Finite Group Databasebeta

← #13126874

Subgroups — #13126874

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#11719255C211yesmaximal, characteristic
2#11719247C211yesmaximal, characteristic, complemented
3C13×#435C211yesmaximal, characteristic, complemented
4#11718798C211yesmaximal, characteristic, complemented
5#11718792C211yesmaximal, characteristic, complemented
6#11718775C211yesmaximal, characteristic, complemented
7#11718774C211yesmaximal, characteristic, complemented
8#11718506C211yesmaximal, characteristic, complemented
9#11718503C211yesmaximal, characteristic, complemented
10#11718398C211yesmaximal, characteristic, complemented
11#11718394C211yesmaximal, characteristic, complemented
12#11718392C211yesmaximal, characteristic, complemented
13#11718384C211yesmaximal, characteristic, complemented
14#11718375C211yesmaximal, characteristic, complemented
15#11718371C211yesmaximal, characteristic, complemented
16C2×#6127C2211yescharacteristic
17C22×D52C2211yescharacteristic
18C2×C13×M16C2211yescharacteristic
19C22×C8×C13C2211yescharacteristic, complemented
20C4×D4×C13C2211yescharacteristic
21#88191—21no—
22#88190—21no—
23#88184C2211yescharacteristic
24#88180C2211yescharacteristic
25#88180C2211yescharacteristic, complemented
26#88178C2211yescharacteristic
27#88178C2211yescharacteristic
28#88178C2211yescharacteristic, complemented
29C2×Dic52C2211yescharacteristic, complemented
30C2×#6095C2211yescharacteristic
31C2×#6095C2211yescharacteristic
32#88148—21no—
33#88141—21no—
34#88138—21no—
35C22⋊C4×D13—21no—
36#88133—21no—
37#88133—21no—
38#88129C2211yescharacteristic
39C4×D52C2211yescharacteristic
40#88123C2211yescharacteristic, complemented
41C4×Dic26C2211yescharacteristic, complemented
42C13×C4⋊C8C2211yescharacteristic, complemented
43C13×C22⋊C8C2211yescharacteristic
44C13×C22⋊C8C2211yescharacteristic, complemented
45C13×#97C2211yescharacteristic, complemented
46#88061C2211yescharacteristic
47#88061C2211yescharacteristic
48#88061C2211yescharacteristic
49#88061C2211yescharacteristic
50#88061C2211yescharacteristic
51#88061C2211yescharacteristic
52#88058C2211yescharacteristic, complemented
53#88057C2211yescharacteristic, complemented
54#88057C2211yescharacteristic, complemented
55#88056C2211yescharacteristic, complemented
56#88056C2211yescharacteristic, complemented
57#88056C2211yescharacteristic, complemented
58#88056C2211yescharacteristic, complemented
59C23×D13—21no—
60C2×D4×C13D411yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C2×C22⋊D13—21no—
64C2×C22⋊D13—21no—
65#6127—22no—
66#6127—41no—
67C2×D52—22no—
68C2×D52—21no—
69C2×D52—41no—
70C2×D52C2311yescharacteristic
71C2×D52C2311yescharacteristic
72C2×C4×D13—21no—
73C2×C4×D13—21no—
74C2×Dic26—21no—
75C2×Dic26C2311yescharacteristic
76C2×Dic26C2311yescharacteristic
77C13×M16—41no—
78C2×C8×C13—41no—
79C2×C8×C13C2311yescharacteristic
80C2×C8×C13C2311yescharacteristic
81C2×C8×C13C2311yescharacteristic
82C2×C8×C13C2311yescharacteristic
83C13×C4⋊C4D411yescharacteristic
84C13×C22⋊C4D411yescharacteristic
85C13×C22⋊C4D411yescharacteristic
86C42×C13C2311yescharacteristic
87C22⋊Dic13—21no—
88C22⋊Dic13—21no—
89C22⋊Dic13—21no—
90C22⋊Dic13—21no—
91C22⋊Dic13—21no—
92#6103—21no—
93#6103—21no—
