Finite Group Databasebeta

← #13127073

Subgroups — #13127073

Order 1664.

460 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719321C211yesmaximal, characteristic, complemented
2#11719314C211yesmaximal, characteristic, complemented
3C13×#469C211yesmaximal, characteristic, complemented
4#11718817C211yesmaximal, characteristic, complemented
5#11718811C211yesmaximal, characteristic, complemented
6#11718792C211yesmaximal, characteristic, complemented
7#11718789C211yesmaximal, characteristic, complemented
8#11718697C211yesmaximal, characteristic, complemented
9#11718696C211yesmaximal, characteristic, complemented
10#11718531C211yesmaximal, characteristic, complemented
11#11718527C211yesmaximal, characteristic, complemented
12#11718443C211yesmaximal, characteristic, complemented
13#11718431C211yesmaximal, characteristic, complemented
14#11718421C211yesmaximal, characteristic, complemented
15#11718417C211yesmaximal, characteristic, complemented
16C2×D4×D13—21no—
17C2×D4×D13C2211yescharacteristic
18C22×D52C2211yescharacteristic
19C2×C13×D8C2211yescharacteristic, complemented
20C2×C13×M16C2211yescharacteristic, complemented
21C13×#121C2211yescharacteristic
22C13×#121C2211yescharacteristic, complemented
23#88194C2211yescharacteristic
24#88193—21no—
25#88192C2211yescharacteristic, complemented
26#88191—21no—
27#88190—21no—
28D4×Dic13C2211yescharacteristic, complemented
29C2×#6104C2211yescharacteristic
30C2×#6104C2211yescharacteristic, complemented
31C4×C22⋊D13C2211yescharacteristic
32#88180C2211yescharacteristic, complemented
33C2×#6094C2211yescharacteristic, complemented
34#88149C2211yescharacteristic
35#88147C2211yescharacteristic
36#88146C2211yescharacteristic, complemented
37#88142C2211yescharacteristic, complemented
38#88139—21no—
39#88138—21no—
40#88136—21no—
41#88131—21no—
42C13×#106C2211yescharacteristic, complemented
43C13×#102C2211yescharacteristic, complemented
44C13×#102C2211yescharacteristic, complemented
45#88072C2211yescharacteristic, complemented
46#88072C2211yescharacteristic, complemented
47C22⋊#1055C2211yescharacteristic, complemented
48#88061C2211yescharacteristic
49#88061C2211yescharacteristic
50#88061C2211yescharacteristic, complemented
51#88061C2211yescharacteristic, complemented
52#88060C2211yescharacteristic, complemented
53#88054C2211yescharacteristic, complemented
54C8×Dic13C2211yescharacteristic, complemented
55#88049C2211yescharacteristic
56#88049C2211yescharacteristic, complemented
57#88048C2211yescharacteristic, complemented
58#88047C2211yescharacteristic, complemented
59C23×D13—21no—
60C23×D13—21no—
61C2×D4×C13—21no—
62C2×D4×C13—21no—
63C2×D4×C13C2311yescharacteristic
64C2×D4×C13C2311yescharacteristic
65C22×C4×C13C2311yescharacteristic
66C2×C22⋊D13—21no—
67C2×C22⋊D13—21no—
68C2×C22⋊D13—21no—
69C2×C22⋊D13—21no—
70C2×C22⋊D13D411yescharacteristic
71C22×Dic13—21no—
72D4×D13—22no—
73D4×D13—41no—
74D4×D13—44no—
75C2×D52—22no—
76C2×D52—21no—
77C2×D52—21no—
78C2×D52—41no—
79C2×D52C2311yescharacteristic
80C2×D52C2311yescharacteristic
81C2×C4×D13—21no—
82C2×C4×D13C2311yescharacteristic
83C2×Dic26—21no—
84C13×D8—41no—
85C13×M16—41no—
86C2×C8×C13C2311yescharacteristic
87C2×C8×C13C2311yescharacteristic
88C13×C4⋊C4C2311yescharacteristic
89C13×C4⋊C4C2311yescharacteristic
90C13×C22⋊C4—21no—
91C13×C22⋊C4—21no—
92C22⋊Dic13—21no—
93C22⋊Dic13—21no—
94C22⋊Dic13—21no—
95C22⋊Dic13D411yescharacteristic
96#6104—22no—
97#6104—41no—
98#6103—21no—
99#6103—21no—
100#6103—21no—
101#6103D411yescharacteristic
