Finite Group Databasebeta

← #13126763

Subgroups — #13126763

Order 1664.

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

normal subgroups only

This group has 398 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
1#11719439C211yesmaximal, characteristic, complemented
2#11719431C211yesmaximal, characteristic, complemented
3C13×#487C211yesmaximal, characteristic, complemented
4#11718745C211yesmaximal, characteristic, complemented
5#11718744C211yesmaximal, characteristic, complemented
6#11718475C212yesmaximal, complemented
7#11718472C212yesmaximal, complemented
8#11718468C212yesmaximal, complemented
9#11718465C212yesmaximal, complemented
10C4×D104C211yesmaximal, characteristic, complemented
11C8×D52C211yesmaximal, characteristic, complemented
12C2×#6131C2212yes—
13C13×C4⋊Q8C2211yescharacteristic
14C13×C4⋊Q8C2211yescharacteristic
15#88201—22no—
16#88200C2212yes—
17C2×#6106C2212yes—
18C2×D104C2211yescharacteristic
19C2×C8×D13C2212yes—
20#88149—21no—
21#88149—21no—
22#88149C2212yes—
23#88148—22no—
24#88146—21no—
25#88146C2212yes—
26C4⋊C4×D13—21no—
27C4×D52C2211yescharacteristic
28C4×D52C2211yescharacteristic
29C4×D52C2211yescharacteristic
30C13×#103C2212yes—
31C13×#103C2212yes—
32C4×C8×C13C2211yescharacteristic
33#88075C2212yes—
34#88061C2211yescharacteristic
35#88061C2211yescharacteristic
36#88060C2212yes—
37#88058C2211yescharacteristic
38#88049C2212yes—
39#88048C2212yes—
40C4⋊#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×Q8×C13C2312yes—
43#6131—24no—
44#6131—42no—
45C2×D52—22no—
46C2×D52—22no—
47C2×D52D411yescharacteristic
48C2×D52C2311yescharacteristic
49C2×D52C2311yescharacteristic
50C2×C4×D13—21no—
51C2×C4×D13—21no—
52C2×C4×D13—22no—
53C2×C4×D13C2312yes—
54C2×C8×C13C2311yescharacteristic
55C2×C8×C13C2311yescharacteristic
56C13×C4⋊C4—21no—
57C13×C4⋊C4—21no—
58C13×C4⋊C4—21no—
59C13×C4⋊C4C2312yes—
60C42×C13C2311yescharacteristic
61#6106—42no—
62#6103—22no—
63#6103—22no—
64#6103—21no—
65#6103—21no—
66#6103—22no—
67#6103D412yes—
68C4⋊Dic13D411yescharacteristic
69C4⋊Dic13C2311yescharacteristic
70C4⋊Dic13C2311yescharacteristic
71#6101—22no—
72C4×Dic13—22no—
73C2×#1055C2312yes—
74D104—22no—
75C8×D13—42no—
76#3303—131nomaximal, Sylow
77C22×D13—21no—
78C22×D13—21no—
79C22×D13C2×D412yes—
80Q8×C13—22no—
81Q8×C13—22no—
82Q8×C13—81no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13C2×D411yescharacteristic
86C2×C4×C13C2×D411yescharacteristic
87C2×C4×C13C2411yescharacteristic
88C2×Dic13—21no—
89C2×Dic13—21no—
90C2×Dic13C2×D412yes—
91D52—22no—
92D52—21no—
93D52—21no—
94D52—21no—
95D52—44no—
96D52—82no—
97D52#4112yes—
98C4×D13—22no—
99C4×D13—22no—
100C4×D13—44no—
101C4×D13—42no—
102C4×D13—42no—
103C8×C13—21no—
104C8×C13—21no—
105#1055—22no—
106#555—131no—
107#547—131no—
108#487D1311yescharacteristic, complemented
109#485—132no—
110#476—131no—
111#465—132no—
112#461—131no—
113#449—132no—
114C4×D8—131no—
115C8×D4—131no—
116#416—132no—
117C22×C13C22×D411yescharacteristic
118C2×D13—22no—
119C2×D13—22no—
120C2×D13—22no—
121C2×D13—22no—
122C2×D13—41no—
123C2×D13—41no—
124C2×D13—41no—
125C2×D13—41no—
126C2×D13—41no—
127C4×C13—21no—
128C4×C13—42no—
