Finite Group Databasebeta

← #13125191

Subgroups — #13125191

Order 1664.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719420C211yesmaximal, characteristic
2#11719394C211yesmaximal, characteristic, complemented
3C13×#490C211yesmaximal, characteristic, complemented
4#11718731C211yesmaximal, characteristic, complemented
5#11718729C211yesmaximal, characteristic, complemented
6#11718433C211yesmaximal, characteristic, complemented
7#11718432C211yesmaximal, characteristic, complemented
8#11718431C211yesmaximal, characteristic, complemented
9D13×#102C211yesmaximal, characteristic, complemented
10#11718429C211yesmaximal, characteristic, complemented
11#11718426C211yesmaximal, characteristic, complemented
12#11718425C211yesmaximal, characteristic, complemented
13#11718421C211yesmaximal, characteristic, complemented
14#11718375C211yesmaximal, characteristic, complemented
15#11718369C211yesmaximal, characteristic, complemented
16C2×#6129C2211yescharacteristic
17C2×D4×D13C2211yescharacteristic
18C13×#127C2211yescharacteristic
19C13×#125C2211yescharacteristic, complemented
20#88194C2211yescharacteristic
21#88193—21no—
22#88193—21no—
23#88191—21no—
24#88191—21no—
25#88190C2211yescharacteristic
26C2×#6094C2211yescharacteristic
27C2×C8×D13C2211yescharacteristic
28#88151—21no—
29#88150—21no—
30#88146C2211yescharacteristic
31C4⋊C4×D13C2211yescharacteristic
32#88144C2211yescharacteristic, complemented
33#88143—21no—
34#88142—21no—
35#88142C2211yescharacteristic, complemented
36#88129C2211yescharacteristic
37#88126C2211yescharacteristic
38#88123C2211yescharacteristic, complemented
39C13×#102C2211yescharacteristic
40C13×#102C2211yescharacteristic
41C13×#102C2211yescharacteristic, complemented
42C13×#102C2211yescharacteristic, complemented
43C13×#97C2211yescharacteristic, complemented
44#88072C2211yescharacteristic
45#88072C2211yescharacteristic
46#88072C2211yescharacteristic, complemented
47#88072C2211yescharacteristic, complemented
48#88061C2211yescharacteristic
49#88061C2211yescharacteristic
50#88056C2211yescharacteristic, complemented
51#88056C2211yescharacteristic, complemented
52#88055C2211yescharacteristic, complemented
53C8×Dic13C2211yescharacteristic, complemented
54#88050C2211yescharacteristic, complemented
55#88050C2211yescharacteristic, complemented
56#88049C2211yescharacteristic
57#88049C2211yescharacteristic
58C4×#1055C2211yescharacteristic, complemented
59C23×D13—21no—
60C2×D4×C13—21no—
61C2×D4×C13—21no—
62C2×D4×C13C2311yescharacteristic
63C2×D4×C13C2311yescharacteristic
64C2×C22⋊D13—21no—
65C2×C22⋊D13—21no—
66C2×C22⋊D13—21no—
67C2×C22⋊D13—21no—
68C22×Dic13—21no—
69#6129—22no—
70#6129—22no—
71D4×D13—22no—
72D4×D13—22no—
73C2×D52C2311yescharacteristic
74C2×C4×D13—21no—
75C2×C4×D13C2311yescharacteristic
76C2×Dic26—21no—
77C2×Dic26—21no—
78C2×Dic26C2311yescharacteristic
79C2×C8×C13C2311yescharacteristic
80C2×C8×C13C2311yescharacteristic
81C13×C4⋊C4—21no—
82C13×C4⋊C4—21no—
83C13×C4⋊C4C2311yescharacteristic
84C13×C4⋊C4C2311yescharacteristic
85C42×C13C2311yescharacteristic
86C22⋊Dic13—21no—
87C22⋊Dic13—21no—
88#6103—21no—
89#6103—21no—
90#6103—21no—
91#6103D411yescharacteristic
92#6103D411yescharacteristic
93C4⋊Dic13—21no—
