Finite Group Databasebeta

← #13127162

Subgroups — #13127162

Order 1664.

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

normal subgroups only

This group has 430 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#11719431C211yesmaximal, characteristic, complemented
2#11719423C211yesmaximal, characteristic, complemented
3C13×#486C211yesmaximal, characteristic, complemented
4#11718755C211yesmaximal, characteristic, complemented
5#11718733C211yesmaximal, characteristic, complemented
6#11718443C212yesmaximal, complemented
7#11718442C212yesmaximal, complemented
8#11718438C212yesmaximal, complemented
9#11718432C212yesmaximal, complemented
10C4×#6095C211yesmaximal, characteristic, complemented
11#11718349C211yesmaximal, characteristic, complemented
12C2×#6131—21no—
13C2×#6129C2212yes—
14C13×C4⋊Q8C2211yescharacteristic
15C13×#127C2211yescharacteristic
16#88200—21no—
17#88194—21no—
18#88193—22no—
19#88192C2212yes—
20D4×Dic13—21no—
21C2×#6104C2212yes—
22C2×#6095C2211yescharacteristic
23C2×#6094C2212yes—
24#88149C2212yes—
25#88148—22no—
26C4⋊C4×D13C2212yes—
27C4×D52C2211yescharacteristic
28C4×D52C2211yescharacteristic
29C4×Dic26C2211yescharacteristic
30C13×#102C2212yes—
31C13×#102C2212yes—
32C4×C8×C13C2211yescharacteristic
33#88072C2212yes—
34#88061C2211yescharacteristic
35#88060C2212yes—
36#88057C2211yescharacteristic
37#88056C2211yescharacteristic
38#88050C2212yes—
39#88048C2212yes—
40C4⋊#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×D4×C13—21no—
43C2×D4×C13—21no—
44C2×D4×C13C2312yes—
45C2×C22⋊D13—22no—
46C2×C22⋊D13—22no—
47C22×Dic13—22no—
48#6131—44no—
49#6129—24no—
50#6129—42no—
51C2×D52—22no—
52C2×D52D411yescharacteristic
53C2×D52C2311yescharacteristic
54C2×C4×D13—22no—
55C2×C4×D13—21no—
56C2×C4×D13C2312yes—
57C2×Dic26C2311yescharacteristic
58C2×C8×C13C2311yescharacteristic
59C2×C8×C13C2311yescharacteristic
60C13×C4⋊C4—21no—
61C13×C4⋊C4C2312yes—
62C42×C13C2311yescharacteristic
63C22⋊Dic13—22no—
64#6104—42no—
65#6103—21no—
66#6103—22no—
67#6103D412yes—
68C4⋊Dic13D411yescharacteristic
69C4⋊Dic13C2311yescharacteristic
70C4⋊Dic13C2311yescharacteristic
71#6101—21no—
72#6101—22no—
73C4×Dic13—21no—
74C2×#1055C2312yes—
75#6095—22no—
76#6094—42no—
77#3332—131nomaximal, Sylow
78C23×C13—22no—
79C22×D13—21no—
80C22×D13C2×D412yes—
81Q8×C13—42no—
82D4×C13—22no—
83D4×C13—22no—
84D4×C13—42no—
85D4×C13—81no—
86C2×C4×C13—22no—
87C2×C4×C13C2×D411yescharacteristic
88C2×C4×C13C2×D411yescharacteristic
89C2×C4×C13C2411yescharacteristic
90C22⋊D13—44no—
91C22⋊D13—82no—
92C2×Dic13—21no—
93C2×Dic13—21no—
94C2×Dic13—21no—
95C2×Dic13—44no—
96C2×Dic13C2×D412yes—
97D52—22no—
98D52—21no—
99D52—21no—
100D52—44no—
101C4×D13—22no—
102C4×D13—22no—
103C4×D13—44no—
104C4×D13—42no—
105Dic26—21no—
106Dic26#4112yescomplemented
107C8×C13—21no—
108C8×C13—21no—
109#1055—22no—
110#550—131no—
111#547—131no—
112#486D1311yescharacteristic, complemented
113#481—132no—
114#475—131no—
115#469—132no—
116#459—131no—
117#449—132no—
118C4×SD16—131no—
119#436—131no—
120#417—132no—
121C22×C13—42no—
122C22×C13—42no—
123C22×C13—42no—
124C22×C13C22×D411yescharacteristic
125C2×D13—22no—
126C2×D13—22no—
127C2×D13—22no—
128C2×D13—41no—
129C2×D13—41no—
130C2×D13—41no—
131C4×C13—21no—
132C4×C13—42no—
