Finite Group Databasebeta

← #13125834

Subgroups — #13125834

Order 1664.

400 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 111 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
1#11719433C211yesmaximal, characteristic, complemented
2D13×#124C211yesmaximal, characteristic
3C13×#497C211yesmaximal, characteristic, complemented
4#11718847C212yesmaximal, complemented
5#11718846C212yesmaximal, complemented
6#11718830C212yesmaximal
7#11718827C212yesmaximal, complemented
8#11718747C211yesmaximal, characteristic, complemented
9#11718716C211yesmaximal, characteristic, complemented
10#11718375C211yesmaximal, characteristic, complemented
11#11718366C211yesmaximal, characteristic, complemented
12C2×Q8×D13C2211yescharacteristic
13C2×D4×D13C2211yescharacteristic
14C2×C13×Q16C2212yescomplemented
15C2×C13×SD16C2212yes—
16C13×C4⋊Q8C2211yescharacteristic, complemented
17C13×#124C2211yescharacteristic
18#88201C2211yescharacteristic
19#88200C2212yes—
20Q8×Dic13C2212yescomplemented
21C2×#6107C2212yescomplemented
22C2×#6106C2212yes—
23#88190C2211yescharacteristic
24#88151—21no—
25#88146—21no—
26#88144—21no—
27#88141—21no—
28#88139—21no—
29#88139—21no—
30C22⋊C4×D13—21no—
31C22⋊C4×D13—21no—
32#88129C2211yescharacteristic
33C42×D13C2211yescharacteristic
34#88123C2211yescharacteristic, complemented
35C13×#97C2211yescharacteristic, complemented
36#88075C2212yescomplemented
37#88072C2212yes—
38#88061C2212yes—
39#88060C2212yes—
40#88056C2212yescomplemented
41#88054C2212yescomplemented
42#88043C2211yescharacteristic, complemented
43C23×D13—21no—
44C2×Q8×C13C2311yescharacteristic
45C2×Q8×C13C2312yes—
46C2×D4×C13C2311yescharacteristic
47C2×C22⋊D13—21no—
48Q8×D13—42no—
49D4×D13—42no—
50C2×D52C2311yescharacteristic
51C2×C4×D13—21no—
52C2×C4×D13D411yescharacteristic
53C2×C4×D13D411yescharacteristic
54C2×C4×D13C2311yescharacteristic
55C2×Dic26—21no—
56C2×Dic26—21no—
57C2×Dic26C2311yescharacteristic
58C13×Q16—42no—
59C13×SD16—42no—
60C2×C8×C13C2312yes—
61C13×C4⋊C4—21no—
62C13×C4⋊C4—21no—
63C13×C22⋊C4—21no—
64C13×C22⋊C4—21no—
65C42×C13C2311yescharacteristic
66C22⋊Dic13—21no—
67C22⋊Dic13—21no—
68#6107—42no—
69#6106—42no—
70#6103—22no—
71#6103—21no—
72#6103—21no—
73#6103—21no—
74#6103—21no—
75C4⋊Dic13—21no—
76C4⋊Dic13—22no—
77C4⋊Dic13C2312yes—
78#6101—22no—
79C4×Dic13—22no—
80C4×Dic13D411yescharacteristic
81C4×Dic13D411yescharacteristic
82C4×Dic13C2311yescharacteristic
83C2×#1055C2312yes—
84#3215—131nomaximal, Sylow
85C23×C13—21no—
86C22×D13—21no—
87C22×D13—42no—
88C22×D13—42no—
89C22×D13—42no—
90C22×D13C2×D411yescharacteristic
91Q8×C13—22no—
92Q8×C13—22no—
93Q8×C13—22no—
94D4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—21no—
97C2×C4×C13C2×D411yescharacteristic
98C2×C4×C13C2×D411yescharacteristic
99C2×C4×C13C2411yescharacteristic
100C22⋊D13—42no—
101C2×Dic13—22no—
102C2×Dic13—21no—
103C2×Dic13C2×D411yescharacteristic
104C2×Dic13C2×D411yescharacteristic
105C2×Dic13C2×D411yescharacteristic
106D52—22no—
107C4×D13—22no—
108C4×D13—22no—
109C4×D13—41no—
110C4×D13—42no—
111Dic26—22no—
112Dic26—42no—
113Dic26—42no—
114C8×C13—22no—
115#1055—22no—
116#533—131no—
117C2×#124—131no—
118#497—131no—
119#497D1311yescharacteristic, complemented
120#489—131no—
121#489—131no—
122#464—132no—
123#464—132no—
124#451—132no—
125#450—132no—
126#432—131no—
127C22×C13—41no—
128C22×C13—41no—
129C22×C13—41no—
130C22×C13C22×D411yescharacteristic
131C2×D13—21no—
132C2×D13—21no—
133C2×D13—41no—
134C2×D13—41no—
135C2×D13—41no—
136C2×D13—84no—
137C2×D13#13712yes—
138C4×C13—21no—
139C4×C13—21no—
140C4×C13—41no—
141C4×C13—42no—
