Finite Group Databasebeta

← #13125858

Subgroups — #13125858

Order 1664.

490 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 115 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×#127C211yesmaximal, characteristic, complemented
2#11719285C211yesmaximal, characteristic, complemented
3C13×#460C211yesmaximal, characteristic, complemented
4#11718837C212yesmaximal, complemented
5#11718830C212yesmaximal, complemented
6#11718733C211yesmaximal, characteristic, complemented
7#11718688C211yesmaximal, characteristic, complemented
8#11718504C211yesmaximal, characteristic, complemented
9#11718496C211yesmaximal, characteristic, complemented
10#11718434C212yesmaximal, complemented
11#11718425C212yesmaximal, complemented
12C2×D4×D13—21no—
13C2×D4×D13—21no—
14C2×D4×D13C2212yes—
15C2×C13×SD16C2212yescomplemented
16C13×#127C2211yescharacteristic
17C4×Q8×C13C2211yescharacteristic, complemented
18#88201C2211yescharacteristic, complemented
19#88200C2211yescharacteristic
20C2×#6106C2212yescomplemented
21#88194—21no—
22#88194—21no—
23#88194C2212yes—
24C2×#6104C2212yescomplemented
25C2×D104C2212yescomplemented
26#88152—21no—
27#88149C2211yescharacteristic
28#88148—21no—
29#88144C2211yescharacteristic, complemented
30#88128C2211yescharacteristic
31C4×D52—21no—
32C4×D52C2211yescharacteristic, complemented
33#88126—21no—
34C42×D13C2211yescharacteristic
35C13×C4⋊C8C2211yescharacteristic, complemented
36C13×#102C2212yescomplemented
37#88072C2212yescomplemented
38#88061C2212yescomplemented
39#88060C2212yes—
40#88055C2212yescomplemented
41#88049C2212yescomplemented
42C4⋊#1055C2211yescharacteristic, complemented
43C23×D13—22no—
44C2×Q8×C13C2311yescharacteristic
45C2×D4×C13—21no—
46C2×D4×C13—21no—
47C2×D4×C13C2312yes—
48C2×C22⋊D13—22no—
49C2×C22⋊D13—22no—
50C2×C22⋊D13—22no—
51D4×D13—42no—
52D4×D13—42no—
53D4×D13—44no—
54D4×D13—44no—
55C2×D52—21no—
56C2×D52—21no—
57C2×D52—21no—
58C2×D52C2311yescharacteristic
59C2×D52C2312yes—
60C2×C4×D13—21no—
61C2×C4×D13D411yescharacteristic
62C2×C4×D13D411yescharacteristic
63C2×C4×D13C2311yescharacteristic
64C13×SD16—42no—
65C2×C8×C13C2312yes—
66C13×C4⋊C4—21no—
67C13×C4⋊C4C2311yescharacteristic
68C42×C13—21no—
69C42×C13C2311yescharacteristic
70#6106—42no—
71#6104—42no—
72#6103—21no—
73#6103—21no—
74#6103—21no—
75#6103—21no—
76#6103—21no—
77C4⋊Dic13—21no—
78C4⋊Dic13C2311yescharacteristic
79#6101—21no—
80#6101—21no—
81C4×Dic13D411yescharacteristic
82C4×Dic13D411yescharacteristic
83C4×Dic13C2311yescharacteristic
84C2×#1055C2312yes—
85D104—42no—
86#3217—131nomaximal, Sylow
87C23×C13—22no—
88C22×D13—21no—
89C22×D13—22no—
90C22×D13—44no—
91C22×D13—44no—
92C22×D13—44no—
93C22×D13C2×D411yescharacteristic
94Q8×C13—21no—
95Q8×C13—21no—
96D4×C13—22no—
97D4×C13—22no—
98D4×C13—42no—
99D4×C13—42no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13C2×D411yescharacteristic
103C2×C4×C13C2×D411yescharacteristic
104C2×C4×C13C2411yescharacteristic
105C22⋊D13—44no—
106C22⋊D13—44no—
107C22⋊D13—44no—
108C2×Dic13—21no—
109C2×Dic13C2×D411yescharacteristic
110C2×Dic13C2×D411yescharacteristic
111C2×Dic13C2×D411yescharacteristic
112D52—21no—
113D52—22no—
114D52—21no—
115D52—22no—
116D52—42no—
117D52—42no—
118D52—42no—
119C4×D13—22no—
120C4×D13—22no—
121C4×D13—21no—
122C4×D13—21no—
123C4×D13—42no—
124C8×C13—22no—
125#1055—22no—
126C2×#127—131no—
127#529—131no—
128#496—132no—
129#490—132no—
130#460—131no—
131#460D1311yescharacteristic, complemented
132#459—131no—
133#459—131no—
134#450—132no—
135#447—132no—
136#432—131no—
137C22×C13—42no—
138C22×C13—42no—
139C22×C13—42no—
140C22×C13C22×D411yescharacteristic
141C2×D13—21no—
142C2×D13—21no—
143C2×D13—42no—
144C2×D13—41no—
145C2×D13—41no—
146C2×D13—42no—
147C2×D13—42no—
148C2×D13—41no—
149C2×D13—88no—
150C2×D13AGL(1,ℤ/8)12yes—
151C4×C13—21no—
152C4×C13—41no—
153C4×C13—41no—
154C4×C13AGL(1,ℤ/8)12yes—
155C4×C13H(5,𝔽2)11yescharacteristic
156C4×C13H(5,𝔽2)11yescharacteristic
157Dic13—21no—
158Dic13—21no—
159Dic13—21no—
160Dic13—41no—
