Finite Group Databasebeta

← #13127129

Subgroups — #13127129

Order 1664.

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

normal subgroups only

This group has 386 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
2#11719432C211yesmaximal, characteristic, complemented
3C13×#487C211yesmaximal, characteristic, complemented
4#11718752C211yesmaximal, characteristic, complemented
5#11718744C211yesmaximal, characteristic, complemented
6#11718476C212yesmaximal, complemented
7#11718473C212yesmaximal, complemented
8#11718467C212yesmaximal, complemented
9#11718463C212yesmaximal, complemented
10C4×#6095C211yesmaximal, characteristic, complemented
11#11718349C211yesmaximal, characteristic, complemented
12C2×Q8×D13C2212yes—
13C13×C4⋊Q8C2211yescharacteristic
14C13×C4⋊Q8C2211yescharacteristic
15#88201—22no—
16#88200C2212yes—
17C2×#6106C2212yes—
18C2×#6095C2211yescharacteristic
19C2×#6094C2212yes—
20#88150—22no—
21#88149—21no—
22#88149C2212yes—
23#88147—21no—
24#88146—21no—
25#88146C2212yes—
26#88142—21no—
27C4×D52C2211yescharacteristic
28C4×D52C2211yescharacteristic
29C4×Dic26C2211yescharacteristic
30C13×#103C2212yes—
31C13×#103C2212yes—
32C4×C8×C13C2211yescharacteristic
33#88075C2212yes—
34#88061C2211yescharacteristic
35#88060C2212yes—
36#88057C2211yescharacteristic
37#88056C2211yescharacteristic
38#88050C2212yes—
39#88047C2212yes—
40C4⋊#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×Q8×C13C2312yes—
43Q8×D13—24no—
44Q8×D13—42no—
45C2×D52—22no—
46C2×D52D411yescharacteristic
47C2×D52C2311yescharacteristic
48C2×C4×D13—22no—
49C2×C4×D13—21no—
50C2×C4×D13C2312yes—
51C2×Dic26—22no—
52C2×Dic26C2311yescharacteristic
53C2×C8×C13C2311yescharacteristic
54C2×C8×C13C2311yescharacteristic
55C13×C4⋊C4—21no—
56C13×C4⋊C4—21no—
57C13×C4⋊C4—21no—
58C13×C4⋊C4C2312yes—
59C42×C13C2311yescharacteristic
60#6106—42no—
61#6103—22no—
62#6103—22no—
63#6103—21no—
64#6103—22no—
65#6103D412yes—
66C4⋊Dic13D411yescharacteristic
67C4⋊Dic13C2311yescharacteristic
68C4⋊Dic13C2311yescharacteristic
69#6101—21no—
70#6101—22no—
71C4×Dic13—21no—
72C4×Dic13—22no—
73C2×#1055C2312yes—
74#6095—22no—
75#6094—42no—
76#3329—131nomaximal, Sylow
77C22×D13—21no—
78C22×D13C2×D412yes—
79Q8×C13—22no—
80Q8×C13—22no—
81Q8×C13—81no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13C2×D411yescharacteristic
85C2×C4×C13C2×D411yescharacteristic
86C2×C4×C13C2411yescharacteristic
87C2×Dic13—21no—
88C2×Dic13—21no—
89C2×Dic13—21no—
90C2×Dic13C2×D412yes—
91D52—22no—
92D52—21no—
93D52—21no—
94D52—82no—
95C4×D13—22no—
96C4×D13—22no—
97C4×D13—44no—
98C4×D13—42no—
99Dic26—21no—
100Dic26—44no—
101Dic26#4112yes—
102C8×C13—21no—
103C8×C13—21no—
104#1055—22no—
105#555—131no—
106D4×Q8—131no—
107#487D1311yescharacteristic, complemented
108#485—132no—
109#477—131no—
110#468—132no—
111#461—131no—
112#448—132no—
113C4×SD16—131no—
114#436—131no—
115#419—132no—
116C22×C13C22×D411yescharacteristic
117C2×D13—22no—
118C2×D13—22no—
119C2×D13—22no—
120C2×D13—41no—
121C2×D13—41no—
122C2×D13—41no—
123C4×C13—21no—
124C4×C13—42no—
125C4×C13—42no—
126C4×C13#13712yes—
