Finite Group Databasebeta

← #13126113

Subgroups — #13126113

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×#542C211yesmaximal, characteristic
2#11719224C211yesmaximal, characteristic, complemented
3#11718741C211yesmaximal, characteristic, complemented
4#11718739C211yesmaximal, characteristic, complemented
5#11718717C211yesmaximal, characteristic, complemented
6#11718716C211yesmaximal, characteristic, complemented
7#11718706C211yesmaximal, characteristic, complemented
8#11718705C211yesmaximal, characteristic, complemented
9#11718696C211yesmaximal, characteristic
10#11718694C211yesmaximal, characteristic
11#11718683C211yesmaximal, characteristic, complemented
12#11718682C211yesmaximal, characteristic, complemented
13#11718670C211yesmaximal, characteristic, complemented
14#11718668C211yesmaximal, characteristic, complemented
15#11718661C211yesmaximal, characteristic, complemented
16C13×C4⋊Q8C2211yescharacteristic
17C13×#126—21no—
18C13×#124—21no—
19C13×#124C2211yescharacteristic
20C13×#123—21no—
21C13×C22⋊Q8—21no—
22C13×C22⋊Q8C2211yescharacteristic
23C13×#121C2211yescharacteristic
24C4×Q8×C13C2211yescharacteristic
25C4×D4×C13C2211yescharacteristic
26C13×#117C2211yescharacteristic
27#88180C2211yescharacteristic
28C2×C4⋊Dic13C2211yescharacteristic
29#88144—21no—
30#88142—21no—
31#88132—21no—
32#88132—21no—
33#88124C2211yescharacteristic
34#88124C2211yescharacteristic
35#88123C2211yescharacteristic
36#88123C2211yescharacteristic
37#88075C2211yescharacteristic
38#88075C2211yescharacteristic
39#88075C2211yescharacteristic
40#88075C2211yescharacteristic
41#88072C2211yescharacteristic
42#88072C2211yescharacteristic
43#88072C2211yescharacteristic
44#88072C2211yescharacteristic
45C22⋊#1055C2211yescharacteristic
46C22⋊#1055C2211yescharacteristic
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×C13C2311yescharacteristic
61C2×D4×C13—21no—
62C2×D4×C13C2311yescharacteristic
63C22×C4×C13—21no—
64C22×C4×C13C2311yescharacteristic
65C22×Dic13—21no—
66C2×Dic26—21no—
67C2×Dic26—21no—
68C13×C4⋊C4—21no—
69C13×C4⋊C4—21no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4D411yescharacteristic
72C13×C4⋊C4D411yescharacteristic
73C13×C4⋊C4C2311yescharacteristic
74C13×C4⋊C4C2311yescharacteristic
75C13×C22⋊C4—21no—
76C13×C22⋊C4—21no—
77C13×C22⋊C4—21no—
78C13×C22⋊C4—21no—
79C13×C22⋊C4—21no—
80C13×C22⋊C4D411yescharacteristic
81C13×C22⋊C4D411yescharacteristic
82C42×C13—21no—
83C42×C13C2311yescharacteristic
84C42×C13C2311yescharacteristic
85C22⋊Dic13—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13—21no—
88C4⋊Dic13—21no—
89C4⋊Dic13C2311yescharacteristic
90C4⋊Dic13C2311yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92C4⋊Dic13C2311yescharacteristic
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97C4×Dic13—21no—
98C2×#1055C2311yescharacteristic
99C2×#1055C2311yescharacteristic
100C2×#1055C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102#3243—131nomaximal, Sylow
103C23×C13—21no—
104C23×C13C2×D411yescharacteristic
105Q8×C13—21no—
106Q8×C13—21no—
107Q8×C13—81no—
108D4×C13—21no—
109D4×C13—21no—
110D4×C13—81no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—81no—
117C2×C4×C13C2×D411yescharacteristic
118C2×C4×C13C2×D411yescharacteristic
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2×D411yescharacteristic
121C2×C4×C13C2×D411yescharacteristic
122C2×C4×C13C2411yescharacteristic
