Finite Group Databasebeta

← #13124960

Subgroups — #13124960

Order 1664.

424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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#11719430C211yesmaximal, characteristic
2C4×Q8×D13C211yesmaximal, characteristic, complemented
3C13×#477C211yesmaximal, characteristic, complemented
4#11718752C211yesmaximal, characteristic, complemented
5#11718688C211yesmaximal, characteristic, complemented
6#11718550C212yesmaximal, complemented
7#11718543C212yesmaximal, complemented
8#11718509C211yesmaximal, characteristic, complemented
9#11718496C211yesmaximal, characteristic, complemented
10#11718478C212yesmaximal, complemented
11#11718467C212yesmaximal, complemented
12C2×#6131—21no—
13C2×Q8×D13C2211yescharacteristic
14C13×C4⋊Q8C2211yescharacteristic
15C4×Q8×C13C2211yescharacteristic
16#88201—21no—
17Q8×Dic13C2211yescharacteristic
18C2×#6106C2212yes—
19C2×#6095C2212yes—
20#88149—21no—
21#88149C2212yes—
22#88147—21no—
23#88147C2212yes—
24C4⋊C4×D13—21no—
25C4⋊C4×D13C2211yescharacteristic
26#88141—21no—
27#88141C2211yescharacteristic
28#88128C2211yescharacteristic
29C42×D13—21no—
30C42×D13C2211yescharacteristic
31C4×Dic26—21no—
32C4×Dic26C2211yescharacteristic
33C13×#107C2212yes—
34C13×C4⋊C8C2211yescharacteristic
35C13×#103C2212yes—
36#88061C2212yes—
37#88060C2212yes—
38#88055C2212yes—
39#88050C2212yes—
40#88049C2212yes—
41#88047C2212yes—
42C4⋊#1055C2211yescharacteristic
43C2×Q8×C13—21no—
44C2×Q8×C13C2311yescharacteristic
45#6131—44no—
46Q8×D13—22no—
47Q8×D13—22no—
48C2×D52—22no—
49C2×D52—21no—
50C2×D52—21no—
51C2×D52C2312yes—
52C2×C4×D13—21no—
53C2×C4×D13—21no—
54C2×C4×D13—22no—
55C2×C4×D13D411yescharacteristic
56C2×C4×D13D411yescharacteristic
57C2×C4×D13C2311yescharacteristic
58C2×Dic26—21no—
59C2×Dic26C2311yescharacteristic
60C2×C8×C13C2312yes—
61C13×C4⋊C4—21no—
62C13×C4⋊C4—21no—
63C13×C4⋊C4C2312yes—
64C13×C4⋊C4C2311yescharacteristic
65C42×C13—21no—
66C42×C13C2311yescharacteristic
67#6106—24no—
68#6103—22no—
69#6103—22no—
70C4⋊Dic13—21no—
71C4⋊Dic13C2311yescharacteristic
72#6101—21no—
73#6101—21no—
74#6101—21no—
75C4×Dic13—21no—
76C4×Dic13—21no—
77C4×Dic13—21no—
78C4×Dic13D411yescharacteristic
79C4×Dic13D411yescharacteristic
80C4×Dic13C2311yescharacteristic
81C2×#1055C2312yes—
82#6095—24no—
83#3112—131nomaximal, Sylow
84C22×D13—22no—
85C22×D13C2×D411yescharacteristic
86Q8×C13—21no—
87Q8×C13—42no—
88Q8×C13#4112yescomplemented
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—22no—
92C2×C4×C13C2×D411yescharacteristic
93C2×C4×C13C2×D411yescharacteristic
94C2×C4×C13C2411yescharacteristic
95C2×Dic13—21no—
96C2×Dic13—21no—
97C2×Dic13C2×D411yescharacteristic
98C2×Dic13C2×D411yescharacteristic
99C2×Dic13C2×D411yescharacteristic
100D52—22no—
101D52—22no—
102D52—42no—
103D52—44no—
104D52—42no—
105C4×D13—24no—
106C4×D13—22no—
107C4×D13—22no—
108C4×D13—21no—
109C4×D13—21no—
110C4×D13—44no—
111C4×D13—42no—
112Dic26—24no—
113Dic26—21no—
114Dic26#4112yescomplemented
115C8×C13—22no—
116#1055—22no—
117#532—131no—
118C2×C4×Q8—131no—
119#480—132no—
120#477—131no—
121#477D1311yescharacteristic, complemented
122#460—131no—
123#460—131no—
124#448—132no—
125#440—132no—
126#440—132no—
127#432—131no—
128C22×C13C22×D411yescharacteristic
129C2×D13—21no—
130C2×D13—21no—
131C2×D13—42no—
132C2×D13—42no—
133C2×D13—42no—
134C2×D13AGL(1,ℤ/8)12yes—
135C4×C13—22no—
136C4×C13—21no—
137C4×C13—42no—
138C4×C13—41no—
