Finite Group Databasebeta

← #13125470

Subgroups — #13125470

Order 1664.

362 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#11719348C211yesmaximal, characteristic, complemented
2#11719308C211yesmaximal, characteristic, complemented
3C13×#468C211yesmaximal, characteristic, complemented
4#11718829C211yesmaximal, characteristic, complemented
5#11718825C211yesmaximal, characteristic, complemented
6#11718795C211yesmaximal, characteristic, complemented
7#11718783C211yesmaximal, characteristic, complemented
8#11718712C211yesmaximal, characteristic, complemented
9#11718699C211yesmaximal, characteristic
10#11718550C211yesmaximal, characteristic, complemented
11#11718535C211yesmaximal, characteristic, complemented
12#11718456C211yesmaximal, characteristic, complemented
13#11718451C211yesmaximal, characteristic, complemented
14#11718426C211yesmaximal, characteristic, complemented
15#11718417C211yesmaximal, characteristic, complemented
16C2×C13×SD16C2211yescharacteristic
17C2×C13×M16C2211yescharacteristic
18C13×C22⋊Q8C2211yescharacteristic
19C13×#121C2211yescharacteristic
20#88201C2211yescharacteristic
21Q8×Dic13C2211yescharacteristic
22C2×#6107C2211yescharacteristic
23#88190—21no—
24#88190C2211yescharacteristic
25#88189—21no—
26D4×Dic13C2211yescharacteristic
27C2×#6104C2211yescharacteristic
28#88184C2211yescharacteristic
29#88180C2211yescharacteristic
30#88178C2211yescharacteristic
31C22×#1055C2211yescharacteristic
32C2×#6095C2211yescharacteristic
33#88152—21no—
34#88151—21no—
35#88147C2211yescharacteristic
36#88142C2211yescharacteristic
37#88142C2211yescharacteristic
38#88141C2211yescharacteristic
39#88139—21no—
40#88137—21no—
41#88133—21no—
42#88132—21no—
43C13×#107C2211yescharacteristic
44C13×#103C2211yescharacteristic
45C13×#102C2211yescharacteristic
46#88075C2211yescharacteristic
47#88072C2211yescharacteristic
48#88061C2211yescharacteristic
49#88058C2211yescharacteristic
50#88056C2211yescharacteristic
51#88055C2211yescharacteristic
52#88055C2211yescharacteristic
53C8×Dic13C2211yescharacteristic
54C8×Dic13C2211yescharacteristic
55#88050C2211yescharacteristic
56#88049C2211yescharacteristic
57#88047C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×D4×C13—21no—
61C2×D4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C2×C22⋊D13—21no—
64C22×Dic13—21no—
65C2×D52C2311yescharacteristic
66C2×C4×D13—21no—
67C2×Dic26—21no—
68C2×Dic26—21no—
69C2×Dic26C2311yescharacteristic
70C13×SD16—22no—
71C13×M16—22no—
72C2×C8×C13C2311yescharacteristic
73C2×C8×C13C2311yescharacteristic
74C13×C4⋊C4—21no—
75C13×C4⋊C4C2311yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C22⋊C4—21no—
78C13×C22⋊C4—21no—
79C22⋊Dic13—21no—
80C22⋊Dic13—21no—
81C22⋊Dic13—21no—
82C22⋊Dic13—21no—
83C22⋊Dic13D411yescharacteristic
84C22⋊Dic13D411yescharacteristic
85#6107—22no—
86#6104—22no—
87#6103—21no—
88#6103—21no—
89#6103—21no—
90#6103—21no—
91C4⋊Dic13—21no—
92C4⋊Dic13D411yescharacteristic
93C4⋊Dic13D411yescharacteristic
94C4⋊Dic13C2311yescharacteristic
95C4⋊Dic13C2311yescharacteristic
96#6101—21no—
97#6101—21no—
98#6101—21no—
99#6101—21no—
100C4×Dic13—21no—
101C4×Dic13—21no—
102C4×Dic13C2311yescharacteristic
103C4×Dic13C2311yescharacteristic
104C2×#1055—22no—
105C2×#1055C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107#6095—22no—
108#3175—131nomaximal, Sylow
109C23×C13—21no—
110C23×C13C2×D411yescharacteristic
111C22×D13—21no—
112Q8×C13—21no—
113Q8×C13—21no—
114D4×C13—21no—
115D4×C13—21no—
116D4×C13—81no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13C2×D411yescharacteristic
123C2×C4×C13C2411yescharacteristic
124C22⋊D13—81no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—81no—
129C2×Dic13C2×D411yescharacteristic
130C2×Dic13C2×D411yescharacteristic
131C2×Dic13C2×D411yescharacteristic
132C2×Dic13C2×D411yescharacteristic
133D52—21no—
134D52—21no—
135C4×D13—81no—
136Dic26—21no—
137Dic26—21no—
138Dic26—81no—
139Dic26—81no—
140C8×C13—21no—
141C8×C13#4112yes—
142#1055—21no—
143#1055#4112yes—
144#542—131no—
145#542—131no—
146#500—131no—
147#495—131no—
148#489—131no—
149#489—131no—
150#468—131no—
151#468D1311yescharacteristic, complemented
152#467—131no—
153#466—131no—
154#440—131no—
