Group #16819113 — subgroups

Subgroups — #16819113

Order 3712.

198 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 61 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	#14271561	C₂	1	1	yes	maximal, characteristic, complemented
3	#14271535	C₂	1	1	yes	maximal, characteristic
4	#14271535	C₂	1	1	yes	maximal, characteristic
5	#14271513	C₂	1	1	yes	maximal, characteristic, complemented
6	#14270885	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#486	C₂	1	1	yes	maximal, characteristic
8	C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₂₉×#127	C₂²	1	1	yes	characteristic
10	C₂×#90783	—	2	2	no	—
11	C₂×#90783	—	2	2	no	—
12	#11745231	C₂²	1	1	yes	characteristic
13	#11745231	C₂²	1	1	yes	characteristic
14	C₂₉×#102	—	2	2	no	—
15	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
16	#11745183	—	2	2	no	—
17	#11745165	—	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×Dic₅₈	—	2	1	no	—
26	C₂×Dic₅₈	—	2	1	no	—
27	C₂×C₈×C₂₉	D₄	1	2	yes	—
28	C₄⋊C₄×C₂₉	—	2	1	no	—
29	C₄⋊C₄×C₂₉	—	2	1	no	—
30	C₄²×C₂₉	C₂³	1	1	yes	characteristic
31	#90783	—	4	4	no	—
32	#90783	—	4	4	no	—
33	C₄⋊Dic₂₉	—	2	1	no	—
34	C₄⋊Dic₂₉	—	2	1	no	—
35	C₄⋊Dic₂₉	—	2	1	no	—
36	C₄⋊Dic₂₉	—	2	1	no	—
37	C₂×#6597	D₄	1	2	yes	—
38	C₂×#6597	D₄	1	2	yes	—
39	C₂³×C₂₉	—	4	1	no	—
40	Q₈×C₂₉	—	4	2	no	—
41	D₄×C₂₉	—	4	2	no	—
42	D₄×C₂₉	—	4	2	no	—
43	D₄×C₂₉	—	4	2	no	—
44	C₂×C₄×C₂₉	—	4	1	no	—
45	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
48	C₂×Dic₂₉	—	4	1	no	—
49	C₂×Dic₂₉	—	4	1	no	—
50	Dic₅₈	—	4	2	no	—
51	Dic₅₈	—	4	2	no	—
52	C₈×C₂₉	—	2	2	no	—
53	#6597	—	2	2	no	—
54	#6597	SD₁₆	1	4	yes	complemented
55	#1714	—	29	1	no	maximal, Sylow
56	C₂²×C₂₉	—	8	1	no	—
57	C₂²×C₂₉	—	8	1	no	—
58	C₂²×C₂₉	—	8	1	no	—
59	C₂²×C₂₉	#127	1	1	yes	characteristic
60	C₄×C₂₉	—	8	1	no	—
61	C₄×C₂₉	C₂×SD₁₆	1	2	yes	—
62	C₄×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
63	C₄×C₂₉	#137	1	2	yes	—
64	Dic₂₉	—	8	1	no	—
65	Dic₂₉	—	8	1	no	—
66	#500	—	29	1	no	—
67	#498	—	29	1	no	—
68	#492	—	29	1	no	—
69	#492	—	29	1	no	—
70	#487	—	29	1	no	—
71	#486	D₂₉	1	1	yes	characteristic
72	#322	—	29	1	no	—
73	C₂×C₂₉	—	16	1	no	—
74	C₂×C₂₉	#492	1	1	yes	characteristic
75	C₂×C₂₉	#496	1	1	yes	characteristic
76	C₂×C₂₉	#497	1	1	yes	characteristic
77	C₂×SD₁₆	—	58	2	no	—
78	C₂×SD₁₆	—	58	2	no	—
79	C₄⋊Q₈	—	29	1	no	—
80	C₄⋊Q₈	—	29	1	no	—
81	C₄⋊Q₈	C₂×D₂₉	1	1	yes	characteristic
82	#127	C₂×D₂₉	1	1	yes	characteristic
83	#107	—	58	2	no	—
84	#106	—	58	2	no	—
85	#103	—	58	2	no	—
86	#102	—	2	2	no	—
87	C₄×C₈	—	29	1	no	—
88	C₄×C₈	—	29	1	no	—
89	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
90	C₂₉	#1714	1	1	yes	characteristic, complemented, Sylow
91	C₂×Q₈	—	2	1	no	—
92	C₂×Q₈	—	58	1	no	—
93	C₂×Q₈	—	58	1	no	—
94	C₂×D₄	—	2	1	no	—
95	C₂×D₄	—	2	1	no	—
96	C₂×D₄	—	2	1	no	—
97	SD₁₆	—	116	4	no	—
98	SD₁₆	—	116	4	no	—
99	C₂×C₈	—	29	2	no	—
100	C₂×C₈	—	29	2	no	—
101	C₂×C₈	C₂²⋊D₂₉	1	2	yes	—
102	C₄⋊C₄	—	2	1	no	—
103	C₄⋊C₄	—	2	1	no	—
104	C₄⋊C₄	—	58	1	no	—
105	C₄⋊C₄	—	58	1	no	—
106	C₄⋊C₄	—	58	1	no	—
107	C₄⋊C₄	—	58	1	no	—
108	C₄²	C₂²×D₂₉	1	1	yes	characteristic
109	C₂³	—	4	1	no	—
110	Q₈	—	4	2	no	—
111	Q₈	—	116	2	no	—
112	Q₈	—	116	2	no	—
113	D₄	—	4	2	no	—
114	D₄	—	4	2	no	—
115	D₄	—	4	2	no	—
116	C₂×C₄	—	4	1	no	—
117	C₂×C₄	—	116	1	no	—
118	C₂×C₄	—	116	1	no	—
119	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
120	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
121	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
122	C₈	—	2	2	no	—
123	C₈	—	29	4	no	—
124	C₈	—	58	2	no	—
125	C₂²	—	8	1	no	—
126	C₂²	—	8	1	no	—
127	C₂²	—	8	1	no	—
128	C₂²	#11745302	1	1	yes	characteristic
129	C₄	—	8	1	no	—
130	C₄	—	232	1	no	—
131	C₄	—	232	1	no	—
132	C₄	#11745273	1	2	yes	—
133	C₄	SD₁₆×D₂₉	1	2	yes	—
134	C₄	#11745313	1	2	yes	—
135	C₂	—	16	1	no	—
136	C₂	#14271534	1	1	yes	characteristic
137	C₂	#14271551	1	1	yes	characteristic
138	C₂	#14271558	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271566

