Finite Group Databasebeta

← #13127366

Subgroups — #13127366

Order 1664.

336 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#552C211yesmaximal, characteristic
2#11719247C211yesmaximal, characteristic
3#11718726C211yesmaximal, characteristic, complemented
4#11718724C211yesmaximal, characteristic, complemented
5#11718713C211yesmaximal, characteristic, complemented
6#11718712C211yesmaximal, characteristic, complemented
7#11718706C211yesmaximal, characteristic, complemented
8#11718706C211yesmaximal, characteristic, complemented
9#11718691C211yesmaximal, characteristic, complemented
10#11718682C211yesmaximal, characteristic, complemented
11#11718672C211yesmaximal, characteristic
12#11718659C211yesmaximal, characteristic, complemented
13#11718657C211yesmaximal, characteristic, complemented
14#11718631C211yesmaximal, characteristic, complemented
15#11718625C211yesmaximal, characteristic, complemented
16C13×#126—21no—
17C13×#125—21no—
18C13×#125C2211yescharacteristic
19C13×#123—21no—
20C13×C22⋊Q8C2211yescharacteristic
21C13×C22⋊Q8C2211yescharacteristic
22C4×Q8×C13C2211yescharacteristic
23C4×D4×C13C2211yescharacteristic
24C13×#117—21no—
25C13×#117C2211yescharacteristic
26C2×C13×C4⋊C4C2211yescharacteristic
27C2×#6107C2211yescharacteristic
28#88190—21no—
29#88180C2211yescharacteristic
30#88180C2211yescharacteristic
31#88178C2211yescharacteristic
32#88178C2211yescharacteristic
33C2×#6099C2211yescharacteristic
34C22×#1055C2211yescharacteristic
35#88141—21no—
36#88133—21no—
37#88133—21no—
38#88123C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40#88075C2211yescharacteristic
41#88075C2211yescharacteristic
42#88075C2211yescharacteristic
43C22⋊#1055C2211yescharacteristic
44C22⋊#1055C2211yescharacteristic
45#88050C2211yescharacteristic
46#88050C2211yescharacteristic
47#88050C2211yescharacteristic
48#88048C2211yescharacteristic
49#88048C2211yescharacteristic
50#88048C2211yescharacteristic
51#88048C2211yescharacteristic
52#88047C2211yescharacteristic
53#88047C2211yescharacteristic
54#88047C2211yescharacteristic
55#88047C2211yescharacteristic
56#88047C2211yescharacteristic
57C4⋊#1055C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×D4×C13D411yescharacteristic
61C22×C4×C13—21no—
62C22×C4×C13C2311yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C2×Dic26—21no—
65C2×Dic26C2311yescharacteristic
66C13×C4⋊C4—21no—
67C13×C4⋊C4—21no—
68C13×C4⋊C4—21no—
69C13×C4⋊C4—21no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4D411yescharacteristic
73C13×C4⋊C4C2311yescharacteristic
74C13×C4⋊C4C2311yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C13×C22⋊C4—21no—
77C13×C22⋊C4—21no—
78C13×C22⋊C4—21no—
79C13×C22⋊C4D411yescharacteristic
80C13×C22⋊C4D411yescharacteristic
81C42×C13—21no—
82C42×C13—21no—
83C42×C13C2311yescharacteristic
84C22⋊Dic13—21no—
85C22⋊Dic13—21no—
86C22⋊Dic13—21no—
87C22⋊Dic13—21no—
88#6107—22no—
89C4⋊Dic13—21no—
90C4⋊Dic13C2311yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92C4⋊Dic13C2311yescharacteristic
93#6101—21no—
94#6101—21no—
95#6101—21no—
96C4×Dic13—21no—
97C4×Dic13—21no—
98C4×Dic13—21no—
99#6099—22no—
100C2×#1055—22no—
101C2×#1055C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105#3349—131nomaximal, Sylow
106C23×C13C2×D411yescharacteristic
107C23×C13C2×D411yescharacteristic
108Q8×C13—21no—
109Q8×C13—21no—
110D4×C13—41no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—42no—
120C2×C4×C13C2×D411yescharacteristic
121C2×C4×C13C2×D411yescharacteristic
122C2×C4×C13C2×D411yescharacteristic
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2411yescharacteristic
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129Dic26—21no—
130Dic26—21no—
131Dic26—42no—
132#1055—21no—
133#1055—21no—
134#1055—21no—
135#1055#4112yes—
136#556—131no—
137#552D1311yescharacteristic
138#501—131no—
139#485—131no—
140#485—131no—
141#485—131no—
142#484—131no—
143#479—131no—
144#477—131no—
145#470—131no—
146#467—131no—
