Finite Group Databasebeta

← #13127160

Subgroups — #13127160

Order 1664.

430 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 117 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#11719282C211yesmaximal, characteristic, complemented
3C13×#475C211yesmaximal, characteristic, complemented
4#11718749C211yesmaximal, characteristic, complemented
5C4×#6106C211yesmaximal, characteristic, complemented
6#11718526C212yesmaximal, complemented
7#11718524C212yesmaximal, complemented
8#11718504C211yesmaximal, characteristic, complemented
9#11718499C211yesmaximal, characteristic, complemented
10#11718472C212yesmaximal, complemented
11#11718464C212yesmaximal, complemented
12C2×#6131—21no—
13C2×#6131C2212yes—
14C13×C4⋊Q8C2211yescharacteristic
15C4×Q8×C13C2211yescharacteristic
16#88200—21no—
17C2×#6106C2211yescharacteristic
18C2×D104C2212yes—
19C2×#6094C2212yes—
20#88149—22no—
21#88149C2212yes—
22#88149C2212yes—
23#88148—22no—
24C4⋊C4×D13C2212yes—
25#88128—21no—
26#88128C2211yescharacteristic
27C4×D52—21no—
28C4×D52C2211yescharacteristic
29C4×D52C2211yescharacteristic
30C13×#106C2212yes—
31C13×C4⋊C8C2211yescharacteristic
32C13×#103C2212yes—
33#88075C2211yescharacteristic
34#88061C2212yes—
35#88060C2212yes—
36#88049C2211yescharacteristic
37#88049C2212yes—
38#88049C2212yes—
39#88048C2211yescharacteristic
40C4×#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×Q8×C13C2311yescharacteristic
43#6131—24no—
44#6131—42no—
45#6131—44no—
46C2×D52—22no—
47C2×D52—22no—
48C2×D52—21no—
49C2×D52—22no—
50C2×D52—21no—
51C2×D52D411yescharacteristic
52C2×D52C2311yescharacteristic
53C2×D52C2312yes—
54C2×C4×D13—22no—
55C2×C4×D13—21no—
56C2×C4×D13—22no—
57C2×C4×D13C2312yes—
58C2×C8×C13C2312yes—
59C13×C4⋊C4—21no—
60C13×C4⋊C4—21no—
61C13×C4⋊C4C2312yes—
62C13×C4⋊C4C2311yescharacteristic
63C42×C13—21no—
64C42×C13C2311yescharacteristic
65#6106—22no—
66#6103—21no—
67#6103—22no—
68#6103—22no—
69#6103D412yes—
70C4⋊Dic13D411yescharacteristic
71C4⋊Dic13C2311yescharacteristic
72#6101—22no—
73C2×#1055C2311yescharacteristic
74C2×#1055C2311yescharacteristic
75D104—42no—
76#6094—42no—
77#3332—131nomaximal, Sylow
78C22×D13—21no—
79C22×D13—22no—
80C22×D13C2×D412yes—
81Q8×C13—21no—
82Q8×C13—42no—
83Q8×C13#4112yescomplemented
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×Dic13C2×D412yes—
92D52—22no—
93D52—21no—
94D52—22no—
95D52—21no—
96D52—22no—
97D52—44no—
98D52—44no—
99D52—42no—
100D52—81no—
101D52—82no—
102C4×D13—22no—
103C4×D13—22no—
104C4×D13—44no—
105C4×D13—44no—
106C4×D13—42no—
107C8×C13—22no—
108#1055—21no—
109#1055—21no—
110#550—131no—
111#547—131no—
112#486—131no—
113#481—132no—
114#475D1311yescharacteristic, complemented
115#469—132no—
116#459—131no—
117#449—132no—
118C4×SD16—131no—
119#436—131no—
120#417—132no—
121C22×C13C22×D411yescharacteristic
122C2×D13—22no—
123C2×D13—22no—
124C2×D13—22no—
125C2×D13—42no—
126C2×D13—41no—
127C2×D13—41no—
128C2×D13—42no—
129C2×D13—42no—
130C2×D13—41no—
131C4×C13—22no—
132C4×C13—21no—
133C4×C13—42no—
134C4×C13—41no—
135C4×C13AGL(1,ℤ/8)12yes—
136C4×C13C2×#4111yescharacteristic
137C4×C13H(5,𝔽2)11yescharacteristic
138Dic13—22no—
