Finite Group Databasebeta

← #13126633

Subgroups — #13126633

Order 1664.

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

normal subgroups only

This group has 476 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
1C13×#576C211yesmaximal, characteristic, complemented
2#11719540C212yesmaximal, complemented
3#11719474C211yesmaximal, characteristic, complemented
4#11718902C212yesmaximal, complemented
5#11718860C212yesmaximal, complemented
6#11718859C212yesmaximal, complemented
7#11718857C211yesmaximal, characteristic, complemented
8#11718821C211yesmaximal, characteristic, complemented
9#11718812C211yesmaximal, characteristic, complemented
10#11718805C211yesmaximal, characteristic, complemented
11#11718803C211yesmaximal, characteristic, complemented
12C13×H(5,𝔽2)C2212yescomplemented
13#88256C2212yescomplemented
14C13×AGL(1,ℤ/8)—22no—
15C13×AGL(1,ℤ/8)C2212yescomplemented
16C13×#135—21no—
17C13×#135C2211yescharacteristic
18C2×C13×D8—21no—
19C2×C13×D8C2211yescharacteristic, complemented
20C13×#131C2211yescharacteristic, complemented
21#88204—22no—
22#88204C2211yescharacteristic
23#88203—22no—
24#88203C2212yescomplemented
25#88203C2212yescomplemented
26#88202C2212yescomplemented
27#88194C2212yescomplemented
28#88186—22no—
29#88186C2212yescomplemented
30C2×#6104—22no—
31C2×#6104C2212yescomplemented
32#88173—21no—
33#88168—22no—
34D8×D13—21no—
35C2×D104C2211yescharacteristic, complemented
36#88155C2211yescharacteristic, complemented
37#88077C2211yescharacteristic, complemented
38#88077C2212yescomplemented
39#88073C2212yescomplemented
40#88065C2211yescharacteristic, complemented
41#88063C2212yescomplemented
42#88062C2211yescharacteristic, complemented
43#88059C2211yescharacteristic, complemented
44C8×Dic13C2211yescharacteristic, complemented
45C13×#41—22no—
46C13×#41—22no—
47C13×#41C2312yes—
48C13×#41C2311yescharacteristic
49C2×D4×C13—22no—
50C2×D4×C13—22no—
51C2×D4×C13—42no—
52C2×D4×C13C2312yes—
53C2×C22⋊D13—42no—
54#6131—22no—
55D4×D13—22no—
56D4×D13—42no—
57#6127—22no—
58#6127C2311yescharacteristic
59C2×D52—22no—
60C2×D52C2312yes—
61C13×Q16D411yescharacteristic, complemented
62C13×SD16—22no—
63C13×SD16D412yescomplemented
64C13×D8—22no—
65C13×D8—21no—
66C13×D8—21no—
67C13×D8D411yescharacteristic, complemented
68C13×M16—21no—
69C13×M16C2311yescharacteristic
70C2×C8×C13—21no—
71C2×C8×C13C2311yescharacteristic
72#6107D411yescharacteristic, complemented
73#6106—22no—
74#6106—22no—
75#6106D411yescharacteristic, complemented
76#6105—22no—
77#6105D411yescharacteristic, complemented
78#6104—22no—
79#6104—22no—
80#6104—22no—
81#6104—22no—
82#6104—22no—
83#6104D411yescharacteristic, complemented
84C4×Dic13C2311yescharacteristic
85#6099—22no—
86#6099C2311yescharacteristic
87#6099C2312yes—
88C2×#1055—22no—
89C2×#1055C2311yescharacteristic
90D104—21no—
91D104—21no—
92#6094—21no—
93C8×D13—21no—
94#3292—131nomaximal, Sylow
95C23×C13—22no—
96C23×C13—42no—
97C22×D13—22no—
98C22×D13—42no—
99Q8×C13C2×D411yescharacteristic
100Q8×C13C2×D412yes—
101D4×C13—22no—
102D4×C13—21no—
103D4×C13—22no—
104D4×C13—22no—
105D4×C13—42no—
106D4×C13—42no—
107D4×C13C2×D411yescharacteristic
108D4×C13C2×D412yes—
109C2×C4×C13—22no—
110C2×C4×C13—21no—
111C2×C4×C13—42no—
112C2×C4×C13C2411yescharacteristic
113C22⋊D13—21no—
114C22⋊D13—42no—
115C22⋊D13—84no—
116C2×Dic13—21no—
117D52—22no—
118D52—22no—
119D52—42no—
120D52C2×D411yescharacteristic
121C4×D13—21no—
122C4×D13—42no—
123Dic26C2×D411yescharacteristic
124C8×C13—21no—
125C8×C13C2×D411yescharacteristic
126C8×C13C2×D411yescharacteristic
