Finite Group Databasebeta

← #13124778

Subgroups — #13124778

Order 1664.

462 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 127 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
1D13×#117C211yesmaximal, characteristic, complemented
2C2×#88149C211yesmaximal, characteristic
3C13×#428C211yesmaximal, characteristic, complemented
4#11718792C211yesmaximal, characteristic, complemented
5#11718787C211yesmaximal, characteristic, complemented
6#11718662C211yesmaximal, characteristic, complemented
7#11718625C211yesmaximal, characteristic, complemented
8#11718546C212yesmaximal, complemented
9#11718543C212yesmaximal, complemented
10#11718527C212yesmaximal, complemented
11#11718524C212yesmaximal, complemented
12C22×D52—21no—
13C22×D52C2211yescharacteristic
14C22×C4×D13C2211yescharacteristic
15C2×C13×M16C2211yescharacteristic
16C13×#117C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
18C2×#6103—21no—
19#88180C2211yescharacteristic
20C2×#6099C2211yescharacteristic
21#88149—21no—
22#88149—21no—
23#88149C2212yes—
24#88149C2212yes—
25#88146C2211yescharacteristic, complemented
26#88146C2211yescharacteristic, complemented
27C4⋊C4×D13C2211yescharacteristic, complemented
28C4⋊C4×D13C2211yescharacteristic, complemented
29C22⋊C4×D13—21no—
30#88131—21no—
31#88126—21no—
32C42×D13—21no—
33C13×#107C2212yescomplemented
34C13×#106C2212yescomplemented
35#88061C2212yescomplemented
36#88061C2212yescomplemented
37#88060C2212yescomplemented
38#88060C2212yescomplemented
39#88049C2212yescomplemented
40#88049C2212yescomplemented
41#88048C2212yescomplemented
42#88047C2212yescomplemented
43C23×D13—21no—
44C23×D13D411yescharacteristic
45C22×C4×C13—21no—
46C22×C4×C13C2311yescharacteristic
47C22×Dic13D411yescharacteristic
48C2×D52—22no—
49C2×D52—22no—
50C2×D52—22no—
51C2×D52—22no—
52C2×D52—21no—
53C2×D52—44no—
54C2×D52C2312yes—
55C2×C4×D13—22no—
56C2×C4×D13—22no—
57C2×C4×D13—21no—
58C2×C4×D13—21no—
59C2×C4×D13D411yescharacteristic
60C2×C4×D13D411yescharacteristic
61C2×C4×D13C2311yescharacteristic
62C2×C4×D13C2311yescharacteristic
63C13×M16—22no—
64C2×C8×C13C2312yes—
65C13×C4⋊C4—21no—
66C13×C4⋊C4C2311yescharacteristic
67C13×C4⋊C4C2312yes—
68C13×C4⋊C4C2311yescharacteristic
69C13×C22⋊C4—21no—
70C42×C13—21no—
71C22⋊Dic13—21no—
72#6103—21no—
73#6103—21no—
74#6103—22no—
75#6103—22no—
76C4⋊Dic13C2311yescharacteristic
77C4⋊Dic13C2311yescharacteristic
78#6101—21no—
79#6101—21no—
80C4×Dic13—21no—
81C4×Dic13—21no—
82C4×Dic13—21no—
83#6099—22no—
84C2×#1055C2312yes—
85#3094—131nomaximal, Sylow
86C23×C13C2×D411yescharacteristic
87C22×D13—22no—
88C22×D13—22no—
89C22×D13—22no—
90C22×D13—41no—
91C22×D13—42no—
92C22×D13—42no—
93C22×D13—42no—
94C22×D13C2×D411yescharacteristic
95C22×D13C2×D411yescharacteristic
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—22no—
99C2×C4×C13—42no—
100C2×C4×C13C2×D411yescharacteristic
101C2×C4×C13#4112yes—
102C2×C4×C13#4112yes—
103C2×C4×C13C2411yescharacteristic
104C2×Dic13—22no—
105C2×Dic13—21no—
106C2×Dic13—21no—
107C2×Dic13C2×D411yescharacteristic
108C2×Dic13C2×D411yescharacteristic
109D52—22no—
110D52—22no—
111D52—44no—
112D52—44no—
113D52—42no—
114C4×D13—22no—
115C4×D13—22no—
116C4×D13—21no—
117C4×D13—21no—
118C4×D13—21no—
119C4×D13—21no—
120C4×D13—42no—
121C4×D13—42no—
122C8×C13—22no—
123#1055—22no—
124C2×#121—131no—
125C2×#117—131no—
126#482—132no—
127#482—132no—
128#481—132no—
129#480—132no—
130#428—131no—
131#428D1311yescharacteristic, complemented
132#418—131no—
133#418—131no—
134#407—131no—
135C22×C13—21no—
136C22×C13—21no—
137C22×C13#12312yes—
138C22×C13C22×D411yescharacteristic
139C2×D13—21no—
140C2×D13—21no—
141C2×D13—21no—
142C2×D13—21no—
143C2×D13—21no—
144C2×D13—44no—
145C2×D13—42no—
146C2×D13—42no—
147C2×D13—42no—
148C2×D13—84no—
149C2×D13AGL(1,ℤ/8)12yes—
150C4×C13—41no—
151C4×C13—42no—
152C4×C13—41no—
153C4×C13#12312yes—
154C4×C13C2×#4111yescharacteristic
155C4×C13C2×#4111yescharacteristic