102C4⋊Dic13C2311yescharacteristic
103C4⋊Dic13C2311yescharacteristic
104#6101—21no—
105#6101D411yescharacteristic
106C4×Dic13—21no—
107C4×Dic13—21no—
108C4×Dic13C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111#6094—41no—
112#3325—131nomaximal, Sylow
113C23×C13—21no—
114C23×C13—21no—
115C23×C13C2×D411yescharacteristic
116C22×D13—21no—
117C22×D13—21no—
118C22×D13—42no—
119C22×D13—42no—
120C22×D13—42no—
121C22×D13—42no—
122C22×D13—81no—
123C22×D13—81no—
124C22×D13C2×D411yescharacteristic
125D4×C13—21no—
126D4×C13—21no—
127D4×C13—21no—
128D4×C13—21no—
129D4×C13—42no—
130D4×C13—81no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13C2×D411yescharacteristic
136C2×C4×C13C2411yescharacteristic
137C22⋊D13—22no—
138C22⋊D13—42no—
139C22⋊D13—42no—
140C22⋊D13—81no—
141C22⋊D13—81no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—42no—
145C2×Dic13C2×D411yescharacteristic
146C2×Dic13C2×D411yescharacteristic
147C2×Dic13C2×D411yescharacteristic
148D52—21no—
149D52—21no—
150D52—21no—
151D52—42no—
152D52—42no—
153D52#4112yes—
154C4×D13—21no—
155C4×D13—21no—
156C4×D13—42no—
157Dic26—81no—
158C8×C13—21no—
159C8×C13—21no—
160#1055—21no—
161#1055—21no—
162#555—131no—
163D42—131no—
164#486—131no—
165#482—131no—
166#482—131no—
167#476—131no—
168#469—131no—
169#469D1311yescharacteristic, complemented
170#459—131no—
171#447—131no—
172#447—131no—
173C4×D8—131no—
174#436—131no—
175#418—131no—
176#418—131no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—41no—
186C22×C13C22×D411yescharacteristic
187C2×D13—21no—
188C2×D13—22no—
189C2×D13—21no—
190C2×D13—21no—
191C2×D13—41no—
192C2×D13—41no—
193C2×D13—41no—
194C2×D13—41no—
195C2×D13—41no—
196C2×D13—84no—
197C2×D13—84no—
198C4×C13—21no—
199C4×C13—41no—
200C4×C13—41no—
201C4×C13C2×#4111yescharacteristic
202C4×C13H(5,𝔽2)11yescharacteristic
203Dic13—21no—
204Dic13—21no—
205Dic13—41no—
206Dic13—41no—
207Dic13AGL(1,ℤ/8)12yes—
208C22×D4—131no—
209C22×D4—131no—
210C22×D4—261no—
211C2×D8—131no—
212C2×D8—131no—
213C2×D8C2×D1311yescharacteristic, complemented
214C2×M16—131no—
215C2×M16C2×D1311yescharacteristic, complemented
216C4⋊Q8—131no—
217#127—131no—
218#124—261no—
219#124—261no—
220#121—131no—
221#121—131no—
222#121—261no—
223#121—261no—
224#121C2×D1311yescharacteristic
225#121C2×D1311yescharacteristic, complemented
226#120—261no—
227#120—261no—
228C4×D4—131no—
229C4×D4—131no—
230C4×D4—131no—
231#117—131no—
232#117—131no—
233#117—261no—
234#107—131no—
235#106—131no—
236#106C2×D1311yescharacteristic, complemented
237C4⋊C8—131no—
238#102—131no—
239#102—131no—
240#102—131no—
241#102—131no—
242#102—131no—
243#102—131no—
244#102—131no—
245#102—131no—
246#102C2×D1311yescharacteristic, complemented
247#102C2×D1311yescharacteristic, complemented
248C22⋊C8—131no—
249C22⋊C8—131no—
250C4×C8—131no—
251C2×C13—41no—
252C2×C13—81no—
253C2×C13—81no—
254C2×C13#54611yescharacteristic
255C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
256C2×C13#57611yescharacteristic
257D13—41no—
258D13—42no—
259D13—81no—
260C24—261no—
261C24—261no—
262C2×Q8—261no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—131no—
266C2×D4—131no—
267C2×D4—131no—
268C2×D4—262no—
269C2×D4—261no—
270C2×D4—261no—
271C2×D4—261no—
272C2×D4—261no—
273C2×D4—262no—
274C2×D4—261no—
275C2×D4—261no—
276C2×D4—521no—
277C2×D4—521no—
278C2×D4—524no—
279C2×D4C22×D1311yescharacteristic
280C2×D4C22×D1311yescharacteristic
281C22×C4—131no—
282C22×C4—261no—
283C22×C4—261no—
284C22×C4C22×D1311yescharacteristic
