Group #16818871 — subgroups

Subgroups — #16818871

Order 3712.

150 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 57 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	#14271455	C₂	1	1	yes	maximal, characteristic
2	#14271370	C₂	1	1	yes	maximal, characteristic
3	C₈×Dic₅₈	C₂	1	1	yes	maximal, characteristic
4	#14270914	C₂	1	1	yes	maximal, characteristic
5	#14270912	C₂	1	1	yes	maximal, characteristic
6	#14270909	C₂	1	1	yes	maximal, characteristic
7	C₂₉×#498	C₂	1	1	yes	maximal, characteristic
8	C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×#90785	—	2	1	no	—
11	C₄×Dic₅₈	C₂²	1	1	yes	characteristic
12	C₂₉×#106	—	2	1	no	—
13	C₂₉×#106	—	2	1	no	—
14	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
15	#11745183	—	2	1	no	—
16	#11745162	—	2	1	no	—
17	C₈×Dic₂₉	—	2	1	no	—
18	#11745158	—	2	1	no	—
19	#11745155	—	2	1	no	—
20	C₄⋊#6597	C₂²	1	1	yes	characteristic
21	C₄⋊#6597	C₂²	1	1	yes	characteristic
22	C₄⋊#6597	C₂²	1	1	yes	characteristic
23	C₂×Q₈×C₂₉	—	2	1	no	—
24	C₂×Q₈×C₂₉	—	2	1	no	—
25	C₂×Dic₅₈	D₄	1	1	yes	characteristic
26	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
27	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
28	C₄⋊C₄×C₂₉	—	2	1	no	—
29	C₄⋊C₄×C₂₉	—	2	1	no	—
30	C₄⋊C₄×C₂₉	—	2	1	no	—
31	C₄⋊C₄×C₂₉	—	2	1	no	—
32	C₄²×C₂₉	C₂³	1	1	yes	characteristic
33	#90785	—	4	2	no	—
34	C₄⋊Dic₂₉	D₄	1	1	yes	characteristic
35	#90779	—	2	1	no	—
36	C₄×Dic₂₉	—	2	1	no	—
37	C₂×#6597	—	2	1	no	—
38	C₂×#6597	—	2	1	no	—
39	C₂×#6597	—	2	1	no	—
40	Q₈×C₂₉	—	4	1	no	—
41	Q₈×C₂₉	—	4	1	no	—
42	Q₈×C₂₉	—	8	1	no	—
43	C₂×C₄×C₂₉	—	4	1	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	#41	1	1	yes	characteristic
48	C₂×Dic₂₉	—	2	1	no	—
49	C₂×Dic₂₉	—	2	1	no	—
50	Dic₅₈	—	2	1	no	—
51	Dic₅₈	SD₁₆	1	2	yes	—
52	C₈×C₂₉	—	2	1	no	—
53	C₈×C₂₉	Q₁₆	1	2	yes	complemented
54	#6597	—	4	1	no	—
55	#6597	—	4	1	no	—
56	#6597	—	4	1	no	—
57	#1672	—	29	1	no	maximal, Sylow
58	C₂²×C₂₉	#121	1	1	yes	characteristic
59	C₄×C₂₉	—	2	1	no	—
60	C₄×C₂₉	—	8	1	no	—
61	C₄×C₂₉	—	8	1	no	—
62	C₄×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
63	C₄×C₂₉	C₂×Q₁₆	1	1	yes	characteristic
64	C₄×C₂₉	#135	1	1	yes	characteristic
