Finite Group Databasebeta

← #13126861

Subgroups — #13126861

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
1D4×C22⋊D13C211yesmaximal, characteristic
2#11719347C211yesmaximal, characteristic, complemented
3C13×#450C211yesmaximal, characteristic, complemented
4C2×#88072C211yesmaximal, characteristic, complemented
5#11718835C211yesmaximal, characteristic, complemented
6#11718830C211yesmaximal, characteristic, complemented
7#11718825C211yesmaximal, characteristic, complemented
8#11718824C211yesmaximal, characteristic, complemented
9#11718709C211yesmaximal, characteristic, complemented
10#11718445C211yesmaximal, characteristic, complemented
11#11718431C211yesmaximal, characteristic, complemented
12#11718427C211yesmaximal, characteristic, complemented
13#11718425C211yesmaximal, characteristic, complemented
14#11718397C211yesmaximal, characteristic, complemented
15#11718391C211yesmaximal, characteristic, complemented
16C22×D4×C13C2211yescharacteristic
17C22×C22⋊D13—21no—
18C2×D4×D13C2211yescharacteristic
19C2×C13×SD16C2211yescharacteristic
20C2×C13×SD16C2211yescharacteristic, complemented
21C13×C22⋊Q8C2211yescharacteristic, complemented
22#88207—21no—
23#88200C2211yescharacteristic, complemented
24Q8×Dic13C2211yescharacteristic, complemented
25C2×#6106C2211yescharacteristic, complemented
26#88194C2211yescharacteristic
27#88193—21no—
28#88192C2211yescharacteristic
29#88191—21no—
30D4×Dic13C2211yescharacteristic
31#88184C2211yescharacteristic
32C4×C22⋊D13C2211yescharacteristic
33C2×C4⋊Dic13C2211yescharacteristic, complemented
34C22×#1055C2211yescharacteristic, complemented
35C2×#6094C2211yescharacteristic, complemented
36#88152—21no—
37#88146C2211yescharacteristic, complemented
38#88144—21no—
39#88144C2211yescharacteristic, complemented
40#88140—21no—
41#88131—21no—
42C13×#102C2211yescharacteristic
43C13×#102C2211yescharacteristic, complemented
44C13×C22⋊C8C2211yescharacteristic, complemented
45#88075C2211yescharacteristic, complemented
46#88072C2211yescharacteristic
47#88072C2211yescharacteristic
48#88072C2211yescharacteristic, complemented
49#88072C2211yescharacteristic, complemented
50#88061C2211yescharacteristic, complemented
51#88061C2211yescharacteristic, complemented
52#88060C2211yescharacteristic, complemented
53#88058C2211yescharacteristic, complemented
54#88058C2211yescharacteristic, complemented
55#88055C2211yescharacteristic, complemented
56#88054C2211yescharacteristic, complemented
57#88049C2211yescharacteristic, complemented
58#88048C2211yescharacteristic, complemented
59C24×C13—21no—
60C23×D13—21no—
61C2×Q8×C13C2311yescharacteristic
62C2×D4×C13—22no—
63C2×D4×C13—21no—
64C2×D4×C13—41no—
65C2×D4×C13C2311yescharacteristic
66C2×D4×C13C2311yescharacteristic
67C22×C4×C13C2311yescharacteristic
68C2×C22⋊D13—21no—
69C2×C22⋊D13—21no—
70C2×C22⋊D13—21no—
71C2×C22⋊D13—21no—
72C2×C22⋊D13—21no—
73C2×C22⋊D13—44no—
74C2×C22⋊D13D411yescharacteristic
75C22×Dic13—21no—
76C22×Dic13—21no—
77D4×D13—22no—
78D4×D13—41no—
79C2×D52C2311yescharacteristic
80C2×C4×D13C2311yescharacteristic
81C13×SD16—22no—
82C13×SD16—41no—
83C2×C8×C13C2311yescharacteristic
