Finite Group Databasebeta

← #13126008

Subgroups — #13126008

Order 1664.

334 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
1D13×#125C211yesmaximal, characteristic, complemented
2#11719285C211yesmaximal, characteristic
3C13×#479C211yesmaximal, characteristic, complemented
4#11718727C211yesmaximal, characteristic, complemented
5#11718683C211yesmaximal, characteristic, complemented
6#11718543C211yesmaximal, characteristic
7#11718539C211yesmaximal, characteristic, complemented
8#11718524C211yesmaximal, characteristic
9#11718519C211yesmaximal, characteristic, complemented
10#11718508C211yesmaximal, characteristic, complemented
11#11718494C211yesmaximal, characteristic, complemented
12#11718470C211yesmaximal, characteristic, complemented
13#11718466C211yesmaximal, characteristic, complemented
14#11718461C211yesmaximal, characteristic, complemented
15#11718461C211yesmaximal, characteristic, complemented
16C13×#125C2211yescharacteristic
17C4×Q8×C13C2211yescharacteristic
18#88201C2211yescharacteristic
19#88200C2211yescharacteristic
20#88152—21no—
21#88149C2211yescharacteristic
22#88148—21no—
23C4⋊C4×D13—21no—
24C4⋊C4×D13—21no—
25C4⋊C4×D13C2211yescharacteristic
26C4⋊C4×D13C2211yescharacteristic
27#88144C2211yescharacteristic
28#88144C2211yescharacteristic
29#88144C2211yescharacteristic
30#88143—21no—
31#88143—21no—
32C4×D52—21no—
33C4×D52C2211yescharacteristic
34#88126—21no—
35C42×D13C2211yescharacteristic
36#88124C2211yescharacteristic
37C13×#107C2211yescharacteristic
38C13×#106C2211yescharacteristic
39C13×C4⋊C8C2211yescharacteristic
40C13×#103C2211yescharacteristic
41C13×#103C2211yescharacteristic
42#88075C2211yescharacteristic
43#88075C2211yescharacteristic
44#88061C2211yescharacteristic
45#88061C2211yescharacteristic
46#88060C2211yescharacteristic
47#88060C2211yescharacteristic
48#88058C2211yescharacteristic
49#88057C2211yescharacteristic
50C8×Dic13C2211yescharacteristic
51C8×Dic13C2211yescharacteristic
52#88049C2211yescharacteristic
53#88049C2211yescharacteristic
54#88048C2211yescharacteristic
55#88048C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×D52—21no—
61C2×D52C2311yescharacteristic
62C2×C4×D13—21no—
63C2×C4×D13—21no—
64C2×C4×D13—21no—
65C2×C4×D13D411yescharacteristic
66C2×C4×D13D411yescharacteristic
67C2×C4×D13C2311yescharacteristic
68C2×C8×C13C2311yescharacteristic
69C2×C8×C13C2311yescharacteristic
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4C2311yescharacteristic
74C13×C4⋊C4C2311yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C42×C13—21no—
77C42×C13C2311yescharacteristic
78#6103—21no—
79#6103—21no—
80#6103—21no—
81#6103—21no—
82#6103—21no—
83C4⋊Dic13—21no—
84C4⋊Dic13—21no—
85C4⋊Dic13—21no—
86C4⋊Dic13C2311yescharacteristic
87C4⋊Dic13C2311yescharacteristic
88C4⋊Dic13C2311yescharacteristic
89#6101—21no—
90#6101—21no—
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97C4×Dic13D411yescharacteristic
98C4×Dic13D411yescharacteristic
99C4×Dic13C2311yescharacteristic
100C2×#1055C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102#3232—131nomaximal, Sylow
103C22×D13—21no—
104C22×D13C2×D411yescharacteristic
105Q8×C13—21no—
106Q8×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13C2×D411yescharacteristic
112C2×C4×C13C2×D411yescharacteristic
113C2×C4×C13C2411yescharacteristic
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13C2×D411yescharacteristic
118C2×Dic13C2×D411yescharacteristic
119C2×Dic13C2×D411yescharacteristic
120D52—21no—
121D52—21no—
122D52—42no—
123C4×D13—22no—
124C4×D13—21no—
125C4×D13—21no—
126C4×D13—41no—
127C4×D13—42no—
128C4×D13—42no—
129C4×D13—42no—
130C8×C13—21no—
131C8×C13—21no—
132#1055—21no—
133#1055—21no—
134#529—131no—
135C2×#125—131no—
136#499—131no—
137#499—131no—
138#488—131no—
139#488—131no—
140#484—131no—
141#483—131no—
142#481—131no—
143#480—131no—
144#479—131no—
145#479D1311yescharacteristic, complemented
146#478—131no—
147#478—131no—
148#431—131no—
