Finite Group Databasebeta

← #13125697

Subgroups — #13125697

Order 1664.

442 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 117 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×#535C211yesmaximal, characteristic, complemented
2#11719535C211yesmaximal, characteristic, complemented
3#11718895C211yesmaximal, characteristic, complemented
4#11718878C212yesmaximal, complemented
5#11718700C212yesmaximal, complemented
6#11718699C212yesmaximal, complemented
7#11718697C212yesmaximal, complemented
8#11718696C212yesmaximal, complemented
9#11718664C212yesmaximal, complemented
10C2×C13×#41C2211yescharacteristic
11C22×D4×C13C2211yescharacteristic, complemented
12C22×D52C2211yescharacteristic, complemented
13C13×#127—21no—
14C13×#124—21no—
15C13×#121C2212yes—
16C13×#121C2212yescomplemented
17C13×#120—21no—
18C13×#120—21no—
19C13×#117C2211yescharacteristic, complemented
20#88201—21no—
21#88194—21no—
22#88191—21no—
23#88191—21no—
24C2×#6104C2212yes—
25C2×#6104C2212yes—
26#88184C2212yes—
27#88184C2212yescomplemented
28#88180C2211yescharacteristic, complemented
29C2×#6099C2211yescharacteristic, complemented
30C22×#1055C2211yescharacteristic, complemented
31#88072C2212yescomplemented
32#88072C2212yescomplemented
33C22⋊#1055C2212yescomplemented
34C22⋊#1055C2212yescomplemented
35#88049C2212yescomplemented
36#88049C2212yescomplemented
37#88048C2212yescomplemented
38#88047C2212yescomplemented
39C24×C13—21no—
40C23×D13—21no—
41C13×#41—41no—
42C13×#41—41no—
43C2×Q8×C13D411yescharacteristic
44C2×D4×C13—22no—
45C2×D4×C13—22no—
46C2×D4×C13—21no—
47C2×D4×C13—41no—
48C2×D4×C13—41no—
49C2×D4×C13D411yescharacteristic
50C2×D4×C13D411yescharacteristic
51C2×D4×C13D411yescharacteristic
52C2×D4×C13C2312yes—
53C22×C4×C13C2311yescharacteristic
54C22×C4×C13C2311yescharacteristic
55C22×C4×C13C2311yescharacteristic
56C2×C22⋊D13—22no—
57C2×C22⋊D13—22no—
58C2×D52—21no—
59C2×D52—41no—
60C2×D52—41no—
61C2×D52C2312yes—
62C13×C4⋊C4C2312yes—
63C13×C22⋊C4—21no—
64C13×C22⋊C4—22no—
65C13×C22⋊C4—22no—
66C42×C13—21no—
67C22⋊Dic13—21no—
68#6104—42no—
69#6104—42no—
70#6103—22no—
71#6103—22no—
72C4⋊Dic13C2312yes—
73C4×Dic13—21no—
74#6099—41no—
75C2×#1055—41no—
76C2×#1055C2312yes—
77C2×#1055C2312yes—
78#3199—131nomaximal, Sylow
79C23×C13—22no—
80C23×C13—42no—
81C23×C13—82no—
82C23×C13C2×D411yescharacteristic
83C23×C13C2×D411yescharacteristic
84C23×C13C2×D411yescharacteristic
85C22×D13—22no—
86C22×D13—42no—
87C22×D13—82no—
88Q8×C13—41no—
89D4×C13—22no—
90D4×C13—22no—
91D4×C13—41no—
92D4×C13—41no—
93D4×C13—41no—
94D4×C13—42no—
95D4×C13—82no—
96D4×C13—82no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—22no—
104C2×C4×C13C2×D411yescharacteristic
105C2×C4×C13C2×D411yescharacteristic
106C2×C4×C13C2×D411yescharacteristic
107C2×C4×C13C2411yescharacteristic
108C22⋊D13—82no—
109C22⋊D13—82no—
110C2×Dic13—22no—
111D52—22no—
112D52—22no—
113D52—42no—
114#1055—22no—
115#1055—22no—
116#535—131no—
117#535D1311yescharacteristic, complemented
118#482—132no—
119#482—132no—
120#469—132no—
121#466—132no—
122#447—132no—
123#447—132no—
124#408—131no—
125C22×C13—21no—
126C22×C13—21no—
127C22×C13—21no—
128C22×C13—22no—
129C22×C13—22no—
130C22×C13—22no—
131C22×C13—42no—
132C22×C13—42no—
133C22×C13—42no—
134C22×C13—84no—
135C22×C13C22×D411yescharacteristic
136C2×D13—42no—
137C2×D13—42no—
138C2×D13—42no—
139C2×D13—84no—
140C4×C13—21no—
141C4×C13—21no—
142C4×C13—21no—
143C4×C13—42no—
144C4×C13H(5,𝔽2)11yescharacteristic
145C4×C13H(5,𝔽2)11yescharacteristic
146Dic13—42no—
147C2×#41C2×D1311yescharacteristic
148C22×D4—131no—
149C22×D4C2×D1311yescharacteristic, complemented
