Finite Group Databasebeta

← #13120536

Subgroups — #13120536

Order 1664.

476 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 141 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×#125C211yesmaximal, characteristic, complemented
2C2×#88126C211yesmaximal, characteristic
3#11718654C211yesmaximal, characteristic
4#11718653C211yesmaximal, characteristic
5#11718651C212yesmaximal
6#11718650C212yesmaximal
7#11718643C211yesmaximal, characteristic, complemented
8#11718641C211yesmaximal, characteristic, complemented
9#11718639C212yesmaximal, complemented
10#11718633C212yesmaximal, complemented
11#11718593C211yesmaximal, characteristic, complemented
12C22×C4×D13C2211yescharacteristic
13C13×#125—24no—
14C2×C13×C4⋊C4C2212yes—
15C2×C13×C4⋊C4C2212yes—
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
18C2×C42×C13C2211yescharacteristic
19C2×#6103C2211yescharacteristic
20C2×#6103C2211yescharacteristic
21C2×#6103C2212yes—
22C2×#6103C2212yes—
23C2×#6101C2211yescharacteristic
24C2×#6101C2211yescharacteristic
25C2×#6101C2212yes—
26C2×#6101C2212yes—
27C2×C4×Dic13C2211yescharacteristic
28C2×C4×Dic13C2212yes—
29#88126—24no—
30#88071C2212yes—
31#88071C2211yescharacteristic
32#88071C2211yescharacteristic
33#88071C2212yes—
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37C23×D13C2311yescharacteristic
38C22×C4×C13C2312yes—
39C22×C4×C13C2312yes—
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2311yescharacteristic
42C22×C4×C13C2311yescharacteristic
43C22×Dic13C2312yes—
44C22×Dic13C2311yescharacteristic
45C22×Dic13C2311yescharacteristic
46C22×Dic13C2312yes—
47C22×Dic13C2311yescharacteristic
48C2×C4×D13—22no—
49C2×C4×D13—22no—
50C2×C4×D13—22no—
51C13×C4⋊C4—24no—
52C13×C4⋊C4—24no—
53C13×C4⋊C4—22no—
54C13×C4⋊C4—22no—
55C42×C13D414yes—
56#6103—24no—
57#6103—22no—
58#6103—22no—
59#6103—24no—
60#6101—22no—
61#6101—22no—
62#6101—24no—
63#6101—24no—
64C4×Dic13—22no—
65C4×Dic13—24no—
66#2611—131nomaximal, Sylow
67C23×C13C2411yescharacteristic
68C22×D13—21no—
69C22×D13—22no—
70C22×D13—21no—
71C22×D13—22no—
72C22×D13#4112yes—
73C2×C4×C13—22no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13C2×D412yes—
84C2×C4×C13C2×D412yes—
85C2×C4×C13C2×D412yes—
86C2×Dic13—21no—
87C2×Dic13—22no—
88C2×Dic13—21no—
89C2×Dic13—22no—
90C2×Dic13—21no—
91C2×Dic13—21no—
92C2×Dic13—22no—
93C2×Dic13—22no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13#4114yes—
98C2×Dic13#4112yes—
99C4×D13—28no—
100C2×#125D1311yescharacteristic, complemented
101C2×#117—131no—
102#400—131no—
103#399—131no—
104#398—131no—
105#397—131no—
106#389—132no—
107#388—132no—
108#387—132no—
109#385—132no—
110#376—131no—
111C22×C13C22×D411yescharacteristic
112C22×C13C2×#4111yescharacteristic
113C22×C13C2×#4111yescharacteristic
114C22×C13C2×#4112yes—
115C22×C132−1+412yes—
116C2×D13—22no—
117C2×D13—24no—
118C2×D13—41no—
119C2×D13—41no—
120C2×D13—42no—
121C4×C13—22no—
