Finite Group Databasebeta

← #13128946

Subgroups — #13128946

Order 1664.

1030 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
1C13×#548C211yesmaximal, characteristic, complemented
2#11719539C211yesmaximal, characteristic, complemented
3#41×Dic13C211yesmaximal, characteristic, complemented
4#11719522C211yesmaximal, characteristic, complemented
5#11719517C211yesmaximal, characteristic, complemented
6#11719387C213yesmaximal, complemented
7#11719386C213yesmaximal, complemented
8#11719344C213yesmaximal, complemented
9#11719329C213yesmaximal, complemented
10#11719324C213yesmaximal, complemented
11#11719319C213yesmaximal, complemented
12#11719279C211yesmaximal, characteristic, complemented
13#11719275C211yesmaximal, characteristic, complemented
14#11719268C213yesmaximal, complemented
15#11719243C213yesmaximal, complemented
16C2×C13×#41C2211yescharacteristic
17C22×Q8×C13C2211yescharacteristic
18C2×#6131C2211yescharacteristic
19C13×#124C2213yes—
20C13×C22⋊Q8C2213yes—
21C13×#121C2213yes—
22C4×Q8×C13C2211yescharacteristic
23C4×D4×C13C2213yes—
24#88201C2213yes—
25#88200C2213yes—
26Q8×Dic13C2211yescharacteristic
27Q8×Dic13C2211yescharacteristic
28Q8×Dic13C2213yes—
29Q8×Dic13C2213yes—
30Q8×Dic13C2211yescharacteristic
31#88194C2213yes—
32#88193C2213yes—
33#88192C2216yes—
34#88192C2213yes—
35#88189C2213yes—
36D4×Dic13C2213yes—
37D4×Dic13C2213yes—
38#88184C2213yes—
39#88184C2213yes—
40C4×C22⋊D13C2213yes—
41C4×C22⋊D13C2213yes—
42#88180C2213yes—
43#88180C2213yes—
44#88180C2213yes—
45C2×C4×Dic13C2213yes—
46#88152C2213yes—
47#88147C2213yes—
48#88146C2216yes—
49C4⋊C4×D13C2213yes—
50#88144C2213yes—
51#88144C2213yes—
52#88143C2213yes—
53#88140C2213yes—
54#88140C2216yes—
55#88139C2213yes—
56#88139C2216yes—
57#88137C2216yes—
58#88135C2216yes—
59#88133C2211yescharacteristic
60#88133C2216yes—
61#88132C2213yes—
62C4×D52C2213yes—
63#88126C2213yes—
64#88123C2213yes—
65C4×Dic26C2213yes—
66C13×#41—24no—
67C2×Q8×C13—24no—
68C2×Q8×C13C2313yes—
69C2×Q8×C13C2311yescharacteristic
70C2×D4×C13C2313yes—
71C2×D4×C13C2313yes—
72C22×C4×C13C2313yes—
73C22×C4×C13C2313yes—
74C2×C22⋊D13C2316yes—
75C2×C22⋊D13C2313yes—
76C2×C22⋊D13C2313yes—
77C22×Dic13C2313yes—
78C22×Dic13C2313yes—
79#6131—24no—
80C2×D52C2313yes—
81C2×C4×D13C2313yes—
82C2×C4×D13C2316yes—
83C2×Dic26C2313yes—
84C13×C4⋊C4C2313yes—
85C13×C4⋊C4C2313yes—
86C13×C22⋊C4C2313yes—
87C13×C22⋊C4C2316yes—
88C13×C22⋊C4C2311yescharacteristic
89C42×C13C2313yes—
90C22⋊Dic13C2313yes—
91C22⋊Dic13C2316yes—
92C22⋊Dic13C2311yescharacteristic
93C22⋊Dic13C2311yescharacteristic
94C22⋊Dic13C2313yes—
95#6103C2313yes—
96#6103C2313yes—
97#6103C2313yes—
98#6103C2316yes—
99#6103C2313yes—
100C4⋊Dic13C2311yescharacteristic
101C4⋊Dic13C2316yes—
102C4⋊Dic13C2313yes—
103C4⋊Dic13C2313yes—
104C4⋊Dic13C2313yes—
