Finite Group Databasebeta

← #13126431

Subgroups — #13126431

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×#88165C212yesmaximal, complemented
2#11719422C211yesmaximal, characteristic, complemented
3#11719260C211yesmaximal, characteristic, complemented
4C13×#459C211yesmaximal, characteristic, complemented
5#11718819C212yesmaximal, complemented
6#11718737C211yesmaximal, characteristic, complemented
7C4×#6104C211yesmaximal, characteristic, complemented
8#11718502C211yesmaximal, characteristic, complemented
9#11718499C211yesmaximal, characteristic, complemented
10#11718441C212yesmaximal, complemented
11#11718437C212yesmaximal, complemented
12C2×#6129C2212yescomplemented
13C2×D4×D13—21no—
14C2×D4×D13C2212yes—
15C2×C13×D8C2212yescomplemented
16C13×#127C2211yescharacteristic
17C4×D4×C13C2211yescharacteristic, complemented
18#88192—21no—
19#88192C2212yes—
20#88191—22no—
21C2×#6105C2212yescomplemented
22C2×#6105C2212yescomplemented
23C2×#6104C2211yescharacteristic
24#88184—21no—
25C2×C4⋊Dic13—21no—
26#88165—28no—
27C2×#6095C2212yes—
28C2×#6094C2212yescomplemented
29#88151C2212yescomplemented
30#88140—22no—
31C4×D52C2211yescharacteristic
32C4×D52C2211yescharacteristic
33#88123C2211yescharacteristic, complemented
34C13×C4⋊C8C2211yescharacteristic, complemented
35C13×#102C2212yescomplemented
36#88072C2211yescharacteristic, complemented
37#88060C2212yescomplemented
38#88056C2212yescomplemented
39#88049C2211yescharacteristic
40#88047C2211yescharacteristic, complemented
41C4×#1055C2211yescharacteristic, complemented
42C23×D13—22no—
43C2×D4×C13—21no—
44C2×D4×C13—21no—
45C2×D4×C13C2312yes—
46C2×D4×C13C2311yescharacteristic
47C22×C4×C13—21no—
48C2×C22⋊D13—22no—
49C2×C22⋊D13—22no—
50C2×C22⋊D13—22no—
51C22×Dic13—22no—
52#6129—24no—
53#6129—42no—
54D4×D13—24no—
55D4×D13—42no—
56D4×D13—44no—
57C2×D52D411yescharacteristic
58C2×D52C2311yescharacteristic
59C2×C4×D13—21no—
60C2×C4×D13C2312yes—
61C2×Dic26C2312yes—
62C13×D8—24no—
63C2×C8×C13C2312yes—
64C13×C4⋊C4C2311yescharacteristic
65C13×C22⋊C4—21no—
66C42×C13C2311yescharacteristic
67C22⋊Dic13—22no—
68#6105—24no—
69#6105—42no—
70#6104D414yescomplemented
71#6103—22no—
72#6103—21no—
73#6103D412yes—
74C4⋊Dic13—21no—
75C4⋊Dic13—21no—
76C4⋊Dic13—22no—
77C4⋊Dic13D411yescharacteristic
78C4⋊Dic13C2311yescharacteristic
79C2×#1055C2311yescharacteristic
80C2×#1055C2311yescharacteristic
81#6095—24no—
82#6094—24no—
83#3272—131nomaximal, Sylow
84C23×C13—21no—
85C23×C13—22no—
86C22×D13—21no—
87C22×D13—44no—
88C22×D13—44no—
89C22×D13—82no—
90C22×D13C2×D412yes—
91D4×C13—22no—
92D4×C13—21no—
93D4×C13—22no—
94D4×C13—42no—
95D4×C13—81no—
96D4×C13C2×D412yescomplemented
97C2×C4×C13—21no—
98C2×C4×C13—42no—
99C2×C4×C13C2×D411yescharacteristic
100C2×C4×C13C2×D411yescharacteristic
101C2×C4×C13C2411yescharacteristic
102C22⋊D13—44no—
103C22⋊D13—44no—
104C22⋊D13—44no—
105C2×Dic13—22no—
106C2×Dic13—21no—
107C2×Dic13—44no—
108C2×Dic13C2×D412yes—
109D52—22no—
110D52—21no—
111D52C2×D412yes—
112C4×D13—22no—
113C4×D13—22no—
114C4×D13—42no—
115Dic26—22no—
116Dic26—22no—
117C8×C13—22no—
118#1055—21no—
119#1055C2×D412yescomplemented
120C2×AGL(1,ℤ/8)—132no—
121#547—131no—
122D42—131no—
123#492—131no—
124#468—132no—
125#461—131no—
126#459D1311yescharacteristic, complemented
127#450—132no—
128#449—132no—
129C4×D8—131no—
130#436—131no—
131C22×C13—22no—
132C22×C13—41no—
133C22×C13—41no—
134C22×C13—42no—
135C22×C13—42no—
136C22×C13—42no—
137C22×C13C22×D411yescharacteristic
138C2×D13—22no—
139C2×D13—22no—
140C2×D13—22no—
141C2×D13—22no—
142C2×D13—41no—
143C2×D13—41no—
144C2×D13—88no—
145C4×C13—21no—
146C4×C13—41no—
147C4×C13AGL(1,ℤ/8)12yescomplemented
148C4×C13C22×D411yescharacteristic
149C4×C13H(5,𝔽2)11yescharacteristic
150Dic13—22no—
151Dic13—42no—
152Dic13—41no—
153C2×#41—132no—
154C22×D4—132no—
155C22×D4—261no—
