Finite Group Databasebeta

← #13128844

Subgroups — #13128844

Order 1664.

1010 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×#548C211yesmaximal, characteristic, complemented
2#11719536C211yesmaximal, characteristic, complemented
3#41×Dic13C211yesmaximal, characteristic, complemented
4Q8×C22⋊D13C211yesmaximal, characteristic, complemented
5#11719517C211yesmaximal, characteristic, complemented
6#11719387C213yesmaximal, complemented
7#11719376C213yesmaximal, complemented
8#11719346C213yesmaximal, complemented
9#11719327C213yesmaximal, complemented
10#11719321C213yesmaximal, complemented
11#11719308C213yesmaximal, complemented
12#11719277C211yesmaximal, characteristic, complemented
13Q8×Dic26C211yesmaximal, characteristic, complemented
14#11719247C213yesmaximal, complemented
15#11719243C213yesmaximal, complemented
16C2×C13×#41C2211yescharacteristic
17C22×Q8×C13C2211yescharacteristic
18C2×Q8×D13C2211yescharacteristic
19C13×#124C2213yes—
20C13×C22⋊Q8C2213yes—
21C13×#121C2213yes—
22C4×Q8×C13C2211yescharacteristic
23C4×D4×C13C2213yes—
24#88200C2213yes—
25Q8×Dic13C2211yescharacteristic
26Q8×Dic13C2211yescharacteristic
27Q8×Dic13C2213yes—
28Q8×Dic13C2213yes—
29Q8×Dic13C2211yescharacteristic
30#88198C2213yes—
31#88193C2213yes—
32#88192C2213yes—
33#88190C2216yes—
34#88190C2213yes—
35#88189C2213yes—
36D4×Dic13C2213yes—
37D4×Dic13C2213yes—
38C4×C22⋊D13C2213yes—
39C4×C22⋊D13C2213yes—
40#88180C2213yes—
41#88180C2213yes—
42#88180C2213yes—
43#88178C2213yes—
44#88178C2213yes—
45C2×C4×Dic13C2213yes—
46#88152C2213yes—
47#88146C2213yes—
48#88143C2213yes—
49#88142C2213yes—
50#88142C2213yes—
51#88141C2216yes—
52#88141C2213yes—
53#88140C2213yes—
54#88139C2211yescharacteristic
55#88139C2216yes—
56#88133C2213yes—
57#88133C2216yes—
58#88133C2216yes—
59#88132C2213yes—
60#88132C2216yes—
61#88131C2216yes—
62#88126C2213yes—
63#88123C2213yes—
64C4×Dic26C2213yes—
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⋊D13C2311yescharacteristic
75C2×C22⋊D13C2313yes—
76C22×Dic13C2313yes—
77C22×Dic13C2313yes—
78Q8×D13—24no—
79C2×C4×D13C2313yes—
80C2×Dic26C2311yescharacteristic
81C2×Dic26C2313yes—
82C2×Dic26C2316yes—
83C13×C4⋊C4C2313yes—
84C13×C4⋊C4C2313yes—
85C13×C22⋊C4C2316yes—
86C13×C22⋊C4C2313yes—
87C13×C22⋊C4C2311yescharacteristic
88C42×C13C2313yes—
89C22⋊Dic13C2316yes—
90C22⋊Dic13C2313yes—
91C22⋊Dic13C2316yes—
92C22⋊Dic13C2313yes—
93C22⋊Dic13C2313yes—
94C22⋊Dic13C2311yescharacteristic
95#6103C2311yescharacteristic
96#6103C2313yes—
97#6103C2313yes—
98#6103C2311yescharacteristic
99C4⋊Dic13C2313yes—
100C4⋊Dic13C2313yes—
101C4⋊Dic13C2313yes—
102C4⋊Dic13C2313yes—
103C4⋊Dic13C2313yes—