84C2×C8×C13C2311yescharacteristic
85C13×C4⋊C4—21no—
86C13×C4⋊C4C2311yescharacteristic
87C13×C22⋊C4—21no—
88C22⋊Dic13—21no—
89C22⋊Dic13—21no—
90C22⋊Dic13D411yescharacteristic
91#6106—41no—
92#6103—21no—
93#6103—21no—
94#6103—21no—
95#6103D411yescharacteristic
96C4⋊Dic13—21no—
97C4⋊Dic13—21no—
98C4⋊Dic13—21no—
99C4⋊Dic13C2311yescharacteristic
100C4⋊Dic13C2311yescharacteristic
101C4⋊Dic13C2311yescharacteristic
102#6101—21no—
103#6101—21no—
104#6101D411yescharacteristic
105C4×Dic13—21no—
106C4×Dic13—21no—
107C4×Dic13C2311yescharacteristic
108C2×#1055—41no—
109C2×#1055C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111#6094—41no—
112#3310—131nomaximal, Sylow
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—42no—
116C23×C13—42no—
117C23×C13—81no—
118C23×C13C2×D411yescharacteristic
119C22×D13—21no—
120C22×D13—42no—
121C22×D13—42no—
122C22×D13—81no—
123C22×D13C2×D411yescharacteristic
124Q8×C13—21no—
125Q8×C13—21no—
126D4×C13—21no—
127D4×C13—21no—
128D4×C13—21no—
129D4×C13—42no—
130D4×C13#4112yes—
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—42no—
141C22⋊D13—42no—
142C22⋊D13—81no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—42no—
147C2×Dic13—42no—
148C2×Dic13C2×D411yescharacteristic
149C2×Dic13C2×D411yescharacteristic
150C2×Dic13C2×D411yescharacteristic
151D52—21no—
152D52—21no—
153C4×D13—21no—
154C4×D13—21no—
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#468—131no—
166#465—131no—
167#460—131no—
168#450—131no—
169#450D1311yescharacteristic, complemented
170#440—131no—
171#435—131no—
172#418—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—84no—
183C22×C13AGL(1,ℤ/8)12yes—
184C22×C13C22×D411yescharacteristic
185C2×D13—21no—
186C2×D13—21no—
187C2×D13—21no—
188C2×D13—41no—
189C2×D13—41no—
190C2×D13—41no—
191C2×D13—84no—
192C4×C13—21no—
193C4×C13—41no—
194C4×C13—41no—
195C4×C13C2×#4111yescharacteristic
196C4×C13H(5,𝔽2)11yescharacteristic
197Dic13—21no—
198Dic13—21no—
199Dic13—21no—
200Dic13—41no—
201Dic13—41no—
202Dic13—41no—
203C22×D4—131no—
204C22×D4—261no—
205C22×D4C2×D1311yescharacteristic
206C2×SD16—131no—
207C2×SD16C2×D1311yescharacteristic
208C2×SD16C2×D1311yescharacteristic, complemented
209C2×M16—131no—
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—131no—
220#121—261no—
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#107—131no—
231#106—131no—
232C4⋊C8—131no—
233#103—131no—
234#102—131no—
235#102—131no—
236#102—131no—
237#102—131no—
238#102—131no—
239#102—131no—
240#102—131no—
241#102C2×D1311yescharacteristic
242#102C2×D1311yescharacteristic, complemented
243C22⋊C8—131no—
244C22⋊C8C2×D1311yescharacteristic, complemented
245#97—131no—
246C2×C13—22no—
247C2×C13—42no—
248C2×C13—81no—
249C2×C13#54611yescharacteristic
250C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
251C2×C13#57711yescharacteristic
252D13—41no—
253D13—81no—
254C24—21no—
255C24—261no—
256C2×Q8C22×D1311yescharacteristic
257C2×D4—22no—
258C2×D4—21no—
259C2×D4—41no—
260C2×D4—131no—
261C2×D4—131no—
262C2×D4—261no—
263C2×D4—261no—
264C2×D4—261no—
265C2×D4—262no—
266C2×D4—261no—
267C2×D4—261no—
268C2×D4—521no—
269C2×D4—524no—
270C2×D4C22×D1311yescharacteristic
