Finite Group Databasebeta

← #13125797

Subgroups — #13125797

Order 1664.

410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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×#529C211yesmaximal, characteristic, complemented
2C2×#88129C211yesmaximal, characteristic, complemented
3#11718729C212yesmaximal, complemented
4#11718720C212yesmaximal, complemented
5#11718711C211yesmaximal, characteristic, complemented
6#11718707C211yesmaximal, characteristic, complemented
7#11718701C211yesmaximal, characteristic, complemented
8#11718697C211yesmaximal, characteristic
9#11718689C212yesmaximal, complemented
10#11718677C212yesmaximal, complemented
11#11718586C211yesmaximal, characteristic, complemented
12C22×D52C2211yescharacteristic
13C22×Dic26C2211yescharacteristic
14C13×#126—21no—
15C13×#125C2211yescharacteristic, complemented
16C13×#124C2211yescharacteristic, complemented
17C13×#123—21no—
18C13×C22⋊Q8C2211yescharacteristic
19C13×#121C2211yescharacteristic
20C4×Q8×C13C2211yescharacteristic, complemented
21C4×D4×C13—21no—
22C4×D4×C13C2211yescharacteristic, complemented
23C13×#117—21no—
24C2×C42×C13C2211yescharacteristic
25C2×#6107C2212yescomplemented
26C2×#6106C2212yes—
27C2×#6105C2212yescomplemented
28C2×#6104C2212yes—
29C2×#6103—21no—
30C2×#6103—21no—
31#88129—21no—
32#88129—21no—
33#88129C2212yes—
34#88129C2212yes—
35C22⋊#1055C2211yescharacteristic
36C22⋊#1055C2211yescharacteristic
37#88050C2212yescomplemented
38#88050C2212yescomplemented
39#88049C2212yes—
40#88049C2212yes—
41C4⋊#1055C2212yescomplemented
42C4×#1055C2212yescomplemented
43C23×D13—21no—
44C2×Q8×C13C2311yescharacteristic
45C2×D4×C13—21no—
46C2×D4×C13C2311yescharacteristic
47C22×C4×C13—21no—
48C22×C4×C13D411yescharacteristic
49C22×C4×C13D411yescharacteristic
50C22×C4×C13C2311yescharacteristic
51C22×Dic13—21no—
52C2×D52—21no—
53C2×D52—42no—
54C2×D52C2312yes—
55C2×Dic26—21no—
56C2×Dic26—42no—
57C2×Dic26C2312yes—
58C13×C4⋊C4—21no—
59C13×C4⋊C4—21no—
60C13×C4⋊C4—21no—
61C13×C4⋊C4—21no—
62C13×C4⋊C4C2311yescharacteristic
63C13×C4⋊C4C2311yescharacteristic
64C13×C22⋊C4—21no—
65C13×C22⋊C4—21no—
66C13×C22⋊C4—21no—
67C13×C22⋊C4—21no—
68C13×C22⋊C4—21no—
69C42×C13—21no—
70C42×C13D411yescharacteristic
71C42×C13D411yescharacteristic
72C42×C13C2311yescharacteristic
73C42×C13C2311yescharacteristic
74#6107—42no—
75#6106—42no—
76#6105—42no—
77#6104—42no—
78#6103—22no—
79#6103—22no—
80#6103—22no—
81#6103—22no—
82C2×#1055C2312yes—
83C2×#1055C2312yes—
84#3211—131nomaximal, Sylow
85C23×C13—21no—
86C23×C13C2×D411yescharacteristic
87C22×D13—22no—
88C22×D13—42no—
89C22×D13—42no—
90C22×D13—42no—
91Q8×C13—22no—
92D4×C13—22no—
93D4×C13—42no—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—41no—
100C2×C4×C13—42no—
101C2×C4×C13C2×D411yescharacteristic
102C2×C4×C13C2×D411yescharacteristic
103C2×C4×C13C2×D411yescharacteristic
104C2×C4×C13C2×D411yescharacteristic
105C2×C4×C13C2×D411yescharacteristic
106C2×C4×C13C2411yescharacteristic
107C2×Dic13—22no—
108C2×Dic13—42no—
109D52—22no—
110D52—22no—
111D52—42no—
112Dic26—22no—
113Dic26—22no—
114Dic26—42no—
115#1055—22no—
116#1055—22no—
117#529D1311yescharacteristic, complemented
118C2×#124—131no—
119#495—132no—
120#488—132no—
121#464—132no—
122#463—132no—
123#451—131no—
124#450—131no—
125#448—131no—
126#447—131no—
127#431—131no—
128C22×C13—21no—
129C22×C13—21no—
130C22×C13—41no—
131C22×C13—41no—
132C22×C13—41no—
133C22×C13#13512yes—
134C22×C13C22×D411yescharacteristic
135C2×D13—42no—
136C2×D13—42no—
137C2×D13—42no—
138C2×D13—84no—
139C4×C13—21no—
140C4×C13—21no—
141C4×C13—21no—
142C4×C13—21no—
143C4×C13—21no—
144C4×C13—41no—
145C4×C13—41no—
146C4×C13—41no—
147C4×C13H(5,𝔽2)12yes—
148Dic13—42no—
149C22×Q8—131no—
150C22×D4—131no—
151C2×Q16—132no—
152C2×SD16—132no—
