Group #16818788 — subgroups

Subgroups — #16818788

Order 3712.

206 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 45 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	#14271913	C₂	1	1	yes	maximal, characteristic, complemented
2	#14271527	C₂	1	2	yes	maximal, complemented
3	#14270904	C₂	1	2	yes	maximal, complemented
4	#14270903	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#496	C₂	1	1	yes	maximal, characteristic
6	C₂×SD₁₆×C₂₉	—	2	1	no	—
7	C₂×D₈×C₂₉	—	2	1	no	—
8	C₂₉×#127	C₂²	1	1	yes	characteristic
9	C₂₉×#124	C₂²	1	1	yes	characteristic
10	#11745306	—	2	1	no	—
11	#11745297	—	2	1	no	—
12	#11745241	—	2	2	no	—
13	#11745240	—	2	2	no	—
14	#11745232	C₂²	1	2	yes	—
15	C₂₉×#97	C₂²	1	1	yes	characteristic
16	#11745180	—	2	2	no	—
17	#11745180	—	2	2	no	—
18	#11745151	C₂²	1	2	yes	—
19	C₂×Q₈×C₂₉	D₄	1	1	yes	characteristic
20	C₂×D₄×C₂₉	—	2	1	no	—
21	C₂×D₄×C₂₉	—	2	2	no	—
22	C₂×D₄×C₂₉	D₄	1	1	yes	characteristic
23	C₂²×Dic₂₉	—	2	1	no	—
24	C₂×Dic₅₈	—	2	1	no	—
25	SD₁₆×C₂₉	—	4	2	no	—
26	D₈×C₂₉	—	4	2	no	—
27	C₂×C₈×C₂₉	—	2	1	no	—
28	C₂²⋊C₄×C₂₉	—	2	2	no	—
29	C₄²×C₂₉	C₂³	1	1	yes	characteristic
30	C₂²⋊Dic₂₉	—	2	2	no	—
31	C₂²⋊Dic₂₉	—	2	1	no	—
32	C₄⋊Dic₂₉	D₄	1	2	yes	—
33	C₄⋊Dic₂₉	D₄	1	2	yes	—
34	#90779	—	2	2	no	—
35	#90779	—	2	2	no	—
36	#90779	—	2	2	no	—
37	C₄×Dic₂₉	—	2	1	no	—
38	C₂×#6597	—	2	2	no	—
39	C₂³×C₂₉	—	2	1	no	—
40	C₂³×C₂₉	—	4	1	no	—
41	Q₈×C₂₉	—	4	1	no	—
42	D₄×C₂₉	—	4	1	no	—
43	D₄×C₂₉	—	4	1	no	—
44	D₄×C₂₉	—	4	1	no	—
45	D₄×C₂₉	—	4	4	no	—
46	C₂×C₄×C₂₉	—	2	1	no	—
47	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
48	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
49	C₂×Dic₂₉	—	2	2	no	—
50	C₂×Dic₂₉	—	2	2	no	—
51	C₂×Dic₂₉	—	8	1	no	—
52	Dic₅₈	—	8	1	no	—
53	C₈×C₂₉	—	2	2	no	—
54	#6597	—	4	2	no	—
55	#1657	—	29	1	no	maximal, Sylow
56	C₂²×C₂₉	—	4	1	no	—
57	C₂²×C₂₉	—	4	2	no	—
58	C₂²×C₂₉	—	8	1	no	—
59	C₂²×C₂₉	—	8	2	no	—
60	C₂²×C₂₉	#120	1	1	yes	characteristic
61	C₄×C₂₉	—	2	1	no	—