155#440—131no—
156C4×Q16—131no—
157C4×D8—131no—
158#405—131no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13C22×D411yescharacteristic
166C2×D13—41no—
167C2×D13—41no—
168C2×D13—41no—
169C4×C13—21no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13C2×#4111yescharacteristic
174C4×C13C2×#4111yescharacteristic
175Dic13—21no—
176Dic13—21no—
177Dic13—21no—
178Dic13—21no—
179Dic13—41no—
180Dic13—41no—
181Dic13—41no—
182C2×Q16—131no—
183C2×SD16—131no—
184C2×SD16C2×D1311yescharacteristic
185C2×D8—131no—
186C2×M16C2×D1311yescharacteristic
187C22×C8—131no—
188C4⋊Q8—131no—
189C4⋊Q8—131no—
190#126—261no—
191#126—261no—
192#124—131no—
193#124—131no—
194#124—261no—
195#124—261no—
196#123—261no—
197#123—261no—
198C22⋊Q8—131no—
199C22⋊Q8—261no—
200C22⋊Q8—261no—
201C22⋊Q8C2×D1311yescharacteristic
202#121—131no—
203#121C2×D1311yescharacteristic
204C4×Q8—131no—
205C4×Q8—131no—
206C4×D4—131no—
207C4×D4—131no—
208#117—131no—
209#107—131no—
210#107—131no—
211#107—131no—
212#107C2×D1311yescharacteristic
213#103—131no—
214#103—131no—
215#103—131no—
216#103C2×D1311yescharacteristic
217#102—131no—
218#102—131no—
219#102—131no—
220#102C2×D1311yescharacteristic
221#97—131no—
222#97—131no—
223C4×C8—131no—
224C4×C8—131no—
225C2×C13—41no—
226C2×C13—81no—
227C2×C13#53211yescharacteristic
228C2×C13#57611yescharacteristic
229C2×C13#57811yescharacteristic
230D13—81no—
231C2×Q8—131no—
232C2×Q8—261no—
233C2×Q8—261no—
234C2×Q8C22×D1311yescharacteristic
235C2×D4—21no—
236C2×D4—131no—
237C2×D4—261no—
238C2×D4C22×D1311yescharacteristic
239C22×C4—261no—
240C22×C4—261no—
241C22×C4C22×D1311yescharacteristic
242Q16—262no—
243SD16—22no—
244SD16—262no—
245D8—262no—
246M16—22no—
247C2×C8—131no—
248C2×C8—131no—
249C2×C8—262no—
250C2×C8C22×D1311yescharacteristic
251C2×C8C22×D1311yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—131no—
254C4⋊C4—131no—
255C4⋊C4—131no—
256C4⋊C4—131no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4—261no—
261C4⋊C4—261no—
262C4⋊C4C22×D1311yescharacteristic
263C4⋊C4C22×D1311yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—131no—
267C22⋊C4—131no—
268C22⋊C4—261no—
269C22⋊C4—261no—
270C22⋊C4—261no—
271C22⋊C4—261no—
272C22⋊C4—261no—
273C22⋊C4—261no—
274C22⋊C4—261no—
275C22⋊C4—261no—
276C42—131no—
277C42—131no—
278C42—261no—
279C42—261no—
280C13#317511yescharacteristic, complemented, Sylow
281C23—21no—
282C23—261no—
283C23D4×D1311yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—261no—
287Q8—261no—
288Q8—1041no—
289Q8—1041no—
290D4—21no—
291D4—21no—
292D4—81no—
293D4—261no—
294D4—261no—
295D4—1041no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—131no—
302C2×C4—131no—
303C2×C4—131no—
304C2×C4—131no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—1041no—
309C2×C4—1041no—
310C2×C4D4×D1311yescharacteristic
311C2×C4C23×D1311yescharacteristic
312C8—21no—
313C8—132no—
314C8—261no—
315C8#612912yes—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—521no—
323C22—521no—
324C22—521no—
325C22C2×D4×D1311yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—261no—
331C4—261no—
332C4—261no—
333C4—261no—
334C4—521no—
335C4—521no—
336C4—521no—
337C4C2×#612911yescharacteristic
338C4#41×D1311yescharacteristic
339C2—41no—
340C2—81no—
341C2—1041no—
342C2#1171930111yescharacteristic
343C2#1171947911yescharacteristic
344C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#468C2
socleC22×C13C22×D4
prime radical#11718699C2
hypercenter#468D13
hypocenterC13#3175
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #11719348C2semidirect
2. #11719308C2semidirect
3. C13×#468C2semidirect
4. #11718829C2semidirect
5. #11718825C2semidirect
6. #11718795C2semidirect
7. #11718783C2semidirect
8. #11718712C2semidirect
10. #11718550C2semidirect
11. #11718535C2semidirect
12. #11718456C2semidirect
13. #11718451C2semidirect
14. #11718426C2semidirect
15. #11718417C2semidirect
151. #468D13semidirect
280. C13#3175semidirect

Maximal subgroups

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

subgroupindex
#117193482
#117193082
C13×#4682
#117188292
#117188252
#117187952
#117187832
#117187122
#117186992
#117185502
#117185352
#117184562
#117184512
#117184262
#117184172
#317513