Finite Group Databasebeta

← #13125193

Subgroups — #13125193

Order 1664.

404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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#11719535C211yesmaximal, characteristic
2#11719205C211yesmaximal, characteristic, complemented
3C13×#417C211yesmaximal, characteristic, complemented
4#11718894C211yesmaximal, characteristic, complemented
5#11718792C211yesmaximal, characteristic, complemented
6#11718783C211yesmaximal, characteristic, complemented
7C2×#88049C211yesmaximal, characteristic, complemented
8#11718461C212yesmaximal, complemented
9#11718456C212yesmaximal, complemented
10#11718425C212yesmaximal, complemented
11#11718421C212yesmaximal, complemented
12C2×C13×#41C2211yescharacteristic
13C22×D52C2211yescharacteristic
14C2×C13×M16C2211yescharacteristic
15C2×C13×C4⋊C4C2211yescharacteristic
16#88201C2212yes—
17#88194C2212yes—
18#88191—22no—
19#88184—21no—
20#88184—21no—
21#88180C2211yescharacteristic
22#88180C2211yescharacteristic
23#88178—22no—
24C22×#1055C2211yescharacteristic
25#88144—21no—
26#88144C2212yescomplemented
27#88142—21no—
28#88142C2212yescomplemented
29C13×#103C2212yescomplemented
30C13×#102C2212yescomplemented
31#88075C2211yescharacteristic, complemented
32#88075C2211yescharacteristic, complemented
33#88072C2211yescharacteristic, complemented
34#88072C2211yescharacteristic, complemented
35#88061C2212yes—
36#88061C2212yes—
37#88055C2212yescomplemented
38C8×Dic13C2212yescomplemented
39#88049C2212yes—
40#88049C2212yes—
41C23×D13—21no—
42C13×#41—22no—
43C13×#41—22no—
44C2×Q8×C13C2311yescharacteristic
45C2×D4×C13—21no—
46C2×D4×C13C2311yescharacteristic
47C22×C4×C13—21no—
48C22×C4×C13—21no—
49C22×C4×C13C2311yescharacteristic
50C2×C22⋊D13—22no—
51C2×C22⋊D13—22no—
52C2×D52—22no—
53C2×D52—22no—
54C2×D52—21no—
55C2×D52C2312yes—
56C2×Dic26—22no—
57C13×M16—22no—
58C2×C8×C13C2312yes—
59C13×C4⋊C4—21no—
60C13×C4⋊C4C2312yes—
61C22⋊Dic13—21no—
62C22⋊Dic13D412yes—
63#6103—22no—
64#6103—22no—
65C4⋊Dic13—22no—
66C4⋊Dic13D411yescharacteristic
67C4⋊Dic13D411yescharacteristic
68C4⋊Dic13C2311yescharacteristic
69C4⋊Dic13C2311yescharacteristic
70#6101—22no—
71#6101—22no—
72C4×Dic13—21no—
73C4×Dic13C2312yes—
74C2×#1055—22no—
75C2×#1055C2311yescharacteristic
76C2×#1055C2311yescharacteristic
77#3136—131nomaximal, Sylow
78C23×C13—21no—
79C23×C13C2×D411yescharacteristic
80C22×D13—22no—
81C22×D13—42no—
82C22×D13—81no—
83C22×D13—81no—
84Q8×C13—21no—
85Q8×C13—21no—
86D4×C13—21no—
87D4×C13—21no—
88D4×C13—42no—
89C2×C4×C13—22no—
90C2×C4×C13—21no—
91C2×C4×C13—42no—
92C2×C4×C13—81no—
93C2×C4×C13C2×D411yescharacteristic
94C2×C4×C13#4112yes—
95C2×C4×C13#4112yes—
96C2×C4×C13C2411yescharacteristic
97C22⋊D13—82no—
98C22⋊D13—82no—
99C2×Dic13—21no—
100C2×Dic13—21no—
101C2×Dic13C2×D412yes—
102C2×Dic13C2×D412yes—
103D52—22no—
104D52—22no—
105D52—42no—
106Dic26—82no—
107C8×C13—22no—
108#1055—21no—
109#1055—21no—
110#544—131no—
111#535—131no—
112#490—132no—
113#489—132no—
114#488—132no—
115#486—132no—
116#418—131no—
117#417D1311yescharacteristic, complemented
118#416—131no—
119C2×#102—131no—
120#405—131no—
121C22×C13—21no—
122C22×C13—21no—
123C22×C13—41no—
124C22×C13—41no—
125C22×C13—41no—
126C22×C13#12412yes—
127C22×C13C22×D411yescharacteristic
128C2×D13—42no—
129C2×D13—42no—
130C2×D13—42no—
131C2×D13—84no—
132C4×C13—41no—
133C4×C13—42no—
134C4×C13#12412yes—
135C4×C13C2×#4111yescharacteristic
136C4×C13C2×#4111yescharacteristic
