Finite Group Databasebeta

← #13127186

Subgroups — #13127186

Order 1664.

388 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719340C211yesmaximal, characteristic, complemented
2#11719212C211yesmaximal, characteristic
3C13×#483C211yesmaximal, characteristic, complemented
4#11718709C211yesmaximal, characteristic, complemented
5C2×#88048C211yesmaximal, characteristic, complemented
6#11718531C211yesmaximal, characteristic, complemented
7#11718524C211yesmaximal, characteristic, complemented
8D13×#106C211yesmaximal, characteristic, complemented
9#11718516C211yesmaximal, characteristic, complemented
10#11718468C211yesmaximal, characteristic, complemented
11#11718466C211yesmaximal, characteristic, complemented
12#11718452C211yesmaximal, characteristic, complemented
13#11718449C211yesmaximal, characteristic, complemented
14#11718396C211yesmaximal, characteristic, complemented
15#11718386C211yesmaximal, characteristic, complemented
16C2×#6127—21no—
17C13×C22⋊Q8C2211yescharacteristic
18C2×C13×C4⋊C4C2211yescharacteristic
19#88200C2211yescharacteristic
20Q8×Dic13C2211yescharacteristic
21C2×#6106C2211yescharacteristic
22#88184C2211yescharacteristic
23#88183—21no—
24C4×C22⋊D13C2211yescharacteristic
25C2×C4⋊Dic13C2211yescharacteristic
26C22×#1055C2211yescharacteristic
27C2×C8×D13C2211yescharacteristic
28#88151—21no—
29#88150—21no—
30#88149C2211yescharacteristic
31#88148—21no—
32#88147C2211yescharacteristic
33C4⋊C4×D13C2211yescharacteristic
34C4⋊C4×D13C2211yescharacteristic
35#88143—21no—
36#88142C2211yescharacteristic
37#88142C2211yescharacteristic
38#88135—21no—
39#88132—21no—
40C13×#106C2211yescharacteristic
41C13×#106C2211yescharacteristic
42C13×#103C2211yescharacteristic
43C13×#103C2211yescharacteristic
44C13×C22⋊C8C2211yescharacteristic
45#88075C2211yescharacteristic
46#88061C2211yescharacteristic
47#88061C2211yescharacteristic
48#88060C2211yescharacteristic
49#88057C2211yescharacteristic
50#88057C2211yescharacteristic
51#88054C2211yescharacteristic
52C8×Dic13C2211yescharacteristic
53#88049C2211yescharacteristic
54#88048C2211yescharacteristic
55#88048C2211yescharacteristic
56#88048C2211yescharacteristic
57#88048C2211yescharacteristic
58#88048C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C22×C4×C13—21no—
61C22×C4×C13C2311yescharacteristic
62C2×C22⋊D13—21no—
63C2×C22⋊D13D411yescharacteristic
64C22×Dic13—21no—
65#6127—44no—
66C2×D52—21no—
67C2×D52C2311yescharacteristic
68C2×C4×D13—21no—
69C2×C4×D13—21no—
70C2×C4×D13—21no—
71C2×C4×D13C2311yescharacteristic
72C2×Dic26—21no—
73C2×Dic26—21no—
74C2×C8×C13C2311yescharacteristic
75C2×C8×C13C2311yescharacteristic
76C13×C4⋊C4—21no—
77C13×C4⋊C4—21no—
78C13×C4⋊C4C2311yescharacteristic
79C13×C4⋊C4C2311yescharacteristic
80C13×C4⋊C4C2311yescharacteristic
81C13×C22⋊C4—21no—
82C22⋊Dic13D411yescharacteristic
83#6106—22no—
84#6103—21no—
85#6103—21no—
86#6103—21no—
87#6103—21no—
88#6103D411yescharacteristic
89C4⋊Dic13—21no—
90C4⋊Dic13—21no—
91C4⋊Dic13C2311yescharacteristic
92C4⋊Dic13C2311yescharacteristic
93C4⋊Dic13C2311yescharacteristic
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101—21no—
99#6101D411yescharacteristic
100C4×Dic13—21no—
101C4×Dic13C2311yescharacteristic
102C2×#1055—22no—
103C2×#1055C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105C8×D13—22no—
106#3335—131nomaximal, Sylow
107C23×C13C2×D411yescharacteristic
108C22×D13—21no—
109C22×D13C2×D411yescharacteristic
110Q8×C13—21no—
111Q8×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—42no—
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2411yescharacteristic
121C22⋊D13—42no—
122C22⋊D13SD1614yescomplemented
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—81no—
127C2×Dic13C2×D411yescharacteristic
128C2×Dic13C2×D411yescharacteristic
129C2×Dic13C2×D411yescharacteristic
130D52—21no—
131D52—21no—
132D52—42no—
133C4×D13—21no—
134C4×D13—21no—
135C4×D13—42no—
136C4×D13—42no—
137C4×D13—81no—
138Dic26—42no—
139Dic26—81no—
140C8×C13—21no—
141C8×C13—21no—
142#1055—21no—
143#1055#4112yescomplemented
144#554—131no—
145#547—131no—
146#498—131no—
147#483—131no—
148#483D1311yescharacteristic, complemented
149#481—131no—
150#481—131no—
151#476—131no—
152#475—131no—
153#465—131no—
154#465—131no—
155C4×SD16—131no—
156C8×D4—131no—
157C2×#106—131no—
