Finite Group Databasebeta

← #13125551

Subgroups — #13125551

Order 1664.

402 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719283C211yesmaximal, characteristic, complemented
2#11719253C211yesmaximal, characteristic
3C13×#440C211yesmaximal, characteristic, complemented
4#11718836C211yesmaximal, characteristic, complemented
5#11718835C211yesmaximal, characteristic, complemented
6#11718687C211yesmaximal, characteristic, complemented
7#11718679C211yesmaximal, characteristic, complemented
8#11718547C211yesmaximal, characteristic, complemented
9#11718535C211yesmaximal, characteristic, complemented
10#11718473C211yesmaximal, characteristic, complemented
11#11718453C211yesmaximal, characteristic, complemented
12#11718441C211yesmaximal, characteristic, complemented
13#11718421C211yesmaximal, characteristic, complemented
14#11718371C211yesmaximal, characteristic, complemented
15#11718368C211yesmaximal, characteristic, complemented
16C2×#6127—21no—
17C2×C13×SD16C2211yescharacteristic
18C4×Q8×C13C2211yescharacteristic
19C4×D4×C13C2211yescharacteristic
20#88200C2211yescharacteristic
21#88198C2211yescharacteristic
22C2×#6106C2211yescharacteristic
23#88194C2211yescharacteristic
24#88192C2211yescharacteristic
25C2×#6105C2211yescharacteristic
26C4×C22⋊D13—21no—
27C2×#6095C2211yescharacteristic
28C2×#6094C2211yescharacteristic
29C2×#6094C2211yescharacteristic
30#88151C2211yescharacteristic
31#88150—21no—
32#88149C2211yescharacteristic
33#88143—21no—
34#88142C2211yescharacteristic
35#88142C2211yescharacteristic
36#88139—21no—
37#88138—21no—
38C4×D52C2211yescharacteristic
39#88126—21no—
40C42×D13C2211yescharacteristic
41C4×Dic26—21no—
42C4×Dic26C2211yescharacteristic
43C13×#107C2211yescharacteristic
44C13×#103C2211yescharacteristic
45C13×#102C2211yescharacteristic
46C13×#97C2211yescharacteristic
47#88075C2211yescharacteristic
48#88072C2211yescharacteristic
49#88061C2211yescharacteristic
50#88058C2211yescharacteristic
51#88056C2211yescharacteristic
52C8×Dic13C2211yescharacteristic
53C8×Dic13C2211yescharacteristic
54#88050C2211yescharacteristic
55#88049C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×D4×C13C2311yescharacteristic
61C22×C4×C13—21no—
62C2×C22⋊D13—21no—
63C2×C22⋊D13—21no—
64C2×C22⋊D13—21no—
65#6127—44no—
66C2×D52—21no—
67C2×D52C2311yescharacteristic
68C2×C4×D13—21no—
69C2×C4×D13D411yescharacteristic
70C2×C4×D13D411yescharacteristic
71C2×C4×D13C2311yescharacteristic
72C2×Dic26—21no—
73C2×Dic26—21no—
74C2×Dic26C2311yescharacteristic
75C13×SD16—22no—
76C2×C8×C13C2311yescharacteristic
77C2×C8×C13C2311yescharacteristic
78C13×C4⋊C4—21no—
79C13×C4⋊C4C2311yescharacteristic
80C13×C4⋊C4C2311yescharacteristic
81C13×C22⋊C4—21no—
82C42×C13—21no—
83C42×C13C2311yescharacteristic
84C22⋊Dic13—21no—
85#6106—22no—
86#6105—22no—
87#6103—21no—
88#6103—21no—
89#6103—21no—
90#6103—21no—
91C4⋊Dic13—21no—
92C4⋊Dic13C2311yescharacteristic
93C4⋊Dic13C2311yescharacteristic
94#6101—21no—
95#6101—21no—
96#6101—21no—
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—
107#6094—22no—
108#6094—22no—
109#3182—131nomaximal, Sylow
110C23×C13—21no—
111C22×D13—21no—
112C22×D13C2×D411yescharacteristic
113Q8×C13—21no—
114Q8×C13—21no—
115D4×C13—21no—
116D4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—42no—
121C2×C4×C13C2×D411yescharacteristic
122C2×C4×C13C2×D411yescharacteristic
123C2×C4×C13C2411yescharacteristic
124C22⋊D13—42no—
125C22⋊D13—42no—
126C22⋊D13—42no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13C2×D411yescharacteristic
131C2×Dic13C2×D411yescharacteristic
132C2×Dic13C2×D411yescharacteristic
133D52—21no—
134D52—21no—
135D52—42no—
136C4×D13—21no—
137C4×D13—21no—
138C4×D13—22no—
139C4×D13—22no—
140C4×D13—42no—
141Dic26—21no—
142Dic26—21no—
143Dic26—42no—
144Dic26—42no—
145C8×C13—21no—
146C8×C13#4112yescomplemented
147#1055—21no—
148#1055#4112yescomplemented
149#533—131no—
150#532—131no—
151#500—131no—
152#492—131no—
153#487—131no—
154#486—131no—
155#468—131no—
156#468—131no—
157#468—131no—
158#468—131no—
159#440—131no—
160#440—131no—
161#440—131no—
162#440D1311yescharacteristic, complemented
163C4×M16—131no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13—41no—
167C22×C13C22×D411yescharacteristic
168C2×D13—21no—
169C2×D13—21no—
170C2×D13—21no—
171C2×D13—41no—
