Group #16819083 — subgroups

Subgroups — #16819083

Order 3712.

224 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 65 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	#14271566	C₂	1	1	yes	maximal, characteristic, complemented
2	#14271539	C₂	1	1	yes	maximal, characteristic
3	#14271537	C₂	1	1	yes	maximal, characteristic, complemented
4	#14271535	C₂	1	1	yes	maximal, characteristic, complemented
5	#14271510	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×#6597	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#486	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₂₉×#127	C₂²	1	1	yes	characteristic
10	C₂×#90784	—	2	2	no	—
11	C₂×#90783	—	2	2	no	—
12	C₂×#90782	—	2	2	no	—
13	#11745236	C₂²	1	1	yes	characteristic
14	#11745231	C₂²	1	1	yes	characteristic
15	C₂₉×#102	—	2	2	no	—
16	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
17	#11745169	—	2	2	no	—
18	#11745155	—	2	2	no	—
19	C₄×#6597	C₂²	1	1	yes	characteristic
20	C₄×#6597	C₂²	1	1	yes	characteristic
21	C₂×Q₈×C₂₉	—	2	1	no	—
22	C₂×D₄×C₂₉	—	2	1	no	—
23	C₂×D₄×C₂₉	—	2	1	no	—
24	C₂×D₄×C₂₉	—	2	1	no	—
25	C₂×D₁₁₆	—	2	1	no	—
26	C₂×D₁₁₆	—	2	1	no	—
27	C₂×D₁₁₆	—	2	1	no	—
28	C₂×Dic₅₈	—	2	1	no	—
29	C₂×C₈×C₂₉	D₄	1	2	yes	—
30	C₄⋊C₄×C₂₉	—	2	1	no	—
31	C₄⋊C₄×C₂₉	—	2	1	no	—
32	C₄²×C₂₉	C₂³	1	1	yes	characteristic
33	#90784	—	4	4	no	—
34	#90783	—	4	4	no	—
35	#90782	—	4	4	no	—
36	C₄⋊Dic₂₉	—	2	1	no	—
37	C₄⋊Dic₂₉	—	2	1	no	—
38	C₂×#6597	D₄	1	2	yes	—
39	C₂×#6597	D₄	1	2	yes	—
40	C₂³×C₂₉	—	4	1	no	—
41	C₂²×D₂₉	—	4	1	no	—
42	Q₈×C₂₉	—	4	2	no	—
43	D₄×C₂₉	—	4	2	no	—
44	D₄×C₂₉	—	4	2	no	—
45	D₄×C₂₉	—	4	2	no	—
46	C₂×C₄×C₂₉	—	4	1	no	—
47	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
50	C₂×Dic₂₉	—	4	1	no	—
51	D₁₁₆	—	4	2	no	—
52	D₁₁₆	—	4	2	no	—
53	D₁₁₆	—	4	2	no	—
54	Dic₅₈	—	4	2	no	—
55	C₈×C₂₉	—	2	2	no	—
56	#6597	D₈	1	4	yes	complemented
57	#6597	SD₁₆	1	4	yes	complemented
58	#1706	—	29	1	no	maximal, Sylow
59	C₂²×C₂₉	—	8	1	no	—
60	C₂²×C₂₉	—	8	1	no	—
61	C₂²×C₂₉	—	8	1	no	—
62	C₂²×C₂₉	#127	1	1	yes	characteristic
63	C₂×D₂₉	—	8	1	no	—
64	C₂×D₂₉	—	8	1	no	—
65	C₂×D₂₉	—	8	1	no	—
66	C₄×C₂₉	—	8	1	no	—
67	C₄×C₂₉	C₂×D₈	1	2	yes	—
68	C₄×C₂₉	C₂×SD₁₆	1	2	yes	—
