Finite Group Databasebeta

← #13125519

Subgroups — #13125519

Order 1664.

374 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719240C211yesmaximal, characteristic, complemented
2#11719239C211yesmaximal, characteristic, complemented
3C13×#405C211yesmaximal, characteristic, complemented
4#11718796C211yesmaximal, characteristic, complemented
5#11718795C211yesmaximal, characteristic, complemented
6#11718776C211yesmaximal, characteristic, complemented
7#11718775C211yesmaximal, characteristic, complemented
8#11718373C211yesmaximal, characteristic, complemented
9#11718372C211yesmaximal, characteristic, complemented
10#11718371C211yesmaximal, characteristic, complemented
11#11718363C211yesmaximal, characteristic, complemented
12#11718358C211yesmaximal, characteristic, complemented
13#11718355C211yesmaximal, characteristic, complemented
14C4×D104C211yesmaximal, characteristic, complemented
15C4×#6095C211yesmaximal, characteristic, complemented
16C2×C13×M16C2211yescharacteristic
17C22×C8×C13C2211yescharacteristic
18C13×#117C2211yescharacteristic
19#88184C2211yescharacteristic
20#88184C2211yescharacteristic
21#88184C2211yescharacteristic
22#88178C2211yescharacteristic
23C2×D104C2211yescharacteristic
24C2×D104C2211yescharacteristic
25C2×#6095C2211yescharacteristic
26C2×#6095C2211yescharacteristic
27#88152—21no—
28#88150—21no—
29#88148—21no—
30#88148—21no—
31#88139—21no—
32#88138—21no—
33#88138—21no—
34#88137—21no—
35#88129C2211yescharacteristic
36#88128C2211yescharacteristic
37C4×D52C2211yescharacteristic
38C4×D52C2211yescharacteristic
39C4×D52C2211yescharacteristic
40#88124C2211yescharacteristic
41#88123C2211yescharacteristic
42C4×Dic26C2211yescharacteristic
43C13×#97C2211yescharacteristic
44C13×#97C2211yescharacteristic
45C4×C8×C13C2211yescharacteristic
46C4×C8×C13C2211yescharacteristic
47#88061C2211yescharacteristic
48#88061C2211yescharacteristic
49#88061C2211yescharacteristic
50#88061C2211yescharacteristic
51#88061C2211yescharacteristic
52#88061C2211yescharacteristic
53#88058C2211yescharacteristic
54#88058C2211yescharacteristic
55#88057C2211yescharacteristic
56#88057C2211yescharacteristic
57#88056C2211yescharacteristic
58#88056C2211yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C2×C22⋊D13—21no—
61C2×C22⋊D13—21no—
62C2×C22⋊D13—21no—
63C2×D52—21no—
64C2×D52—21no—
65C2×D52C2311yescharacteristic
66C2×D52C2311yescharacteristic
67C2×D52C2311yescharacteristic
68C2×C4×D13—21no—
69C2×C4×D13—21no—
70C2×C4×D13—21no—
71C2×Dic26—21no—
72C2×Dic26C2311yescharacteristic
73C13×M16—22no—
74C2×C8×C13—22no—
75C2×C8×C13C2311yescharacteristic
76C2×C8×C13C2311yescharacteristic
77C2×C8×C13C2311yescharacteristic
78C2×C8×C13C2311yescharacteristic
79C13×C4⋊C4D411yescharacteristic
80C13×C4⋊C4D411yescharacteristic
81C13×C22⋊C4D411yescharacteristic
82C13×C22⋊C4D411yescharacteristic
83C42×C13C2311yescharacteristic
84C42×C13C2311yescharacteristic
85C22⋊Dic13—21no—
86#6103—21no—
87#6103—21no—
88#6103—21no—
89#6103—21no—