161C22×D4—132no—
162C22×D4—261no—
163C22×D4—261no—
164C2×SD16—132no—
165C2×SD16C2×D1312yescomplemented
166C2×D8—132no—
167C2×D8—132no—
168#127—132no—
169#127—131no—
170#127—261no—
171#127—261no—
172#127C2×D1311yescharacteristic
173#126—261no—
174#125—131no—
175#124—131no—
176#123—261no—
177C22⋊Q8—131no—
178#121—131no—
179C4×Q8C2×D1311yescharacteristic, complemented
180C4×D4—131no—
181C4×D4—261no—
182#117—261no—
183C2×C42—131no—
184C4⋊C8—131no—
185C4⋊C8C2×D1311yescharacteristic, complemented
186#102—132no—
187#102—132no—
188#102—132no—
189#102C2×D1312yescomplemented
190C22⋊C8—132no—
191#97—132no—
192C2×C13—82no—
193C2×C13#53511yescharacteristic
194C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
195C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
196D13—22no—
197D13—81no—
198D13—82no—
199C24—262no—
200C2×Q8C22×D1311yescharacteristic
201C2×D4—21no—
202C2×D4—21no—
203C2×D4—132no—
204C2×D4—131no—
205C2×D4—261no—
206C2×D4—262no—
207C2×D4—262no—
208C2×D4—262no—
209C2×D4—261no—
210C2×D4—261no—
211C2×D4—522no—
212C2×D4—522no—
213C2×D4—524no—
214C2×D4—524no—
215C2×D4C22×D1312yes—
216C22×C4—131no—
217C22×C4—131no—
218C22×C4—131no—
219C22×C4—261no—
220SD16—42no—
221SD16—522no—
222D8—522no—
223D8—522no—
224C2×C8—132no—
225C2×C8C22×D1312yes—
226C4⋊C4—21no—
227C4⋊C4—131no—
228C4⋊C4—261no—
229C4⋊C4—261no—
230C4⋊C4—261no—
231C4⋊C4C22×D1311yescharacteristic
232C22⋊C4—261no—
233C22⋊C4—261no—
234C22⋊C4—261no—
235C22⋊C4—261no—
236C22⋊C4—261no—
237C42—21no—
238C42—131no—
239C42—131no—
240C42—131no—
241C42C22×D1311yescharacteristic
242C13#321711yescharacteristic, complemented, Sylow
243C23—22no—
244C23—131no—
245C23—261no—
246C23—262no—
247C23—524no—
248C23—524no—
249C23—524no—
250Q8—21no—
251Q8—21no—
252D4—22no—
253D4—22no—
254D4—42no—
255D4—42no—
256D4—261no—
257D4—262no—
258D4—261no—
259D4—262no—
260D4—522no—
261D4—522no—
262D4—524no—
263D4—524no—
264D4—524no—
265D4—522no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—131no—
269C2×C4—131no—
270C2×C4—131no—
271C2×C4—262no—
272C2×C4—262no—
273C2×C4—261no—
274C2×C4—261no—
275C2×C4—261no—
276C2×C4—522no—
277C2×C4D4×D1311yescharacteristic
278C2×C4D4×D1311yescharacteristic
279C2×C4C23×D1311yescharacteristic
280C8—22no—
281C8—262no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—132no—
286C22—261no—
287C22—261no—
288C22—521no—
289C22—522no—
290C22—522no—
291C22—521no—
292C22—522no—
293C22—521no—
294C22—1048no—
295C22C2×D4×D1311yescharacteristic
296C4—21no—
297C4—41no—
298C4—41no—
299C4—261no—
300C4—261no—
301C4—261no—
302C4—521no—
303C4#8816812yes—
304C4#8825111yescharacteristic
305C4#8825611yescharacteristic
306C2—82no—
307C2—262no—
308C2—1042no—
309C2—1041no—
310C2#1171931211yescharacteristic
311C2C2×#8816811yescharacteristic
312C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#460C2
socleC22×C13C22×D4
hypercenter#460D13
hypocenterC13#3217
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. D13×#127C2semidirect
2. #11719285C2semidirect
3. C13×#460C2semidirect
4. #11718837C2semidirect
5. #11718830C2semidirect
6. #11718733C2semidirect
7. #11718688C2semidirect
8. #11718504C2semidirect
9. #11718496C2semidirect
10. #11718434C2semidirect
11. #11718425C2semidirect
15. C2×C13×SD16C22semidirect
17. C4×Q8×C13C22semidirect
18. #88201C22semidirect
20. C2×#6106C22semidirect
24. C2×#6104C22semidirect
25. C2×D104C22semidirect
29. #88144C22semidirect
32. C4×D52C22semidirect
35. C13×C4⋊C8C22semidirect
36. C13×#102C22semidirect
37. #88072C22semidirect
38. #88061C22semidirect
40. #88055C22semidirect
41. #88049C22semidirect
42. C4⋊#1055C22semidirect
131. #460D13semidirect
165. C2×SD16C2×D13semidirect
179. C4×Q8C2×D13semidirect
185. C4⋊C8C2×D13semidirect
189. #102C2×D13semidirect
242. C13#3217semidirect

Maximal subgroups

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

subgroupindex
D13×#1272
#117192852
C13×#4602
#117188372
#117188302
#117187332
#117186882
#117185042
#117184962
#117184342
#117184252
#321713