Finite Group Databasebeta

← #13125637

Subgroups — #13125637

Order 1664.

462 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13×C22⋊Q8C211yesmaximal, characteristic, complemented
2D13×#121C211yesmaximal, characteristic
3C13×#468C211yesmaximal, characteristic, complemented
4#11718831C211yesmaximal, characteristic, complemented
5#11718830C211yesmaximal, characteristic, complemented
6#11718795C211yesmaximal, characteristic, complemented
7#11718787C211yesmaximal, characteristic, complemented
8#11718710C211yesmaximal, characteristic, complemented
9#11718703C211yesmaximal, characteristic, complemented
10#11718545C211yesmaximal, characteristic, complemented
11#11718543C211yesmaximal, characteristic, complemented
12#11718470C211yesmaximal, characteristic, complemented
13#11718467C211yesmaximal, characteristic, complemented
14#11718437C211yesmaximal, characteristic, complemented
15#11718435C211yesmaximal, characteristic, complemented
16C2×Q8×D13C2211yescharacteristic, complemented
17C2×D4×D13—21no—
18C2×D4×D13C2211yescharacteristic
19C22×C4×D13C2211yescharacteristic
20C2×C13×SD16C2211yescharacteristic, complemented
21C2×C13×M16C2211yescharacteristic, complemented
22C13×C22⋊Q8C2211yescharacteristic, complemented
23C13×#121C2211yescharacteristic
24#88200C2211yescharacteristic
25C2×#6106C2211yescharacteristic, complemented
26#88193—21no—
27#88192C2211yescharacteristic
28C2×#6105C2211yescharacteristic, complemented
29#88184C2211yescharacteristic
30#88178C2211yescharacteristic, complemented
31C2×#6099C2211yescharacteristic, complemented
32C2×#6095C2211yescharacteristic, complemented
33#88151C2211yescharacteristic
34#88150—21no—
35#88149C2211yescharacteristic
36C4⋊C4×D13—21no—
37C4⋊C4×D13C2211yescharacteristic
38C4⋊C4×D13C2211yescharacteristic, complemented
39#88138—21no—
40C22⋊C4×D13—21no—
41C22⋊C4×D13—21no—
42#88132—21no—
43C13×#107C2211yescharacteristic, complemented
44C13×#103C2211yescharacteristic, complemented
45C13×#102C2211yescharacteristic, complemented
46#88075C2211yescharacteristic, complemented
47#88072C2211yescharacteristic, complemented
48#88061C2211yescharacteristic, complemented
49#88060C2211yescharacteristic
50#88060C2211yescharacteristic
51#88060C2211yescharacteristic, complemented
52#88060C2211yescharacteristic, complemented
53#88058C2211yescharacteristic, complemented
54#88056C2211yescharacteristic, complemented
55#88050C2211yescharacteristic, complemented
56#88049C2211yescharacteristic, complemented
57#88047C2211yescharacteristic, complemented
58#88047C2211yescharacteristic, complemented
59C23×D13—21no—
60C23×D13D411yescharacteristic
61C2×Q8×C13C2311yescharacteristic
62C2×D4×C13—21no—
63C2×D4×C13C2311yescharacteristic
64C22×C4×C13C2311yescharacteristic
65C2×C22⋊D13—21no—
66C2×C22⋊D13—21no—
67C2×C22⋊D13—21no—
68C22×Dic13D411yescharacteristic
69Q8×D13—41no—
70Q8×D13—41no—
71D4×D13—41no—
72D4×D13—41no—
73D4×D13—44no—
74C2×D52—21no—
75C2×D52C2311yescharacteristic
76C2×C4×D13—21no—
77C2×C4×D13—21no—
78C2×C4×D13—21no—
79C2×C4×D13—41no—
80C2×C4×D13—41no—
81C2×C4×D13D411yescharacteristic
82C2×C4×D13D411yescharacteristic
83C2×C4×D13C2311yescharacteristic
84C2×C4×D13C2311yescharacteristic
85C2×Dic26—21no—
86C2×Dic26C2311yescharacteristic
87C13×SD16—41no—
88C13×M16—41no—
89C2×C8×C13C2311yescharacteristic
90C2×C8×C13C2311yescharacteristic
91C13×C4⋊C4—21no—
92C13×C4⋊C4C2311yescharacteristic
93C13×C4⋊C4C2311yescharacteristic
94C13×C22⋊C4—21no—
95C13×C22⋊C4—21no—
96C22⋊Dic13—21no—
97C22⋊Dic13—21no—
98#6106—41no—
99#6105—41no—
100#6103—21no—
101#6103—21no—
102#6103—21no—
103#6103—21no—