285D8—41no—
286D8—262no—
287D8—521no—
288M16—41no—
289M16—521no—
290C2×C8—131no—
291C2×C8—131no—
292C2×C8C22×D1311yescharacteristic
293C2×C8C22×D1311yescharacteristic
294C4⋊C4—131no—
295C4⋊C4—131no—
296C4⋊C4—131no—
297C4⋊C4—261no—
298C4⋊C4C22×D1311yescharacteristic
299C4⋊C4C22×D1311yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—131no—
303C22⋊C4—131no—
304C22⋊C4—261no—
305C22⋊C4—261no—
306C22⋊C4—261no—
307C22⋊C4—261no—
308C22⋊C4—261no—
309C22⋊C4—261no—
310C42—131no—
311C42—261no—
312C42—261no—
313C13#332511yescharacteristic, complemented, Sylow
314C23—21no—
315C23—21no—
316C23—131no—
317C23—261no—
318C23—261no—
319C23—522no—
320C23—522no—
321C23—522no—
322C23—522no—
323C23—1041no—
324C23—1041no—
325C23D4×D1311yescharacteristic
326Q8—1041no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—42no—
332D4—81no—
333D4—132no—
334D4—262no—
335D4—261no—
336D4—261no—
337D4—261no—
338D4—522no—
339D4—522no—
340D4—522no—
341D4—522no—
342D4—1041no—
343D4—1041no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—131no—
349C2×C4—131no—
350C2×C4—131no—
351C2×C4—261no—
352C2×C4—261no—
353C2×C4—261no—
354C2×C4—261no—
355C2×C4—522no—
356C2×C4—522no—
357C2×C4D4×D1311yescharacteristic
358C2×C4C23×D1311yescharacteristic
359C8—21no—
360C8—21no—
361C8—261no—
362C8—261no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—261no—
373C22—261no—
374C22—261no—
375C22—262no—
376C22—521no—
377C22—521no—
378C22—521no—
379C22—521no—
380C22—521no—
381C22—1044no—
382C22—1044no—
383C22C2×D4×D1311yescharacteristic
384C4—21no—
385C4—41no—
386C4—41no—
387C4—132no—
388C4—261no—
389C4—261no—
390C4—521no—
391C4—521no—
392C4#8825111yescharacteristic
393C4#41×D1311yescharacteristic
394C2—41no—
395C2—81no—
396C2—81no—
397C2—521no—
398C2—522no—
399C2—1041no—
400C2#1171931511yescharacteristic
401C2D13×AGL(1,ℤ/8)11yescharacteristic
402C2#1171947911yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#469C2
socleC22×C13C22×D4
hypercenter#469D13
hypocenterC13#3325
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #11719321C2semidirect
2. #11719314C2semidirect
3. C13×#469C2semidirect
4. #11718817C2semidirect
5. #11718811C2semidirect
6. #11718792C2semidirect
7. #11718789C2semidirect
8. #11718697C2semidirect
9. #11718696C2semidirect
10. #11718531C2semidirect
11. #11718527C2semidirect
12. #11718443C2semidirect
13. #11718431C2semidirect
14. #11718421C2semidirect
15. #11718417C2semidirect
19. C2×C13×D8C22semidirect
20. C2×C13×M16C22semidirect
22. C13×#121C22semidirect
25. #88192C22semidirect
28. D4×Dic13C22semidirect
30. C2×#6104C22semidirect
32. #88180C22semidirect
33. C2×#6094C22semidirect
36. #88146C22semidirect
37. #88142C22semidirect
42. C13×#106C22semidirect
43. C13×#102C22semidirect
44. C13×#102C22semidirect
45. #88072C22semidirect
46. #88072C22semidirect
47. C22⋊#1055C22semidirect
50. #88061C22semidirect
51. #88061C22semidirect
52. #88060C22semidirect
53. #88054C22semidirect
54. C8×Dic13C22semidirect
56. #88049C22semidirect
57. #88048C22semidirect
58. #88047C22semidirect
169. #469D13semidirect
213. C2×D8C2×D13semidirect
215. C2×M16C2×D13semidirect
225. #121C2×D13semidirect
236. #106C2×D13semidirect
246. #102C2×D13semidirect
247. #102C2×D13semidirect
313. C13#3325semidirect

Maximal subgroups

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

subgroupindex
#117193212
#117193142
C13×#4692
#117188172
#117188112
#117187922
#117187892
#117186972
#117186962
#117185312
#117185272
#117184432
#117184312
#117184212
#117184172
#332513