Finite Group Databasebeta

← #13126017

Subgroups — #13126017

Order 1664.

332 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#11719184C211yesmaximal, characteristic
2#11719175C211yesmaximal, characteristic, complemented
3C13×#431C211yesmaximal, characteristic, complemented
4#11718512C211yesmaximal, characteristic, complemented
5#11718511C211yesmaximal, characteristic, complemented
6#11718507C211yesmaximal, characteristic, complemented
7#11718503C211yesmaximal, characteristic, complemented
8#11718398C212yesmaximal
9#11718384C212yesmaximal, complemented
10#11718358C212yesmaximal, complemented
11#11718344C212yesmaximal, complemented
12C2×C42×C13C2211yescharacteristic
13#88184C2211yescharacteristic
14#88183—21no—
15C4×C22⋊D13—21no—
16#88180C2212yes—
17#88178—21no—
18#88178—21no—
19#88178C2211yescharacteristic
20#88130—21no—
21#88129C2211yescharacteristic
22C4×D52C2211yescharacteristic
23#88126—21no—
24#88124C2212yes—
25#88124C2211yescharacteristic
26#88123C2211yescharacteristic
27#88123C2211yescharacteristic
28C4×Dic26—21no—
29C4×Dic26—21no—
30C4×Dic26C2211yescharacteristic
31C13×C4⋊C8C2211yescharacteristic
32C13×C4⋊C8C2211yescharacteristic
33C13×C22⋊C8C2212yes—
34C4×C8×C13C2212yes—
35#88061C2212yes—
36#88061C2212yes—
37#88058C2212yes—
38#88058C2212yes—
39#88057C2212yes—
40#88057C2212yes—
41#88056C2212yes—
42#88056C2212yes—
43C22×C4×C13D411yescharacteristic
44C22×C4×C13D411yescharacteristic
45C22×C4×C13C2311yescharacteristic
46C2×C22⋊D13—21no—
47C2×D52C2311yescharacteristic
48C2×C4×D13—21no—
49C2×Dic26—21no—
50C2×Dic26—21no—
51C2×Dic26C2311yescharacteristic
52C2×C8×C13C2312yes—
53C2×C8×C13C2312yes—
54C42×C13D411yescharacteristic
55C42×C13D411yescharacteristic
56C42×C13C2311yescharacteristic
57C42×C13C2311yescharacteristic
58C22⋊Dic13—22no—
59C22⋊Dic13—21no—
60#6103—21no—
61#6103—21no—
62#6103—21no—
63#6103—21no—
64C4⋊Dic13—21no—
65C4⋊Dic13—21no—
66C4⋊Dic13C2311yescharacteristic
67C4⋊Dic13C2312yes—
68C4⋊Dic13C2312yes—
69C4⋊Dic13C2311yescharacteristic
70#6101—22no—
71#6101—22no—
72#6101—21no—
73#6101—21no—
74#6101—21no—
75#6101—21no—
76C4×Dic13—22no—
77C4×Dic13—21no—
78#3233—131nomaximal, Sylow
79C23×C13C2×D411yescharacteristic
80C22×D13—21no—
81C2×C4×C13—22no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—41no—
85C2×C4×C13C2×D411yescharacteristic
86C2×C4×C13C2×D411yescharacteristic
87C2×C4×C13C2×D411yescharacteristic
88C2×C4×C13C2×D411yescharacteristic
89C2×C4×C13C2×D411yescharacteristic
90C2×C4×C13C2411yescharacteristic
91C22⋊D13—42no—
92C2×Dic13—21no—
93C2×Dic13—22no—
94C2×Dic13—22no—
95C2×Dic13—21no—
96C2×Dic13—21no—
97D52—21no—
98D52—21no—
99C4×D13—42no—
100Dic26—21no—
101Dic26—21no—
102Dic26—42no—
103Dic26—42no—
104C8×C13—22no—
105C8×C13—22no—
106#533—131no—
107#529—131no—
108#499—132no—
109#488—132no—
110#485—132no—
111#482—132no—
112#477—131no—
113#476—131no—
114#475—131no—
115#474—131no—
116#431D1311yescharacteristic, complemented
117C22×C13—21no—
118C22×C13—21no—
119C22×C13—21no—
120C22×C13C22×D411yescharacteristic
121C2×D13—41no—
122C2×D13—41no—
123C2×D13—41no—
124C4×C13—21no—
125C4×C13—21no—
126C4×C13—21no—
127C4×C13—21no—
128C4×C13#13512yes—
129C4×C132−1+411yescharacteristic