147#441—131no—
148#435—131no—
149#428—131no—
150#427—131no—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13C22×D411yescharacteristic
158C4×C13—21no—
159C4×C13—21no—
160C4×C13—21no—
161C4×C13—21no—
162C4×C13—41no—
163C4×C13—41no—
164C4×C13—41no—
165C4×C13—41no—
166C4×C13C2×#4111yescharacteristic
167C4×C132−1+411yescharacteristic
168Dic13—41no—
169Dic13—41no—
170Dic13—41no—
171Dic13—41no—
172C2×Q16—131no—
173C2×M16—131no—
174C22×C8—131no—
175C4⋊Q8—131no—
176#126—21no—
177#126—261no—
178#126—261no—
179#125—21no—
180#125C2×D1311yescharacteristic
181#124—261no—
182#123—21no—
183C22⋊Q8—131no—
184C22⋊Q8—131no—
185C22⋊Q8C2×D1311yescharacteristic
186C22⋊Q8C2×D1311yescharacteristic
187C4×Q8—131no—
188C4×Q8—261no—
189C4×Q8C2×D1311yescharacteristic
190C4×D4C2×D1311yescharacteristic
191#117—21no—
192#117—131no—
193#117—131no—
194#117C2×D1311yescharacteristic
195C2×C4⋊C4C2×D1311yescharacteristic
196#107—131no—
197#107—131no—
198#107—131no—
199#107—131no—
200#107—131no—
201#106—131no—
202#106—131no—
203#106—131no—
204#106—131no—
205C4⋊C8—131no—
206#103—131no—
207#103—131no—
208#103—131no—
209#103—131no—
210#103—131no—
211#103—131no—
212C22⋊C8—131no—
213C22⋊C8—131no—
214#97—131no—
215C2×C13—41no—
216C2×C13—41no—
217C2×C13#54711yescharacteristic
218C2×C13#57511yescharacteristic
219C2×C13#57811yescharacteristic
220C2×Q8—131no—
221C2×Q8—261no—
222C2×Q8C22×D1311yescharacteristic
223C2×D4C22⋊D1311yescharacteristic
224C22×C4—21no—
225C22×C4C22×D1311yescharacteristic
226C22×C4C22×D1311yescharacteristic
227Q16—262no—
228M16—262no—
229C2×C8—131no—
230C2×C8—131no—
231C2×C8—131no—
232C2×C8—131no—
233C2×C8—262no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—131no—
241C4⋊C4—131no—
242C4⋊C4—131no—
243C4⋊C4—261no—
244C4⋊C4—261no—
245C4⋊C4—261no—
246C4⋊C4—261no—
247C4⋊C4C22⋊D1311yescharacteristic
248C4⋊C4C22×D1311yescharacteristic
249C4⋊C4C22×D1311yescharacteristic
250C4⋊C4C22×D1311yescharacteristic
251C22⋊C4—21no—
252C22⋊C4—21no—
253C22⋊C4—21no—
254C22⋊C4—261no—
255C22⋊C4—261no—
256C22⋊C4—261no—
257C22⋊C4—261no—
258C22⋊C4C22⋊D1311yescharacteristic
259C22⋊C4C22⋊D1311yescharacteristic
260C42—21no—
261C42—21no—
262C42—261no—
263C42—261no—
264C42—261no—
265C42C22×D1311yescharacteristic
266C13#334911yescharacteristic, complemented, Sylow
267C23C2×C22⋊D1311yescharacteristic
268C23C2×C22⋊D1311yescharacteristic
269Q8—21no—
270Q8—21no—
271Q8—261no—
272Q8—261no—
273Q8—522no—
274D4—41no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—42no—
284C2×C4—261no—
285C2×C4—261no—
286C2×C4—261no—
287C2×C4—261no—
288C2×C4C2×C22⋊D1311yescharacteristic
289C2×C4C2×C22⋊D1311yescharacteristic
290C2×C4C2×C22⋊D1311yescharacteristic
291C2×C4C2×C22⋊D1311yescharacteristic
292C2×C4C23×D1311yescharacteristic
293C8—132no—
294C8—261no—
295C8—261no—
296C8—261no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22C22×C22⋊D1311yescharacteristic
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—521no—
313C4—521no—
314C4—521no—
315C4—521no—
316C4#41×D1311yescharacteristic
317C4#8825711yescharacteristic
318C2—41no—
319C2—41no—
320C2#1171952711yescharacteristic
321C2#1171952911yescharacteristic
322C2#1171954311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#552C2
socleC22×C13C22×D4
prime radicalC2×D4×C13D4
hypercenter#552D13
hypocenterC13#3349
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
3. #11718726C2semidirect
4. #11718724C2semidirect
5. #11718713C2semidirect
6. #11718712C2semidirect
7. #11718706C2semidirect
8. #11718706C2semidirect
9. #11718691C2semidirect
10. #11718682C2semidirect
12. #11718659C2semidirect
13. #11718657C2semidirect
14. #11718631C2semidirect
15. #11718625C2semidirect
266. C13#3349semidirect

Maximal subgroups

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

subgroupindex
C13×#5522
#117192472
#117187262
#117187242
#117187132
#117187122
#117187062
#117186912
#117186822
#117186722
#117186592
#117186572
#117186312
#117186252
#334913