90#6103—21no—
91#6103—21no—
92#6103—21no—
93#6103—21no—
94C4⋊Dic13—21no—
95C4⋊Dic13C2311yescharacteristic
96C4⋊Dic13C2311yescharacteristic
97C4⋊Dic13C2311yescharacteristic
98C4⋊Dic13C2311yescharacteristic
99#6101—21no—
100#6101—21no—
101#6101—21no—
102#6101—21no—
103C4×Dic13—21no—
104D104—22no—
105D104—22no—
106#6095—22no—
107#6095—22no—
108#3179—131nomaximal, Sylow
109C23×C13C2×D411yescharacteristic
110C22×D13—21no—
111C22×D13—21no—
112C22×D13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13C2×D411yescharacteristic
116C2×C4×C13C2×D411yescharacteristic
117C2×C4×C13C2×D411yescharacteristic
118C2×C4×C13C2×D411yescharacteristic
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2411yescharacteristic
121C22⋊D13—81no—
122C22⋊D13—81no—
123C22⋊D13—81no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129D52—21no—
130D52—21no—
131D52—21no—
132D52—21no—
133D52—21no—
134D52—21no—
135D52—81no—
136D52—81no—
137C4×D13—81no—
138C4×D13—81no—
139C4×D13—81no—
140Dic26—21no—
141Dic26—21no—
142Dic26—81no—
143C8×C13—21no—
144C8×C13—21no—
145C8×C13#4112yes—
146C8×C13#4112yes—
147#542—131no—
148#540—131no—
149#501—131no—
150#496—131no—
151#488—131no—
152#486—131no—
153#469—131no—
154#468—131no—
155#466—131no—
156#465—131no—
157#442—131no—
158#440—131no—
159C4×SD16—131no—
160C4×D8—131no—
161#405D1311yescharacteristic, complemented
162C22×C13—21no—
163C22×C13—21no—
164C22×C13—21no—
165C22×C13C22×D411yescharacteristic
166C2×D13—41no—
167C2×D13—41no—
168C2×D13—41no—
169C2×D13—41no—
170C2×D13—41no—
171C2×D13—41no—
172C2×D13—41no—
173C2×D13—41no—
174C2×D13—41no—
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—21no—
178C4×C13—21no—
179C4×C13—21no—
180C4×C13C2×#4111yescharacteristic
181C4×C13C2×#4111yescharacteristic
182Dic13—41no—
183Dic13—41no—
184Dic13—41no—
185Dic13—41no—
186Dic13—41no—
187C2×SD16—131no—
188C2×SD16—131no—
189C2×D8—131no—
190C2×D8—131no—
191C2×M16C2×D1311yescharacteristic
192C22×C8C2×D1311yescharacteristic
193C4⋊Q8—131no—
194#127—131no—
195#126—261no—
196#125—131no—
197#124—131no—
198#124—261no—
199#123—261no—
200#123—261no—
201#123—261no—
202C22⋊Q8—131no—
203C22⋊Q8—261no—
204#121—131no—
205#121—131no—
206#121—131no—
207#121—261no—
208#121—261no—
209C4×Q8—131no—
210C4×D4—131no—
211C4×D4—131no—
212C4×D4—131no—
213#117C2×D1311yescharacteristic
214#107—131no—
215#107—131no—
216#106—131no—
217#106—131no—
218#103—131no—
219#103—131no—
220#102—131no—
221#102—131no—
222#102—131no—
223#102—131no—
224#102—131no—
225#102—131no—
226#97C2×D1311yescharacteristic
227#97C2×D1311yescharacteristic
228C4×C8C2×D1311yescharacteristic
229C4×C8C2×D1311yescharacteristic
230C2×C13—41no—
231C2×C13#53211yescharacteristic
232C2×C13#57611yescharacteristic
233C2×C13#57711yescharacteristic
234D13—81no—
235D13—81no—
236D13—81no—
237C2×Q8—131no—
238C2×Q8—261no—
239C2×D4—131no—
240C2×D4—131no—
241C2×D4—131no—
242C2×D4—261no—
243C2×D4—261no—
244C2×D4—261no—
245C2×D4—261no—
246C2×D4—261no—
247C22×C4—261no—
248C22×C4—261no—
