Finite Group Databasebeta

← #13126803

Subgroups — #13126803

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#11719335C211yesmaximal, characteristic, complemented
2#11719316C211yesmaximal, characteristic, complemented
3C13×#465C211yesmaximal, characteristic, complemented
4#11718833C211yesmaximal, characteristic, complemented
5#11718826C211yesmaximal, characteristic, complemented
6C2×#88061C211yesmaximal, characteristic, complemented
7#11718772C211yesmaximal, characteristic, complemented
8#11718704C211yesmaximal, characteristic, complemented
9#11718697C211yesmaximal, characteristic, complemented
10#11718531C211yesmaximal, characteristic, complemented
11#11718524C211yesmaximal, characteristic, complemented
12#11718464C211yesmaximal, characteristic, complemented
13#11718456C211yesmaximal, characteristic, complemented
14#11718446C211yesmaximal, characteristic, complemented
15#11718443C211yesmaximal, characteristic, complemented
16C2×#6131C2211yescharacteristic
17C2×#6129—21no—
18C22×D52C2211yescharacteristic
19C2×C13×SD16C2211yescharacteristic, complemented
20C22×C8×C13C2211yescharacteristic
21C13×C22⋊Q8C2211yescharacteristic
22C13×#121C2211yescharacteristic
23#88201C2211yescharacteristic
24#88192C2211yescharacteristic, complemented
25#88189—21no—
26D4×Dic13C2211yescharacteristic, complemented
27C2×#6104C2211yescharacteristic
28C2×#6104C2211yescharacteristic
29C4×C22⋊D13C2211yescharacteristic
30C2×C4⋊Dic13C2211yescharacteristic
31C2×#6094C2211yescharacteristic, complemented
32#88149—21no—
33#88149C2211yescharacteristic
34#88148—21no—
35#88147C2211yescharacteristic
36C4⋊C4×D13C2211yescharacteristic, complemented
37#88142C2211yescharacteristic, complemented
38#88137—21no—
39#88136—21no—
40C22⋊C4×D13—21no—
41#88132—21no—
42C13×#106C2211yescharacteristic, complemented
43C13×#103C2211yescharacteristic, complemented
44C13×#102C2211yescharacteristic, complemented
45#88075C2211yescharacteristic, complemented
46#88075C2211yescharacteristic, complemented
47C22⋊#1055C2211yescharacteristic
48#88061C2211yescharacteristic
49#88061C2211yescharacteristic
50#88061C2211yescharacteristic
51#88061C2211yescharacteristic
52#88060C2211yescharacteristic, complemented
53#88055C2211yescharacteristic, complemented
54#88054C2211yescharacteristic, complemented
55#88049C2211yescharacteristic
56#88049C2211yescharacteristic
57#88048C2211yescharacteristic, complemented
58#88048C2211yescharacteristic, complemented
59C23×D13—21no—
60C2×Q8×C13C2311yescharacteristic
61C2×D4×C13—21no—
62C2×D4×C13C2311yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C2×C22⋊D13—21no—
65C2×C22⋊D13D411yescharacteristic
66C22×Dic13—21no—
67C22×Dic13—21no—
68#6131—22no—
69#6131—41no—
70#6129—44no—
71C2×D52—22no—
72C2×D52—21no—
73C2×D52—21no—
74C2×D52—21no—
75C2×D52—41no—
76C2×D52C2311yescharacteristic
77C2×D52C2311yescharacteristic
78C2×C4×D13—21no—
79C2×C4×D13—21no—
80C2×C4×D13—21no—
81C2×C4×D13C2311yescharacteristic
82C2×Dic26—21no—
83C13×SD16—41no—
84C2×C8×C13—41no—
85C2×C8×C13C2311yescharacteristic
86C2×C8×C13C2311yescharacteristic
87C13×C4⋊C4—21no—
88C13×C4⋊C4C2311yescharacteristic
89C13×C4⋊C4C2311yescharacteristic
90C13×C22⋊C4—21no—
91C13×C22⋊C4—21no—
92C22⋊Dic13—21no—
93C22⋊Dic13—21no—
94C22⋊Dic13D411yescharacteristic
95#6104—22no—
96#6104—41no—
97#6103—21no—
98#6103—21no—
99#6103—21no—
100#6103—21no—
101#6103D411yescharacteristic
102C4⋊Dic13—21no—
103C4⋊Dic13C2311yescharacteristic
104C4⋊Dic13C2311yescharacteristic
105#6101—21no—
106#6101—21no—
107#6101D411yescharacteristic
108C4×Dic13C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111#6094—41no—
112#3306—131nomaximal, Sylow
113C23×C13—21no—
114C23×C13C2×D411yescharacteristic
115C22×D13—21no—
116C22×D13—21no—
117C22×D13—42no—
118C22×D13—42no—
119C22×D13—81no—
120C22×D13C2×D411yescharacteristic
121Q8×C13—21no—
122Q8×C13—21no—
123D4×C13—21no—
124D4×C13—21no—
125D4×C13—42no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13C2×D411yescharacteristic
132C2×C4×C13C2411yescharacteristic
133C22⋊D13—22no—
134C22⋊D13—42no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—42no—
138C2×Dic13—42no—
139C2×Dic13C2×D411yescharacteristic
140C2×Dic13C2×D411yescharacteristic
141C2×Dic13C2×D411yescharacteristic
142D52—21no—
143D52—21no—
144D52—21no—
145D52—42no—
146D52—42no—
147D52—81no—
148D52#4112yescomplemented
149C4×D13—21no—
150C4×D13—21no—
151C4×D13—42no—
152C4×D13—42no—
153C4×D13—81no—
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#465D1311yescharacteristic, complemented
