Group #16820317 — subgroups

Subgroups — #16820317

Order 3712.

412 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 113 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×#11745180	C₂	1	4	yes	maximal, complemented
2	C₂×#11745151	C₂	1	1	yes	maximal, characteristic, complemented
3	#14271029	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₉×#127	C₂	1	1	yes	maximal, characteristic
5	C₂²×D₄×C₂₉	—	2	2	no	—
6	C₂²×D₄×C₂₉	C₂²	1	2	yes	—
7	C₂₉×#127	—	2	2	no	—
8	C₂₉×#127	C₄	1	4	yes	complemented
9	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₂₉	C₂²	1	2	yes	—
11	C₂²×#6597	C₂²	1	2	yes	—
12	#11745180	—	2	8	no	—
13	#11745179	—	2	2	no	—
14	#11745151	—	2	2	no	—
15	C₂⁴×C₂₉	—	2	2	no	—
16	C₂×D₄×C₂₉	—	2	8	no	—
17	C₂×D₄×C₂₉	—	2	4	no	—
18	C₂×D₄×C₂₉	—	2	2	no	—
19	C₂×D₄×C₂₉	—	2	4	no	—
20	C₂×D₄×C₂₉	—	4	8	no	—
21	C₂×D₄×C₂₉	C₂×C₄	1	4	yes	—
22	C₂²×C₄×C₂₉	D₄	1	2	yes	—
23	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
24	C₂²×Dic₂₉	—	2	2	no	—
25	C₄²×C₂₉	C₂×C₄	1	2	yes	—
26	C₄²×C₂₉	D₄	1	2	yes	—
27	C₄⋊Dic₂₉	—	2	4	no	—
28	C₂×#6597	—	2	2	no	—
29	C₂×#6597	—	2	2	no	—
30	C₂×#6597	D₄	1	4	yes	complemented
31	C₂³×C₂₉	—	2	4	no	—
32	C₂³×C₂₉	—	4	2	no	—
33	C₂³×C₂₉	—	4	2	no	—
34	C₂³×C₂₉	—	4	8	no	—
35	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
36	D₄×C₂₉	—	2	8	no	—
37	D₄×C₂₉	—	4	16	no	—
38	D₄×C₂₉	—	4	4	no	—
39	C₂×C₄×C₂₉	—	2	4	no	—
40	C₂×C₄×C₂₉	C₂²⋊C₄	1	4	yes	—
41	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
43	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₂₉	#41	1	2	yes	—
45	C₂×Dic₂₉	—	4	2	no	—
46	C₂×Dic₂₉	—	4	4	no	—
47	#6597	—	2	4	no	—
48	#1961	—	29	1	no	maximal, Sylow
49	C₂²×C₂₉	—	4	4	no	—
50	C₂²×C₂₉	—	4	8	no	—
51	C₂²×C₂₉	—	8	4	no	—
52	C₂²×C₂₉	—	8	4	no	—
53	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
54	C₂²×C₂₉	#124	1	1	yes	characteristic
55	C₂²×C₂₉	#127	1	1	yes	characteristic
56	C₂²×C₂₉	AGL(1,ℤ/8)	1	4	yes	—
57	C₄×C₂₉	—	2	4	no	—
58	C₄×C₂₉	C₄×D₄	1	2	yes	—
59	C₄×C₂₉	#121	1	2	yes	—
60	Dic₂₉	—	8	2	no	—
61	C₂×#127	D₂₉	1	1	yes	characteristic
62	C₂×#102	—	29	4	no	—
63	C₂×#97	—	29	1	no	—
64	#382	—	29	1	no	—
65	C₂×C₂₉	—	8	4	no	—
66	C₂×C₂₉	#390	1	1	yes	characteristic
67	C₂×C₂₉	#418	1	2	yes	—
68	C₂×C₂₉	#490	1	2	yes	—
69	C₂×C₂₉	#496	1	2	yes	—
70	C₂²×D₄	—	2	2	no	—
71	C₂²×D₄	C₂×D₂₉	1	2	yes	—
72	C₂²×C₈	—	29	2	no	—
73	#127	—	2	2	no	—
74	#127	Dic₂₉	1	4	yes	complemented
75	C₂×C₄⋊C₄	—	29	2	no	—
76	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
77	#102	—	58	8	no	—
78	#97	—	58	2	no	—
79	#95	—	58	2	no	—
80	C₂₉	#1961	1	1	yes	characteristic, complemented, Sylow
81	C₂⁴	—	2	2	no	—
82	C₂×D₄	—	2	8	no	—
83	C₂×D₄	—	2	4	no	—
84	C₂×D₄	—	2	4	no	—
85	C₂×D₄	—	2	2	no	—
86	C₂×D₄	—	4	8	no	—
87	C₂×D₄	C₂×Dic₂₉	1	4	yes	—
88	C₂²×C₄	—	58	2	no	—
89	C₂²×C₄	C₂²⋊D₂₉	1	2	yes	—
90	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
91	C₂×C₈	—	29	4	no	—
92	C₂×C₈	—	58	2	no	—
93	C₂×C₈	—	58	2	no	—
94	C₄⋊C₄	—	58	4	no	—
95	C₄²	C₂×Dic₂₉	1	2	yes	—
96	C₄²	C₂²⋊D₂₉	1	2	yes	—
97	C₂³	—	2	4	no	—
98	C₂³	—	4	8	no	—
99	C₂³	—	4	2	no	—
100	C₂³	—	4	2	no	—
101	C₂³	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
102	D₄	—	2	8	no	—
103	D₄	—	4	16	no	—
104	D₄	—	4	4	no	—
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	—	116	4	no	—
107	C₂×C₄	—	116	2	no	—
108	C₂×C₄	C₂²⋊Dic₂₉	1	4	yes	—
109	C₂×C₄	D₄×D₂₉	1	2	yes	—
110	C₂×C₄	#90807	1	2	yes	—
111	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
112	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
113	C₈	—	58	4	no	—
114	C₂²	—	4	4	no	—
115	C₂²	—	4	8	no	—
116	C₂²	—	8	4	no	—
117	C₂²	—	8	4	no	—
118	C₂²	#11745294	1	4	yes	—
119	C₂²	#11745298	1	1	yes	characteristic
120	C₂²	#11745302	1	1	yes	characteristic
121	C₂²	C₂×C₂²⋊Dic₂₉	1	1	yes	characteristic
122	C₄	—	2	4	no	—
123	C₄	—	232	2	no	—
124	C₄	D₄×Dic₂₉	1	2	yes	—
125	C₄	#11745300	1	2	yes	—
126	C₂	—	8	4	no	—
127	C₂	#14271066	1	1	yes	characteristic
128	C₂	#14271168	1	2	yes	—
129	C₂	#14271527	1	2	yes	—
130	C₂	#14271550	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745180