139Dic13—41no—
140C2×#41—132no—
141C2×#41—261no—
142C2×SD16—131no—
143C2×D8—132no—
144C2×M16—132no—
145C4⋊Q8C2×D1311yescharacteristic
146#127—131no—
147#127—261no—
148#123—262no—
149C22⋊Q8—261no—
150#121—132no—
151#121—132no—
152#121—262no—
153C4×Q8C2×D1311yescharacteristic
154C4×D4—131no—
155C4×D4—131no—
156C4×D4—261no—
157C2×C4⋊C4—132no—
158#106—131no—
159#106C2×D1312yes—
160C4⋊C8C2×D1311yescharacteristic
161#103—131no—
162#103C2×D1312yes—
163#102—132no—
164#102—132no—
165#102—131no—
166#102—132no—
167C22⋊C8—132no—
168C4×C8—131no—
169C2×C13#54611yescharacteristic
170C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
171C2×C13#57711yescharacteristic
172D13—42no—
173D13—82no—
174D13—81no—
175#41—264no—
176#41—522no—
177#41—524no—
178C2×Q8—21no—
179C2×Q8C22×D1311yescharacteristic
180C2×D4—131no—
181C2×D4—132no—
182C2×D4—131no—
183C2×D4—262no—
184C2×D4—262no—
185C2×D4—262no—
186C2×D4—261no—
187C2×D4—261no—
188C22×C4—132no—
189C22×C4—262no—
190C22×C4—262no—
191C22×C4—261no—
192SD16—262no—
193D8—522no—
194M16—522no—
195C2×C8—131no—
196C2×C8—131no—
197C2×C8C22×D1312yes—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—131no—
201C4⋊C4—131no—
202C4⋊C4—262no—
203C4⋊C4C22×D1312yes—
204C4⋊C4C22×D1311yescharacteristic
205C22⋊C4—132no—
206C22⋊C4—262no—
207C22⋊C4—262no—
208C22⋊C4—261no—
209C42—21no—
210C42C22×D1311yescharacteristic
211C13#333211yescharacteristic, complemented, Sylow
212C23—132no—
213C23—261no—
214C23—262no—
215Q8—21no—
216Q8—42no—
217Q8#613112yescomplemented
218D4—262no—
219D4—261no—
220D4—262no—
221D4—261no—
222D4—262no—
223D4—524no—
224D4—524no—
225D4—522no—
226D4—1041no—
227D4—1042no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—132no—
232C2×C4—262no—
233C2×C4—262no—
234C2×C4—261no—
235C2×C4—524no—
236C2×C4—524no—
237C2×C4—522no—
238C2×C4D4×D1311yescharacteristic
239C2×C4D4×D1311yescharacteristic
240C2×C4C23×D1311yescharacteristic
241C8—22no—
242C8—261no—
243C8—261no—
244C22—262no—
245C22—262no—
246C22—262no—
247C22—521no—
248C22—522no—
249C22—522no—
250C22—521no—
251C22—522no—
252C22—521no—
253C22C2×D4×D1311yescharacteristic
254C4—21no—
255C4—22no—
256C4—42no—
257C4—41no—
258C4—262no—
259C4—521no—
260C4#8816812yes—
261C4C2×#613111yescharacteristic
262C4#8825611yescharacteristic
263C2—522no—
264C2—1041no—
265C2—1042no—
266C2#1171933511yescharacteristic
267C2C2×#8816811yescharacteristic
268C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#475C2
socleC22×C13C22×D4
hypercenter#475D13
hypocenterC13#3332
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #11719431C2semidirect
2. #11719282C2semidirect
3. C13×#475C2semidirect
4. #11718749C2semidirect
5. C4×#6106C2semidirect
6. #11718526C2semidirect
7. #11718524C2semidirect
8. #11718504C2semidirect
9. #11718499C2semidirect
10. #11718472C2semidirect
11. #11718464C2semidirect
83. Q8×C13#41semidirect
114. #475D13semidirect
211. C13#3332semidirect
217. Q8#6131semidirect

Maximal subgroups

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

subgroupindex
#117194312
#117192822
C13×#4752
#117187492
C4×#61062
#117185262
#117185242
#117185042
#117184992
#117184722
#117184642
#333213