149C22×C13C22×D411yescharacteristic
150C2×D13—21no—
151C2×D13—21no—
152C2×D13—41no—
153C2×D13—41no—
154C2×D13—41no—
155C2×D13#13512yes—
156C4×C13—21no—
157C4×C13—21no—
158C4×C13—41no—
159C4×C13—41no—
160C4×C13—41no—
161C4×C13—41no—
162C4×C132−1+411yescharacteristic
163C4×C132−1+411yescharacteristic
164Dic13—21no—
165Dic13—21no—
166Dic13—21no—
167Dic13—41no—
168Dic13—41no—
169Dic13—41no—
170#126—261no—
171#125—131no—
172#125—131no—
173#125—131no—
174#125—131no—
175#125—261no—
176#125—261no—
177#125C2×D1311yescharacteristic
178#124—131no—
179#123—261no—
180C22⋊Q8—131no—
181#121—131no—
182C4×Q8C2×D1311yescharacteristic
183C4×D4—131no—
184C4×D4—261no—
185#117—261no—
186C2×C4⋊C4—131no—
187C2×C4⋊C4—131no—
188C2×C4⋊C4—261no—
189C2×C4⋊C4—261no—
190C2×C42—131no—
191#107—131no—
192#107—131no—
193#107—131no—
194#107C2×D1311yescharacteristic
195#106—131no—
196#106—131no—
197#106—131no—
198#106C2×D1311yescharacteristic
199C4⋊C8—131no—
200C4⋊C8C2×D1311yescharacteristic
201#103—131no—
202#103—131no—
203#103C2×D1311yescharacteristic
204#103C2×D1311yescharacteristic
205#102—131no—
206#102—131no—
207#102—131no—
208#102—131no—
209C22⋊C8—131no—
210C22⋊C8—131no—
211C4×C8—131no—
212C4×C8—131no—
213C2×C13#53611yescharacteristic
214C2×C13C2×#13511yescharacteristic
215C2×C13#57511yescharacteristic
216D13—22no—
217D13—81no—
218C2×Q8C22×D1311yescharacteristic
219C2×D4—131no—
220C2×D4—261no—
221C22×C4—131no—
222C22×C4—131no—
223C22×C4—131no—
224C22×C4—261no—
225C22×C4—261no—
226C22×C4—261no—
227C2×C8—131no—
228C2×C8—131no—
229C2×C8C22×D1311yescharacteristic
230C2×C8C22×D1311yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—131no—
235C4⋊C4—131no—
236C4⋊C4—131no—
237C4⋊C4—261no—
238C4⋊C4—261no—
239C4⋊C4—261no—
240C4⋊C4—261no—
241C4⋊C4—261no—
242C4⋊C4—261no—
243C4⋊C4—261no—
244C4⋊C4—261no—
245C4⋊C4—261no—
246C4⋊C4—261no—
247C4⋊C4—261no—
248C4⋊C4C22×D1311yescharacteristic
249C4⋊C4C22×D1311yescharacteristic
250C4⋊C4C22×D1311yescharacteristic
251C22⋊C4—261no—
252C22⋊C4—261no—
253C22⋊C4—261no—
254C22⋊C4—261no—
255C22⋊C4—261no—
256C42—21no—
257C42—131no—
258C42—131no—
259C42—131no—
260C42C22×D1311yescharacteristic
261C13#323211yescharacteristic, complemented, Sylow
262C23—131no—
263C23—261no—
264Q8—21no—
265Q8—21no—
266D4—261no—
267D4—261no—
268D4—522no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—131no—
274C2×C4—131no—
275C2×C4—131no—
276C2×C4—262no—
277C2×C4—261no—
278C2×C4—261no—
279C2×C4—261no—
280C2×C4—261no—
281C2×C4—261no—
282C2×C4—521no—
283C2×C4—522no—
284C2×C4—522no—
285C2×C4—522no—
286C2×C4D4×D1311yescharacteristic
287C2×C4D4×D1311yescharacteristic
288C2×C4C23×D1311yescharacteristic
289C8—21no—
290C8—21no—
291C8—261no—
292C8—261no—
293C22—132no—
294C22—261no—
295C22—261no—
296C22—521no—
297C22—521no—
298C22—521no—
299C22C2×D4×D1311yescharacteristic
300C4—21no—
301C4—21no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—261no—
307C4—261no—
308C4—261no—
309C4—521no—
310C4—521no—
311C4—521no—
312C4#8825411yescharacteristic
313C4#8825711yescharacteristic
314C2—262no—
315C2—1041no—
316C2#1171933311yescharacteristic
317C2D13×#13511yescharacteristic
318C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#479C2
socleC22×C13C22×D4
prime radical#88149C22
hypercenter#479D13
hypocenterC13#3232
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. D13×#125C2semidirect
3. C13×#479C2semidirect
4. #11718727C2semidirect
5. #11718683C2semidirect
7. #11718539C2semidirect
9. #11718519C2semidirect
10. #11718508C2semidirect
11. #11718494C2semidirect
12. #11718470C2semidirect
13. #11718466C2semidirect
14. #11718461C2semidirect
15. #11718461C2semidirect
145. #479D13semidirect
261. C13#3232semidirect

Maximal subgroups

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

subgroupindex
D13×#1252
#117192852
C13×#4792
#117187272
#117186832
#117185432
#117185392
#117185242
#117185192
#117185082
#117184942
#117184702
#117184662
#117184612
#323213