62	C₄×C₂₉	—	2	2	no	—
63	C₄×C₂₉	—	4	1	no	—
64	Dic₂₉	—	4	2	no	—
65	Dic₂₉	—	4	2	no	—
66	#563	—	29	1	no	—
67	#496	D₂₉	1	1	yes	characteristic
68	#490	—	29	2	no	—
69	#330	—	29	2	no	—
70	#329	—	29	1	no	—
71	C₂×C₂₉	—	8	1	no	—
72	C₂×C₂₉	—	16	1	no	—
73	C₂×C₂₉	#453	1	1	yes	characteristic
74	C₂×C₂₉	#454	1	2	yes	—
75	C₂×SD₁₆	—	2	1	no	—
76	C₂×D₈	—	2	1	no	—
77	C₄⋊Q₈	—	58	1	no	—
78	#127	C₂×D₂₉	1	1	yes	characteristic
79	#126	—	58	2	no	—
80	#125	—	29	2	no	—
81	#124	C₂×D₂₉	1	1	yes	characteristic
82	#123	—	58	1	no	—
83	C₂²⋊Q₈	—	58	2	no	—
84	#102	—	58	2	no	—
85	#102	—	58	2	no	—
86	#97	—	29	2	no	—
87	#97	C₂×D₂₉	1	1	yes	characteristic
88	C₂₉	#1657	1	1	yes	characteristic, complemented, Sylow
89	C₂×Q₈	—	58	1	no	—
90	C₂×Q₈	C₂²⋊D₂₉	1	1	yes	characteristic
91	C₂×D₄	—	2	2	no	—
92	C₂×D₄	—	2	1	no	—
93	C₂×D₄	C₂²⋊D₂₉	1	1	yes	characteristic
94	C₂²×C₄	—	58	1	no	—
95	SD₁₆	—	4	2	no	—
96	D₈	—	4	2	no	—
97	C₂×C₈	—	2	1	no	—
98	C₂×C₈	—	58	2	no	—
99	C₄⋊C₄	—	29	2	no	—
100	C₄⋊C₄	—	29	2	no	—
101	C₄⋊C₄	—	58	2	no	—
102	C₄⋊C₄	—	58	2	no	—
103	C₄⋊C₄	—	58	2	no	—
104	C₂²⋊C₄	—	2	2	no	—
105	C₂²⋊C₄	—	58	2	no	—
106	C₂²⋊C₄	—	58	1	no	—
107	C₄²	—	58	1	no	—
108	C₄²	C₂²×D₂₉	1	1	yes	characteristic
109	C₂³	—	2	1	no	—
110	C₂³	—	4	1	no	—
111	Q₈	—	4	1	no	—
112	Q₈	—	232	1	no	—
113	D₄	—	4	1	no	—
114	D₄	—	4	1	no	—
115	D₄	—	4	1	no	—
116	D₄	—	4	4	no	—
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	—	58	2	no	—
119	C₂×C₄	—	58	2	no	—
120	C₂×C₄	—	232	1	no	—
121	C₂×C₄	D₄×D₂₉	1	2	yes	—
122	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
123	C₈	—	2	2	no	—
124	C₈	—	116	2	no	—
125	C₂²	—	4	1	no	—
126	C₂²	—	4	2	no	—
127	C₂²	—	8	1	no	—
128	C₂²	—	8	2	no	—
129	C₂²	#11745299	1	1	yes	characteristic
130	C₄	—	2	1	no	—
131	C₄	—	2	2	no	—
132	C₄	—	4	1	no	—
133	C₄	—	116	2	no	—
134	C₄	—	116	2	no	—
135	C₂	—	8	1	no	—
136	C₂	—	16	1	no	—
137	C₂	#14271330	1	1	yes	characteristic
138	C₂	#14271334	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14271913