130C4×C132−1+411yescharacteristic
131Dic13—41no—
132Dic13—42no—
133Dic13—41no—
134Dic13—42no—
135Dic13—41no—
136C4⋊Q8—131no—
137C4⋊Q8—131no—
138#126—261no—
139#125—131no—
140#125—132no—
141#124—131no—
142#123—261no—
143C22⋊Q8—131no—
144C22⋊Q8—261no—
145C22⋊Q8—261no—
146#121—131no—
147C4×Q8—131no—
148C4×Q8—261no—
149C4×Q8—261no—
150C4×D4—131no—
151C4×D4—261no—
152#117—132no—
153#117—261no—
154C2×C42C2×D1311yescharacteristic
155#107—132no—
156#107—132no—
157#106—132no—
158#106—132no—
159C4⋊C8C2×D1311yescharacteristic
160C4⋊C8C2×D1311yescharacteristic
161#103—132no—
162#103—132no—
163#102—132no—
164#102—132no—
165C22⋊C8C2×D1312yes—
166C4×C8C2×D1312yes—
167C2×C13—41no—
168C2×C13#53611yescharacteristic
169C2×C13C2×#13511yescharacteristic
170C2×C13#57511yescharacteristic
171D13—81no—
172C2×Q8—131no—
173C2×Q8—261no—
174C2×Q8—261no—
175C2×D4—131no—
176C2×D4—261no—
177C22×C4—261no—
178C22×C4D5211yescharacteristic
179C22×C4D5211yescharacteristic
180C22×C4C22×D1311yescharacteristic
181C2×C8C22×D1312yes—
182C2×C8C22×D1312yes—
183C4⋊C4—132no—
184C4⋊C4—132no—
185C4⋊C4—131no—
186C4⋊C4—131no—
187C4⋊C4—261no—
188C4⋊C4—261no—
189C4⋊C4—261no—
190C4⋊C4—261no—
191C4⋊C4—262no—
192C4⋊C4—262no—
193C4⋊C4—261no—
194C4⋊C4—261no—
195C22⋊C4—262no—
196C22⋊C4—261no—
197C22⋊C4—261no—
198C22⋊C4—261no—
199C22⋊C4—261no—
200C22⋊C4—261no—
201C42—262no—
202C42—261no—
203C42D5211yescharacteristic
204C42D5211yescharacteristic
205C42C22×D1311yescharacteristic
206C42C22×D1311yescharacteristic
207C13#323311yescharacteristic, complemented, Sylow
208C23—261no—
209C23C2×D5211yescharacteristic
210Q8—261no—
211Q8—261no—
212Q8—522no—
213Q8—522no—
214D4—261no—
215D4—261no—
216D4—522no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—41no—
221C2×C4—261no—
222C2×C4—261no—
223C2×C4—262no—
224C2×C4—262no—
225C2×C4—261no—
226C2×C4—522no—
227C2×C4C2×D5211yescharacteristic
228C2×C4C2×D5211yescharacteristic
229C2×C4C2×D5211yescharacteristic
230C2×C4C2×D5211yescharacteristic
231C2×C4C2×D5211yescharacteristic
232C2×C4C23×D1311yescharacteristic
233C8—22no—
234C8—22no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—521no—
239C22—521no—
240C22—521no—
241C22C22×D5211yescharacteristic
242C4—21no—
243C4—21no—
244C4—21no—
245C4—21no—
246C4—521no—
247C4—522no—
248C4—521no—
249C4—522no—
250C4—521no—
251C4#8815812yes—
252C4#8825711yescharacteristic
253C4#8825711yescharacteristic
254C2—41no—
255C2—1041no—
256C2#1171923111yescharacteristic
257C2C2×#8815811yescharacteristic
258C2#1171945311yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#431C2
socleC22×C13C22×D4
prime radical#88184C22
hypercenter#431D13
hypocenterC13#3233
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #11719175C2semidirect
3. C13×#431C2semidirect
4. #11718512C2semidirect
5. #11718511C2semidirect
6. #11718507C2semidirect
7. #11718503C2semidirect
9. #11718384C2semidirect
10. #11718358C2semidirect
11. #11718344C2semidirect
116. #431D13semidirect
207. C13#3233semidirect

Maximal subgroups

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

subgroupindex
#117191842
#117191752
C13×#4312
#117185122
#117185112
#117185072
#117185032
#117183982
#117183842
#117183582
#117183442
#323313