Finite Group Databasebeta

← #13125986

Subgroups — #13125986

Order 1664.

360 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 123 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
1D13×C4⋊Q8C211yesmaximal, characteristic
2#11719283C211yesmaximal, characteristic
3C13×#477C211yesmaximal, characteristic, complemented
4#11718752C211yesmaximal, characteristic, complemented
5#11718682C211yesmaximal, characteristic, complemented
6#11718545C212yesmaximal
7#11718535C212yesmaximal, complemented
8#11718511C211yesmaximal, characteristic, complemented
9#11718494C211yesmaximal, characteristic
10#11718470C212yesmaximal
11#11718453C212yesmaximal, complemented
12C2×Q8×D13—21no—
13C13×C4⋊Q8C2211yescharacteristic
14C4×Q8×C13C2211yescharacteristic
15#88200C2211yescharacteristic
16#88198—21no—
17#88198C2211yescharacteristic
18#88151C2211yescharacteristic
19#88150—21no—
20C4⋊C4×D13—21no—
21C4⋊C4×D13C2212yes—
22#88143—21no—
23#88142—21no—
24#88142C2212yes—
25#88142C2211yescharacteristic
26#88126—21no—
27C42×D13C2211yescharacteristic
28#88123C2211yescharacteristic
29C4×Dic26—21no—
30C4×Dic26C2211yescharacteristic
31C13×#107C2212yes—
32C13×C4⋊C8C2211yescharacteristic
33C13×#103C2212yes—
34#88075C2212yes—
35#88060C2212yes—
36#88058C2212yes—
37#88056C2212yes—
38C8×Dic13C2212yes—
39#88050C2212yes—
40#88047C2212yes—
41#88047C2212yes—
42C4⋊#1055C2211yescharacteristic
43C2×Q8×C13—21no—
44C2×Q8×C13C2311yescharacteristic
45Q8×D13—44no—
46C2×C4×D13—22no—
47C2×C4×D13D411yescharacteristic
48C2×C4×D13D411yescharacteristic
49C2×C4×D13C2311yescharacteristic
50C2×Dic26—21no—
51C2×Dic26—21no—
52C2×Dic26—22no—
53C2×Dic26C2311yescharacteristic
54C2×C8×C13C2312yes—
55C13×C4⋊C4—21no—
56C13×C4⋊C4—21no—
57C13×C4⋊C4C2312yes—
58C13×C4⋊C4C2311yescharacteristic
59C42×C13—21no—
60C42×C13C2311yescharacteristic
61#6103—21no—
62#6103—21no—
63C4⋊Dic13—21no—
64C4⋊Dic13—21no—
65C4⋊Dic13C2312yes—
66C4⋊Dic13C2311yescharacteristic
67#6101—21no—
68#6101—21no—
69#6101—21no—
70#6101—21no—
71#6101—21no—
72#6101—22no—
73#6101—22no—
74C4×Dic13—21no—
75C4×Dic13D411yescharacteristic
76C4×Dic13D411yescharacteristic
77C4×Dic13C2311yescharacteristic
78C2×#1055C2312yes—
79#3230—131nomaximal, Sylow
80C22×D13C2×D411yescharacteristic
81Q8×C13—21no—
82Q8×C13—21no—
83Q8×C13—42no—
84C2×C4×C13—21no—
85C2×C4×C13—22no—
86C2×C4×C13—21no—
87C2×C4×C13C2×D411yescharacteristic
88C2×C4×C13C2×D411yescharacteristic
89C2×C4×C13C2411yescharacteristic
90C2×Dic13—21no—
91C2×Dic13—21no—
92C2×Dic13—22no—
93C2×Dic13C2×D411yescharacteristic
94C2×Dic13C2×D411yescharacteristic
95C2×Dic13C2×D411yescharacteristic
96C4×D13—21no—
97C4×D13—21no—
98C4×D13—22no—
99C4×D13—44no—
100C4×D13Q1614yes—
101Dic26—21no—
102Dic26—21no—
103Dic26—42no—
104Dic26—42no—
105Dic26—44no—
106C8×C13—22no—
107#1055—22no—
108#533—131no—
109C2×C4⋊Q8—131no—
110#500—132no—
111#487—132no—
112#484—132no—
113#484—132no—
114#477—131no—
115#477—131no—
116#477—131no—
117#477D1311yescharacteristic, complemented
118#431—131no—
119C22×C13C22×D411yescharacteristic
120C2×D13—21no—
121C2×D13—21no—
122C2×D13C2×Q1612yes—
123C4×C13—21no—
124C4×C13—41no—