127#1055—21no—
128#1055—22no—
129#1055C2×D411yescharacteristic
130#1055C2×D411yescharacteristic
131#576—132no—
132#576—131no—
133#576D1311yescharacteristic, complemented
134#493—131no—
135#472—132no—
136#472—131no—
137#472—131no—
138#453—132no—
139#453—132no—
140#443—131no—
141#443—131no—
142C22×C13—22no—
143C22×C13—21no—
144C22×C13—42no—
145C22×C13—82no—
146C22×C13—162no—
147C22×C13H(5,𝔽2)11yescharacteristic
148C2×D13—21no—
149C2×D13—42no—
150C2×D13—82no—
151C2×D13—162no—
152C4×C13—22no—
153C4×C13—21no—
154C4×C13C22×D411yescharacteristic
155C4×C13C22×D411yescharacteristic
156Dic13—22no—
157Dic13—21no—
158H(5,𝔽2)—132no—
159H(5,𝔽2)C2×D1312yescomplemented
160AGL(1,ℤ/8)—22no—
161AGL(1,ℤ/8)—132no—
162AGL(1,ℤ/8)—132no—
163AGL(1,ℤ/8)—132no—
164AGL(1,ℤ/8)—262no—
165AGL(1,ℤ/8)—262no—
166AGL(1,ℤ/8)—262no—
167AGL(1,ℤ/8)C2×D1312yescomplemented
168#135—21no—
169#135—131no—
170#135—262no—
171#135—261no—
172#135C2×D1311yescharacteristic
173C2×D8—21no—
174C2×D8—132no—
175C2×D8—131no—
176C2×D8—262no—
177C2×D8—261no—
178C2×D8C2×D1311yescharacteristic, complemented
179#131—132no—
180#131—131no—
181#131C2×D1311yescharacteristic, complemented
182#127—132no—
183#108—131no—
184#108—131no—
185#104—131no—
186#104—132no—
187#104—131no—
188#100—132no—
189#100—132no—
190C4×C8—131no—
191C2×C13—21no—
192C2×C13—42no—
193C2×C13—41no—
194C2×C13—82no—
195C2×C13D4211yescharacteristic
196D13—41no—
197D13—82no—
198#41—22no—
199#41—22no—
200#41—131no—
201#41—262no—
202#41—262no—
203#41C22×D1311yescharacteristic
204#41C22×D1312yes—
205C2×D4—22no—
206C2×D4—22no—
207C2×D4—42no—
208C2×D4—132no—
209C2×D4—262no—
210C2×D4—262no—
211C2×D4—522no—
212C2×D4—522no—
213C2×D4C22×D1312yes—
214Q16—131no—
215Q16C22⋊D1311yescharacteristic, complemented
216SD16—22no—
217SD16—131no—
218SD16—131no—
219SD16—262no—
220SD16—262no—
221SD16—262no—
222SD16C22⋊D1312yescomplemented
223D8—22no—
224D8—21no—
225D8—21no—
226D8—131no—
227D8—262no—
228D8—262no—
229D8—262no—
230D8—262no—
231D8—262no—
232D8—261no—
233D8—261no—
234D8C22⋊D1311yescharacteristic, complemented
235M16—21no—
236M16—132no—
237M16—131no—
238M16—262no—
239M16—261no—
240M16C22×D1311yescharacteristic
241C2×C8—21no—
242C2×C8—131no—
243C2×C8—262no—
244C2×C8—261no—
245C2×C8C22×D1311yescharacteristic
246C42—131no—
247C13#329211yescharacteristic, complemented, Sylow
248C23—22no—
249C23—42no—
250C23—262no—
251C23—522no—
252Q8—131no—
253Q8D4×D1311yescharacteristic
254Q8C2×C22⋊D1312yes—
255D4—21no—
256D4—22no—
257D4—22no—
258D4—22no—
259D4—42no—
260D4—42no—
261D4—131no—
262D4—261no—
263D4—262no—
264D4—262no—
265D4—522no—
266D4—522no—
267D4—1044no—
268D4D4×D1311yescharacteristic
269D4C2×C22⋊D1312yes—
270C2×C4—22no—
271C2×C4—21no—
272C2×C4—42no—
273C2×C4—261no—
274C2×C4—261no—
275C2×C4—522no—
276C2×C4C23×D1311yescharacteristic
277C8—21no—
278C8—131no—
279C8—131no—
280C8—262no—
281C8—261no—
282C8C2×C22⋊D1311yescharacteristic
283C8C2×C22⋊D1311yescharacteristic
284C22—21no—
285C22—22no—
286C22—42no—
287C22—82no—
288C22—162no—
289C22—261no—
290C22—522no—
291C22—1042no—
292C22—2082no—
293C22#8825111yescharacteristic
294C4—21no—
295C4—22no—
296C4—262no—
297C4—261no—
298C4C2×D4×D1311yescharacteristic
299C4C22×C22⋊D1311yescharacteristic
300C2—21no—
301C2—41no—
302C2—42no—
303C2—82no—
304C2—521no—
305C2—1042no—
306C2D4×C22⋊D1311yescharacteristic
subgroupG/H
centerC2D4×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#576C2
socleC2×C13D42
hypercenter#576D13
hypocenterC13#3292
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ #576

