Finite Group Databasebeta

← #13126852

Subgroups — #13126852

Order 1664.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719344C211yesmaximal, characteristic, complemented
2#11719314C211yesmaximal, characteristic
3C13×#468C211yesmaximal, characteristic, complemented
4#11718830C211yesmaximal, characteristic, complemented
5#11718824C211yesmaximal, characteristic, complemented
6#11718792C211yesmaximal, characteristic, complemented
7#11718788C211yesmaximal, characteristic, complemented
8#11718707C211yesmaximal, characteristic, complemented
9#11718696C211yesmaximal, characteristic, complemented
10#11718552C211yesmaximal, characteristic, complemented
11#11718543C211yesmaximal, characteristic, complemented
12#11718478C211yesmaximal, characteristic, complemented
13#11718468C211yesmaximal, characteristic, complemented
14D13×#102C211yesmaximal, characteristic, complemented
15#11718425C211yesmaximal, characteristic, complemented
16C2×D4×D13—21no—
17C2×D4×D13C2211yescharacteristic
18C22×D52C2211yescharacteristic
19C2×C13×SD16C2211yescharacteristic, complemented
20C2×C13×M16C2211yescharacteristic, complemented
21C13×C22⋊Q8C2211yescharacteristic, complemented
22C13×#121C2211yescharacteristic
23#88200C2211yescharacteristic, complemented
24Q8×Dic13C2211yescharacteristic, complemented
25C2×#6106C2211yescharacteristic
26C2×#6106C2211yescharacteristic, complemented
27#88194C2211yescharacteristic
28#88191—21no—
29C4×C22⋊D13C2211yescharacteristic
30#88180C2211yescharacteristic, complemented
31C2×C8×D13C2211yescharacteristic, complemented
32#88149C2211yescharacteristic
33#88147C2211yescharacteristic
34#88146—21no—
35C4⋊C4×D13C2211yescharacteristic, complemented
36#88144C2211yescharacteristic, complemented
37#88143—21no—
38#88138—21no—
39#88137—21no—
40#88136—21no—
41#88133—21no—
42C13×#107C2211yescharacteristic, complemented
43C13×#103C2211yescharacteristic, 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#88055C2211yescharacteristic, complemented
54#88054C2211yescharacteristic, complemented
55#88049C2211yescharacteristic
56#88049C2211yescharacteristic, complemented
57#88048C2211yescharacteristic, complemented
58#88047C2211yescharacteristic, complemented
59C23×D13—21no—
60C23×D13—21no—
61C2×Q8×C13C2311yescharacteristic
62C2×D4×C13—21no—
63C2×D4×C13C2311yescharacteristic
64C22×C4×C13C2311yescharacteristic
65C2×C22⋊D13—21no—
66C2×C22⋊D13—21no—
67C2×C22⋊D13—21no—
68C2×C22⋊D13D411yescharacteristic
69D4×D13—22no—
70D4×D13—41no—
71D4×D13—44no—
72C2×D52—22no—
73C2×D52—21no—
74C2×D52—21no—
75C2×D52—41no—
76C2×D52C2311yescharacteristic
77C2×D52C2311yescharacteristic
78C2×C4×D13—21no—
79C2×C4×D13—21no—
80C2×C4×D13C2311yescharacteristic
81C13×SD16—41no—
82C13×M16—41no—
83C2×C8×C13C2311yescharacteristic
84C2×C8×C13C2311yescharacteristic
85C13×C4⋊C4—21no—
86C13×C4⋊C4C2311yescharacteristic
87C13×C4⋊C4C2311yescharacteristic
88C13×C22⋊C4—21no—
89C13×C22⋊C4—21no—
90C22⋊Dic13—21no—
91C22⋊Dic13D411yescharacteristic
92#6106—22no—
93#6106—41no—
94#6103—21no—
95#6103—21no—
96#6103—21no—
97#6103D411yescharacteristic
98C4⋊Dic13—21no—
99C4⋊Dic13—21no—
100C4⋊Dic13C2311yescharacteristic
101C4⋊Dic13C2311yescharacteristic
102#6101—21no—
103#6101—21no—
104#6101—21no—
105#6101D411yescharacteristic
106C4×Dic13—21no—
107C4×Dic13—21no—
