Finite Group Databasebeta

← #13126435

Subgroups — #13126435

Order 1664.

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

normal subgroups only

This group has 546 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
1C2×#88168C212yesmaximal, complemented
2#11719431C211yesmaximal, characteristic, complemented
3#11719422C211yesmaximal, characteristic, complemented
4C13×#492C211yesmaximal, characteristic, complemented
5#11718835C212yesmaximal, complemented
6#11718833C212yesmaximal, complemented
7#11718830C212yesmaximal, complemented
8#11718744C211yesmaximal, characteristic, complemented
9#11718733C211yesmaximal, characteristic, complemented
10C4×D104C211yesmaximal, characteristic, complemented
11#11718349C211yesmaximal, characteristic, complemented
12C2×#6131C2212yescomplemented
13C2×D4×D13—21no—
14C2×D4×D13C2212yes—
15C2×C13×SD16C2212yescomplemented
16C2×C13×SD16C2212yescomplemented
17C13×C4⋊Q8C2211yescharacteristic, complemented
18C13×#127C2211yescharacteristic
19#88200C2212yescomplemented
20C2×#6106C2212yes—
21#88192—21no—
22#88192C2212yes—
23#88191—22no—
24C2×#6104C2212yescomplemented
25#88168—28no—
26C2×D104C2211yescharacteristic
27C2×#6094C2212yescomplemented
28#88149—21no—
29#88148—22no—
30C4⋊C4×D13—21no—
31C4×D52C2211yescharacteristic
32C4×D52C2211yescharacteristic
33C4×D52C2211yescharacteristic, complemented
34C4×C8×C13C2211yescharacteristic, complemented
35#88075C2212yescomplemented
36#88072C2212yescomplemented
37#88061C2211yescharacteristic
38#88061C2211yescharacteristic, complemented
39#88060C2212yescomplemented
40#88058C2211yescharacteristic, complemented
41C4⋊#1055C2211yescharacteristic, complemented
42C23×D13—22no—
43C2×Q8×C13C2312yes—
44C2×D4×C13—21no—
45C2×D4×C13—21no—
46C2×D4×C13C2312yes—
47C2×C22⋊D13—22no—
48C2×C22⋊D13—22no—
49#6131—24no—
50#6131—42no—
51D4×D13—24no—
52D4×D13—42no—
53D4×D13—44no—
54C2×D52—22no—
55C2×D52D411yescharacteristic
56C2×D52C2311yescharacteristic
57C2×D52C2311yescharacteristic
58C2×C4×D13—21no—
59C2×C4×D13—21no—
60C2×C4×D13—22no—
61C2×C4×D13C2312yes—
62C13×SD16—24no—
63C13×SD16—42no—
64C2×C8×C13C2311yescharacteristic
65C2×C8×C13C2311yescharacteristic
66C13×C4⋊C4—21no—
67C13×C4⋊C4—21no—
68C42×C13C2311yescharacteristic
69C22⋊Dic13—22no—
70#6106—24no—
71#6104—24no—
72#6103—22no—
73#6103—21no—
74#6103—21no—
75#6103D412yes—
76C4⋊Dic13D411yescharacteristic
77C4⋊Dic13C2311yescharacteristic
78C4⋊Dic13C2311yescharacteristic
79#6101—22no—
80C2×#1055C2312yes—
81D104D414yescomplemented
82#6094—24no—
83#3272—131nomaximal, Sylow
84C23×C13—22no—
85C22×D13—21no—
86C22×D13—21no—
87C22×D13—44no—
88C22×D13—44no—
89C22×D13—82no—
90C22×D13C2×D412yes—
91Q8×C13—22no—
92Q8×C13—22no—
93D4×C13—22no—
94D4×C13—22no—
95D4×C13—42no—
96D4×C13—81no—
97C2×C4×C13—22no—
98C2×C4×C13C2×D411yescharacteristic
99C2×C4×C13C2×D411yescharacteristic
100C2×C4×C13C2411yescharacteristic
101C22⋊D13—44no—
102C22⋊D13—44no—
103C2×Dic13—21no—
104C2×Dic13—21no—
105C2×Dic13C2×D412yes—
106D52—22no—
107D52—21no—
108D52—21no—
109D52—44no—
110D52C2×D412yes—
111D52C2×D412yescomplemented
112C4×D13—22no—
113C4×D13—22no—
114C4×D13—44no—
115C4×D13—42no—
116C4×D13—42no—
117C8×C13—21no—
118C8×C13C2×D412yescomplemented
119#1055—22no—
120C2×AGL(1,ℤ/8)—132no—
121#547—131no—
122D42—131no—
123#492D1311yescharacteristic, complemented
124#468—132no—
125#461—131no—
126#459—131no—
127#450—132no—
128#449—132no—
129C4×D8—131no—
130#436—131no—
131C22×C13—42no—
132C22×C13—42no—
133C22×C13—42no—
134C22×C13C22×D411yescharacteristic
135C2×D13—22no—
136C2×D13—22no—
137C2×D13—22no—
138C2×D13—22no—
139C2×D13—22no—
140C2×D13—41no—
141C2×D13—41no—
142C2×D13—41no—
143C2×D13—41no—
144C2×D13—88no—
145C4×C13—21no—
146C4×C13—42no—
147C4×C13AGL(1,ℤ/8)12yescomplemented
148C4×C13C22×D411yescharacteristic
149C4×C13H(5,𝔽2)11yescharacteristic
150Dic13—22no—
151Dic13—41no—
152Dic13—41no—
153C2×#41—132no—
154C22×D4—132no—
155C22×D4—261no—
156AGL(1,ℤ/8)—268no—
