Finite Group Databasebeta

← #13128836

Subgroups — #13128836

Order 1664.

1122 conjugacy classes of subgroups.

The subgroup lattice has 364 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#11719539C211yesmaximal, characteristic, complemented
4#11719282C211yesmaximal, characteristic, complemented
5#11719279C211yesmaximal, characteristic, complemented
6C4×#6131C211yesmaximal, characteristic, complemented
7#11719274C211yesmaximal, characteristic, complemented
8#11719267C213yesmaximal, complemented
9#11719263C213yesmaximal, complemented
10#11719258C213yesmaximal, complemented
11#11719253C213yesmaximal, complemented
12#11719240C213yesmaximal, complemented
13#11719233C213yesmaximal, complemented
14#11719219C213yesmaximal, complemented
15#11719212C213yesmaximal, complemented
16C2×C13×#41C2211yescharacteristic
17C2×#6131C2211yescharacteristic
18C2×#6131C2211yescharacteristic
19C2×#6127C2216yes—
20C4×Q8×C13C2211yescharacteristic
21C4×Q8×C13C2211yescharacteristic
22C4×D4×C13C2213yes—
23C4×D4×C13C2213yes—
24C13×#117C2213yes—
25C2×C13×C4⋊C4C2213yes—
26Q8×Dic13C2211yescharacteristic
27Q8×Dic13C2211yescharacteristic
28#88194C2213yes—
29#88194C2213yes—
30#88192C2213yes—
31#88192C2213yes—
32#88184C2213yes—
33#88184C2213yes—
34#88184C2216yes—
35#88183C2216yes—
36C4×C22⋊D13C2213yes—
37C4×C22⋊D13C2213yes—
38C4×C22⋊D13C2216yes—
39#88152C2213yes—
40#88150C2213yes—
41#88149C2213yes—
42#88149C2213yes—
43#88148C2216yes—
44#88148C2213yes—
45#88147C2213yes—
46#88147C2213yes—
47#88146C2213yes—
48C4⋊C4×D13C2213yes—
49#88144C2213yes—
50#88143C2211yescharacteristic
51#88142C2213yes—
52#88139C2213yes—
53#88138C2213yes—
54#88138C2216yes—
55#88138C2216yes—
56#88137C2213yes—
57#88133C2213yes—
58#88128C2213yes—
59C4×D52C2213yes—
60C4×D52C2213yes—
61C4×D52C2213yes—
62#88126C2213yes—
63C42×D13C2213yes—
64#88124C2213yes—
65C4×Dic26C2213yes—
66C13×#41—24no—
67C2×Q8×C13C2311yescharacteristic
68C2×D4×C13C2313yes—
69C22×C4×C13C2313yes—
70C22×C4×C13C2316yes—
71C2×C22⋊D13C2313yes—
72C2×C22⋊D13C2313yes—
73C2×C22⋊D13C2316yes—
74C2×C22⋊D13C2316yes—
75#6131—24no—
76#6131—24no—
77#6127—412no—
78C2×D52C2313yes—
79C2×D52C2313yes—
80C2×D52C2313yes—
81C2×D52C2316yes—
82C2×C4×D13C2313yes—
83C2×C4×D13C2313yes—
84C2×C4×D13C2313yes—
85C2×C4×D13C2313yes—
86C2×C4×D13C2316yes—
87C2×Dic26C2313yes—
88C13×C4⋊C4C2313yes—
89C13×C4⋊C4C2311yescharacteristic
90C13×C4⋊C4C2313yes—
91C13×C4⋊C4C2313yes—
92C13×C22⋊C4C2313yes—
93C13×C22⋊C4C2313yes—
94C42×C13C2313yes—
95C42×C13C2313yes—
96C22⋊Dic13C2313yes—
97C22⋊Dic13C2313yes—
98#6103C2313yes—
99#6103C2313yes—
100#6103C2313yes—
101#6103C2316yes—
102#6103C2313yes—
103#6103C2313yes—
104#6103C2313yes—
105C4⋊Dic13C2313yes—
106C4⋊Dic13C2313yes—
107C4⋊Dic13C2313yes—
108C4⋊Dic13C2311yescharacteristic
109#6101C2311yescharacteristic
