Group #16819217 — subgroups

Subgroups — #16819217

Order 3712.

372 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 137 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	C₂²×#90772	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆×D₂₉	C₂	1	2	yes	maximal
3	#14270928	C₂	1	1	yes	maximal, characteristic, complemented
4	#14270927	C₂	1	2	yes	maximal, complemented
5	C₂₉×#341	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×D₂₉	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₂₉	C₂²	1	2	yes	—
8	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
9	C₂×#90777	C₂²	1	2	yes	—
10	C₂²×#6597	C₂²	1	1	yes	characteristic
11	M₁₆×D₂₉	—	2	4	no	—
12	M₁₆×D₂₉	C₄	1	8	yes	—
13	C₂×#90772	—	2	2	no	—
14	C₂×#90772	—	2	4	no	—
15	C₂×#90772	C₄	1	4	yes	—
16	C₂×C₈×D₂₉	—	2	2	no	—
17	C₂³×D₂₉	Q₈	1	1	yes	characteristic
18	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
19	C₂²×Dic₂₉	Q₈	1	1	yes	characteristic
20	C₂×C₄×D₂₉	C₂×C₄	1	2	yes	—
21	C₂×C₄×D₂₉	C₂×C₄	1	4	yes	—
22	C₂×C₄×D₂₉	D₄	1	2	yes	—
23	C₂×C₄×D₂₉	D₄	1	4	yes	—
24	M₁₆×C₂₉	—	2	2	no	—
25	M₁₆×C₂₉	C₂×C₄	1	4	yes	—
26	C₂×C₈×C₂₉	—	2	2	no	—
27	C₂×C₈×C₂₉	—	2	2	no	—
28	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
29	#90777	—	2	2	no	—
30	#90777	C₂×C₄	1	4	yes	—
31	C₂×#6597	—	2	2	no	—
32	C₂×#6597	—	2	2	no	—
33	C₂×#6597	C₂×C₄	1	2	yes	—
34	#90772	—	2	8	no	—
35	#90772	—	2	8	no	—
36	C₈×D₂₉	—	2	8	no	—
37	C₂³×C₂₉	C₂×Q₈	1	1	yes	characteristic
38	C₂²×D₂₉	—	4	2	no	—
39	C₂²×D₂₉	C₄⋊C₄	1	2	yes	—
40	C₂²×D₂₉	C₄⋊C₄	1	4	yes	—
41	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
43	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
44	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
45	C₂×Dic₂₉	C₄⋊C₄	1	4	yes	—
46	C₂×Dic₂₉	C₄⋊C₄	1	2	yes	—
47	C₄×D₂₉	C₄²	1	4	yes	—
48	C₄×D₂₉	C₂²⋊C₄	1	4	yes	—
49	C₄×D₂₉	C₂²⋊C₄	1	4	yes	—
50	C₄×D₂₉	C₂²⋊C₄	1	4	yes	—
51	C₈×C₂₉	—	2	4	no	—
52	C₈×C₂₉	—	2	2	no	—
53	#6597	—	2	4	no	—
54	#6597	—	2	2	no	—
55	#1738	—	29	1	no	maximal, Sylow
56	C₂²×C₂₉	—	2	2	no	—
57	C₂²×C₂₉	C₂×C₄⋊C₄	1	2	yes	—
58	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
59	C₂×D₂₉	—	2	4	no	—
60	C₂×D₂₉	—	4	4	no	—
61	C₂×D₂₉	#95	1	4	yes	—