125C4×C13—42no—
126C4×C13—41no—
127C4×C13C2×Q1612yes—
128C4×C132−1+411yescharacteristic
129C4×C132−1+411yescharacteristic
130Dic13—21no—
131Dic13—41no—
132Dic13—42no—
133Dic13—41no—
134Dic13C2×Q1612yes—
135Dic13AGL(1,ℤ/8)12yes—
136C22×Q8—261no—
137C4⋊Q8—132no—
138C4⋊Q8—131no—
139C4⋊Q8—131no—
140C4⋊Q8—131no—
141C4⋊Q8—261no—
142C4⋊Q8—261no—
143C4⋊Q8C2×D1311yescharacteristic
144#125—261no—
145C22⋊Q8—131no—
146C22⋊Q8—131no—
147C22⋊Q8—261no—
148C4×Q8—131no—
149C4×Q8—261no—
150C4×Q8C2×D1311yescharacteristic
151#117—261no—
152C2×C4⋊C4—132no—
153C2×C4⋊C4—261no—
154C2×C42—131no—
155#107—132no—
156#107—132no—
157#107—132no—
158#107C2×D1312yes—
159C4⋊C8—131no—
160C4⋊C8C2×D1311yescharacteristic
161#103—132no—
162#103—132no—
163#103—132no—
164#103C2×D1312yes—
165C22⋊C8—132no—
166C4×C8—132no—
167C2×C13#53611yescharacteristic
168C2×C13C22×Q1611yescharacteristic
169C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
170D13—22no—
171C2×Q8—21no—
172C2×Q8—131no—
173C2×Q8—261no—
174C2×Q8—262no—
175C2×Q8—261no—
176C2×Q8—524no—
177C2×Q8C22×D1311yescharacteristic
178C22×C4—131no—
179C22×C4—131no—
180C22×C4—131no—
181C22×C4—262no—
182C2×C8—132no—
183C2×C8C22×D1312yes—
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4—132no—
187C4⋊C4—131no—
188C4⋊C4—262no—
189C4⋊C4—262no—
190C4⋊C4—261no—
191C4⋊C4—261no—
192C4⋊C4—261no—
193C4⋊C4—261no—
194C4⋊C4—261no—
195C4⋊C4—261no—
196C4⋊C4—261no—
197C4⋊C4C22×D1312yes—
198C4⋊C4C22×D1311yescharacteristic
199C22⋊C4—261no—
200C22⋊C4—261no—
201C42—21no—
202C42—131no—
203C42—131no—
204C42—131no—
205C42—261no—
206C42C22×D1311yescharacteristic
207C13#323011yescharacteristic, complemented, Sylow
208C23—131no—
209Q8—21no—
210Q8—21no—
211Q8—42no—
212Q8—261no—
213Q8—261no—
214Q8—522no—
215Q8—522no—
216Q8—524no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—131no—
221C2×C4—131no—
222C2×C4—134no—
223C2×C4—131no—
224C2×C4—262no—
225C2×C4—261no—
226C2×C4—261no—
227C2×C4—261no—
228C2×C4—261no—
229C2×C4—262no—
230C2×C4—524no—
231C2×C4D4×D1311yescharacteristic
232C2×C4D4×D1311yescharacteristic
233C2×C4C23×D1311yescharacteristic
234C8—22no—
235C8—262no—
236C22—132no—
237C22—261no—
238C22—261no—
239C22C2×D4×D1311yescharacteristic
240C4—21no—
241C4—42no—
242C4—41no—
243C4—41no—
244C4—132no—
245C4—132no—
246C4—261no—
247C4—522no—
248C4—521no—
249C4—521no—
250C4Q16×D1312yes—
251C4#8825411yescharacteristic
252C4#8825711yescharacteristic
253C2—262no—
254C2#1171933311yescharacteristic
255C2C2×Q16×D1311yescharacteristic
256C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#477C2
socleC22×C13C22×D4
prime radicalC22×D13C2×D4
hypercenter#477D13
hypocenterC13#3230
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
3. C13×#477C2semidirect
4. #11718752C2semidirect
5. #11718682C2semidirect
7. #11718535C2semidirect
8. #11718511C2semidirect
11. #11718453C2semidirect
117. #477D13semidirect
207. C13#3230semidirect

Maximal subgroups

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

subgroupindex
D13×C4⋊Q82
#117192832
C13×#4772
#117187522
#117186822
#117185452
#117185352
#117185112
#117184942
#117184702
#117184532
#323013