Finite Group Databasebeta

← #13128912

Subgroups — #13128912

Order 1664.

1104 conjugacy classes of subgroups.

The subgroup lattice has 362 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#11719532C211yesmaximal, characteristic, complemented
4#11719522C211yesmaximal, characteristic, complemented
5C2×Q8×Dic13C211yesmaximal, characteristic, complemented
6#11719387C213yesmaximal, complemented
7#11719386C213yesmaximal, complemented
8#11719348C213yesmaximal, complemented
9#11719340C213yesmaximal, complemented
10#11719316C213yesmaximal, complemented
11#11719301C213yesmaximal, complemented
12#11719279C211yesmaximal, characteristic, complemented
13Q8×Dic26C211yesmaximal, characteristic, complemented
14#11719260C213yesmaximal, complemented
15#11719243C213yesmaximal, complemented
16C2×C13×#41C2211yescharacteristic
17C22×Q8×C13C2211yescharacteristic
18C2×#6131C2211yescharacteristic
19C2×#6129C2216yes—
20C13×#124C2213yes—
21C13×C22⋊Q8C2213yes—
22C13×#121C2213yes—
23C4×Q8×C13C2211yescharacteristic
24C4×D4×C13C2213yes—
25#88201C2213yes—
26#88200C2213yes—
27Q8×Dic13C2211yescharacteristic
28Q8×Dic13C2211yescharacteristic
29Q8×Dic13C2213yes—
30Q8×Dic13C2213yes—
31Q8×Dic13C2211yescharacteristic
32#88194C2213yes—
33#88193C2213yes—
34#88192C2213yes—
35#88189C2213yes—
36D4×Dic13C2213yes—
37D4×Dic13C2213yes—
38#88184C2213yes—
39#88184C2213yes—
40C4×C22⋊D13C2213yes—
41C4×C22⋊D13C2213yes—
42#88180C2213yes—
43C2×C4⋊Dic13C2213yes—
44C2×C4⋊Dic13C2213yes—
45C2×C4×Dic13C2213yes—
46#88152C2213yes—
47#88151C2216yes—
48#88147C2213yes—
49C4⋊C4×D13C2213yes—
50#88143C2213yes—
51#88142C2213yes—
52#88142C2213yes—
53#88140C2213yes—
54#88140C2216yes—
55#88139C2213yes—
56#88139C2216yes—
57#88137C2216yes—
58#88135C2216yes—
59#88133C2213yes—
60#88132C2211yescharacteristic
61#88132C2216yes—
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⋊D13C2313yes—
75C2×C22⋊D13C2313yes—
76C2×C22⋊D13C2316yes—
77C22×Dic13C2311yescharacteristic
78C22×Dic13C2313yes—
79C22×Dic13C2316yes—
80#6131—24no—
81#6129—412no—
82C2×D52C2313yes—
83C2×C4×D13C2313yes—
84C2×C4×D13C2316yes—
85C2×Dic26C2311yescharacteristic
86C2×Dic26C2316yes—
87C13×C4⋊C4C2313yes—
88C13×C4⋊C4C2313yes—
89C13×C22⋊C4C2316yes—
90C13×C22⋊C4C2311yescharacteristic
91C13×C22⋊C4C2313yes—
92C42×C13C2313yes—
93C22⋊Dic13C2313yes—
94C22⋊Dic13C2311yescharacteristic
95C22⋊Dic13C2313yes—
96C22⋊Dic13C2313yes—
97#6103C2313yes—
98#6103C2313yes—
99#6103C2316yes—
100#6103C2313yes—
101#6103C2313yes—
102C4⋊Dic13C2313yes—
103C4⋊Dic13C2313yes—
104C4⋊Dic13C2313yes—
105C4⋊Dic13C2313yes—
106C4⋊Dic13C2316yes—
107C4⋊Dic13C2311yescharacteristic
108C4⋊Dic13C2313yes—
109#6101C2313yes—
110#6101C2313yes—
111#6101C2311yescharacteristic
112#6101C2313yes—
113#6101C2313yes—
114#6101C2311yescharacteristic
