Finite Group Databasebeta

← #13128821

Subgroups — #13128821

Order 1664.

1012 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#520C211yesmaximal, characteristic, complemented
2#11719536C211yesmaximal, characteristic, complemented
3#11719536C211yesmaximal, characteristic, complemented
4Q8×D52C211yesmaximal, characteristic, complemented
5#11719277C211yesmaximal, characteristic, complemented
6C4×Q8×D13C211yesmaximal, characteristic, complemented
7#11719274C211yesmaximal, characteristic, complemented
8#11719266C213yesmaximal, complemented
9#11719263C213yesmaximal, complemented
10#11719262C213yesmaximal, complemented
11#11719247C213yesmaximal, complemented
12#11719233C213yesmaximal, complemented
13#11719223C213yesmaximal, complemented
14#11719218C213yesmaximal, complemented
15#11719216C213yesmaximal, complemented
16C2×C13×#41C2211yescharacteristic
17C2×Q8×D13C2211yescharacteristic
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#88192C2213yes—
28#88192C2213yes—
29#88190C2213yes—
30#88190C2213yes—
31#88183C2216yes—
32C4×C22⋊D13C2213yes—
33C4×C22⋊D13C2216yes—
34C4×C22⋊D13C2213yes—
35#88180C2216yes—
36#88178C2213yes—
37#88178C2216yes—
38#88178C2213yes—
39#88152C2213yes—
40#88151C2213yes—
41#88151C2213yes—
42#88150C2213yes—
43#88148C2211yescharacteristic
44#88146C2213yes—
45C4⋊C4×D13C2213yes—
46#88144C2213yes—
47#88143C2216yes—
48#88143C2213yes—
49#88142C2213yes—
50#88141C2213yes—
51#88141C2213yes—
52#88139C2213yes—
53#88138C2213yes—
54#88137C2213yes—
55#88133C2216yes—
56#88133C2216yes—
57#88133C2213yes—
58C4×D52C2213yes—
59#88126C2213yes—
60C42×D13C2213yes—
61#88124C2213yes—
62#88123C2213yes—
63C4×Dic26C2213yes—
64C4×Dic26C2213yes—
65C4×Dic26C2213yes—
66C13×#41—24no—
67C2×Q8×C13C2311yescharacteristic
68C2×D4×C13C2313yes—
69C22×C4×C13C2313yes—
70C22×C4×C13C2316yes—
71C2×C22⋊D13C2313yes—
72C2×C22⋊D13C2313yes—
73Q8×D13—24no—
74Q8×D13—24no—
75C2×D52C2311yescharacteristic
76C2×C4×D13C2311yescharacteristic
77C2×C4×D13C2313yes—
78C2×C4×D13C2313yes—
79C2×C4×D13C2313yes—
80C2×Dic26C2313yes—
81C2×Dic26C2313yes—
82C2×Dic26C2313yes—
83C13×C4⋊C4C2313yes—
84C13×C4⋊C4C2313yes—
85C13×C4⋊C4C2311yescharacteristic
86C13×C4⋊C4C2313yes—
87C13×C22⋊C4C2313yes—
88C13×C22⋊C4C2313yes—
89C42×C13C2313yes—
90C42×C13C2313yes—
91C22⋊Dic13C2316yes—
92C22⋊Dic13C2316yes—
93C22⋊Dic13C2313yes—
94C22⋊Dic13C2313yes—
95#6103C2311yescharacteristic
96#6103C2313yes—
97#6103C2313yes—
98#6103C2313yes—
99#6103C2311yescharacteristic
100#6103C2311yescharacteristic
101C4⋊Dic13C2313yes—
102C4⋊Dic13C2313yes—
103C4⋊Dic13C2313yes—
104C4⋊Dic13C2313yes—
105C4⋊Dic13C2316yes—
106#6101C2311yescharacteristic