94C4⋊Dic13—21no—
95C4⋊Dic13C2311yescharacteristic
96C4⋊Dic13C2311yescharacteristic
97#6101—21no—
98#6101—21no—
99#6101—21no—
100#6101D411yescharacteristic
101#6101D411yescharacteristic
102C4×Dic13—21no—
103C4×Dic13C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106#6094—22no—
107C8×D13—22no—
108#3136—131nomaximal, Sylow
109C23×C13—21no—
110C23×C13—21no—
111C22×D13—21no—
112C22×D13—42no—
113C22×D13—81no—
114C22×D13—81no—
115C22×D13C2×D411yescharacteristic
116D4×C13—21no—
117D4×C13—21no—
118D4×C13—21no—
119D4×C13—21no—
120D4×C13—81no—
121D4×C13—81no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13C2×D411yescharacteristic
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2411yescharacteristic
127C22⋊D13—42no—
128C22⋊D13—42no—
129C22⋊D13—81no—
130C22⋊D13—81no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—42no—
135C2×Dic13C2×D411yescharacteristic
136C2×Dic13C2×D411yescharacteristic
137C2×Dic13C2×D411yescharacteristic
138D52—21no—
139D52—21no—
140C4×D13—81no—
141C4×D13#4112yes—
142C4×D13#4112yes—
143Dic26—21no—
144Dic26—21no—
145Dic26—81no—
146Dic26—81no—
147C8×C13—21no—
148C8×C13—21no—
149#1055—21no—
150#1055—21no—
151#544—131no—
152#535—131no—
153#490—131no—
154#490D1311yescharacteristic, complemented
155#489—131no—
156#489—131no—
157#488—131no—
158#488—131no—
159#486—131no—
160#486—131no—
161#418—131no—
162#417—131no—
163#416—131no—
164C2×#102—131no—
165#405—131no—
166C22×C13—41no—
167C22×C13—41no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13C22×D411yescharacteristic
173C2×D13—21no—
174C2×D13—21no—
175C2×D13—41no—
176C2×D13—41no—
177C2×D13—41no—
178C2×D13—84no—
179C2×D13#12412yes—
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—41no—
183C4×C13—41no—
184C4×C13C2×#4111yescharacteristic
185C4×C13C2×#4111yescharacteristic
186Dic13—21no—
187Dic13—21no—
188Dic13—41no—
189Dic13—41no—
190Dic13—41no—
191Dic13#12412yes—
192C2×#41—131no—
193C22×D4—131no—
194C2×M16—131no—
195C22×C8—131no—
196C4⋊Q8—131no—
197C4⋊Q8—131no—
198C4⋊Q8—261no—
199#127—131no—
200#127C2×D1311yescharacteristic
201#125—131no—
202#125—261no—
203#125C2×D1311yescharacteristic, complemented
204#124—131no—
205#124—131no—
206C22⋊Q8—261no—
207C22⋊Q8—261no—
208#121—261no—
209#121—261no—
210#120—261no—
211#120—261no—
212#117—131no—
213#117—131no—
214C2×C4⋊C4—131no—
215#103—131no—
216#103—131no—
217#103—131no—
218#103—131no—
219#102—131no—
220#102—131no—
221#102—131no—
222#102—131no—
223#102—131no—
224#102—131no—
225#102—131no—
226#102—131no—
227#102C2×D1311yescharacteristic
228#102C2×D1311yescharacteristic
229#102C2×D1311yescharacteristic, complemented
230#102C2×D1311yescharacteristic, complemented
231#97—131no—
232#97C2×D1311yescharacteristic, complemented
233C4×C8—131no—
234C4×C8—131no—
235C2×C13—81no—
236C2×C13—81no—
237C2×C13C2×#12411yescharacteristic
238C2×C13#57611yescharacteristic
239C2×C13#57711yescharacteristic
240D13—22no—
241D13—81no—
242C24—261no—
243#41—262no—
244#41—262no—
245C2×Q8—131no—
246C2×Q8—261no—
247C2×Q8—261no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4—131no—
251C2×D4—262no—
252C2×D4—262no—
253C2×D4—261no—
254C2×D4—261no—
255C2×D4—261no—
256C2×D4—261no—
257C2×D4C22×D1311yescharacteristic
