Finite Group Databasebeta

← #13126867

Subgroups — #13126867

Order 1664.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719346C211yesmaximal, characteristic, complemented
2#11719335C211yesmaximal, characteristic
3C13×#470C211yesmaximal, characteristic, complemented
4#11718848C211yesmaximal, characteristic, complemented
5#11718846C211yesmaximal, characteristic, complemented
6#11718792C211yesmaximal, characteristic, complemented
7#11718788C211yesmaximal, characteristic, complemented
8#11718707C211yesmaximal, characteristic, complemented
9#11718706C211yesmaximal, characteristic, complemented
10#11718531C211yesmaximal, characteristic, complemented
11#11718527C211yesmaximal, characteristic, complemented
12#11718478C211yesmaximal, characteristic, complemented
13#11718468C211yesmaximal, characteristic, complemented
14#11718465C211yesmaximal, characteristic, complemented
15#11718456C211yesmaximal, characteristic, complemented
16C2×#6131C2211yescharacteristic
17C22×D52C2211yescharacteristic
18C2×C13×Q16C2211yescharacteristic, complemented
19C2×C13×M16C2211yescharacteristic
20C13×C22⋊Q8C2211yescharacteristic
21C13×C22⋊Q8C2211yescharacteristic
22#88201C2211yescharacteristic
23#88200C2211yescharacteristic, complemented
24Q8×Dic13C2211yescharacteristic, complemented
25C2×#6106C2211yescharacteristic
26C2×#6106C2211yescharacteristic
27C4×C22⋊D13C2211yescharacteristic
28#88180C2211yescharacteristic
29C2×C8×D13C2211yescharacteristic, complemented
30#88152—21no—
31#88149—21no—
32#88149C2211yescharacteristic
33#88148—21no—
34#88147C2211yescharacteristic
35#88146C2211yescharacteristic, complemented
36#88142C2211yescharacteristic, complemented
37#88141—21no—
38#88139—21no—
39#88136—21no—
40C22⋊C4×D13—21no—
41#88133—21no—
42C13×#106C2211yescharacteristic, complemented
43C13×#103C2211yescharacteristic, complemented
44C13×#103C2211yescharacteristic, complemented
45#88075C2211yescharacteristic, complemented
46#88075C2211yescharacteristic, complemented
47C22⋊#1055C2211yescharacteristic
48#88061C2211yescharacteristic
49#88061C2211yescharacteristic
50#88061C2211yescharacteristic
51#88061C2211yescharacteristic
52#88060C2211yescharacteristic, complemented
53#88055C2211yescharacteristic, complemented
54#88054C2211yescharacteristic, complemented
55#88049C2211yescharacteristic
56#88049C2211yescharacteristic
57#88048C2211yescharacteristic, complemented
58#88047C2211yescharacteristic, complemented
59C23×D13—21no—
60C2×Q8×C13C2311yescharacteristic
61C2×Q8×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C2×C22⋊D13D411yescharacteristic
64#6131—22no—
65#6131—41no—
66C2×D52—22no—
67C2×D52—21no—
68C2×D52—21no—
69C2×D52—21no—
70C2×D52—41no—
71C2×D52C2311yescharacteristic
72C2×D52C2311yescharacteristic
73C2×C4×D13—21no—
74C2×C4×D13—21no—
75C2×C4×D13C2311yescharacteristic
76C2×Dic26—21no—
77C13×Q16—41no—
78C13×M16—41no—
79C2×C8×C13C2311yescharacteristic
80C2×C8×C13C2311yescharacteristic
81C13×C4⋊C4—21no—
82C13×C4⋊C4—21no—
83C13×C4⋊C4C2311yescharacteristic
84C13×C4⋊C4C2311yescharacteristic
85C13×C22⋊C4—21no—
86C13×C22⋊C4—21no—
87C22⋊Dic13—21no—
88C22⋊Dic13D411yescharacteristic
89#6106—22no—
90#6106—41no—