94#6103—21no—
95#6103—21no—
96C4⋊Dic13—21no—
97C4⋊Dic13C2311yescharacteristic
98C4⋊Dic13C2311yescharacteristic
99C4⋊Dic13C2311yescharacteristic
100C4⋊Dic13C2311yescharacteristic
101#6101—21no—
102#6101—21no—
103#6101—21no—
104#6101—21no—
105C4×Dic13—21no—
106C4×Dic13—21no—
107C4×Dic13—21no—
108Dic52—41no—
109#6095—22no—
110#6095—41no—
111#3311—131nomaximal, Sylow
112C23×C13C2×D411yescharacteristic
113C23×C13C2×D411yescharacteristic
114C22×D13—21no—
115C22×D13—21no—
116C22×D13—42no—
117C22×D13—42no—
118C22×D13—81no—
119D4×C13—41no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13C2×D411yescharacteristic
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2×D411yescharacteristic
127C2×C4×C13C2×D411yescharacteristic
128C2×C4×C13C2411yescharacteristic
129C22⋊D13—42no—
130C22⋊D13—81no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137D52—21no—
138D52—21no—
139D52—21no—
140D52—42no—
141D52#4112yes—
142C4×D13—42no—
143C4×D13—81no—
144Dic26—21no—
145Dic26—21no—
146Dic26—21no—
147Dic26—21no—
148Dic26—42no—
149C8×C13—21no—
150C8×C13—21no—
151C8×C13—21no—
152C8×C13—21no—
153#556—131no—
154#546—131no—
155#489—131no—
156#485—131no—
157#482—131no—
158#476—131no—
159#470—131no—
160#465—131no—
161#464—131no—
162#452—131no—
163#450—131no—
164#440—131no—
165#435D1311yescharacteristic, complemented
166#418—131no—
167#416—131no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13C22×D411yescharacteristic
175C2×D13—22no—
176C2×D13—41no—
177C2×D13—41no—
178C2×D13—41no—
179C2×D13—41no—
180C2×D13—41no—
181C2×D13—84no—
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13C2×#4111yescharacteristic
187C4×C13H(5,𝔽2)11yescharacteristic
188Dic13—41no—
189Dic13—41no—
190Dic13—41no—
191Dic13—41no—
192Dic13—41no—
193Dic13—41no—
194C2×#41—131no—
195C22×D4—131no—
196C2×Q16—131no—
197C2×SD16—131no—
198C2×SD16—131no—
199C2×M16C2×D1311yescharacteristic
200C22×C8C2×D1311yescharacteristic, complemented
201C4⋊Q8—131no—
202#126—261no—
203#126—261no—
204#124—131no—
205#124—261no—
206#123—261no—
207C22⋊Q8—131no—
208C22⋊Q8—131no—
209C22⋊Q8—131no—
210#121—131no—
211#121—261no—
212#120—261no—
213C4×Q8—131no—
214C4×Q8—261no—
215C4×D4—131no—
216C4×D4C2×D1311yescharacteristic
217#117—131no—
218#117—131no—
219C2×C22⋊C4—261no—
220#107—131no—
221#106—131no—
222#106—131no—
223C4⋊C8C2×D1311yescharacteristic, complemented
224#103—131no—
225#103—131no—
226#103—131no—
227#103—131no—
228#102—131no—
229#102—131no—
230#102—131no—
231#102—131no—
232#102—131no—
233#102—131no—
234C22⋊C8C2×D1311yescharacteristic
235C22⋊C8C2×D1311yescharacteristic, complemented
236#97C2×D1311yescharacteristic, complemented
237C2×C13—41no—
238C2×C13—41no—
239C2×C13#54611yescharacteristic
240C2×C13#57511yescharacteristic
241C2×C13#57711yescharacteristic
242D13—42no—
243D13—81no—
244C24—261no—
245#41—262no—
246#41—521no—
247C2×Q8—131no—
248C2×Q8—131no—
249C2×Q8—261no—
250C2×D4—131no—
251C2×D4—131no—
252C2×D4—262no—
253C2×D4—261no—
254C2×D4—261no—
255C2×D4—261no—
256C2×D4—521no—
257C2×D4D5211yescharacteristic
258C22×C4—261no—
259C22×C4—261no—
260C22×C4C22×D1311yescharacteristic
261C22×C4C22×D1311yescharacteristic
262Q16—521no—
263SD16—262no—
264SD16—521no—
265M16—41no—
266C2×C8—41no—