62	C₄×C₂₉	C₂×C₄²	1	1	yes	characteristic
63	C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
64	C₄×C₂₉	C₂×C₂²⋊C₄	1	2	yes	—
65	Dic₂₉	#95	1	4	yes	—
66	C₂²×M₁₆	—	29	1	no	—
67	C₂²×M₁₆	—	29	2	no	—
68	#341	—	29	2	no	—
69	#341	—	29	1	no	—
70	#341	D₂₉	1	1	yes	characteristic, complemented
71	C₂×C₂₉	—	2	2	no	—
72	C₂×C₂₉	C₂×#95	1	1	yes	characteristic
73	C₂×C₂₉	#430	1	2	yes	—
74	D₂₉	—	2	4	no	—
75	C₂³×C₄	—	29	1	no	—
76	C₂×M₁₆	—	29	4	no	—
77	C₂×M₁₆	—	29	2	no	—
78	C₂×M₁₆	—	29	8	no	—
79	C₂×M₁₆	—	58	4	no	—
80	C₂×M₁₆	—	58	2	no	—
81	C₂×M₁₆	—	58	4	no	—
82	C₂×M₁₆	C₂×D₂₉	1	2	yes	—
83	C₂²×C₈	—	29	1	no	—
84	C₂²×C₈	—	58	2	no	—
85	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
86	C₂₉	#1738	1	1	yes	characteristic, complemented, Sylow
87	C₂⁴	—	29	1	no	—
88	C₂²×C₄	—	29	1	no	—
89	C₂²×C₄	—	29	4	no	—
90	C₂²×C₄	—	29	2	no	—
91	C₂²×C₄	—	29	4	no	—
92	C₂²×C₄	—	29	2	no	—
93	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
94	M₁₆	—	2	2	no	—
95	M₁₆	—	29	4	no	—
96	M₁₆	—	58	8	no	—
97	M₁₆	—	58	8	no	—
98	M₁₆	—	58	2	no	—
99	M₁₆	C₄×D₂₉	1	4	yes	—
100	C₂×C₈	—	2	2	no	—
101	C₂×C₈	—	2	2	no	—
102	C₂×C₈	—	29	2	no	—
103	C₂×C₈	—	58	8	no	—
104	C₂×C₈	—	58	2	no	—
105	C₂×C₈	—	58	2	no	—
106	C₂×C₈	C₄×D₂₉	1	2	yes	—
107	C₂³	—	29	2	no	—
108	C₂³	—	29	4	no	—
109	C₂³	—	116	2	no	—
110	C₂³	Q₈×D₂₉	1	1	yes	characteristic
111	C₂×C₄	—	29	4	no	—
112	C₂×C₄	—	29	2	no	—
113	C₂×C₄	—	29	4	no	—
114	C₂×C₄	—	29	4	no	—
115	C₂×C₄	—	29	4	no	—
116	C₂×C₄	—	29	4	no	—
117	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
118	C₂×C₄	C₂×C₄×D₂₉	1	2	yes	—
119	C₂×C₄	D₄×D₂₉	1	2	yes	—
120	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
121	C₈	—	2	2	no	—
122	C₈	—	2	4	no	—
123	C₈	—	58	2	no	—
124	C₈	—	58	4	no	—
125	C₂²	—	2	2	no	—
126	C₂²	—	29	4	no	—
127	C₂²	—	58	4	no	—
128	C₂²	—	116	4	no	—
129	C₂²	C₄⋊C₄×D₂₉	1	2	yes	—
130	C₂²	C₄⋊C₄×D₂₉	1	1	yes	characteristic
131	C₄	—	29	4	no	—
132	C₄	C₄²×D₂₉	1	1	yes	characteristic
133	C₄	C₂²⋊C₄×D₂₉	1	1	yes	characteristic
134	C₄	C₂²⋊C₄×D₂₉	1	2	yes	—
135	C₂	—	2	2	no	—
136	C₂	—	58	4	no	—
137	C₂	#95×D₂₉	1	1	yes	characteristic
138	C₂	#14271210	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#90772