69	C₄×C₂₉	#135	1	2	yes	—
70	Dic₂₉	—	8	1	no	—
71	#500	—	29	1	no	—
72	#493	—	29	1	no	—
73	#492	—	29	1	no	—
74	#492	—	29	1	no	—
75	#486	—	29	1	no	—
76	#486	D₂₉	1	1	yes	characteristic, complemented
77	C₈²	—	29	1	no	—
78	C₂×C₂₉	—	16	1	no	—
79	C₂×C₂₉	#492	1	1	yes	characteristic
80	C₂×C₂₉	#493	1	1	yes	characteristic
81	C₂×C₂₉	#495	1	1	yes	characteristic
82	D₂₉	—	16	1	no	—
83	C₂×SD₁₆	—	58	2	no	—
84	C₂×SD₁₆	—	58	2	no	—
85	C₂×D₈	—	58	2	no	—
86	C₄⋊Q₈	—	29	1	no	—
87	C₄⋊Q₈	C₂×D₂₉	1	1	yes	characteristic
88	#127	—	29	1	no	—
89	#127	C₂×D₂₉	1	1	yes	characteristic
90	#107	—	58	2	no	—
91	#102	—	2	2	no	—
92	#102	—	58	2	no	—
93	C₄×C₈	—	29	1	no	—
94	C₄×C₈	—	29	1	no	—
95	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
96	C₂₉	#1706	1	1	yes	characteristic, complemented, Sylow
97	C₂×Q₈	—	2	1	no	—
98	C₂×Q₈	—	58	1	no	—
99	C₂×D₄	—	2	1	no	—
100	C₂×D₄	—	2	1	no	—
101	C₂×D₄	—	2	1	no	—
102	C₂×D₄	—	58	1	no	—
103	C₂×D₄	—	58	1	no	—
104	C₂×D₄	—	58	1	no	—
105	SD₁₆	—	116	4	no	—
106	SD₁₆	—	116	4	no	—
107	D₈	—	116	4	no	—
108	C₂×C₈	—	29	2	no	—
109	C₂×C₈	—	29	2	no	—
110	C₂×C₈	C₂²⋊D₂₉	1	2	yes	—
111	C₄⋊C₄	—	2	1	no	—
112	C₄⋊C₄	—	2	1	no	—
113	C₄⋊C₄	—	58	1	no	—
114	C₄⋊C₄	—	58	1	no	—
115	C₄²	C₂²×D₂₉	1	1	yes	characteristic
116	C₂³	—	4	1	no	—
117	C₂³	—	116	1	no	—
118	Q₈	—	4	2	no	—
119	Q₈	—	116	2	no	—
120	D₄	—	4	2	no	—
121	D₄	—	4	2	no	—
122	D₄	—	4	2	no	—
123	D₄	—	116	2	no	—
124	D₄	—	116	2	no	—
125	D₄	—	116	2	no	—
126	C₂×C₄	—	4	1	no	—
127	C₂×C₄	—	116	1	no	—
128	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
129	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
130	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
131	C₈	—	2	2	no	—
132	C₈	—	29	4	no	—
133	C₈	—	29	4	no	—
134	C₂²	—	8	1	no	—
135	C₂²	—	8	1	no	—
136	C₂²	—	8	1	no	—
137	C₂²	—	232	1	no	—
138	C₂²	—	232	1	no	—
139	C₂²	—	232	1	no	—
140	C₂²	#11745302	1	1	yes	characteristic
141	C₄	—	8	1	no	—
142	C₄	—	232	1	no	—
143	C₄	D₈×D₂₉	1	2	yes	—
144	C₄	SD₁₆×D₂₉	1	2	yes	—
145	C₄	#11745312	1	2	yes	—
146	C₂	—	16	1	no	—
147	C₂	—	464	1	no	—
148	C₂	#14271534	1	1	yes	characteristic
149	C₂	#14271538	1	1	yes	characteristic
150	C₂	#14271545	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271566