142C4×C13H(5,𝔽2)12yes—
143Dic13—21no—
144Dic13—21no—
145Dic13—21no—
146Dic13—41no—
147Dic13—42no—
148C22×Q8—131no—
149C22×D4—131no—
150C2×Q16—132no—
151C2×Q16C2×D1312yescomplemented
152C2×SD16—132no—
153C2×SD16C2×D1312yes—
154C4⋊Q8—131no—
155C4⋊Q8C2×D1311yescharacteristic, complemented
156#125—261no—
157#124—131no—
158#124—131no—
159#124—131no—
160#124—261no—
161#124—261no—
162#124C2×D1311yescharacteristic
163C22⋊Q8—132no—
164C22⋊Q8—261no—
165C4×Q8—132no—
166C4×Q8—261no—
167#117—261no—
168C2×C22⋊C4—261no—
169C2×C22⋊C4—261no—
170C2×C42—131no—
171C4⋊C8—132no—
172#103—132no—
173#103—132no—
174#102—132no—
175#102—132no—
176C22⋊C8—132no—
177#97—131no—
178#97C2×D1311yescharacteristic, complemented
179C2×C13—81no—
180C2×C13#53511yescharacteristic
181C2×C13C2×#13711yescharacteristic
182C2×C13#57511yescharacteristic
183D13—22no—
184D13—81no—
185C24—261no—
186C2×Q8—131no—
187C2×Q8—261no—
188C2×Q8—261no—
189C2×Q8—522no—
190C2×Q8C22×D1311yescharacteristic
191C2×Q8C22×D1312yes—
192C2×D4—131no—
193C2×D4—261no—
194C2×D4—522no—
195C2×D4C22×D1311yescharacteristic
196C22×C4—131no—
197C22×C4—131no—
198C22×C4—131no—
199C22×C4—261no—
200Q16—42no—
201Q16—522no—
202SD16—42no—
203SD16—522no—
204C2×C8—132no—
205C2×C8C22×D1312yes—
206C4⋊C4—21no—
207C4⋊C4—21no—
208C4⋊C4—132no—
209C4⋊C4—262no—
210C4⋊C4—262no—
211C4⋊C4—261no—
212C22⋊C4—21no—
213C22⋊C4—21no—
214C22⋊C4—261no—
215C22⋊C4—261no—
216C22⋊C4—262no—
217C22⋊C4—261no—
218C22⋊C4—261no—
219C22⋊C4—261no—
220C22⋊C4—261no—
221C42—131no—
222C42—131no—
223C42—131no—
224C42—262no—
225C42C22×D1311yescharacteristic
226C13#321511yescharacteristic, complemented, Sylow
227C23—21no—
228C23—131no—
229C23—261no—
230C23—522no—
231C23—522no—
232C23—522no—
233Q8—22no—
234Q8—22no—
235Q8—22no—
236Q8—262no—
237Q8—522no—
238Q8—522no—
239D4—22no—
240D4—262no—
241D4—522no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—131no—
245C2×C4—131no—
246C2×C4—131no—
247C2×C4—262no—
248C2×C4—262no—
249C2×C4—262no—
250C2×C4—261no—
251C2×C4—521no—
252C2×C4—522no—
253C2×C4D4×D1311yescharacteristic
254C2×C4D4×D1311yescharacteristic
255C2×C4C23×D1311yescharacteristic
256C8—22no—
257C8—262no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—132no—
262C22—261no—
263C22—261no—
264C22—521no—
265C22—521no—
266C22—521no—
267C22—1044no—
268C22C2×D4×D1311yescharacteristic
269C4—21no—
270C4—21no—
271C4—41no—
272C4—42no—
273C4—261no—
274C4—261no—
275C4—261no—
276C4—522no—
277C4—521no—
278C4#8825112yes—
279C2—81no—
280C2—262no—
281C2—1041no—
282C2#1171942011yescharacteristic
283C2D13×#13711yescharacteristic
284C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#497C2
socleC22×C13C22×D4
prime radicalC2×D4×D13C22
hypercenter#497D13
hypocenterC13#3215
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. #11719433C2semidirect
3. C13×#497C2semidirect
4. #11718847C2semidirect
5. #11718846C2semidirect
7. #11718827C2semidirect
8. #11718747C2semidirect
9. #11718716C2semidirect
10. #11718375C2semidirect
11. #11718366C2semidirect
14. C2×C13×Q16C22semidirect
16. C13×C4⋊Q8C22semidirect
20. Q8×Dic13C22semidirect
21. C2×#6107C22semidirect
34. #88123C22semidirect
35. C13×#97C22semidirect
36. #88075C22semidirect
40. #88056C22semidirect
41. #88054C22semidirect
42. #88043C22semidirect
119. #497D13semidirect
151. C2×Q16C2×D13semidirect
155. C4⋊Q8C2×D13semidirect
178. #97C2×D13semidirect
226. C13#3215semidirect

Maximal subgroups

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

subgroupindex
#117194332
D13×#1242
C13×#4972
#117188472
#117188462
#117188302
#117188272
#117187472
#117187162
#117183752
#117183662
#321513