C₂

yes

maximal, characteristic

C₂×M₁₆×D₂₉

C₂

yes

maximal

#14270928

C₂

yes

maximal, characteristic, complemented

#14270927

C₂

yes

maximal, complemented

C₂₉×#341

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₂₉

C₂²

yes

characteristic

C₂×M₁₆×C₂₉

C₂²

yes

—

C₂²×C₈×C₂₉

C₂²

yes

characteristic

C₂×#90777

C₂²

yes

—

C₂²×#6597

C₂²

yes

characteristic

M₁₆×D₂₉

—

M₁₆×D₂₉

C₄

yes

—

C₂×#90772

—

C₂×#90772

—

C₂×#90772

C₄

yes

—

C₂×C₈×D₂₉

—

C₂³×D₂₉

Q₈

yes

characteristic

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

Q₈

yes

characteristic

C₂×C₄×D₂₉

C₂×C₄

yes

—

C₂×C₄×D₂₉

C₂×C₄

yes

—

C₂×C₄×D₂₉

D₄

yes

—

C₂×C₄×D₂₉

D₄

yes

—

M₁₆×C₂₉

—

M₁₆×C₂₉

C₂×C₄

yes

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

#90777

—

#90777

C₂×C₄

yes

—

C₂×#6597

—

C₂×#6597

—

C₂×#6597

C₂×C₄

yes

—

#90772

—

#90772

—

C₈×D₂₉

—

C₂³×C₂₉

C₂×Q₈

yes

characteristic

C₂²×D₂₉

—

C₂²×D₂₉

C₄⋊C₄

yes

—

C₂²×D₂₉

C₄⋊C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×Dic₂₉

C₄⋊C₄

yes

—

C₂×Dic₂₉

C₄⋊C₄

yes

—

C₄×D₂₉

C₄²

yes

—

C₄×D₂₉

C₂²⋊C₄

yes

—

C₄×D₂₉

C₂²⋊C₄

yes

—

C₄×D₂₉

C₂²⋊C₄

yes

—

C₈×C₂₉

—

C₈×C₂₉

—

—

—

—

C₂²×C₂₉

—

C₂²×C₂₉

C₂×C₄⋊C₄

yes

—

C₂²×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

#95

yes

—

C₄×C₂₉

C₂×C₄²

yes

characteristic

C₄×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₂₉

C₂×C₂²⋊C₄

yes

—

Dic₂₉

#95

yes

—

C₂²×M₁₆

—

C₂²×M₁₆

—

#341

—

#341

—

#341

D₂₉

yes

characteristic, complemented

C₂×C₂₉

—

C₂×C₂₉

C₂×#95

yes

characteristic

C₂×C₂₉

#430

yes

—

D₂₉

—

C₂³×C₄

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₂₉

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×D₂₉

yes

characteristic

C₂₉

#1738

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

C₄×D₂₉

yes

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

C₄×D₂₉

yes

—

107

C₂³

—

108

C₂³

—

109

C₂³

—

116

—

110

C₂³

Q₈×D₂₉

yes

characteristic

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

118

C₂×C₄

C₂×C₄×D₂₉

yes

—

119

C₂×C₄

D₄×D₂₉

yes

—

120

C₂×C₄

D₄×D₂₉

yes

characteristic

121

C₈

—

122

C₈

—

123

C₈

—

124

C₈

—

125

C₂²

—

126

C₂²

—

127

C₂²

—

128

C₂²

—

116

—

129

C₂²

C₄⋊C₄×D₂₉

yes

—

130

C₂²

C₄⋊C₄×D₂₉

yes

characteristic

131

C₄

—

132

C₄

C₄²×D₂₉

yes

characteristic

133

C₄

C₂²⋊C₄×D₂₉

yes

characteristic

134

C₄

C₂²⋊C₄×D₂₉

yes

—

135

C₂

—

136

C₂

—

137

C₂

#95×D₂₉

yes

characteristic

138

C₂

#14271210

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₂₉
commutator	C₄×C₂₉	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂₉×#341	C₂
socle	C₂²×C₂₉	C₂×C₄⋊C₄
prime radical	C₂³×D₂₉	Q₈
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	#341	D₂₉
hypocenter	C₂₉	#1738
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂×C₄

D₄×D₂₉

commutator

C₄×C₂₉

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂₉×#341

C₂

socle

C₂²×C₂₉

C₂×C₄⋊C₄

prime radical

C₂³×D₂₉

Q₈

cosocle

C₂²×C₄×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
3. #14270928	C₂	semidirect
4. #14270927	C₂	semidirect
5. C₂₉×#341	C₂	semidirect
70. #341	D₂₉	semidirect
86. C₂₉	#1738	semidirect

H ≅ G/N

type

3. #14270928

C₂

semidirect

4. #14270927

C₂

semidirect

5. C₂₉×#341

C₂

semidirect

70. #341

D₂₉

semidirect

86. C₂₉

#1738

semidirect

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

subgroup	index
C₂²×#90772	2
C₂×M₁₆×D₂₉	2
#14270928	2
#14270927	2
C₂₉×#341	2
#1738	29

subgroup

index

C₂²×#90772

C₂×M₁₆×D₂₉

#14270928

#14270927

C₂₉×#341

#1738

Subgroups — #16819217

Conjugacy classes of subgroups

Complements

Maximal subgroups