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—81no—
128Dic26—81no—
129Dic26—81no—
130#1055—21no—
131#1055—21no—
132#1055—21no—
133#1055—21no—
134#544—131no—
135#542D1311yescharacteristic
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×C13—41no—
153C22×C13—41no—
154C22×C13—41no—
155C22×C13C22×D411yescharacteristic
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×C132−1+411yescharacteristic
165C4×C132−1+411yescharacteristic
166Dic13—41no—
167Dic13—41no—
168Dic13—41no—
169Dic13—41no—
170C4⋊Q8—131no—
171C4⋊Q8—131no—
172C4⋊Q8—261no—
173C4⋊Q8C2×D1311yescharacteristic
174#126—21no—
175#125—131no—
176#125—131no—
177#125—261no—
178#124—21no—
179#124C2×D1311yescharacteristic
180#123—21no—
181C22⋊Q8—21no—
182C22⋊Q8—261no—
183C22⋊Q8—261no—
184C22⋊Q8C2×D1311yescharacteristic
185#121C2×D1311yescharacteristic
186C4×Q8C2×D1311yescharacteristic
187C4×D4C2×D1311yescharacteristic
188#117—131no—
189#117C2×D1311yescharacteristic
190C2×C4⋊C4—131no—
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—81no—
215C2×C13#53611yescharacteristic
216C2×C13#57611yescharacteristic
217C2×C13#57811yescharacteristic
218C2×Q8—21no—
219C2×Q8—261no—
220C2×Q8—261no—
221C2×Q8C22×D1311yescharacteristic
222C2×D4—21no—
223C2×D4C22×D1311yescharacteristic
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—131no—
235C4⋊C4—131no—
236C4⋊C4—131no—
237C4⋊C4—131no—
238C4⋊C4—261no—
239C4⋊C4—261no—
240C4⋊C4—261no—
241C4⋊C4—261no—
242C4⋊C4—261no—
243C4⋊C4—261no—
244C4⋊C4—261no—
245C4⋊C4C22⋊D1311yescharacteristic
246C4⋊C4C22⋊D1311yescharacteristic
247C4⋊C4C22×D1311yescharacteristic
248C4⋊C4C22×D1311yescharacteristic
249C22⋊C4—21no—
250C22⋊C4—21no—
251C22⋊C4—21no—
252C22⋊C4—21no—
253C22⋊C4—21no—
254C22⋊C4—261no—
255C22⋊C4C22⋊D1311yescharacteristic
256C22⋊C4C22⋊D1311yescharacteristic
257C42—21no—
258C42—261no—
259C42C22×D1311yescharacteristic
260C42C22×D1311yescharacteristic
261C13#324311yescharacteristic, complemented, Sylow
262C23—21no—
263C23C2×C22⋊D1311yescharacteristic
264Q8—21no—
265Q8—21no—
266Q8—81no—
267Q8—1041no—
268Q8—1041no—
269D4—21no—
270D4—21no—
271D4—81no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—81no—
278C2×C4—261no—
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—41no—
297C22—41no—
298C22—41no—
299C22C22×C22⋊D1311yescharacteristic
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—521no—
309C4—521no—
310C4—521no—
311C4—521no—
312C4#8825711yescharacteristic
313C4#8825711yescharacteristic
314C2—41no—
315C2—81no—
316C2#1171953011yescharacteristic
317C2#1171954011yescharacteristic
318C2#1171954311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#542C2
socleC22×C13C22×D4
prime radicalC13×#121C22
hypercenter#542D13
hypocenterC13#3243
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
2. #11719224C2semidirect
3. #11718741C2semidirect
4. #11718739C2semidirect
5. #11718717C2semidirect
6. #11718716C2semidirect
7. #11718706C2semidirect
8. #11718705C2semidirect
11. #11718683C2semidirect
12. #11718682C2semidirect
13. #11718670C2semidirect
14. #11718668C2semidirect
15. #11718661C2semidirect
261. C13#3243semidirect

Maximal subgroups

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

subgroupindex
C13×#5422
#117192242
#117187412
#117187392
#117187172
#117187162
#117187062
#117187052
#117186962
#117186942
#117186832
#117186822
#117186702
#117186682
#117186612
#324313