Finite Group Databasebeta

← #13123191

Subgroups — #13123191

Order 1664.

752 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 752 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#124C211yesmaximal, characteristic, complemented
2C2×#88201C211yesmaximal, characteristic, complemented
3C2×#88198C211yesmaximal, characteristic, complemented
4C2×#88194C211yesmaximal, characteristic
5C2×#88190C211yesmaximal, characteristic, complemented
6C2×#88129C211yesmaximal, characteristic, complemented
7#11718618C218yesmaximal, complemented
8C42×Dic13C211yesmaximal, characteristic, complemented
9C22×Q8×C13C2211yescharacteristic
10C22×D4×C13C2211yescharacteristic
11C22×C22⋊D13C2214yes—
12C22×D52C2211yescharacteristic
13C22×Dic26C2211yescharacteristic
14C13×#124—24no—
15C2×C13×C22⋊C4C2214yes—
16C2×C42×C13C2211yescharacteristic
17C2×C22⋊Dic13C2214yes—
18#88201—24no—
19#88198—24no—
20#88194—24no—
21#88190—24no—
22C2×#6103C2214yes—
23C2×#6103C2214yes—
24C2×#6101C2214yes—
25C2×C4×Dic13C2214yes—
26C2×C4×Dic13C2211yescharacteristic
27C2×C4×Dic13C2211yescharacteristic
28#88129—24no—
29C24×C13C2312yes—
30C23×D13C2312yes—
31C2×Q8×C13—22no—
32C2×Q8×C13—22no—
33C2×Q8×C13—22no—
34C2×D4×C13—22no—
35C2×D4×C13—22no—
36C2×D4×C13—22no—
37C22×C4×C13C2312yes—
38C22×C4×C13C2312yes—
39C22×C4×C13C2311yescharacteristic
40C2×C22⋊D13—28no—
41C2×C22⋊D13—216no—
42C22×Dic13C2312yes—
43C22×Dic13C2312yes—
44C22×Dic13C2312yes—
45C2×D52—22no—
46C2×D52—22no—
47C2×D52—22no—
48C2×Dic26—22no—
49C2×Dic26—22no—
50C2×Dic26—22no—
51C13×C22⋊C4—28no—
52C42×C13D414yescomplemented
53C22⋊Dic13—28no—
54#6103—28no—
55#6103—28no—
56#6101—28no—
57C4×Dic13—28no—
58C4×Dic13D414yes—
59C4×Dic13D414yescomplemented
60#2858—131nomaximal, Sylow
61C23×C13—22no—
62C23×C13—22no—
63C23×C13—22no—
64C23×C13—28no—
65C23×C13C2411yescharacteristic
66C22×D13—22no—
67C22×D13—22no—
68C22×D13—22no—
69C22×D13—28no—
70Q8×C13—44no—
71D4×C13—44no—
72C2×C4×C13—24no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13—22no—
76C2×C4×C13C2×D414yes—
77C2×C4×C13C2×D412yes—
78C2×C4×C13C2×D412yes—
79C2×C4×C13C2×D412yes—
80C22⋊D13—416no—
81C2×Dic13—24no—
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—22no—
85C2×Dic13C2×D414yes—
86C2×Dic13C2×D414yes—
87C2×Dic13#4118yes—
88D52—44no—
89Dic26—44no—
90C2×C4⋊Q8—131no—
91C2×#127—131no—
92C2×#124—131no—
93C2×#124—131no—
94C2×#124—131no—
95C2×#124D1311yescharacteristic, complemented
96#390—138no—
97C43—131no—
98C22×C13—44no—
99C22×C13—42no—
100C22×C13—44no—
101C22×C13—44no—
102C22×C13C22×D411yescharacteristic
103C22×C13C22×D411yescharacteristic
104C22×C13C22×D411yescharacteristic
105C22×C13C2×#4114yes—
106C2×D13—44no—
107C2×D13—42no—
108C2×D13—44no—
109C2×D13—44no—
110C4×C13—24no—
111C4×C13—42no—
112C4×C13#12714yes—
113Dic13—24no—
114Dic13—42no—