C₂

yes

maximal, characteristic, complemented

#14271561

C₂

yes

maximal, characteristic, complemented

#14271535

C₂

yes

maximal, characteristic

#14271535

C₂

yes

maximal, characteristic

#14271513

C₂

yes

maximal, characteristic, complemented

#14270885

C₂

yes

maximal, characteristic, complemented

C₂₉×#486

C₂

yes

maximal, characteristic

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×Dic₅₈

—

C₂×Dic₅₈

—

C₂×C₈×C₂₉

D₄

yes

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄²×C₂₉

C₂³

yes

characteristic

#90783

—

#90783

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₂×#6597

D₄

yes

—

C₂×#6597

D₄

yes

—

C₂³×C₂₉

—

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

—

C₂×Dic₂₉

—

Dic₅₈

—

Dic₅₈

—

C₈×C₂₉

—

#6597

—

#6597

SD₁₆

yes

complemented

#1714

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

#127

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

C₂×SD₁₆

yes

—

C₄×C₂₉

AGL(1,ℤ/8)

yes

—

C₄×C₂₉

#137

yes

—

Dic₂₉

—

Dic₂₉

—

—

—

—

—

—

D₂₉

yes

characteristic

#322

—

C₂×C₂₉

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×SD₁₆

—

C₂×SD₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₂₉

yes

characteristic

#127

C₂×D₂₉

yes

—

—

—

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₂₉

yes

characteristic

C₂₉

#1714

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

SD₁₆

—

116

—

SD₁₆

—

116

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

C₂²⋊D₂₉

yes

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄²

C₂²×D₂₉

yes

characteristic

109

C₂³

—

110

Q₈

—

111

Q₈

—

116

—

112

Q₈

—

116

—

113

D₄

—

114

D₄

—

115

D₄

—

116

C₂×C₄

—

117

C₂×C₄

—

116

—

118

C₂×C₄

—

116

—

119

C₂×C₄

D₄×D₂₉

yes

characteristic

120

C₂×C₄

D₄×D₂₉

yes

characteristic

121

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

122

C₈

—

123

C₈

—

124

C₈

—

125

C₂²

—

126

C₂²

—

127

C₂²

—

128

C₂²

#11745302

yes

characteristic

129

C₄

—

130

C₄

—

232

—

131

C₄

—

232

—

132

C₄

#11745273

yes

—

133

C₄

SD₁₆×D₂₉

yes

—

134

C₄

#11745313

yes

—

135

C₂

—

136

C₂

#14271534

yes

characteristic

137

C₂

#14271551

yes

characteristic

138

C₂

#14271558

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	C₂₉×#127	C₂²
hypercenter	#486	D₂₉
hypocenter	C₂₉	#1714
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

socle

C₂²×C₂₉

#127

prime radical

C₂₉×#127

C₂²

D₂₉

C₂₉

G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #486

N	H ≅ G/N	type
1. #14271566	C₂	semidirect
2. #14271561	C₂	semidirect
5. #14271513	C₂	semidirect
6. #14270885	C₂	semidirect
54. #6597	SD₁₆	semidirect
90. C₂₉	#1714	semidirect

H ≅ G/N

type

1. #14271566

C₂

semidirect

2. #14271561

C₂

semidirect

5. #14271513

C₂

semidirect

6. #14270885

C₂

semidirect

54. #6597

SD₁₆

semidirect

90. C₂₉

#1714

semidirect

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

subgroup	index
#14271566	2
#14271561	2
#14271535	2
#14271513	2
#14270885	2
C₂₉×#486	2
#1714	29

subgroup

index

C₂₉×#486

Subgroups — #16819113

Conjugacy classes of subgroups

Complements

Maximal subgroups