Finite Group Databasebeta

← #13124775

Subgroups — #13124775

Order 1664.

462 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13×#121C211yesmaximal, characteristic
2D13×#117C211yesmaximal, characteristic, complemented
3C13×#482C211yesmaximal, characteristic, complemented
4#11718696C211yesmaximal, characteristic, complemented
5#11718664C211yesmaximal, characteristic, complemented
6#11718543C211yesmaximal, characteristic, complemented
7#11718542C211yesmaximal, characteristic, complemented
8#11718524C211yesmaximal, characteristic, complemented
9#11718522C211yesmaximal, characteristic, complemented
10#11718438C211yesmaximal, characteristic, complemented
11#11718435C211yesmaximal, characteristic, complemented
12#11718431C211yesmaximal, characteristic, complemented
13#11718431C211yesmaximal, characteristic, complemented
14#11718398C211yesmaximal, characteristic, complemented
15#11718387C211yesmaximal, characteristic, complemented
16C2×D4×D13—21no—
17C2×D4×D13C2211yescharacteristic
18C22×C4×D13C2211yescharacteristic
19C13×#121C2211yescharacteristic
20C13×#117C2211yescharacteristic, complemented
21#88193—21no—
22#88192C2211yescharacteristic
23#88184C2211yescharacteristic
24#88180C2211yescharacteristic, complemented
25C2×#6094C2211yescharacteristic
26C2×#6094C2211yescharacteristic
27#88149C2211yescharacteristic
28#88146C2211yescharacteristic
29#88146C2211yescharacteristic
30C4⋊C4×D13C2211yescharacteristic
31C4⋊C4×D13C2211yescharacteristic, complemented
32C4⋊C4×D13C2211yescharacteristic, complemented
33#88138—21no—
34C22⋊C4×D13—21no—
35C22⋊C4×D13—21no—
36#88131—21no—
37#88126—21no—
38C42×D13—21no—
39C13×#107C2211yescharacteristic, complemented
40C13×#106C2211yescharacteristic, complemented
41C13×#102C2211yescharacteristic, complemented
42C13×#102C2211yescharacteristic, complemented
43C13×C22⋊C8C2211yescharacteristic, complemented
44#88072C2211yescharacteristic, complemented
45#88072C2211yescharacteristic, complemented
46C22⋊#1055C2211yescharacteristic, complemented
47#88061C2211yescharacteristic, complemented
48#88061C2211yescharacteristic, complemented
49#88060C2211yescharacteristic, complemented
50#88060C2211yescharacteristic, complemented
51#88058C2211yescharacteristic, complemented
52#88057C2211yescharacteristic, complemented
53#88049C2211yescharacteristic, complemented
54#88049C2211yescharacteristic, complemented
55#88048C2211yescharacteristic, complemented
56#88048C2211yescharacteristic, complemented
57#88047C2211yescharacteristic, complemented
58#88047C2211yescharacteristic, complemented
59C23×D13—21no—
60C23×D13D411yescharacteristic
61C2×D4×C13—21no—
62C2×D4×C13C2311yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C2×C22⋊D13—21no—
65C2×C22⋊D13—21no—
66C2×C22⋊D13—21no—
67C22×Dic13D411yescharacteristic
68D4×D13—22no—
69D4×D13—22no—
70D4×D13—44no—
71C2×D52—21no—
72C2×D52C2311yescharacteristic
73C2×C4×D13—22no—
74C2×C4×D13—22no—
75C2×C4×D13—21no—
76C2×C4×D13—21no—
77C2×C4×D13—21no—
78C2×C4×D13D411yescharacteristic
79C2×C4×D13D411yescharacteristic
80C2×C4×D13C2311yescharacteristic
81C2×C4×D13C2311yescharacteristic
82C2×C8×C13C2311yescharacteristic
83C2×C8×C13C2311yescharacteristic
84C13×C4⋊C4C2311yescharacteristic
85C13×C4⋊C4C2311yescharacteristic
86C13×C4⋊C4C2311yescharacteristic
87C13×C22⋊C4—21no—
88C13×C22⋊C4—21no—
89C42×C13—21no—
90C22⋊Dic13—21no—
91C22⋊Dic13—21no—
92#6103—21no—
93#6103—21no—
94#6103—21no—
95#6103—21no—