104C4⋊Dic13—21no—
105C4⋊Dic13C2311yescharacteristic
106C4⋊Dic13C2311yescharacteristic
107#6101—21no—
108#6101—21no—
109#6101—21no—
110#6101—21no—
111#6099—41no—
112C2×#1055C2311yescharacteristic
113C2×#1055C2311yescharacteristic
114#6095—41no—
115#3193—131nomaximal, Sylow
116C23×C13—21no—
117C23×C13C2×D411yescharacteristic
118C22×D13—22no—
119C22×D13—22no—
120C22×D13—21no—
121C22×D13—41no—
122C22×D13—42no—
123C22×D13—42no—
124C22×D13—42no—
125C22×D13C2×D411yescharacteristic
126C22×D13C2×D411yescharacteristic
127Q8×C13—21no—
128Q8×C13—21no—
129D4×C13—21no—
130D4×C13—21no—
131D4×C13—42no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13C2×D411yescharacteristic
138C2×C4×C13C2411yescharacteristic
139C22⋊D13—42no—
140C22⋊D13—42no—
141C22⋊D13—42no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—41no—
146C2×Dic13C2×D411yescharacteristic
147C2×Dic13C2×D411yescharacteristic
148D52—21no—
149D52—21no—
150D52—42no—
151C4×D13—21no—
152C4×D13—21no—
153C4×D13—21no—
154C4×D13—21no—
155C4×D13—41no—
156C4×D13—41no—
157C4×D13—42no—
158C4×D13—42no—
159C4×D13—42no—
160Dic26—21no—
161Dic26—21no—
162Dic26—42no—
163C8×C13—21no—
164C8×C13—21no—
165#1055—21no—
166#1055—21no—
167C2×C22⋊Q8—131no—
168C2×#121—131no—
169#484—131no—
170#484—131no—
171#480—131no—
172#480—131no—
173#468—131no—
174#468—131no—
175#468—131no—
176#468D1311yescharacteristic, complemented
177#450—131no—
178#450—131no—
179#448—131no—
180#448—131no—
181#407—131no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—41no—
186C22×C13—41no—
187C22×C13—41no—
188C22×C13C22×D411yescharacteristic
189C2×D13—21no—
190C2×D13—21no—
191C2×D13—21no—
192C2×D13—21no—
193C2×D13—44no—
194C2×D13—41no—
195C2×D13—41no—
196C2×D13—41no—
197C2×D13—84no—
198C2×D13AGL(1,ℤ/8)12yes—
199C2×D13#13712yes—
200C4×C13—21no—
201C4×C13—41no—
202C4×C13—41no—
203C4×C13—41no—
204C4×C13H(5,𝔽2)11yescharacteristic
205C4×C13H(5,𝔽2)11yescharacteristic
206Dic13—21no—
207Dic13—21no—
208Dic13—41no—
209Dic13—41no—
210Dic13—41no—
211C22×Q8—131no—
212C22×D4—131no—
213C22×D4—261no—
214C23×C4—131no—
215C2×SD16—131no—
216C2×SD16—131no—
217C2×SD16—131no—
218C2×SD16C2×D1311yescharacteristic, complemented
219C2×M16—131no—
220C2×M16C2×D1311yescharacteristic, complemented
221C22⋊Q8—131no—
222C22⋊Q8—131no—
223C22⋊Q8—131no—
224C22⋊Q8—261no—
225C22⋊Q8—261no—
226C22⋊Q8C2×D1311yescharacteristic, complemented
227#121—131no—
228#121—131no—
229#121—131no—
230#121—261no—
231#121—261no—
232#121C2×D1311yescharacteristic
233C2×C4⋊C4—131no—
234C2×C4⋊C4—131no—
235C2×C4⋊C4—261no—
236C2×C22⋊C4—261no—
237C2×C22⋊C4—261no—
238#107—131no—
239#107—131no—
240#107—131no—
241#107C2×D1311yescharacteristic, complemented
242#103—131no—
243#103—131no—
244#103—131no—
245#103C2×D1311yescharacteristic, complemented
246#102—131no—
247#102—131no—
248#102—131no—
249#102C2×D1311yescharacteristic, complemented
250C22⋊C8—131no—
251C22⋊C8—131no—
252C22⋊C8—131no—
253C22⋊C8—131no—
254C2×C13—41no—
255C2×C13—81no—
256C2×C13#53411yescharacteristic
257C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
258C2×C13C2×#13711yescharacteristic
259D13—22no—
260D13—22no—
261D13—81no—
262C24—131no—
263C24—261no—
264C2×Q8—131no—
265C2×Q8—261no—
266C2×Q8—521no—
267C2×Q8—521no—
268C2×Q8C22×D1311yescharacteristic
269C2×D4—21no—
270C2×D4—131no—
271C2×D4—261no—
272C2×D4—261no—
273C2×D4—261no—
274C2×D4—261no—
275C2×D4—521no—
276C2×D4—521no—
277C2×D4—524no—
278C2×D4C22×D1311yescharacteristic
279C22×C4—131no—
280C22×C4—131no—
281C22×C4—131no—
282C22×C4—131no—
283C22×C4—131no—
284C22×C4—261no—
285C22×C4—261no—
286C22×C4—261no—
287C22×C4—521no—