107#6101C2313yes—
108#6101C2313yes—
109#6101C2316yes—
110#6101C2316yes—
111#6101C2313yes—
112#6101C2313yes—
113#6101C2313yes—
114C4×Dic13C2313yes—
115C4×Dic13C2313yes—
116C4×Dic13C2313yes—
117C4×Dic13C2316yes—
118C4×Dic13C2313yes—
119#3516—131nomaximal, Sylow
120C23×C13C2413yes—
121C22×D13C2411yescharacteristic
122C22×D13C2411yescharacteristic
123Q8×C13#4114yes—
124D4×C13—26no—
125C2×C4×C13—26no—
126C2×C4×C13—46no—
127C2×C4×C13C2411yescharacteristic
128C2×C4×C13C2413yes—
129C2×C4×C13C2411yescharacteristic
130C2×C4×C13C2411yescharacteristic
131C2×C4×C13C2413yes—
132C2×C4×C13C2413yes—
133C22⋊D13—26no—
134C22⋊D13—43no—
135C2×Dic13C2411yescharacteristic
136C2×Dic13C2413yes—
137C2×Dic13C2411yescharacteristic
138C2×Dic13C2413yes—
139C2×Dic13C2413yes—
140C2×Dic13C2413yes—
141D52—22no—
142C4×D13—22no—
143C4×D13—26no—
144C4×D13—26no—
145C4×D13—43no—
146Dic26—26no—
147Dic26—26no—
148Dic26—43no—
149#557—131no—
150#556—133no—
151#554—133no—
152#553—133no—
153#552—133no—
154D4×Q8—131no—
155#548—131no—
156#548—131no—
157#542—133no—
158#541—133no—
159#529—133no—
160#529—133no—
161#520D1311yescharacteristic, complemented
162#519—131no—
163C2×C4×Q8—131no—
164C22×C13—23no—
165C22×C13—23no—
166C22×C13—23no—
167C22×C13C2511yescharacteristic
168C2×D13—21no—
169C2×D13—21no—
170C2×D13—21no—
171C2×D13—21no—
172C2×D13—21no—
173C2×D132−1+412yes—
174C4×C13—21no—
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—23no—
178C4×C13—23no—
179C4×C13C2×#4116yes—
180Dic13—23no—
181Dic13—23no—
182Dic13—21no—
183Dic13—23no—
184Dic13—21no—
185Dic13—23no—
186C2×#41C2×D1311yescharacteristic
187C22×Q8—131no—
188C22×Q8—131no—
189C4⋊Q8—133no—
190C4⋊Q8—133no—
191#126—133no—
192#126—136no—
193#126—133no—
194#126—136no—
195#125—133no—
196#125—133no—
197#125—136no—
198#125—133no—
199#124—133no—
200#124—133no—
201#124—133no—
202#123—136no—
203#123—131no—
204#123—133no—
205C22⋊Q8—133no—
206C22⋊Q8—133no—
207C22⋊Q8—136no—
208C22⋊Q8—133no—
209C22⋊Q8—133no—
210C22⋊Q8—133no—
211#121—133no—
212#121—133no—
213#121—133no—
214C4×Q8—131no—
215C4×Q8—131no—
216C4×Q8—133no—
217C4×Q8—133no—
218C4×Q8—133no—
219C4×Q8—133no—
220C4×Q8—133no—
221C4×Q8C2×D1311yescharacteristic
222C4×Q8C2×D1311yescharacteristic
223C4×D4—133no—
224C4×D4—133no—
225C4×D4—136no—
226C4×D4—133no—
227C4×D4C2×D1313yes—
228C4×D4C2×D1313yes—
229#117—136no—
230#117—133no—
231#117—133no—
232#117C2×D1313yes—
233C2×C4⋊C4—133no—
234C2×C4⋊C4C2×D1313yes—
235C2×C42—133no—
236C2×C13—43no—
237C2×C13C22×#4111yescharacteristic
238C2×C13C2×2−1+411yescharacteristic
239C2×C13#58511yescharacteristic
240D13—22no—
241D13—41no—
242#41—24no—
243C2×Q8—133no—
244C2×Q8—133no—
