Finite Group Databasebeta

← #13126061

Subgroups — #13126061

Order 1664.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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, complemented
2#11719285C211yesmaximal, characteristic
3C13×#477C211yesmaximal, characteristic, complemented
4#11718745C211yesmaximal, characteristic, complemented
5#11718682C211yesmaximal, characteristic, complemented
6#11718543C212yesmaximal
7#11718537C212yesmaximal, complemented
8#11718503C211yesmaximal, characteristic, complemented
9#11718496C211yesmaximal, characteristic, complemented
10#11718466C212yesmaximal, complemented
11#11718456C212yesmaximal, complemented
12C2×Q8×D13—21no—
13C13×C4⋊Q8C2211yescharacteristic
14C4×Q8×C13C2211yescharacteristic
15#88201C2211yescharacteristic
16#88200C2211yescharacteristic
17#88198—21no—
18#88152—21no—
19#88149C2211yescharacteristic
20#88148—21no—
21C4⋊C4×D13—21no—
22C4⋊C4×D13C2212yes—
23#88144C2211yescharacteristic
24#88142—21no—
25#88142C2212yes—
26C4×D52—21no—
27C4×D52C2211yescharacteristic
28#88126—21no—
29C42×D13C2211yescharacteristic
30#88123C2211yescharacteristic
31C13×#107C2212yes—
32C13×C4⋊C8C2211yescharacteristic
33C13×#103C2212yes—
34#88075C2212yes—
35#88061C2212yes—
36#88060C2212yes—
37#88057C2212yes—
38#88055C2212yes—
39#88049C2212yes—
40#88048C2212yes—
41#88047C2212yes—
42C4⋊#1055C2211yescharacteristic
43C2×Q8×C13—21no—
44C2×Q8×C13C2311yescharacteristic
45Q8×D13—44no—
46C2×D52—21no—
47C2×D52C2311yescharacteristic
48C2×C4×D13—22no—
49C2×C4×D13—21no—
50C2×C4×D13D411yescharacteristic
51C2×C4×D13D411yescharacteristic
52C2×C4×D13C2311yescharacteristic
53C2×Dic26—21no—
54C2×Dic26—22no—
55C2×C8×C13C2312yes—
56C13×C4⋊C4—21no—
57C13×C4⋊C4—21no—
58C13×C4⋊C4C2312yes—
59C13×C4⋊C4C2311yescharacteristic
60C42×C13—21no—
61C42×C13C2311yescharacteristic
62#6103—21no—
63#6103—21no—
64#6103—21no—
65#6103—21no—
66#6103—21no—
67C4⋊Dic13—21no—
68C4⋊Dic13—21no—
69C4⋊Dic13C2312yes—
70C4⋊Dic13C2311yescharacteristic
71#6101—21no—
72#6101—21no—
73#6101—22no—
74#6101—22no—
75C4×Dic13D411yescharacteristic
76C4×Dic13D411yescharacteristic
77C4×Dic13C2311yescharacteristic
78C2×#1055C2312yes—
79#3238—131nomaximal, Sylow
80C22×D13—21no—
81C22×D13C2×D411yescharacteristic
82Q8×C13—21no—
83Q8×C13—21no—
84Q8×C13—42no—
85C2×C4×C13—22no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13C2×D411yescharacteristic
89C2×C4×C13C2×D411yescharacteristic
90C2×C4×C13C2411yescharacteristic
91C2×Dic13—21no—
92C2×Dic13—22no—
93C2×Dic13C2×D411yescharacteristic
94C2×Dic13C2×D411yescharacteristic
95C2×Dic13C2×D411yescharacteristic
96D52—21no—
97D52—21no—
98D52—42no—
99C4×D13—22no—
100C4×D13—22no—
101C4×D13—21no—
102C4×D13—21no—
103C4×D13—44no—
104C4×D13—42no—
105Dic26—44no—
106Dic26—42no—
107C8×C13—22no—
108#1055—22no—
109C2×C4⋊Q8—131no—
110#529—131no—
111#501—132no—
112#489—132no—
113#483—132no—
114#480—132no—
115#477—131no—
116#477D1311yescharacteristic, complemented
117#476—131no—
118#476—131no—
119#432—131no—
120C22×C13C22×D411yescharacteristic
121C2×D13—21no—
122C2×D13—21no—
123C2×D13—41no—
124C2×D13—41no—
125C2×D13—41no—
126C2×D13AGL(1,ℤ/8)12yes—
127C4×C13—21no—
128C4×C13—41no—
129C4×C13—42no—
