Finite Group Databasebeta

← #13126797

Subgroups — #13126797

Order 1664.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#546C211yesmaximal, characteristic, complemented
2#11719260C211yesmaximal, characteristic, complemented
3#11718899C211yesmaximal, characteristic, complemented
4#11718893C211yesmaximal, characteristic, complemented
5#11718878C211yesmaximal, characteristic, complemented
6C2×#88072C211yesmaximal, characteristic, complemented
7#11718718C211yesmaximal, characteristic, complemented
8#11718716C211yesmaximal, characteristic, complemented
9#11718709C211yesmaximal, characteristic, complemented
10#11718704C211yesmaximal, characteristic, complemented
11#11718700C211yesmaximal, characteristic, complemented
12#11718695C211yesmaximal, characteristic, complemented
13#11718675C211yesmaximal, characteristic, complemented
14#11718672C211yesmaximal, characteristic, complemented
15#11718669C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C22×D4×C13C2211yescharacteristic
18C2×#6129—21no—
19C13×#124C2211yescharacteristic
20C13×#123—21no—
21C13×C22⋊Q8C2211yescharacteristic
22C13×#121—21no—
23C13×#121C2211yescharacteristic
24C13×#120—21no—
25C4×D4×C13C2211yescharacteristic
26C4×D4×C13C2211yescharacteristic
27C2×C13×C22⋊C4—21no—
28C2×#6106C2211yescharacteristic, complemented
29C2×#6104C2211yescharacteristic
30C2×#6104C2211yescharacteristic
31#88184C2211yescharacteristic
32#88184C2211yescharacteristic, complemented
33C2×C4⋊Dic13C2211yescharacteristic
34C2×C4⋊Dic13C2211yescharacteristic, complemented
35C2×#6099C2211yescharacteristic, complemented
36C22×#1055C2211yescharacteristic
37#88151—21no—
38#88140—21no—
39#88140—21no—
40C4×D52C2211yescharacteristic, complemented
41#88123C2211yescharacteristic, complemented
42#88075C2211yescharacteristic, complemented
43#88075C2211yescharacteristic, complemented
44#88075C2211yescharacteristic, complemented
45#88072C2211yescharacteristic
46#88072C2211yescharacteristic
47#88072C2211yescharacteristic
48#88072C2211yescharacteristic
49#88072C2211yescharacteristic
50#88072C2211yescharacteristic
51C22⋊#1055C2211yescharacteristic
52C22⋊#1055C2211yescharacteristic, complemented
53#88049C2211yescharacteristic, complemented
54#88048C2211yescharacteristic, complemented
55#88048C2211yescharacteristic, complemented
56#88048C2211yescharacteristic, complemented
57C4⋊#1055C2211yescharacteristic, complemented
58#88043C2211yescharacteristic, complemented
59C24×C13—21no—
60C13×#41—22no—
61C13×#41—41no—
62C2×Q8×C13C2311yescharacteristic
63C2×D4×C13—22no—
64C2×D4×C13—21no—
65C2×D4×C13—21no—
66C2×D4×C13—21no—
67C2×D4×C13—41no—
68C2×D4×C13D411yescharacteristic
69C2×D4×C13C2311yescharacteristic
70C2×D4×C13C2311yescharacteristic
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13C2311yescharacteristic
74C22×C4×C13C2311yescharacteristic
75C2×C22⋊D13—21no—
76C2×C22⋊D13—21no—
77C22×Dic13—21no—
78C22×Dic13—21no—
79#6129—44no—
80C2×D52C2311yescharacteristic
81C2×C4×D13—21no—
82C2×Dic26—21no—
83C13×C4⋊C4—21no—
84C13×C4⋊C4D411yescharacteristic
85C13×C4⋊C4C2311yescharacteristic
86C13×C22⋊C4—21no—
87C13×C22⋊C4—21no—
88C13×C22⋊C4—21no—
89C13×C22⋊C4—21no—
90C13×C22⋊C4—21no—
91C13×C22⋊C4D411yescharacteristic
92C13×C22⋊C4D411yescharacteristic
93C42×C13C2311yescharacteristic
94#6106—41no—
95#6104—22no—