156AGL(1,ℤ/8)—268no—
157C2×SD16—132no—
158C2×SD16—132no—
159C2×SD16—132no—
160C2×D8—131no—
161C2×D8C2×D1312yescomplemented
162C2×M16—132no—
163C4⋊Q8—131no—
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×D4C2×D1311yescharacteristic, complemented
174C2×C4⋊C4—261no—
175#107—131no—
176C4⋊C8C2×D1311yescharacteristic, complemented
177#103—132no—
178#102—131no—
179#102—131no—
180#102C2×D1312yescomplemented
181C22⋊C8—132no—
182C4×C8—131no—
183C2×C13—42no—
184C2×C13—82no—
185C2×C13D4211yescharacteristic
186C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
187C2×C13#57711yescharacteristic
188D13—42no—
189D13—42no—
190C24—262no—
191#41—264no—
192#41—522no—
193C2×Q8—132no—
194C2×D4—21no—
195C2×D4—21no—
196C2×D4—131no—
197C2×D4—131no—
198C2×D4—262no—
199C2×D4—264no—
200C2×D4—262no—
201C2×D4—262no—
202C2×D4—522no—
203C2×D4—524no—
204C2×D4C22×D1312yes—
205C2×D4C22×D1311yescharacteristic
206C22×C4—21no—
207C22×C4—132no—
208C22×C4—262no—
209C22×C4—261no—
210SD16—264no—
211SD16—264no—
212SD16—522no—
213D8—24no—
214D8—134no—
215M16—264no—
216C2×C8—131no—
217C2×C8—131no—
218C2×C8C22×D1312yes—
219C4⋊C4—131no—
220C4⋊C4—131no—
221C4⋊C4—262no—
222C4⋊C4—261no—
223C4⋊C4—261no—
224C4⋊C4C22×D1311yescharacteristic
225C22⋊C4—21no—
226C22⋊C4—132no—
227C22⋊C4—262no—
228C22⋊C4—262no—
229C22⋊C4—261no—
230C42C22×D1311yescharacteristic
231C13#327211yescharacteristic, complemented, Sylow
232C23—21no—
233C23—22no—
234C23—132no—
235C23—261no—
236C23—524no—
237C23—524no—
238C23—1042no—
239Q8—262no—
240Q8—262no—
241D4—22no—
242D4—21no—
243D4—22no—
244D4—42no—
245D4—81no—
246D4—132no—
247D4—262no—
248D4—261no—
249D4—524no—
250D4—524no—
251D4—524no—
252D4D4×D1312yescomplemented
253C2×C4—21no—
254C2×C4—42no—
255C2×C4—132no—
256C2×C4—262no—
257C2×C4—262no—
258C2×C4—261no—
259C2×C4—262no—
260C2×C4—524no—
261C2×C4—522no—
262C2×C4D4×D1311yescharacteristic
263C2×C4D4×D1311yescharacteristic
264C2×C4C23×D1311yescharacteristic
265C8—22no—
266C8—132no—
267C8—261no—
268C22—22no—
269C22—41no—
270C22—41no—
271C22—42no—
272C22—42no—
273C22—42no—
274C22—262no—
275C22—262no—
276C22—262no—
277C22—262no—
278C22—521no—
279C22—521no—
280C22—1048no—
281C22C2×D4×D1311yescharacteristic
282C4—21no—
283C4—41no—
284C4—262no—
285C4—521no—
286C4—522no—
287C4#8816512yescomplemented
288C4C2×D4×D1311yescharacteristic
289C4#8825611yescharacteristic
290C2—42no—
291C2—82no—
292C2—522no—
293C2—522no—
294C2#1171931411yescharacteristic
295C2C2×#8816511yescharacteristic
296C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#459C2
socleC22×C13C22×D4
hypercenter#459D13
hypocenterC13#3272
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#88165C2semidirect
2. #11719422C2semidirect
3. #11719260C2semidirect
4. C13×#459C2semidirect
5. #11718819C2semidirect
6. #11718737C2semidirect
7. C4×#6104C2semidirect
8. #11718502C2semidirect
9. #11718499C2semidirect
10. #11718441C2semidirect
11. #11718437C2semidirect
12. C2×#6129C22semidirect
15. C2×C13×D8C22semidirect
17. C4×D4×C13C22semidirect
21. C2×#6105C22semidirect
22. C2×#6105C22semidirect
28. C2×#6094C22semidirect
29. #88151C22semidirect
33. #88123C22semidirect
34. C13×C4⋊C8C22semidirect
35. C13×#102C22semidirect
36. #88072C22semidirect
37. #88060C22semidirect
38. #88056C22semidirect
40. #88047C22semidirect
41. C4×#1055C22semidirect
70. #6104D4semidirect
96. D4×C13C2×D4semidirect
119. #1055C2×D4semidirect
126. #459D13semidirect
147. C4×C13AGL(1,ℤ/8)semidirect
161. C2×D8C2×D13semidirect
173. C4×D4C2×D13semidirect
176. C4⋊C8C2×D13semidirect
180. #102C2×D13semidirect
231. C13#3272semidirect
252. D4D4×D13semidirect
287. C4#88165semidirect

Maximal subgroups

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

subgroupindex
C2×#881652
#117194222
#117192602
C13×#4592
#117188192
#117187372
C4×#61042
#117185022
#117184992
#117184412
#117184372
#327213