Finite Group Databasebeta

← #13126013

Subgroups — #13126013

Order 1664.

332 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 113 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#11719433C211yesmaximal, characteristic, complemented
2#11719262C211yesmaximal, characteristic
3C13×#474C211yesmaximal, characteristic, complemented
4#11718755C211yesmaximal, characteristic, complemented
5#11718669C211yesmaximal, characteristic, complemented
6#11718549C212yesmaximal, complemented
7#11718539C212yesmaximal, complemented
8#11718511C211yesmaximal, characteristic, complemented
9#11718494C211yesmaximal, characteristic, complemented
10#11718445C212yesmaximal
11#11718429C212yesmaximal, complemented
12C13×C4⋊Q8C2211yescharacteristic
13C4×D4×C13C2211yescharacteristic
14#88200—21no—
15Q8×Dic13—21no—
16#88192C2211yescharacteristic
17#88190C2211yescharacteristic
18C4×C22⋊D13—21no—
19#88180—21no—
20#88151—21no—
21#88151C2211yescharacteristic
22#88146C2212yes—
23#88144C2212yes—
24#88144C2211yescharacteristic
25#88141—21no—
26#88137—21no—
27#88133—21no—
28C42×D13C2211yescharacteristic
29#88123C2211yescharacteristic
30C4×Dic26C2211yescharacteristic
31C13×#107C2212yes—
32C13×C4⋊C8C2211yescharacteristic
33C13×#102C2212yes—
34#88072C2212yes—
35#88060C2212yes—
36#88058C2212yes—
37#88056C2212yes—
38C8×Dic13C2212yes—
39#88050C2212yes—
40#88048C2212yes—
41#88048C2212yes—
42C4⋊#1055C2211yescharacteristic
43C2×Q8×C13—21no—
44C2×D4×C13C2311yescharacteristic
45C22×C4×C13—21no—
46C2×C22⋊D13—21no—
47C2×C4×D13D411yescharacteristic
48C2×C4×D13D411yescharacteristic
49C2×C4×D13C2311yescharacteristic
50C2×Dic26—21no—
51C2×Dic26C2311yescharacteristic
52C2×C8×C13C2312yes—
53C13×C4⋊C4—21no—
54C13×C4⋊C4C2312yes—
55C13×C4⋊C4C2311yescharacteristic
56C13×C22⋊C4—21no—
57C42×C13C2311yescharacteristic
58C22⋊Dic13—21no—
59C22⋊Dic13—21no—
60C22⋊Dic13—21no—
61#6103—21no—
62#6103—22no—
63C4⋊Dic13—21no—
64C4⋊Dic13—21no—
65C4⋊Dic13—21no—
66C4⋊Dic13—22no—
67C4⋊Dic13C2312yes—
68C4⋊Dic13C2311yescharacteristic
69#6101—21no—
70#6101—21no—
71#6101—22no—
72C4×Dic13—21no—
73C4×Dic13—22no—
74C4×Dic13D411yescharacteristic
75C4×Dic13D411yescharacteristic
76C4×Dic13C2311yescharacteristic
77C2×#1055C2312yes—
78#3233—131nomaximal, Sylow
79C23×C13—21no—
80C22×D13C2×D411yescharacteristic
81Q8×C13—42no—
82D4×C13—21no—
83D4×C13—21no—
84C2×C4×C13—22no—
85C2×C4×C13—21no—
86C2×C4×C13—42no—
87C2×C4×C13C2×D411yescharacteristic
88C2×C4×C13C2×D411yescharacteristic
89C2×C4×C13C2411yescharacteristic
90C22⋊D13—42no—
91C2×Dic13—21no—
92C2×Dic13—22no—
93C2×Dic13—21no—
94C2×Dic13C2×D411yescharacteristic
95C2×Dic13C2×D411yescharacteristic
96C2×Dic13C2×D411yescharacteristic
97C4×D13—22no—
98C4×D13—21no—
99C4×D13—21no—
100C4×D13—41no—
101Dic26—21no—
102Dic26—21no—
103Dic26—42no—
104C8×C13—22no—
105#1055—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#474D1311yescharacteristic, complemented
116#431—131no—
117C22×C13—41no—
118C22×C13—41no—
119C22×C13—41no—
120C22×C13C22×D411yescharacteristic
121C2×D13—21no—
122C2×D13—21no—