130C4×C13—41no—
131C4×C13#13712yes—
132C4×C132−1+411yescharacteristic
133C4×C132−1+411yescharacteristic
134Dic13—21no—
135Dic13—21no—
136Dic13—21no—
137Dic13—42no—
138Dic13—41no—
139C22×Q8—261no—
140C4⋊Q8—132no—
141C4⋊Q8—131no—
142C4⋊Q8—261no—
143C4⋊Q8—261no—
144C4⋊Q8C2×D1311yescharacteristic
145#126—261no—
146#125—131no—
147#124—131no—
148#123—261no—
149C22⋊Q8—131no—
150#121—131no—
151C4×Q8C2×D1311yescharacteristic
152C4×D4—131no—
153C4×D4—261no—
154#117—261no—
155C2×C4⋊C4—132no—
156C2×C4⋊C4—261no—
157C2×C42—131no—
158#107—132no—
159#107C2×D1312yes—
160#106—132no—
161#106—132no—
162C4⋊C8—131no—
163C4⋊C8C2×D1311yescharacteristic
164#103—132no—
165#103C2×D1312yes—
166#102—132no—
167#102—132no—
168C22⋊C8—132no—
169#97—132no—
170C2×C13#53611yescharacteristic
171C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
172C2×C13C2×#13711yescharacteristic
173D13—22no—
174D13—81no—
175C2×Q8—21no—
176C2×Q8—262no—
177C2×Q8—261no—
178C2×Q8—524no—
179C2×Q8C22×D1311yescharacteristic
180C2×D4—131no—
181C2×D4—261no—
182C22×C4—131no—
183C22×C4—131no—
184C22×C4—131no—
185C22×C4—262no—
186C22×C4—261no—
187C2×C8—132no—
188C2×C8C22×D1312yes—
189C4⋊C4—21no—
190C4⋊C4—21no—
191C4⋊C4—132no—
192C4⋊C4—131no—
193C4⋊C4—262no—
194C4⋊C4—262no—
195C4⋊C4—261no—
196C4⋊C4—261no—
197C4⋊C4—261no—
198C4⋊C4—261no—
199C4⋊C4C22×D1312yes—
200C4⋊C4C22×D1311yescharacteristic
201C22⋊C4—261no—
202C22⋊C4—261no—
203C22⋊C4—261no—
204C22⋊C4—261no—
205C22⋊C4—261no—
206C42—21no—
207C42—131no—
208C42—131no—
209C42—131no—
210C42C22×D1311yescharacteristic
211C13#323811yescharacteristic, complemented, Sylow
212C23—131no—
213C23—261no—
214Q8—21no—
215Q8—21no—
216Q8—42no—
217Q8—522no—
218Q8—524no—
219D4—261no—
220D4—261no—
221D4—522no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—131no—
226C2×C4—131no—
227C2×C4—131no—
228C2×C4—262no—
229C2×C4—262no—
230C2×C4—261no—
231C2×C4—261no—
232C2×C4—261no—
233C2×C4—262no—
234C2×C4—524no—
235C2×C4—522no—
236C2×C4D4×D1311yescharacteristic
237C2×C4D4×D1311yescharacteristic
238C2×C4C23×D1311yescharacteristic
239C8—22no—
240C8—262no—
241C22—132no—
242C22—261no—
243C22—261no—
244C22—521no—
245C22—521no—
246C22—521no—
247C22C2×D4×D1311yescharacteristic
248C4—21no—
249C4—42no—
250C4—41no—
251C4—41no—
252C4—261no—
253C4—261no—
254C4—261no—
255C4—521no—
256C4—522no—
257C4#8817212yes—
258C4#8825411yescharacteristic
259C4#8825711yescharacteristic
260C2—262no—
261C2—1041no—
262C2#1171933311yescharacteristic
263C2C2×#8817211yescharacteristic
264C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#477C2
socleC22×C13C22×D4
prime radical#88149C22
hypercenter#477D13
hypocenterC13#3238
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
1. D13×C4⋊Q8C2semidirect
3. C13×#477C2semidirect
4. #11718745C2semidirect
5. #11718682C2semidirect
7. #11718537C2semidirect
8. #11718503C2semidirect
9. #11718496C2semidirect
10. #11718466C2semidirect
11. #11718456C2semidirect
116. #477D13semidirect
211. C13#3238semidirect

Maximal subgroups

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

subgroupindex
D13×C4⋊Q82
#117192852
C13×#4772
#117187452
#117186822
#117185432
#117185372
#117185032
#117184962
#117184662
#117184562
#323813