150C2×D8—132no—
151C2×D8—132no—
152C2×M16—131no—
153C22×C8—131no—
154#127—21no—
155#127—261no—
156#124—21no—
157#124—261no—
158#121—132no—
159#121—132no—
160#121C2×D1312yes—
161#121C2×D1312yescomplemented
162#120—21no—
163#120—21no—
164#120—261no—
165#120—261no—
166#117—131no—
167#117C2×D1311yescharacteristic, complemented
168#107—132no—
169#106—132no—
170#102—132no—
171#102—132no—
172#102—132no—
173#102—132no—
174C22⋊C8—132no—
175C22⋊C8—132no—
176C2×C13—41no—
177C2×C13—41no—
178C2×C13—41no—
179C2×C13—82no—
180C2×C13#53411yescharacteristic
181C2×C13#57612yes—
182D13—82no—
183C24—21no—
184C24—261no—
185#41—41no—
186#41—41no—
187C2×Q8C22⋊D1311yescharacteristic
188C2×D4—22no—
189C2×D4—22no—
190C2×D4—21no—
191C2×D4—41no—
192C2×D4—41no—
193C2×D4—132no—
194C2×D4—262no—
195C2×D4—262no—
196C2×D4—261no—
197C2×D4—521no—
198C2×D4—521no—
199C2×D4C22⋊D1311yescharacteristic
200C2×D4C22⋊D1311yescharacteristic
201C2×D4C22⋊D1311yescharacteristic
202C2×D4C22×D1312yes—
203C22×C4C22×D1311yescharacteristic
204C22×C4C22×D1311yescharacteristic
205C22×C4C22×D1311yescharacteristic
206D8—522no—
207D8—522no—
208M16—521no—
209C2×C8—132no—
210C2×C8—132no—
211C2×C8—521no—
212C4⋊C4—132no—
213C4⋊C4C22×D1312yes—
214C22⋊C4—21no—
215C22⋊C4—22no—
216C22⋊C4—22no—
217C22⋊C4—261no—
218C22⋊C4—262no—
219C22⋊C4—262no—
220C42—21no—
221C42—261no—
222C13#319911yescharacteristic, complemented, Sylow
223C23—22no—
224C23—42no—
225C23—82no—
226C23—262no—
227C23—522no—
228C23—1042no—
229C23C2×C22⋊D1311yescharacteristic
230C23C2×C22⋊D1311yescharacteristic
231C23C2×C22⋊D1311yescharacteristic
232Q8—41no—
233D4—22no—
234D4—22no—
235D4—41no—
236D4—41no—
237D4—41no—
238D4—42no—
239D4—82no—
240D4—82no—
241D4—262no—
242D4—262no—
243D4—522no—
244D4—1042no—
245D4—1042no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—262no—
254C2×C4C2×C22⋊D1311yescharacteristic
255C2×C4C2×C22⋊D1311yescharacteristic
256C2×C4C2×C22⋊D1311yescharacteristic
257C2×C4C23×D1311yescharacteristic
258C8—262no—
259C8—262no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—22no—
264C22—22no—
265C22—22no—
266C22—42no—
267C22—42no—
268C22—42no—
269C22—84no—
270C22—522no—
271C22—522no—
272C22—522no—
273C22—1044no—
274C22C22×C22⋊D1311yescharacteristic
275C4—21no—
276C4—21no—
277C4—21no—
278C4—42no—
279C4—522no—
280C4#8825111yescharacteristic
281C4#8825111yescharacteristic
282C2—41no—
283C2—41no—
284C2—41no—
285C2—82no—
286C2—1042no—
287C2#1171950911yescharacteristic
288C2#1171954012yes—
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#535C2
socleC22×C13C22×D4
hypercenter#535D13
hypocenterC13#3199
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C13×#535C2semidirect
2. #11719535C2semidirect
3. #11718895C2semidirect
4. #11718878C2semidirect
5. #11718700C2semidirect
6. #11718699C2semidirect
7. #11718697C2semidirect
8. #11718696C2semidirect
9. #11718664C2semidirect
11. C22×D4×C13C22semidirect
12. C22×D52C22semidirect
16. C13×#121C22semidirect
19. C13×#117C22semidirect
27. #88184C22semidirect
28. #88180C22semidirect
29. C2×#6099C22semidirect
30. C22×#1055C22semidirect
31. #88072C22semidirect
32. #88072C22semidirect
33. C22⋊#1055C22semidirect
34. C22⋊#1055C22semidirect
35. #88049C22semidirect
36. #88049C22semidirect
37. #88048C22semidirect
38. #88047C22semidirect
117. #535D13semidirect
149. C22×D4C2×D13semidirect
161. #121C2×D13semidirect
167. #117C2×D13semidirect
222. C13#3199semidirect

Maximal subgroups

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

subgroupindex
C13×#5352
#117195352
#117188952
#117188782
#117187002
#117186992
#117186972
#117186962
#117186642
#319913