108C4×Dic13C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111C8×D13—41no—
112#3310—131nomaximal, Sylow
113C23×C13—21no—
114C23×C13C2×D411yescharacteristic
115C22×D13—21no—
116C22×D13—21no—
117C22×D13—42no—
118C22×D13—42no—
119C22×D13—42no—
120C22×D13—42no—
121C22×D13—81no—
122C22×D13—81no—
123C22×D13C2×D411yescharacteristic
124Q8×C13—21no—
125Q8×C13—21no—
126D4×C13—21no—
127D4×C13—21no—
128D4×C13—42no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13C2×D411yescharacteristic
135C2×C4×C13C2411yescharacteristic
136C22⋊D13—22no—
137C22⋊D13—42no—
138C22⋊D13—42no—
139C22⋊D13—81no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13C2×D411yescharacteristic
143C2×Dic13C2×D411yescharacteristic
144C2×Dic13C2×D411yescharacteristic
145D52—21no—
146D52—21no—
147D52—21no—
148D52—42no—
149D52—42no—
150D52#4112yes—
151C4×D13—21no—
152C4×D13—21no—
153C4×D13—42no—
154C4×D13—42no—
155C8×C13—21no—
156C8×C13—21no—
157#1055—21no—
158#1055—21no—
159#552—131no—
160D42—131no—
161#490—131no—
162#482—131no—
163#480—131no—
164#478—131no—
165#468D1311yescharacteristic, complemented
166#465—131no—
167#460—131no—
168#450—131no—
169#450—131no—
170#440—131no—
171#435—131no—
172#418—131no—
173C2×#102—131no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13C22×D411yescharacteristic
181C2×D13—21no—
182C2×D13—21no—
183C2×D13—22no—
184C2×D13—41no—
185C2×D13—41no—
186C2×D13—41no—
187C2×D13—41no—
188C2×D13—41no—
189C2×D13—84no—
190C2×D13—84no—
191C2×D13AGL(1,ℤ/8)12yes—
192C4×C13—21no—
193C4×C13—41no—
194C4×C13—41no—
195C4×C13—41no—
196C4×C13C2×#4111yescharacteristic
197C4×C13H(5,𝔽2)11yescharacteristic
198Dic13—21no—
199Dic13—21no—
200Dic13—21no—
201Dic13—41no—
202Dic13—41no—
203C22×D4—131no—
204C22×D4—131no—
205C22×D4—261no—
206C2×SD16—131no—
207C2×SD16—131no—
208C2×SD16C2×D1311yescharacteristic, complemented
209C2×M16C2×D1311yescharacteristic, complemented
210C22×C8—131no—
211#127—131no—
212#126—261no—
213#125—131no—
214#125—261no—
215#123—261no—
216C22⋊Q8—131no—
217C22⋊Q8C2×D1311yescharacteristic, complemented
218#121—131no—
219#121—261no—
220#121C2×D1311yescharacteristic
221#120—261no—
222#120—261no—
223C4×Q8—131no—
224C4×D4—131no—
225C4×D4—131no—
226#117—131no—
227#117—261no—
228C2×C4⋊C4—131no—
229#107—131no—
230#107C2×D1311yescharacteristic, complemented
231#106—131no—
232C4⋊C8—131no—
233#103C2×D1311yescharacteristic, complemented
234#102—131no—
235#102—131no—
236#102—131no—
237#102—131no—
238#102—131no—
239#102—131no—
240#102—131no—
241#102—131no—
242#102C2×D1311yescharacteristic, complemented
243C22⋊C8—131no—
244C22⋊C8—131no—
245#97—131no—
246C2×C13—41no—
247C2×C13—81no—
248C2×C13#54611yescharacteristic
249C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
250C2×C13#57711yescharacteristic
251D13—22no—
252D13—42no—
253D13—81no—
254C24—261no—
255C24—261no—
256C2×Q8C22×D1311yescharacteristic
257C2×D4—21no—
258C2×D4—131no—
259C2×D4—131no—
260C2×D4—131no—
261C2×D4—262no—
262C2×D4—261no—
263C2×D4—261no—
264C2×D4—261no—
265C2×D4—261no—
266C2×D4—262no—
267C2×D4—261no—
268C2×D4—521no—
269C2×D4—521no—
270C2×D4—524no—
271C2×D4C22×D1311yescharacteristic
272C22×C4—131no—
273C22×C4—261no—
274C22×C4—261no—
275C22×C4C22×D1311yescharacteristic
276SD16—41no—
277SD16—262no—
278SD16—521no—
279M16—41no—
280C2×C8—131no—
281C2×C8—131no—
282C2×C8—521no—
283C2×C8C22×D1311yescharacteristic
