Finite Group Databasebeta

← #13124757

Subgroups — #13124757

Order 1664.

458 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 129 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#11719533C211yesmaximal, characteristic
2C2×C4⋊C4×D13C211yesmaximal, characteristic, complemented
3C13×#417C211yesmaximal, characteristic, complemented
4#11718893C211yesmaximal, characteristic, complemented
5#11718787C211yesmaximal, characteristic, complemented
6#11718782C211yesmaximal, characteristic, complemented
7#11718625C211yesmaximal, characteristic, complemented
8#11718470C212yesmaximal, complemented
9#11718466C212yesmaximal, complemented
10#11718438C212yesmaximal, complemented
11#11718435C212yesmaximal, complemented
12C2×C13×#41C2211yescharacteristic
13C22×C4×D13—21no—
14C22×C4×D13C2211yescharacteristic
15C2×C13×M16C2211yescharacteristic
16C2×C13×C4⋊C4C2211yescharacteristic
17#88200C2211yescharacteristic
18#88200C2211yescharacteristic
19#88192C2211yescharacteristic
20#88192C2211yescharacteristic
21#88191—21no—
22#88189—21no—
23C4×C22⋊D13—21no—
24C4×C22⋊D13—21no—
25#88180C2211yescharacteristic
26C2×C4⋊Dic13C2211yescharacteristic
27C2×#6101—21no—
28C2×#6099C2211yescharacteristic
29C4⋊C4×D13—21no—
30C4⋊C4×D13—21no—
31C4⋊C4×D13C2212yes—
32C4⋊C4×D13C2212yes—
33C13×#103C2212yescomplemented
34C13×#102C2212yescomplemented
35#88075C2212yescomplemented
36#88072C2212yescomplemented
37#88060C2212yes—
38#88060C2212yes—
39#88058C2212yescomplemented
40#88057C2212yescomplemented
41#88048C2212yescomplemented
42#88047C2212yescomplemented
43C23×D13D411yescharacteristic
44C13×#41—22no—
45C13×#41—22no—
46C2×Q8×C13C2311yescharacteristic
47C2×D4×C13—21no—
48C2×D4×C13C2311yescharacteristic
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13C2311yescharacteristic
52C2×C22⋊D13—21no—
53C2×C22⋊D13—21no—
54C22×Dic13—21no—
55C22×Dic13D411yescharacteristic
56C2×C4×D13—22no—
57C2×C4×D13—22no—
58C2×C4×D13—22no—
59C2×C4×D13—22no—
60C2×C4×D13—44no—
61C2×C4×D13D411yescharacteristic
62C2×C4×D13D411yescharacteristic
63C2×C4×D13C2311yescharacteristic
64C2×C4×D13C2311yescharacteristic
65C13×M16—22no—
66C2×C8×C13C2312yes—
67C13×C4⋊C4—21no—
68C13×C4⋊C4C2312yes—
69C22⋊Dic13—21no—
70C22⋊Dic13—21no—
71C22⋊Dic13—21no—
72#6103—21no—
73#6103—21no—
74C4⋊Dic13—21no—
75C4⋊Dic13C2312yes—
76C4⋊Dic13C2311yescharacteristic
77C4⋊Dic13C2311yescharacteristic
78#6101—22no—
79#6101—22no—
80#6101—21no—
81#6101—21no—
82C4×Dic13—21no—
83#6099—22no—
84C2×#1055C2312yes—
85#3092—131nomaximal, Sylow
86C23×C13—21no—
87C23×C13C2×D411yescharacteristic
88C22×D13—22no—
89C22×D13—22no—
90C22×D13—22no—
91C22×D13C2×D411yescharacteristic
92C22×D13C2×D411yescharacteristic
93Q8×C13—21no—
94Q8×C13—21no—
95D4×C13—21no—
96D4×C13—21no—
97D4×C13—42no—
98C2×C4×C13—21no—
99C2×C4×C13—22no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13C2×D411yescharacteristic
103C2×C4×C13#4112yes—
104C2×C4×C13#4112yes—
105C2×C4×C13C2411yescharacteristic
106C22⋊D13—42no—
107C22⋊D13—42no—
108C2×Dic13—22no—
109C2×Dic13—21no—
110C2×Dic13—21no—
111C2×Dic13—22no—
112C2×Dic13—42no—
113C2×Dic13C2×D411yescharacteristic
114C2×Dic13C2×D411yescharacteristic
115C4×D13—22no—
116C4×D13—22no—
117C4×D13—21no—
118C4×D13—21no—
119C4×D13—21no—
120C4×D13—21no—
121C4×D13—44no—
122C4×D13—44no—
123C8×C13—22no—
124#1055—22no—
125#525—131no—
126C22×C4⋊C4—131no—
127#484—132no—
128#483—132no—
129#481—132no—
130#480—132no—
131#428—131no—
132#428—131no—
133#417—131no—
134#417D1311yescharacteristic, complemented
135#407—131no—
136C22×C13—21no—
137C22×C13—21no—
138C22×C13—41no—
139C22×C13—41no—
140C22×C13—41no—
141C22×C13#12312yes—
142C22×C13C22×D411yescharacteristic
143C2×D13—28no—
144C2×D13—21no—
145C2×D13—21no—
146C2×D13—21no—
147C2×D13—21no—
148C2×D13AGL(1,ℤ/8)12yes—
149C2×D13#13712yes—
150C4×C13—41no—
151C4×C13—42no—
152C4×C13#12312yes—
153C4×C13C2×#4111yescharacteristic