245C2×Q8—133no—
246C2×Q8—264no—
247C2×Q8—264no—
248C2×Q8C22×D1311yescharacteristic
249C2×D4—133no—
250C2×D4—133no—
251C2×D4—131no—
252C2×D4C22×D1313yes—
253C22×C4—131no—
254C22×C4—133no—
255C22×C4—133no—
256C22×C4—133no—
257C22×C4C22×D1313yes—
258C22×C4C22×D1316yes—
259C4⋊C4—133no—
260C4⋊C4—136no—
261C4⋊C4—133no—
262C4⋊C4—133no—
263C4⋊C4—133no—
264C4⋊C4—133no—
265C4⋊C4—136no—
266C4⋊C4—133no—
267C4⋊C4—133no—
268C4⋊C4—136no—
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—136no—
279C22⋊C4—133no—
280C22⋊C4—133no—
281C22⋊C4—131no—
282C22⋊C4—131no—
283C22⋊C4—133no—
284C22⋊C4—131no—
285C22⋊C4—133no—
286C22⋊C4C22×D1313yes—
287C22⋊C4C22×D1313yes—
288C42—133no—
289C42—133no—
290C42—133no—
291C42—136no—
292C42—133no—
293C42C22×D1313yes—
294C42C22×D1313yes—
295C13#351611yescharacteristic, complemented, Sylow
296C23—131no—
297C23—131no—
298C23C23×D1313yes—
299Q8—266no—
300Q8—266no—
301Q8—523no—
302Q8#612714yes—
303D4—26no—
304D4—262no—
305D4—266no—
306D4—523no—
307C2×C4—26no—
308C2×C4—46no—
309C2×C4—131no—
310C2×C4—131no—
311C2×C4—133no—
312C2×C4—133no—
313C2×C4—133no—
314C2×C4—133no—
315C2×C4—262no—
316C2×C4—266no—
317C2×C4—266no—
318C2×C4—523no—
319C2×C4C23×D1311yescharacteristic
320C2×C4C23×D1313yes—
321C2×C4C23×D1311yescharacteristic
322C2×C4C23×D1313yes—
323C2×C4C23×D1311yescharacteristic
324C2×C4C23×D1313yes—
325C22—23no—
326C22—23no—
327C22—23no—
328C22—132no—
329C22—261no—
330C22—261no—
331C22—261no—
332C22—261no—
333C22—261no—
334C22C24×D1311yescharacteristic
335C4—21no—
336C4—23no—
337C4—23no—
338C4—21no—
339C4—21no—
340C4—263no—
341C4—263no—
342C4—263no—
343C4—261no—
344C4—261no—
345C4—263no—
346C4C2×#612716yes—
347C2—43no—
348C2—262no—
349C2—521no—
350C2C22×#612711yescharacteristic
351C2#1171965011yescharacteristic
352C2D13×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D13
commutator, socle, cosocleC22×C13C25
FittingC13×#520C2
hypercenter#520D13
hypocenterC13#3516
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. #11719536C2semidirect
3. #11719536C2semidirect
4. Q8×D52C2semidirect
5. #11719277C2semidirect
6. C4×Q8×D13C2semidirect
7. #11719274C2semidirect
8. #11719266C2semidirect
9. #11719263C2semidirect
10. #11719262C2semidirect
11. #11719247C2semidirect
12. #11719233C2semidirect
13. #11719223C2semidirect
14. #11719218C2semidirect
15. #11719216C2semidirect
161. #520D13semidirect
295. C13#3516semidirect

Maximal subgroups

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

subgroupindex
C13×#5202
#117195362
Q8×D522
#117192772
C4×Q8×D132
#117192742
#117192662
#117192632
#117192622
#117192472
#117192332
#117192232
#117192182
#117192162
#351613