122C4×C13—22no—
123C4×C13—22no—
124C4×C13—42no—
125C4×C13—42no—
126Dic13—22no—
127Dic13—24no—
128Dic13—41no—
129Dic13—41no—
130Dic13—42no—
131C23×C4—131no—
132#125—24no—
133#117—264no—
134C2×C4⋊C4—131no—
135C2×C4⋊C4—131no—
136C2×C4⋊C4—132no—
137C2×C4⋊C4—132no—
138C2×C4⋊C4C2×D1312yes—
139C2×C4⋊C4C2×D1312yes—
140C2×C4⋊C4C2×D1311yescharacteristic
141C2×C4⋊C4C2×D1311yescharacteristic
142C2×C22⋊C4—131no—
143C2×C22⋊C4—131no—
144C2×C22⋊C4—132no—
145C2×C22⋊C4—132no—
146C2×C42—131no—
147C2×C42—132no—
148C2×C42C2×D1311yescharacteristic
149#95—132no—
150#95—131no—
151#95—131no—
152#95—132no—
153#95—132no—
154#95—132no—
155#95—132no—
156C2×C13#52511yescharacteristic
157C2×C13#53211yescharacteristic
158C2×C13#53611yescharacteristic
159C2×C13#55212yes—
160C2×C13#55212yes—
161D13—42no—
162C24—131no—
163C22×C4—132no—
164C22×C4—131no—
165C22×C4—132no—
166C22×C4—131no—
167C22×C4—131no—
168C22×C4—262no—
169C22×C4—262no—
170C22×C4—262no—
171C22×C4C22×D1312yes—
172C22×C4C22×D1312yes—
173C22×C4C22×D1311yescharacteristic
174C22×C4C22×D1311yescharacteristic
175C22×C4C22×D1311yescharacteristic
176C4⋊C4—24no—
177C4⋊C4—24no—
178C4⋊C4—22no—
179C4⋊C4—22no—
180C4⋊C4—264no—
181C4⋊C4—264no—
182C4⋊C4—262no—
183C4⋊C4—262no—
184C22⋊C4—264no—
185C22⋊C4—264no—
186C22⋊C4—262no—
187C22⋊C4—262no—
188C42—264no—
189C42—262no—
190C42C22⋊D1314yes—
191C13#261111yescharacteristic, complemented, Sylow
192C23—132no—
193C23—262no—
194C23—262no—
195C23—261no—
196C23—261no—
197C23C23×D1311yescharacteristic
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—134no—
209C2×C4—132no—
210C2×C4—268no—
211C2×C4—262no—
212C2×C4—262no—
213C2×C4—261no—
214C2×C4—261no—
215C2×C4—262no—
216C2×C4—262no—
217C2×C4—262no—
218C2×C4—262no—
219C2×C4—262no—
220C2×C4—261no—
221C2×C4—261no—
222C2×C4C2×C22⋊D1312yes—
223C2×C4C2×C22⋊D1312yes—
224C2×C4C2×C22⋊D1312yes—
225C22—262no—
226C22—264no—
227C22—521no—
228C22—521no—
229C22—522no—
230C22#8825412yes—
231C22#41×D1311yescharacteristic
232C22#41×D1311yescharacteristic
233C22#41×D1312yes—
234C22C22×C22⋊D1311yescharacteristic
235C4—22no—
236C4—22no—
237C4—22no—
238C4—42no—
239C4—42no—
240C4—262no—
241C4—264no—
242C4—521no—
243C4—521no—
244C4—522no—
245C2—522no—
246C2#1171939812yes—
247C2#1171939812yes—
248C2#1171952111yescharacteristic
249C2#1171953311yescharacteristic
250C2#1171953711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×#125C2
prime radicalC23×D13C23
hypercenterC2×#125D13
hypocenterC13#2611
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. C2×C13×#125C2semidirect
7. #11718643C2semidirect
8. #11718641C2semidirect
9. #11718639C2semidirect
10. #11718633C2semidirect
11. #11718593C2semidirect
100. C2×#125D13semidirect
191. C13#2611semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1252
C2×#881262
#117186542
#117186532
#117186512
#117186502
#117186432
#117186412
#117186392
#117186332
#117185932
#261113