Finite Group Databasebeta

← #13124783

Subgroups — #13124783

Order 1664.

410 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13×C22⋊Q8C211yesmaximal, characteristic
2D13×#117C211yesmaximal, characteristic
3C13×#485C211yesmaximal, characteristic, complemented
4#11718706C211yesmaximal, characteristic, complemented
5#11718657C211yesmaximal, characteristic, complemented
6#11718545C211yesmaximal, characteristic, complemented
7#11718542C211yesmaximal, characteristic, complemented
8#11718523C211yesmaximal, characteristic, complemented
9#11718522C211yesmaximal, characteristic, complemented
10#11718470C211yesmaximal, characteristic, complemented
11#11718466C211yesmaximal, characteristic, complemented
12#11718463C211yesmaximal, characteristic, complemented
13#11718463C211yesmaximal, characteristic, complemented
14#11718387C211yesmaximal, characteristic
15#11718384C211yesmaximal, characteristic, complemented
16C2×Q8×D13C2211yescharacteristic
17C22×C4×D13C2211yescharacteristic
18C13×C22⋊Q8C2211yescharacteristic
19C13×#117C2211yescharacteristic
20#88200C2211yescharacteristic
21#88180C2211yescharacteristic
22#88178C2211yescharacteristic
23C2×#6094C2211yescharacteristic
24C2×#6094C2211yescharacteristic
25#88151C2211yescharacteristic
26#88150—21no—
27#88146C2211yescharacteristic
28#88146C2211yescharacteristic
29C4⋊C4×D13—21no—
30C4⋊C4×D13C2211yescharacteristic
31C4⋊C4×D13C2211yescharacteristic
32C4⋊C4×D13C2211yescharacteristic
33C22⋊C4×D13—21no—
34C22⋊C4×D13—21no—
35#88132—21no—
36#88131—21no—
37#88126—21no—
38C42×D13—21no—
39C13×#107C2211yescharacteristic, complemented
40C13×#106C2211yescharacteristic, complemented
41C13×#103C2211yescharacteristic, complemented
42C13×#103C2211yescharacteristic, complemented
43C13×C22⋊C8C2211yescharacteristic
44#88075C2211yescharacteristic, complemented
45#88075C2211yescharacteristic, complemented
46C22⋊#1055C2211yescharacteristic
47#88060C2211yescharacteristic
48#88060C2211yescharacteristic
49#88058C2211yescharacteristic, complemented
50#88057C2211yescharacteristic, complemented
51#88056C2211yescharacteristic, complemented
52#88056C2211yescharacteristic, complemented
53#88050C2211yescharacteristic, complemented
54#88050C2211yescharacteristic, complemented
55#88048C2211yescharacteristic, complemented
56#88048C2211yescharacteristic, complemented
57#88047C2211yescharacteristic, complemented
58#88047C2211yescharacteristic, complemented
59C23×D13D411yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C22×Dic13D411yescharacteristic
63Q8×D13—22no—
64Q8×D13—22no—
65C2×C4×D13—22no—
66C2×C4×D13—22no—
67C2×C4×D13—21no—
68C2×C4×D13—21no—
69C2×C4×D13—21no—
70C2×C4×D13—21no—
71C2×C4×D13D411yescharacteristic
72C2×C4×D13D411yescharacteristic
73C2×C4×D13C2311yescharacteristic
74C2×C4×D13C2311yescharacteristic
75C2×Dic26—21no—
76C2×Dic26C2311yescharacteristic
77C2×C8×C13C2311yescharacteristic
78C2×C8×C13C2311yescharacteristic
79C13×C4⋊C4—21no—
80C13×C4⋊C4C2311yescharacteristic
81C13×C4⋊C4C2311yescharacteristic
82C13×C4⋊C4C2311yescharacteristic
83C13×C22⋊C4—21no—
84C13×C22⋊C4—21no—
85C42×C13—21no—
