Finite Group Databasebeta

← #13126015

Subgroups — #13126015

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
1C13×#533C211yesmaximal, characteristic, complemented
2#11719184C211yesmaximal, characteristic
3#11718755C211yesmaximal, characteristic, complemented
4#11718752C211yesmaximal, characteristic, complemented
5#11718748C211yesmaximal, characteristic, complemented
6#11718745C211yesmaximal, characteristic, complemented
7#11718729C212yesmaximal, complemented
8#11718725C212yesmaximal, complemented
9#11718664C212yesmaximal
10#11718657C212yesmaximal, complemented
11#11718586C211yesmaximal, characteristic, complemented
12C13×C4⋊Q8C2211yescharacteristic
13C13×C4⋊Q8C2211yescharacteristic
14C13×#125C2212yes—
15C13×C22⋊Q8—21no—
16C13×C22⋊Q8—21no—
17C4×Q8×C13—21no—
18C4×Q8×C13—21no—
19C13×#117C2212yes—
20C2×C42×C13C2211yescharacteristic
21#88184C2211yescharacteristic
22#88183—21no—
23C4×C22⋊D13—21no—
24#88178C2211yescharacteristic
25#88130—21no—
26#88129C2211yescharacteristic
27C4×D52C2211yescharacteristic
28#88126—21no—
29#88124C2211yescharacteristic
30C4×Dic26C2211yescharacteristic
31C22⋊#1055C2212yes—
32#88050C2212yes—
33#88050C2212yes—
34#88049C2212yes—
35#88049C2212yes—
36#88048C2212yes—
37#88048C2212yes—
38#88047C2212yes—
39#88047C2212yes—
40C4⋊#1055C2211yescharacteristic
41C4⋊#1055C2211yescharacteristic
42C4×#1055C2212yes—
43C2×Q8×C13—21no—
44C2×Q8×C13—21no—
45C22×C4×C13D411yescharacteristic
46C22×C4×C13D411yescharacteristic
47C22×C4×C13C2311yescharacteristic
48C2×C22⋊D13—21no—
49C2×D52C2311yescharacteristic
50C2×C4×D13—21no—
51C2×Dic26C2311yescharacteristic
52C13×C4⋊C4—22no—
53C13×C4⋊C4—22no—
54C13×C4⋊C4—21no—
55C13×C4⋊C4—21no—
56C13×C4⋊C4C2312yes—
57C13×C4⋊C4C2312yes—
58C13×C22⋊C4—22no—
59C42×C13—22no—
60C42×C13D411yescharacteristic
61C42×C13D411yescharacteristic
62C42×C13C2311yescharacteristic
63C42×C13C2311yescharacteristic
64C22⋊Dic13—21no—
65#6103—21no—
66#6103—21no—
67#6103—21no—
68#6103—21no—
69C4⋊Dic13C2311yescharacteristic
70C4⋊Dic13C2311yescharacteristic
71#6101—21no—
72#6101—21no—
73#6101—21no—
74#6101—21no—
75C4×Dic13—21no—
76C2×#1055C2312yes—
77C2×#1055C2312yes—
78#3233—131nomaximal, Sylow
79C23×C13C2×D411yescharacteristic
80C22×D13—21no—
81Q8×C13—42no—
82Q8×C13—42no—
83C2×C4×C13—22no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—41no—
89C2×C4×C13C2×D411yescharacteristic
90C2×C4×C13C2×D411yescharacteristic
91C2×C4×C13C2×D411yescharacteristic
92C2×C4×C13C2×D411yescharacteristic
93C2×C4×C13C2×D411yescharacteristic
94C2×C4×C13C2411yescharacteristic
95C22⋊D13—42no—
96C2×Dic13—21no—
97C2×Dic13—21no—
98C2×Dic13—21no—
99D52—21no—
100D52—21no—
101C4×D13—42no—
102Dic26—21no—
103Dic26—21no—
104#1055—22no—
105#1055—22no—
106#533D1311yescharacteristic, complemented
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#431—131no—
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—42no—
129C4×C13—42no—
130C4×C13#13512yes—
131C4×C132−1+411yescharacteristic
132C4×C132−1+411yescharacteristic
133Dic13—41no—
134Dic13—41no—
135Dic13—41no—
