Finite Group Databasebeta

← #13126801

Subgroups — #13126801

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
1#11719511C211yesmaximal, characteristic, complemented
2#11719316C211yesmaximal, characteristic, complemented
3C13×#447C211yesmaximal, characteristic, complemented
4C2×#88072C211yesmaximal, characteristic, complemented
5#11718820C211yesmaximal, characteristic, complemented
6#11718819C211yesmaximal, characteristic, complemented
7#11718814C211yesmaximal, characteristic, complemented
8#11718813C211yesmaximal, characteristic, complemented
9#11718702C211yesmaximal, characteristic, complemented
10#11718438C211yesmaximal, characteristic, complemented
11#11718432C211yesmaximal, characteristic, complemented
12#11718426C211yesmaximal, characteristic, complemented
13#11718422C211yesmaximal, characteristic, complemented
14#11718391C211yesmaximal, characteristic, complemented
15#11718382C211yesmaximal, characteristic, complemented
16C22×D4×C13C2211yescharacteristic
17C2×#6129—21no—
18C2×#6129C2211yescharacteristic
19C2×C13×D8C2211yescharacteristic
20C2×C13×D8C2211yescharacteristic
21C13×#121C2211yescharacteristic
22#88207—21no—
23C2×C22⋊Dic13—21no—
24#88193—21no—
25#88192C2211yescharacteristic
26#88192C2211yescharacteristic, complemented
27#88190C2211yescharacteristic
28#88189—21no—
29#88189—21no—
30D4×Dic13C2211yescharacteristic
31D4×Dic13C2211yescharacteristic, complemented
32C2×#6105C2211yescharacteristic, complemented
33C4×C22⋊D13C2211yescharacteristic
34C2×C4⋊Dic13C2211yescharacteristic
35#88178C2211yescharacteristic
36C22×#1055C2211yescharacteristic
37C2×#6094C2211yescharacteristic, complemented
38C4⋊C4×D13C2211yescharacteristic, complemented
39#88142C2211yescharacteristic, complemented
40#88137—21no—
41#88132—21no—
42C13×#102C2211yescharacteristic
43C13×#102C2211yescharacteristic
44C13×C22⋊C8C2211yescharacteristic
45#88072C2211yescharacteristic
46#88072C2211yescharacteristic
47#88072C2211yescharacteristic
48#88072C2211yescharacteristic
49#88072C2211yescharacteristic, complemented
50#88060C2211yescharacteristic, complemented
51#88057C2211yescharacteristic, complemented
52#88057C2211yescharacteristic, complemented
53#88056C2211yescharacteristic, complemented
54#88056C2211yescharacteristic, complemented
55#88055C2211yescharacteristic, complemented
56#88054C2211yescharacteristic, complemented
57#88050C2211yescharacteristic, complemented
58#88048C2211yescharacteristic, complemented
59C24×C13—21no—
60C2×D4×C13—22no—
61C2×D4×C13—21no—
62C2×D4×C13—21no—
63C2×D4×C13—41no—
64C2×D4×C13C2311yescharacteristic
65C2×D4×C13C2311yescharacteristic
66C2×D4×C13C2311yescharacteristic
67C22×C4×C13C2311yescharacteristic
68C2×C22⋊D13—21no—
69C2×C22⋊D13—21no—
70C2×C22⋊D13—21no—
71C2×C22⋊D13D411yescharacteristic
72C22×Dic13—21no—
73C22×Dic13—21no—
74C22×Dic13—21no—
75C22×Dic13—21no—
76#6129—22no—
77#6129—41no—
78#6129—44no—
79C2×C4×D13—21no—
80C2×C4×D13C2311yescharacteristic
81C2×Dic26—21no—
82C2×Dic26C2311yescharacteristic
83C13×D8—22no—
84C13×D8—41no—
85C2×C8×C13C2311yescharacteristic
86C2×C8×C13C2311yescharacteristic
87C13×C4⋊C4C2311yescharacteristic
88C13×C22⋊C4—21no—
89C22⋊Dic13—21no—
90C22⋊Dic13—21no—
91C22⋊Dic13—21no—
