Finite Group Databasebeta

← #13125806

Subgroups — #13125806

Order 1664.

410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 113 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×#88201C211yesmaximal, characteristic, complemented
2#11719329C211yesmaximal, characteristic, complemented
3C13×#451C211yesmaximal, characteristic, complemented
4#11718888C211yesmaximal, characteristic, complemented
5#11718852C212yesmaximal, complemented
6#11718846C212yesmaximal, complemented
7#11718707C211yesmaximal, characteristic, complemented
8#11718480C212yesmaximal, complemented
9#11718461C212yesmaximal, complemented
10#11718393C211yesmaximal, characteristic
11#11718379C211yesmaximal, characteristic, complemented
12C22×Q8×C13C2211yescharacteristic
13C22×D52C2211yescharacteristic
14C2×C13×Q16C2212yescomplemented
15C13×C22⋊Q8C2211yescharacteristic
16#88201—21no—
17#88201—21no—
18#88201C2212yes—
19#88201C2212yes—
20#88201C2211yescharacteristic, complemented
21Q8×Dic13C2211yescharacteristic, complemented
22C2×#6106C2212yes—
23C2×#6106C2212yescomplemented
24#88184C2211yescharacteristic
25C2×#6103—21no—
26C2×#6103—21no—
27C2×C4×Dic13C2211yescharacteristic
28C2×D104C2212yes—
29#88152—21no—
30#88147C2211yescharacteristic, complemented
31#88146—21no—
32#88144C2211yescharacteristic, complemented
33#88140—21no—
34#88135—21no—
35C13×#103C2212yescomplemented
36C13×C22⋊C8C2211yescharacteristic
37#88075C2212yescomplemented
38C22⋊#1055C2211yescharacteristic
39#88061C2212yes—
40#88054C2212yescomplemented
41C8×Dic13C2212yescomplemented
42#88049C2212yes—
43C23×D13—21no—
44C2×Q8×C13—21no—
45C2×Q8×C13—42no—
46C2×Q8×C13C2312yes—
47C2×Q8×C13C2311yescharacteristic
48C22×C4×C13—21no—
49C22×C4×C13C2311yescharacteristic
50C2×C22⋊D13—21no—
51C22×Dic13D411yescharacteristic
52C22×Dic13D411yescharacteristic
53C2×D52—21no—
54C2×D52—42no—
55C2×D52C2311yescharacteristic
56C2×D52C2312yes—
57C2×C4×D13—21no—
58C13×Q16—42no—
59C2×C8×C13C2312yes—
60C13×C4⋊C4—21no—
61C13×C4⋊C4C2311yescharacteristic
62C13×C22⋊C4—21no—
63#6106—42no—
64#6106—42no—
65#6103—21no—
66#6103—21no—
67#6103—21no—
68#6103—21no—
69#6103—22no—
70#6103—22no—
71#6103—22no—
72#6103—22no—
73C4⋊Dic13—21no—
74C4⋊Dic13—21no—
75C4⋊Dic13C2311yescharacteristic
76#6101—21no—
77C4×Dic13—21no—
78C4×Dic13D411yescharacteristic
79C4×Dic13D411yescharacteristic
80C4×Dic13C2311yescharacteristic
81C4×Dic13C2311yescharacteristic
82C2×#1055C2312yes—
83D104—42no—
84#3211—131nomaximal, Sylow
85C23×C13C2×D411yescharacteristic
86C22×D13—21no—
87C22×D13—22no—
88C22×D13—42no—
89C22×D13—42no—
90C22×D13—42no—
91Q8×C13—22no—
92Q8×C13—22no—
93Q8×C13—22no—
94Q8×C13—42no—
95C2×C4×C13—22no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—22no—
99C2×C4×C13—42no—
100C2×C4×C13C2×D411yescharacteristic
101C2×C4×C13C2411yescharacteristic
102C22⋊D13—42no—
103C2×Dic13—22no—
104C2×Dic13—21no—
105C2×Dic13—41no—
106C2×Dic13C2×D411yescharacteristic
107C2×Dic13C2×D411yescharacteristic
108C2×Dic13C2×D411yescharacteristic
109C2×Dic13C2×D411yescharacteristic
110D52—22no—
111D52—22no—
112D52—22no—
113D52—42no—
114C4×D13—42no—
115C8×C13—22no—
116#1055—22no—
117#529—131no—
118C2×#124—131no—
119#495—132no—
120#488—132no—
121#464—132no—
122#463—132no—
123#451D1311yescharacteristic, complemented
124#450—131no—
125#448—131no—
126#447—131no—
127#431—131no—
128C22×C13—21no—
129C22×C13—21no—
130C22×C13#13512yes—
131C22×C13C22×D411yescharacteristic
132C2×D13—42no—
133C2×D13—41no—
134C2×D13—41no—
135C2×D13—42no—
136C2×D13—41no—
137C2×D13—42no—
138C2×D13—84no—
139C4×C13—21no—
140C4×C13—42no—
141C4×C13—41no—