133C4×C13AGL(1,ℤ/8)12yes—
134C4×C13C2×#4111yescharacteristic
135C4×C13H(5,𝔽2)11yescharacteristic
136Dic13—22no—
137Dic13—22no—
138Dic13—41no—
139Dic13—41no—
140C2×#41—132no—
141C2×#41—261no—
142C2×SD16—131no—
143C2×D8—132no—
144C2×M16—132no—
145C4⋊Q8C2×D1311yescharacteristic
146#127—261no—
147#127C2×D1311yescharacteristic
148#123—262no—
149C22⋊Q8—261no—
150#121—132no—
151#121—132no—
152#121—262no—
153C4×Q8—131no—
154C4×D4—131no—
155C4×D4—131no—
156C4×D4—261no—
157C2×C4⋊C4—132no—
158#106—131no—
159#106—132no—
160C4⋊C8—131no—
161#103—131no—
162#103—132no—
163#102—132no—
164#102—131no—
165#102C2×D1312yes—
166#102C2×D1312yes—
167C22⋊C8—132no—
168C4×C8C2×D1311yescharacteristic
169C2×C13—82no—
170C2×C13#54611yescharacteristic
171C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
172C2×C13#57711yescharacteristic
173D13—42no—
174D13—81no—
175#41—264no—
176#41—522no—
177#41—524no—
178C2×Q8—21no—
179C2×Q8—131no—
180C2×D4—21no—
181C2×D4—21no—
182C2×D4—131no—
183C2×D4—131no—
184C2×D4—262no—
185C2×D4—262no—
186C2×D4—262no—
187C2×D4C22×D1312yes—
188C22×C4—132no—
189C22×C4—262no—
190C22×C4—262no—
191C22×C4—261no—
192SD16—262no—
193D8—522no—
194M16—522no—
195C2×C8—132no—
196C2×C8C22×D1311yescharacteristic
197C2×C8C22×D1311yescharacteristic
198C4⋊C4—21no—
199C4⋊C4—131no—
200C4⋊C4—131no—
201C4⋊C4—131no—
202C4⋊C4—262no—
203C4⋊C4—261no—
204C4⋊C4C22×D1312yes—
205C22⋊C4—132no—
206C22⋊C4—262no—
207C22⋊C4—262no—
208C22⋊C4—261no—
209C42—261no—
210C42C22×D1311yescharacteristic
211C13#333211yescharacteristic, complemented, Sylow
212C23—22no—
213C23—132no—
214C23—261no—
215Q8—42no—
216Q8—132no—
217Q8—261no—
218D4—22no—
219D4—22no—
220D4—42no—
221D4—81no—
222D4—262no—
223D4—261no—
224D4—261no—
225D4—524no—
226D4—524no—
227D4—1042no—
228C2×C4—22no—
229C2×C4—132no—
230C2×C4—261no—
231C2×C4—262no—
232C2×C4—262no—
233C2×C4—261no—
234C2×C4—261no—
235C2×C4—524no—
236C2×C4—524no—
237C2×C4—522no—
238C2×C4D4×D1311yescharacteristic
239C2×C4D4×D1311yescharacteristic
240C2×C4C23×D1311yescharacteristic
241C8—21no—
242C8—21no—
243C8—262no—
244C22—42no—
245C22—42no—
246C22—42no—
247C22—262no—
248C22—262no—
249C22—262no—
250C22—521no—
251C22—521no—
252C22—521no—
253C22C2×D4×D1311yescharacteristic
254C4—21no—
255C4—42no—
256C4—262no—
257C4—262no—
258C4—521no—
259C4—521no—
260C4#8816512yes—
261C4#41×D1311yescharacteristic
262C4#8825611yescharacteristic
263C2—82no—
264C2—522no—
265C2—1041no—
266C2#1171938111yescharacteristic
267C2C2×#8816511yescharacteristic
268C2#1171946711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#486C2
socleC22×C13C22×D4
hypercenter#486D13
hypocenterC13#3332
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #11719431C2semidirect
2. #11719423C2semidirect
3. C13×#486C2semidirect
4. #11718755C2semidirect
5. #11718733C2semidirect
6. #11718443C2semidirect
7. #11718442C2semidirect
8. #11718438C2semidirect
9. #11718432C2semidirect
10. C4×#6095C2semidirect
11. #11718349C2semidirect
106. Dic26#41semidirect
112. #486D13semidirect
211. C13#3332semidirect

Maximal subgroups

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

subgroupindex
#117194312
#117194232
C13×#4862
#117187552
#117187332
#117184432
#117184422
#117184382
#117184322
C4×#60952
#117183492
#333213