C₂

yes

maximal, complemented

C₂×#11745151

C₂

yes

maximal, characteristic, complemented

#14271029

C₂

yes

maximal, characteristic, complemented

C₂×C₂₉×#127

C₂

yes

maximal, characteristic

C₂²×D₄×C₂₉

—

C₂²×D₄×C₂₉

C₂²

yes

—

C₂₉×#127

—

C₂₉×#127

C₄

yes

complemented

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₂₉

C₂²

yes

—

C₂²×#6597

C₂²

yes

—

#11745180

—

#11745179

—

#11745151

—

C₂⁴×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

D₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

—

C₄²×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

D₄

yes

—

C₄⋊Dic₂₉

—

C₂×#6597

—

C₂×#6597

—

C₂×#6597

D₄

yes

complemented

C₂³×C₂₉

—

C₂³×C₂₉

—

C₂³×C₂₉

—

C₂³×C₂₉

—

C₂³×C₂₉

C₂×D₄

yes

characteristic

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²⋊C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

#41

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

#6597

—

#1961

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

C₂×C₂²⋊C₄

yes

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₂²×C₂₉

yes

—

C₄×C₂₉

—

C₄×C₂₉

C₄×D₄

yes

—

C₄×C₂₉

#121

yes

—

Dic₂₉

—

C₂×#127

D₂₉

yes

characteristic

C₂×#102

—

C₂×#97

—

#382

—

C₂×C₂₉

—

C₂×C₂₉

#390

yes

characteristic

C₂×C₂₉

#418

yes

—

C₂×C₂₉

#490

yes

—

C₂×C₂₉

#496

yes

—

C₂²×D₄

—

C₂²×D₄

C₂×D₂₉

yes

—

C₂²×C₈

—

#127

—

#127

Dic₂₉

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₂₉

yes

—

—

—

C₂₉

#1961

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

C₂×Dic₂₉

yes

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₂₉

yes

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄²

C₂×Dic₂₉

yes

—

C₄²

C₂²⋊D₂₉

yes

—

C₂³

—

C₂³

—

C₂³

—

100

C₂³

—

101

C₂³

C₂×C₂²⋊D₂₉

yes

characteristic

102

D₄

—

103

D₄

—

104

D₄

—

105

C₂×C₄

—

106

C₂×C₄

—

116

—

107

C₂×C₄

—

116

—

108

C₂×C₄

C₂²⋊Dic₂₉

yes

—

109

C₂×C₄

D₄×D₂₉

yes

—

110

C₂×C₄

#90807

yes

—

111

C₂×C₄

C₂²×Dic₂₉

yes

characteristic

112

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

113

C₈

—

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

C₂²

#11745294

yes

—

119

C₂²

#11745298

yes

characteristic

120

C₂²

#11745302

yes

characteristic

121

C₂²

C₂×C₂²⋊Dic₂₉

yes

characteristic

122

C₄

—

123

C₄

—

232

—

124

C₄

D₄×Dic₂₉

yes

—

125

C₄

#11745300

yes

—

126

C₂

—

127

C₂

#14271066

yes

characteristic

128

C₂

#14271168

yes

—

129

C₂

#14271527

yes

—

130

C₂

#14271550

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₂₉
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting, prime radical	C₂×C₂₉×#127	C₂
socle	C₂³×C₂₉	C₂×D₄
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	C₂×#127	D₂₉
hypocenter	C₂₉	#1961
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#127

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₂₉

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting, prime radical

C₂×C₂₉×#127

C₂

socle

C₂³×C₂₉

C₂×D₄

cosocle

C₂²×C₄×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#127

N	H ≅ G/N	type
1. C₂×#11745180	C₂	semidirect
2. C₂×#11745151	C₂	semidirect
3. #14271029	C₂	semidirect
8. C₂₉×#127	C₄	semidirect
30. C₂×#6597	D₄	semidirect
74. #127	Dic₂₉	semidirect
80. C₂₉	#1961	semidirect

H ≅ G/N

type

1. C₂×#11745180

C₂

semidirect

2. C₂×#11745151

C₂

semidirect

3. #14271029

C₂

semidirect

8. C₂₉×#127

C₄

semidirect

30. C₂×#6597

D₄

semidirect

74. #127

Dic₂₉

semidirect

80. C₂₉

#1961

semidirect

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

subgroup	index
C₂×#11745180	2
C₂×#11745151	2
#14271029	2
C₂×C₂₉×#127	2
#1961	29

subgroup

index

C₂×C₂₉×#127

Subgroups — #16820317

Conjugacy classes of subgroups

Complements

Maximal subgroups