271C2×D4C22×D1311yescharacteristic
272C22×C4—131no—
273C22×C4—261no—
274C22×C4—261no—
275C22×C4C22×D1311yescharacteristic
276SD16—22no—
277SD16—41no—
278SD16—521no—
279M16—521no—
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—131no—
290C4⋊C4—261no—
291C4⋊C4—261no—
292C4⋊C4—261no—
293C4⋊C4—261no—
294C4⋊C4—261no—
295C4⋊C4C22×D1311yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—131no—
298C22⋊C4—131no—
299C22⋊C4—261no—
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—21no—
310C23—42no—
311C23—42no—
312C23—81no—
313C23—131no—
314C23—261no—
315C23—522no—
316C23—522no—
317C23—1041no—
318C23D4×D1311yescharacteristic
319Q8—21no—
320Q8—21no—
321D4—21no—
322D4—21no—
323D4—21no—
324D4—42no—
325D4—262no—
326D4—261no—
327D4—261no—
328D4—522no—
329D4—522no—
330D4—522no—
331D4—522no—
332D4—1041no—
333D4#612912yes—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—131no—
339C2×C4—131no—
340C2×C4—131no—
341C2×C4—261no—
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—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—84no—
363C22—261no—
364C22—261no—
365C22—261no—
366C22—521no—
367C22—521no—
368C22—521no—
369C22—1044no—
370C22#8816812yes—
371C22C2×D4×D1311yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—261no—
376C4—261no—
377C4—261no—
378C4—521no—
379C4—521no—
380C4—521no—
381C4C2×#612911yescharacteristic
382C4#8825111yescharacteristic
383C2—22no—
384C2—42no—
385C2—81no—
386C2—521no—
387C2—1041no—
388C2#1171929611yescharacteristic
389C2C2×#8816811yescharacteristic
390C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#450C2
socleC22×C13C22×D4
prime radicalD4×C22⋊D13C2
hypercenter#450D13
hypocenterC13#3310
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
2. #11719347C2semidirect
3. C13×#450C2semidirect
4. C2×#88072C2semidirect
5. #11718835C2semidirect
6. #11718830C2semidirect
7. #11718825C2semidirect
8. #11718824C2semidirect
9. #11718709C2semidirect
10. #11718445C2semidirect
11. #11718431C2semidirect
12. #11718427C2semidirect
13. #11718425C2semidirect
14. #11718397C2semidirect
15. #11718391C2semidirect
20. C2×C13×SD16C22semidirect
21. C13×C22⋊Q8C22semidirect
23. #88200C22semidirect
24. Q8×Dic13C22semidirect
25. C2×#6106C22semidirect
33. C2×C4⋊Dic13C22semidirect
34. C22×#1055C22semidirect
35. C2×#6094C22semidirect
37. #88146C22semidirect
39. #88144C22semidirect
43. C13×#102C22semidirect
44. C13×C22⋊C8C22semidirect
45. #88075C22semidirect
48. #88072C22semidirect
49. #88072C22semidirect
50. #88061C22semidirect
51. #88061C22semidirect
52. #88060C22semidirect
53. #88058C22semidirect
54. #88058C22semidirect
55. #88055C22semidirect
56. #88054C22semidirect
57. #88049C22semidirect
58. #88048C22semidirect
169. #450D13semidirect
208. C2×SD16C2×D13semidirect
217. C22⋊Q8C2×D13semidirect
242. #102C2×D13semidirect
244. C22⋊C8C2×D13semidirect
307. C13#3310semidirect

Maximal subgroups

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

subgroupindex
D4×C22⋊D132
#117193472
C13×#4502
C2×#880722
#117188352
#117188302
#117188252
#117188242
#117187092
#117184452
#117184312
#117184272
#117184252
#117183972
#117183912
#331013