Group #16816899 — subgroups

Subgroups — C₂₉×#3185 #16816899

Order 3712.

358 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 184 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	C₂₉×#533	C₂	1	2	yes	maximal
2	C₂₉×#498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#494	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#487	C₂	1	2	yes	maximal, complemented
5	C₂₉×#470	C₂	1	4	yes	maximal
6	C₂₉×#441	C₂	1	4	yes	maximal, complemented
7	C₄×M₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₁₆×C₂₉	C₂²	1	4	yes	—
9	C₂×M₁₆×C₂₉	C₂²	1	2	yes	—
10	C₂₉×C₄⋊Q₈	C₂²	1	2	yes	—
11	C₂₉×C₄⋊Q₈	C₂²	1	2	yes	—
12	C₂₉×#125	—	2	2	no	—
13	C₂₉×C₂²⋊Q₈	—	2	2	no	—
14	C₂₉×C₂²⋊Q₈	C₂²	1	4	yes	—
15	C₄×Q₈×C₂₉	—	2	2	no	—
16	C₄×Q₈×C₂₉	C₂²	1	4	yes	—
17	C₂₉×#117	—	2	2	no	—
18	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
19	C₂₉×#106	C₂²	1	4	yes	—
20	C₂₉×#103	C₂²	1	8	yes	—
21	C₂₉×#97	C₂²	1	2	yes	—
22	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
23	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
24	C₂×Q₈×C₂₉	—	2	2	no	—
25	C₂×Q₈×C₂₉	C₂³	1	4	yes	—
26	C₂²×C₄×C₂₉	D₄	1	2	yes	—
27	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
28	Q₁₆×C₂₉	—	2	8	no	—
29	M₁₆×C₂₉	—	2	4	no	—
30	C₂×C₈×C₂₉	C₂³	1	2	yes	—
31	C₂×C₈×C₂₉	C₂³	1	2	yes	—
32	C₄⋊C₄×C₂₉	—	2	2	no	—
33	C₄⋊C₄×C₂₉	—	2	2	no	—
34	C₄⋊C₄×C₂₉	—	2	2	no	—
35	C₄⋊C₄×C₂₉	—	2	4	no	—
36	C₄⋊C₄×C₂₉	—	2	4	no	—
37	C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
38	C₂²⋊C₄×C₂₉	—	2	4	no	—
39	C₄²×C₂₉	—	2	4	no	—
40	C₄²×C₂₉	D₄	1	2	yes	—
41	C₄²×C₂₉	C₂³	1	1	yes	characteristic
42	C₄²×C₂₉	C₂³	1	1	yes	characteristic
43	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
44	Q₈×C₂₉	—	2	8	no	—
45	Q₈×C₂₉	—	4	4	no	—
46	C₂×C₄×C₂₉	—	2	4	no	—
47	C₂×C₄×C₂₉	—	2	2	no	—
48	C₂×C₄×C₂₉	—	2	4	no	—
49	C₂×C₄×C₂₉	—	2	4	no	—
50	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
51	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
53	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
54	C₈×C₂₉	—	2	2	no	—
55	C₈×C₂₉	#41	1	4	yes	—
56	#3185	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
57	C₂²×C₂₉	—	2	1	no	—
58	C₂²×C₂₉	—	2	2	no	—
59	C₂²×C₂₉	C₂²×D₄	1	1	yes	characteristic
60	C₄×C₂₉	—	2	1	no	—
61	C₄×C₂₉	—	2	2	no	—
62	C₄×C₂₉	—	4	4	no	—
63	C₄×C₂₉	—	4	4	no	—