104C4⋊Dic13C2313yes—
105#6101C2313yes—
106#6101C2313yes—
107#6101C2313yes—
108#6101C2313yes—
109#6101C2313yes—
110#6101C2316yes—
111#6101C2313yes—
112C4×Dic13C2316yes—
113C4×Dic13C2313yes—
114C4×Dic13C2313yes—
115C4×Dic13C2313yes—
116C4×Dic13C2316yes—
117C4×Dic13C2313yes—
118C4×Dic13C2311yescharacteristic
119#3518—131nomaximal, Sylow
120C23×C13C2411yescharacteristic
121C23×C13C2413yes—
122C22×D13C2411yescharacteristic
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—22no—
135C22⋊D13—43no—
136C2×Dic13—26no—
137C2×Dic13—43no—
138C2×Dic13C2413yes—
139C2×Dic13C2411yescharacteristic
140C2×Dic13C2411yescharacteristic
141C2×Dic13C2413yes—
142C2×Dic13C2413yes—
143C2×Dic13C2413yes—
144C2×Dic13C2411yescharacteristic
145C4×D13—26no—
146Dic26—26no—
147Dic26—22no—
148Dic26—46no—
149Q82—131no—
150#556—133no—
151#556—133no—
152#556—133no—
153#555—133no—
154D4×Q8—131no—
155#548—131no—
156#548D1311yescharacteristic, complemented
157#542—133no—
158#542—133no—
159#533—133no—
160#529—133no—
161#519—131no—
162#519—131no—
163C4×#41—131no—
164C22×C13—21no—
165C22×C13—23no—
166C22×C13—23no—
167C22×C13—21no—
168C22×C13—23no—
169C22×C13—21no—
170C22×C13C2511yescharacteristic
171C2×D13—21no—
172C2×D13—21no—
173C2×D13—21no—
174C4×C13—21no—
175C4×C13—23no—
176C4×C13—21no—
177C4×C13—23no—
178C4×C13C2×#4116yes—
179Dic13—23no—
180Dic13—21no—
181Dic13—23no—
182Dic13—23no—
183Dic13—23no—
184Dic13—21no—
185Dic132−1+412yes—
186C2×#41C2×D1311yescharacteristic
187C22×Q8—131no—
188C22×Q8C2×D1311yescharacteristic
189C4⋊Q8—133no—
190C4⋊Q8—133no—
191C4⋊Q8—133no—
192C4⋊Q8—133no—
193#126—133no—
194#126—133no—
195#126—136no—
196#126—136no—
197#125—133no—
198#124—133no—
199#124—136no—
200#124—131no—
201#124—136no—
202#124C2×D1313yes—
203#123—133no—
204#123—133no—
205C22⋊Q8—133no—
206C22⋊Q8—133no—
207C22⋊Q8—133no—
208C22⋊Q8—133no—
209C22⋊Q8—136no—
210C22⋊Q8C2×D1313yes—
211#121—133no—
212#121—133no—
213#121C2×D1313yes—
214C4×Q8—131no—
215C4×Q8—131no—
216C4×Q8—133no—
217C4×Q8—131no—
218C4×Q8—133no—
219C4×Q8—133no—
220C4×Q8—136no—
221C4×Q8—133no—
222C4×Q8—133no—
223C4×Q8C2×D1311yescharacteristic
224C4×D4—133no—
225C4×D4—133no—
226C4×D4—133no—
227C4×D4—133no—
228C4×D4C2×D1313yes—
229#117—133no—
230#117—133no—
231#117—133no—
232#117—133no—
233#117—136no—
234#117—133no—
235C2×C42—133no—
236C2×C13—41no—
237C2×C13—43no—
238C2×C13C22×#4111yescharacteristic
239C2×C13C2×2−1+411yescharacteristic
240C2×C13#58511yescharacteristic
241D13—41no—
242#41—24no—
243C2×Q8—24no—
244C2×Q8—131no—
245C2×Q8—133no—
246C2×Q8—136no—
247C2×Q8—264no—
248C2×Q8C22×D1313yes—
249C2×Q8C22×D1311yescharacteristic
250C2×D4—131no—
251C2×D4—133no—
