Finite Group Databasebeta

← #13125857

Subgroups — #13125857

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
1C2×#88194C211yesmaximal, characteristic, complemented
2#11719329C211yesmaximal, characteristic, complemented
3C13×#450C211yesmaximal, characteristic, complemented
4#11718878C211yesmaximal, characteristic, complemented
5#11718837C212yesmaximal, complemented
6#11718824C212yesmaximal, complemented
7#11718707C211yesmaximal, characteristic, complemented
8#11718447C212yesmaximal, complemented
9#11718425C212yesmaximal, complemented
10#11718393C211yesmaximal, characteristic, complemented
11#11718380C211yesmaximal, characteristic, complemented
12C22×D4×C13C2211yescharacteristic
13C22×C22⋊D13—21no—
14C22×C22⋊D13—21no—
15C22×D52C2211yescharacteristic
16C2×C13×SD16C2212yescomplemented
17C13×C22⋊Q8C2211yescharacteristic
18#88201C2211yescharacteristic, complemented
19Q8×Dic13C2211yescharacteristic, complemented
20C2×#6106C2212yescomplemented
21#88194—21no—
22#88194—21no—
23#88194C2212yes—
24#88194C2212yes—
25C2×#6104C2212yescomplemented
26#88184C2211yescharacteristic
27C2×C4×Dic13C2211yescharacteristic
28C2×D104C2212yescomplemented
29#88152—21no—
30#88147C2211yescharacteristic, complemented
31#88146—21no—
32#88144C2211yescharacteristic, complemented
33#88140—21no—
34#88135—21no—
35C13×#102C2212yescomplemented
36C13×C22⋊C8C2211yescharacteristic
37#88072C2212yescomplemented
38C22⋊#1055C2211yescharacteristic
39#88061C2212yescomplemented
40#88055C2212yescomplemented
41#88054C2212yescomplemented
42#88049C2212yescomplemented
43C24×C13—21no—
44C23×D13—21no—
45C2×Q8×C13C2311yescharacteristic
46C2×D4×C13—21no—
47C2×D4×C13—42no—
48C2×D4×C13C2312yes—
49C22×C4×C13C2311yescharacteristic
50C2×C22⋊D13—21no—
51C2×C22⋊D13—22no—
52C2×C22⋊D13—22no—
53C2×C22⋊D13—22no—
54C2×C22⋊D13—22no—
55C2×C22⋊D13—44no—
56C2×C22⋊D13—44no—
57C22×Dic13D411yescharacteristic
58C22×Dic13D411yescharacteristic
59C2×D52—21no—
60C2×D52—42no—
61C2×D52C2311yescharacteristic
62C2×D52C2312yes—
63C2×C4×D13—21no—
64C13×SD16—42no—
65C2×C8×C13C2312yes—
66C13×C4⋊C4—21no—
67C13×C4⋊C4C2311yescharacteristic
68C13×C22⋊C4—21no—
69#6106—42no—
70#6104—42no—
71#6103—21no—
72#6103—21no—
73#6103—21no—
74#6103—21no—
75C4⋊Dic13—21no—
76C4⋊Dic13—21no—
77C4⋊Dic13C2311yescharacteristic
78#6101—21no—
79C4×Dic13—21no—
80C4×Dic13D411yescharacteristic
81C4×Dic13D411yescharacteristic
82C4×Dic13C2311yescharacteristic
83C4×Dic13C2311yescharacteristic
84C2×#1055C2312yes—
85D104—42no—
86#3217—131nomaximal, Sylow
87C23×C13—22no—
88C23×C13—42no—
89C23×C13—42no—
90C23×C13—42no—
91C23×C13C2×D411yescharacteristic
92C22×D13—21no—
93C22×D13—22no—
94C22×D13—42no—
95C22×D13—42no—
96C22×D13—42no—
97Q8×C13—22no—
98D4×C13—22no—
99D4×C13—22no—
100D4×C13—42no—
101C2×C4×C13—22no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13C2×D411yescharacteristic
105C2×C4×C13C2411yescharacteristic
106C22⋊D13—44no—
107C22⋊D13—44no—
108C22⋊D13—44no—
109C22⋊D13—42no—
110C22⋊D13—44no—
111C2×Dic13—22no—
112C2×Dic13—22no—
113C2×Dic13—21no—
114C2×Dic13C2×D411yescharacteristic
115C2×Dic13C2×D411yescharacteristic
116C2×Dic13C2×D411yescharacteristic
117C2×Dic13C2×D411yescharacteristic
118D52—22no—
119D52—22no—
120D52—22no—
121D52—42no—
122C4×D13—42no—
123C8×C13—22no—
124#1055—22no—
125C2×#127—131no—
126#529—131no—
127#496—132no—
128#490—132no—
129#460—132no—
130#459—132no—
131#450—131no—
132#450D1311yescharacteristic, complemented
133#447—131no—
134#447—131no—
135#432—131no—
136C22×C13—21no—
137C22×C13—21no—
138C22×C13—42no—
139C22×C13—42no—
140C22×C13—42no—
141C22×C13—84no—
142C22×C13AGL(1,ℤ/8)12yes—
143C22×C13C22×D411yescharacteristic
144C2×D13—42no—
145C2×D13—41no—
146C2×D13—41no—
147C2×D13—42no—
148C2×D13—42no—
149C2×D13—41no—
150C2×D13—84no—
151C4×C13—21no—
152C4×C13—41no—
153C4×C13—41no—
154C4×C13H(5,𝔽2)12yes—
155Dic13—21no—
156Dic13—21no—