288C22×C4—521no—
289C22×C4C22×D1311yescharacteristic
290SD16—41no—
291SD16—521no—
292SD16—521no—
293SD16—521no—
294M16—41no—
295M16—521no—
296C2×C8—131no—
297C2×C8—131no—
298C2×C8C22×D1311yescharacteristic
299C2×C8C22×D1311yescharacteristic
300C4⋊C4—21no—
301C4⋊C4—131no—
302C4⋊C4—131no—
303C4⋊C4—261no—
304C4⋊C4—261no—
305C4⋊C4—261no—
306C4⋊C4—261no—
307C4⋊C4—261no—
308C4⋊C4C22×D1311yescharacteristic
309C4⋊C4C22×D1311yescharacteristic
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—261no—
313C22⋊C4—261no—
314C22⋊C4—261no—
315C22⋊C4—261no—
316C22⋊C4—261no—
317C22⋊C4—261no—
318C13#319311yescharacteristic, complemented, Sylow
319C23—21no—
320C23—131no—
321C23—131no—
322C23—262no—
323C23—262no—
324C23—261no—
325C23—521no—
326C23—522no—
327C23—522no—
328C23—522no—
329C23D4×D1311yescharacteristic
330Q8—21no—
331Q8—21no—
332Q8—261no—
333Q8—261no—
334Q8—522no—
335D4—21no—
336D4—21no—
337D4—42no—
338D4—261no—
339D4—261no—
340D4—522no—
341D4—522no—
342D4—522no—
343D4—522no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—131no—
350C2×C4—131no—
351C2×C4—261no—
352C2×C4—261no—
353C2×C4—261no—
354C2×C4—261no—
355C2×C4—261no—
356C2×C4—261no—
357C2×C4—261no—
358C2×C4—521no—
359C2×C4—521no—
360C2×C4—522no—
361C2×C4—522no—
362C2×C4—522no—
363C2×C4—521no—
364C2×C4D4×D1311yescharacteristic
365C2×C4C23×D1311yescharacteristic
366C8—21no—
367C8—21no—
368C8—261no—
369C8—261no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—132no—
377C22—132no—
378C22—261no—
379C22—261no—
380C22—261no—
381C22—261no—
382C22—524no—
383C22—521no—
384C22—521no—
385C22—521no—
386C22—1044no—
387C22C2×D4×D1311yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—261no—
393C4—261no—
394C4—521no—
395C4—521no—
396C4—521no—
397C4#8825111yescharacteristic
398C4#8825611yescharacteristic
399C2—41no—
400C2—81no—
401C2—262no—
402C2—262no—
403C2—1041no—
404C2#1171931011yescharacteristic
405C2D13×AGL(1,ℤ/8)11yescharacteristic
406C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#468C2
socleC22×C13C22×D4
prime radicalD13×#121C2
hypercenter#468D13
hypocenterC13#3193
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. D13×C22⋊Q8C2semidirect
3. C13×#468C2semidirect
4. #11718831C2semidirect
5. #11718830C2semidirect
6. #11718795C2semidirect
7. #11718787C2semidirect
8. #11718710C2semidirect
9. #11718703C2semidirect
10. #11718545C2semidirect
11. #11718543C2semidirect
12. #11718470C2semidirect
13. #11718467C2semidirect
14. #11718437C2semidirect
15. #11718435C2semidirect
16. C2×Q8×D13C22semidirect
20. C2×C13×SD16C22semidirect
21. C2×C13×M16C22semidirect
22. C13×C22⋊Q8C22semidirect
25. C2×#6106C22semidirect
28. C2×#6105C22semidirect
30. #88178C22semidirect
31. C2×#6099C22semidirect
32. C2×#6095C22semidirect
38. C4⋊C4×D13C22semidirect
43. C13×#107C22semidirect
44. C13×#103C22semidirect
45. C13×#102C22semidirect
46. #88075C22semidirect
47. #88072C22semidirect
48. #88061C22semidirect
51. #88060C22semidirect
52. #88060C22semidirect
53. #88058C22semidirect
54. #88056C22semidirect
55. #88050C22semidirect
56. #88049C22semidirect
57. #88047C22semidirect
58. #88047C22semidirect
176. #468D13semidirect
218. C2×SD16C2×D13semidirect
220. C2×M16C2×D13semidirect
226. C22⋊Q8C2×D13semidirect
241. #107C2×D13semidirect
245. #103C2×D13semidirect
249. #102C2×D13semidirect
318. C13#3193semidirect

Maximal subgroups

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

subgroupindex
D13×C22⋊Q82
D13×#1212
C13×#4682
#117188312
#117188302
#117187952
#117187872
#117187102
#117187032
#117185452
#117185432
#117184702
#117184672
#117184372
#117184352
#319313