142C4×C13—41no—
143C4×C13H(5,𝔽2)12yes—
144Dic13—21no—
145Dic13—21no—
146Dic13—21no—
147Dic13—21no—
148Dic13—41no—
149C22×Q8C2×D1311yescharacteristic
150C22×D4—131no—
151C2×Q16C2×D1312yescomplemented
152C2×SD16—132no—
153C2×SD16—132no—
154C2×D8—132no—
155#126—261no—
156#125—131no—
157#124—132no—
158#124—132no—
159#124—131no—
160#124—261no—
161#124—261no—
162#123—261no—
163C22⋊Q8C2×D1311yescharacteristic
164#121—131no—
165C4×Q8—131no—
166C4×D4—131no—
167C4×D4—261no—
168#117—261no—
169C2×C22⋊C4—261no—
170C2×C22⋊C4—261no—
171C2×C42—131no—
172C4⋊C8—132no—
173#103—132no—
174#103C2×D1312yescomplemented
175#102—132no—
176#102—132no—
177C22⋊C8—131no—
178C22⋊C8C2×D1311yescharacteristic
179C4×C8—132no—
180C2×C13—22no—
181C2×C13#53511yescharacteristic
182C2×C13C2×#13511yescharacteristic
183C2×C13#57511yescharacteristic
184D13—81no—
185D13—82no—
186C24—261no—
187C2×Q8—21no—
188C2×Q8—42no—
189C2×Q8C22×D1312yes—
190C2×Q8C22×D1311yescharacteristic
191C2×D4—132no—
192C2×D4—131no—
193C2×D4—261no—
194C2×D4—261no—
195C2×D4—522no—
196C22×C4—21no—
197C22×C4—131no—
198C22×C4—131no—
199C22×C4—261no—
200C22×C4C22×D1311yescharacteristic
201Q16—42no—
202SD16—522no—
203SD16—522no—
204D8—522no—
205C2×C8—132no—
206C2×C8C22×D1312yes—
207C4⋊C4—21no—
208C4⋊C4—131no—
209C4⋊C4—261no—
210C4⋊C4—261no—
211C4⋊C4—261no—
212C4⋊C4C22×D1311yescharacteristic
213C22⋊C4—21no—
214C22⋊C4—262no—
215C22⋊C4—262no—
216C22⋊C4—262no—
217C22⋊C4—262no—
218C22⋊C4—261no—
219C22⋊C4—261no—
220C22⋊C4—261no—
221C22⋊C4—261no—
222C42—131no—
223C42—131no—
224C42—131no—
225C42—131no—
226C42—261no—
227C13#321111yescharacteristic, complemented, Sylow
228C23—261no—
229C23—262no—
230C23—522no—
231C23—522no—
232C23—522no—
233C23D4×D1311yescharacteristic
234Q8—22no—
235Q8—22no—
236Q8—22no—
237Q8—42no—
238D4—262no—
239D4—262no—
240D4—262no—
241D4—522no—
242D4—522no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—42no—
248C2×C4—131no—
249C2×C4—131no—
250C2×C4—131no—
251C2×C4—131no—
252C2×C4—262no—
253C2×C4—261no—
254C2×C4—522no—
255C2×C4—521no—
256C2×C4D4×D1311yescharacteristic
257C2×C4C23×D1311yescharacteristic
258C8—22no—
259C8—262no—
260C22—21no—
261C22—21no—
262C22—521no—
263C22—522no—
264C22—521no—
265C22—522no—
266C22—522no—
267C22—521no—
268C22—1044no—
269C22#8817312yes—
270C22C2×D4×D1311yescharacteristic
271C4—21no—
272C4—41no—
273C4—42no—
274C4—41no—
275C4—261no—
276C4—261no—
277C4—261no—
278C4—261no—
279C4—521no—
280C4#8825112yes—
281C2—22no—
282C2—1042no—
283C2—1041no—
284C2#1171929711yescharacteristic
285C2C2×#8817311yescharacteristic
286C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#451C2
socleC22×C13C22×D4
prime radical#11718393C2
hypercenter#451D13
hypocenterC13#3211
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. C2×#88201C2semidirect
2. #11719329C2semidirect
3. C13×#451C2semidirect
4. #11718888C2semidirect
5. #11718852C2semidirect
6. #11718846C2semidirect
7. #11718707C2semidirect
8. #11718480C2semidirect
9. #11718461C2semidirect
11. #11718379C2semidirect
14. C2×C13×Q16C22semidirect
20. #88201C22semidirect
21. Q8×Dic13C22semidirect
23. C2×#6106C22semidirect
30. #88147C22semidirect
32. #88144C22semidirect
35. C13×#103C22semidirect
37. #88075C22semidirect
40. #88054C22semidirect
41. C8×Dic13C22semidirect
123. #451D13semidirect
151. C2×Q16C2×D13semidirect
174. #103C2×D13semidirect
227. C13#3211semidirect

Maximal subgroups

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

subgroupindex
C2×#882012
#117193292
C13×#4512
#117188882
#117188522
#117188462
#117187072
#117184802
#117184612
#117183932
#117183792
#321113