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—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13AGL(1,ℤ/8)12yes—
180C22×C13C22×D411yescharacteristic
181C2×D13—21no—
182C2×D13—22no—
183C2×D13—21no—
184C2×D13—21no—
185C2×D13—41no—
186C2×D13—41no—
187C2×D13—41no—
188C2×D13—41no—
189C2×D13—41no—
190C2×D13—84no—
191C4×C13—21no—
192C4×C13—41no—
193C4×C13—41no—
194C4×C13—41no—
195C4×C13C2×#4111yescharacteristic
196C4×C13H(5,𝔽2)11yescharacteristic
197Dic13—21no—
198Dic13—21no—
199Dic13—21no—
200Dic13—41no—
201Dic13—41no—
202C2×#41—131no—
203C2×#41—261no—
204C22×D4—131no—
205C2×SD16C2×D1311yescharacteristic, complemented
206C2×D8—131no—
207C2×D8—131no—
208C2×M16—131no—
209C22×C8C2×D1311yescharacteristic
210C4⋊Q8—131no—
211#124—131no—
212#123—261no—
213#123—261no—
214#123—261no—
215C22⋊Q8—261no—
216C22⋊Q8C2×D1311yescharacteristic
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#106C2×D1311yescharacteristic, complemented
231C4⋊C8—131no—
232#103—131no—
233#103—131no—
234#103C2×D1311yescharacteristic, complemented
235#102—131no—
236#102—131no—
237#102—131no—
238#102—131no—
239#102—131no—
240#102—131no—
241#102C2×D1311yescharacteristic, complemented
242C22⋊C8—131no—
243C22⋊C8—131no—
244#97—131no—
245C2×C13—22no—
246C2×C13—81no—
247C2×C13#54611yescharacteristic
248C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
249C2×C13#57711yescharacteristic
250D13—41no—
251D13—42no—
252D13—81no—
253C24—261no—
254#41—262no—
255#41—521no—
256#41—524no—
257C2×Q8—261no—
258C2×Q8C22×D1311yescharacteristic
259C2×D4—21no—
260C2×D4—131no—
261C2×D4—131no—
262C2×D4—131no—
263C2×D4—262no—
264C2×D4—261no—
265C2×D4—261no—
266C2×D4—261no—
267C2×D4—261no—
268C2×D4—521no—
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—41no—
278D8—262no—
279D8—521no—
280M16—521no—
281C2×C8—41no—
282C2×C8—131no—
283C2×C8—131no—
284C2×C8C22×D1311yescharacteristic
285C2×C8C22×D1311yescharacteristic
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—131no—
298C22⋊C4—131no—
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—131no—
309C23—261no—
310C23—261no—
311C23—522no—
312C23—522no—
313C23—1041no—
314C23D4×D1311yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—522no—
318D4—21no—
319D4—21no—
320D4—42no—
321D4—132no—
322D4—262no—
323D4—261no—
324D4—261no—
325D4—261no—
326D4—522no—
327D4—522no—
328D4—522no—
329D4—1041no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—131no—
336C2×C4—131no—
337C2×C4—131no—
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—41no—
356C22—41no—
357C22—41no—
358C22—261no—
359C22—261no—
360C22—261no—
361C22—262no—
362C22—521no—
363C22—521no—
364C22—521no—
365C22—521no—
366C22—521no—
367C22—1044no—
368C22#8816812yes—
369C22C2×D4×D1311yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—261no—
375C4—261no—
376C4—261no—
377C4—521no—
378C4—521no—
379C4#8825111yescharacteristic
380C4#41×D1311yescharacteristic
381C2—22no—
382C2—81no—
383C2—521no—
384C2—522no—
385C2—1041no—
386C2#1171931511yescharacteristic
387C2C2×#8816811yescharacteristic
388C2#1171947511yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#465C2
socleC22×C13C22×D4
hypercenter#465D13
hypocenterC13#3306
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #11719335C2semidirect
2. #11719316C2semidirect
3. C13×#465C2semidirect
4. #11718833C2semidirect
5. #11718826C2semidirect
6. C2×#88061C2semidirect
7. #11718772C2semidirect
8. #11718704C2semidirect
9. #11718697C2semidirect
10. #11718531C2semidirect
11. #11718524C2semidirect
12. #11718464C2semidirect
13. #11718456C2semidirect
14. #11718446C2semidirect
15. #11718443C2semidirect
19. C2×C13×SD16C22semidirect
24. #88192C22semidirect
26. D4×Dic13C22semidirect
31. C2×#6094C22semidirect
36. C4⋊C4×D13C22semidirect
37. #88142C22semidirect
42. C13×#106C22semidirect
43. C13×#103C22semidirect
44. C13×#102C22semidirect
45. #88075C22semidirect
46. #88075C22semidirect
52. #88060C22semidirect
53. #88055C22semidirect
54. #88054C22semidirect
57. #88048C22semidirect
58. #88048C22semidirect
148. D52#41semidirect
166. #465D13semidirect
205. C2×SD16C2×D13semidirect
230. #106C2×D13semidirect
234. #103C2×D13semidirect
241. #102C2×D13semidirect
306. C13#3306semidirect

Maximal subgroups

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

subgroupindex
#117193352
#117193162
C13×#4652
#117188332
#117188262
C2×#880612
#117187722
#117187042
#117186972
#117185312
#117185242
#117184642
#117184562
#117184462
#117184432
#330613