Finite Group Databasebeta

← #13126089

Subgroups — #13126089

Order 1664.

332 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#544C211yesmaximal, characteristic, complemented
2#11719240C211yesmaximal, characteristic
3#11718749C211yesmaximal, characteristic, complemented
4#11718748C211yesmaximal, characteristic, complemented
5#11718745C211yesmaximal, characteristic, complemented
6#11718741C211yesmaximal, characteristic, complemented
7#11718728C211yesmaximal, characteristic, complemented
8#11718727C211yesmaximal, characteristic, complemented
9#11718727C211yesmaximal, characteristic, complemented
10#11718725C211yesmaximal, characteristic, complemented
11#11718664C211yesmaximal, characteristic, complemented
12#11718664C211yesmaximal, characteristic, complemented
13#11718661C211yesmaximal, characteristic, complemented
14#11718629C211yesmaximal, characteristic, complemented
15#11718628C211yesmaximal, characteristic, complemented
16C13×C4⋊Q8—21no—
17C13×C4⋊Q8C2211yescharacteristic
18C13×C4⋊Q8C2211yescharacteristic
19C13×#125—21no—
20C13×#125C2211yescharacteristic
21C13×#125C2211yescharacteristic
22C13×C22⋊Q8—21no—
23C13×C22⋊Q8—21no—
24C13×#117C2211yescharacteristic
25C13×#117C2211yescharacteristic
26C2×C13×C4⋊C4C2211yescharacteristic
27#88184C2211yescharacteristic
28#88184C2211yescharacteristic
29#88148—21no—
30#88148—21no—
31#88138—21no—
32#88138—21no—
33#88128C2211yescharacteristic
34C4×D52C2211yescharacteristic
35C4×D52C2211yescharacteristic
36#88124C2211yescharacteristic
37C22⋊#1055C2211yescharacteristic
38C22⋊#1055C2211yescharacteristic
39#88049C2211yescharacteristic
40#88049C2211yescharacteristic
41#88049C2211yescharacteristic
42#88049C2211yescharacteristic
43#88049C2211yescharacteristic
44#88049C2211yescharacteristic
45#88049C2211yescharacteristic
46#88049C2211yescharacteristic
47#88048C2211yescharacteristic
48#88048C2211yescharacteristic
49#88048C2211yescharacteristic
50#88048C2211yescharacteristic
51#88047C2211yescharacteristic
52#88047C2211yescharacteristic
53#88047C2211yescharacteristic
54#88047C2211yescharacteristic
55C4⋊#1055C2211yescharacteristic
56C4⋊#1055C2211yescharacteristic
57#88043C2211yescharacteristic
58C4×#1055C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13C2311yescharacteristic
63C2×C22⋊D13—21no—
64C2×C22⋊D13—21no—
65C2×D52—21no—
66C2×D52—21no—
67C2×D52C2311yescharacteristic
68C2×D52C2311yescharacteristic
69C2×C4×D13—21no—
70C2×C4×D13—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4—21no—
75C13×C4⋊C4—21no—
76C13×C4⋊C4—21no—
77C13×C4⋊C4—21no—
78C13×C4⋊C4D411yescharacteristic
79C13×C4⋊C4D411yescharacteristic
80C13×C4⋊C4C2311yescharacteristic
81C13×C4⋊C4C2311yescharacteristic
82C13×C4⋊C4C2311yescharacteristic
83C13×C4⋊C4C2311yescharacteristic
84C13×C22⋊C4—21no—
85C13×C22⋊C4D411yescharacteristic
86C13×C22⋊C4D411yescharacteristic
87C42×C13—21no—
88C42×C13C2311yescharacteristic
89C42×C13C2311yescharacteristic
90#6103—21no—
91#6103—21no—
92#6103—21no—
93#6103—21no—
94C4⋊Dic13C2311yescharacteristic
95C4⋊Dic13C2311yescharacteristic
96#6101—21no—
97#6101—21no—
98C2×#1055C2311yescharacteristic
99C2×#1055C2311yescharacteristic
100C2×#1055C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102#3241—131nomaximal, Sylow
103C23×C13C2×D411yescharacteristic
104C22×D13—21no—
105C22×D13—21no—
106Q8×C13—81no—
107Q8×C13—81no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—81no—
115C2×C4×C13C2×D411yescharacteristic
116C2×C4×C13C2×D411yescharacteristic
117C2×C4×C13C2×D411yescharacteristic
118C2×C4×C13C2×D411yescharacteristic
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2411yescharacteristic
121C22⋊D13—81no—
122C22⋊D13—81no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125D52—21no—
126D52—21no—
127D52—21no—
128D52—21no—
129D52—81no—
130D52—81no—
131C4×D13—81no—
132C4×D13—81no—
133#1055—21no—
134#1055—21no—
135#1055—21no—
136#1055—21no—
137#544D1311yescharacteristic, complemented
138#540—131no—
139#501—131no—
140#499—131no—
141#490—131no—
142#486—131no—
143#482—131no—
144#482—131no—
145#481—131no—
146#480—131no—
147#478—131no—
148#478—131no—
149#476—131no—
150#474—131no—
151#433—131no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13—21no—
