Finite Group Databasebeta

← #13127625

Subgroups — #13127625

Order 1664.

384 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719432C211yesmaximal, characteristic, complemented
2#11719386C211yesmaximal, characteristic, complemented
3C13×#489C211yesmaximal, characteristic, complemented
4#11718745C211yesmaximal, characteristic, complemented
5#11718718C211yesmaximal, characteristic, complemented
6#11718480C211yesmaximal, characteristic, complemented
7#11718456C211yesmaximal, characteristic, complemented
8#11718452C211yesmaximal, characteristic, complemented
9#11718449C211yesmaximal, characteristic, complemented
10#11718447C211yesmaximal, characteristic
11#11718446C211yesmaximal, characteristic, complemented
12#11718422C211yesmaximal, characteristic, complemented
13#11718421C211yesmaximal, characteristic, complemented
14#11718372C211yesmaximal, characteristic, complemented
15#11718362C211yesmaximal, characteristic, complemented
16C2×Q8×D13—21no—
17C13×C4⋊Q8C2211yescharacteristic
18C13×#124C2211yescharacteristic
19#88201C2211yescharacteristic
20#88200—21no—
21Q8×Dic13C2211yescharacteristic
22C2×#6106C2211yescharacteristic
23#88194C2211yescharacteristic
24D4×Dic13C2211yescharacteristic
25C2×#6104C2211yescharacteristic
26C2×D104C2211yescharacteristic
27#88150—21no—
28#88150—21no—
29#88147C2211yescharacteristic
30#88147C2211yescharacteristic
31#88142C2211yescharacteristic
32#88142C2211yescharacteristic
33#88140—21no—
34#88139—21no—
35#88137—21no—
36#88135—21no—
37C4×D52C2211yescharacteristic
38C4×D52C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40C13×#103C2211yescharacteristic
41C13×#103C2211yescharacteristic
42C13×#102C2211yescharacteristic
43C13×#102C2211yescharacteristic
44C13×#97C2211yescharacteristic
45#88075C2211yescharacteristic
46#88072C2211yescharacteristic
47#88061C2211yescharacteristic
48#88061C2211yescharacteristic
49#88057C2211yescharacteristic
50#88055C2211yescharacteristic
51#88054C2211yescharacteristic
52#88054C2211yescharacteristic
53C8×Dic13C2211yescharacteristic
54#88049C2211yescharacteristic
55#88049C2211yescharacteristic
56#88048C2211yescharacteristic
57#88048C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13C2311yescharacteristic
61C2×D4×C13C2311yescharacteristic
62C2×C22⋊D13—21no—
63C2×C22⋊D13—21no—
64C22×Dic13—21no—
65Q8×D13—44no—
66C2×D52C2311yescharacteristic
67C2×D52C2311yescharacteristic
68C2×C4×D13—21no—
69C2×C4×D13—21no—
70C2×C4×D13—21no—
71C2×C4×D13—21no—
72C2×Dic26—21no—
73C2×Dic26—21no—
74C2×Dic26D411yescharacteristic
75C2×C8×C13C2311yescharacteristic
76C2×C8×C13C2311yescharacteristic
77C13×C4⋊C4—21no—
78C13×C4⋊C4C2311yescharacteristic
79C13×C4⋊C4C2311yescharacteristic
80C13×C22⋊C4—21no—
81C13×C22⋊C4—21no—
82C42×C13C2311yescharacteristic
83C22⋊Dic13—21no—
84#6106—22no—
85#6104—22no—
86#6103—21no—
87#6103—21no—
88#6103—21no—
89#6103—21no—
90#6103—21no—
91#6103—21no—
92C4⋊Dic13—21no—
93C4⋊Dic13D411yescharacteristic
94C4⋊Dic13C2311yescharacteristic
95C4⋊Dic13C2311yescharacteristic
96#6101—21no—
97#6101—21no—
98#6101D411yescharacteristic
99#6101D411yescharacteristic
100C4×Dic13—21no—
101C4×Dic13C2311yescharacteristic
102C4×Dic13C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105D104—22no—
106#3373—131nomaximal, Sylow
107C23×C13—21no—
108C22×D13—21no—
109C22×D13—21no—
110Q8×C13—21no—
111Q8×C13—21no—
112Q8×C13—42no—
113D4×C13—21no—
114D4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13C2×D411yescharacteristic
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2411yescharacteristic
121C22⋊D13—42no—
122C22⋊D13—81no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—81no—
126C2×Dic13C2×D411yescharacteristic
127C2×Dic13C2×D411yescharacteristic
128C2×Dic13C2×D411yescharacteristic
129C2×Dic13C2×D411yescharacteristic
130D52—21no—
131D52—21no—
132D52—21no—
133D52#4112yes—
134C4×D13—42no—
135C4×D13—42no—
136C4×D13—42no—
137C4×D13—81no—
138Dic26—22no—
139Dic26—42no—
140Dic26—42no—
141C8×C13—21no—
142C8×C13—21no—
143#1055—21no—
144#1055—21no—
145#559—131no—
146D4×Q8—131no—
147#489—131no—
148#489D1311yescharacteristic, complemented
149#486—131no—
150#476—131no—
151#476—131no—
152#475—131no—
153#463—131no—
154#463—131no—
155#459—131no—
156#446—131no—
157#442—131no—
158#442—131no—