96C4⋊Dic13C2311yescharacteristic
97C4⋊Dic13C2311yescharacteristic
98C4⋊Dic13C2311yescharacteristic
99#6101—21no—
100#6101—21no—
101#6101—21no—
102C4×Dic13—21no—
103C4×Dic13—21no—
104C4×Dic13—21no—
105C2×#1055C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107#6094—22no—
108#6094—22no—
109#3094—131nomaximal, Sylow
110C23×C13—21no—
111C23×C13C2×D411yescharacteristic
112C22×D13—22no—
113C22×D13—22no—
114C22×D13—21no—
115C22×D13—41no—
116C22×D13—42no—
117C22×D13—42no—
118C22×D13—42no—
119C22×D13C2×D411yescharacteristic
120C22×D13C2×D411yescharacteristic
121D4×C13—21no—
122D4×C13—21no—
123D4×C13—42no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13C2×D411yescharacteristic
130C2×C4×C13C2411yescharacteristic
131C22⋊D13—42no—
132C22⋊D13—42no—
133C22⋊D13—42no—
134C2×Dic13—22no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13C2×D411yescharacteristic
139C2×Dic13C2×D411yescharacteristic
140D52—21no—
141D52—21no—
142D52—42no—
143C4×D13—22no—
144C4×D13—21no—
145C4×D13—21no—
146C4×D13—22no—
147C4×D13—42no—
148C4×D13—42no—
149C4×D13—42no—
150C4×D13#4112yes—
151C4×D13#4112yes—
152C8×C13—21no—
153C8×C13—21no—
154#1055—21no—
155#1055—21no—
156C2×#121—131no—
157C2×#117—131no—
158#482—131no—
159#482—131no—
160#482—131no—
161#482D1311yescharacteristic, complemented
162#481—131no—
163#481—131no—
164#480—131no—
165#480—131no—
166#428—131no—
167#428—131no—
168#418—131no—
169#418—131no—
170#407—131no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13C22×D411yescharacteristic
178C2×D13—21no—
179C2×D13—21no—
180C2×D13—21no—
181C2×D13—21no—
182C2×D13—44no—
183C2×D13—41no—
184C2×D13—41no—
185C2×D13—41no—
186C2×D13—84no—
187C2×D13#12312yes—
188C2×D13AGL(1,ℤ/8)12yes—
189C4×C13—21no—
190C4×C13—41no—
191C4×C13—41no—
192C4×C13—41no—
193C4×C13C2×#4111yescharacteristic
194C4×C13C2×#4111yescharacteristic
195Dic13—21no—
196Dic13—41no—
197Dic13—41no—
198Dic13—41no—
199Dic13#12312yes—
200C22×D4—131no—
201C22×D4—261no—
202C23×C4—131no—
203C2×M16—131no—
204C2×M16—131no—
205#121—131no—
206#121—131no—
207#121—131no—
208#121—261no—
209#121—261no—
210#121C2×D1311yescharacteristic
211#117—131no—
212#117—131no—
213#117—131no—
214#117—261no—
215#117—261no—
216#117C2×D1311yescharacteristic, complemented
217C2×C4⋊C4—131no—
218C2×C4⋊C4—131no—
219C2×C4⋊C4—131no—
220C2×C22⋊C4—261no—
221C2×C22⋊C4—261no—
222C2×C42—261no—
223#107—131no—
224#107—131no—
225#107—131no—
226#107C2×D1311yescharacteristic, complemented
227#106—131no—
228#106—131no—
229#106—131no—
230#106C2×D1311yescharacteristic, complemented
231#102—131no—
232#102—131no—
233#102—131no—
234#102—131no—
235#102—131no—
236#102—131no—
237#102C2×D1311yescharacteristic, complemented
238#102C2×D1311yescharacteristic, complemented
239C22⋊C8—131no—
240C22⋊C8—131no—
241C22⋊C8—131no—
242C22⋊C8C2×D1311yescharacteristic, complemented
243C2×C13—41no—
244C2×C13—81no—
245C2×C13C2×#12311yescharacteristic
246C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
247C2×C13#57511yescharacteristic
248D13—22no—
249D13—22no—
250D13—81no—
251C24—131no—
252C24—261no—
253C2×D4—21no—
254C2×D4—131no—
255C2×D4—261no—
256C2×D4—262no—
257C2×D4—262no—
258C2×D4—261no—
259C2×D4—261no—
260C2×D4—261no—
261C2×D4—524no—
262C2×D4C22×D1311yescharacteristic
263C22×C4—131no—
264C22×C4—131no—
265C22×C4—131no—
266C22×C4—131no—
267C22×C4—131no—
268C22×C4—262no—
269C22×C4—262no—
270C22×C4—261no—
271C22×C4—261no—
272C22×C4—261no—
273C22×C4C22×D1311yescharacteristic