64	C₄×C₂₉	#137	1	4	yes	—
65	C₄×C₂₉	C₂×#41	1	2	yes	—
66	#533	C₂×C₂₉	1	2	yes	—
67	#498	C₂×C₂₉	1	1	yes	characteristic, complemented
68	#494	C₂×C₂₉	1	1	yes	characteristic, complemented
69	#487	C₂×C₂₉	1	2	yes	complemented
70	#470	C₂×C₂₉	1	4	yes	—
71	#441	C₂×C₂₉	1	4	yes	complemented
72	C₄×M₁₆	C₂×C₂₉	1	1	yes	characteristic
73	C₂×C₂₉	—	4	1	no	—
74	C₂×C₂₉	#532	1	1	yes	characteristic
75	C₂×C₂₉	C₂×#137	1	2	yes	—
76	C₂×Q₁₆	C₂²×C₂₉	1	4	yes	—
77	C₂×M₁₆	C₂²×C₂₉	1	2	yes	—
78	C₄⋊Q₈	C₂²×C₂₉	1	2	yes	—
79	C₄⋊Q₈	C₂²×C₂₉	1	2	yes	—
80	#125	—	2	2	no	—
81	C₂²⋊Q₈	—	2	2	no	—
82	C₂²⋊Q₈	C₂²×C₂₉	1	4	yes	—
83	C₄×Q₈	—	2	2	no	—
84	C₄×Q₈	C₂²×C₂₉	1	4	yes	—
85	#117	—	2	2	no	—
86	C₂×C₄²	C₂²×C₂₉	1	1	yes	characteristic
87	#106	C₂²×C₂₉	1	4	yes	—
88	#103	C₂²×C₂₉	1	8	yes	—
89	#97	C₂²×C₂₉	1	2	yes	—
90	C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
91	C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
92	C₂₉	#3185	1	1	yes	characteristic, direct product factor, Sylow
93	C₂×Q₈	—	2	2	no	—
94	C₂×Q₈	C₂³×C₂₉	1	4	yes	—
95	C₂²×C₄	D₄×C₂₉	1	2	yes	—
96	C₂²×C₄	C₂³×C₂₉	1	1	yes	characteristic
97	Q₁₆	—	2	8	no	—
98	M₁₆	—	2	4	no	—
99	C₂×C₈	C₂³×C₂₉	1	2	yes	—
100	C₂×C₈	C₂³×C₂₉	1	2	yes	—
101	C₄⋊C₄	—	2	2	no	—
102	C₄⋊C₄	—	2	2	no	—
103	C₄⋊C₄	—	2	2	no	—
104	C₄⋊C₄	—	2	4	no	—
105	C₄⋊C₄	—	2	4	no	—
106	C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
107	C₂²⋊C₄	—	2	4	no	—
108	C₄²	—	2	4	no	—
109	C₄²	D₄×C₂₉	1	2	yes	—
110	C₄²	C₂³×C₂₉	1	1	yes	characteristic
111	C₄²	C₂³×C₂₉	1	1	yes	characteristic
112	C₂³	C₂×D₄×C₂₉	1	1	yes	characteristic
113	Q₈	—	2	8	no	—
114	Q₈	—	4	4	no	—
115	C₂×C₄	—	2	4	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	4	no	—
118	C₂×C₄	—	2	4	no	—
119	C₂×C₄	C₂×D₄×C₂₉	1	2	yes	—
120	C₂×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
121	C₂×C₄	C₂×D₄×C₂₉	1	2	yes	—
122	C₂×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
123	C₈	—	2	2	no	—
124	C₈	#41×C₂₉	1	4	yes	—
125	C₂²	—	2	1	no	—
126	C₂²	—	2	2	no	—
127	C₂²	C₂²×D₄×C₂₉	1	1	yes	characteristic
128	C₄	—	2	1	no	—
129	C₄	—	2	2	no	—
130	C₄	—	4	4	no	—
131	C₄	—	4	4	no	—
132	C₄	C₂₉×#137	1	4	yes	—
133	C₄	C₂×#41×C₂₉	1	2	yes	—
134	C₂	—	4	1	no	—
135	C₂	C₂₉×#532	1	1	yes	characteristic
136	C₂	C₂×C₂₉×#137	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂₉×#533