136C4⋊Q8C2×D1311yescharacteristic
137C4⋊Q8C2×D1311yescharacteristic
138#126—261no—
139#125—131no—
140#125C2×D1312yes—
141#124—131no—
142#123—261no—
143C22⋊Q8—21no—
144C22⋊Q8—21no—
145C22⋊Q8—131no—
146#121—131no—
147C4×Q8—21no—
148C4×Q8—21no—
149C4×Q8—131no—
150C4×D4—131no—
151C4×D4—261no—
152#117—261no—
153#117C2×D1312yes—
154C2×C42C2×D1311yescharacteristic
155#107—132no—
156#107—132no—
157#106—132no—
158#106—132no—
159C4⋊C8—131no—
160C4⋊C8—131no—
161#103—132no—
162#103—132no—
163#102—132no—
164#102—132no—
165C22⋊C8—132no—
166C4×C8—132no—
167C2×C13—41no—
168C2×C13#53611yescharacteristic
169C2×C13C2×#13511yescharacteristic
170C2×C13#57511yescharacteristic
171D13—81no—
172C2×Q8—21no—
173C2×Q8—21no—
174C2×Q8—131no—
175C2×D4—131no—
176C2×D4—261no—
177C22×C4—261no—
178C22×C4C22⋊D1311yescharacteristic
179C22×C4C22⋊D1311yescharacteristic
180C22×C4C22×D1311yescharacteristic
181C2×C8—132no—
182C2×C8—132no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—131no—
188C4⋊C4—131no—
189C4⋊C4—261no—
190C4⋊C4—261no—
191C4⋊C4—261no—
192C4⋊C4—261no—
193C4⋊C4C22×D1312yes—
194C4⋊C4C22×D1312yes—
195C22⋊C4—22no—
196C22⋊C4—261no—
197C22⋊C4—261no—
198C22⋊C4—261no—
199C22⋊C4—261no—
200C22⋊C4—261no—
201C42—22no—
202C42—261no—
203C42C22⋊D1311yescharacteristic
204C42C22⋊D1311yescharacteristic
205C42C22×D1311yescharacteristic
206C42C22×D1311yescharacteristic
207C13#323311yescharacteristic, complemented, Sylow
208C23—261no—
209C23C2×C22⋊D1311yescharacteristic
210Q8—42no—
211Q8—42no—
212Q8—261no—
213Q8—261no—
214D4—261no—
215D4—261no—
216D4—522no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—261no—
224C2×C4—261no—
225C2×C4—261no—
226C2×C4—522no—
227C2×C4C2×C22⋊D1311yescharacteristic
228C2×C4C2×C22⋊D1311yescharacteristic
229C2×C4C2×C22⋊D1311yescharacteristic
230C2×C4C2×C22⋊D1311yescharacteristic
231C2×C4C2×C22⋊D1311yescharacteristic
232C2×C4C23×D1311yescharacteristic
233C8—262no—
234C8—262no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—521no—
239C22—521no—
240C22—521no—
241C22C22×C22⋊D1311yescharacteristic
242C4—21no—
243C4—21no—
244C4—21no—
245C4—21no—
246C4—42no—
247C4—42no—
248C4—521no—
249C4—521no—
250C4—521no—
251C4#8820412yes—
252C4#8825411yescharacteristic
253C4#8825411yescharacteristic
254C2—41no—
255C2—1041no—
256C2#1171952111yescharacteristic
257C2C2×#8820411yescharacteristic
258C2#1171952711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#533C2
socleC22×C13C22×D4
prime radical#88184C22
hypercenter#533D13
hypocenterC13#3233
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
1. C13×#533C2semidirect
3. #11718755C2semidirect
4. #11718752C2semidirect
5. #11718748C2semidirect
6. #11718745C2semidirect
7. #11718729C2semidirect
8. #11718725C2semidirect
10. #11718657C2semidirect
11. #11718586C2semidirect
106. #533D13semidirect
207. C13#3233semidirect

Maximal subgroups

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

subgroupindex
C13×#5332
#117191842
#117187552
#117187522
#117187482
#117187452
#117187292
#117187252
#117186642
#117186572
#117185862
#323313