91#6103—21no—
92#6103—21no—
93#6103—21no—
94#6103—21no—
95#6103—21no—
96#6103—21no—
97#6103D411yescharacteristic
98C4⋊Dic13—21no—
99C4⋊Dic13C2311yescharacteristic
100C4⋊Dic13C2311yescharacteristic
101#6101—21no—
102#6101—21no—
103#6101D411yescharacteristic
104C4×Dic13—21no—
105C4×Dic13—21no—
106C4×Dic13—21no—
107C4×Dic13C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110C8×D13—41no—
111#3311—131nomaximal, Sylow
112C23×C13C2×D411yescharacteristic
113C22×D13—21no—
114C22×D13—21no—
115C22×D13—42no—
116C22×D13—42no—
117C22×D13—81no—
118C22×D13C2×D411yescharacteristic
119Q8×C13—21no—
120Q8×C13—21no—
121Q8×C13—21no—
122Q8×C13—21no—
123C2×C4×C13—21no—
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—41no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13C2×D411yescharacteristic
135C2×Dic13C2×D411yescharacteristic
136C2×Dic13C2×D411yescharacteristic
137D52—21no—
138D52—21no—
139D52—21no—
140D52—42no—
141D52—42no—
142D52—81no—
143D52#4112yes—
144C4×D13—21no—
145C4×D13—21no—
146C4×D13—42no—
147C4×D13—81no—
148Dic26—42no—
149C8×C13—21no—
150C8×C13—21no—
151#1055—21no—
152#1055—21no—
153#556—131no—
154#546—131no—
155#489—131no—
156#485—131no—
157#482—131no—
158#476—131no—
159#470D1311yescharacteristic, complemented
160#465—131no—
161#464—131no—
162#452—131no—
163#450—131no—
164#440—131no—
165#435—131no—
166#418—131no—
167#416—131no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13C22×D411yescharacteristic
172C2×D13—21no—
173C2×D13—22no—
174C2×D13—21no—
175C2×D13—21no—
176C2×D13—41no—
177C2×D13—41no—
178C2×D13—41no—
179C2×D13—41no—
180C2×D13—41no—
181C2×D13—84no—
182C4×C13—21no—
183C4×C13—41no—
184C4×C13—41no—
185C4×C13—41no—
186C4×C13—41no—
187C4×C13C2×#4111yescharacteristic
188C4×C13H(5,𝔽2)11yescharacteristic
189Dic13—21no—
190Dic13—21no—
191Dic13—21no—
192Dic13—41no—
193Dic13—41no—
194C2×#41—131no—
195C22×D4—131no—
196C2×Q16C2×D1311yescharacteristic, complemented
197C2×SD16—131no—
198C2×SD16—131no—
199C2×M16C2×D1311yescharacteristic
200C22×C8—131no—
201C4⋊Q8—131no—
202#126—261no—
203#126—261no—
204#124—131no—
205#124—261no—
206#123—261no—
207C22⋊Q8—131no—
208C22⋊Q8C2×D1311yescharacteristic
209C22⋊Q8C2×D1311yescharacteristic
210#121—131no—
211#121—261no—
212#120—261no—
213C4×Q8—131no—
214C4×Q8—261no—
215C4×D4—131no—
216C4×D4—131no—
217#117—131no—
218#117—131no—
219C2×C22⋊C4—261no—
220#107—131no—
221#106—131no—
222#106C2×D1311yescharacteristic, complemented
223C4⋊C8—131no—
224#103—131no—
225#103—131no—
226#103C2×D1311yescharacteristic, complemented
227#103C2×D1311yescharacteristic, complemented
228#102—131no—
229#102—131no—
230#102—131no—
231#102—131no—
232#102—131no—
233#102—131no—
234C22⋊C8—131no—
235C22⋊C8—131no—
236#97—131no—
237C2×C13—41no—
238C2×C13#54611yescharacteristic
239C2×C13#57511yescharacteristic
240C2×C13#57711yescharacteristic
241D13—41no—
242D13—42no—
243D13—81no—
244C24—261no—
245#41—262no—
246#41—521no—
247C2×Q8—261no—
248C2×Q8C22×D1311yescharacteristic
249C2×Q8C22×D1311yescharacteristic
250C2×D4—131no—
251C2×D4—131no—
252C2×D4—131no—
253C2×D4—262no—
254C2×D4—261no—
255C2×D4—261no—
256C2×D4—261no—
257C2×D4—521no—
258C22×C4—131no—
259C22×C4—261no—
260C22×C4—261no—
