Group #16819618 — subgroups

Subgroups — #16819618

Order 3712.

248 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 109 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×C₈×Dic₂₉	C₂	1	1	yes	maximal, characteristic
2	#14271032	C₂	1	2	yes	maximal
3	#14270926	C₂	1	1	yes	maximal, characteristic
4	#14270925	C₂	1	2	yes	maximal
5	C₂₉×#340	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₂₉	C₂²	1	2	yes	—
9	C₂×#90779	—	2	2	no	—
10	C₂×#90779	—	2	2	no	—
11	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
12	C₂²×#6597	C₂²	1	1	yes	characteristic
13	C₈×Dic₂₉	C₄	1	4	yes	complemented
14	C₂²×C₄×C₂₉	—	2	2	no	—
15	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
16	C₂²×Dic₂₉	—	2	2	no	—
17	C₂²×Dic₂₉	D₄	1	1	yes	characteristic
18	C₂²×Dic₂₉	D₄	1	1	yes	characteristic
19	C₂×C₈×C₂₉	—	2	2	no	—
20	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
21	C₄⋊C₄×C₂₉	—	2	2	no	—
22	C₄⋊C₄×C₂₉	—	2	2	no	—
23	C₄⋊Dic₂₉	—	2	2	no	—
24	C₄⋊Dic₂₉	—	2	2	no	—
25	#90779	—	4	4	no	—
26	#90779	—	4	4	no	—
27	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
28	C₄×Dic₂₉	Q₈	1	2	yes	—
29	C₂×#6597	—	2	2	no	—
30	C₂×#6597	C₂×C₄	1	2	yes	—
31	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₂₉	—	4	2	no	—
33	C₂×C₄×C₂₉	—	4	2	no	—
34	C₂×C₄×C₂₉	—	4	2	no	—
35	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
37	C₂×C₄×C₂₉	#41	1	2	yes	—
38	C₂×C₄×C₂₉	#41	1	2	yes	—
39	C₂×Dic₂₉	—	4	2	no	—
40	C₂×Dic₂₉	—	4	2	no	—
41	C₂×Dic₂₉	—	4	2	no	—
42	C₂×Dic₂₉	C₄⋊C₄	1	2	yes	—
43	C₂×Dic₂₉	C₄⋊C₄	1	2	yes	—
44	C₂×Dic₂₉	D₈	1	2	yes	—
45	C₂×Dic₂₉	SD₁₆	1	4	yes	—
46	C₂×Dic₂₉	Q₁₆	1	2	yes	—
47	C₈×C₂₉	—	2	2	no	—
48	#6597	—	2	2	no	—
49	#1834	—	29	1	no	maximal, Sylow
50	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₂²×C₂₉	#124	1	2	yes	—
52	C₂²×C₂₉	C₂×D₈	1	1	yes	characteristic
53	C₂²×C₂₉	C₂×SD₁₆	1	2	yes	—
54	C₂²×C₂₉	C₂×Q₁₆	1	1	yes	characteristic
55	C₄×C₂₉	—	8	2	no	—
56	C₄×C₂₉	#117	1	1	yes	characteristic
57	C₄×C₂₉	#117	1	1	yes	characteristic
58	C₄×C₂₉	#125	1	2	yes	—
59	Dic₂₉	—	8	2	no	—
60	Dic₂₉	#106	1	4	yes	—
61	Dic₂₉	#107	1	4	yes	—
62	C₂×C₄×C₈	—	29	1	no	—
63	#384	—	29	2	no	—
64	#340	—	29	1	no	—
65	#340	—	29	2	no	—
66	#340	D₂₉	1	1	yes	characteristic
67	C₂×C₂₉	#382	1	1	yes	characteristic
68	C₂×C₂₉	C₂×#106	1	1	yes	characteristic
69	C₂×C₂₉	C₂×#107	1	1	yes	characteristic
70	C₂×C₂₉	#486	1	2	yes	—
71	C₂×C₂₉	#487	1	2	yes	—
72	C₂²×C₈	—	29	1	no	—
73	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
74	C₂×C₄⋊C₄	—	29	2	no	—
75	C₂×C₄⋊C₄	—	58	2	no	—
76	C₂×C₄⋊C₄	—	58	2	no	—
77	C₂×C₄⋊C₄	C₂×D₂₉	1	2	yes	—
78	C₂×C₄²	—	29	1	no	—
79	C₄×C₈	—	29	4	no	—
80	C₂₉	#1834	1	1	yes	characteristic, complemented, Sylow
81	C₂²×C₄	—	2	2	no	—
82	C₂²×C₄	—	29	1	no	—
83	C₂²×C₄	—	29	1	no	—
84	C₂²×C₄	—	58	2	no	—
85	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
86	C₂×C₈	—	2	2	no	—
87	C₂×C₈	—	29	2	no	—
88	C₂×C₈	—	58	2	no	—
89	C₂×C₈	C₄×D₂₉	1	2	yes	—
90	C₄⋊C₄	—	2	2	no	—
91	C₄⋊C₄	—	2	2	no	—
92	C₄⋊C₄	—	58	2	no	—
93	C₄⋊C₄	—	58	2	no	—
94	C₄⋊C₄	—	116	4	no	—
95	C₄⋊C₄	—	116	4	no	—
96	C₄²	—	29	2	no	—
97	C₄²	—	29	2	no	—
98	C₂³	D₄×D₂₉	1	1	yes	characteristic
99	C₂×C₄	—	4	2	no	—
100	C₂×C₄	—	4	2	no	—
101	C₂×C₄	—	4	2	no	—
102	C₂×C₄	—	29	2	no	—
103	C₂×C₄	—	29	2	no	—
104	C₂×C₄	—	29	2	no	—
105	C₂×C₄	—	29	4	no	—
106	C₂×C₄	—	29	2	no	—
107	C₂×C₄	—	116	2	no	—
108	C₂×C₄	—	116	2	no	—
109	C₂×C₄	—	116	2	no	—
110	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
111	C₂×C₄	#90805	1	2	yes	—
112	C₂×C₄	#90807	1	2	yes	—
113	C₂×C₄	Q₈×D₂₉	1	1	yes	characteristic
114	C₈	—	2	2	no	—
115	C₈	—	58	2	no	—
116	C₂²	#11745247	1	2	yes	—
117	C₂²	C₄⋊C₄×D₂₉	1	1	yes	characteristic
118	C₂²	D₈×D₂₉	1	1	yes	characteristic
119	C₂²	SD₁₆×D₂₉	1	2	yes	—
120	C₂²	Q₁₆×D₂₉	1	1	yes	characteristic
121	C₄	—	8	2	no	—
122	C₄	—	29	4	no	—
123	C₄	—	29	4	no	—
124	C₄	—	232	2	no	—
125	C₄	#11745234	1	1	yes	characteristic
126	C₄	#11745239	1	1	yes	characteristic
127	C₄	#11745251	1	2	yes	—
128	C₂	#14271027	1	1	yes	characteristic
129	C₂	#106×D₂₉	1	1	yes	characteristic
130	C₂	#107×D₂₉	1	1	yes	characteristic
131	C₂	#14271508	1	2	yes	—
132	C₂	#14271512	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₈×Dic₂₉

