Finite Group Databasebeta

← #13127604

Subgroups — #13127604

Order 1664.

344 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#557C211yesmaximal, characteristic, complemented
2#11719290C211yesmaximal, characteristic
3#11718750C211yesmaximal, characteristic, complemented
4#11718745C211yesmaximal, characteristic, complemented
5#11718729C211yesmaximal, characteristic, complemented
6#11718728C211yesmaximal, characteristic
7#11718727C211yesmaximal, characteristic, complemented
8#11718724C211yesmaximal, characteristic, complemented
9#11718691C211yesmaximal, characteristic, complemented
10#11718689C211yesmaximal, characteristic, complemented
11#11718689C211yesmaximal, characteristic, complemented
12#11718688C211yesmaximal, characteristic
13#11718687C211yesmaximal, characteristic, complemented
14C4×#6106C211yesmaximal, characteristic, complemented
15#11718685C211yesmaximal, characteristic, complemented
16C13×C4⋊Q8—21no—
17C13×C4⋊Q8C2211yescharacteristic
18C13×#125—21no—
19C13×#125—21no—
20C13×#125C2211yescharacteristic
21C13×#125C2211yescharacteristic
22C4×Q8×C13—21no—
23C4×Q8×C13C2211yescharacteristic
24C4×Q8×C13C2211yescharacteristic
25C4×Q8×C13C2211yescharacteristic
26C4×Q8×C13C2211yescharacteristic
27#88201—21no—
28C2×#6107C2211yescharacteristic
29C2×#6106C2211yescharacteristic
30C2×#6106C2211yescharacteristic
31#88148—21no—
32#88148—21no—
33#88147—21no—
34#88129C2211yescharacteristic
35#88129C2211yescharacteristic
36#88128C2211yescharacteristic
37C4×D52C2211yescharacteristic
38C4×D52C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40#88075C2211yescharacteristic
41#88050C2211yescharacteristic
42#88050C2211yescharacteristic
43#88050C2211yescharacteristic
44#88049C2211yescharacteristic
45#88049C2211yescharacteristic
46#88049C2211yescharacteristic
47#88049C2211yescharacteristic
48#88049C2211yescharacteristic
49#88049C2211yescharacteristic
50#88048C2211yescharacteristic
51#88048C2211yescharacteristic
52#88047C2211yescharacteristic
53C4⋊#1055C2211yescharacteristic
54C4⋊#1055C2211yescharacteristic
55C4⋊#1055C2211yescharacteristic
56#88043C2211yescharacteristic
57#88043C2211yescharacteristic
58C4×#1055C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13D411yescharacteristic
61C2×Q8×C13C2311yescharacteristic
62C2×D52—21no—
63C2×D52—21no—
64C2×D52C2311yescharacteristic
65C2×D52C2311yescharacteristic
66C2×C4×D13—21no—
67C2×C4×D13—21no—
68C2×Dic26C2311yescharacteristic
69C13×C4⋊C4—21no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4—21no—
75C13×C4⋊C4—21no—
76C13×C4⋊C4—21no—
77C13×C4⋊C4D411yescharacteristic
78C13×C4⋊C4D411yescharacteristic
79C13×C4⋊C4D411yescharacteristic
80C13×C4⋊C4C2311yescharacteristic
81C13×C4⋊C4C2311yescharacteristic
82C13×C4⋊C4C2311yescharacteristic
83C42×C13—21no—
84C42×C13—21no—
85C42×C13—21no—
86C42×C13C2311yescharacteristic
87C42×C13C2311yescharacteristic
88C42×C13C2311yescharacteristic
89#6107—22no—
90#6106—22no—
91#6106—22no—
92#6103—21no—
93#6103—21no—
94#6103—21no—
95#6103—21no—
96#6103—21no—
97#6103—21no—
98C4⋊Dic13C2311yescharacteristic
99#6101—21no—
100C4×Dic13—21no—
101C2×#1055C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105#3371—131nomaximal, Sylow
106C22×D13—21no—
107C22×D13—21no—
108Q8×C13—21no—
109Q8×C13—41no—
110Q8×C13—42no—
111Q8×C13#4112yes—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13C2×D411yescharacteristic
117C2×C4×C13C2×D411yescharacteristic
118C2×C4×C13C2×D411yescharacteristic
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2×D411yescharacteristic
121C2×C4×C13C2×D411yescharacteristic
122C2×C4×C13C2411yescharacteristic
123C2×Dic13—21no—
124C2×Dic13—21no—
125D52—21no—
126D52—21no—
127D52—21no—
128D52—21no—
129D52—42no—
130D52—81no—
131C4×D13—81no—
132C4×D13—81no—
133Dic26—21no—
134Dic26—21no—
135#1055—21no—
136#1055—21no—
137#1055—21no—
138#1055—21no—
139#559—131no—
140#557D1311yescharacteristic, complemented
141#490—131no—
142#489—131no—
143#488—131no—
144#479—131no—
145#478—131no—
146#476—131no—
147#464—131no—
148#464—131no—
149#460—131no—
150#446—131no—
151#441—131no—
152#440—131no—