115C4×Dic13C2313yes—
116C4×Dic13C2313yes—
117C4×Dic13C2313yes—
118C4×Dic13C2313yes—
119C4×Dic13C2313yes—
120#3522—131nomaximal, Sylow
121C23×C13C2413yes—
122C23×C13C2411yescharacteristic
123C22×D13C2413yes—
124Q8×C13—26no—
125Q8×C13#4114yescomplemented
126D4×C13—26no—
127D4×C13—26no—
128C2×C4×C13—26no—
129C2×C4×C13—26no—
130C2×C4×C13C2413yes—
131C2×C4×C13C2413yes—
132C2×C4×C13C2411yescharacteristic
133C2×C4×C13C2411yescharacteristic
134C2×C4×C13C2413yes—
135C22⋊D13—26no—
136C22⋊D13—26no—
137C22⋊D13—46no—
138C2×Dic13—26no—
139C2×Dic13—22no—
140C2×Dic13—46no—
141C2×Dic13C2411yescharacteristic
142C2×Dic13C2411yescharacteristic
143C2×Dic13C2413yes—
144C2×Dic13C2413yes—
145C2×Dic13C2413yes—
146C2×Dic13C2411yescharacteristic
147C2×Dic13C2411yescharacteristic
148D52—26no—
149C4×D13—26no—
150C4×D13—46no—
151Dic26—22no—
152Dic26—46no—
153#559—133no—
154Q82—131no—
155#554—133no—
156#550—131no—
157#548—131no—
158#548D1311yescharacteristic, complemented
159#547—133no—
160#547—133no—
161#542—133no—
162#542—133no—
163#532—133no—
164#529—133no—
165#520—131no—
166#520—131no—
167C2×C4×Q8—131no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—23no—
171C22×C13—23no—
172C22×C13—23no—
173C22×C13H(5,𝔽2)12yes—
174C22×C13C2511yescharacteristic
175C2×D13—23no—
176C2×D13—23no—
177C2×D13—23no—
178C4×C13—21no—
179C4×C13—23no—
180C4×C13—23no—
181C4×C13—21no—
182C4×C13C2×#4116yes—
183Dic13—21no—
184Dic13—23no—
185Dic13—23no—
186Dic13—23no—
187Dic13—21no—
188Dic13—21no—
189Dic132−1+412yes—
190C2×#41—131no—
191C2×#41—136no—
192C2×#41C2×D1311yescharacteristic
193C22×Q8C2×D1311yescharacteristic
194C4⋊Q8—133no—
195C4⋊Q8—133no—
196C4⋊Q8—133no—
197#127—133no—
198#126—133no—
199#126—133no—
200#125—133no—
201#124—133no—
202#124—133no—
203#124—136no—
204#124C2×D1313yes—
205#123—133no—
206#123—133no—
207#123—136no—
208#123—136no—
209C22⋊Q8—133no—
210C22⋊Q8—136no—
211C22⋊Q8—131no—
212C22⋊Q8—136no—
213C22⋊Q8C2×D1313yes—
214#121—133no—
215#121—133no—
216#121—133no—
217#121—133no—
218#121C2×D1313yes—
219C4×Q8—131no—
220C4×Q8—133no—
221C4×Q8—131no—
222C4×Q8—133no—
223C4×Q8—131no—
224C4×Q8—133no—
225C4×Q8C2×D1311yescharacteristic
226C4×D4—133no—
227C4×D4—133no—
228C4×D4—133no—
229C4×D4—133no—
230C4×D4—133no—
231C4×D4—136no—
232C4×D4—133no—
233C4×D4C2×D1313yes—
234#117—133no—
235#117—133no—
236C2×C4⋊C4—133no—
237C2×C4⋊C4—133no—
238C2×C4⋊C4—133no—
239C2×C42—133no—
240C2×C13—22no—
241C2×C13—43no—
242C2×C13C22×#4111yescharacteristic
243C2×C13C2×H(5,𝔽2)11yescharacteristic
244C2×C13C2×2−1+411yescharacteristic
245D13—43no—
246#41—24no—
247#41—264no—
248#41—5212no—
249C2×Q8—24no—
250C2×Q8—131no—
251C2×Q8—136no—
252C2×Q8C22×D1313yes—
253C2×Q8C22×D1311yescharacteristic
254C2×D4—133no—
255C2×D4—133no—