C₂

yes

maximal

C₂₉×#498

C₂

yes

maximal, characteristic, complemented

C₂₉×#494

C₂

yes

maximal, characteristic, complemented

C₂₉×#487

C₂

yes

maximal, complemented

C₂₉×#470

C₂

yes

maximal

C₂₉×#441

C₂

yes

maximal, complemented

C₄×M₁₆×C₂₉

C₂

yes

maximal, characteristic

C₂×Q₁₆×C₂₉

C₂²

yes

—

C₂×M₁₆×C₂₉

C₂²

yes

—

C₂₉×C₄⋊Q₈

C₂²

yes

—

C₂₉×C₄⋊Q₈

C₂²

yes

—

C₂₉×#125

—

C₂₉×C₂²⋊Q₈

—

C₂₉×C₂²⋊Q₈

C₂²

yes

—

C₄×Q₈×C₂₉

—

C₄×Q₈×C₂₉

C₂²

yes

—

C₂₉×#117

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂₉×#106

C₂²

yes

—

C₂₉×#103

C₂²

yes

—

C₂₉×#97

C₂²

yes

—

C₄×C₈×C₂₉

C₂²

yes

characteristic

C₄×C₈×C₂₉

C₂²

yes

characteristic

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

C₂³

yes

—

C₂²×C₄×C₂₉

D₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

Q₁₆×C₂₉

—

M₁₆×C₂₉

—

C₂×C₈×C₂₉

C₂³

yes

—

C₂×C₈×C₂₉

C₂³

yes

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

C₂³

yes

—

C₂²⋊C₄×C₂₉

—

C₄²×C₂₉

—

C₄²×C₂₉

D₄

yes

—

C₄²×C₂₉

C₂³

yes

characteristic

C₄²×C₂₉

C₂³

yes

characteristic

C₂³×C₂₉

C₂×D₄

yes

characteristic

Q₈×C₂₉

—

Q₈×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂⁴

yes

characteristic

C₈×C₂₉

—

C₈×C₂₉

#41

yes

—

#3185

C₂₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

C₂²×D₄

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

#137

yes

—

C₄×C₂₉

C₂×#41

yes

—

#533

C₂×C₂₉

yes

—

#498

C₂×C₂₉

yes

characteristic, complemented

#494

C₂×C₂₉

yes

characteristic, complemented

#487

C₂×C₂₉

yes

complemented

#470

C₂×C₂₉

yes

—

#441

C₂×C₂₉

yes

complemented

C₄×M₁₆

C₂×C₂₉

yes

characteristic

C₂×C₂₉

—

C₂×C₂₉

#532

yes

characteristic

C₂×C₂₉

C₂×#137

yes

—

C₂×Q₁₆

C₂²×C₂₉

yes

—

C₂×M₁₆

C₂²×C₂₉

yes

—

C₄⋊Q₈

C₂²×C₂₉

yes

—

C₄⋊Q₈

C₂²×C₂₉

yes

—

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

C₂²×C₂₉

yes

—

C₄×Q₈

—

C₄×Q₈

C₂²×C₂₉

yes

—

#117

—

C₂×C₄²

C₂²×C₂₉

yes

characteristic

#106

C₂²×C₂₉

yes

—

#103

C₂²×C₂₉

yes

—

#97

C₂²×C₂₉

yes

—

C₄×C₈

C₂²×C₂₉

yes

characteristic

C₄×C₈

C₂²×C₂₉

yes

characteristic

C₂₉

#3185

yes

characteristic, direct product factor, Sylow

C₂×Q₈

—

C₂×Q₈

C₂³×C₂₉

yes

—

C₂²×C₄

D₄×C₂₉

yes

—

C₂²×C₄

C₂³×C₂₉

yes

characteristic

Q₁₆

—

M₁₆

—

C₂×C₈

C₂³×C₂₉

yes

—

100

C₂×C₈

C₂³×C₂₉

yes

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

C₂³×C₂₉

yes

—

107

C₂²⋊C₄

—

108

C₄²

—

109

C₄²

D₄×C₂₉

yes

—

110

C₄²

C₂³×C₂₉

yes

characteristic

111

C₄²

C₂³×C₂₉

yes

characteristic

112

C₂³

C₂×D₄×C₂₉

yes

characteristic

113

Q₈

—

114

Q₈

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

C₂×D₄×C₂₉

yes

—

120

C₂×C₄

C₂×D₄×C₂₉

yes

characteristic

121

C₂×C₄

C₂×D₄×C₂₉

yes

—

122

C₂×C₄

C₂⁴×C₂₉

yes

characteristic

123

C₈

—

124

C₈

#41×C₂₉

yes

—

125

C₂²

—

126

C₂²

—

127

C₂²

C₂²×D₄×C₂₉

yes

characteristic

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

—

132

C₄

C₂₉×#137

yes

—

133

C₄

C₂×#41×C₂₉

yes

—

134

C₂

—

135

C₂

C₂₉×#532

yes

characteristic

136

C₂

C₂×C₂₉×#137

yes

—

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
prime radical	C₂³×C₂₉	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₂₉

C₂²×D₄

commutator, Frattini, cosocle

C₂×C₄

C₂⁴×C₂₉

prime radical

C₂³×C₂₉

C₂×D₄

LCS

G ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

N	H ≅ G/N	type
2. C₂₉×#498	C₂	semidirect
3. C₂₉×#494	C₂	semidirect
4. C₂₉×#487	C₂	semidirect
6. C₂₉×#441	C₂	semidirect
56. #3185	C₂₉	direct (N × H)
67. #498	C₂×C₂₉	semidirect
68. #494	C₂×C₂₉	semidirect
69. #487	C₂×C₂₉	semidirect
71. #441	C₂×C₂₉	semidirect
92. C₂₉	#3185	direct (N × H)

H ≅ G/N

type

2. C₂₉×#498

C₂

semidirect

3. C₂₉×#494

C₂

semidirect

4. C₂₉×#487

C₂

semidirect

6. C₂₉×#441

C₂

semidirect

56. #3185

C₂₉

direct (N × H)

67. #498

C₂×C₂₉

semidirect

68. #494

C₂×C₂₉

semidirect

69. #487

C₂×C₂₉

semidirect

71. #441

C₂×C₂₉

semidirect

92. C₂₉

#3185

direct (N × H)

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

subgroup	index
C₂₉×#533	2
C₂₉×#498	2
C₂₉×#494	2
C₂₉×#487	2
C₂₉×#470	2
C₂₉×#441	2
C₄×M₁₆×C₂₉	2
#3185	29

subgroup

index

C₂₉×#533

C₂₉×#498

C₂₉×#494

C₂₉×#487

C₂₉×#470

C₂₉×#441

C₄×M₁₆×C₂₉

#3185

Subgroups — C₂₉×#3185 #16816899

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C29×#3185 #16816899

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#3185 #16816899