C₂

yes

maximal, characteristic, complemented

#14271527

C₂

yes

maximal, complemented

#14270904

C₂

yes

maximal, complemented

#14270903

C₂

yes

maximal, characteristic, complemented

C₂₉×#496

C₂

yes

maximal, characteristic

C₂×SD₁₆×C₂₉

—

C₂×D₈×C₂₉

—

C₂₉×#127

C₂²

yes

characteristic

C₂₉×#124

C₂²

yes

—

—

—

—

C₂²

yes

—

C₂₉×#97

C₂²

yes

—

—

C₂²

yes

—

C₂×Q₈×C₂₉

D₄

yes

characteristic

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

D₄

yes

characteristic

C₂²×Dic₂₉

—

C₂×Dic₅₈

—

SD₁₆×C₂₉

—

D₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂²⋊C₄×C₂₉

—

C₄²×C₂₉

C₂³

yes

characteristic

C₂²⋊Dic₂₉

—

C₂²⋊Dic₂₉

—

C₄⋊Dic₂₉

D₄

yes

—

C₄⋊Dic₂₉

D₄

yes

—

#90779

—

#90779

—

#90779

—

C₄×Dic₂₉

—

C₂×#6597

—

C₂³×C₂₉

—

C₂³×C₂₉

—

Q₈×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

Dic₅₈

—

C₈×C₂₉

—

#6597

—

#1657

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

#120

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

Dic₂₉

—

Dic₂₉

—

#563

—

#496

D₂₉

yes

—

—

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

#453

yes

characteristic

C₂×C₂₉

#454

yes

—

C₂×SD₁₆

—

C₂×D₈

—

C₄⋊Q₈

—

#127

C₂×D₂₉

yes

—

—

C₂×D₂₉

yes

characteristic

#123

—

C₂²⋊Q₈

—

—

—

—

C₂×D₂₉

yes

characteristic

C₂₉

#1657

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

C₂²⋊D₂₉

yes

characteristic

C₂×D₄

—

C₂×D₄

—

C₂×D₄

C₂²⋊D₂₉

yes

characteristic

C₂²×C₄

—

SD₁₆

—

D₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₂²⋊C₄

—

105

C₂²⋊C₄

—

106

C₂²⋊C₄

—

107

C₄²

—

108

C₄²

C₂²×D₂₉

yes

characteristic

109

C₂³

—

110

C₂³

—

111

Q₈

—

112

Q₈

—

232

—

113

D₄

—

114

D₄

—

115

D₄

—

116

D₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

232

—

121

C₂×C₄

D₄×D₂₉

yes

—

122

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

123

C₈

—

124

C₈

—

116

—

125

C₂²

—

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

#11745299

yes

characteristic

130

C₄

—

131

C₄

—

132

C₄

—

133

C₄

—

116

—

134

C₄

—

116

—

135

C₂

—

136

C₂

—

137

C₂

#14271330

yes

characteristic

138

C₂

#14271334

yes

—

	subgroup	G/H
center	C₂²	#11745299
commutator, cosocle	C₄²×C₂₉	C₂³
Frattini	C₄²	C₂²×D₂₉
Fitting, prime radical	C₂₉×#496	C₂
socle	C₂²×C₂₉	#120
hypercenter	#496	D₂₉
hypocenter	C₂₉	#1657
LCS	G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #496

subgroup

G/H

center

C₂²

#11745299

commutator, cosocle

C₄²×C₂₉

C₂³

Frattini

C₄²

C₂²×D₂₉

Fitting, prime radical

C₂₉×#496

C₂

C₂²×C₂₉

D₂₉

C₂₉

G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #496

N	H ≅ G/N	type
1. #14271913	C₂	semidirect
2. #14271527	C₂	semidirect
3. #14270904	C₂	semidirect
4. #14270903	C₂	semidirect
88. C₂₉	#1657	semidirect

H ≅ G/N

type

1. #14271913

C₂

semidirect

2. #14271527

C₂

semidirect

3. #14270904

C₂

semidirect

4. #14270903

C₂

semidirect

88. C₂₉

#1657

semidirect

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

subgroup	index
#14271913	2
#14271527	2
#14270904	2
#14270903	2
C₂₉×#496	2
#1657	29

subgroup

index

C₂₉×#496

Subgroups — #16818788

Conjugacy classes of subgroups

Complements

Maximal subgroups