110#6101C2313yes—
111#6101C2316yes—
112#6101C2311yescharacteristic
113#6101C2313yes—
114#6101C2311yescharacteristic
115#6101C2311yescharacteristic
116C4×Dic13C2313yes—
117C4×Dic13C2313yes—
118C4×Dic13C2311yescharacteristic
119C4×Dic13C2313yes—
120#3517—131nomaximal, Sylow
121C23×C13C2413yes—
122C22×D13C2413yes—
123C22×D13C2413yes—
124Q8×C13#4114yescomplemented
125D4×C13—26no—
126C2×C4×C13—26no—
127C2×C4×C13—46no—
128C2×C4×C13C2411yescharacteristic
129C2×C4×C13C2413yes—
130C2×C4×C13C2411yescharacteristic
131C2×C4×C13C2413yes—
132C2×C4×C13C2411yescharacteristic
133C2×C4×C13C2413yes—
134C22⋊D13—26no—
135C22⋊D13—46no—
136C22⋊D13—46no—
137C22⋊D13—43no—
138C2×Dic13C2411yescharacteristic
139C2×Dic13C2411yescharacteristic
140C2×Dic13C2413yes—
141C2×Dic13C2413yes—
142C2×Dic13C2411yescharacteristic
143C2×Dic13C2411yescharacteristic
144D52—26no—
145D52—26no—
146D52—43no—
147D52—46no—
148C4×D13—26no—
149C4×D13—26no—
150C4×D13—26no—
151C4×D13—43no—
152C4×D13—46no—
153Dic26—26no—
154#557—131no—
155#553—133no—
156#553—133no—
157#550—131no—
158#550—131no—
159#550—131no—
160#550—133no—
161#547—133no—
162#540—133no—
163#540—133no—
164#532—133no—
165#529—133no—
166#520—131no—
167#520D1311yescharacteristic, complemented
168C4×#41—131no—
169C22×C13—23no—
170C22×C13—23no—
171C22×C13—23no—
172C22×C13C2511yescharacteristic
173C2×D13—23no—
174C2×D13—23no—
175C2×D13—23no—
176C2×D13—23no—
177C2×D13—23no—
178C2×D13—23no—
179C4×C13—21no—
180C4×C13—23no—
181C4×C13—23no—
182C4×C13—21no—
183C4×C13—21no—
184C4×C13C2×#4116yes—
185Dic13—21no—
186Dic13—21no—
187Dic13—23no—
188Dic13—23no—
189Dic13—21no—
190Dic13H(5,𝔽2)12yes—
191C2×#41—131no—
192C2×#41—131no—
193C2×#41—136no—
194C2×#41C2×D1311yescharacteristic
195C4⋊Q8—133no—
196#127—133no—
197#127—133no—
198#127—133no—
199#126—133no—
200#126—133no—
201#125—131no—
202#125—133no—
203#125—133no—
204#124—133no—
205#123—136no—
206#123—133no—
207#123—136no—
208#123—133no—
209C22⋊Q8—133no—
210#121—133no—
211#121—133no—
212#121—133no—
213#121—136no—
214#121—133no—
215#121—133no—
216#121—133no—
217#121—133no—
218#121—136no—
219#121—136no—
220C4×Q8—131no—
221C4×Q8—131no—
222C4×Q8—133no—
223C4×Q8C2×D1311yescharacteristic
224C4×Q8C2×D1311yescharacteristic
225C4×D4—133no—
226C4×D4—133no—
227C4×D4—136no—
228C4×D4—133no—
229C4×D4—133no—
230C4×D4—133no—
231C4×D4—133no—
232C4×D4—133no—
233C4×D4C2×D1313yes—
234C4×D4C2×D1313yes—
235#117—133no—
236#117—133no—
237#117C2×D1313yes—
238C2×C4⋊C4—133no—
239C2×C4⋊C4C2×D1313yes—
240C2×C42—133no—
241C2×C13—43no—
242C2×C13C22×#4111yescharacteristic
243C2×C13C2×H(5,𝔽2)11yescharacteristic
244C2×C13#58511yescharacteristic
245D13—43no—
246D13—43no—
247#41—24no—
248#41—264no—
249#41—264no—
250#41—5212no—
251C2×Q8—133no—
252C2×Q8C22×D1311yescharacteristic
253C2×D4—133no—
254C2×D4—136no—
