Finite Group Databasebeta

← #13128937

Subgroups — #13128937

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×#520C211yesmaximal, characteristic, complemented
2#11719539C211yesmaximal, characteristic, complemented
3#11719536C211yesmaximal, characteristic, complemented
4#11719281C211yesmaximal, characteristic, complemented
5C4×#6131C211yesmaximal, characteristic, complemented
6#11719277C211yesmaximal, characteristic, complemented
7#11719275C211yesmaximal, characteristic, complemented
8#11719268C213yesmaximal, complemented
9#11719267C213yesmaximal, complemented
10#11719264C213yesmaximal, complemented
11#11719262C213yesmaximal, complemented
12#11719239C213yesmaximal, complemented
13#11719233C213yesmaximal, complemented
14#11719219C213yesmaximal, complemented
15#11719218C213yesmaximal, complemented
16C2×C13×#41C2211yescharacteristic
17C2×#6131C2211yescharacteristic
18C2×Q8×D13C2211yescharacteristic
19C4×Q8×C13C2211yescharacteristic
20C4×Q8×C13C2211yescharacteristic
21C4×D4×C13C2213yes—
22C4×D4×C13C2213yes—
23C13×#117C2213yes—
24C2×C13×C4⋊C4C2213yes—
25Q8×Dic13C2211yescharacteristic
26Q8×Dic13C2211yescharacteristic
27#88194C2213yes—
28#88192C2213yes—
29#88192C2213yes—
30#88190C2213yes—
31#88184C2213yes—
32#88184C2216yes—
33#88183C2216yes—
34C4×C22⋊D13C2213yes—
35C4×C22⋊D13C2213yes—
36C4×C22⋊D13C2216yes—
37#88180C2216yes—
38#88178C2213yes—
39#88152C2216yes—
40#88152C2211yescharacteristic
41#88151C2213yes—
42#88150C2213yes—
43#88149C2213yes—
44#88148C2213yes—
45#88147C2213yes—
46#88146C2213yes—
47#88146C2213yes—
48#88144C2213yes—
49#88144C2213yes—
50#88143C2213yes—
51#88141C2213yes—
52#88139C2213yes—
53#88139C2216yes—
54#88138C2213yes—
55#88137C2213yes—
56#88137C2216yes—
57#88133C2213yes—
58#88129C2213yes—
59C4×D52C2213yes—
60C4×D52C2213yes—
61#88126C2213yes—
62C42×D13C2213yes—
63#88123C2213yes—
64C4×Dic26C2213yes—
65C4×Dic26C2213yes—
66C13×#41—24no—
67C2×Q8×C13C2311yescharacteristic
68C2×D4×C13C2313yes—
69C22×C4×C13C2313yes—
70C22×C4×C13C2316yes—
71C2×C22⋊D13C2313yes—
72C2×C22⋊D13C2316yes—
73C2×C22⋊D13C2313yes—
74#6131—24no—
75Q8×D13—24no—
76C2×D52C2313yes—
77C2×D52C2313yes—
78C2×C4×D13C2313yes—
79C2×C4×D13C2313yes—
80C2×C4×D13C2313yes—
81C2×C4×D13C2313yes—
82C2×Dic26C2313yes—
83C2×Dic26C2313yes—
84C13×C4⋊C4C2313yes—
85C13×C4⋊C4C2313yes—
86C13×C4⋊C4C2313yes—
87C13×C4⋊C4C2311yescharacteristic
88C13×C22⋊C4C2313yes—
89C13×C22⋊C4C2313yes—
90C42×C13C2313yes—
91C42×C13C2313yes—
92C22⋊Dic13C2313yes—
93C22⋊Dic13C2313yes—
94C22⋊Dic13C2316yes—
95#6103C2311yescharacteristic
96#6103C2313yes—
97#6103C2311yescharacteristic
98#6103C2313yes—
99#6103C2316yes—
100#6103C2316yes—
101#6103C2311yescharacteristic
102#6103C2313yes—
103C4⋊Dic13C2311yescharacteristic
104C4⋊Dic13C2313yes—
105C4⋊Dic13C2313yes—
106C4⋊Dic13C2316yes—