252C2×D4C22×D1313yes—
253C2×D4C22×D1313yes—
254C22×C4—133no—
255C22×C4—133no—
256C22×C4—133no—
257C22×C4C22×D1313yes—
258C22×C4C22×D1313yes—
259C4⋊C4—133no—
260C4⋊C4—133no—
261C4⋊C4—133no—
262C4⋊C4—133no—
263C4⋊C4—133no—
264C4⋊C4—133no—
265C4⋊C4—133no—
266C4⋊C4—133no—
267C4⋊C4—133no—
268C4⋊C4—133no—
269C4⋊C4—136no—
270C4⋊C4—133no—
271C4⋊C4—133no—
272C4⋊C4C22×D1313yes—
273C4⋊C4C22×D1313yes—
274C22⋊C4—133no—
275C22⋊C4—131no—
276C22⋊C4—136no—
277C22⋊C4—136no—
278C22⋊C4—133no—
279C22⋊C4—133no—
280C22⋊C4—133no—
281C22⋊C4—131no—
282C22⋊C4—131no—
283C22⋊C4—133no—
284C22⋊C4C22×D1316yes—
285C22⋊C4C22×D1311yescharacteristic
286C22⋊C4C22×D1313yes—
287C42—131no—
288C42—133no—
289C42—133no—
290C42—133no—
291C42—136no—
292C42—136no—
293C42—133no—
294C42C22×D1313yes—
295C13#351811yescharacteristic, complemented, Sylow
296C23—131no—
297C23C23×D1311yescharacteristic
298C23C23×D1313yes—
299Q8—26no—
300Q8—262no—
301Q8—266no—
302Q8—526no—
303Q8#612914yes—
304D4—26no—
305D4—43no—
306D4—262no—
307D4—523no—
308C2×C4—26no—
309C2×C4—26no—
310C2×C4—131no—
311C2×C4—133no—
312C2×C4—131no—
313C2×C4—131no—
314C2×C4—133no—
315C2×C4—133no—
316C2×C4—133no—
317C2×C4—266no—
318C2×C4—266no—
319C2×C4—523no—
320C2×C4C23×D1311yescharacteristic
321C2×C4C23×D1313yes—
322C2×C4C23×D1313yes—
323C2×C4C23×D1311yescharacteristic
324C2×C4C23×D1313yes—
325C22—21no—
326C22—23no—
327C22—23no—
328C22—21no—
329C22—23no—
330C22—21no—
331C22—261no—
332C22—261no—
333C22—261no—
334C22C24×D1311yescharacteristic
335C4—21no—
336C4—23no—
337C4—23no—
338C4—21no—
339C4—132no—
340C4—263no—
341C4—261no—
342C4—263no—
343C4—263no—
344C4—263no—
345C4—261no—
346C4C2×#612916yes—
347C2—41no—
348C2—43no—
349C2—521no—
350C2C22×#612911yescharacteristic
351C2#1171964811yescharacteristic
352C2D13×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D13
commutator, socle, cosocleC22×C13C25
FittingC13×#548C2
hypercenter#548D13
hypocenterC13#3518
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. #11719536C2semidirect
3. #41×Dic13C2semidirect
4. Q8×C22⋊D13C2semidirect
5. #11719517C2semidirect
6. #11719387C2semidirect
7. #11719376C2semidirect
8. #11719346C2semidirect
9. #11719327C2semidirect
10. #11719321C2semidirect
11. #11719308C2semidirect
12. #11719277C2semidirect
13. Q8×Dic26C2semidirect
14. #11719247C2semidirect
15. #11719243C2semidirect
156. #548D13semidirect
295. C13#3518semidirect

Maximal subgroups

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

subgroupindex
C13×#5482
#117195362
#41×Dic132
Q8×C22⋊D132
#117195172
#117193872
#117193762
#117193462
#117193272
#117193212
#117193082
#117192772
Q8×Dic262
#117192472
#117192432
#351813