137Dic13—22no—
138Dic13—22no—
139Dic13—41no—
140Dic13—41no—
141C2×#41C2×D1311yescharacteristic
142C22×D4—131no—
143C2×M16C2×D1311yescharacteristic
144C22×C8—131no—
145C4⋊Q8—132no—
146C4⋊Q8—261no—
147#127—132no—
148#125—132no—
149#125—261no—
150#124—132no—
151C22⋊Q8—262no—
152#121—261no—
153#121—261no—
154#120—262no—
155#117—131no—
156#117—131no—
157C2×C4⋊C4C2×D1311yescharacteristic
158#103—131no—
159#103—131no—
160#103C2×D1312yescomplemented
161#102—131no—
162#102—131no—
163#102—132no—
164#102—132no—
165#102—132no—
166#102—132no—
167#102C2×D1312yescomplemented
168#97—132no—
169C4×C8—132no—
170C2×C13—22no—
171C2×C13—81no—
172C2×C13C2×#12411yescharacteristic
173C2×C13#57611yescharacteristic
174C2×C13#57711yescharacteristic
175D13—82no—
176C24—261no—
177#41—22no—
178#41—22no—
179C2×Q8—262no—
180C2×Q8C22×D1311yescharacteristic
181C2×D4—21no—
182C2×D4—132no—
183C2×D4—262no—
184C2×D4—262no—
185C2×D4—262no—
186C2×D4—261no—
187C2×D4—262no—
188C2×D4C22×D1311yescharacteristic
189C22×C4—21no—
190C22×C4—21no—
191C22×C4C22×D1311yescharacteristic
192M16—22no—
193C2×C8—131no—
194C2×C8—131no—
195C2×C8—262no—
196C2×C8C22×D1312yes—
197C4⋊C4—21no—
198C4⋊C4—131no—
199C4⋊C4—131no—
200C4⋊C4—131no—
201C4⋊C4—131no—
202C4⋊C4—262no—
203C4⋊C4—262no—
204C4⋊C4—262no—
205C4⋊C4C22×D1312yes—
206C22⋊C4—132no—
207C22⋊C4—262no—
208C22⋊C4—262no—
209C22⋊C4—261no—
210C42—132no—
211C42—261no—
212C13#313611yescharacteristic, complemented, Sylow
213C23—21no—
214C23—262no—
215C23—522no—
216C23—1041no—
217C23—1041no—
218C23D4×D1311yescharacteristic
219Q8—21no—
220Q8—21no—
221Q8—1042no—
222D4—21no—
223D4—21no—
224D4—42no—
225D4—262no—
226D4—262no—
227D4—522no—
228D4—1042no—
229D4—1042no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—42no—
233C2×C4—81no—
234C2×C4—132no—
235C2×C4—132no—
236C2×C4—261no—
237C2×C4—261no—
238C2×C4#612712yes—
239C2×C4D4×D1311yescharacteristic
240C2×C4#612912yes—
241C2×C4C23×D1311yescharacteristic
242C8—22no—
243C8—261no—
244C8—261no—
245C22—21no—
246C22—21no—
247C22—41no—
248C22—41no—
249C22—41no—
250C22—522no—
251C22—522no—
252C22—522no—
253C22—1044no—
254C22#8813912yes—
255C22C2×D4×D1311yescharacteristic
256C4—41no—
257C4—42no—
258C4—262no—
259C4—262no—
260C4—521no—
261C4—521no—
262C4#8813912yes—
263C4C2×#612711yescharacteristic
264C4C2×#612911yescharacteristic
265C2—22no—
266C2—81no—
267C2—1042no—
268C2C2×#8813911yescharacteristic
269C2#1171947911yescharacteristic
270C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#417C2
socleC22×C13C22×D4
prime radical#11719535C2
hypercenter#417D13
hypocenterC13#3136
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. #11719205C2semidirect
3. C13×#417C2semidirect
4. #11718894C2semidirect
5. #11718792C2semidirect
6. #11718783C2semidirect
7. C2×#88049C2semidirect
8. #11718461C2semidirect
9. #11718456C2semidirect
10. #11718425C2semidirect
11. #11718421C2semidirect
26. #88144C22semidirect
28. #88142C22semidirect
29. C13×#103C22semidirect
30. C13×#102C22semidirect
31. #88075C22semidirect
32. #88075C22semidirect
33. #88072C22semidirect
34. #88072C22semidirect
37. #88055C22semidirect
38. C8×Dic13C22semidirect
117. #417D13semidirect
160. #103C2×D13semidirect
167. #102C2×D13semidirect
212. C13#3136semidirect

Maximal subgroups

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

subgroupindex
#117195352
#117192052
C13×#4172
#117188942
#117187922
#117187832
C2×#880492
#117184612
#117184562
#117184252
#117184212
#313613