123C2×D13—21no—
124C4×C13—21no—
125C4×C13—41no—
126C4×C13—42no—
127C4×C13#13512yes—
128C4×C132−1+411yescharacteristic
129C4×C132−1+411yescharacteristic
130Dic13—21no—
131Dic13—21no—
132Dic13—21no—
133Dic13—41no—
134Dic13—42no—
135Dic13—41no—
136C4⋊Q8—131no—
137C4⋊Q8C2×D1311yescharacteristic
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—261no—
151C4×D4C2×D1311yescharacteristic
152#117—132no—
153#117—261no—
154C2×C42—131no—
155#107—132no—
156#107C2×D1312yes—
157#106—132no—
158#106—132no—
159C4⋊C8—131no—
160C4⋊C8C2×D1311yescharacteristic
161#103—132no—
162#103—132no—
163#102—132no—
164#102C2×D1312yes—
165C22⋊C8—132no—
166C4×C8—132no—
167C2×C13—81no—
168C2×C13#53611yescharacteristic
169C2×C13C2×#13511yescharacteristic
170C2×C13#57511yescharacteristic
171D13—41no—
172C2×Q8—21no—
173C2×Q8—131no—
174C2×Q8—261no—
175C2×D4—261no—
176C2×D4C22×D1311yescharacteristic
177C22×C4—21no—
178C22×C4—131no—
179C22×C4—131no—
180C22×C4—131no—
181C2×C8—132no—
182C2×C8C22×D1312yes—
183C4⋊C4—21no—
184C4⋊C4—132no—
185C4⋊C4—131no—
186C4⋊C4—261no—
187C4⋊C4—261no—
188C4⋊C4—261no—
189C4⋊C4—262no—
190C4⋊C4—262no—
191C4⋊C4—261no—
192C4⋊C4—261no—
193C4⋊C4C22×D1312yes—
194C4⋊C4C22×D1311yescharacteristic
195C22⋊C4—21no—
196C22⋊C4—262no—
197C22⋊C4—261no—
198C22⋊C4—261no—
199C22⋊C4—261no—
200C22⋊C4—261no—
201C42—131no—
202C42—131no—
203C42—131no—
204C42—262no—
205C42—261no—
206C42C22×D1311yescharacteristic
207C13#323311yescharacteristic, complemented, Sylow
208C23—21no—
209C23—131no—
210Q8—42no—
211Q8—261no—
212Q8—261no—
213Q8—522no—
214D4—21no—
215D4—21no—
216D4—522no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—42no—
220C2×C4—131no—
221C2×C4—131no—
222C2×C4—131no—
223C2×C4—262no—
224C2×C4—261no—
225C2×C4—261no—
226C2×C4—261no—
227C2×C4—261no—
228C2×C4—262no—
229C2×C4—521no—
230C2×C4D4×D1311yescharacteristic
231C2×C4D4×D1311yescharacteristic
232C2×C4C23×D1311yescharacteristic
233C8—22no—
234C8—262no—
235C22—41no—
236C22—41no—
237C22—41no—
238C22—261no—
239C22—261no—
240C22—261no—
241C22C2×D4×D1311yescharacteristic
242C4—21no—
243C4—41no—
244C4—42no—
245C4—261no—
246C4—261no—
247C4—261no—
248C4—521no—
249C4—522no—
250C4—521no—
251C4#8816612yes—
252C4#8825411yescharacteristic
253C4#8825711yescharacteristic
254C2—81no—
255C2—521no—
256C2#1171933311yescharacteristic
257C2C2×#8816611yescharacteristic
258C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#474C2
socleC22×C13C22×D4
prime radical#88192C22
hypercenter#474D13
hypocenterC13#3233
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #11719433C2semidirect
3. C13×#474C2semidirect
4. #11718755C2semidirect
5. #11718669C2semidirect
6. #11718549C2semidirect
7. #11718539C2semidirect
8. #11718511C2semidirect
9. #11718494C2semidirect
11. #11718429C2semidirect
115. #474D13semidirect
207. C13#3233semidirect

Maximal subgroups

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

subgroupindex
#117194332
#117192622
C13×#4742
#117187552
#117186692
#117185492
#117185392
#117185112
#117184942
#117184452
#117184292
#323313