139C4×C13#13712yes—
140C4×C13C2×#4111yescharacteristic
141C4×C13C2×#4111yescharacteristic
142Dic13—21no—
143Dic13—22no—
144Dic13—21no—
145Dic13—21no—
146Dic13—41no—
147C2×#41—261no—
148C22×Q8—131no—
149C2×SD16—132no—
150C2×SD16—132no—
151C4⋊Q8C2×D1311yescharacteristic
152#127—131no—
153#124—261no—
154#121—132no—
155#121—261no—
156C4×Q8—131no—
157C4×Q8—131no—
158C4×Q8—131no—
159C4×Q8—261no—
160C4×Q8—261no—
161C4×Q8C2×D1311yescharacteristic
162C4×D4—132no—
163C4×D4—261no—
164C2×C4⋊C4—131no—
165C2×C4⋊C4—261no—
166C2×C42—131no—
167C2×C42—261no—
168#107—132no—
169#107C2×D1312yes—
170C4⋊C8—131no—
171C4⋊C8C2×D1311yescharacteristic
172#103—132no—
173#103C2×D1312yes—
174#102—132no—
175#102—132no—
176C22⋊C8—132no—
177#97—132no—
178C2×C13#52511yescharacteristic
179C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
180C2×C13C2×#13711yescharacteristic
181D13—22no—
182D13—82no—
183#41—524no—
184C2×Q8—21no—
185C2×Q8—131no—
186C2×Q8—261no—
187C2×Q8—262no—
188C2×Q8—262no—
189C2×Q8C22×D1311yescharacteristic
190C2×D4—132no—
191C2×D4—262no—
192C2×D4—261no—
193C2×D4—261no—
194C22×C4—131no—
195C22×C4—131no—
196C22×C4—131no—
197C22×C4—262no—
198C22×C4—261no—
199C22×C4—261no—
200SD16—264no—
201SD16—264no—
202C2×C8—132no—
203C2×C8C22×D1312yes—
204C4⋊C4—21no—
205C4⋊C4—21no—
206C4⋊C4—131no—
207C4⋊C4—261no—
208C4⋊C4—261no—
209C4⋊C4—261no—
210C4⋊C4—261no—
211C4⋊C4C22×D1311yescharacteristic
212C4⋊C4C22×D1312yes—
213C22⋊C4—262no—
214C22⋊C4—262no—
215C42—21no—
216C42—131no—
217C42—131no—
218C42—131no—
219C42—261no—
220C42—261no—
221C42—261no—
222C42C22×D1311yescharacteristic
223C13#311211yescharacteristic, complemented, Sylow
224C23—131no—
225C23—262no—
226Q8—21no—
227Q8—42no—
228Q8—132no—
229Q8—264no—
230Q8—261no—
231Q8#613112yescomplemented
232D4—262no—
233D4—262no—
234D4—522no—
235D4—524no—
236D4—522no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—131no—
241C2×C4—131no—
242C2×C4—131no—
243C2×C4—262no—
244C2×C4—264no—
245C2×C4—261no—
246C2×C4—262no—
247C2×C4—261no—
248C2×C4—261no—
249C2×C4—261no—
250C2×C4—524no—
251C2×C4—522no—
252C2×C4D4×D1311yescharacteristic
253C2×C4D4×D1311yescharacteristic
254C2×C4C23×D1311yescharacteristic
255C8—22no—
256C8—262no—
257C22—132no—
258C22—261no—
259C22—261no—
260C22—522no—
261C22—522no—
262C22—522no—
263C22C2×D4×D1311yescharacteristic
264C4—21no—
265C4—22no—
266C4—41no—
267C4—42no—
268C4—261no—
269C4—261no—
270C4—261no—
271C4—262no—
272C4—521no—
273C4#8817212yes—
274C4C2×#613111yescharacteristic
275C4#41×D1311yescharacteristic
276C2—262no—
277C2—1042no—
278C2#1171933211yescharacteristic
279C2C2×#8817211yescharacteristic
280C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#477C2
socleC22×C13C22×D4
prime radical#11719430C2
hypercenter#477D13
hypocenterC13#3112
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
2. C4×Q8×D13C2semidirect
3. C13×#477C2semidirect
4. #11718752C2semidirect
5. #11718688C2semidirect
6. #11718550C2semidirect
7. #11718543C2semidirect
8. #11718509C2semidirect
9. #11718496C2semidirect
10. #11718478C2semidirect
11. #11718467C2semidirect
88. Q8×C13#41semidirect
114. Dic26#41semidirect
121. #477D13semidirect
223. C13#3112semidirect
231. Q8#6131semidirect

Maximal subgroups

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

subgroupindex
#117194302
C4×Q8×D132
C13×#4772
#117187522
#117186882
#117185502
#117185432
#117185092
#117184962
#117184782
#117184672
#311213