284C2×C8C22×D1311yescharacteristic
285C4⋊C4—21no—
286C4⋊C4—131no—
287C4⋊C4—131no—
288C4⋊C4—131no—
289C4⋊C4—261no—
290C4⋊C4—261no—
291C4⋊C4—261no—
292C4⋊C4—261no—
293C4⋊C4—261no—
294C4⋊C4C22×D1311yescharacteristic
295C4⋊C4C22×D1311yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—131no—
299C22⋊C4—131no—
300C22⋊C4—261no—
301C22⋊C4—261no—
302C22⋊C4—261no—
303C22⋊C4—261no—
304C42—131no—
305C42—261no—
306C42—261no—
307C13#331011yescharacteristic, complemented, Sylow
308C23—21no—
309C23—131no—
310C23—261no—
311C23—261no—
312C23—522no—
313C23—522no—
314C23—522no—
315C23—522no—
316C23—1041no—
317C23—1041no—
318C23D4×D1311yescharacteristic
319Q8—21no—
320Q8—21no—
321D4—21no—
322D4—21no—
323D4—42no—
324D4—132no—
325D4—262no—
326D4—261no—
327D4—261no—
328D4—261no—
329D4—522no—
330D4—522no—
331D4—522no—
332D4—522no—
333D4—1041no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—131no—
340C2×C4—131no—
341C2×C4—131no—
342C2×C4—261no—
343C2×C4—261no—
344C2×C4—261no—
345C2×C4—261no—
346C2×C4—522no—
347C2×C4—522no—
348C2×C4D4×D1311yescharacteristic
349C2×C4C23×D1311yescharacteristic
350C8—21no—
351C8—21no—
352C8—261no—
353C8—261no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—132no—
361C22—261no—
362C22—261no—
363C22—262no—
364C22—521no—
365C22—521no—
366C22—521no—
367C22—521no—
368C22—521no—
369C22—1044no—
370C22—1044no—
371C22C2×D4×D1311yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—261no—
377C4—261no—
378C4—261no—
379C4—521no—
380C4—521no—
381C4#8825111yescharacteristic
382C4#41×D1311yescharacteristic
383C2—41no—
384C2—81no—
385C2—262no—
386C2—522no—
387C2—1041no—
388C2#1171931511yescharacteristic
389C2D13×AGL(1,ℤ/8)11yescharacteristic
390C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#468C2
socleC22×C13C22×D4
prime radical#11719314C2
hypercenter#468D13
hypocenterC13#3310
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #11719344C2semidirect
3. C13×#468C2semidirect
4. #11718830C2semidirect
5. #11718824C2semidirect
6. #11718792C2semidirect
7. #11718788C2semidirect
8. #11718707C2semidirect
9. #11718696C2semidirect
10. #11718552C2semidirect
11. #11718543C2semidirect
12. #11718478C2semidirect
13. #11718468C2semidirect
14. D13×#102C2semidirect
15. #11718425C2semidirect
19. C2×C13×SD16C22semidirect
20. C2×C13×M16C22semidirect
21. C13×C22⋊Q8C22semidirect
23. #88200C22semidirect
24. Q8×Dic13C22semidirect
26. C2×#6106C22semidirect
30. #88180C22semidirect
31. C2×C8×D13C22semidirect
35. C4⋊C4×D13C22semidirect
36. #88144C22semidirect
42. C13×#107C22semidirect
43. C13×#103C22semidirect
44. C13×#102C22semidirect
45. #88072C22semidirect
46. #88072C22semidirect
47. C22⋊#1055C22semidirect
50. #88061C22semidirect
51. #88061C22semidirect
52. #88060C22semidirect
53. #88055C22semidirect
54. #88054C22semidirect
56. #88049C22semidirect
57. #88048C22semidirect
58. #88047C22semidirect
165. #468D13semidirect
208. C2×SD16C2×D13semidirect
209. C2×M16C2×D13semidirect
217. C22⋊Q8C2×D13semidirect
230. #107C2×D13semidirect
233. #103C2×D13semidirect
242. #102C2×D13semidirect
307. C13#3310semidirect

Maximal subgroups

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

subgroupindex
#117193442
#117193142
C13×#4682
#117188302
#117188242
#117187922
#117187882
#117187072
#117186962
#117185522
#117185432
#117184782
#117184682
D13×#1022
#117184252
#331013