159C4×SD16—131no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13C22×D411yescharacteristic
164C2×D13—22no—
165C2×D13—41no—
166C2×D13—41no—
167C2×D13—41no—
168C2×D13—41no—
169C2×D13—41no—
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13—41no—
175C4×C13C2×#4111yescharacteristic
176C4×C132−1+411yescharacteristic
177Dic13—21no—
178Dic13—21no—
179Dic13—21no—
180Dic13—41no—
181Dic13—41no—
182Dic13AGL(1,ℤ/8)12yes—
183C22×Q8—261no—
184C2×SD16—131no—
185C2×D8—131no—
186C2×D8—131no—
187C4⋊Q8—131no—
188C4⋊Q8—131no—
189C4⋊Q8C2×D1311yescharacteristic
190#127—131no—
191#124—131no—
192#124—261no—
193#124C2×D1311yescharacteristic
194#123—261no—
195#123—261no—
196C22⋊Q8—261no—
197C22⋊Q8—261no—
198C22⋊Q8—261no—
199C4×Q8—131no—
200C4×Q8—131no—
201C4×D4—131no—
202C4×D4—131no—
203C4×D4—131no—
204C4×D4—131no—
205C4×D4—131no—
206C4×D4—261no—
207#106—131no—
208#106—131no—
209#106—131no—
210C4⋊C8—131no—
211C4⋊C8—131no—
212C4⋊C8—131no—
213#103—131no—
214#103C2×D1311yescharacteristic
215#103C2×D1311yescharacteristic
216#102—131no—
217#102—131no—
218#102—131no—
219#102—131no—
220#102—131no—
221#102C2×D1311yescharacteristic
222#102C2×D1311yescharacteristic
223#97—131no—
224#97C2×D1311yescharacteristic
225C4×C8—131no—
226C2×C13—81no—
227C2×C13#54811yescharacteristic
228C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
229C2×C13#57711yescharacteristic
230D13—42no—
231D13—81no—
232C2×Q8—21no—
233C2×Q8—131no—
234C2×Q8—261no—
235C2×Q8—261no—
236C2×Q8—524no—
237C2×Q8C22×D1311yescharacteristic
238C2×D4—131no—
239C2×D4—131no—
240C2×D4—261no—
241C2×D4—261no—
242C2×D4C22×D1311yescharacteristic
243C22×C4—261no—
244C22×C4—261no—
245C22×C4—261no—
246C22×C4—261no—
247C22×C4—261no—
248SD16—262no—
249D8—262no—
250D8—262no—
251C2×C8—131no—
252C2×C8—131no—
253C2×C8C22×D1311yescharacteristic
254C2×C8C22×D1311yescharacteristic
255C4⋊C4—21no—
256C4⋊C4—131no—
257C4⋊C4—131no—
258C4⋊C4—131no—
259C4⋊C4—131no—
260C4⋊C4—131no—
261C4⋊C4—261no—
262C4⋊C4—261no—
263C4⋊C4—261no—
264C4⋊C4C22×D1311yescharacteristic
265C4⋊C4C22×D1311yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—261no—
269C22⋊C4—261no—
270C22⋊C4—261no—
271C22⋊C4—261no—
272C22⋊C4—261no—
273C22⋊C4—261no—
274C22⋊C4—261no—
275C42—131no—
276C42—131no—
277C42—261no—
278C42C22×D1311yescharacteristic
279C13#337311yescharacteristic, complemented, Sylow
280C23—21no—
281C23—261no—
282C23—261no—
283Q8—21no—
284Q8—21no—
285Q8—42no—
286Q8—262no—
287Q8—522no—
288Q8—522no—
289D4—21no—
290D4—21no—
291D4—132no—
292D4—261no—
293D4—261no—
294D4—261no—
295D4—522no—
296D4—1041no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—131no—
301C2×C4—131no—
302C2×C4—131no—
303C2×C4—131no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—522no—
307C2×C4—522no—
308C2×C4—522no—
309C2×C4—1041no—
310C2×C4—1041no—
311C2×C4D4×D1311yescharacteristic
312C2×C4D4×D1311yescharacteristic
313C2×C4C23×D1311yescharacteristic
314C8—21no—
315C8—21no—
316C8—261no—
317C8—261no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—262no—
322C22—521no—
323C22—521no—
324C22—521no—
325C22—521no—
326C22—521no—
327C22C2×D4×D1311yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—132no—
334C4—261no—
335C4—261no—
336C4—261no—
337C4—521no—
338C4—521no—
339C4#41×D1311yescharacteristic
340C4#8825711yescharacteristic
341C2—81no—
342C2—522no—
343C2—1041no—
344C2#1171938211yescharacteristic
345C2D13×AGL(1,ℤ/8)11yescharacteristic
346C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#489C2
socleC22×C13C22×D4
prime radical#11718447C2
hypercenter#489D13
hypocenterC13#3373
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #11719432C2semidirect
2. #11719386C2semidirect
3. C13×#489C2semidirect
4. #11718745C2semidirect
5. #11718718C2semidirect
6. #11718480C2semidirect
7. #11718456C2semidirect
8. #11718452C2semidirect
9. #11718449C2semidirect
11. #11718446C2semidirect
12. #11718422C2semidirect
13. #11718421C2semidirect
14. #11718372C2semidirect
15. #11718362C2semidirect
148. #489D13semidirect
279. C13#3373semidirect

Maximal subgroups

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

subgroupindex
#117194322
#117193862
C13×#4892
#117187452
#117187182
#117184802
#117184562
#117184522
#117184492
#117184472
#117184462
#117184222
#117184212
#117183722
#117183622
#337313