Finite Group Databasebeta

← #13126119

Subgroups — #13126119

Order 1664.

320 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#544C211yesmaximal, characteristic, complemented
2#11719239C211yesmaximal, characteristic
3#11718752C211yesmaximal, characteristic, complemented
4#11718750C211yesmaximal, characteristic, complemented
5#11718748C211yesmaximal, characteristic, complemented
6#11718739C211yesmaximal, characteristic, complemented
7#11718729C211yesmaximal, characteristic, complemented
8#11718727C211yesmaximal, characteristic, complemented
9#11718726C211yesmaximal, characteristic, complemented
10#11718724C211yesmaximal, characteristic, complemented
11#11718664C211yesmaximal, characteristic
12#11718661C211yesmaximal, characteristic, complemented
13#11718657C211yesmaximal, characteristic, complemented
14#11718631C211yesmaximal, characteristic, complemented
15#11718628C211yesmaximal, characteristic
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#88178C2211yescharacteristic
29#88152—21no—
30#88150—21no—
31#88139—21no—
32#88137—21no—
33#88129C2211yescharacteristic
34C4×D52C2211yescharacteristic
35#88123C2211yescharacteristic
36C4×Dic26C2211yescharacteristic
37C22⋊#1055C2211yescharacteristic
38C22⋊#1055C2211yescharacteristic
39#88050C2211yescharacteristic
40#88050C2211yescharacteristic
41#88050C2211yescharacteristic
42#88050C2211yescharacteristic
43#88049C2211yescharacteristic
44#88049C2211yescharacteristic
45#88049C2211yescharacteristic
46#88049C2211yescharacteristic
47#88048C2211yescharacteristic
48#88048C2211yescharacteristic
49#88047C2211yescharacteristic
50#88047C2211yescharacteristic
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×D52C2311yescharacteristic
65C2×C4×D13—21no—
66C2×Dic26—21no—
67C2×Dic26C2311yescharacteristic
68C13×C4⋊C4—21no—
69C13×C4⋊C4—21no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4—21no—
75C13×C4⋊C4D411yescharacteristic
76C13×C4⋊C4D411yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C13×C4⋊C4C2311yescharacteristic
79C13×C4⋊C4C2311yescharacteristic
80C13×C4⋊C4C2311yescharacteristic
81C13×C22⋊C4—21no—
82C13×C22⋊C4D411yescharacteristic
83C13×C22⋊C4D411yescharacteristic
84C42×C13—21no—
85C42×C13C2311yescharacteristic
86C42×C13C2311yescharacteristic
87C22⋊Dic13—21no—
88#6103—21no—
89#6103—21no—
90#6103—21no—
91#6103—21no—
92C4⋊Dic13—21no—
93C4⋊Dic13C2311yescharacteristic
94C4⋊Dic13C2311yescharacteristic
95#6101—21no—
96#6101—21no—
97C4×Dic13—21no—
98C2×#1055C2311yescharacteristic
99C2×#1055C2311yescharacteristic
100C2×#1055C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102#3243—131nomaximal, Sylow
103C23×C13C2×D411yescharacteristic
104C22×D13—21no—
105Q8×C13—81no—
106Q8×C13—81no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—81no—
114C2×C4×C13C2×D411yescharacteristic
115C2×C4×C13C2×D411yescharacteristic
116C2×C4×C13C2×D411yescharacteristic
117C2×C4×C13C2×D411yescharacteristic
118C2×C4×C13C2×D411yescharacteristic
119C2×C4×C13C2411yescharacteristic
120C22⋊D13—81no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124D52—21no—
125D52—21no—
126C4×D13—81no—
127Dic26—21no—
128Dic26—21no—
129Dic26—81no—
130#1055—21no—
131#1055—21no—
132#1055—21no—
133#1055—21no—
134#544D1311yescharacteristic, complemented
135#542—131no—
136#501—131no—
137#500—131no—
138#489—131no—
139#488—131no—
140#485—131no—
141#484—131no—
142#482—131no—
143#480—131no—
144#479—131no—
145#478—131no—
146#477—131no—
147#474—131no—
148#433—131no—
149C22×C13—21no—
150C22×C13—21no—
151C22×C13—21no—
152C22×C13C22×D411yescharacteristic
153C2×D13—41no—
154C2×D13—41no—
155C2×D13—41no—
156C4×C13—21no—
157C4×C13—21no—
158C4×C13—21no—
159C4×C13—21no—
160C4×C13—21no—
161C4×C13—41no—