96#6104—41no—
97#6103—21no—
98#6103—21no—
99#6103—21no—
100C4⋊Dic13—21no—
101C4⋊Dic13—21no—
102C4⋊Dic13—21no—
103C4⋊Dic13C2311yescharacteristic
104C4⋊Dic13C2311yescharacteristic
105C4⋊Dic13C2311yescharacteristic
106#6099—41no—
107C2×#1055—41no—
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111C2×#1055C2311yescharacteristic
112#3306—131nomaximal, Sylow
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—42no—
116C23×C13—42no—
117C23×C13—81no—
118C23×C13C2×D411yescharacteristic
119C23×C13C2×D411yescharacteristic
120C22×D13—21no—
121Q8×C13—21no—
122Q8×C13—21no—
123D4×C13—22no—
124D4×C13—21no—
125D4×C13—21no—
126D4×C13—21no—
127D4×C13—42no—
128D4×C13—42no—
129D4×C13—81no—
130D4×C13#4112yescomplemented
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—42no—
138C2×C4×C13—81no—
139C2×C4×C13C2×D411yescharacteristic
140C2×C4×C13C2×D411yescharacteristic
141C2×C4×C13C2×D411yescharacteristic
142C2×C4×C13C2×D411yescharacteristic
143C2×C4×C13C2411yescharacteristic
144C22⋊D13—42no—
145C22⋊D13—42no—
146C2×Dic13—21no—
147C2×Dic13—21no—
148C2×Dic13—21no—
149C2×Dic13—42no—
150C2×Dic13—42no—
151D52—21no—
152D52—21no—
153C4×D13—42no—
154Dic26—42no—
155#1055—21no—
156#1055—21no—
157#1055—21no—
158#1055—21no—
159#547—131no—
160#546D1311yescharacteristic, complemented
161#489—131no—
162#483—131no—
163#481—131no—
164#476—131no—
165#469—131no—
166#465—131no—
167#463—131no—
168#449—131no—
169#447—131no—
170#442—131no—
171#435—131no—
172#417—131no—
173C2×#102—131no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—22no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—84no—
186C22×C13AGL(1,ℤ/8)12yes—
187C22×C13C22×D411yescharacteristic
188C2×D13—41no—
189C2×D13—41no—
190C2×D13—41no—
191C4×C13—21no—
192C4×C13—21no—
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—41no—
196C4×C13—41no—
197C4×C13C2×#4111yescharacteristic
198C4×C13H(5,𝔽2)11yescharacteristic
199Dic13—41no—
200Dic13—41no—
201Dic13—41no—
202C2×#41—261no—
203C2×#41C2×D1311yescharacteristic
204C22×D4C2×D1311yescharacteristic
205C2×SD16—131no—
206C2×D8—131no—
207C2×D8—131no—
208C2×M16—131no—
209C22×C8—131no—
210C4⋊Q8—131no—
211#124C2×D1311yescharacteristic
212#123—21no—
213#123—261no—
214#123—261no—
215C22⋊Q8—261no—
216C22⋊Q8C2×D1311yescharacteristic
217#121—21no—
218#121—131no—
219#121—131no—
220#121C2×D1311yescharacteristic
221#120—21no—
222C4×D4—131no—
223C4×D4C2×D1311yescharacteristic
224C4×D4C2×D1311yescharacteristic
225C2×C4⋊C4—131no—
226C2×C4⋊C4—131no—
227C2×C22⋊C4—21no—
228#106—131no—
229#106—131no—
230#106—131no—
231C4⋊C8—131no—
232#103—131no—
233#103—131no—
234#103—131no—
235#102—131no—
236#102—131no—
237#102—131no—
238#102—131no—
239#102—131no—
240#102—131no—
241#102—131no—
242C22⋊C8—131no—
243C22⋊C8—131no—
244#97—131no—
245C2×C13—22no—
246C2×C13—41no—
247C2×C13—42no—
248C2×C13—81no—
249C2×C13#54611yescharacteristic
250C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
251C2×C13#57711yescharacteristic
252D13—81no—
253C24—21no—
254#41—22no—
255#41—41no—
256#41—524no—
257C2×Q8—261no—
258C2×Q8C22×D1311yescharacteristic
259C2×D4—22no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—131no—
265C2×D4—261no—
266C2×D4—261no—
267C2×D4C22⋊D1311yescharacteristic
268C2×D4C22×D1311yescharacteristic
269C2×D4C22×D1311yescharacteristic