153C2×SD16—132no—
154C2×D8—132no—
155#126—21no—
156#125C2×D1311yescharacteristic, complemented
157#124—132no—
158#124—132no—
159#124—261no—
160#124—261no—
161#124C2×D1311yescharacteristic, complemented
162#123—21no—
163C22⋊Q8C2×D1311yescharacteristic
164#121C2×D1311yescharacteristic
165C4×Q8C2×D1311yescharacteristic, complemented
166C4×D4—21no—
167C4×D4C2×D1311yescharacteristic, complemented
168#117—21no—
169C2×C22⋊C4—261no—
170C2×C22⋊C4—261no—
171C2×C42C2×D1311yescharacteristic
172C4⋊C8—132no—
173#103—132no—
174#103—132no—
175#102—132no—
176#102—132no—
177C22⋊C8—131no—
178C22⋊C8—131no—
179C4×C8—132no—
180C2×C13—22no—
181C2×C13—81no—
182C2×C13#53511yescharacteristic
183C2×C13C2×#13511yescharacteristic
184C2×C13#57511yescharacteristic
185D13—82no—
186C24—261no—
187C2×Q8—132no—
188C2×Q8—261no—
189C2×Q8—522no—
190C2×Q8C22×D1311yescharacteristic
191C2×D4—21no—
192C2×D4—132no—
193C2×D4—261no—
194C2×D4—522no—
195C2×D4C22×D1311yescharacteristic
196C22×C4—21no—
197C22×C4—261no—
198C22×C4C22⋊D1311yescharacteristic
199C22×C4C22⋊D1311yescharacteristic
200C22×C4C22×D1311yescharacteristic
201Q16—522no—
202SD16—522no—
203SD16—522no—
204D8—522no—
205C2×C8—132no—
206C2×C8—132no—
207C4⋊C4—21no—
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—21no—
211C4⋊C4C22×D1311yescharacteristic
212C4⋊C4C22×D1311yescharacteristic
213C22⋊C4—21no—
214C22⋊C4—21no—
215C22⋊C4—21no—
216C22⋊C4—21no—
217C22⋊C4—21no—
218C22⋊C4—262no—
219C22⋊C4—262no—
220C22⋊C4—262no—
221C22⋊C4—262no—
222C42—21no—
223C42C22⋊D1311yescharacteristic
224C42C22⋊D1311yescharacteristic
225C42C22×D1311yescharacteristic
226C42C22×D1311yescharacteristic
227C13#321111yescharacteristic, complemented, Sylow
228C23—21no—
229C23—262no—
230C23—522no—
231C23—522no—
232C23—522no—
233C23C2×C22⋊D1311yescharacteristic
234Q8—22no—
235Q8—262no—
236Q8—262no—
237Q8—522no—
238D4—22no—
239D4—42no—
240D4—262no—
241D4—262no—
242D4—522no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—262no—
251C2×C4—522no—
252C2×C4C2×C22⋊D1311yescharacteristic
253C2×C4C2×C22⋊D1311yescharacteristic
254C2×C4C2×C22⋊D1311yescharacteristic
255C2×C4C2×C22⋊D1311yescharacteristic
256C2×C4C2×C22⋊D1311yescharacteristic
257C2×C4C23×D1311yescharacteristic
258C8—262no—
259C8—262no—
260C22—21no—
261C22—21no—
262C22—41no—
263C22—41no—
264C22—41no—
265C22—522no—
266C22—522no—
267C22—522no—
268C22—1044no—
269C22#8820412yes—
270C22C22×C22⋊D1311yescharacteristic
271C4—21no—
272C4—21no—
273C4—21no—
274C4—21no—
275C4—21no—
276C4—41no—
277C4—41no—
278C4—41no—
279C4—522no—
280C4#8825612yes—
281C2—22no—
282C2—81no—
283C2—1042no—
284C2C2×#8820411yescharacteristic
285C2#1171952711yescharacteristic
286C2#1171953511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#529C2
socleC22×C13C22×D4
prime radical#11718697C2
hypercenter#529D13
hypocenterC13#3211
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C13×#529C2semidirect
2. C2×#88129C2semidirect
3. #11718729C2semidirect
4. #11718720C2semidirect
5. #11718711C2semidirect
6. #11718707C2semidirect
7. #11718701C2semidirect
9. #11718689C2semidirect
10. #11718677C2semidirect
11. #11718586C2semidirect
15. C13×#125C22semidirect
16. C13×#124C22semidirect
20. C4×Q8×C13C22semidirect
22. C4×D4×C13C22semidirect
25. C2×#6107C22semidirect
27. C2×#6105C22semidirect
37. #88050C22semidirect
38. #88050C22semidirect
41. C4⋊#1055C22semidirect
42. C4×#1055C22semidirect
117. #529D13semidirect
156. #125C2×D13semidirect
161. #124C2×D13semidirect
165. C4×Q8C2×D13semidirect
167. C4×D4C2×D13semidirect
227. C13#3211semidirect

Maximal subgroups

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

subgroupindex
C13×#5292
C2×#881292
#117187292
#117187202
#117187112
#117187072
#117187012
#117186972
#117186892
#117186772
#117185862
#321113