156Dic13—21no—
157Dic13—21no—
158Dic13—41no—
159Dic13—41no—
160C22×D4—131no—
161C22×D4—261no—
162C23×C4—131no—
163C2×M16—131no—
164C2×M16C2×D1311yescharacteristic
165#121—132no—
166#121—132no—
167#121—261no—
168#121—261no—
169#117—131no—
170#117—131no—
171#117—131no—
172#117—261no—
173#117—261no—
174#117C2×D1311yescharacteristic
175C2×C4⋊C4—131no—
176C2×C4⋊C4—131no—
177C2×C4⋊C4C2×D1311yescharacteristic
178C2×C22⋊C4—261no—
179C2×C22⋊C4—261no—
180C2×C42—261no—
181#107—132no—
182#107C2×D1312yescomplemented
183#106—132no—
184#106C2×D1312yescomplemented
185#102—132no—
186#102—132no—
187#102—132no—
188#102—132no—
189C22⋊C8—132no—
190C22⋊C8—132no—
191C2×C13—22no—
192C2×C13C2×#12311yescharacteristic
193C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
194C2×C13#57511yescharacteristic
195D13—22no—
196D13—41no—
197D13—82no—
198C24—131no—
199C24—261no—
200C2×D4—132no—
201C2×D4—262no—
202C2×D4—262no—
203C2×D4—262no—
204C2×D4—261no—
205C2×D4—262no—
206C2×D4—524no—
207C22×C4—21no—
208C22×C4—131no—
209C22×C4—131no—
210C22×C4—131no—
211C22×C4—131no—
212C22×C4—131no—
213C22×C4—261no—
214C22×C4—261no—
215C22×C4—262no—
216C22×C4—262no—
217C22×C4C22×D1311yescharacteristic
218M16—22no—
219M16—262no—
220C2×C8—132no—
221C2×C8C22×D1312yes—
222C4⋊C4—21no—
223C4⋊C4—131no—
224C4⋊C4—131no—
225C4⋊C4—261no—
226C4⋊C4—261no—
227C4⋊C4C22×D1311yescharacteristic
228C4⋊C4C22×D1311yescharacteristic
229C4⋊C4C22×D1312yes—
230C22⋊C4—21no—
231C22⋊C4—262no—
232C22⋊C4—262no—
233C22⋊C4—261no—
234C22⋊C4—261no—
235C22⋊C4—261no—
236C42—21no—
237C42—261no—
238C42—261no—
239C42—261no—
240C13#309411yescharacteristic, complemented, Sylow
241C23—131no—
242C23—131no—
243C23—262no—
244C23—262no—
245C23—262no—
246C23—521no—
247C23—522no—
248C23—522no—
249C23—522no—
250C23D4×D1311yescharacteristic
251D4—262no—
252D4—262no—
253D4—524no—
254D4—524no—
255D4—522no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—42no—
260C2×C4—131no—
261C2×C4—131no—
262C2×C4—262no—
263C2×C4—262no—
264C2×C4—262no—
265C2×C4—261no—
266C2×C4—261no—
267C2×C4—261no—
268C2×C4—261no—
269C2×C4—261no—
270C2×C4—261no—
271C2×C4—522no—
272C2×C4—522no—
273C2×C4#612712yes—
274C2×C4D4×D1311yescharacteristic
275C2×C4#613112yes—
276C2×C4C23×D1311yescharacteristic
277C8—22no—
278C8—262no—
279C22—21no—
280C22—21no—
281C22—132no—
282C22—261no—
283C22—261no—
284C22—261no—
285C22—261no—
286C22—261no—
287C22—524no—
288C22—522no—
289C22—522no—
290C22—522no—
291C22—1044no—
292C22#8814812yes—
293C22C2×D4×D1311yescharacteristic
294C4—42no—
295C4—41no—
296C4—41no—
297C4—261no—
298C4—261no—
299C4—521no—
300C4—521no—
301C4#8814812yes—
302C4C2×#612711yescharacteristic
303C4C2×#613111yescharacteristic
304C2—22no—
305C2—262no—
306C2—521no—
307C2—1042no—
308C2C2×#8814811yescharacteristic
309C2D13×AGL(1,ℤ/8)11yescharacteristic
310C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#428C2
socleC22×C13C22×D4
prime radicalC2×#88149C2
hypercenter#428D13
hypocenterC13#3094
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. D13×#117C2semidirect
3. C13×#428C2semidirect
4. #11718792C2semidirect
5. #11718787C2semidirect
6. #11718662C2semidirect
7. #11718625C2semidirect
8. #11718546C2semidirect
9. #11718543C2semidirect
10. #11718527C2semidirect
11. #11718524C2semidirect
25. #88146C22semidirect
26. #88146C22semidirect
27. C4⋊C4×D13C22semidirect
28. C4⋊C4×D13C22semidirect
33. C13×#107C22semidirect
34. C13×#106C22semidirect
35. #88061C22semidirect
36. #88061C22semidirect
37. #88060C22semidirect
38. #88060C22semidirect
39. #88049C22semidirect
40. #88049C22semidirect
41. #88048C22semidirect
42. #88047C22semidirect
131. #428D13semidirect
182. #107C2×D13semidirect
184. #106C2×D13semidirect
240. C13#3094semidirect

Maximal subgroups

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

subgroupindex
D13×#1172
C2×#881492
C13×#4282
#117187922
#117187872
#117186622
#117186252
#117185462
#117185432
#117185272
#117185242
#309413