162C4×C13—41no—
163C4×C13—41no—
164C4×C13—41no—
165C4×C132−1+411yescharacteristic
166C4×C132−1+411yescharacteristic
167Dic13—41no—
168Dic13—41no—
169Dic13—41no—
170C4⋊Q8—21no—
171C4⋊Q8—131no—
172C4⋊Q8C2×D1311yescharacteristic
173C4⋊Q8C2×D1311yescharacteristic
174#126—261no—
175#125—21no—
176#125C2×D1311yescharacteristic
177#125C2×D1311yescharacteristic
178#124—131no—
179#124—261no—
180#123—261no—
181C22⋊Q8—21no—
182C22⋊Q8—21no—
183C22⋊Q8—131no—
184C22⋊Q8—261no—
185#121—131no—
186C4×Q8—131no—
187C4×D4—131no—
188#117C2×D1311yescharacteristic
189#117C2×D1311yescharacteristic
190C2×C4⋊C4C2×D1311yescharacteristic
191#107—131no—
192#107—131no—
193#107—131no—
194#107—131no—
195#107—131no—
196#107—131no—
197#106—131no—
198#106—131no—
199C4⋊C8—131no—
200C4⋊C8—131no—
201#103—131no—
202#103—131no—
203#103—131no—
204#103—131no—
205#102—131no—
206#102—131no—
207#102—131no—
208#102—131no—
209C22⋊C8—131no—
210C22⋊C8—131no—
211#97—131no—
212C4×C8—131no—
213C2×C13—41no—
214C2×C13#53611yescharacteristic
215C2×C13#57611yescharacteristic
216C2×C13#57811yescharacteristic
217D13—81no—
218C2×Q8—21no—
219C2×Q8—21no—
220C2×Q8—131no—
221C2×Q8—261no—
222C2×D4—131no—
223C2×D4—261no—
224C22×C4—21no—
225C22×C4—261no—
226C22×C4C22×D1311yescharacteristic
227C2×C8—131no—
228C2×C8—131no—
229C2×C8—131no—
230C2×C8—131no—
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—131no—
239C4⋊C4—131no—
240C4⋊C4—261no—
241C4⋊C4—261no—
242C4⋊C4—261no—
243C4⋊C4C22⋊D1311yescharacteristic
244C4⋊C4C22⋊D1311yescharacteristic
245C4⋊C4C22×D1311yescharacteristic
246C4⋊C4C22×D1311yescharacteristic
247C4⋊C4C22×D1311yescharacteristic
248C4⋊C4C22×D1311yescharacteristic
249C22⋊C4—21no—
250C22⋊C4—261no—
251C22⋊C4—261no—
252C22⋊C4—261no—
253C22⋊C4—261no—
254C22⋊C4—261no—
255C22⋊C4C22⋊D1311yescharacteristic
256C22⋊C4C22⋊D1311yescharacteristic
257C42—21no—
258C42—261no—
259C42C22×D1311yescharacteristic
260C42C22×D1311yescharacteristic
261C13#324311yescharacteristic, complemented, Sylow
262C23—261no—
263C23C2×C22⋊D1311yescharacteristic
264Q8—81no—
265Q8—81no—
266Q8—261no—
267Q8—261no—
268Q8—1041no—
269D4—261no—
270D4—261no—
271D4—1041no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—81no—
279C2×C4—261no—
280C2×C4—261no—
281C2×C4—261no—
282C2×C4—1041no—
283C2×C4C2×C22⋊D1311yescharacteristic
284C2×C4C2×C22⋊D1311yescharacteristic
285C2×C4C2×C22⋊D1311yescharacteristic
286C2×C4C2×C22⋊D1311yescharacteristic
287C2×C4C2×C22⋊D1311yescharacteristic
288C2×C4C23×D1311yescharacteristic
289C8—261no—
290C8—261no—
291C8—261no—
292C8—261no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—521no—
297C22—521no—
298C22—521no—
299C22C22×C22⋊D1311yescharacteristic
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—521no—
310C4—521no—
311C4—521no—
312C4#8825411yescharacteristic
313C4#8825411yescharacteristic
314C2—41no—
315C2—1041no—
316C2#1171952111yescharacteristic
317C2#1171954011yescharacteristic
318C2#1171954311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#544C2
socleC22×C13C22×D4
prime radical#88184C22
hypercenter#544D13
hypocenterC13#3243
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. #11718752C2semidirect
4. #11718750C2semidirect
5. #11718748C2semidirect
6. #11718739C2semidirect
7. #11718729C2semidirect
8. #11718727C2semidirect
9. #11718726C2semidirect
10. #11718724C2semidirect
12. #11718661C2semidirect
13. #11718657C2semidirect
14. #11718631C2semidirect
134. #544D13semidirect
261. C13#3243semidirect

Maximal subgroups

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

subgroupindex
C13×#5442
#117192392
#117187522
#117187502
#117187482
#117187392
#117187292
#117187272
#117187262
#117187242
#117186642
#117186612
#117186572
#117186312
#117186282
#324313