127C4×C13C2×#4111yescharacteristic
128C4×C13H(5,𝔽2)11yescharacteristic
129Dic13—22no—
130Dic13—22no—
131Dic13—41no—
132Dic13—41no—
133C22×Q8—132no—
134C2×SD16—132no—
135C2×SD16—131no—
136C2×M16—132no—
137C4⋊Q8—261no—
138C4⋊Q8C2×D1311yescharacteristic
139C4⋊Q8C2×D1311yescharacteristic
140#124—262no—
141C22⋊Q8—132no—
142C22⋊Q8—262no—
143#121—132no—
144#121—261no—
145C4×Q8—131no—
146C4×D4—131no—
147C4×D4—131no—
148C4×D4—261no—
149#117—132no—
150#117—261no—
151#107—132no—
152#106—131no—
153C4⋊C8—131no—
154#103—132no—
155#103—131no—
156#103—132no—
157#103C2×D1312yes—
158#103C2×D1312yes—
159#102—131no—
160C22⋊C8—132no—
161C4×C8C2×D1311yescharacteristic
162C2×C13#54611yescharacteristic
163C2×C13C2×#13711yescharacteristic
164C2×C13#57711yescharacteristic
165D13—42no—
166D13—81no—
167C2×Q8—21no—
168C2×Q8—131no—
169C2×Q8—262no—
170C2×Q8—264no—
171C2×Q8—522no—
172C2×Q8C22×D1312yes—
173C2×D4—131no—
174C2×D4—131no—
175C2×D4—262no—
176C22×C4—132no—
177C22×C4—262no—
178C22×C4—261no—
179SD16—262no—
180SD16—522no—
181M16—522no—
182C2×C8—132no—
183C2×C8C22×D1311yescharacteristic
184C2×C8C22×D1311yescharacteristic
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—131no—
189C4⋊C4—131no—
190C4⋊C4—131no—
191C4⋊C4—262no—
192C4⋊C4—261no—
193C4⋊C4C22×D1312yes—
194C22⋊C4—132no—
195C22⋊C4—262no—
196C22⋊C4—262no—
197C22⋊C4—262no—
198C22⋊C4—261no—
199C42—262no—
200C42—261no—
201C42C22×D1311yescharacteristic
202C13#332911yescharacteristic, complemented, Sylow
203C23—132no—
204C23—261no—
205Q8—22no—
206Q8—22no—
207Q8—81no—
208Q8—132no—
209Q8—261no—
210Q8—524no—
211D4—262no—
212D4—261no—
213D4—261no—
214D4—1042no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—132no—
218C2×C4—261no—
219C2×C4—262no—
220C2×C4—262no—
221C2×C4—261no—
222C2×C4—261no—
223C2×C4—524no—
224C2×C4—522no—
225C2×C4D4×D1311yescharacteristic
226C2×C4D4×D1311yescharacteristic
227C2×C4C23×D1311yescharacteristic
228C8—21no—
229C8—21no—
230C8—262no—
231C22—262no—
232C22—262no—
233C22—262no—
234C22—521no—
235C22—521no—
236C22—521no—
237C22C2×D4×D1311yescharacteristic
238C4—21no—
239C4—42no—
240C4—42no—
241C4—262no—
242C4—262no—
243C4—521no—
244C4—521no—
245C4#8817212yes—
246C4#41×D1311yescharacteristic
247C4#8825611yescharacteristic
248C2—522no—
249C2—1041no—
250C2#1171938111yescharacteristic
251C2#1171946711yescharacteristic
252C2C2×#8817211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#487C2
socleC22×C13C22×D4
prime radical#11719439C2
hypercenter#487D13
hypocenterC13#3329
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
2. #11719432C2semidirect
3. C13×#487C2semidirect
4. #11718752C2semidirect
5. #11718744C2semidirect
6. #11718476C2semidirect
7. #11718473C2semidirect
8. #11718467C2semidirect
9. #11718463C2semidirect
10. C4×#6095C2semidirect
11. #11718349C2semidirect
107. #487D13semidirect
202. C13#3329semidirect

Maximal subgroups

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

subgroupindex
#117194392
#117194322
C13×#4872
#117187522
#117187442
#117184762
#117184732
#117184672
#117184632
C4×#60952
#117183492
#332913