Finite Group Databasebeta

← #13127065

Subgroups — #13127065

Order 1664.

448 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#11719314C211yesmaximal, characteristic
2#11719238C211yesmaximal, characteristic, complemented
3C13×#482C211yesmaximal, characteristic, complemented
4#11718703C211yesmaximal, characteristic, complemented
5#11718662C211yesmaximal, characteristic, complemented
6#11718551C211yesmaximal, characteristic, complemented
7#11718547C211yesmaximal, characteristic, complemented
8#11718527C211yesmaximal, characteristic, complemented
9#11718513C211yesmaximal, characteristic, complemented
10#11718437C211yesmaximal, characteristic, complemented
11#11718431C211yesmaximal, characteristic, complemented
12#11718423C211yesmaximal, characteristic, complemented
13#11718421C211yesmaximal, characteristic, complemented
14#11718392C211yesmaximal, characteristic, complemented
15#11718390C211yesmaximal, characteristic, complemented
16C2×D4×D13—21no—
17C2×D4×D13C2211yescharacteristic
18C22×D52C2211yescharacteristic
19C13×#121C2211yescharacteristic
20C13×#117C2211yescharacteristic, complemented
21#88194C2211yescharacteristic
22#88191—21no—
23C2×#6105C2211yescharacteristic, complemented
24C4×C22⋊D13C2211yescharacteristic
25#88178C2211yescharacteristic, complemented
26C2×#6099C2211yescharacteristic, complemented
27C2×#6095C2211yescharacteristic
28C2×#6095C2211yescharacteristic, complemented
29C2×#6094C2211yescharacteristic, complemented
30#88151C2211yescharacteristic, complemented
31#88149C2211yescharacteristic
32#88147C2211yescharacteristic
33#88146C2211yescharacteristic, complemented
34#88142C2211yescharacteristic, complemented
35#88141C2211yescharacteristic, complemented
36#88139—21no—
37#88138—21no—
38#88136—21no—
39#88133—21no—
40#88130—21no—
41C4×Dic26—21no—
42C13×#107C2211yescharacteristic, complemented
43C13×#106C2211yescharacteristic, complemented
44C13×#102C2211yescharacteristic, complemented
45C13×#102C2211yescharacteristic, complemented
46C13×C22⋊C8C2211yescharacteristic, complemented
47#88072C2211yescharacteristic, complemented
48#88061C2211yescharacteristic
49#88061C2211yescharacteristic, complemented
50#88060C2211yescharacteristic, complemented
51#88054C2211yescharacteristic, complemented
52C8×Dic13C2211yescharacteristic, complemented
53#88050C2211yescharacteristic, complemented
54#88049C2211yescharacteristic
55#88049C2211yescharacteristic
56#88049C2211yescharacteristic, complemented
57#88049C2211yescharacteristic, complemented
58#88047C2211yescharacteristic, complemented
59C23×D13—21no—
60C23×D13—21no—
61C2×D4×C13—21no—
62C2×D4×C13C2311yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C2×C22⋊D13—21no—
65C2×C22⋊D13—21no—
66C2×C22⋊D13—21no—
67C2×C22⋊D13D411yescharacteristic
68D4×D13—22no—
69D4×D13—41no—
70D4×D13—44no—
71C2×D52—22no—
72C2×D52—21no—
73C2×D52—21no—
74C2×D52—41no—
75C2×D52C2311yescharacteristic
76C2×D52C2311yescharacteristic
77C2×C4×D13—21no—
78C2×C4×D13C2311yescharacteristic
79C2×Dic26—21no—
80C2×Dic26C2311yescharacteristic
81C2×C8×C13C2311yescharacteristic
82C2×C8×C13C2311yescharacteristic