258C2×D4C22×D1311yescharacteristic
259C22×C4—131no—
260C22×C4—261no—
261C22×C4—261no—
262M16—262no—
263C2×C8—131no—
264C2×C8—131no—
265C2×C8—262no—
266C2×C8C22×D1311yescharacteristic
267C2×C8C22×D1311yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—131no—
271C4⋊C4—131no—
272C4⋊C4—131no—
273C4⋊C4—131no—
274C4⋊C4—261no—
275C4⋊C4—261no—
276C4⋊C4—261no—
277C4⋊C4—261no—
278C4⋊C4—261no—
279C4⋊C4C22×D1311yescharacteristic
280C4⋊C4C22×D1311yescharacteristic
281C22⋊C4—131no—
282C22⋊C4—131no—
283C22⋊C4—261no—
284C22⋊C4—261no—
285C22⋊C4—261no—
286C22⋊C4—261no—
287C22⋊C4—261no—
288C42—131no—
289C42—261no—
290C42C22×D1311yescharacteristic
291C13#313611yescharacteristic, complemented, Sylow
292C23—21no—
293C23—21no—
294C23—131no—
295C23—261no—
296C23—522no—
297C23—1041no—
298C23—1041no—
299Q8—261no—
300Q8—261no—
301Q8—1041no—
302Q8—1041no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—81no—
308D4—81no—
309D4—261no—
310D4—261no—
311D4—522no—
312D4—522no—
313D4—1041no—
314D4—1041no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—131no—
318C2×C4—132no—
319C2×C4—132no—
320C2×C4—131no—
321C2×C4—131no—
322C2×C4—261no—
323C2×C4—261no—
324C2×C4—261no—
325C2×C4—522no—
326C2×C4—1041no—
327C2×C4D4×D1311yescharacteristic
328C2×C4D4×D1311yescharacteristic
329C2×C4C23×D1311yescharacteristic
330C8—21no—
331C8—21no—
332C8—261no—
333C8—261no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—132no—
341C22—261no—
342C22—261no—
343C22—521no—
344C22—521no—
345C22—521no—
346C22—1044no—
347C22C2×D4×D1311yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—132no—
353C4—261no—
354C4—261no—
355C4—521no—
356C4—521no—
357C4—521no—
358C4#41×D1311yescharacteristic
359C4#41×D1311yescharacteristic
360C2—81no—
361C2—81no—
362C2—262no—
363C2—1041no—
364C2D13×#12411yescharacteristic
365C2#1171947911yescharacteristic
366C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#490C2
socleC22×C13C22×D4
prime radical#11719420C2
hypercenter#490D13
hypocenterC13#3136
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
2. #11719394C2semidirect
3. C13×#490C2semidirect
4. #11718731C2semidirect
5. #11718729C2semidirect
6. #11718433C2semidirect
7. #11718432C2semidirect
8. #11718431C2semidirect
9. D13×#102C2semidirect
10. #11718429C2semidirect
11. #11718426C2semidirect
12. #11718425C2semidirect
13. #11718421C2semidirect
14. #11718375C2semidirect
15. #11718369C2semidirect
19. C13×#125C22semidirect
32. #88144C22semidirect
35. #88142C22semidirect
38. #88123C22semidirect
41. C13×#102C22semidirect
42. C13×#102C22semidirect
43. C13×#97C22semidirect
46. #88072C22semidirect
47. #88072C22semidirect
50. #88056C22semidirect
51. #88056C22semidirect
52. #88055C22semidirect
53. C8×Dic13C22semidirect
54. #88050C22semidirect
55. #88050C22semidirect
58. C4×#1055C22semidirect
154. #490D13semidirect
203. #125C2×D13semidirect
229. #102C2×D13semidirect
230. #102C2×D13semidirect
232. #97C2×D13semidirect
291. C13#3136semidirect

Maximal subgroups

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

subgroupindex
#117194202
#117193942
C13×#4902
#117187312
#117187292
#117184332
#117184322
#117184312
D13×#1022
#117184292
#117184262
#117184252
#117184212
#117183752
#117183692
#313613