Finite Group Databasebeta

← #13125635

Subgroups — #13125635

Order 1664.

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

normal subgroups only

This group has 514 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×#121C211yesmaximal, characteristic, complemented
2C2×#88149C211yesmaximal, characteristic, complemented
3C13×#481C211yesmaximal, characteristic, complemented
4#11718697C211yesmaximal, characteristic, complemented
5#11718629C211yesmaximal, characteristic, complemented
6#11718526C212yesmaximal, complemented
7#11718524C212yesmaximal, complemented
8#11718443C212yesmaximal, complemented
9#11718434C212yesmaximal, complemented
10#11718393C211yesmaximal, characteristic, complemented
11#11718387C211yesmaximal, characteristic, complemented
12C2×D4×D13—21no—
13C2×D4×D13C2211yescharacteristic, complemented
14C22×D52—21no—
15C22×D52C2211yescharacteristic, complemented
16C22×C4×D13C2211yescharacteristic
17C13×#121C2211yescharacteristic
18C2×C13×C4⋊C4C2211yescharacteristic, complemented
19#88193—21no—
20#88192C2211yescharacteristic, complemented
21C2×#6104C2212yescomplemented
22#88184C2211yescharacteristic
23C2×#6103—21no—
24C2×D104C2212yescomplemented
25C2×#6094C2212yescomplemented
26#88149—21no—
27#88149—21no—
28#88149C2212yes—
29#88149C2212yescomplemented
30#88149C2211yescharacteristic, complemented
31C4⋊C4×D13C2211yescharacteristic, complemented
32#88138—21no—
33C22⋊C4×D13—21no—
34C13×#106C2212yescomplemented
35C13×#102C2212yescomplemented
36C13×C22⋊C8C2211yescharacteristic, complemented
37C22⋊#1055C2211yescharacteristic, complemented
38#88061C2212yescomplemented
39#88060C2212yescomplemented
40#88049C2212yescomplemented
41#88049C2212yescomplemented
42#88048C2212yescomplemented
43C23×D13—21no—
44C23×D13—21no—
45C23×D13D411yescharacteristic
46C2×D4×C13—21no—
47C2×D4×C13C2311yescharacteristic
48C22×C4×C13—21no—
49C22×C4×C13C2311yescharacteristic
50C2×C22⋊D13—21no—
51C2×C22⋊D13—21no—
52C2×C22⋊D13—21no—
53C22×Dic13D411yescharacteristic
54D4×D13—42no—
55D4×D13—44no—
56C2×D52—21no—
57C2×D52—22no—
58C2×D52—22no—
59C2×D52—21no—
60C2×D52—42no—
61C2×D52—44no—
62C2×D52C2312yes—
63C2×D52C2311yescharacteristic
64C2×C4×D13—21no—
65C2×C4×D13—42no—
66C2×C4×D13D411yescharacteristic
67C2×C4×D13D411yescharacteristic
68C2×C4×D13C2311yescharacteristic
69C2×C4×D13C2311yescharacteristic
70C2×C8×C13C2312yes—
71C13×C4⋊C4—21no—
72C13×C4⋊C4C2312yes—
73C13×C4⋊C4C2311yescharacteristic
74C13×C22⋊C4—21no—
75C22⋊Dic13—21no—
76#6104—42no—
77#6103—21no—
78#6103—21no—
79#6103—22no—
80#6103—22no—
81C4⋊Dic13C2311yescharacteristic
82#6101—21no—
83C2×#1055C2312yes—
84D104—42no—
85#6094—42no—
86#3192—131nomaximal, Sylow
87C23×C13—21no—
88C23×C13C2×D411yescharacteristic
89C22×D13—22no—
90C22×D13—22no—
91C22×D13—22no—
92C22×D13—21no—
93C22×D13—41no—
94C22×D13—42no—
95C22×D13—42no—