C₂

yes

maximal, characteristic, complemented

#14271539

C₂

yes

maximal, characteristic

#14271537

C₂

yes

maximal, characteristic, complemented

#14271535

C₂

yes

maximal, characteristic, complemented

#14271510

C₂

yes

maximal, characteristic, complemented

C₈×#6597

C₂

yes

maximal, characteristic, complemented

C₂₉×#486

C₂

yes

maximal, characteristic, complemented

C₂₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂₉×#127

C₂²

yes

—

—

—

C₂²

yes

characteristic

#11745231

C₂²

yes

characteristic

C₂₉×#102

—

C₄×C₈×C₂₉

C₂²

yes

—

—

C₂²

yes

characteristic

C₄×#6597

C₂²

yes

characteristic

C₂×Q₈×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₁₁₆

—

C₂×D₁₁₆

—

C₂×D₁₁₆

—

C₂×Dic₅₈

—

C₂×C₈×C₂₉

D₄

yes

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄²×C₂₉

C₂³

yes

—

—

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₂×#6597

D₄

yes

—

C₂×#6597

D₄

yes

—

C₂³×C₂₉

—

C₂²×D₂₉

—

Q₈×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×Dic₂₉

—

D₁₁₆

—

D₁₁₆

—

D₁₁₆

—

Dic₅₈

—

C₈×C₂₉

—

#6597

D₈

yes

complemented

#6597

SD₁₆

yes

complemented

#1706

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

#127

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₂×D₈

yes

—

C₄×C₂₉

C₂×SD₁₆

yes

—

C₄×C₂₉

#135

yes

—

Dic₂₉

—

—

—

—

—

—

D₂₉

yes

characteristic, complemented

C₈²

—

C₂×C₂₉

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

D₂₉

—

C₂×SD₁₆

—

C₂×SD₁₆

—

C₂×D₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₂₉

yes

characteristic

#127

—

#127

C₂×D₂₉

yes

—

—

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₂₉

yes

characteristic

C₂₉

#1706

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

100

C₂×D₄

—

101

C₂×D₄

—

102

C₂×D₄

—

103

C₂×D₄

—

104

C₂×D₄

—

105

SD₁₆

—

116

—

106

SD₁₆

—

116

—

107

D₈

—

116

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

C₂²⋊D₂₉

yes

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₄²

C₂²×D₂₉

yes

characteristic

116

C₂³

—

117

C₂³

—

116

—

118

Q₈

—

119

Q₈

—

116

—

120

D₄

—

121

D₄

—

122

D₄

—

123

D₄

—

116

—

124

D₄

—

116

—

125

D₄

—

116

—

126

C₂×C₄

—

127

C₂×C₄

—

116

—

128

C₂×C₄

D₄×D₂₉

yes

characteristic

129

C₂×C₄

D₄×D₂₉

yes

characteristic

130

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

131

C₈

—

132

C₈

—

133

C₈

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

232

—

138

C₂²

—

232

—

139

C₂²

—

232

—

140

C₂²

#11745302

yes

characteristic

141

C₄

—

142

C₄

—

232

—

143

C₄

D₈×D₂₉

yes

—

144

C₄

SD₁₆×D₂₉

yes

—

145

C₄

#11745312

yes

—

146

C₂

—

147

C₂

—

464

—

148

C₂

#14271534

yes

characteristic

149

C₂

#14271538

yes

characteristic

150

C₂

#14271545

yes

characteristic

	subgroup	G/H
center	C₂²	#11745302
commutator, cosocle	C₄²×C₂₉	C₂³
Frattini	C₄²	C₂²×D₂₉
Fitting	C₂₉×#486	C₂
socle	C₂²×C₂₉	#127
prime radical	#14271539	C₂
hypercenter	#486	D₂₉
hypocenter	C₂₉	#1706
LCS	G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #486

subgroup

G/H

center

C₂²

#11745302

commutator, cosocle

C₄²×C₂₉

C₂³

Frattini

C₄²

C₂²×D₂₉

Fitting

C₂₉×#486

C₂

C₂²×C₂₉

C₂

D₂₉

C₂₉

G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #486

N	H ≅ G/N	type
1. #14271566	C₂	semidirect
3. #14271537	C₂	semidirect
4. #14271535	C₂	semidirect
5. #14271510	C₂	semidirect
6. C₈×#6597	C₂	semidirect
7. C₂₉×#486	C₂	semidirect
56. #6597	D₈	semidirect
57. #6597	SD₁₆	semidirect
76. #486	D₂₉	semidirect
96. C₂₉	#1706	semidirect

H ≅ G/N

type

1. #14271566

C₂

semidirect

3. #14271537

C₂

semidirect

4. #14271535

C₂

semidirect

5. #14271510

C₂

semidirect

6. C₈×#6597

C₂

semidirect

7. C₂₉×#486

C₂

semidirect

56. #6597

D₈

semidirect

57. #6597

SD₁₆

semidirect

76. #486

D₂₉

semidirect

96. C₂₉

#1706

semidirect

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

subgroup	index
#14271566	2
#14271539	2
#14271537	2
#14271535	2
#14271510	2
C₈×#6597	2
C₂₉×#486	2
#1706	29

subgroup

index

C₂₉×#486

Subgroups — #16819083

Conjugacy classes of subgroups

Complements

Maximal subgroups