65	C₄×C₂₉	#137	1	1	yes	characteristic
66	Dic₂₉	—	2	2	no	—
67	Dic₂₉	—	4	1	no	—
68	#498	D₂₉	1	1	yes	characteristic
69	#477	—	29	1	no	—
70	#462	—	29	1	no	—
71	C₈×Q₈	—	29	1	no	—
72	#334	—	29	1	no	—
73	#333	—	29	1	no	—
74	#332	—	29	1	no	—
75	C₂×C₂₉	#462	1	1	yes	characteristic
76	C₂×C₂₉	#465	1	1	yes	characteristic
77	C₂×C₂₉	#471	1	1	yes	characteristic
78	C₂×Q₁₆	—	58	1	no	—
79	C₄⋊Q₈	C₂×D₂₉	1	1	yes	characteristic
80	C₄⋊Q₈	C₂×D₂₉	1	1	yes	characteristic
81	C₄×Q₈	—	29	1	no	—
82	#107	—	58	1	no	—
83	#106	—	2	1	no	—
84	#106	—	2	1	no	—
85	C₄⋊C₈	—	29	1	no	—
86	C₄⋊C₈	—	29	1	no	—
87	C₄⋊C₈	—	29	1	no	—
88	C₄⋊C₈	—	58	1	no	—
89	#103	—	58	1	no	—
90	#103	—	58	1	no	—
91	C₄×C₈	—	58	1	no	—
92	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
93	C₂₉	#1672	1	1	yes	characteristic, complemented, Sylow
94	C₂×Q₈	—	2	1	no	—
95	C₂×Q₈	—	2	1	no	—
96	C₂×Q₈	—	29	1	no	—
97	Q₁₆	—	116	2	no	—
98	C₂×C₈	—	58	1	no	—
99	C₂×C₈	—	58	1	no	—
100	C₂×C₈	—	58	1	no	—
101	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
102	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
103	C₄⋊C₄	—	2	1	no	—
104	C₄⋊C₄	—	2	1	no	—
105	C₄⋊C₄	—	2	1	no	—
106	C₄⋊C₄	—	2	1	no	—
107	C₄⋊C₄	—	29	1	no	—
108	C₄⋊C₄	—	58	1	no	—
109	C₄²	—	58	1	no	—
110	C₄²	C₂²×D₂₉	1	1	yes	characteristic
111	Q₈	—	4	1	no	—
112	Q₈	—	4	1	no	—
113	Q₈	—	8	1	no	—
114	Q₈	—	29	2	no	—
115	Q₈	—	58	1	no	—
116	C₂×C₄	—	4	1	no	—
117	C₂×C₄	—	4	1	no	—
118	C₂×C₄	—	58	1	no	—
119	C₂×C₄	—	58	1	no	—
120	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
121	C₂×C₄	#90807	1	1	yes	characteristic
122	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
123	C₈	—	2	1	no	—
124	C₈	—	116	1	no	—
125	C₈	—	116	1	no	—
126	C₈	—	116	1	no	—
127	C₈	#90785	1	2	yes	complemented
128	C₂²	#11745300	1	1	yes	characteristic
129	C₄	—	2	1	no	—
130	C₄	—	8	1	no	—
131	C₄	—	8	1	no	—
132	C₄	—	58	2	no	—
133	C₄	—	116	1	no	—
134	C₄	SD₁₆×D₂₉	1	1	yes	characteristic
135	C₄	#11745278	1	1	yes	characteristic
136	C₄	#11745304	1	1	yes	characteristic
137	C₄	C₂×#90785	1	1	yes	characteristic
138	C₂	#14271370	1	1	yes	characteristic
139	C₂	#14271389	1	1	yes	characteristic
140	C₂	#14271423	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271455