96C22×D13—42no—
97C22×D13—42no—
98C22×D13—42no—
99C22×D13—42no—
100C22×D13C2×D411yescharacteristic
101C22×D13C2×D411yescharacteristic
102D4×C13—22no—
103D4×C13—42no—
104C2×C4×C13—22no—
105C2×C4×C13—21no—
106C2×C4×C13—22no—
107C2×C4×C13—42no—
108C2×C4×C13C2×D411yescharacteristic
109C2×C4×C13C2411yescharacteristic
110C22⋊D13—42no—
111C22⋊D13—42no—
112C22⋊D13—42no—
113C2×Dic13—21no—
114C2×Dic13—41no—
115C2×Dic13C2×D411yescharacteristic
116C2×Dic13C2×D411yescharacteristic
117D52—22no—
118D52—22no—
119D52—22no—
120D52—42no—
121D52—44no—
122D52—42no—
123D52—44no—
124C4×D13—22no—
125C4×D13—22no—
126C4×D13—41no—
127C4×D13—41no—
128C4×D13—42no—
129C8×C13—22no—
130#1055—22no—
131C2×#121—131no—
132C2×#121—131no—
133#481—131no—
134#481—132no—
135#481D1311yescharacteristic, complemented
136#469—132no—
137#469—132no—
138#447—131no—
139#447—132no—
140#447—131no—
141#407—131no—
142C22×C13—21no—
143C22×C13—21no—
144C22×C13—41no—
145C22×C13—41no—
146C22×C13—41no—
147C22×C13AGL(1,ℤ/8)12yes—
148C22×C13C22×D411yescharacteristic
149C2×D13—21no—
150C2×D13—21no—
151C2×D13—21no—
152C2×D13—21no—
153C2×D13—21no—
154C2×D13—44no—
155C2×D13—42no—
156C2×D13—41no—
157C2×D13—42no—
158C2×D13—41no—
159C2×D13—42no—
160C2×D13—41no—
161C2×D13—84no—
162C2×D13—84no—
163C2×D13AGL(1,ℤ/8)12yes—
164C4×C13—21no—
165C4×C13—41no—
166C4×C13—42no—
167C4×C13H(5,𝔽2)12yes—
168Dic13—21no—
169Dic13—21no—
170Dic13—41no—
171C22×D4—131no—
172C22×D4—131no—
173C22×D4—261no—
174C22×D4—261no—
175C23×C4—131no—
176C2×D8—132no—
177C2×D8—132no—
178C2×M16—132no—
179#121—131no—
180#121—131no—
181#121—132no—
182#121—131no—
183#121—132no—
184#121—261no—
185#121—261no—
186#121—261no—
187#121—261no—
188#121C2×D1311yescharacteristic
189C2×C4⋊C4—131no—
190C2×C4⋊C4C2×D1311yescharacteristic, complemented
191C2×C22⋊C4—261no—
192C2×C22⋊C4—261no—
193#106—132no—
194#106C2×D1312yescomplemented
195#102—132no—
196#102—132no—
197#102—132no—
198#102C2×D1312yescomplemented
199C22⋊C8—131no—
200C22⋊C8—132no—
201C22⋊C8C2×D1311yescharacteristic, complemented
202C2×C13—22no—
203C2×C13—81no—
204C2×C13#53411yescharacteristic
205C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
206C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
207D13—22no—
208D13—41no—
209D13—82no—
210D13—81no—
211C24—131no—
212C24—261no—
213C24—261no—
214C2×D4—21no—
215C2×D4—132no—
216C2×D4—131no—
217C2×D4—261no—
218C2×D4—262no—
219C2×D4—262no—
220C2×D4—261no—
221C2×D4—261no—
222C2×D4—261no—
223C2×D4—261no—
224C2×D4—522no—
225C2×D4—524no—
226C2×D4—522no—
227C2×D4—524no—
228C2×D4C22×D1311yescharacteristic
229C22×C4—21no—
230C22×C4—131no—
231C22×C4—131no—
232C22×C4—131no—
233C22×C4—131no—
234C22×C4—131no—
235C22×C4—261no—
236C22×C4—522no—
237C22×C4C22×D1311yescharacteristic
238D8—522no—
239D8—522no—
240M16—522no—
241C2×C8—132no—
242C2×C8C22×D1312yes—
243C4⋊C4—21no—