115Dic13#12418yescomplemented
116C22×Q8—131no—
117C22×Q8C2×D1311yescharacteristic
118C22×D4—134no—
119C22×D4—131no—
120C22×D4C2×D1311yescharacteristic
121C4⋊Q8—264no—
122#127—264no—
123#124—24no—
124#124—264no—
125#124—264no—
126#124—264no—
127C2×C4⋊C4—134no—
128C2×C22⋊C4—134no—
129C2×C22⋊C4—134no—
130C2×C22⋊C4—134no—
131C2×C22⋊C4C2×D1314yes—
132C2×C42—131no—
133C2×C42—131no—
134C2×C42—134no—
135C2×C42C2×D1311yescharacteristic
136C2×C13—82no—
137C2×C13C2×#12412yes—
138C2×C13C2×#12711yescharacteristic
139C2×C13#53212yes—
140C2×C13#53212yes—
141D13—82no—
142C24—132no—
143C24C22×D1312yes—
144C2×Q8—22no—
145C2×Q8—22no—
146C2×Q8—22no—
147C2×Q8—262no—
148C2×Q8—262no—
149C2×Q8—262no—
150C2×D4—22no—
151C2×D4—22no—
152C2×D4—22no—
153C2×D4—268no—
154C2×D4—2616no—
155C2×D4—262no—
156C2×D4—262no—
157C2×D4—262no—
158C22×C4—132no—
159C22×C4—132no—
160C22×C4—132no—
161C22×C4C22×D1312yes—
162C22×C4C22×D1312yes—
163C22×C4C22×D1311yescharacteristic
164C4⋊C4—268no—
165C22⋊C4—28no—
166C22⋊C4—268no—
167C22⋊C4—268no—
168C22⋊C4—268no—
169C42—134no—
170C42—134no—
171C42—268no—
172C42C22⋊D1314yescomplemented
173C13#285811yescharacteristic, complemented, Sylow
174C23—22no—
175C23—22no—
176C23—28no—
177C23—22no—
178C23—262no—
179C23—262no—
180C23—268no—
181C23—262no—
182C23C23×D1311yescharacteristic
183Q8—44no—
184Q8—524no—
185D4—44no—
186D4—5216no—
187D4—524no—
188C2×C4—24no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—134no—
193C2×C4—138no—
194C2×C4—134no—
195C2×C4—264no—
196C2×C4—262no—
197C2×C4—262no—
198C2×C4—262no—
199C2×C4D4×D1312yes—
200C2×C4D4×D1312yes—
201C2×C4C2×C22⋊D1314yes—
202C2×C4C2×C22⋊D1312yes—
203C22—42no—
204C22—44no—
205C22—44no—
206C22—44no—
207C22—522no—
208C22—524no—
209C22—524no—
210C22—524no—
211C22C2×D4×D1311yescharacteristic
212C22C2×D4×D1311yescharacteristic
213C22#41×D1314yes—
214C22C22×C22⋊D1311yescharacteristic
215C4—24no—
216C4—42no—
217C4—138no—
218C4—264no—
219C4—522no—
220C4#8819414yes—
221C2—82no—
222C2—1042no—
223C2#1171937312yes—
224C2D13×#12412yes—
225C2C2×#8819411yescharacteristic
226C2#1171953712yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×#124C2
prime radicalC2×#88194C2
hypercenterC2×#124D13
hypocenterC13#2858
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#124

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C13×#124C2semidirect
2. C2×#88201C2semidirect
3. C2×#88198C2semidirect
5. C2×#88190C2semidirect
6. C2×#88129C2semidirect
7. #11718618C2semidirect
8. C42×Dic13C2semidirect
52. C42×C13D4semidirect
59. C4×Dic13D4semidirect
95. C2×#124D13semidirect
115. Dic13#124semidirect
172. C42C22⋊D13semidirect
173. C13#2858semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1242
C2×#882012
C2×#881982
C2×#881942
C2×#881902
C2×#881292
#117186182
C42×Dic132
#285813