Finite Group Databasebeta

← #13126011

Subgroups — #13126011

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×#529C211yesmaximal, characteristic
2#11719175C211yesmaximal, characteristic, complemented
3#11718725C212yesmaximal, complemented
4#11718717C212yesmaximal, complemented
5#11718706C212yesmaximal, complemented
6#11718696C212yesmaximal
7#11718682C211yesmaximal, characteristic, complemented
8#11718681C211yesmaximal, characteristic, complemented
9#11718669C211yesmaximal, characteristic, complemented
10#11718668C211yesmaximal, characteristic, complemented
11#11718586C211yesmaximal, characteristic, complemented
12C13×#126—21no—
13C13×#125C2211yescharacteristic
14C13×#124C2211yescharacteristic
15C13×#123—21no—
16C13×C22⋊Q8C2211yescharacteristic
17C13×#121C2211yescharacteristic
18C4×Q8×C13C2211yescharacteristic
19C4×D4×C13—21no—
20C4×D4×C13C2211yescharacteristic
21C13×#117—21no—
22C2×C42×C13C2211yescharacteristic
23#88180C2212yes—
24#88178—21no—
25#88178—21no—
26#88124C2212yes—
27#88123C2211yescharacteristic
28#88123C2211yescharacteristic
29C4×Dic26—21no—
30C4×Dic26—21no—
31#88075C2212yes—
32#88075C2212yes—
33#88072C2212yes—
34#88072C2212yes—
35C22⋊#1055C2212yes—
36#88048C2212yes—
37#88048C2212yes—
38#88047C2212yes—
39#88047C2212yes—
40C4⋊#1055C2211yescharacteristic
41C4⋊#1055C2211yescharacteristic
42C4×#1055C2212yes—
43C2×Q8×C13C2311yescharacteristic
44C2×D4×C13—21no—
45C2×D4×C13C2311yescharacteristic
46C22×C4×C13—21no—
47C22×C4×C13D411yescharacteristic
48C22×C4×C13D411yescharacteristic
49C22×C4×C13C2311yescharacteristic
50C2×Dic26—21no—
51C2×Dic26—21no—
52C13×C4⋊C4—21no—
53C13×C4⋊C4—21no—
54C13×C4⋊C4—21no—
55C13×C4⋊C4—21no—
56C13×C4⋊C4C2311yescharacteristic
57C13×C4⋊C4C2311yescharacteristic
58C13×C22⋊C4—21no—
59C13×C22⋊C4—21no—
60C13×C22⋊C4—21no—
61C13×C22⋊C4—21no—
62C13×C22⋊C4—21no—
63C42×C13—21no—
64C42×C13D411yescharacteristic
65C42×C13D411yescharacteristic
66C42×C13C2311yescharacteristic
67C42×C13C2311yescharacteristic
68C22⋊Dic13—22no—
69C4⋊Dic13—21no—
70C4⋊Dic13—21no—
71C4⋊Dic13C2312yes—
72C4⋊Dic13C2312yes—
73#6101—22no—
74#6101—22no—
75C4×Dic13—22no—
76C2×#1055C2312yes—
77C2×#1055C2312yes—
78#3233—131nomaximal, Sylow
79C23×C13—21no—
80C23×C13C2×D411yescharacteristic
81Q8×C13—21no—
82Q8×C13—21no—
83D4×C13—21no—
84D4×C13—21no—
85D4×C13—42no—
86C2×C4×C13—22no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—41no—
93C2×C4×C13—42no—
94C2×C4×C13C2×D411yescharacteristic
95C2×C4×C13C2×D411yescharacteristic
96C2×C4×C13C2×D411yescharacteristic
97C2×C4×C13C2×D411yescharacteristic
98C2×C4×C13C2×D411yescharacteristic
99C2×C4×C13C2411yescharacteristic
100C2×Dic13—22no—
101C2×Dic13—22no—
102Dic26—42no—
103Dic26—42no—
104#1055—22no—
105#1055—22no—
106#533—131no—
107#529D1311yescharacteristic
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×C13—41no—
121C22×C13—41no—
122C22×C13—41no—
123C22×C13C22×D411yescharacteristic
124C4×C13—21no—
