Finite Group Databasebeta

← #13125532

Subgroups — #13125532

Order 1664.

410 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719262C211yesmaximal, characteristic, complemented
2#11719253C211yesmaximal, characteristic, complemented
3C13×#442C211yesmaximal, characteristic, complemented
4#11718818C211yesmaximal, characteristic, complemented
5#11718815C211yesmaximal, characteristic, complemented
6#11718679C211yesmaximal, characteristic, complemented
7#11718675C211yesmaximal, characteristic, complemented
8#11718525C211yesmaximal, characteristic, complemented
9#11718517C211yesmaximal, characteristic, complemented
10#11718439C211yesmaximal, characteristic, complemented
11#11718436C211yesmaximal, characteristic, complemented
12#11718426C211yesmaximal, characteristic, complemented
13#11718425C211yesmaximal, characteristic, complemented
14#11718371C211yesmaximal, characteristic, complemented
15D13×#97C211yesmaximal, characteristic, complemented
16C2×#6127—21no—
17C2×C13×D8C2211yescharacteristic
18C4×D4×C13C2211yescharacteristic
19C4×D4×C13C2211yescharacteristic
20#88194C2211yescharacteristic
21#88192C2211yescharacteristic
22#88192C2211yescharacteristic
23#88190C2211yescharacteristic
24C2×#6105C2211yescharacteristic
25C2×#6104C2211yescharacteristic
26C4×C22⋊D13—21no—
27C4×C22⋊D13—21no—
28#88180—21no—
29C2×#6095C2211yescharacteristic
30C2×C8×D13C2211yescharacteristic
31C2×C8×D13C2211yescharacteristic
32#88151C2211yescharacteristic
33#88149C2211yescharacteristic
34#88144C2211yescharacteristic
35#88142C2211yescharacteristic
36#88139—21no—
37#88138—21no—
38#88137—21no—
39#88133—21no—
40C4×D52C2211yescharacteristic
41C42×D13C2211yescharacteristic
42C4×Dic26C2211yescharacteristic
43C13×#106C2211yescharacteristic
44C13×#102C2211yescharacteristic
45C13×#102C2211yescharacteristic
46C13×#97C2211yescharacteristic
47#88072C2211yescharacteristic
48#88072C2211yescharacteristic
49#88061C2211yescharacteristic
50#88058C2211yescharacteristic
51#88056C2211yescharacteristic
52#88055C2211yescharacteristic
53#88055C2211yescharacteristic
54#88050C2211yescharacteristic
55#88049C2211yescharacteristic
56#88048C2211yescharacteristic
57#88047C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×D4×C13C2311yescharacteristic
60C2×D4×C13C2311yescharacteristic
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C2×C22⋊D13—21no—
64C2×C22⋊D13—21no—
65C2×C22⋊D13—21no—
66C2×C22⋊D13—21no—
67#6127—44no—
68C2×D52—21no—
69C2×D52C2311yescharacteristic
70C2×C4×D13—21no—
71C2×C4×D13D411yescharacteristic
72C2×C4×D13D411yescharacteristic
73C2×C4×D13C2311yescharacteristic
74C2×Dic26—21no—
75C2×Dic26C2311yescharacteristic
76C13×D8—22no—
77C2×C8×C13C2311yescharacteristic
78C2×C8×C13C2311yescharacteristic
79C13×C4⋊C4C2311yescharacteristic
80C13×C4⋊C4C2311yescharacteristic
81C13×C22⋊C4—21no—
82C13×C22⋊C4—21no—
83C42×C13C2311yescharacteristic
84C22⋊Dic13—21no—
85C22⋊Dic13—21no—
86C22⋊Dic13—21no—
87C22⋊Dic13—21no—
88#6105—22no—
89#6104—22no—
90#6103—21no—
91#6103—21no—
92#6103—21no—
93C4⋊Dic13—21no—
94C4⋊Dic13—21no—
95C4⋊Dic13C2311yescharacteristic
96C4⋊Dic13C2311yescharacteristic
97#6101—21no—
98#6101—21no—
99#6101—21no—
100C4×Dic13—21no—
101C4×Dic13D411yescharacteristic
102C4×Dic13D411yescharacteristic
103C4×Dic13C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106#6095—22no—
107C8×D13—22no—
108C8×D13—22no—
109#3180—131nomaximal, Sylow
110C23×C13—21no—
111C23×C13—21no—
112C22×D13—21no—
113C22×D13C2×D411yescharacteristic
114D4×C13—21no—
115D4×C13—21no—
116D4×C13—21no—
117D4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13C2×D411yescharacteristic
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2411yescharacteristic
125C22⋊D13—42no—
126C22⋊D13—42no—
127C22⋊D13—42no—
128C22⋊D13—42no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13C2×D411yescharacteristic
133C2×Dic13C2×D411yescharacteristic
134C2×Dic13C2×D411yescharacteristic
135D52—21no—
136D52—21no—
137D52—42no—
138C4×D13—22no—
139C4×D13—21no—
140C4×D13—21no—
141C4×D13—41no—
142C4×D13—42no—
143Dic26—21no—
144Dic26—21no—
145Dic26—42no—
146C8×C13—21no—
147C8×C13#4112yescomplemented
148#1055—21no—
149#1055#4112yescomplemented
150#532—131no—
151#529—131no—
152#501—131no—
153#496—131no—
154#490—131no—
155#489—131no—
156#466—131no—
157#466—131no—
158#465—131no—
159#465—131no—
160#442—131no—
161#442D1311yescharacteristic, complemented
162#440—131no—
163#440—131no—
164C2×#97—131no—
165C22×C13—41no—
166C22×C13—41no—