105C4⋊Dic13C2313yes—
106C4⋊Dic13C2313yes—
107#6101C2313yes—
108#6101C2313yes—
109#6101C2311yescharacteristic
110#6101C2313yes—
111#6101C2313yes—
112#6101C2311yescharacteristic
113C4×Dic13C2313yes—
114C4×Dic13C2313yes—
115C4×Dic13C2313yes—
116C4×Dic13C2316yes—
117C4×Dic13C2311yescharacteristic
118C4×Dic13C2313yes—
119#3524—131nomaximal, Sylow
120C23×C13C2411yescharacteristic
121C23×C13C2413yes—
122C22×D13C2413yes—
123Q8×C13—26no—
124Q8×C13#4114yes—
125D4×C13—26no—
126D4×C13—43no—
127C2×C4×C13—26no—
128C2×C4×C13—26no—
129C2×C4×C13C2411yescharacteristic
130C2×C4×C13C2413yes—
131C2×C4×C13C2413yes—
132C2×C4×C13C2411yescharacteristic
133C2×C4×C13C2413yes—
134C22⋊D13—43no—
135C22⋊D13—46no—
136C22⋊D13—43no—
137C2×Dic13—43no—
138C2×Dic13—43no—
139C2×Dic13C2411yescharacteristic
140C2×Dic13C2411yescharacteristic
141C2×Dic13C2413yes—
142C2×Dic13C2411yescharacteristic
143C2×Dic13C2413yes—
144C2×Dic13C2413yes—
145C2×Dic13C2411yescharacteristic
146D52—26no—
147C4×D13—26no—
148C4×D13—46no—
149Dic26—43no—
150#559—133no—
151#557—131no—
152#555—133no—
153#553—133no—
154#552—133no—
155#550—131no—
156#548—131no—
157#548D1311yescharacteristic, complemented
158#542—133no—
159#540—133no—
160#529—133no—
161#529—133no—
162#520—131no—
163#519—131no—
164C4×#41—131no—
165C22×C13—21no—
166C22×C13—23no—
167C22×C13—23no—
168C22×C13—23no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13C2511yescharacteristic
172C2×D13—23no—
173C2×D13—23no—
174C2×D13—23no—
175C4×C13—21no—
176C4×C13—23no—
177C4×C13—21no—
178C4×C13—23no—
179C4×C13C2×#4116yes—
180Dic13—21no—
181Dic13—23no—
182Dic13—23no—
183Dic13—23no—
184Dic13—21no—
185Dic13—21no—
186Dic13—21no—
187C2×#41—131no—
188C2×#41C2×D1311yescharacteristic
189C22×Q8C2×D1311yescharacteristic
190C4⋊Q8—133no—
191#127—133no—
192#126—133no—
193#126—131no—
194#126—136no—
195#125—133no—
196#125—133no—
197#125—133no—
198#124—133no—
199#124—133no—
200#124—136no—
201#124C2×D1313yes—
202#123—133no—
203#123—136no—
204#123—133no—
205#123—136no—
206C22⋊Q8—133no—
207C22⋊Q8—133no—
208C22⋊Q8C2×D1313yes—
209#121—133no—
210#121—136no—
211#121—133no—
212#121—133no—
213#121—133no—
214#121C2×D1313yes—
215C4×Q8—131no—
216C4×Q8—131no—
217C4×Q8—133no—
218C4×Q8—131no—
219C4×Q8—133no—
220C4×Q8—133no—
221C4×Q8C2×D1311yescharacteristic
222C4×D4—133no—
223C4×D4—133no—
224C4×D4—133no—
225C4×D4—133no—
226C4×D4—133no—
227C4×D4—136no—
228C4×D4—133no—
229C4×D4C2×D1313yes—
230#117—133no—
231#117—133no—
232#117—133no—
233#117—136no—
234#117—133no—
235C2×C4⋊C4—133no—
236C2×C42—133no—
237C2×C13—41no—
238C2×C13—43no—
239C2×C13C22×#4111yescharacteristic
240C2×C13#58511yescharacteristic
241C2×C13#58511yescharacteristic
242D13—43no—
243#41—24no—
244#41—264no—
245C2×Q8—24no—
246C2×Q8—133no—
247C2×Q8C22×D1313yes—