83C13×C4⋊C4C2311yescharacteristic
84C13×C4⋊C4C2311yescharacteristic
85C13×C4⋊C4C2311yescharacteristic
86C13×C22⋊C4—21no—
87C13×C22⋊C4—21no—
88C42×C13—21no—
89C22⋊Dic13—21no—
90C22⋊Dic13D411yescharacteristic
91#6105—41no—
92#6103—21no—
93#6103—21no—
94#6103—21no—
95#6103—21no—
96#6103D411yescharacteristic
97C4⋊Dic13—21no—
98C4⋊Dic13C2311yescharacteristic
99#6101—21no—
100#6101—21no—
101#6101—21no—
102#6101D411yescharacteristic
103C4×Dic13—21no—
104C4×Dic13—21no—
105C4×Dic13C2311yescharacteristic
106#6099—41no—
107C2×#1055C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109#6095—22no—
110#6095—41no—
111#6094—41no—
112#3324—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
124D4×C13—21no—
125D4×C13—21no—
126D4×C13—42no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13C2×D411yescharacteristic
133C2×C4×C13C2411yescharacteristic
134C22⋊D13—22no—
135C22⋊D13—42no—
136C22⋊D13—42no—
137C22⋊D13—81no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13C2×D411yescharacteristic
141C2×Dic13C2×D411yescharacteristic
142C2×Dic13C2×D411yescharacteristic
143D52—21no—
144D52—21no—
145D52—21no—
146D52—42no—
147D52—42no—
148D52#4112yes—
149C4×D13—21no—
150C4×D13—21no—
151C4×D13—42no—
152Dic26—21no—
153Dic26—21no—
154Dic26—42no—
155C8×C13—21no—
156C8×C13—21no—
157#1055—21no—
158#1055—21no—
159#556—131no—
160D42—131no—
161#486—131no—
162#482—131no—
163#482D1311yescharacteristic, complemented
164#474—131no—
165#468—131no—
166#468—131no—
167#460—131no—
168#450—131no—
169#450—131no—
170C4×SD16—131no—
171#436—131no—
172#418—131no—
173#418—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—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—
191C2×D13—84no—
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—41no—
201Dic13—41no—
202Dic13AGL(1,ℤ/8)12yes—
203C22×D4—131no—
204C22×D4—131no—
205C22×D4—261no—
206C2×SD16—131no—
207C2×SD16—131no—
208C2×SD16—131no—
209C2×M16—131no—
210C2×M16—131no—
211C4⋊Q8—131no—
212#127—131no—
213#126—261no—
214#126—261no—
215#124—261no—
216C22⋊Q8—131no—
217C22⋊Q8—131no—
218#121—131no—
219#121—261no—
220#121C2×D1311yescharacteristic
221#120—261no—
222#120—261no—
223C4×Q8—131no—
224C4×Q8—261no—
225C4×D4—131no—
226C4×D4—131no—
227#117—131no—
228#117C2×D1311yescharacteristic, complemented
229#107—131no—
230#107C2×D1311yescharacteristic, complemented
231#106C2×D1311yescharacteristic, complemented
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, complemented
242#102C2×D1311yescharacteristic, complemented
243C22⋊C8—131no—
244C22⋊C8C2×D1311yescharacteristic, complemented
245C4×C8—131no—
246C2×C13—41no—
247C2×C13—81no—
248C2×C13#54611yescharacteristic
249C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
250C2×C13#57711yescharacteristic
251D13—41no—
252D13—42no—
253D13—81no—
254C24—261no—
255C24—261no—
256C2×Q8—131no—
257C2×Q8—261no—
258C2×D4—21no—
259C2×D4—131no—
260C2×D4—131no—
261C2×D4—131no—
262C2×D4—262no—
263C2×D4—261no—
264C2×D4—261no—
265C2×D4—261no—
266C2×D4—261no—
267C2×D4—262no—
268C2×D4—261no—
269C2×D4—521no—
270C2×D4—521no—
271C2×D4—524no—
272C2×D4C22×D1311yescharacteristic