172C2×D13—41no—
173C2×D13—41no—
174C4×C13—21no—
175C4×C13—21no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13C2×#4111yescharacteristic
180C4×C13C2×#4111yescharacteristic
181Dic13—21no—
182Dic13—41no—
183Dic13—41no—
184Dic13—41no—
185Dic13AGL(1,ℤ/8)12yes—
186Dic13#13712yes—
187C2×#41—261no—
188C2×SD16—131no—
189C2×SD16—131no—
190C2×SD16—131no—
191C2×SD16C2×D1311yescharacteristic
192C2×M16—131no—
193C2×M16—131no—
194C4⋊Q8—131no—
195C4⋊Q8—131no—
196C4⋊Q8—131no—
197#127—131no—
198#125—261no—
199#124—261no—
200C22⋊Q8—131no—
201C22⋊Q8—131no—
202C22⋊Q8—261no—
203#121—131no—
204#121—131no—
205#121—261no—
206C4×Q8—131no—
207C4×Q8—261no—
208C4×Q8C2×D1311yescharacteristic
209C4×D4—131no—
210C4×D4—261no—
211C4×D4C2×D1311yescharacteristic
212#117—261no—
213C2×C42—131no—
214#107—131no—
215#107—131no—
216#107—131no—
217#107C2×D1311yescharacteristic
218#103—131no—
219#103—131no—
220#103—131no—
221#103C2×D1311yescharacteristic
222#102—131no—
223#102—131no—
224#102—131no—
225#102C2×D1311yescharacteristic
226#97—131no—
227#97C2×D1311yescharacteristic
228C4×C8—131no—
229C4×C8—131no—
230C2×C13—81no—
231C2×C13#53211yescharacteristic
232C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
233C2×C13C2×#13711yescharacteristic
234D13—41no—
235D13—81no—
236#41—524no—
237C2×Q8—131no—
238C2×Q8—261no—
239C2×Q8—261no—
240C2×Q8C22×D1311yescharacteristic
241C2×D4—131no—
242C2×D4—261no—
243C2×D4—261no—
244C2×D4—261no—
245C2×D4—261no—
246C2×D4C22×D1311yescharacteristic
247C22×C4—21no—
248C22×C4—131no—
249C22×C4—131no—
250C22×C4—131no—
251C22×C4—261no—
252SD16—22no—
253SD16—262no—
254SD16—262no—
255SD16—262no—
256M16—262no—
257M16—262no—
258C2×C8—131no—
259C2×C8—131no—
260C2×C8C22×D1311yescharacteristic
261C2×C8C22×D1311yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—131no—
264C4⋊C4—131no—
265C4⋊C4—261no—
266C4⋊C4—261no—
267C4⋊C4—261no—
268C4⋊C4—261no—
269C4⋊C4—261no—
270C4⋊C4—261no—
271C4⋊C4—261no—
272C4⋊C4C22×D1311yescharacteristic
273C4⋊C4C22×D1311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—261no—
276C22⋊C4—261no—
277C22⋊C4—261no—
278C22⋊C4—261no—
279C22⋊C4—261no—
280C42—21no—
281C42—131no—
282C42—131no—
283C42—131no—
284C42—261no—
285C42C22×D1311yescharacteristic
286C13#318211yescharacteristic, complemented, Sylow
287C23—21no—
288C23—131no—
289C23—261no—
290Q8—21no—
291Q8—21no—
292Q8—261no—
293Q8—261no—
294Q8—522no—
295Q8—522no—
296D4—21no—
297D4—21no—
298D4—261no—
299D4—261no—
300D4—522no—
301D4—522no—
302D4—522no—
303D4—522no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—131no—
309C2×C4—131no—
310C2×C4—131no—
311C2×C4—262no—
312C2×C4—262no—
313C2×C4—261no—
314C2×C4—261no—
315C2×C4—261no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—522no—
319C2×C4D4×D1311yescharacteristic
320C2×C4D4×D1311yescharacteristic
321C2×C4C23×D1311yescharacteristic
322C8—21no—
323C8—132no—
324C8—261no—
325C8#612712yescomplemented
326C22—41no—
327C22—41no—
328C22—41no—
329C22—261no—
330C22—261no—
331C22—261no—
332C22—521no—
333C22—521no—
334C22—521no—
335C22C2×D4×D1311yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—132no—
342C4—132no—
343C4—261no—
344C4—521no—
345C4—521no—
346C4—521no—
347C4C2×#612711yescharacteristic
348C4#41×D1311yescharacteristic
349C2—81no—
350C2—521no—
351C2—1041no—
352C2#1171925311yescharacteristic
353C2D13×AGL(1,ℤ/8)11yescharacteristic
354C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#440C2
socleC22×C13C22×D4
prime radical#11719253C2
hypercenter#440D13
hypocenterC13#3182
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #11719283C2semidirect
3. C13×#440C2semidirect
4. #11718836C2semidirect
5. #11718835C2semidirect
6. #11718687C2semidirect
7. #11718679C2semidirect
8. #11718547C2semidirect
9. #11718535C2semidirect
10. #11718473C2semidirect
11. #11718453C2semidirect
12. #11718441C2semidirect
13. #11718421C2semidirect
14. #11718371C2semidirect
15. #11718368C2semidirect
146. C8×C13#41semidirect
148. #1055#41semidirect
162. #440D13semidirect
286. C13#3182semidirect
325. C8#6127semidirect

Maximal subgroups

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

subgroupindex
#117192832
#117192532
C13×#4402
#117188362
#117188352
#117186872
#117186792
#117185472
#117185352
#117184732
#117184532
#117184412
#117184212
#117183712
#117183682
#318213