107C4⋊Dic13C2313yes—
108#6101C2313yes—
109#6101C2313yes—
110#6101C2313yes—
111#6101C2313yes—
112#6101C2311yescharacteristic
113#6101C2313yes—
114C4×Dic13C2313yes—
115C4×Dic13C2313yes—
116C4×Dic13C2316yes—
117C4×Dic13C2311yescharacteristic
118C4×Dic13C2313yes—
119#3524—131nomaximal, Sylow
120C23×C13C2413yes—
121C22×D13C2411yescharacteristic
122C22×D13C2413yes—
123Q8×C13#4114yes—
124D4×C13—26no—
125C2×C4×C13—26no—
126C2×C4×C13—46no—
127C2×C4×C13C2413yes—
128C2×C4×C13C2411yescharacteristic
129C2×C4×C13C2411yescharacteristic
130C2×C4×C13C2413yes—
131C2×C4×C13C2411yescharacteristic
132C2×C4×C13C2413yes—
133C22⋊D13—43no—
134C22⋊D13—46no—
135C22⋊D13—43no—
136C2×Dic13C2411yescharacteristic
137C2×Dic13C2411yescharacteristic
138C2×Dic13C2411yescharacteristic
139C2×Dic13C2413yes—
140C2×Dic13C2413yes—
141C2×Dic13C2413yes—
142D52—26no—
143D52—43no—
144C4×D13—26no—
145C4×D13—26no—
146C4×D13—43no—
147C4×D13—43no—
148Dic26—26no—
149Dic26—43no—
150#559—133no—
151#557—131no—
152#555—133no—
153#553—133no—
154#552—133no—
155#550—131no—
156#548—131no—
157#548—131no—
158#542—133no—
159#540—133no—
160#529—133no—
161#529—133no—
162#520D1311yescharacteristic, complemented
163#519—131no—
164C4×#41—131no—
165C22×C13—23no—
166C22×C13—23no—
167C22×C13—23no—
168C22×C13C2511yescharacteristic
169C2×D13—21no—
170C2×D13—23no—
171C2×D13—23no—
172C2×D13—23no—
173C2×D13—21no—
174C2×D13—21no—
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—21no—
178C4×C13—23no—
179C4×C13—23no—
180C4×C13C2×#4116yes—
181Dic13—23no—
182Dic13—21no—
183Dic13—23no—
184Dic13—23no—
185Dic13—21no—
186Dic13—21no—
187C2×#41—131no—
188C2×#41C2×D1311yescharacteristic
189C22×Q8—131no—
190C4⋊Q8—133no—
191#127—133no—
192#126—131no—
193#126—136no—
194#126—133no—
195#125—133no—
196#125—133no—
197#125—133no—
198#124—133no—
199#124—133no—
200#124—136no—
201#124—133no—
202#123—136no—
203#123—133no—
204#123—136no—
205#123—133no—
206C22⋊Q8—133no—
207C22⋊Q8—133no—
208C22⋊Q8—133no—
209#121—133no—
210#121—133no—
211#121—136no—
212#121—133no—
213#121—133no—
214#121—133no—
215C4×Q8—131no—
216C4×Q8—131no—
217C4×Q8—133no—
218C4×Q8—133no—
219C4×Q8—133no—
220C4×Q8C2×D1311yescharacteristic
221C4×Q8C2×D1311yescharacteristic
222C4×D4—133no—
223C4×D4—133no—
224C4×D4—136no—
225C4×D4—133no—
226C4×D4—133no—
227C4×D4—133no—
228C4×D4C2×D1313yes—
229C4×D4C2×D1313yes—
230#117—136no—
231#117—133no—
232#117—133no—
233#117—133no—
234#117C2×D1313yes—
235C2×C4⋊C4C2×D1313yes—
236C2×C42—133no—
237C2×C13—43no—
238C2×C13C22×#4111yescharacteristic
239C2×C13#58511yescharacteristic
240C2×C13#58511yescharacteristic
241D13—41no—
242D13—43no—
243#41—24no—
244#41—264no—
245C2×Q8—133no—
246C2×Q8—133no—
247C2×Q8—264no—
248C2×Q8C22×D1311yescharacteristic
249C2×D4—133no—
250C2×D4—136no—
251C2×D4—133no—
252C2×D4—133no—