86C22⋊Dic13—21no—
87C22⋊Dic13—21no—
88#6103—21no—
89#6103—21no—
90#6103—21no—
91#6103—21no—
92C4⋊Dic13—21no—
93C4⋊Dic13C2311yescharacteristic
94C4⋊Dic13C2311yescharacteristic
95C4⋊Dic13C2311yescharacteristic
96#6101—21no—
97#6101—21no—
98#6101—21no—
99#6101—21no—
100#6101—21no—
101C4×Dic13—21no—
102C4×Dic13—21no—
103C4×Dic13—21no—
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106#6094—22no—
107#6094—22no—
108#3095—131nomaximal, Sylow
109C23×C13C2×D411yescharacteristic
110C22×D13—22no—
111C22×D13—22no—
112C22×D13—41no—
113C22×D13C2×D411yescharacteristic
114C22×D13C2×D411yescharacteristic
115Q8×C13—21no—
116Q8×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2411yescharacteristic
125C2×Dic13—22no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13C2×D411yescharacteristic
131C2×Dic13C2×D411yescharacteristic
132C4×D13—22no—
133C4×D13—21no—
134C4×D13—21no—
135C4×D13—22no—
136C4×D13—42no—
137C4×D13—42no—
138C4×D13—42no—
139C4×D13—42no—
140C4×D13#4112yes—
141C4×D13#4112yes—
142Dic26—21no—
143Dic26—21no—
144Dic26—42no—
145C8×C13—21no—
146C8×C13—21no—
147#1055—21no—
148#1055—21no—
149C2×C22⋊Q8—131no—
150C2×#117—131no—
151#485—131no—
152#485—131no—
153#485—131no—
154#485D1311yescharacteristic, complemented
155#484—131no—
156#484—131no—
157#483—131no—
158#483—131no—
159#428—131no—
160#428—131no—
161#419—131no—
162#419—131no—
163#407—131no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13C22×D411yescharacteristic
168C2×D13—21no—
169C2×D13—21no—
170C2×D13—21no—
171C2×D13—21no—
172C2×D13—44no—
173C2×D13#12312yes—
174C2×D13#13712yes—
175C4×C13—21no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13—41no—
180C4×C13C2×#4111yescharacteristic
181C4×C13C2×#4111yescharacteristic
182Dic13—21no—
183Dic13—41no—
184Dic13—41no—
185Dic13—41no—
186Dic13—41no—
187Dic13#12312yes—
188C22×Q8—131no—
189C23×C4—131no—
190C2×M16—131no—
191C2×M16—131no—
192C22⋊Q8—131no—
193C22⋊Q8—131no—
194C22⋊Q8—131no—
195C22⋊Q8—261no—
196C22⋊Q8—261no—
197C22⋊Q8C2×D1311yescharacteristic
198#117—131no—
199#117—131no—
200#117—131no—
201#117—261no—
202#117—261no—
203#117C2×D1311yescharacteristic
204C2×C4⋊C4—131no—
205C2×C4⋊C4—131no—
206C2×C4⋊C4—131no—
207C2×C4⋊C4—261no—
208C2×C22⋊C4—261no—
209C2×C22⋊C4—261no—
210C2×C42—261no—
211#107—131no—
212#107—131no—
213#107—131no—
214#107C2×D1311yescharacteristic, complemented
215#106—131no—
216#106—131no—
217#106—131no—
218#106C2×D1311yescharacteristic, complemented
219#103—131no—
220#103—131no—
221#103—131no—
222#103—131no—
223#103—131no—
224#103—131no—
225#103C2×D1311yescharacteristic, complemented
226#103C2×D1311yescharacteristic, complemented
227C22⋊C8—131no—
228C22⋊C8—131no—
229C22⋊C8—131no—
230C22⋊C8C2×D1311yescharacteristic
231C2×C13—41no—
232C2×C13C2×#12311yescharacteristic
233C2×C13C2×#13711yescharacteristic
234C2×C13#57511yescharacteristic
235D13—22no—
236D13—22no—
237C24—131no—
238C2×Q8—131no—
239C2×Q8—261no—
240C2×Q8—262no—
241C2×Q8—262no—
242C2×Q8C22×D1311yescharacteristic
243C22×C4—131no—
244C22×C4—131no—
245C22×C4—131no—
246C22×C4—131no—
247C22×C4—131no—
248C22×C4—262no—
249C22×C4—262no—
250C22×C4—261no—