157C2×SD16—132no—
158C2×SD16C2×D1312yescomplemented
159C2×SD16C2×D1312yescomplemented
160C2×D8—132no—
161C2×D8—131no—
162C2×M16—132no—
163C4⋊Q8C2×D1311yescharacteristic, complemented
164#127C2×D1311yescharacteristic
165#123—262no—
166C22⋊Q8—132no—
167#121—132no—
168#121—261no—
169#121—261no—
170#120—262no—
171C4×D4—131no—
172C4×D4—131no—
173C4×D4—131no—
174C2×C4⋊C4—261no—
175#107—131no—
176C4⋊C8—131no—
177#103—132no—
178#102—132no—
179#102—131no—
180#102—131no—
181C22⋊C8—132no—
182C4×C8C2×D1311yescharacteristic, complemented
183C2×C13—82no—
184C2×C13D4211yescharacteristic
185C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
186C2×C13#57711yescharacteristic
187D13—42no—
188D13—42no—
189D13—42no—
190C24—262no—
191#41—264no—
192#41—522no—
193C2×Q8C22×D1312yes—
194C2×D4—21no—
195C2×D4—21no—
196C2×D4—131no—
197C2×D4—131no—
198C2×D4—131no—
199C2×D4—262no—
200C2×D4—262no—
201C2×D4—264no—
202C2×D4—262no—
203C2×D4—522no—
204C2×D4—524no—
205C2×D4C22×D1312yes—
206C22×C4—132no—
207C22×C4—262no—
208C22×C4—261no—
209C22×C4—261no—
210SD16—24no—
211SD16—42no—
212SD16—264no—
213D8—134no—
214D8—264no—
215M16—264no—
216C2×C8—132no—
217C2×C8C22×D1311yescharacteristic
218C2×C8C22×D1311yescharacteristic
219C4⋊C4—21no—
220C4⋊C4—21no—
221C4⋊C4—131no—
222C4⋊C4—131no—
223C4⋊C4—131no—
224C4⋊C4—262no—
225C22⋊C4—132no—
226C22⋊C4—262no—
227C22⋊C4—262no—
228C22⋊C4—261no—
229C22⋊C4—261no—
230C42C22×D1311yescharacteristic
231C13#327211yescharacteristic, complemented, Sylow
232C23—22no—
233C23—132no—
234C23—261no—
235C23—261no—
236C23—524no—
237C23—524no—
238C23—1042no—
239Q8—22no—
240Q8—22no—
241D4—22no—
242D4—22no—
243D4—42no—
244D4—81no—
245D4—132no—
246D4—132no—
247D4—262no—
248D4—261no—
249D4—261no—
250D4—524no—
251D4—524no—
252D4—524no—
253C2×C4—22no—
254C2×C4—132no—
255C2×C4—262no—
256C2×C4—262no—
257C2×C4—261no—
258C2×C4—261no—
259C2×C4—524no—
260C2×C4—522no—
261C2×C4—522no—
262C2×C4D4×D1311yescharacteristic
263C2×C4D4×D1311yescharacteristic
264C2×C4C23×D1311yescharacteristic
265C8—21no—
266C8—262no—
267C8D4×D1312yescomplemented
268C22—42no—
269C22—42no—
270C22—42no—
271C22—262no—
272C22—262no—
273C22—262no—
274C22—262no—
275C22—262no—
276C22—521no—
277C22—521no—
278C22—521no—
279C22—521no—
280C22—1048no—
281C22C2×D4×D1311yescharacteristic
282C4—21no—
283C4—42no—
284C4—262no—
285C4—521no—
286C4—521no—
287C4#8816812yescomplemented
288C4C2×D4×D1311yescharacteristic
289C4#8825111yescharacteristic
290C2—82no—
291C2—522no—
292C2—522no—
293C2—522no—
294C2#1171942211yescharacteristic
295C2C2×#8816811yescharacteristic
296C2#1171946711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#492C2
socleC22×C13C22×D4
hypercenter#492D13
hypocenterC13#3272
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. C2×#88168C2semidirect
2. #11719431C2semidirect
3. #11719422C2semidirect
4. C13×#492C2semidirect
5. #11718835C2semidirect
6. #11718833C2semidirect
7. #11718830C2semidirect
8. #11718744C2semidirect
9. #11718733C2semidirect
10. C4×D104C2semidirect
11. #11718349C2semidirect
12. C2×#6131C22semidirect
15. C2×C13×SD16C22semidirect
16. C2×C13×SD16C22semidirect
17. C13×C4⋊Q8C22semidirect
19. #88200C22semidirect
24. C2×#6104C22semidirect
27. C2×#6094C22semidirect
33. C4×D52C22semidirect
34. C4×C8×C13C22semidirect
35. #88075C22semidirect
36. #88072C22semidirect
38. #88061C22semidirect
39. #88060C22semidirect
40. #88058C22semidirect
41. C4⋊#1055C22semidirect
81. D104D4semidirect
111. D52C2×D4semidirect
118. C8×C13C2×D4semidirect
123. #492D13semidirect
147. C4×C13AGL(1,ℤ/8)semidirect
158. C2×SD16C2×D13semidirect
159. C2×SD16C2×D13semidirect
163. C4⋊Q8C2×D13semidirect
182. C4×C8C2×D13semidirect
231. C13#3272semidirect
267. C8D4×D13semidirect
287. C4#88168semidirect

Maximal subgroups

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

subgroupindex
C2×#881682
#117194312
#117194222
C13×#4922
#117188352
#117188332
#117188302
#117187442
#117187332
C4×D1042
#117183492
#327213