153C4×SD16—131no—
154C22×C13C22×D411yescharacteristic
155C2×D13—41no—
156C2×D13—41no—
157C2×D13—41no—
158C2×D13—41no—
159C2×D13—41no—
160C2×D13—41no—
161C4×C13—22no—
162C4×C13—21no—
163C4×C13—21no—
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—21no—
167C4×C13—21no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13C2×#4111yescharacteristic
172C4×C132−1+411yescharacteristic
173Dic13—41no—
174Dic13—41no—
175C2×Q16—131no—
176C2×SD16—131no—
177C2×SD16—131no—
178C4⋊Q8—21no—
179C4⋊Q8C2×D1311yescharacteristic
180#127—131no—
181#125—21no—
182#125—21no—
183#125C2×D1311yescharacteristic
184#125C2×D1311yescharacteristic
185#124—131no—
186#124—131no—
187#124—261no—
188#123—261no—
189#123—261no—
190C4×Q8—21no—
191C4×Q8—131no—
192C4×Q8C2×D1311yescharacteristic
193C4×Q8C2×D1311yescharacteristic
194C4×Q8C2×D1311yescharacteristic
195C4×Q8C2×D1311yescharacteristic
196C4×D4—131no—
197C4×D4—131no—
198C4×D4—261no—
199#107—131no—
200#106—131no—
201#106—131no—
202C4⋊C8—131no—
203C4⋊C8—131no—
204C4⋊C8—131no—
205#103—131no—
206#103—131no—
207#103—131no—
208#103—131no—
209#102—131no—
210#102—131no—
211#102—131no—
212#102—131no—
213#102—131no—
214#102—131no—
215#97—131no—
216#97—131no—
217C4×C8—131no—
218C2×C13#54811yescharacteristic
219C2×C13#57511yescharacteristic
220C2×C13#57711yescharacteristic
221D13—81no—
222D13—81no—
223C2×Q8—21no—
224C2×Q8—131no—
225C2×Q8C22⋊D1311yescharacteristic
226C2×Q8C22×D1311yescharacteristic
227C2×D4—131no—
228C2×D4—131no—
229C2×D4—261no—
230C2×D4—261no—
231C22×C4—261no—
232C22×C4—261no—
233Q16—262no—
234SD16—262no—
235SD16—262no—
236C2×C8—131no—
237C2×C8—131no—
238C2×C8—131no—
239C2×C8—131no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—131no—
249C4⋊C4—261no—
250C4⋊C4C22⋊D1311yescharacteristic
251C4⋊C4C22⋊D1311yescharacteristic
252C4⋊C4C22⋊D1311yescharacteristic
253C4⋊C4C22×D1311yescharacteristic
254C4⋊C4C22×D1311yescharacteristic
255C4⋊C4C22×D1311yescharacteristic
256C22⋊C4—261no—
257C22⋊C4—261no—
258C22⋊C4—261no—
259C22⋊C4—261no—
260C22⋊C4—261no—
261C22⋊C4—261no—
262C42—21no—
263C42—21no—
264C42—21no—
265C42—261no—
266C42C22×D1311yescharacteristic
267C42C22×D1311yescharacteristic
268C42C22×D1311yescharacteristic
269C13#337111yescharacteristic, complemented, Sylow
270C23—261no—
271C23—261no—
272Q8—21no—
273Q8—41no—
274Q8—42no—
275Q8—261no—
276Q8—261no—
277Q8#613112yes—
278D4—261no—
279D4—261no—
280D4—261no—
281D4—261no—
282D4—522no—
283D4—1041no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—1041no—
291C2×C4—1041no—
292C2×C4C2×C22⋊D1311yescharacteristic
293C2×C4C2×C22⋊D1311yescharacteristic
294C2×C4C2×C22⋊D1311yescharacteristic
295C2×C4C2×C22⋊D1311yescharacteristic
296C2×C4C2×C22⋊D1311yescharacteristic
297C2×C4C2×C22⋊D1311yescharacteristic
298C2×C4C23×D1311yescharacteristic
299C8—261no—
300C8—261no—
301C8—261no—
302C8—261no—
303C22—521no—
304C22—521no—
305C22—521no—
306C22—521no—
307C22—521no—
308C22—521no—
309C22C22×C22⋊D1311yescharacteristic
310C4—22no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—521no—
321C4—521no—
322C4C2×#613111yescharacteristic
323C4#8825411yescharacteristic
324C2—1041no—
325C2—1041no—
326C2#1171952211yescharacteristic
327C2#1171952711yescharacteristic
328C2#1171954211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#557C2
socleC22×C13C22×D4
prime radical#88128C22
hypercenter#557D13
hypocenterC13#3371
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

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

NH ≅ G/Ntype
1. C13×#557C2semidirect
3. #11718750C2semidirect
4. #11718745C2semidirect
5. #11718729C2semidirect
7. #11718727C2semidirect
8. #11718724C2semidirect
9. #11718691C2semidirect
10. #11718689C2semidirect
11. #11718689C2semidirect
13. #11718687C2semidirect
14. C4×#6106C2semidirect
15. #11718685C2semidirect
140. #557D13semidirect
269. C13#3371semidirect

Maximal subgroups

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

subgroupindex
C13×#5572
#117192902
#117187502
#117187452
#117187292
#117187282
#117187272
#117187242
#117186912
#117186892
#117186882
#117186872
C4×#61062
#117186852
#337113