251C22×C4—261no—
252C22×C4—261no—
253C22×C4—261no—
254C22×C4C22×D1311yescharacteristic
255M16—262no—
256M16—262no—
257C2×C8—131no—
258C2×C8—131no—
259C2×C8C22×D1311yescharacteristic
260C2×C8C22×D1311yescharacteristic
261C4⋊C4—21no—
262C4⋊C4—131no—
263C4⋊C4—131no—
264C4⋊C4—131no—
265C4⋊C4—261no—
266C4⋊C4—261no—
267C4⋊C4—261no—
268C4⋊C4—261no—
269C4⋊C4—261no—
270C4⋊C4—261no—
271C4⋊C4C22×D1311yescharacteristic
272C4⋊C4C22×D1311yescharacteristic
273C4⋊C4C22×D1311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—261no—
277C22⋊C4—261no—
278C22⋊C4—261no—
279C22⋊C4—261no—
280C22⋊C4—261no—
281C22⋊C4—261no—
282C42—21no—
283C42—261no—
284C42—261no—
285C42—261no—
286C13#309511yescharacteristic, complemented, Sylow
287C23—131no—
288C23—131no—
289C23—262no—
290C23—262no—
291C23—521no—
292C23D4×D1311yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—261no—
296Q8—261no—
297Q8—522no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—131no—
305C2×C4—132no—
306C2×C4—132no—
307C2×C4—131no—
308C2×C4—262no—
309C2×C4—262no—
310C2×C4—262no—
311C2×C4—261no—
312C2×C4—261no—
313C2×C4—261no—
314C2×C4—261no—
315C2×C4—261no—
316C2×C4—261no—
317C2×C4—522no—
318C2×C4—522no—
319C2×C4—522no—
320C2×C4—522no—
321C2×C4D4×D1311yescharacteristic
322C2×C4C23×D1311yescharacteristic
323C8—21no—
324C8—21no—
325C8—261no—
326C8—261no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—132no—
331C22—132no—
332C22—261no—
333C22—261no—
334C22—261no—
335C22—261no—
336C22—524no—
337C22C2×D4×D1311yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—132no—
344C4—261no—
345C4—521no—
346C4—521no—
347C4—521no—
348C4—521no—
349C4#41×D1311yescharacteristic
350C4#41×D1311yescharacteristic
351C2—41no—
352C2—262no—
353C2—262no—
354C2D13×#12311yescharacteristic
355C2#1171947311yescharacteristic
356C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#485C2
socleC22×C13C22×D4
prime radicalC23×D13D4
hypercenter#485D13
hypocenterC13#3095
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. C13×#485C2semidirect
4. #11718706C2semidirect
5. #11718657C2semidirect
6. #11718545C2semidirect
7. #11718542C2semidirect
8. #11718523C2semidirect
9. #11718522C2semidirect
10. #11718470C2semidirect
11. #11718466C2semidirect
12. #11718463C2semidirect
13. #11718463C2semidirect
15. #11718384C2semidirect
39. C13×#107C22semidirect
40. C13×#106C22semidirect
41. C13×#103C22semidirect
42. C13×#103C22semidirect
44. #88075C22semidirect
45. #88075C22semidirect
49. #88058C22semidirect
50. #88057C22semidirect
51. #88056C22semidirect
52. #88056C22semidirect
53. #88050C22semidirect
54. #88050C22semidirect
55. #88048C22semidirect
56. #88048C22semidirect
57. #88047C22semidirect
58. #88047C22semidirect
154. #485D13semidirect
214. #107C2×D13semidirect
218. #106C2×D13semidirect
225. #103C2×D13semidirect
226. #103C2×D13semidirect
286. C13#3095semidirect

Maximal subgroups

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

subgroupindex
D13×C22⋊Q82
D13×#1172
C13×#4852
#117187062
#117186572
#117185452
#117185422
#117185232
#117185222
#117184702
#117184662
#117184632
#117183872
#117183842
#309513