Finite Group Databasebeta

← #13125511

Subgroups — #13125511

Order 1664.

350 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719438C211yesmaximal, characteristic
2#11719436C211yesmaximal, characteristic, complemented
3C13×#487C211yesmaximal, characteristic, complemented
4#11718747C211yesmaximal, characteristic, complemented
5#11718741C211yesmaximal, characteristic, complemented
6#11718478C211yesmaximal, characteristic, complemented
7#11718477C211yesmaximal, characteristic, complemented
8#11718474C211yesmaximal, characteristic, complemented
9#11718473C211yesmaximal, characteristic
10#11718468C211yesmaximal, characteristic
11#11718451C211yesmaximal, characteristic, complemented
12#11718450C211yesmaximal, characteristic, complemented
13#11718449C211yesmaximal, characteristic, complemented
14#11718358C211yesmaximal, characteristic, complemented
15#11718350C211yesmaximal, characteristic, complemented
16C13×C4⋊Q8C2211yescharacteristic
17C13×C4⋊Q8C2211yescharacteristic
18#88201—21no—
19#88200—21no—
20#88200C2211yescharacteristic
21#88200C2211yescharacteristic
22Q8×Dic13C2211yescharacteristic
23Q8×Dic13C2211yescharacteristic
24C2×#6107C2211yescharacteristic
25C2×#6107C2211yescharacteristic
26C2×#6106C2211yescharacteristic
27C2×#6106C2211yescharacteristic
28C2×#6094C2211yescharacteristic
29C2×C8×D13C2211yescharacteristic
30#88152—21no—
31#88152—21no—
32#88152—21no—
33#88151C2211yescharacteristic
34#88149C2211yescharacteristic
35#88148—21no—
36#88147C2211yescharacteristic
37#88143—21no—
38#88143—21no—
39#88141C2211yescharacteristic
40#88129C2211yescharacteristic
41#88126C2211yescharacteristic
42#88124C2211yescharacteristic
43C13×#103C2211yescharacteristic
44C13×#103C2211yescharacteristic
45C13×#103C2211yescharacteristic
46C13×#103C2211yescharacteristic
47C4×C8×C13C2211yescharacteristic
48#88061C2211yescharacteristic
49#88061C2211yescharacteristic
50#88056C2211yescharacteristic
51#88056C2211yescharacteristic
52#88055C2211yescharacteristic
53C8×Dic13C2211yescharacteristic
54#88048C2211yescharacteristic
55#88048C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13C2311yescharacteristic
61C2×Q8×C13C2311yescharacteristic
62C2×D52—21no—
63C2×D52C2311yescharacteristic
64C2×C4×D13—21no—
65C2×C4×D13C2311yescharacteristic
66C2×Dic26C2311yescharacteristic
67C2×C8×C13C2311yescharacteristic
68C2×C8×C13C2311yescharacteristic
69C13×C4⋊C4—21no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4C2311yescharacteristic
73C13×C4⋊C4C2311yescharacteristic
74C42×C13C2311yescharacteristic
75#6107—22no—
76#6107—22no—
77#6106—22no—
78#6106—22no—
79#6103—21no—
80#6103—21no—
81#6103—21no—
82#6103—21no—
83#6103—21no—
84#6103—21no—
85#6103—21no—
86#6103D411yescharacteristic
87#6103D411yescharacteristic
88C4⋊Dic13—21no—
89C4⋊Dic13—21no—
90C4⋊Dic13—21no—
91C4⋊Dic13C2311yescharacteristic
92C4⋊Dic13C2311yescharacteristic
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101D411yescharacteristic
99#6101D411yescharacteristic
100C4×Dic13—21no—
101C4×Dic13—21no—
102C4×Dic13—21no—
103C4×Dic13C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106#6094—22no—
107C8×D13—22no—
108#3178—131nomaximal, Sylow
109C22×D13—21no—
110C22×D13C2×D411yescharacteristic
111Q8×C13—21no—
112Q8×C13—21no—
113Q8×C13—21no—
114Q8×C13—21no—
115Q8×C13—81no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13C2×D411yescharacteristic
121C2×C4×C13C2×D411yescharacteristic
122C2×C4×C13C2411yescharacteristic
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13C2×D411yescharacteristic
127C2×Dic13C2×D411yescharacteristic
128C2×Dic13C2×D411yescharacteristic
129D52—21no—
130D52—21no—
131D52—81no—
132C4×D13—21no—
133C4×D13—21no—
134C4×D13—81no—
135Dic26—21no—
136Dic26—21no—
137C8×C13—21no—
138C8×C13—21no—
139#1055#4112yes—
140#1055#4112yes—
141#542—131no—
142#541—131no—
143#501—131no—
144#497—131no—
145#488—131no—
146#487D1311yescharacteristic, complemented
147#470—131no—
148#468—131no—
149#467—131no—
150#465—131no—
151#441—131no—