244C4⋊C4—131no—
245C4⋊C4—261no—
246C4⋊C4C22×D1311yescharacteristic
247C4⋊C4C22×D1312yes—
248C22⋊C4—21no—
249C22⋊C4—261no—
250C22⋊C4—262no—
251C22⋊C4—262no—
252C22⋊C4—261no—
253C22⋊C4—261no—
254C13#319211yescharacteristic, complemented, Sylow
255C23—21no—
256C23—131no—
257C23—131no—
258C23—262no—
259C23—262no—
260C23—261no—
261C23—262no—
262C23—521no—
263C23—522no—
264C23—522no—
265C23—522no—
266C23—522no—
267C23—522no—
268C23—522no—
269C23D4×D1311yescharacteristic
270D4—22no—
271D4—42no—
272D4—262no—
273D4—262no—
274D4—262no—
275D4—522no—
276D4—524no—
277D4—522no—
278D4—524no—
279D4—522no—
280D4—522no—
281D4—522no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—42no—
286C2×C4—131no—
287C2×C4—131no—
288C2×C4—262no—
289C2×C4—262no—
290C2×C4—261no—
291C2×C4—521no—
292C2×C4—521no—
293C2×C4—522no—
294C2×C4—521no—
295C2×C4D4×D1311yescharacteristic
296C2×C4C23×D1311yescharacteristic
297C8—22no—
298C8—262no—
299C22—21no—
300C22—21no—
301C22—41no—
302C22—41no—
303C22—41no—
304C22—132no—
305C22—261no—
306C22—261no—
307C22—261no—
308C22—261no—
309C22—261no—
310C22—524no—
311C22—521no—
312C22—522no—
313C22—522no—
314C22—521no—
315C22—522no—
316C22—521no—
317C22—1044no—
318C22—1044no—
319C22#8816812yes—
320C22C2×D4×D1311yescharacteristic
321C4—21no—
322C4—41no—
323C4—42no—
324C4—261no—
325C4—261no—
326C4—521no—
327C4#8825612yes—
328C2—22no—
329C2—81no—
330C2—262no—
331C2—521no—
332C2—1041no—
333C2—1042no—
334C2#1171935811yescharacteristic
335C2C2×#8816811yescharacteristic
336C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#481C2
socleC22×C13C22×D4
hypercenter#481D13
hypocenterC13#3192
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. D13×#121C2semidirect
2. C2×#88149C2semidirect
3. C13×#481C2semidirect
4. #11718697C2semidirect
5. #11718629C2semidirect
6. #11718526C2semidirect
7. #11718524C2semidirect
8. #11718443C2semidirect
9. #11718434C2semidirect
10. #11718393C2semidirect
11. #11718387C2semidirect
13. C2×D4×D13C22semidirect
15. C22×D52C22semidirect
18. C2×C13×C4⋊C4C22semidirect
20. #88192C22semidirect
21. C2×#6104C22semidirect
24. C2×D104C22semidirect
25. C2×#6094C22semidirect
29. #88149C22semidirect
30. #88149C22semidirect
31. C4⋊C4×D13C22semidirect
34. C13×#106C22semidirect
35. C13×#102C22semidirect
36. C13×C22⋊C8C22semidirect
37. C22⋊#1055C22semidirect
38. #88061C22semidirect
39. #88060C22semidirect
40. #88049C22semidirect
41. #88049C22semidirect
42. #88048C22semidirect
135. #481D13semidirect
190. C2×C4⋊C4C2×D13semidirect
194. #106C2×D13semidirect
198. #102C2×D13semidirect
201. C22⋊C8C2×D13semidirect
254. C13#3192semidirect

Maximal subgroups

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

subgroupindex
D13×#1212
C2×#881492
C13×#4812
#117186972
#117186292
#117185262
#117185242
#117184432
#117184342
#117183932
#117183872
#319213