157Dic13—21no—
158Dic13—41no—
159Dic13AGL(1,ℤ/8)12yes—
160C22×D4—131no—
161C22×D4—261no—
162C22×D4—261no—
163C22×D4C2×D1311yescharacteristic
164C2×SD16—132no—
165C2×SD16C2×D1312yescomplemented
166C2×D8—132no—
167C2×D8—132no—
168#127—132no—
169#127—132no—
170#127—261no—
171#127—261no—
172#126—261no—
173#125—131no—
174#124—131no—
175#123—261no—
176C22⋊Q8C2×D1311yescharacteristic
177#121—131no—
178C4×Q8—131no—
179C4×D4—131no—
180C4×D4—261no—
181#117—261no—
182C2×C42—131no—
183C4⋊C8—132no—
184#102—132no—
185#102—132no—
186#102—132no—
187#102C2×D1312yescomplemented
188C22⋊C8—131no—
189C22⋊C8C2×D1311yescharacteristic
190#97—132no—
191C2×C13—22no—
192C2×C13—82no—
193C2×C13#53511yescharacteristic
194C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
195C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
196D13—81no—
197D13—82no—
198C24—21no—
199C24—261no—
200C2×Q8C22×D1311yescharacteristic
201C2×D4—21no—
202C2×D4—42no—
203C2×D4—132no—
204C2×D4—131no—
205C2×D4—262no—
206C2×D4—262no—
207C2×D4—262no—
208C2×D4—262no—
209C2×D4—261no—
210C2×D4—261no—
211C2×D4—522no—
212C2×D4—524no—
213C2×D4—524no—
214C2×D4C22×D1312yes—
215C22×C4—131no—
216C22×C4—131no—
217C22×C4—261no—
218C22×C4C22×D1311yescharacteristic
219SD16—42no—
220SD16—522no—
221D8—522no—
222D8—522no—
223C2×C8—132no—
224C2×C8C22×D1312yes—
225C4⋊C4—21no—
226C4⋊C4—131no—
227C4⋊C4—261no—
228C4⋊C4—261no—
229C4⋊C4—261no—
230C4⋊C4C22×D1311yescharacteristic
231C22⋊C4—21no—
232C22⋊C4—261no—
233C22⋊C4—261no—
234C22⋊C4—261no—
235C22⋊C4—261no—
236C42—131no—
237C42—131no—
238C42—131no—
239C42—131no—
240C42—261no—
241C13#321711yescharacteristic, complemented, Sylow
242C23—22no—
243C23—42no—
244C23—42no—
245C23—42no—
246C23—261no—
247C23—262no—
248C23—522no—
249C23—522no—
250C23—522no—
251C23D4×D1311yescharacteristic
252Q8—22no—
253D4—22no—
254D4—22no—
255D4—42no—
256D4—262no—
257D4—262no—
258D4—262no—
259D4—522no—
260D4—524no—
261D4—524no—
262D4—524no—
263D4—524no—
264D4—522no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—131no—
269C2×C4—131no—
270C2×C4—131no—
271C2×C4—131no—
272C2×C4—262no—
273C2×C4—262no—
274C2×C4—261no—
275C2×C4—522no—
276C2×C4D4×D1311yescharacteristic
277C2×C4C23×D1311yescharacteristic
278C8—22no—
279C8—262no—
280C22—21no—
281C22—21no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—84no—
286C22—522no—
287C22—521no—
288C22—521no—
289C22—522no—
290C22—522no—
291C22—521no—
292C22—1044no—
293C22#8816812yes—
294C22C2×D4×D1311yescharacteristic
295C4—21no—
296C4—41no—
297C4—41no—
298C4—132no—
299C4—261no—
300C4—261no—
301C4—261no—
302C4—521no—
303C4#8825112yes—
304C2—22no—
305C2—82no—
306C2—1042no—
307C2—1041no—
308C2#1171929711yescharacteristic
309C2C2×#8816811yescharacteristic
310C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#450C2
socleC22×C13C22×D4
hypercenter#450D13
hypocenterC13#3217
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C2×#88194C2semidirect
2. #11719329C2semidirect
3. C13×#450C2semidirect
4. #11718878C2semidirect
5. #11718837C2semidirect
6. #11718824C2semidirect
7. #11718707C2semidirect
8. #11718447C2semidirect
9. #11718425C2semidirect
10. #11718393C2semidirect
11. #11718380C2semidirect
16. C2×C13×SD16C22semidirect
18. #88201C22semidirect
19. Q8×Dic13C22semidirect
20. C2×#6106C22semidirect
25. C2×#6104C22semidirect
28. C2×D104C22semidirect
30. #88147C22semidirect
32. #88144C22semidirect
35. C13×#102C22semidirect
37. #88072C22semidirect
39. #88061C22semidirect
40. #88055C22semidirect
41. #88054C22semidirect
42. #88049C22semidirect
132. #450D13semidirect
165. C2×SD16C2×D13semidirect
187. #102C2×D13semidirect
241. C13#3217semidirect

Maximal subgroups

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

subgroupindex
C2×#881942
#117193292
C13×#4502
#117188782
#117188372
#117188242
#117187072
#117184472
#117184252
#117183932
#117183802
#321713