167C22×C13—41no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13—41no—
171C22×C13C22×D411yescharacteristic
172C2×D13—21no—
173C2×D13—21no—
174C2×D13—41no—
175C2×D13—41no—
176C2×D13—41no—
177C2×D13AGL(1,ℤ/8)12yes—
178C4×C13—21no—
179C4×C13—21no—
180C4×C13—41no—
181C4×C13—41no—
182C4×C13C2×#4111yescharacteristic
183C4×C13C2×#4111yescharacteristic
184Dic13—21no—
185Dic13—21no—
186Dic13—21no—
187Dic13—41no—
188Dic13—41no—
189Dic13—41no—
190C2×#41—261no—
191C2×SD16—131no—
192C2×SD16—131no—
193C2×D8—131no—
194C2×D8C2×D1311yescharacteristic
195C22×C8—131no—
196C22×C8—131no—
197C4⋊Q8—131no—
198#127—131no—
199#126—261no—
200#125—131no—
201#124—131no—
202#124—261no—
203#123—261no—
204C22⋊Q8—131no—
205#121—131no—
206#121—131no—
207#121—131no—
208#121—261no—
209C4×Q8—131no—
210C4×D4—131no—
211C4×D4—261no—
212C4×D4—261no—
213C4×D4C2×D1311yescharacteristic
214C4×D4C2×D1311yescharacteristic
215#117—261no—
216C2×C42—131no—
217#107—131no—
218#107—131no—
219#106—131no—
220#106C2×D1311yescharacteristic
221#103—131no—
222#103—131no—
223#102—131no—
224#102—131no—
225#102—131no—
226#102—131no—
227#102C2×D1311yescharacteristic
228#102C2×D1311yescharacteristic
229#97—131no—
230#97—131no—
231#97—131no—
232#97C2×D1311yescharacteristic
233C2×C13—81no—
234C2×C13—81no—
235C2×C13#53211yescharacteristic
236C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
237C2×C13#57511yescharacteristic
238D13—22no—
239D13—81no—
240#41—524no—
241C2×Q8—131no—
242C2×Q8—261no—
243C2×D4—131no—
244C2×D4—261no—
245C2×D4—261no—
246C2×D4—261no—
247C2×D4—261no—
248C2×D4—261no—
249C2×D4C22×D1311yescharacteristic
250C2×D4C22×D1311yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—131no—
254C22×C4—131no—
255C22×C4—131no—
256C22×C4—261no—
257SD16—262no—
258SD16—262no—
259D8—22no—
260D8—262no—
261C2×C8—131no—
262C2×C8—131no—
263C2×C8—262no—
264C2×C8—262no—
265C2×C8C22×D1311yescharacteristic
266C2×C8C22×D1311yescharacteristic
267C4⋊C4—131no—
268C4⋊C4—131no—
269C4⋊C4—261no—
270C4⋊C4—261no—
271C4⋊C4—261no—
272C4⋊C4—261no—
273C4⋊C4—261no—
274C4⋊C4C22×D1311yescharacteristic
275C4⋊C4C22×D1311yescharacteristic
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—261no—
279C22⋊C4—261no—
280C22⋊C4—261no—
281C22⋊C4—261no—
282C22⋊C4—261no—
283C22⋊C4—261no—
284C22⋊C4—261no—
285C42—131no—
286C42—131no—
287C42—131no—
288C42—261no—
289C42C22×D1311yescharacteristic
290C13#318011yescharacteristic, complemented, Sylow
291C23—21no—
292C23—21no—
293C23—131no—
294C23—261no—
295Q8—261no—
296Q8—261no—
297Q8—522no—
298D4—21no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—261no—
303D4—261no—
304D4—522no—
305D4—522no—
306D4—522no—
307D4—522no—
308D4—522no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—131no—
314C2×C4—131no—
315C2×C4—131no—
316C2×C4—262no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—261no—
322C2×C4—521no—
323C2×C4—522no—
324C2×C4D4×D1311yescharacteristic
325C2×C4D4×D1311yescharacteristic
326C2×C4C23×D1311yescharacteristic
327C8—21no—
328C8—132no—
329C8—261no—
330C8#612712yescomplemented
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—132no—
338C22—261no—
339C22—261no—
340C22—521no—
341C22—521no—
342C22—521no—
343C22C2×D4×D1311yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—261no—
349C4—261no—
350C4—261no—
351C4—521no—
352C4—521no—
353C4—521no—
354C4C2×#612711yescharacteristic
355C4#41×D1311yescharacteristic
356C2—81no—
357C2—81no—
358C2—262no—
359C2—1041no—
360C2#1171925311yescharacteristic
361C2D13×AGL(1,ℤ/8)11yescharacteristic
362C2#1171947811yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#442C2
socleC22×C13C22×D4
hypercenter#442D13
hypocenterC13#3180
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #11719262C2semidirect
2. #11719253C2semidirect
3. C13×#442C2semidirect
4. #11718818C2semidirect
5. #11718815C2semidirect
6. #11718679C2semidirect
7. #11718675C2semidirect
8. #11718525C2semidirect
9. #11718517C2semidirect
10. #11718439C2semidirect
11. #11718436C2semidirect
12. #11718426C2semidirect
13. #11718425C2semidirect
14. #11718371C2semidirect
15. D13×#97C2semidirect
147. C8×C13#41semidirect
149. #1055#41semidirect
161. #442D13semidirect
290. C13#3180semidirect
330. C8#6127semidirect

Maximal subgroups

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

subgroupindex
#117192622
#117192532
C13×#4422
#117188182
#117188152
#117186792
#117186752
#117185252
#117185172
#117184392
#117184362
#117184262
#117184252
#117183712
D13×#972
#318013