Finite Group Databasebeta

← #13128945

Subgroups — #13128945

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
1C4×C13×#41C211yesmaximal, characteristic, complemented
2#11719539C211yesmaximal, characteristic, complemented
3#11719536C211yesmaximal, characteristic, complemented
4#11719281C211yesmaximal, characteristic, complemented
5#11719279C211yesmaximal, characteristic, complemented
6#11719277C211yesmaximal, characteristic, complemented
7#11719274C211yesmaximal, characteristic, complemented
8#11719267C213yesmaximal, complemented
9#11719266C213yesmaximal, complemented
10#11719264C213yesmaximal, complemented
11#11719263C213yesmaximal, complemented
12#11719237C213yesmaximal, complemented
13#11719234C213yesmaximal, complemented
14#11719184C213yesmaximal, complemented
15#11719184C213yesmaximal, complemented
16C2×C13×#41C2211yescharacteristic
17C2×#6131C2211yescharacteristic
18C2×Q8×D13C2211yescharacteristic
19C4×Q8×C13C2211yescharacteristic
20C4×Q8×C13C2211yescharacteristic
21C4×D4×C13C2213yes—
22C4×D4×C13C2213yes—
23C13×#117C2213yes—
24C2×C42×C13C2213yes—
25Q8×Dic13C2211yescharacteristic
26Q8×Dic13C2211yescharacteristic
27#88194C2213yes—
28#88192C2213yes—
29#88192C2213yes—
30#88190C2213yes—
31#88184C2213yes—
32#88184C2213yes—
33#88183C2213yes—
34#88183C2213yes—
35#88183C2216yes—
36C4×C22⋊D13C2213yes—
37C4×C22⋊D13C2213yes—
38C4×C22⋊D13C2216yes—
39#88178C2213yes—
40#88178C2213yes—
41#88151C2213yes—
42#88149C2213yes—
43#88147C2213yes—
44#88146C2213yes—
45C4⋊C4×D13C2213yes—
46#88144C2213yes—
47#88142C2213yes—
48#88141C2213yes—
49#88139C2216yes—
50#88138C2216yes—
51#88137C2216yes—
52#88133C2216yes—
53#88130C2211yescharacteristic
54#88130C2213yes—
55#88129C2213yes—
56#88129C2213yes—
57C4×D52C2213yes—
58C4×D52C2213yes—
59#88126C2216yes—
60#88126C2213yes—
61#88126C2213yes—
62#88124C2213yes—
63#88124C2213yes—
64C4×Dic26C2213yes—
65C4×Dic26C2213yes—
66C13×#41—24no—
67C2×Q8×C13C2311yescharacteristic
68C2×D4×C13C2313yes—
69C22×C4×C13C2313yes—
70C22×C4×C13C2313yes—
71C22×C4×C13C2313yes—
72C2×C22⋊D13C2313yes—
73C2×C22⋊D13C2313yes—
74C2×C22⋊D13C2316yes—
75#6131—24no—
76Q8×D13—24no—
77C2×D52C2313yes—
78C2×D52C2313yes—
79C2×C4×D13C2313yes—
80C2×C4×D13C2313yes—
81C2×C4×D13C2316yes—
82C2×Dic26C2313yes—
83C2×Dic26C2313yes—
84C13×C4⋊C4C2313yes—
85C13×C4⋊C4C2313yes—
86C13×C22⋊C4C2316yes—
87C42×C13C2313yes—
88C42×C13C2313yes—
89C42×C13C2313yes—
90C42×C13C2311yescharacteristic
91C22⋊Dic13C2313yes—
92C22⋊Dic13C2316yes—
93C22⋊Dic13C2313yes—
94#6103C2311yescharacteristic
95#6103C2313yes—
96#6103C2313yes—
97#6103C2316yes—
98#6103C2313yes—
99#6103C2313yes—
100#6103C2311yescharacteristic
101#6103C2313yes—
102#6103C2311yescharacteristic
103C4⋊Dic13C2313yes—
104C4⋊Dic13C2313yes—
105C4⋊Dic13C2313yes—
106C4⋊Dic13C2313yes—
107#6101C2311yescharacteristic
108#6101C2313yes—
109#6101C2313yes—
110#6101C2311yescharacteristic
111#6101C2313yes—
112#6101C2313yes—
113#6101C2316yes—
114#6101C2313yes—
115#6101C2311yescharacteristic
116C4×Dic13C2316yes—
117C4×Dic13C2313yes—
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—43no—
127C2×C4×C13—43no—
128C2×C4×C13C2413yes—
129C2×C4×C13C2411yescharacteristic
130C2×C4×C13C2411yescharacteristic
131C2×C4×C13C2411yescharacteristic
132C2×C4×C13C2413yes—
133C2×C4×C13C2413yes—
134C22⋊D13—46no—
135C22⋊D13—43no—
136C22⋊D13—43no—
137C2×Dic13C2411yescharacteristic
138C2×Dic13C2413yes—
