Finite Group Databasebeta

← #13125428

Subgroups — #13125428

Order 1664.

408 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 119 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#11719421C211yesmaximal, characteristic, complemented
2#11719385C211yesmaximal, characteristic, complemented
3C13×#496C211yesmaximal, characteristic, complemented
4#11718835C212yesmaximal, complemented
5SD16×Dic13C212yesmaximal, complemented
6#11718820C212yesmaximal, complemented
7D8×Dic13C212yesmaximal, complemented
8#11718732C211yesmaximal, characteristic, complemented
9#11718716C211yesmaximal, characteristic, complemented
10#11718368C211yesmaximal, characteristic, complemented
11#11718363C211yesmaximal, characteristic, complemented
12C2×#6129—21no—
13C2×C13×SD16C2212yes—
14C2×C13×D8C2212yes—
15C13×#127C2211yescharacteristic
16C13×#124C2211yescharacteristic
17#88200C2211yescharacteristic
18Q8×Dic13C2211yescharacteristic
19#88192—21no—
20#88192C2211yescharacteristic
21#88192C2212yes—
22#88190—21no—
23D4×Dic13—21no—
24D4×Dic13C2211yescharacteristic
25D4×Dic13C2212yes—
26C2×#6094C2212yes—
27#88137—21no—
28#88135—21no—
29#88133—21no—
30#88131—21no—
31C42×D13C2211yescharacteristic
32#88124C2211yescharacteristic
33#88123C2211yescharacteristic
34C13×#97C2211yescharacteristic
35#88075C2212yes—
36#88072C2212yes—
37#88072C2212yes—
38#88072C2212yes—
39#88058C2212yes—
40#88057C2212yes—
41C8×Dic13C2212yes—
42#88043C2211yescharacteristic
43C2×Q8×C13C2311yescharacteristic
44C2×D4×C13—21no—
45C2×D4×C13—21no—
46C2×D4×C13C2311yescharacteristic
47C2×D4×C13C2312yes—
48C2×C22⋊D13—21no—
49C2×C22⋊D13—22no—
50C22×Dic13—21no—
51C22×Dic13—22no—
52#6129—44no—
53C2×C4×D13D411yescharacteristic
54C2×C4×D13D411yescharacteristic
55C2×C4×D13C2311yescharacteristic
56C2×Dic26—21no—
57C13×SD16—24no—
58C13×D8—24no—
59C2×C8×C13C2312yes—
60C13×C22⋊C4—21no—
61C13×C22⋊C4—21no—
62C42×C13C2311yescharacteristic
63C22⋊Dic13—21no—
64C22⋊Dic13—21no—
65C22⋊Dic13—22no—
66C22⋊Dic13—22no—
67#6103—21no—
68C4⋊Dic13—21no—
69C4⋊Dic13—21no—
70C4⋊Dic13C2311yescharacteristic
71C4⋊Dic13C2311yescharacteristic
72C4⋊Dic13C2312yes—
73#6101—21no—
74#6101—21no—
75#6101—21no—
76C4×Dic13—21no—
77C4×Dic13D411yescharacteristic
78C4×Dic13D411yescharacteristic
79C4×Dic13C2311yescharacteristic
80C2×#1055C2312yes—
81#6094—24no—
82#3171—131nomaximal, Sylow
83C23×C13—21no—
84C23×C13—22no—
85C22×D13C2×D411yescharacteristic
86Q8×C13—22no—
87D4×C13—22no—
88D4×C13—22no—
89D4×C13—22no—
90D4×C13—42no—
91D4×C13—42no—
92C2×C4×C13—21no—
93C2×C4×C13C2×D411yescharacteristic
94C2×C4×C13C2×D411yescharacteristic
95C2×C4×C13C2411yescharacteristic
96C22⋊D13—44no—
97C22⋊D13—42no—
98C2×Dic13—21no—
99C2×Dic13—21no—
100C2×Dic13—22no—
101C2×Dic13—44no—
102C2×Dic13—42no—
103C2×Dic13C2×D411yescharacteristic
104C2×Dic13C2×D411yescharacteristic
105C2×Dic13C2×D411yescharacteristic
106C4×D13—22no—
107C4×D13—22no—
108C4×D13—41no—
109Dic26—42no—
110C8×C13#4114yescomplemented
111#1055—22no—
112#532—131no—
113#529—131no—
114#501—131no—
115#496D1311yescharacteristic, complemented
116#490—131no—
117#489—131no—
118#469—132no—
119#468—132no—
120C4×SD16—132no—
121C4×D8—132no—
122C4×M16—131no—
123C22×C13—41no—
124C22×C13—42no—
125C22×C13—42no—
126C22×C13—41no—
127C22×C13—41no—
128C22×C13—42no—
129C22×C13C22×D411yescharacteristic
130C2×D13—21no—
131C2×D13—21no—