256C2×D4—136no—
257C2×D4—133no—
258C2×D4C22×D1313yes—
259C2×D4C22×D1313yes—
260C22×C4—131no—
261C22×C4—133no—
262C22×C4—136no—
263C22×C4—133no—
264C22×C4—136no—
265C22×C4C22×D1313yes—
266C22×C4C22×D1313yes—
267C4⋊C4—133no—
268C4⋊C4—133no—
269C4⋊C4—133no—
270C4⋊C4—133no—
271C4⋊C4—133no—
272C4⋊C4—136no—
273C4⋊C4—131no—
274C4⋊C4—131no—
275C4⋊C4—131no—
276C4⋊C4—133no—
277C4⋊C4—133no—
278C4⋊C4—133no—
279C4⋊C4—133no—
280C4⋊C4C22×D1313yes—
281C4⋊C4C22×D1313yes—
282C22⋊C4—133no—
283C22⋊C4—133no—
284C22⋊C4—131no—
285C22⋊C4—133no—
286C22⋊C4—133no—
287C22⋊C4—133no—
288C22⋊C4—133no—
289C22⋊C4—136no—
290C22⋊C4—133no—
291C22⋊C4C22×D1316yes—
292C22⋊C4C22×D1311yescharacteristic
293C22⋊C4C22×D1313yes—
294C42—133no—
295C42—133no—
296C42—133no—
297C42—133no—
298C42—133no—
299C42C22×D1313yes—
300C13#352211yescharacteristic, complemented, Sylow
301C23—133no—
302C23C23×D1313yes—
303C23C23×D1311yescharacteristic
304Q8—26no—
305Q8—262no—
306Q8—526no—
307Q8#612914yescomplemented
308D4—26no—
309D4—26no—
310D4—266no—
311D4—266no—
312D4—266no—
313D4—526no—
314C2×C4—26no—
315C2×C4—26no—
316C2×C4—131no—
317C2×C4—131no—
318C2×C4—131no—
319C2×C4—133no—
320C2×C4—133no—
321C2×C4—133no—
322C2×C4—131no—
323C2×C4—262no—
324C2×C4—266no—
325C2×C4—266no—
326C2×C4—526no—
327C2×C4—526no—
328C2×C4C23×D1313yes—
329C2×C4C23×D1311yescharacteristic
330C2×C4C23×D1313yes—
331C2×C4C23×D1311yescharacteristic
332C2×C4C23×D1313yes—
333C22—21no—
334C22—21no—
335C22—23no—
336C22—23no—
337C22—23no—
338C22—263no—
339C22—263no—
340C22—263no—
341C22#8825612yes—
342C22C24×D1311yescharacteristic
343C4—21no—
344C4—23no—
345C4—23no—
346C4—21no—
347C4—132no—
348C4—261no—
349C4—263no—
350C4—263no—
351C4—263no—
352C4—261no—
353C4—261no—
354C4C2×#612916yes—
355C2—22no—
356C2—43no—
357C2—523no—
358C2C22×#612911yescharacteristic
359C2C2×#8825611yescharacteristic
360C2D13×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D13
commutator, socle, cosocleC22×C13C25
FittingC13×#548C2
hypercenter#548D13
hypocenterC13#3522
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. #11719532C2semidirect
4. #11719522C2semidirect
5. C2×Q8×Dic13C2semidirect
6. #11719387C2semidirect
7. #11719386C2semidirect
8. #11719348C2semidirect
9. #11719340C2semidirect
10. #11719316C2semidirect
11. #11719301C2semidirect
12. #11719279C2semidirect
13. Q8×Dic26C2semidirect
14. #11719260C2semidirect
15. #11719243C2semidirect
125. Q8×C13#41semidirect
158. #548D13semidirect
300. C13#3522semidirect
307. Q8#6129semidirect

Maximal subgroups

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

subgroupindex
C13×#5482
#117195392
#117195322
#117195222
C2×Q8×Dic132
#117193872
#117193862
#117193482
#117193402
#117193162
#117193012
#117192792
Q8×Dic262
#117192602
#117192432
#352213