249C22×C4—261no—
250C22×C4C22×D1311yescharacteristic
251SD16—262no—
252SD16—262no—
253D8—262no—
254D8—262no—
255M16—22no—
256C2×C8—22no—
257C2×C8C22×D1311yescharacteristic
258C2×C8C22×D1311yescharacteristic
259C2×C8C22×D1311yescharacteristic
260C2×C8C22×D1311yescharacteristic
261C4⋊C4—131no—
262C4⋊C4—131no—
263C4⋊C4—131no—
264C4⋊C4—131no—
265C4⋊C4—261no—
266C4⋊C4—261no—
267C4⋊C4—261no—
268C4⋊C4—261no—
269C4⋊C4—261no—
270C4⋊C4D5211yescharacteristic
271C4⋊C4D5211yescharacteristic
272C22⋊C4—261no—
273C22⋊C4—261no—
274C22⋊C4—261no—
275C22⋊C4—261no—
276C22⋊C4—261no—
277C22⋊C4—261no—
278C22⋊C4—261no—
279C22⋊C4—261no—
280C22⋊C4—261no—
281C22⋊C4D5211yescharacteristic
282C22⋊C4D5211yescharacteristic
283C42—261no—
284C42C22×D1311yescharacteristic
285C42C22×D1311yescharacteristic
286C13#317911yescharacteristic, complemented, Sylow
287C23—261no—
288C23—261no—
289C23—261no—
290C23C2×D5211yescharacteristic
291Q8—261no—
292Q8—261no—
293Q8—1041no—
294D4—261no—
295D4—261no—
296D4—261no—
297D4—261no—
298D4—261no—
299D4—261no—
300D4—1041no—
301D4—1041no—
302D4—1041no—
303D4—1041no—
304D4—1041no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—261no—
310C2×C4—261no—
311C2×C4—261no—
312C2×C4—1041no—
313C2×C4—1041no—
314C2×C4—1041no—
315C2×C4C2×D5211yescharacteristic
316C2×C4C2×D5211yescharacteristic
317C2×C4C2×D5211yescharacteristic
318C2×C4C2×D5211yescharacteristic
319C2×C4C2×D5211yescharacteristic
320C2×C4C23×D1311yescharacteristic
321C8—21no—
322C8—21no—
323C8#612712yes—
324C8#612712yes—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—521no—
329C22—521no—
330C22—521no—
331C22—521no—
332C22—521no—
333C22—521no—
334C22—521no—
335C22—521no—
336C22—521no—
337C22C22×D5211yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—521no—
344C4—521no—
345C4—521no—
346C4—521no—
347C4—521no—
348C4C2×#612711yescharacteristic
349C4C2×#612711yescharacteristic
350C2—41no—
351C2—1041no—
352C2—1041no—
353C2—1041no—
354C2#1171918211yescharacteristic
355C2#1171945611yescharacteristic
356C2#1171945711yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#405C2
socleC22×C13C22×D4
hypercenter#405D13
hypocenterC13#3179
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #405

Complements

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

NH ≅ G/Ntype
1. #11719240C2semidirect
2. #11719239C2semidirect
3. C13×#405C2semidirect
4. #11718796C2semidirect
5. #11718795C2semidirect
6. #11718776C2semidirect
7. #11718775C2semidirect
8. #11718373C2semidirect
9. #11718372C2semidirect
10. #11718371C2semidirect
11. #11718363C2semidirect
12. #11718358C2semidirect
13. #11718355C2semidirect
14. C4×D104C2semidirect
15. C4×#6095C2semidirect
161. #405D13semidirect
286. C13#3179semidirect

Maximal subgroups

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

subgroupindex
#117192402
#117192392
C13×#4052
#117187962
#117187952
#117187762
#117187752
#117183732
#117183722
#117183712
#117183632
#117183582
#117183552
C4×D1042
C4×#60952
#317913