92C22⋊Dic13—21no—
93C22⋊Dic13—21no—
94C22⋊Dic13—21no—
95C22⋊Dic13—21no—
96C22⋊Dic13D411yescharacteristic
97#6105—41no—
98#6103D411yescharacteristic
99C4⋊Dic13—21no—
100C4⋊Dic13C2311yescharacteristic
101C4⋊Dic13C2311yescharacteristic
102C4⋊Dic13C2311yescharacteristic
103#6101—21no—
104#6101—21no—
105#6101—21no—
106#6101D411yescharacteristic
107C4×Dic13C2311yescharacteristic
108C2×#1055—41no—
109C2×#1055C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111#6094—41no—
112#3306—131nomaximal, Sylow
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—42no—
117C23×C13—42no—
118C23×C13—81no—
119C23×C13C2×D411yescharacteristic
120C22×D13C2×D411yescharacteristic
121D4×C13—21no—
122D4×C13—21no—
123D4×C13—21no—
124D4×C13—21no—
125D4×C13—21no—
126D4×C13—42no—
127D4×C13—42no—
128D4×C13#4112yescomplemented
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13C2×D411yescharacteristic
133C2×C4×C13C2411yescharacteristic
134C22⋊D13—22no—
135C22⋊D13—42no—
136C22⋊D13—42no—
137C22⋊D13—81no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—42no—
143C2×Dic13—42no—
144C2×Dic13—42no—
145C2×Dic13—81no—
146C2×Dic13C2×D411yescharacteristic
147C2×Dic13C2×D411yescharacteristic
148C2×Dic13C2×D411yescharacteristic
149C4×D13—21no—
150C4×D13—21no—
151C4×D13—42no—
152Dic26—21no—
153Dic26—21no—
154Dic26—42no—
155C8×C13—21no—
156C8×C13—21no—
157#1055—21no—
158#1055—21no—
159#547—131no—
160#546—131no—
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#447D1311yescharacteristic, complemented
170#442—131no—
171#435—131no—
172#417—131no—
173C2×#102—131no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—22no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
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—21no—
189C2×D13—21no—
190C2×D13—21no—
191C4×C13—21no—
192C4×C13—41no—
193C4×C13C2×#4111yescharacteristic
194C4×C13H(5,𝔽2)11yescharacteristic
195Dic13—21no—
196Dic13—21no—
197Dic13—21no—
198Dic13—41no—
199Dic13—41no—
200Dic13—41no—
201Dic13—41no—
202C2×#41—131no—
203C2×#41—261no—
204C22×D4C2×D1311yescharacteristic
205C2×SD16—131no—
206C2×D8C2×D1311yescharacteristic
207C2×D8C2×D1311yescharacteristic
208C2×M16—131no—
209C22×C8—131no—
210C4⋊Q8—131no—
211#124—131no—
212#123—261no—
213#123—261no—
214#123—261no—
215C22⋊Q8—131no—
216C22⋊Q8—261no—
217#121—131no—
218#121—131no—
219#121—261no—
220#121C2×D1311yescharacteristic
221#120—261no—
222C4×D4—131no—
223C4×D4—131no—
224C4×D4—131no—
225C2×C4⋊C4—131no—
226C2×C4⋊C4—131no—
227C2×C22⋊C4—261no—
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#102C2×D1311yescharacteristic
241#102C2×D1311yescharacteristic
242C22⋊C8—131no—
243C22⋊C8C2×D1311yescharacteristic
244#97—131no—
245C2×C13—22no—
246C2×C13—42no—
247C2×C13—81no—
248C2×C13—81no—
249C2×C13#54611yescharacteristic
250C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
251C2×C13#57711yescharacteristic
252D13—41no—
253C24—21no—
254#41—262no—
255#41—521no—
256#41—524no—
257C2×Q8—131no—
258C2×Q8—261no—
259C2×D4—22no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—41no—
263C2×D4—131no—
264C2×D4—261no—
265C2×D4—261no—
266C2×D4—261no—
267C2×D4C22×D1311yescharacteristic
268C2×D4C22×D1311yescharacteristic