267C2×C8C22×D1311yescharacteristic
268C2×C8C22×D1311yescharacteristic
269C2×C8C22×D1311yescharacteristic
270C2×C8C22×D1311yescharacteristic
271C4⋊C4—131no—
272C4⋊C4—131no—
273C4⋊C4—131no—
274C4⋊C4—131no—
275C4⋊C4—261no—
276C4⋊C4—261no—
277C4⋊C4—261no—
278C4⋊C4—261no—
279C4⋊C4—261no—
280C4⋊C4D5211yescharacteristic
281C22⋊C4—261no—
282C22⋊C4—261no—
283C22⋊C4—261no—
284C22⋊C4—261no—
285C22⋊C4—261no—
286C22⋊C4—261no—
287C22⋊C4—261no—
288C22⋊C4—261no—
289C22⋊C4—261no—
290C22⋊C4D5211yescharacteristic
291C22⋊C4D5211yescharacteristic
292C42—261no—
293C42—261no—
294C42—261no—
295C42C22×D1311yescharacteristic
296C13#331111yescharacteristic, complemented, Sylow
297C23—261no—
298C23—261no—
299C23—522no—
300C23—522no—
301C23—1041no—
302C23C2×D5211yescharacteristic
303C23C2×D5211yescharacteristic
304Q8—261no—
305Q8—261no—
306Q8—261no—
307Q8—261no—
308Q8—522no—
309D4—41no—
310D4—132no—
311D4—261no—
312D4—261no—
313D4—261no—
314D4—522no—
315D4—522no—
316D4—1041no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—261no—
322C2×C4—261no—
323C2×C4—261no—
324C2×C4—261no—
325C2×C4—261no—
326C2×C4—261no—
327C2×C4—522no—
328C2×C4—1041no—
329C2×C4C2×D5211yescharacteristic
330C2×C4C2×D5211yescharacteristic
331C2×C4C2×D5211yescharacteristic
332C2×C4C2×D5211yescharacteristic
333C2×C4C23×D1311yescharacteristic
334C8—21no—
335C8—21no—
336C8—21no—
337C8—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—262no—
345C22—521no—
346C22—521no—
347C22—521no—
348C22—521no—
349C22—521no—
350C22—1044no—
351C22C22×D5211yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—521no—
357C4—521no—
358C4—521no—
359C4—521no—
360C4—521no—
361C4—521no—
362C4#8825111yescharacteristic
363C4#41×D1311yescharacteristic
364C2—41no—
365C2—41no—
366C2—522no—
367C2—1041no—
368C2#1171925911yescharacteristic
369C2#1171945311yescharacteristic
370C2#1171945611yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#435C2
socleC22×C13C22×D4
prime radical#11719255C2
hypercenter#435D13
hypocenterC13#3311
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #11719247C2semidirect
3. C13×#435C2semidirect
4. #11718798C2semidirect
5. #11718792C2semidirect
6. #11718775C2semidirect
7. #11718774C2semidirect
8. #11718506C2semidirect
9. #11718503C2semidirect
10. #11718398C2semidirect
11. #11718394C2semidirect
12. #11718392C2semidirect
13. #11718384C2semidirect
14. #11718375C2semidirect
15. #11718371C2semidirect
19. C22×C8×C13C22semidirect
25. #88180C22semidirect
28. #88178C22semidirect
29. C2×Dic52C22semidirect
40. #88123C22semidirect
41. C4×Dic26C22semidirect
42. C13×C4⋊C8C22semidirect
44. C13×C22⋊C8C22semidirect
45. C13×#97C22semidirect
52. #88058C22semidirect
53. #88057C22semidirect
54. #88057C22semidirect
55. #88056C22semidirect
56. #88056C22semidirect
57. #88056C22semidirect
58. #88056C22semidirect
165. #435D13semidirect
200. C22×C8C2×D13semidirect
223. C4⋊C8C2×D13semidirect
235. C22⋊C8C2×D13semidirect
236. #97C2×D13semidirect
296. C13#3311semidirect

Maximal subgroups

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

subgroupindex
#117192552
#117192472
C13×#4352
#117187982
#117187922
#117187752
#117187742
#117185062
#117185032
#117183982
#117183942
#117183922
#117183842
#117183752
#117183712
#331113