C₂

yes

maximal, characteristic

#14271370

C₂

yes

maximal, characteristic

C₈×Dic₅₈

C₂

yes

maximal, characteristic

#14270914

C₂

yes

maximal, characteristic

#14270912

C₂

yes

maximal, characteristic

#14270909

C₂

yes

maximal, characteristic

C₂₉×#498

C₂

yes

maximal, characteristic

C₂₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂×#90785

—

C₄×Dic₅₈

C₂²

yes

characteristic

C₂₉×#106

—

C₂₉×#106

—

C₄×C₈×C₂₉

C₂²

yes

characteristic

#11745183

—

#11745162

—

C₈×Dic₂₉

—

#11745158

—

#11745155

—

C₄⋊#6597

C₂²

yes

characteristic

C₄⋊#6597

C₂²

yes

characteristic

C₄⋊#6597

C₂²

yes

characteristic

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

—

C₂×Dic₅₈

D₄

yes

characteristic

C₂×C₈×C₂₉

D₄

yes

characteristic

C₂×C₈×C₂₉

D₄

yes

characteristic

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄²×C₂₉

C₂³

yes

characteristic

#90785

—

C₄⋊Dic₂₉

D₄

yes

characteristic

#90779

—

C₄×Dic₂₉

—

C₂×#6597

—

C₂×#6597

—

C₂×#6597

—

Q₈×C₂₉

—

Q₈×C₂₉

—

Q₈×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

#41

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

—

Dic₅₈

—

Dic₅₈

SD₁₆

yes

—

C₈×C₂₉

—

C₈×C₂₉

Q₁₆

yes

—

—

—

—

C₂²×C₂₉

yes

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₂×SD₁₆

yes

characteristic

C₄×C₂₉

C₂×Q₁₆

yes

C₄×C₂₉

yes

C₄×C₂₉

yes

Dic₂₉

—

Dic₂₉

—

#498

D₂₉

yes

characteristic

#477

—

#462

—

C₈×Q₈

—

#334

—

#333

—

#332

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×Q₁₆

—

C₄⋊Q₈

C₂×D₂₉

yes

characteristic

C₄⋊Q₈

C₂×D₂₉

yes

characteristic

C₄×Q₈

—

#107

—

#106

—

#106

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

#103

—

#103

—

C₄×C₈

—

C₄×C₈

C₂×D₂₉

yes

characteristic

C₂₉

#1672

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

116

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

C₂²⋊D₂₉

yes

characteristic

102

C₂×C₈

C₂²⋊D₂₉

yes

characteristic

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄²

—

110

C₄²

C₂²×D₂₉

yes

characteristic

111

Q₈

—

112

Q₈

—

113

Q₈

—

114

Q₈

—

115

Q₈

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

D₄×D₂₉

yes

characteristic

121

C₂×C₄

#90807

yes

characteristic

122

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

123

C₈

—

124

C₈

—

116

—

125

C₈

—

116

—

126

C₈

—

116

—

127

C₈

#90785

yes

complemented

128

C₂²

#11745300

yes

characteristic

129

C₄

—

130

C₄

—

131

C₄

—

132

C₄

—

133

C₄

—

116

—

134

C₄

SD₁₆×D₂₉

yes

characteristic

135

C₄

#11745278

yes

characteristic

136

C₄

#11745304

yes

characteristic

137

C₄

C₂×#90785

yes

characteristic

138

C₂

#14271370

yes

characteristic

139

C₂

#14271389

yes

characteristic

140

C₂

#14271423

yes

characteristic

	subgroup	G/H
center	C₂²	#11745300
commutator, cosocle	C₄²×C₂₉	C₂³
Frattini	C₄²	C₂²×D₂₉
Fitting	C₂₉×#498	C₂
socle, prime radical	C₂²×C₂₉	#121
hypercenter	#498	D₂₉
hypocenter	C₂₉	#1672
LCS	G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #498

subgroup

G/H

center

C₂²

#11745300

commutator, cosocle

C₄²×C₂₉

C₂³

Frattini

C₄²

C₂²×D₂₉

Fitting

C₂₉×#498

C₂

C₂²×C₂₉

D₂₉

C₂₉

G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #498

N	H ≅ G/N	type
53. C₈×C₂₉	Q₁₆	semidirect
93. C₂₉	#1672	semidirect
127. C₈	#90785	semidirect

H ≅ G/N

type

53. C₈×C₂₉

Q₁₆

semidirect

93. C₂₉

#1672

semidirect

127. C₈

#90785

semidirect

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

subgroup	index
#14271455	2
#14271370	2
C₈×Dic₅₈	2
#14270914	2
#14270912	2
#14270909	2
C₂₉×#498	2
#1672	29

subgroup

index

C₈×Dic₅₈

C₂₉×#498

Subgroups — #16818871

Conjugacy classes of subgroups

Complements

Maximal subgroups