269C2×D4C22×D1311yescharacteristic
270C22×C4—131no—
271C22×C4—261no—
272C22×C4—261no—
273C22×C4—261no—
274C22×C4—261no—
275C22×C4—261no—
276C22×C4C22×D1311yescharacteristic
277SD16—521no—
278D8—22no—
279D8—41no—
280M16—521no—
281C2×C8—131no—
282C2×C8—131no—
283C2×C8—521no—
284C2×C8C22×D1311yescharacteristic
285C2×C8C22×D1311yescharacteristic
286C4⋊C4—131no—
287C4⋊C4—131no—
288C4⋊C4—131no—
289C4⋊C4—131no—
290C4⋊C4—261no—
291C4⋊C4—261no—
292C4⋊C4—261no—
293C4⋊C4—261no—
294C4⋊C4C22×D1311yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—131no—
297C22⋊C4—131no—
298C22⋊C4—261no—
299C22⋊C4—261no—
300C22⋊C4—261no—
301C22⋊C4—261no—
302C22⋊C4—261no—
303C22⋊C4—261no—
304C22⋊C4—261no—
305C42—131no—
306C13#330611yescharacteristic, complemented, Sylow
307C23—21no—
308C23—21no—
309C23—21no—
310C23—42no—
311C23—42no—
312C23—81no—
313C23—131no—
314C23D4×D1311yescharacteristic
315Q8—261no—
316Q8—261no—
317Q8—522no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—21no—
323D4—42no—
324D4—42no—
325D4—262no—
326D4—522no—
327D4—522no—
328D4—1041no—
329D4#612912yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—131no—
334C2×C4—131no—
335C2×C4—131no—
336C2×C4—261no—
337C2×C4—261no—
338C2×C4—261no—
339C2×C4—261no—
340C2×C4—261no—
341C2×C4—261no—
342C2×C4—522no—
343C2×C4—522no—
344C2×C4—522no—
345C2×C4—522no—
346C2×C4—1041no—
347C2×C4D4×D1311yescharacteristic
348C2×C4C23×D1311yescharacteristic
349C8—21no—
350C8—21no—
351C8—261no—
352C8—261no—
353C22—21no—
354C22—21no—
355C22—22no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—84no—
365C22—261no—
366C22—261no—
367C22—261no—
368C22#8816512yes—
369C22C2×D4×D1311yescharacteristic
370C4—21no—
371C4—41no—
372C4—261no—
373C4—261no—
374C4—261no—
375C4—521no—
376C4—521no—
377C4—521no—
378C4—521no—
379C4C2×#612911yescharacteristic
380C4#8825111yescharacteristic
381C2—22no—
382C2—42no—
383C2—81no—
384C2—81no—
385C2—521no—
386C2#1171929611yescharacteristic
387C2C2×#8816511yescharacteristic
388C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#447C2
socleC22×C13C22×D4
hypercenter#447D13
hypocenterC13#3306
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #11719511C2semidirect
2. #11719316C2semidirect
3. C13×#447C2semidirect
4. C2×#88072C2semidirect
5. #11718820C2semidirect
6. #11718819C2semidirect
7. #11718814C2semidirect
8. #11718813C2semidirect
9. #11718702C2semidirect
10. #11718438C2semidirect
11. #11718432C2semidirect
12. #11718426C2semidirect
13. #11718422C2semidirect
14. #11718391C2semidirect
15. #11718382C2semidirect
26. #88192C22semidirect
31. D4×Dic13C22semidirect
32. C2×#6105C22semidirect
37. C2×#6094C22semidirect
38. C4⋊C4×D13C22semidirect
39. #88142C22semidirect
49. #88072C22semidirect
50. #88060C22semidirect
51. #88057C22semidirect
52. #88057C22semidirect
53. #88056C22semidirect
54. #88056C22semidirect
55. #88055C22semidirect
56. #88054C22semidirect
57. #88050C22semidirect
58. #88048C22semidirect
128. D4×C13#41semidirect
169. #447D13semidirect
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
#117195112
#117193162
C13×#4472
C2×#880722
#117188202
#117188192
#117188142
#117188132
#117187022
#117184382
#117184322
#117184262
#117184222
#117183912
#117183822
#330613