158C2×#106—131no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13C2×SD1612yes—
162C22×C13C22×D411yescharacteristic
163C2×D13—21no—
164C2×D13—21no—
165C2×D13—41no—
166C2×D13—41no—
167C2×D13—41no—
168C2×D13C2×SD1612yes—
169C4×C13—21no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13C2×#4111yescharacteristic
175C4×C132−1+411yescharacteristic
176Dic13—21no—
177Dic13—21no—
178Dic13—41no—
179Dic13—41no—
180Dic13—41no—
181Dic13C2×SD1612yes—
182C2×#41—261no—
183C2×SD16—131no—
184C22×C8—131no—
185C22×C8—131no—
186C4⋊Q8—131no—
187C4⋊Q8—131no—
188#125—261no—
189#123—261no—
190#123—261no—
191C22⋊Q8—131no—
192C22⋊Q8—261no—
193C22⋊Q8—261no—
194C22⋊Q8—261no—
195C22⋊Q8C2×D1311yescharacteristic
196#121—131no—
197#121—131no—
198C4×Q8—131no—
199C4×D4—131no—
200C4×D4—131no—
201C4×D4—261no—
202C2×C4⋊C4—131no—
203C2×C4⋊C4—131no—
204C2×C4⋊C4—131no—
205C2×C4⋊C4C2×D1311yescharacteristic
206#106—131no—
207#106—131no—
208#106—131no—
209#106—131no—
210#106—131no—
211#106—131no—
212#106—131no—
213#106C2×D1311yescharacteristic
214#106C2×D1311yescharacteristic
215C4⋊C8—131no—
216#103—131no—
217#103C2×D1311yescharacteristic
218#103C2×D1311yescharacteristic
219#102—131no—
220#102—131no—
221#102—131no—
222C22⋊C8—131no—
223C22⋊C8C2×D1311yescharacteristic
224C4×C8—131no—
225C2×C13—22no—
226C2×C13#54711yescharacteristic
227C2×C13C22×SD1611yescharacteristic
228C2×C13#57711yescharacteristic
229D13—22no—
230D13—81no—
231#41—524no—
232C2×Q8—261no—
233C2×Q8—261no—
234C2×Q8C22×D1311yescharacteristic
235C2×D4—131no—
236C2×D4—131no—
237C2×D4—261no—
238C2×D4—261no—
239C22×C4—21no—
240C22×C4—131no—
241C22×C4—261no—
242C22×C4—261no—
243C22×C4—261no—
244C22×C4—261no—
245C22×C4C22×D1311yescharacteristic
246SD16—262no—
247C2×C8—131no—
248C2×C8—131no—
249C2×C8—262no—
250C2×C8—262no—
251C2×C8C22×D1311yescharacteristic
252C2×C8C22×D1311yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—131no—
256C4⋊C4—131no—
257C4⋊C4—131no—
258C4⋊C4—131no—
259C4⋊C4—261no—
260C4⋊C4—261no—
261C4⋊C4—261no—
262C4⋊C4—261no—
263C4⋊C4—261no—
264C4⋊C4—261no—
265C4⋊C4—261no—
266C4⋊C4C22×D1311yescharacteristic
267C4⋊C4C22×D1311yescharacteristic
268C4⋊C4C22×D1311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—131no—
271C22⋊C4—131no—
272C22⋊C4—261no—
273C22⋊C4—261no—
274C22⋊C4—261no—
275C22⋊C4—261no—
276C42—131no—
277C42—261no—
278C13#333511yescharacteristic, complemented, Sylow
279C23—131no—
280C23—261no—
281C23D4×D1311yescharacteristic
282Q8—21no—
283Q8—21no—
284Q8—522no—
285Q8—1041no—
286D4—134no—
287D4—261no—
288D4—261no—
289D4—522no—
290D4—522no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—42no—
298C2×C4—131no—
299C2×C4—131no—
300C2×C4—131no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—522no—
307C2×C4—522no—
308C2×C4—1041no—
309C2×C4—1041no—
310C2×C4D4×D1311yescharacteristic
311C2×C4C23×D1311yescharacteristic
312C8—21no—
313C8—21no—
314C8—132no—
315C8—261no—
316C22—21no—
317C22—21no—
318C22—132no—
319C22—261no—
320C22—261no—
321C22—521no—
322C22—521no—
323C22—521no—
324C22SD16×D1312yes—
325C22C2×D4×D1311yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—132no—
332C4—261no—
333C4—261no—
334C4—521no—
335C4—521no—
336C4—521no—
337C4#41×D1311yescharacteristic
338C4#8825711yescharacteristic
339C2—22no—
340C2—262no—
341C2—1041no—
342C2#1171936011yescharacteristic
343C2C2×SD16×D1311yescharacteristic
344C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#483C2
socleC22×C13C22×D4
prime radical#11719212C2
hypercenter#483D13
hypocenterC13#3335
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #11719340C2semidirect
3. C13×#483C2semidirect
4. #11718709C2semidirect
5. C2×#88048C2semidirect
6. #11718531C2semidirect
7. #11718524C2semidirect
8. D13×#106C2semidirect
9. #11718516C2semidirect
10. #11718468C2semidirect
11. #11718466C2semidirect
12. #11718452C2semidirect
13. #11718449C2semidirect
14. #11718396C2semidirect
15. #11718386C2semidirect
122. C22⋊D13SD16semidirect
143. #1055#41semidirect
148. #483D13semidirect
278. C13#3335semidirect

Maximal subgroups

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

subgroupindex
#117193402
#117192122
C13×#4832
#117187092
C2×#880482
#117185312
#117185242
D13×#1062
#117185162
#117184682
#117184662
#117184522
#117184492
#117183962
#117183862
#333513