Complements

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

NH ≅ G/Ntype
1. C13×#576C2semidirect
2. #11719540C2semidirect
3. #11719474C2semidirect
4. #11718902C2semidirect
5. #11718860C2semidirect
6. #11718859C2semidirect
7. #11718857C2semidirect
8. #11718821C2semidirect
9. #11718812C2semidirect
10. #11718805C2semidirect
11. #11718803C2semidirect
12. C13×H(5,𝔽2)C22semidirect
13. #88256C22semidirect
15. C13×AGL(1,ℤ/8)C22semidirect
19. C2×C13×D8C22semidirect
20. C13×#131C22semidirect
24. #88203C22semidirect
25. #88203C22semidirect
26. #88202C22semidirect
27. #88194C22semidirect
29. #88186C22semidirect
31. C2×#6104C22semidirect
35. C2×D104C22semidirect
36. #88155C22semidirect
37. #88077C22semidirect
38. #88077C22semidirect
39. #88073C22semidirect
40. #88065C22semidirect
41. #88063C22semidirect
42. #88062C22semidirect
43. #88059C22semidirect
44. C8×Dic13C22semidirect
61. C13×Q16D4semidirect
63. C13×SD16D4semidirect
67. C13×D8D4semidirect
72. #6107D4semidirect
75. #6106D4semidirect
77. #6105D4semidirect
83. #6104D4semidirect
133. #576D13semidirect
159. H(5,𝔽2)C2×D13semidirect
167. AGL(1,ℤ/8)C2×D13semidirect
178. C2×D8C2×D13semidirect
181. #131C2×D13semidirect
215. Q16C22⋊D13semidirect
222. SD16C22⋊D13semidirect
234. D8C22⋊D13semidirect
247. C13#3292semidirect

Maximal subgroups

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

subgroupindex
C13×#5762
#117195402
#117194742
#117189022
#117188602
#117188592
#117188572
#117188212
#117188122
#117188052
#117188032
#329213