261C22×C4C22×D1311yescharacteristic
262Q16—41no—
263SD16—262no—
264SD16—521no—
265M16—41no—
266C2×C8—131no—
267C2×C8—131no—
268C2×C8—521no—
269C2×C8C22×D1311yescharacteristic
270C2×C8C22×D1311yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—131no—
274C4⋊C4—131no—
275C4⋊C4—131no—
276C4⋊C4—261no—
277C4⋊C4—261no—
278C4⋊C4—261no—
279C4⋊C4C22×D1311yescharacteristic
280C4⋊C4C22×D1311yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—131no—
284C22⋊C4—131no—
285C22⋊C4—261no—
286C22⋊C4—261no—
287C22⋊C4—261no—
288C22⋊C4—261no—
289C22⋊C4—261no—
290C22⋊C4—261no—
291C22⋊C4—261no—
292C42—131no—
293C42—261no—
294C42—261no—
295C42—261no—
296C13#331111yescharacteristic, complemented, Sylow
297C23—131no—
298C23—261no—
299C23—261no—
300C23—522no—
301C23—522no—
302C23—1041no—
303C23D4×D1311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308Q8—522no—
309D4—132no—
310D4—261no—
311D4—261no—
312D4—261no—
313D4—522no—
314D4—522no—
315D4—521no—
316D4—1041no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—131no—
324C2×C4—131no—
325C2×C4—131no—
326C2×C4—261no—
327C2×C4—261no—
328C2×C4—261no—
329C2×C4—261no—
330C2×C4—522no—
331C2×C4—1041no—
332C2×C4D4×D1311yescharacteristic
333C2×C4C23×D1311yescharacteristic
334C8—21no—
335C8—21no—
336C8—261no—
337C8—261no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—261no—
342C22—261no—
343C22—261no—
344C22—262no—
345C22—521no—
346C22—521no—
347C22—521no—
348C22—521no—
349C22—521no—
350C22—1044no—
351C22C2×D4×D1311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—261no—
358C4—261no—
359C4—261no—
360C4—521no—
361C4—521no—
362C4#8825111yescharacteristic
363C4#41×D1311yescharacteristic
364C2—41no—
365C2—521no—
366C2—522no—
367C2—1041no—
368C2#1171931511yescharacteristic
369C2#1171948211yescharacteristic
370C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#470C2
socleC22×C13C22×D4
prime radical#11719335C2
hypercenter#470D13
hypocenterC13#3311
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #11719346C2semidirect
3. C13×#470C2semidirect
4. #11718848C2semidirect
5. #11718846C2semidirect
6. #11718792C2semidirect
7. #11718788C2semidirect
8. #11718707C2semidirect
9. #11718706C2semidirect
10. #11718531C2semidirect
11. #11718527C2semidirect
12. #11718478C2semidirect
13. #11718468C2semidirect
14. #11718465C2semidirect
15. #11718456C2semidirect
18. C2×C13×Q16C22semidirect
23. #88200C22semidirect
24. Q8×Dic13C22semidirect
29. C2×C8×D13C22semidirect
35. #88146C22semidirect
36. #88142C22semidirect
42. C13×#106C22semidirect
43. C13×#103C22semidirect
44. C13×#103C22semidirect
45. #88075C22semidirect
46. #88075C22semidirect
52. #88060C22semidirect
53. #88055C22semidirect
54. #88054C22semidirect
57. #88048C22semidirect
58. #88047C22semidirect
159. #470D13semidirect
196. C2×Q16C2×D13semidirect
222. #106C2×D13semidirect
226. #103C2×D13semidirect
227. #103C2×D13semidirect
296. C13#3311semidirect

Maximal subgroups

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

subgroupindex
#117193462
#117193352
C13×#4702
#117188482
#117188462
#117187922
#117187882
#117187072
#117187062
#117185312
#117185272
#117184782
#117184682
#117184652
#117184562
#331113