154C4×C13C2×#4111yescharacteristic
155Dic13—21no—
156Dic13—21no—
157Dic13—42no—
158Dic13—41no—
159Dic13—41no—
160C2×#41C2×D1311yescharacteristic
161C23×C4—131no—
162C23×C4—261no—
163C2×M16—131no—
164C2×M16C2×D1311yescharacteristic
165#123—261no—
166C22⋊Q8—131no—
167C22⋊Q8—131no—
168#121—131no—
169#121—131no—
170#120—261no—
171C4×D4—261no—
172C4×D4—261no—
173#117—131no—
174C2×C4⋊C4—131no—
175C2×C4⋊C4—132no—
176C2×C4⋊C4—132no—
177C2×C4⋊C4—261no—
178C2×C4⋊C4—261no—
179C2×C4⋊C4—261no—
180C2×C4⋊C4C2×D1311yescharacteristic
181#107—132no—
182#107—132no—
183#106—132no—
184#106—132no—
185#103—132no—
186#103C2×D1312yescomplemented
187#102—132no—
188#102C2×D1312yescomplemented
189C22⋊C8—132no—
190C22⋊C8—132no—
191C2×C13—22no—
192C2×C13—81no—
193C2×C13C2×#12311yescharacteristic
194C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
195C2×C13C2×#13711yescharacteristic
196D13—22no—
197D13—22no—
198C24—131no—
199#41—22no—
200#41—22no—
201C2×Q8C22×D1311yescharacteristic
202C2×D4—21no—
203C2×D4—261no—
204C2×D4—261no—
205C2×D4C22×D1311yescharacteristic
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—131no—
209C22×C4—131no—
210C22×C4—131no—
211C22×C4—131no—
212C22×C4—131no—
213C22×C4—262no—
214C22×C4—262no—
215C22×C4—262no—
216C22×C4—262no—
217C22×C4—261no—
218C22×C4—524no—
219C22×C4C22×D1311yescharacteristic
220M16—22no—
221M16—262no—
222C2×C8—132no—
223C2×C8C22×D1312yes—
224C4⋊C4—21no—
225C4⋊C4—132no—
226C4⋊C4—131no—
227C4⋊C4—131no—
228C4⋊C4—262no—
229C4⋊C4—262no—
230C4⋊C4—261no—
231C4⋊C4—261no—
232C4⋊C4—261no—
233C4⋊C4C22×D1312yes—
234C22⋊C4—261no—
235C22⋊C4—261no—
236C22⋊C4—261no—
237C22⋊C4—261no—
238C22⋊C4—261no—
239C42—261no—
240C13#309211yescharacteristic, complemented, Sylow
241C23—21no—
242C23—131no—
243C23—131no—
244C23—262no—
245C23—262no—
246C23—262no—
247C23D4×D1311yescharacteristic
248Q8—21no—
249Q8—21no—
250D4—21no—
251D4—21no—
252D4—42no—
253D4—522no—
254D4—522no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—131no—
260C2×C4—131no—
261C2×C4—262no—
262C2×C4—262no—
263C2×C4—262no—
264C2×C4—261no—
265C2×C4—261no—
266C2×C4—261no—
267C2×C4—261no—
268C2×C4—261no—
269C2×C4—261no—
270C2×C4—262no—
271C2×C4—524no—
272C2×C4—524no—
273C2×C4—522no—
274C2×C4#612712yes—
275C2×C4D4×D1311yescharacteristic
276C2×C4#612912yes—
277C2×C4C23×D1311yescharacteristic
278C8—22no—
279C8—262no—
280C22—21no—
281C22—21no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—132no—
286C22—132no—
287C22—268no—
288C22—261no—
289C22—261no—
290C22—261no—
291C22—261no—
292C22#8813712yes—
293C22C2×D4×D1311yescharacteristic
294C4—41no—
295C4—42no—
296C4—261no—
297C4—261no—
298C4—522no—
299C4—521no—
300C4—521no—
301C4#8813712yes—
302C4C2×#612711yescharacteristic
303C4C2×#612911yescharacteristic
304C2—22no—
305C2—81no—
306C2—262no—
307C2—262no—
308C2C2×#8813711yescharacteristic
309C2D13×AGL(1,ℤ/8)11yescharacteristic
310C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#417C2
socleC22×C13C22×D4
prime radical#11719533C2
hypercenter#417D13
hypocenterC13#3092
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. C2×C4⋊C4×D13C2semidirect
3. C13×#417C2semidirect
4. #11718893C2semidirect
5. #11718787C2semidirect
6. #11718782C2semidirect
7. #11718625C2semidirect
8. #11718470C2semidirect
9. #11718466C2semidirect
10. #11718438C2semidirect
11. #11718435C2semidirect
33. C13×#103C22semidirect
34. C13×#102C22semidirect
35. #88075C22semidirect
36. #88072C22semidirect
39. #88058C22semidirect
40. #88057C22semidirect
41. #88048C22semidirect
42. #88047C22semidirect
134. #417D13semidirect
186. #103C2×D13semidirect
188. #102C2×D13semidirect
240. C13#3092semidirect

Maximal subgroups

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

subgroupindex
#117195332
C2×C4⋊C4×D132
C13×#4172
#117188932
#117187872
#117187822
#117186252
#117184702
#117184662
#117184382
#117184352
#309213