255C2×D4—133no—
256C2×D4—136no—
257C2×D4—133no—
258C2×D4—133no—
259C2×D4—133no—
260C2×D4—136no—
261C2×D4C22×D1313yes—
262C22×C4—133no—
263C22×C4—133no—
264C22×C4—133no—
265C22×C4—133no—
266C22×C4—136no—
267C22×C4C22×D1313yes—
268C22×C4C22×D1316yes—
269C4⋊C4—133no—
270C4⋊C4—133no—
271C4⋊C4—131no—
272C4⋊C4—133no—
273C4⋊C4—131no—
274C4⋊C4—131no—
275C4⋊C4—131no—
276C4⋊C4—136no—
277C4⋊C4—131no—
278C4⋊C4—133no—
279C4⋊C4—133no—
280C4⋊C4C22×D1313yes—
281C4⋊C4C22×D1313yes—
282C4⋊C4C22×D1313yes—
283C4⋊C4C22×D1311yescharacteristic
284C22⋊C4—133no—
285C22⋊C4—133no—
286C22⋊C4—133no—
287C22⋊C4—136no—
288C22⋊C4—133no—
289C22⋊C4—133no—
290C22⋊C4—133no—
291C22⋊C4—133no—
292C22⋊C4—133no—
293C22⋊C4C22×D1313yes—
294C22⋊C4C22×D1313yes—
295C42—131no—
296C42—133no—
297C42—133no—
298C42—133no—
299C42C22×D1313yes—
300C42C22×D1313yes—
301C13#351711yescharacteristic, complemented, Sylow
302C23—133no—
303C23—133no—
304C23C23×D1313yes—
305Q8—266no—
306Q8#612714yescomplemented
307D4—26no—
308D4—266no—
309D4—266no—
310D4—266no—
311D4—523no—
312D4—526no—
313D4—526no—
314D4—523no—
315D4—526no—
316C2×C4—26no—
317C2×C4—46no—
318C2×C4—131no—
319C2×C4—131no—
320C2×C4—131no—
321C2×C4—133no—
322C2×C4—133no—
323C2×C4—131no—
324C2×C4—266no—
325C2×C4—266no—
326C2×C4—266no—
327C2×C4—523no—
328C2×C4—526no—
329C2×C4C23×D1311yescharacteristic
330C2×C4C23×D1313yes—
331C2×C4C23×D1311yescharacteristic
332C2×C4C23×D1313yes—
333C2×C4C23×D1311yescharacteristic
334C2×C4C23×D1313yes—
335C22—23no—
336C22—23no—
337C22—23no—
338C22—263no—
339C22—263no—
340C22—263no—
341C22—263no—
342C22—263no—
343C22—263no—
344C22C24×D1311yescharacteristic
345C4—21no—
346C4—23no—
347C4—23no—
348C4—21no—
349C4—21no—
350C4—132no—
351C4—261no—
352C4—261no—
353C4—263no—
354C4—263no—
355C4—261no—
356C4C2×#612716yes—
357C2—43no—
358C2—523no—
359C2—523no—
360C2C22×#612711yescharacteristic
361C2D13×H(5,𝔽2)11yescharacteristic
362C2#1171965211yescharacteristic
subgroupG/H
center, FrattiniC22C24×D13
commutator, socle, cosocleC22×C13C25
FittingC13×#520C2
hypercenter#520D13
hypocenterC13#3517
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. #11719539C2semidirect
4. #11719282C2semidirect
5. #11719279C2semidirect
6. C4×#6131C2semidirect
7. #11719274C2semidirect
8. #11719267C2semidirect
9. #11719263C2semidirect
10. #11719258C2semidirect
11. #11719253C2semidirect
12. #11719240C2semidirect
13. #11719233C2semidirect
14. #11719219C2semidirect
15. #11719212C2semidirect
124. Q8×C13#41semidirect
167. #520D13semidirect
301. C13#3517semidirect
306. Q8#6127semidirect

Maximal subgroups

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

subgroupindex
C13×#5202
#117195392
#117192822
#117192792
C4×#61312
#117192742
#117192672
#117192632
#117192582
#117192532
#117192402
#117192332
#117192192
#117192122
#351713