C₂

yes

maximal, characteristic

#14271032

C₂

yes

maximal

#14270926

C₂

yes

maximal, characteristic

#14270925

C₂

yes

maximal

C₂₉×#340

C₂

yes

maximal, characteristic

C₂²×C₈×C₂₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₂₉

C₂²

yes

—

C₂×C₄⋊Dic₂₉

C₂²

yes

—

C₂×#90779

—

C₂×#90779

—

C₂×C₄×Dic₂₉

C₂²

yes

characteristic

C₂²×#6597

C₂²

yes

characteristic

C₈×Dic₂₉

C₄

yes

complemented

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

—

C₂²×Dic₂₉

D₄

yes

characteristic

C₂²×Dic₂₉

D₄

yes

characteristic

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

#90779

—

#90779

—

C₄×Dic₂₉

C₂×C₄

yes

—

C₄×Dic₂₉

Q₈

yes

—

C₂×#6597

—

C₂×#6597

C₂×C₄

yes

—

C₂³×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

#41

yes

—

C₂×C₄×C₂₉

#41

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

C₄⋊C₄

yes

—

C₂×Dic₂₉

C₄⋊C₄

yes

—

C₂×Dic₂₉

D₈

yes

—

C₂×Dic₂₉

SD₁₆

yes

—

C₂×Dic₂₉

Q₁₆

yes

—

C₈×C₂₉

—

#6597

—

#1834

—

maximal, Sylow

C₂²×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₉

#124

yes

—

C₂²×C₂₉

C₂×D₈

yes

characteristic

C₂²×C₂₉

C₂×SD₁₆

yes

—

C₂²×C₂₉

C₂×Q₁₆

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

yes

C₄×C₂₉

yes

C₄×C₂₉

yes

—

Dic₂₉

—

Dic₂₉

#106

yes

—

Dic₂₉

#107

yes

—

C₂×C₄×C₈

—

—

—

—

D₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

—

C₂×C₂₉

#487

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₂₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₂₉

yes

—

C₂×C₄²

—

C₄×C₈

—

C₂₉

#1834

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₂₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

116

—

C₄⋊C₄

—

116

—

C₄²

—

C₄²

—

C₂³

D₄×D₂₉

yes

characteristic

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

116

—

108

C₂×C₄

—

116

—

109

C₂×C₄

—

116

—

110

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

111

C₂×C₄

#90805

yes

—

112

C₂×C₄

#90807

yes

—

113

C₂×C₄

Q₈×D₂₉

yes

characteristic

114

C₈

—

115

C₈

—

116

C₂²

#11745247

yes

—

117

C₂²

C₄⋊C₄×D₂₉

yes

characteristic

118

C₂²

D₈×D₂₉

yes

characteristic

119

C₂²

SD₁₆×D₂₉

yes

—

120

C₂²

Q₁₆×D₂₉

yes

characteristic

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

—

232

—

125

C₄

#11745234

yes

characteristic

126

C₄

#11745239

yes

characteristic

127

C₄

#11745251

yes

—

128

C₂

#14271027

yes

characteristic

129

C₂

#106×D₂₉

yes

characteristic

130

C₂

#107×D₂₉

yes

characteristic

131

C₂

#14271508

yes

—

132

C₂

#14271512

yes

—

	subgroup	G/H
center	C₂³	D₄×D₂₉
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂₉×#340	C₂
socle, prime radical	C₂³×C₂₉	C₂×D₄
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	#340	D₂₉
hypocenter	C₂₉	#1834
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

subgroup

G/H

center

C₂³

D₄×D₂₉

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂₉×#340

C₂

socle, prime radical

C₂³×C₂₉

C₂×D₄

cosocle

C₂²×C₄×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

N	H ≅ G/N	type
13. C₈×Dic₂₉	C₄	semidirect
80. C₂₉	#1834	semidirect

H ≅ G/N

type

13. C₈×Dic₂₉

C₄

semidirect

80. C₂₉

#1834

semidirect

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

subgroup	index
C₂×C₈×Dic₂₉	2
#14271032	2
#14270926	2
#14270925	2
C₂₉×#340	2
#1834	29

subgroup

index

C₂×C₈×Dic₂₉

C₂₉×#340

Subgroups — #16819618

Conjugacy classes of subgroups

Complements

Maximal subgroups