274M16—262no—
275M16—262no—
276C2×C8—131no—
277C2×C8—131no—
278C2×C8C22×D1311yescharacteristic
279C2×C8C22×D1311yescharacteristic
280C4⋊C4—131no—
281C4⋊C4—131no—
282C4⋊C4—131no—
283C4⋊C4—261no—
284C4⋊C4—261no—
285C4⋊C4—261no—
286C4⋊C4C22×D1311yescharacteristic
287C4⋊C4C22×D1311yescharacteristic
288C4⋊C4C22×D1311yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—261no—
292C22⋊C4—261no—
293C22⋊C4—261no—
294C22⋊C4—261no—
295C22⋊C4—261no—
296C22⋊C4—261no—
297C42—21no—
298C42—261no—
299C42—261no—
300C42—261no—
301C13#309411yescharacteristic, complemented, Sylow
302C23—21no—
303C23—131no—
304C23—131no—
305C23—262no—
306C23—262no—
307C23—261no—
308C23—521no—
309C23—522no—
310C23—522no—
311C23—522no—
312C23D4×D1311yescharacteristic
313D4—21no—
314D4—21no—
315D4—42no—
316D4—261no—
317D4—261no—
318D4—522no—
319D4—522no—
320D4—522no—
321D4—522no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—131no—
328C2×C4—132no—
329C2×C4—132no—
330C2×C4—131no—
331C2×C4—262no—
332C2×C4—262no—
333C2×C4—262no—
334C2×C4—261no—
335C2×C4—261no—
336C2×C4—261no—
337C2×C4—261no—
338C2×C4—261no—
339C2×C4—522no—
340C2×C4—522no—
341C2×C4—522no—
342C2×C4D4×D1311yescharacteristic
343C2×C4C23×D1311yescharacteristic
344C8—21no—
345C8—21no—
346C8—261no—
347C8—261no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—132no—
355C22—132no—
356C22—261no—
357C22—261no—
358C22—261no—
359C22—261no—
360C22—524no—
361C22—521no—
362C22—521no—
363C22—521no—
364C22—1044no—
365C22C2×D4×D1311yescharacteristic
366C4—21no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—132no—
371C4—261no—
372C4—521no—
373C4—521no—
374C4—521no—
375C4#41×D1311yescharacteristic
376C4#41×D1311yescharacteristic
377C2—41no—
378C2—81no—
379C2—262no—
380C2—262no—
381C2—1041no—
382C2D13×#12311yescharacteristic
383C2#1171947311yescharacteristic
384C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#482C2
socleC22×C13C22×D4
prime radicalD13×#121C2
hypercenter#482D13
hypocenterC13#3094
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. D13×#117C2semidirect
3. C13×#482C2semidirect
4. #11718696C2semidirect
5. #11718664C2semidirect
6. #11718543C2semidirect
7. #11718542C2semidirect
8. #11718524C2semidirect
9. #11718522C2semidirect
10. #11718438C2semidirect
11. #11718435C2semidirect
12. #11718431C2semidirect
13. #11718431C2semidirect
14. #11718398C2semidirect
15. #11718387C2semidirect
20. C13×#117C22semidirect
24. #88180C22semidirect
31. C4⋊C4×D13C22semidirect
32. C4⋊C4×D13C22semidirect
39. C13×#107C22semidirect
40. C13×#106C22semidirect
41. C13×#102C22semidirect
42. C13×#102C22semidirect
43. C13×C22⋊C8C22semidirect
44. #88072C22semidirect
45. #88072C22semidirect
46. C22⋊#1055C22semidirect
47. #88061C22semidirect
48. #88061C22semidirect
49. #88060C22semidirect
50. #88060C22semidirect
51. #88058C22semidirect
52. #88057C22semidirect
53. #88049C22semidirect
54. #88049C22semidirect
55. #88048C22semidirect
56. #88048C22semidirect
57. #88047C22semidirect
58. #88047C22semidirect
161. #482D13semidirect
216. #117C2×D13semidirect
226. #107C2×D13semidirect
230. #106C2×D13semidirect
237. #102C2×D13semidirect
238. #102C2×D13semidirect
242. C22⋊C8C2×D13semidirect
301. C13#3094semidirect

Maximal subgroups

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

subgroupindex
D13×#1212
D13×#1172
C13×#4822
#117186962
#117186642
#117185432
#117185422
#117185242
#117185222
#117184382
#117184352
#117184312
#117183982
#117183872
#309413