253C2×D4—133no—
254C2×D4C22×D1313yes—
255C22×C4—133no—
256C22×C4—133no—
257C22×C4—133no—
258C22×C4—133no—
259C22×C4C22×D1313yes—
260C22×C4C22×D1316yes—
261C4⋊C4—133no—
262C4⋊C4—133no—
263C4⋊C4—133no—
264C4⋊C4—133no—
265C4⋊C4—133no—
266C4⋊C4—136no—
267C4⋊C4—131no—
268C4⋊C4—133no—
269C4⋊C4—133no—
270C4⋊C4—131no—
271C4⋊C4—133no—
272C4⋊C4C22×D1313yes—
273C4⋊C4C22×D1313yes—
274C4⋊C4C22×D1313yes—
275C4⋊C4C22×D1311yescharacteristic
276C22⋊C4—133no—
277C22⋊C4—136no—
278C22⋊C4—133no—
279C22⋊C4—131no—
280C22⋊C4—133no—
281C22⋊C4—136no—
282C22⋊C4—131no—
283C22⋊C4—131no—
284C22⋊C4—133no—
285C22⋊C4—136no—
286C22⋊C4—133no—
287C22⋊C4C22×D1313yes—
288C22⋊C4C22×D1313yes—
289C42—131no—
290C42—133no—
291C42—133no—
292C42—136no—
293C42—133no—
294C42C22×D1313yes—
295C42C22×D1313yes—
296C13#352411yescharacteristic, complemented, Sylow
297C23—131no—
298C23—133no—
299C23C23×D1313yes—
300Q8—266no—
301Q8—523no—
302Q8#612714yes—
303D4—26no—
304D4—266no—
305D4—523no—
306D4—523no—
307D4—523no—
308D4—526no—
309C2×C4—26no—
310C2×C4—46no—
311C2×C4—131no—
312C2×C4—131no—
313C2×C4—133no—
314C2×C4—131no—
315C2×C4—133no—
316C2×C4—133no—
317C2×C4—266no—
318C2×C4—266no—
319C2×C4—523no—
320C2×C4—523no—
321C2×C4C23×D1313yes—
322C2×C4C23×D1311yescharacteristic
323C2×C4C23×D1311yescharacteristic
324C2×C4C23×D1313yes—
325C2×C4C23×D1311yescharacteristic
326C2×C4C23×D1313yes—
327C22—23no—
328C22—23no—
329C22—23no—
330C22—261no—
331C22—263no—
332C22—263no—
333C22—261no—
334C22—263no—
335C22—261no—
336C22C24×D1311yescharacteristic
337C4—21no—
338C4—23no—
339C4—23no—
340C4—21no—
341C4—21no—
342C4—261no—
343C4—263no—
344C4—261no—
345C4—261no—
346C4—263no—
347C4—263no—
348C4C2×#612716yes—
349C2—43no—
350C2—521no—
351C2—523no—
352C2C22×#612711yescharacteristic
353C2#1171965011yescharacteristic
354C2#1171965211yescharacteristic
subgroupG/H
center, FrattiniC22C24×D13
commutator, socle, cosocleC22×C13C25
FittingC13×#520C2
hypercenter#520D13
hypocenterC13#3524
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #520

Complements

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

NH ≅ G/Ntype
1. C13×#520C2semidirect
2. #11719539C2semidirect
3. #11719536C2semidirect
4. #11719281C2semidirect
5. C4×#6131C2semidirect
6. #11719277C2semidirect
7. #11719275C2semidirect
8. #11719268C2semidirect
9. #11719267C2semidirect
10. #11719264C2semidirect
11. #11719262C2semidirect
12. #11719239C2semidirect
13. #11719233C2semidirect
14. #11719219C2semidirect
15. #11719218C2semidirect
162. #520D13semidirect
296. C13#3524semidirect

Maximal subgroups

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

subgroupindex
C13×#5202
#117195392
#117195362
#117192812
C4×#61312
#117192772
#117192752
#117192682
#117192672
#117192642
#117192622
#117192392
#117192332
#117192192
#117192182
#352413