248C2×Q8C22×D1311yescharacteristic
249C2×D4—133no—
250C2×D4—136no—
251C2×D4—133no—
252C2×D4—133no—
253C2×D4C22×D1313yes—
254C2×D4C22×D1313yes—
255C22×C4—133no—
256C22×C4—133no—
257C22×C4—133no—
258C22×C4—136no—
259C22×C4C22×D1313yes—
260C22×C4C22×D1313yes—
261C4⋊C4—133no—
262C4⋊C4—133no—
263C4⋊C4—131no—
264C4⋊C4—133no—
265C4⋊C4—133no—
266C4⋊C4—133no—
267C4⋊C4—133no—
268C4⋊C4—136no—
269C4⋊C4—131no—
270C4⋊C4—133no—
271C4⋊C4—133no—
272C4⋊C4—131no—
273C4⋊C4—133no—
274C4⋊C4C22×D1313yes—
275C4⋊C4C22×D1313yes—
276C22⋊C4—131no—
277C22⋊C4—133no—
278C22⋊C4—136no—
279C22⋊C4—131no—
280C22⋊C4—133no—
281C22⋊C4—133no—
282C22⋊C4—133no—
283C22⋊C4—133no—
284C22⋊C4—136no—
285C22⋊C4—133no—
286C22⋊C4C22×D1316yes—
287C22⋊C4C22×D1311yescharacteristic
288C22⋊C4C22×D1313yes—
289C42—131no—
290C42—133no—
291C42—133no—
292C42—133no—
293C42—136no—
294C42—133no—
295C42C22×D1313yes—
296C13#352411yescharacteristic, complemented, Sylow
297C23—133no—
298C23C23×D1311yescharacteristic
299C23C23×D1313yes—
300Q8—26no—
301Q8—523no—
302Q8#612914yes—
303D4—26no—
304D4—43no—
305D4—266no—
306D4—523no—
307D4—523no—
308D4—526no—
309C2×C4—26no—
310C2×C4—26no—
311C2×C4—131no—
312C2×C4—133no—
313C2×C4—131no—
314C2×C4—133no—
315C2×C4—131no—
316C2×C4—133no—
317C2×C4—131no—
318C2×C4—266no—
319C2×C4—526no—
320C2×C4—523no—
321C2×C4—523no—
322C2×C4C23×D1311yescharacteristic
323C2×C4C23×D1313yes—
324C2×C4C23×D1311yescharacteristic
325C2×C4C23×D1313yes—
326C2×C4C23×D1313yes—
327C22—21no—
328C22—23no—
329C22—23no—
330C22—21no—
331C22—23no—
332C22—21no—
333C22—263no—
334C22—263no—
335C22—263no—
336C22C24×D1311yescharacteristic
337C4—21no—
338C4—23no—
339C4—23no—
340C4—21no—
341C4—261no—
342C4—263no—
343C4—261no—
344C4—261no—
345C4—261no—
346C4—263no—
347C4—263no—
348C4C2×#612916yes—
349C2—41no—
350C2—43no—
351C2—523no—
352C2C22×#612911yescharacteristic
353C2#1171964811yescharacteristic
354C2#1171965211yescharacteristic
subgroupG/H
center, FrattiniC22C24×D13
commutator, socle, cosocleC22×C13C25
FittingC13×#548C2
hypercenter#548D13
hypocenterC13#3524
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C13×#548C2semidirect
2. #11719539C2semidirect
3. #41×Dic13C2semidirect
4. #11719522C2semidirect
5. #11719517C2semidirect
6. #11719387C2semidirect
7. #11719386C2semidirect
8. #11719344C2semidirect
9. #11719329C2semidirect
10. #11719324C2semidirect
11. #11719319C2semidirect
12. #11719279C2semidirect
13. #11719275C2semidirect
14. #11719268C2semidirect
15. #11719243C2semidirect
157. #548D13semidirect
296. C13#3524semidirect

Maximal subgroups

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

subgroupindex
C13×#5482
#117195392
#41×Dic132
#117195222
#117195172
#117193872
#117193862
#117193442
#117193292
#117193242
#117193192
#117192792
#117192752
#117192682
#117192432
#352413