132C2×D13—21no—
133C4×C13—21no—
134C4×C13—21no—
135C4×C13—41no—
136C4×C13C2×#4112yes—
137Dic13—21no—
138Dic13—21no—
139Dic13—42no—
140Dic13—41no—
141Dic13—41no—
142Dic13AGL(1,ℤ/8)12yes—
143C2×#41—261no—
144C2×SD16C2×D1312yes—
145C2×D8C2×D1312yes—
146C2×M16—132no—
147C4⋊Q8—131no—
148#127C2×D1311yescharacteristic
149#126—261no—
150#125—131no—
151#124—261no—
152#124C2×D1311yescharacteristic
153#123—261no—
154C22⋊Q8—131no—
155#121—131no—
156#121—132no—
157#121—261no—
158C4×Q8—131no—
159C4×D4—131no—
160C4×D4—132no—
161C4×D4—261no—
162C4×D4—261no—
163#117—261no—
164C2×C42—131no—
165#107—132no—
166#106—132no—
167#103—132no—
168#102—132no—
169#102—132no—
170#102—132no—
171#97—131no—
172#97C2×D1311yescharacteristic
173C4×C8—132no—
174C2×C13—82no—
175C2×C13—81no—
176C2×C13#53211yescharacteristic
177C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
178C2×C13#57511yescharacteristic
179D13—41no—
180#41—524no—
181C2×Q8—261no—
182C2×Q8C22×D1311yescharacteristic
183C2×D4—21no—
184C2×D4—21no—
185C2×D4—261no—
186C2×D4—262no—
187C2×D4C22×D1311yescharacteristic
188C2×D4C22×D1312yes—
189C22×C4—131no—
190C22×C4—131no—
191C22×C4—131no—
192C22×C4—261no—
193C22×C4—262no—
194SD16—24no—
195D8—24no—
196M16—264no—
197C2×C8—132no—
198C2×C8C22×D1312yes—
199C4⋊C4—131no—
200C4⋊C4—131no—
201C4⋊C4—132no—
202C4⋊C4—261no—
203C4⋊C4—261no—
204C4⋊C4—261no—
205C4⋊C4—261no—
206C4⋊C4—261no—
207C22⋊C4—21no—
208C22⋊C4—21no—
209C22⋊C4—261no—
210C22⋊C4—261no—
211C22⋊C4—262no—
212C22⋊C4—261no—
213C22⋊C4—262no—
214C42—131no—
215C42—131no—
216C42—131no—
217C42—261no—
218C42C22×D1311yescharacteristic
219C13#317111yescharacteristic, complemented, Sylow
220C23—21no—
221C23—22no—
222C23—131no—
223Q8—22no—
224Q8—522no—
225D4—22no—
226D4—22no—
227D4—22no—
228D4—42no—
229D4—42no—
230D4—522no—
231D4—524no—
232C2×C4—21no—
233C2×C4—131no—
234C2×C4—131no—
235C2×C4—131no—
236C2×C4—262no—
237C2×C4—262no—
238C2×C4—261no—
239C2×C4—261no—
240C2×C4—262no—
241C2×C4—521no—
242C2×C4—522no—
243C2×C4—524no—
244C2×C4D4×D1311yescharacteristic
245C2×C4D4×D1311yescharacteristic
246C2×C4C23×D1311yescharacteristic
247C8—262no—
248C8#612914yescomplemented
249C22—42no—
250C22—41no—
251C22—42no—
252C22—41no—
253C22—41no—
254C22—42no—
255C22—261no—
256C22—261no—
257C22—261no—
258C22C2×D4×D1311yescharacteristic
259C4—21no—
260C4—21no—
261C4—41no—
262C4—132no—
263C4—261no—
264C4—261no—
265C4—521no—
266C4—522no—
267C4—521no—
268C4C2×#612912yes—
269C2—82no—
270C2—81no—
271C2—521no—
272C2#1171942111yescharacteristic
273C2D13×AGL(1,ℤ/8)11yescharacteristic
274C2#1171947811yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#496C2
socleC22×C13C22×D4
hypercenter#496D13
hypocenterC13#3171
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #11719421C2semidirect
2. #11719385C2semidirect
3. C13×#496C2semidirect
4. #11718835C2semidirect
5. SD16×Dic13C2semidirect
6. #11718820C2semidirect
7. D8×Dic13C2semidirect
8. #11718732C2semidirect
9. #11718716C2semidirect
10. #11718368C2semidirect
11. #11718363C2semidirect
110. C8×C13#41semidirect
115. #496D13semidirect
219. C13#3171semidirect
248. C8#6129semidirect

Maximal subgroups

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

subgroupindex
#117194212
#117193852
C13×#4962
#117188352
SD16×Dic132
#117188202
D8×Dic132
#117187322
#117187162
#117183682
#117183632
#317113