Finite Group Databasebeta

← #13125818

Subgroups — #13125818

Order 1664.

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

normal subgroups only

This group has 444 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#11719421C211yesmaximal, characteristic, complemented
2D13×#124C211yesmaximal, characteristic, complemented
3C13×#496C211yesmaximal, characteristic, complemented
4#11718831C212yesmaximal, complemented
5#11718826C212yesmaximal, complemented
6#11718817C212yesmaximal, complemented
7#11718814C212yesmaximal, complemented
8#11718735C211yesmaximal, characteristic, complemented
9#11718716C211yesmaximal, characteristic, complemented
10#11718375C211yesmaximal, characteristic, complemented
11#11718366C211yesmaximal, characteristic, complemented
12C2×Q8×D13C2211yescharacteristic
13C2×#6129—21no—
14C2×D4×D13C2211yescharacteristic
15C2×C13×SD16C2212yescomplemented
16C2×C13×D8C2212yes—
17C13×#127C2211yescharacteristic, complemented
18C13×#124C2211yescharacteristic
19#88201C2211yescharacteristic
20#88192—21no—
21#88192C2212yes—
22#88190—21no—
23#88190C2211yescharacteristic
24D4×Dic13—21no—
25D4×Dic13C2212yescomplemented
26C2×#6105C2212yescomplemented
27C2×#6104C2212yes—
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×D4×C13—21no—
46C2×D4×C13—21no—
47C2×D4×C13C2311yescharacteristic
48C2×D4×C13C2312yes—
49C2×C22⋊D13—22no—
50C2×C22⋊D13—21no—
51C22×Dic13—22no—
52Q8×D13—42no—
53#6129—44no—
54D4×D13—42no—
55C2×D52C2311yescharacteristic
56C2×C4×D13—21no—
57C2×C4×D13D411yescharacteristic
58C2×C4×D13D411yescharacteristic
59C2×C4×D13C2311yescharacteristic
60C2×Dic26—21no—
61C2×Dic26—21no—
62C2×Dic26C2311yescharacteristic
63C13×SD16—42no—
64C13×D8—42no—
65C2×C8×C13C2312yes—
66C13×C22⋊C4—21no—
67C13×C22⋊C4—21no—
68C42×C13C2311yescharacteristic
69C22⋊Dic13—21no—
70C22⋊Dic13—21no—
71C22⋊Dic13—22no—
72C22⋊Dic13—22no—
73#6105—42no—
74#6104—42no—
75#6103—21no—
76#6103—21no—
77#6103—21no—
78#6103—21no—
79C4⋊Dic13—21no—
80C4⋊Dic13C2312yes—
81C4×Dic13D411yescharacteristic
82C4×Dic13D411yescharacteristic
83C4×Dic13C2311yescharacteristic
84C2×#1055C2312yes—
85#3213—131nomaximal, Sylow
86C23×C13—21no—
87C23×C13—22no—
88C22×D13—21no—
89C22×D13—42no—
90C22×D13—42no—
91C22×D13—42no—
92C22×D13C2×D411yescharacteristic
93Q8×C13—22no—
94D4×C13—22no—
95D4×C13—22no—
96D4×C13—22no—
97D4×C13—42no—
98D4×C13—42no—
99C2×C4×C13—21no—
100C2×C4×C13C2×D411yescharacteristic
101C2×C4×C13C2×D411yescharacteristic
102C2×C4×C13C2411yescharacteristic
103C22⋊D13—42no—
104C22⋊D13—44no—
105C2×Dic13—22no—
106C2×Dic13—21no—
107C2×Dic13—44no—
108C2×Dic13C2×D411yescharacteristic
109C2×Dic13C2×D411yescharacteristic
110C2×Dic13C2×D411yescharacteristic
111D52—22no—
112C4×D13—22no—
113C4×D13—22no—
114C4×D13—41no—
115C4×D13—42no—
116Dic26—22no—
117Dic26—42no—
118Dic26—42no—
119C8×C13—22no—
120#1055—22no—
121#532—131no—
122C2×#124—131no—
123#496—131no—
124#496D1311yescharacteristic, complemented
125#489—131no—
126#489—131no—
127#463—132no—
128#463—132no—
129#448—132no—
130#447—132no—
131#432—131no—
132C22×C13—41no—
133C22×C13—42no—
134C22×C13—42no—
135C22×C13—41no—
136C22×C13—42no—
137C22×C13—41no—
138C22×C13C22×D411yescharacteristic
139C2×D13—21no—
140C2×D13—21no—
141C2×D13—41no—
142C2×D13—41no—
143C2×D13—41no—
144C2×D13—84no—
145C2×D13AGL(1,ℤ/8)12yes—
146C4×C13—21no—
147C4×C13—21no—
148C4×C13—41no—
149C4×C13H(5,𝔽2)12yes—
150Dic13—21no—
151Dic13—21no—
152Dic13—21no—
153Dic13—41no—
154Dic13—42no—
155C2×#41—261no—
156C22×Q8—131no—
157C22×D4—131no—
158C2×SD16—132no—
159C2×SD16C2×D1312yescomplemented