125C4×C13—21no—
126C4×C13—21no—
127C4×C13—21no—
128C4×C13—41no—
129C4×C13—41no—
130C4×C13—41no—
131C4×C13#13512yes—
132C4×C132−1+411yescharacteristic
133C4×C132−1+411yescharacteristic
134Dic13—42no—
135Dic13—42no—
136C4⋊Q8—131no—
137C4⋊Q8—131no—
138#126—21no—
139#125—132no—
140#125C2×D1311yescharacteristic
141#124C2×D1311yescharacteristic
142#123—21no—
143C22⋊Q8—261no—
144C22⋊Q8—261no—
145C22⋊Q8C2×D1311yescharacteristic
146#121C2×D1311yescharacteristic
147C4×Q8—261no—
148C4×Q8—261no—
149C4×Q8C2×D1311yescharacteristic
150C4×D4—21no—
151C4×D4C2×D1311yescharacteristic
152#117—21no—
153#117—132no—
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—81no—
169C2×C13#53611yescharacteristic
170C2×C13C2×#13511yescharacteristic
171C2×C13#57511yescharacteristic
172C2×Q8—261no—
173C2×Q8—261no—
174C2×Q8C22×D1311yescharacteristic
175C2×D4—21no—
176C2×D4C22×D1311yescharacteristic
177C22×C4—21no—
178C22×C4C22⋊D1311yescharacteristic
179C22×C4C22⋊D1311yescharacteristic
180C22×C4C22×D1311yescharacteristic
181C2×C8—132no—
182C2×C8—132no—
183C4⋊C4—21no—
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—132no—
188C4⋊C4—132no—
189C4⋊C4—262no—
190C4⋊C4—262no—
191C4⋊C4—261no—
192C4⋊C4—261no—
193C4⋊C4C22×D1311yescharacteristic
194C4⋊C4C22×D1311yescharacteristic
195C22⋊C4—21no—
196C22⋊C4—21no—
197C22⋊C4—21no—
198C22⋊C4—21no—
199C22⋊C4—21no—
200C22⋊C4—262no—
201C42—21no—
202C42—262no—
203C42C22⋊D1311yescharacteristic
204C42C22⋊D1311yescharacteristic
205C42C22×D1311yescharacteristic
206C42C22×D1311yescharacteristic
207C13#323311yescharacteristic, complemented, Sylow
208C23—21no—
209C23C2×C22⋊D1311yescharacteristic
210Q8—21no—
211Q8—21no—
212Q8—522no—
213Q8—522no—
214D4—21no—
215D4—21no—
216D4—42no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—41no—
224C2×C4—42no—
225C2×C4—262no—
226C2×C4—262no—
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—41no—
239C22—41no—
240C22—41no—
241C22C22×C22⋊D1311yescharacteristic
242C4—21no—
243C4—21no—
244C4—21no—
245C4—21no—
246C4—41no—
247C4—41no—
248C4—41no—
249C4—522no—
250C4—522no—
251C4#8820412yes—
252C4#8825711yescharacteristic
253C4#8825711yescharacteristic
254C2—41no—
255C2—81no—
256C2C2×#8820411yescharacteristic
257C2#1171952711yescharacteristic
258C2#1171953011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#529C2
socleC22×C13C22×D4
prime radicalC13×#121C22
hypercenter#529D13
hypocenterC13#3233
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
2. #11719175C2semidirect
3. #11718725C2semidirect
4. #11718717C2semidirect
5. #11718706C2semidirect
7. #11718682C2semidirect
8. #11718681C2semidirect
9. #11718669C2semidirect
10. #11718668C2semidirect
11. #11718586C2semidirect
207. C13#3233semidirect

Maximal subgroups

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

subgroupindex
C13×#5292
#117191752
#117187252
#117187172
#117187062
#117186962
#117186822
#117186812
#117186692
#117186682
#117185862
#323313