂₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₄²×C₂₉

yes

characteristic

C₄²

C₄⋊C₄×C₂₉

yes

characteristic

C₁₆

—

100

C₂³

C₂₉×#100

yes

characteristic

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

C₂₉×#95

yes

characteristic

107

C₂×C₄

C₂₉×#101

yes

characteristic

108

C₂×C₄

C₂₉×#102

yes

—

109

C₂×C₄

C₂₉×#103

yes

—

110

C₈

C₂₉×#102

yes

—

111

C₈

C₂₉×#103

yes

—

112

C₈

C₂₉×#106

yes

—

113

C₈

C₂₉×#107

yes

—

114

C₂²

—

115

C₂²

C₂₉×#331

yes

characteristic

116

C₂²

C₂₉×#333

yes

characteristic

117

C₂²

C₂₉×#343

yes

characteristic

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

C₂₉×#332

yes

—

122

C₄

C₂₉×#340

yes

—

123

C₂

—

124

C₂

—

125

C₂

C₂₉×#1296

yes

characteristic

126

C₂

C₂₉×#1359

yes

—

	subgroup	G/H
center, socle	C₂²×C₂₉	#331
commutator	C₄²	C₄²×C₂₉
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₂₉
prime radical	C₂³×C₂₉	#100
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ C₂×C₄×C₈×C₂₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₂₉

#331

commutator

C₄²

C₄²×C₂₉

Frattini, cosocle

C₂×C₄×C₈

C₂²×C₂₉

prime radical

C₂³×C₂₉

#100

LCS

G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ C₂×C₄×C₈×C₂₉ ◁ G

N	H ≅ G/N	type
8. C₂₉×#364	C₄	semidirect
36. #7268	C₂₉	direct (N × H)
67. #364	C₄×C₂₉	semidirect
84. C₂₉	#7268	direct (N × H)

H ≅ G/N

type

8. C₂₉×#364

C₄

semidirect

36. #7268

C₂₉

direct (N × H)

67. #364

C₄×C₂₉

semidirect

84. C₂₉

#7268

direct (N × H)

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

subgroup	index
C₂×C₂₉×#364	2
C₂₉×#1844	2
#7268	29

subgroup

index

C₂×C₂₉×#364

C₂₉×#1844

#7268

Subgroups — C₂₉×#7268 #20302168

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C29×#7268 #20302168

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#7268 #20302168