152#440—131no—
153C4×Q16—131no—
154C4×SD16—131no—
155#405—131no—
156C22×C13C22×D411yescharacteristic
157C2×D13—21no—
158C2×D13—21no—
159C2×D13—21no—
160C2×D13—41no—
161C2×D13—41no—
162C2×D13—41no—
163C4×C13—21no—
164C4×C13—21no—
165C4×C13—41no—
166C4×C13—41no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13C2×#4111yescharacteristic
170C4×C13C2×#4111yescharacteristic
171Dic13—21no—
172Dic13—21no—
173Dic13—21no—
174Dic13—41no—
175Dic13—41no—
176Dic13—41no—
177C2×Q16—131no—
178C2×Q16—131no—
179C2×SD16—131no—
180C2×SD16—131no—
181C2×M16—131no—
182C22×C8—131no—
183C4⋊Q8C2×D1311yescharacteristic
184C4⋊Q8C2×D1311yescharacteristic
185#126—261no—
186#126—261no—
187#126—261no—
188#125—131no—
189#125—261no—
190#125—261no—
191#124—131no—
192#124—261no—
193#123—261no—
194C22⋊Q8—131no—
195C22⋊Q8—131no—
196C22⋊Q8—131no—
197C22⋊Q8—261no—
198#121—131no—
199C4×Q8—131no—
200C4×Q8—131no—
201C4×Q8—131no—
202C4×D4—131no—
203#117—131no—
204#107—131no—
205#107—131no—
206#106—131no—
207#106—131no—
208#103—131no—
209#103—131no—
210#103C2×D1311yescharacteristic
211#103C2×D1311yescharacteristic
212#103C2×D1311yescharacteristic
213#103C2×D1311yescharacteristic
214#102—131no—
215#102—131no—
216#97—131no—
217#97—131no—
218C4×C8—131no—
219C4×C8C2×D1311yescharacteristic
220C2×C13#53211yescharacteristic
221C2×C13#57711yescharacteristic
222C2×C13#57811yescharacteristic
223D13—41no—
224D13—81no—
225C2×Q8—21no—
226C2×Q8—131no—
227C2×Q8C22×D1311yescharacteristic
228C2×Q8C22×D1311yescharacteristic
229C2×D4—131no—
230C2×D4—261no—
231C22×C4—131no—
232C22×C4—261no—
233Q16—262no—
234Q16—262no—
235SD16—262no—
236SD16—262no—
237M16—262no—
238C2×C8—131no—
239C2×C8—131no—
240C2×C8—262no—
241C2×C8C22×D1311yescharacteristic
242C2×C8C22×D1311yescharacteristic
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—131no—
247C4⋊C4—131no—
248C4⋊C4—131no—
249C4⋊C4—131no—
250C4⋊C4—261no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4C22×D1311yescharacteristic
259C4⋊C4C22×D1311yescharacteristic
260C22⋊C4—131no—
261C22⋊C4—131no—
262C22⋊C4—261no—
263C22⋊C4—261no—
264C22⋊C4—261no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C42—131no—
270C42—261no—
271C42—261no—
272C42—261no—
273C42C22×D1311yescharacteristic
274C13#317811yescharacteristic, complemented, Sylow
275C23—131no—
276C23—261no—
277Q8—21no—
278Q8—21no—
279Q8—21no—
280Q8—21no—
281Q8—81no—
282Q8—261no—
283Q8—261no—
284D4—261no—
285D4—261no—
286D4—1041no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—131no—
292C2×C4—131no—
293C2×C4—131no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—1041no—
300C2×C4D4×D1311yescharacteristic
301C2×C4D4×D1311yescharacteristic
302C2×C4C23×D1311yescharacteristic
303C8—21no—
304C8—21no—
305C8—132no—
306C8—132no—
307C22—261no—
308C22—261no—
309C22—261no—
310C22—521no—
311C22—521no—
312C22—521no—
313C22C2×D4×D1311yescharacteristic
314C4—21no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—261no—
321C4—261no—
322C4—261no—
323C4—521no—
324C4—521no—
325C4—521no—
326C4#41×D1311yescharacteristic
327C4#41×D1311yescharacteristic
328C2—521no—
329C2—1041no—
330C2#1171937311yescharacteristic
331C2#1171946711yescharacteristic
332C2#1171947111yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#487C2
socleC22×C13C22×D4
prime radical#88149C22
hypercenter#487D13
hypocenterC13#3178
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #11719436C2semidirect
3. C13×#487C2semidirect
4. #11718747C2semidirect
5. #11718741C2semidirect
6. #11718478C2semidirect
7. #11718477C2semidirect
8. #11718474C2semidirect
11. #11718451C2semidirect
12. #11718450C2semidirect
13. #11718449C2semidirect
14. #11718358C2semidirect
15. #11718350C2semidirect
146. #487D13semidirect
274. C13#3178semidirect

Maximal subgroups

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

subgroupindex
#117194382
#117194362
C13×#4872
#117187472
#117187412
#117184782
#117184772
#117184742
#117184732
#117184682
#117184512
#117184502
#117184492
#117183582
#117183502
#317813