155C22×C13C22×D411yescharacteristic
156C2×D13—41no—
157C2×D13—41no—
158C2×D13—41no—
159C2×D13—41no—
160C2×D13—41no—
161C2×D13—41no—
162C4×C13—21no—
163C4×C13—21no—
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—21no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C132−1+411yescharacteristic
172C4×C132−1+411yescharacteristic
173Dic13—41no—
174Dic13—41no—
175C4⋊Q8—21no—
176C4⋊Q8C2×D1311yescharacteristic
177C4⋊Q8C2×D1311yescharacteristic
178#127—131no—
179#125—21no—
180#125—131no—
181#125C2×D1311yescharacteristic
182#125C2×D1311yescharacteristic
183#123—261no—
184#123—261no—
185C22⋊Q8—21no—
186C22⋊Q8—21no—
187#121—131no—
188#121—131no—
189#121—261no—
190#121—261no—
191C4×D4—131no—
192C4×D4—131no—
193#117C2×D1311yescharacteristic
194#117C2×D1311yescharacteristic
195C2×C4⋊C4C2×D1311yescharacteristic
196#107—131no—
197#107—131no—
198#107—131no—
199#107—131no—
200#106—131no—
201#106—131no—
202#106—131no—
203#106—131no—
204C4⋊C8—131no—
205C4⋊C8—131no—
206#102—131no—
207#102—131no—
208#102—131no—
209#102—131no—
210#102—131no—
211#102—131no—
212#102—131no—
213#102—131no—
214C22⋊C8—131no—
215C22⋊C8—131no—
216#97—131no—
217C4×C8—131no—
218C2×C13—41no—
219C2×C13#53611yescharacteristic
220C2×C13#57611yescharacteristic
221C2×C13#57711yescharacteristic
222D13—81no—
223D13—81no—
224C2×Q8—21no—
225C2×Q8—21no—
226C2×D4—131no—
227C2×D4—131no—
228C2×D4—261no—
229C2×D4—261no—
230C2×D4—261no—
231C2×D4—261no—
232C22×C4—21no—
233C22×C4—261no—
234C22×C4—261no—
235C22×C4C22×D1311yescharacteristic
236C2×C8—131no—
237C2×C8—131no—
238C2×C8—131no—
239C2×C8—131no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—131no—
248C4⋊C4—131no—
249C4⋊C4—261no—
250C4⋊C4—261no—
251C4⋊C4C22⋊D1311yescharacteristic
252C4⋊C4C22⋊D1311yescharacteristic
253C4⋊C4C22×D1311yescharacteristic
254C4⋊C4C22×D1311yescharacteristic
255C4⋊C4C22×D1311yescharacteristic
256C4⋊C4C22×D1311yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—261no—
259C22⋊C4—261no—
260C22⋊C4—261no—
261C22⋊C4—261no—
262C22⋊C4C22⋊D1311yescharacteristic
263C22⋊C4C22⋊D1311yescharacteristic
264C42—21no—
265C42C22×D1311yescharacteristic
266C42C22×D1311yescharacteristic
267C13#324111yescharacteristic, complemented, Sylow
268C23—261no—
269C23—261no—
270C23C2×C22⋊D1311yescharacteristic
271Q8—81no—
272Q8—81no—
273D4—261no—
274D4—261no—
275D4—261no—
276D4—261no—
277D4—1041no—
278D4—1041no—
279D4—1041no—
280D4—1041no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—81no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—1041no—
291C2×C4—1041no—
292C2×C4C2×C22⋊D1311yescharacteristic
293C2×C4C2×C22⋊D1311yescharacteristic
294C2×C4C2×C22⋊D1311yescharacteristic
295C2×C4C2×C22⋊D1311yescharacteristic
296C2×C4C2×C22⋊D1311yescharacteristic
297C2×C4C23×D1311yescharacteristic
298C8—261no—
299C8—261no—
300C8—261no—
301C8—261no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—521no—
306C22—521no—
307C22—521no—
308C22—521no—
309C22—521no—
310C22—521no—
311C22C22×C22⋊D1311yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—521no—
322C4—521no—
323C4#8825411yescharacteristic
324C4#8825411yescharacteristic
325C2—41no—
326C2—1041no—
327C2—1041no—
328C2#1171952111yescharacteristic
329C2#1171954011yescharacteristic
330C2#1171954211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#544C2
socleC22×C13C22×D4
prime radical#11719240C2
hypercenter#544D13
hypocenterC13#3241
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #544

Complements

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

NH ≅ G/Ntype
1. C13×#544C2semidirect
3. #11718749C2semidirect
4. #11718748C2semidirect
5. #11718745C2semidirect
6. #11718741C2semidirect
7. #11718728C2semidirect
8. #11718727C2semidirect
9. #11718727C2semidirect
10. #11718725C2semidirect
11. #11718664C2semidirect
12. #11718664C2semidirect
13. #11718661C2semidirect
14. #11718629C2semidirect
15. #11718628C2semidirect
137. #544D13semidirect
267. C13#3241semidirect

Maximal subgroups

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

subgroupindex
C13×#5442
#117192402
#117187492
#117187482
#117187452
#117187412
#117187282
#117187272
#117187252
#117186642
#117186612
#117186292
#117186282
#324113