160C2×D8—132no—
161C2×D8C2×D1312yes—
162C4⋊Q8—131no—
163#127C2×D1311yescharacteristic, complemented
164#124—131no—
165#124—131no—
166#124—131no—
167#124—261no—
168#124—261no—
169#124—261no—
170#124C2×D1311yescharacteristic
171#121—132no—
172#121—261no—
173C4×D4—132no—
174C4×D4—261no—
175C2×C22⋊C4—261no—
176C2×C22⋊C4—261no—
177C2×C42—131no—
178C4⋊C8—132no—
179#103—132no—
180#103—132no—
181#102—132no—
182#102—132no—
183C22⋊C8—132no—
184#97—131no—
185#97C2×D1311yescharacteristic, complemented
186C2×C13—81no—
187C2×C13—82no—
188C2×C13#53511yescharacteristic
189C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C13#57511yescharacteristic
191D13—22no—
192D13—81no—
193C24—261no—
194#41—524no—
195C2×Q8—131no—
196C2×Q8—261no—
197C2×Q8—261no—
198C2×Q8—522no—
199C2×Q8C22×D1311yescharacteristic
200C2×D4—21no—
201C2×D4—21no—
202C2×D4—131no—
203C2×D4—261no—
204C2×D4—262no—
205C2×D4—522no—
206C2×D4C22×D1311yescharacteristic
207C2×D4C22×D1312yes—
208C22×C4—131no—
209C22×C4—131no—
210C22×C4—131no—
211C22×C4—261no—
212C22×C4—262no—
213SD16—42no—
214SD16—522no—
215D8—42no—
216D8—522no—
217C2×C8—132no—
218C2×C8C22×D1312yes—
219C4⋊C4—132no—
220C4⋊C4—261no—
221C22⋊C4—21no—
222C22⋊C4—21no—
223C22⋊C4—261no—
224C22⋊C4—261no—
225C22⋊C4—261no—
226C22⋊C4—261no—
227C22⋊C4—262no—
228C22⋊C4—262no—
229C22⋊C4—261no—
230C22⋊C4—261no—
231C42—131no—
232C42—131no—
233C42—131no—
234C42C22×D1311yescharacteristic
235C13#321311yescharacteristic, complemented, Sylow
236C23—21no—
237C23—22no—
238C23—131no—
239C23—261no—
240C23—522no—
241C23—522no—
242C23—522no—
243Q8—22no—
244Q8—262no—
245Q8—522no—
246Q8—522no—
247D4—22no—
248D4—22no—
249D4—22no—
250D4—42no—
251D4—42no—
252D4—262no—
253D4—522no—
254D4—524no—
255C2×C4—21no—
256C2×C4—131no—
257C2×C4—131no—
258C2×C4—131no—
259C2×C4—262no—
260C2×C4—262no—
261C2×C4—261no—
262C2×C4—262no—
263C2×C4—521no—
264C2×C4—522no—
265C2×C4—524no—
266C2×C4D4×D1311yescharacteristic
267C2×C4D4×D1311yescharacteristic
268C2×C4C23×D1311yescharacteristic
269C8—22no—
270C8—262no—
271C22—42no—
272C22—41no—
273C22—42no—
274C22—41no—
275C22—41no—
276C22—42no—
277C22—132no—
278C22—261no—
279C22—261no—
280C22—521no—
281C22—521no—
282C22—521no—
283C22—1044no—
284C22C2×D4×D1311yescharacteristic
285C4—21no—
286C4—21no—
287C4—41no—
288C4—261no—
289C4—261no—
290C4—261no—
291C4—522no—
292C4—521no—
293C4#8825112yes—
294C2—81no—
295C2—82no—
296C2—262no—
297C2—1041no—
298C2#1171942011yescharacteristic
299C2D13×AGL(1,ℤ/8)11yescharacteristic
300C2#1171947811yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#496C2
socleC22×C13C22×D4
hypercenter#496D13
hypocenterC13#3213
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #11719421C2semidirect
2. D13×#124C2semidirect
3. C13×#496C2semidirect
4. #11718831C2semidirect
5. #11718826C2semidirect
6. #11718817C2semidirect
7. #11718814C2semidirect
8. #11718735C2semidirect
9. #11718716C2semidirect
10. #11718375C2semidirect
11. #11718366C2semidirect
15. C2×C13×SD16C22semidirect
17. C13×#127C22semidirect
25. D4×Dic13C22semidirect
26. C2×#6105C22semidirect
34. #88123C22semidirect
35. C13×#97C22semidirect
36. #88075C22semidirect
40. #88056C22semidirect
41. #88054C22semidirect
42. #88043C22semidirect
124. #496D13semidirect
159. C2×SD16C2×D13semidirect
163. #127C2×D13semidirect
185. #97C2×D13semidirect
235. C13#3213semidirect

Maximal subgroups

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

subgroupindex
#117194212
D13×#1242
C13×#4962
#117188312
#117188262
#117188172
#117188142
#117187352
#117187162
#117183752
#117183662
#321313