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—261no—
273C22×C4—261no—
274C22×C4—261no—
275C22×C4C22×D1311yescharacteristic
276C22×C4C22×D1311yescharacteristic
277SD16—521no—
278D8—262no—
279D8—521no—
280M16—521no—
281C2×C8—131no—
282C2×C8—131no—
283C2×C8—131no—
284C2×C8—131no—
285C2×C8—521no—
286C4⋊C4—21no—
287C4⋊C4—131no—
288C4⋊C4—131no—
289C4⋊C4—131no—
290C4⋊C4—261no—
291C4⋊C4—261no—
292C4⋊C4—261no—
293C4⋊C4C22⋊D1311yescharacteristic
294C4⋊C4C22×D1311yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—261no—
301C22⋊C4—261no—
302C22⋊C4—261no—
303C22⋊C4C22⋊D1311yescharacteristic
304C22⋊C4C22⋊D1311yescharacteristic
305C42C22×D1311yescharacteristic
306C13#330611yescharacteristic, complemented, Sylow
307C23—21no—
308C23—21no—
309C23—42no—
310C23—42no—
311C23—81no—
312C23—261no—
313C23C2×C22⋊D1311yescharacteristic
314C23C2×C22⋊D1311yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—522no—
318D4—22no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—42no—
323D4—42no—
324D4—81no—
325D4—261no—
326D4—261no—
327D4—522no—
328D4—522no—
329D4#612912yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—81no—
338C2×C4—261no—
339C2×C4—261no—
340C2×C4—261no—
341C2×C4—522no—
342C2×C4—522no—
343C2×C4—522no—
344C2×C4C2×C22⋊D1311yescharacteristic
345C2×C4C2×C22⋊D1311yescharacteristic
346C2×C4C2×C22⋊D1311yescharacteristic
347C2×C4C2×C22⋊D1311yescharacteristic
348C2×C4C23×D1311yescharacteristic
349C8—261no—
350C8—261no—
351C8—261no—
352C8—261no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—22no—
357C22—21no—
358C22—21no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—84no—
365C22—521no—
366C22—521no—
367C22—521no—
368C22#8820312yes—
369C22C22×C22⋊D1311yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—521no—
377C4—521no—
378C4—521no—
379C4C2×#612911yescharacteristic
380C4#8825111yescharacteristic
381C2—22no—
382C2—41no—
383C2—42no—
384C2—81no—
385C2—1041no—
386C2#1171951111yescharacteristic
387C2C2×#8820311yescharacteristic
388C2#1171954111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#546C2
socleC22×C13C22×D4
hypercenter#546D13
hypocenterC13#3306
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C13×#546C2semidirect
2. #11719260C2semidirect
3. #11718899C2semidirect
4. #11718893C2semidirect
5. #11718878C2semidirect
6. C2×#88072C2semidirect
7. #11718718C2semidirect
8. #11718716C2semidirect
9. #11718709C2semidirect
10. #11718704C2semidirect
11. #11718700C2semidirect
12. #11718695C2semidirect
13. #11718675C2semidirect
14. #11718672C2semidirect
15. #11718669C2semidirect
28. C2×#6106C22semidirect
32. #88184C22semidirect
34. C2×C4⋊Dic13C22semidirect
35. C2×#6099C22semidirect
40. C4×D52C22semidirect
41. #88123C22semidirect
42. #88075C22semidirect
43. #88075C22semidirect
44. #88075C22semidirect
52. C22⋊#1055C22semidirect
53. #88049C22semidirect
54. #88048C22semidirect
55. #88048C22semidirect
56. #88048C22semidirect
57. C4⋊#1055C22semidirect
58. #88043C22semidirect
130. D4×C13#41semidirect
160. #546D13semidirect
306. C13#3306semidirect
329. D4#6129semidirect

Maximal subgroups

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

subgroupindex
C13×#5462
#117192602
#117188992
#117188932
#117188782
C2×#880722
#117187182
#117187162
#117187092
#117187042
#117187002
#117186952
#117186752
#117186722
#117186692
#330613