139C2×Dic13C2411yescharacteristic
140C2×Dic13C2413yes—
141C2×Dic13C2413yes—
142C2×Dic13C2411yescharacteristic
143D52—26no—
144D52—43no—
145C4×D13—26no—
146C4×D13—26no—
147C4×D13—46no—
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#520—131no—
163#519—131no—
164C4×#41D1311yescharacteristic, complemented
165C22×C13—23no—
166C22×C13—23no—
167C22×C13—23no—
168C22×C13C2511yescharacteristic
169C2×D13—21no—
170C2×D13—23no—
171C2×D13—23no—
172C2×D13—21no—
173C2×D13—23no—
174C2×D13—21no—
175C4×C13—21no—
176C4×C13—23no—
177C4×C13—23no—
178C4×C13—21no—
179C4×C13—21no—
180C4×C13C2×#4116yes—
181Dic13—23no—
182Dic13—21no—
183Dic13—21no—
184Dic13—23no—
185Dic13—23no—
186Dic13—21no—
187C2×#41—131no—
188C2×#41C2×D1311yescharacteristic
189C22×Q8—131no—
190C4⋊Q8—133no—
191#127—133no—
192#126—136no—
193#126—131no—
194#126—133no—
195#125—133no—
196#125—133no—
197#125—133no—
198#124—133no—
199#124—136no—
200#124—133no—
201#124—133no—
202#123—136no—
203#123—133no—
204#123—133no—
205#123—136no—
206C22⋊Q8—133no—
207C22⋊Q8—133no—
208C22⋊Q8—133no—
209#121—133no—
210#121—133no—
211#121—133no—
212#121—133no—
213#121—133no—
214#121—136no—
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—133no—
231#117—133no—
232#117—133no—
233#117—136no—
234#117C2×D1313yes—
235C2×C4⋊C4—133no—
236C2×C42C2×D1313yes—
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—136no—
258C22×C4C22×D1313yes—
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—133no—
277C22⋊C4—136no—
278C22⋊C4—133no—
279C22⋊C4—131no—
280C22⋊C4—133no—
281C22⋊C4—133no—
282C22⋊C4—133no—
283C22⋊C4—133no—
284C22⋊C4—136no—
285C22⋊C4—131no—
286C22⋊C4—133no—
287C22⋊C4—131no—
288C22⋊C4C22×D1316yes—
289C42—136no—
290C42—133no—
291C42—133no—
292C42C22×D1311yescharacteristic
293C42C22×D1313yes—
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—43no—
311C2×C4—43no—
312C2×C4—131no—
313C2×C4—133no—
314C2×C4—131no—
315C2×C4—133no—
316C2×C4—133no—
317C2×C4—131no—
318C2×C4—266no—
319C2×C4—266no—
320C2×C4—526no—
321C2×C4C23×D1313yes—
322C2×C4C23×D1311yescharacteristic
323C2×C4C23×D1311yescharacteristic
324C2×C4C23×D1311yescharacteristic
325C2×C4C23×D1313yes—
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—21no—
339C4—21no—
340C4—23no—
341C4—23no—
342C4—261no—
343C4—263no—
344C4—263no—
345C4—261no—
346C4—263no—
347C4—261no—
348C4C2×#612716yes—
349C2—43no—
350C2—521no—
351C2—523no—
352C2C22×#612711yescharacteristic
353C2#1171964811yescharacteristic
354C2#1171964811yescharacteristic
subgroupG/H
center, FrattiniC22C24×D13
commutator, socle, cosocleC22×C13C25
FittingC4×C13×#41C2
hypercenterC4×#41D13
hypocenterC13#3524
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C4×C13×#41C2semidirect
2. #11719539C2semidirect
3. #11719536C2semidirect
4. #11719281C2semidirect
5. #11719279C2semidirect
6. #11719277C2semidirect
7. #11719274C2semidirect
8. #11719267C2semidirect
9. #11719266C2semidirect
10. #11719264C2semidirect
11. #11719263C2semidirect
12. #11719237C2semidirect
13. #11719234C2semidirect
14. #11719184C2semidirect
15. #11719184C2semidirect
164. C4×#41D13semidirect
296. C13#3524semidirect

Maximal subgroups

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

subgroupindex
C4×C13×#412
#117195392
#117195362
#117192812
#117192792
#117192772
#117192742
#117192672
#117192662
#117192642
#117192632
#117192372
#117192342
#117191842
#352413