273C22×C4—131no—
274C22×C4—261no—
275C22×C4C22×D1311yescharacteristic
276SD16—262no—
277SD16—521no—
278SD16—521no—
279M16—521no—
280M16—521no—
281C2×C8—131no—
282C2×C8—131no—
283C2×C8C22×D1311yescharacteristic
284C2×C8C22×D1311yescharacteristic
285C4⋊C4—131no—
286C4⋊C4—131no—
287C4⋊C4—261no—
288C4⋊C4—261no—
289C4⋊C4—261no—
290C4⋊C4—261no—
291C4⋊C4C22×D1311yescharacteristic
292C4⋊C4C22×D1311yescharacteristic
293C4⋊C4C22×D1311yescharacteristic
294C22⋊C4—21no—
295C22⋊C4—21no—
296C22⋊C4—131no—
297C22⋊C4—131no—
298C22⋊C4—261no—
299C22⋊C4—261no—
300C22⋊C4—261no—
301C22⋊C4—261no—
302C22⋊C4—261no—
303C42—21no—
304C42—131no—
305C42—261no—
306C42—261no—
307C13#332411yescharacteristic, 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—261no—
320Q8—261no—
321Q8—522no—
322D4—21no—
323D4—21no—
324D4—42no—
325D4—132no—
326D4—262no—
327D4—261no—
328D4—261no—
329D4—261no—
330D4—522no—
331D4—522no—
332D4—522no—
333D4—522no—
334D4—1041no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—131no—
341C2×C4—131no—
342C2×C4—131no—
343C2×C4—261no—
344C2×C4—261no—
345C2×C4—261no—
346C2×C4—261no—
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—261no—
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—132no—
377C4—261no—
378C4—261no—
379C4—521no—
380C4—521no—
381C4#41×D1311yescharacteristic
382C4#8825611yescharacteristic
383C2—41no—
384C2—81no—
385C2—521no—
386C2—522no—
387C2—1041no—
388C2#1171935911yescharacteristic
389C2#1171947511yescharacteristic
390C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#482C2
socleC22×C13C22×D4
prime radical#11719314C2
hypercenter#482D13
hypocenterC13#3324
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. #11719238C2semidirect
3. C13×#482C2semidirect
4. #11718703C2semidirect
5. #11718662C2semidirect
6. #11718551C2semidirect
7. #11718547C2semidirect
8. #11718527C2semidirect
9. #11718513C2semidirect
10. #11718437C2semidirect
11. #11718431C2semidirect
12. #11718423C2semidirect
13. #11718421C2semidirect
14. #11718392C2semidirect
15. #11718390C2semidirect
20. C13×#117C22semidirect
23. C2×#6105C22semidirect
25. #88178C22semidirect
26. C2×#6099C22semidirect
28. C2×#6095C22semidirect
29. C2×#6094C22semidirect
30. #88151C22semidirect
33. #88146C22semidirect
34. #88142C22semidirect
35. #88141C22semidirect
42. C13×#107C22semidirect
43. C13×#106C22semidirect
44. C13×#102C22semidirect
45. C13×#102C22semidirect
46. C13×C22⋊C8C22semidirect
47. #88072C22semidirect
49. #88061C22semidirect
50. #88060C22semidirect
51. #88054C22semidirect
52. C8×Dic13C22semidirect
53. #88050C22semidirect
56. #88049C22semidirect
57. #88049C22semidirect
58. #88047C22semidirect
163. #482D13semidirect
228. #117C2×D13semidirect
230. #107C2×D13semidirect
231. #106C2×D13semidirect
241. #102C2×D13semidirect
242. #102C2×D13semidirect
244. C22⋊C8C2×D13semidirect
307. C13#3324semidirect

Maximal subgroups

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

subgroupindex
#117193142
#117192382
C13×#4822
#117187032
#117186622
#117185512
#117185472
#117185272
#117185132
#117184372
#117184312
#117184232
#117184212
#117183922
#117183902
#332413