129C4×C13—42no—
130C4×C13#13512yes—
131C4×C13C2×#4111yescharacteristic
132C4×C13H(5,𝔽2)11yescharacteristic
133Dic13—22no—
134Dic13—41no—
135Dic13—41no—
136C2×#41—132no—
137C2×SD16—132no—
138C2×D8—131no—
139C22×C8—132no—
140C4⋊Q8C2×D1311yescharacteristic
141C4⋊Q8C2×D1311yescharacteristic
142#124—262no—
143#123—262no—
144C22⋊Q8—132no—
145#121—132no—
146#121—261no—
147#121—261no—
148C4×D4—131no—
149C4×D4—131no—
150C4×D4—131no—
151#117—132no—
152#117—261no—
153C2×C4⋊C4—261no—
154#107—131no—
155#106—132no—
156C4⋊C8—131no—
157#103—132no—
158#103C2×D1312yes—
159#103C2×D1312yes—
160#102—131no—
161#102—131no—
162#102—132no—
163C22⋊C8—132no—
164C4×C8C2×D1311yescharacteristic
165C2×C13#54611yescharacteristic
166C2×C13C2×#13511yescharacteristic
167C2×C13#57711yescharacteristic
168D13—42no—
169D13—42no—
170D13—81no—
171#41—264no—
172#41—522no—
173C2×Q8—21no—
174C2×Q8C22×D1312yes—
175C2×D4—131no—
176C2×D4—131no—
177C2×D4—131no—
178C2×D4—262no—
179C2×D4—262no—
180C22×C4—132no—
181C22×C4—262no—
182C22×C4—261no—
183C22×C4—261no—
184SD16—522no—
185D8—262no—
186C2×C8—132no—
187C2×C8—522no—
188C2×C8C22×D1311yescharacteristic
189C2×C8C22×D1311yescharacteristic
190C4⋊C4—21no—
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—131no—
194C4⋊C4—131no—
195C4⋊C4—131no—
196C4⋊C4—262no—
197C4⋊C4C22×D1312yes—
198C22⋊C4—132no—
199C22⋊C4—262no—
200C22⋊C4—262no—
201C22⋊C4—262no—
202C22⋊C4—261no—
203C22⋊C4—261no—
204C42—262no—
205C42C22×D1311yescharacteristic
206C13#330311yescharacteristic, complemented, Sylow
207C23—132no—
208C23—261no—
209C23—261no—
210Q8—22no—
211Q8—22no—
212Q8—81no—
213D4—132no—
214D4—262no—
215D4—261no—
216D4—261no—
217D4—261no—
218D4—524no—
219D4—1042no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—132no—
223C2×C4—262no—
224C2×C4—262no—
225C2×C4—261no—
226C2×C4—261no—
227C2×C4—524no—
228C2×C4—522no—
229C2×C4—522no—
230C2×C4D4×D1311yescharacteristic
231C2×C4D4×D1311yescharacteristic
232C2×C4C23×D1311yescharacteristic
233C8—21no—
234C8—21no—
235C8—262no—
236C22—262no—
237C22—262no—
238C22—262no—
239C22—262no—
240C22—521no—
241C22—521no—
242C22—521no—
243C22—521no—
244C22—521no—
245C22C2×D4×D1311yescharacteristic
246C4—21no—
247C4—42no—
248C4—42no—
249C4—262no—
250C4—521no—
251C4—521no—
252C4#8817312yes—
253C4#41×D1311yescharacteristic
254C4#8825611yescharacteristic
255C2—522no—
256C2—522no—
257C2—1041no—
258C2#1171938111yescharacteristic
259C2#1171946711yescharacteristic
260C2C2×#8817311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#487C2
socleC22×C13C22×D4
hypercenter#487D13
hypocenterC13#3303
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #11719439C2semidirect
2. #11719431C2semidirect
3. C13×#487C2semidirect
4. #11718745C2semidirect
5. #11718744C2semidirect
6. #11718475C2semidirect
7. #11718472C2semidirect
8. #11718468C2semidirect
9. #11718465C2semidirect
10. C4×D104C2semidirect
11. C8×D52C2semidirect
108. #487D13semidirect
206. C13#3303semidirect

Maximal subgroups

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

subgroupindex
#117194392
#117194312
C13×#4872
#117187452
#117187442
#117184752
#117184722
#117184682
#117184652
C4×D1042
C8×D522
#330313