Finite Group Databasebeta

← #13125559

Subgroups — #13125559

Order 1664.

370 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#529C211yesmaximal, characteristic, complemented
2#11719184C211yesmaximal, characteristic, complemented
3#11718729C211yesmaximal, characteristic, complemented
4#11718725C211yesmaximal, characteristic, complemented
5#11718720C211yesmaximal, characteristic, complemented
6#11718717C211yesmaximal, characteristic, complemented
7#11718713C211yesmaximal, characteristic, complemented
8#11718710C211yesmaximal, characteristic, complemented
9#11718703C211yesmaximal, characteristic, complemented
10#11718700C211yesmaximal, characteristic
11#11718691C211yesmaximal, characteristic, complemented
12#11718687C211yesmaximal, characteristic, complemented
13#11718679C211yesmaximal, characteristic, complemented
14#11718675C211yesmaximal, characteristic, complemented
15C4×#6099C211yesmaximal, characteristic, complemented
16C13×#126—21no—
17C13×#125C2211yescharacteristic
18C13×#124C2211yescharacteristic
19C13×#123—21no—
20C13×C22⋊Q8C2211yescharacteristic
21C13×#121C2211yescharacteristic
22C4×Q8×C13C2211yescharacteristic
23C4×D4×C13—21no—
24C4×D4×C13C2211yescharacteristic
25C13×#117—21no—
26C2×C42×C13C2211yescharacteristic
27C2×#6107C2211yescharacteristic
28C2×#6106C2211yescharacteristic
29C2×#6105C2211yescharacteristic
30C2×#6104C2211yescharacteristic
31#88184C2211yescharacteristic
32#88183—21no—
33C4×C22⋊D13—21no—
34#88178C2211yescharacteristic
35C2×#6099C2211yescharacteristic
36C2×#6099C2211yescharacteristic
37#88130—21no—
38#88129C2211yescharacteristic
39C4×D52C2211yescharacteristic
40#88126—21no—
41#88124C2211yescharacteristic
42C4×Dic26C2211yescharacteristic
43#88075C2211yescharacteristic
44#88075C2211yescharacteristic
45#88072C2211yescharacteristic
46#88072C2211yescharacteristic
47#88050C2211yescharacteristic
48#88050C2211yescharacteristic
49#88049C2211yescharacteristic
50#88049C2211yescharacteristic
51#88048C2211yescharacteristic
52#88048C2211yescharacteristic
53#88047C2211yescharacteristic
54#88047C2211yescharacteristic
55#88043C2211yescharacteristic
56#88043C2211yescharacteristic
57C4×#1055C2211yescharacteristic
58C4×#1055C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×D4×C13—21no—
61C2×D4×C13C2311yescharacteristic
62C22×C4×C13—21no—
63C22×C4×C13D411yescharacteristic
64C22×C4×C13D411yescharacteristic
65C22×C4×C13C2311yescharacteristic
66C2×C22⋊D13—21no—
67C2×D52C2311yescharacteristic
68C2×C4×D13—21no—
69C2×Dic26C2311yescharacteristic
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4C2311yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C13×C22⋊C4—21no—
77C13×C22⋊C4—21no—
78C13×C22⋊C4—21no—
79C13×C22⋊C4—21no—
80C13×C22⋊C4—21no—
81C42×C13—21no—
82C42×C13D411yescharacteristic
83C42×C13D411yescharacteristic
84C42×C13C2311yescharacteristic
85C42×C13C2311yescharacteristic
86C22⋊Dic13—21no—
87#6107—22no—
88#6106—22no—
89#6105—22no—
90#6104—22no—
91#6103—21no—
92#6103—21no—
93#6103—21no—
94#6103—21no—
95C4⋊Dic13C2311yescharacteristic
96C4⋊Dic13C2311yescharacteristic
97#6101—21no—
98#6101—21no—
99#6101—21no—
100#6101—21no—
101C4×Dic13—21no—
102#6099—22no—
103#6099—22no—
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108#3183—131nomaximal, Sylow
109C23×C13—21no—
110C23×C13C2×D411yescharacteristic
111C22×D13—21no—
112Q8×C13—21no—
113Q8×C13—21no—
114D4×C13—21no—
115D4×C13—21no—
116D4×C13—42no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—42no—
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2×D411yescharacteristic
127C2×C4×C13C2×D411yescharacteristic
128C2×C4×C13C2×D411yescharacteristic
129C2×C4×C13C2×D411yescharacteristic
130C2×C4×C13C2411yescharacteristic
131C22⋊D13—42no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135D52—21no—
136D52—21no—
137C4×D13—42no—
138Dic26—21no—
139Dic26—21no—
140#1055—21no—
141#1055—21no—
142#1055#4112yes—
143#1055#4112yes—
144#529—131no—
145#529D1311yescharacteristic, complemented
146#499—131no—
147#495—131no—
148#488—131no—
149#488—131no—
150#470—131no—
151#469—131no—
152#468—131no—
153#468—131no—
154#442—131no—
155#441—131no—
156#440—131no—
157#440—131no—
158C4×M16—131no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13C22×D411yescharacteristic
166C2×D13—41no—
167C2×D13—41no—
168C2×D13—41no—
169C4×C13—21no—
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—41no—
175C4×C13—41no—
176C4×C13—41no—
177C4×C13C2×#4111yescharacteristic
178C4×C13C2×#4111yescharacteristic
179Dic13—41no—
180Dic13—41no—
181Dic13—41no—
182C2×Q16—131no—
183C2×SD16—131no—
184C2×SD16—131no—
185C2×D8—131no—
186C2×M16—131no—
187C2×M16—131no—
188#126—21no—
189#126—261no—
190#125—131no—
191#125C2×D1311yescharacteristic
192#124—131no—
193#124C2×D1311yescharacteristic
194#123—21no—
195#123—261no—
196C22⋊Q8—131no—
197C22⋊Q8C2×D1311yescharacteristic
198#121—131no—
199#121C2×D1311yescharacteristic
200C4×Q8—131no—
201C4×Q8C2×D1311yescharacteristic
202C4×D4—21no—
203C4×D4—131no—
204C4×D4—261no—
205C4×D4C2×D1311yescharacteristic
206#117—21no—
207#117—261no—
208C2×C42C2×D1311yescharacteristic
209#107—131no—
210#107—131no—
211#106—131no—
212#106—131no—
213#103—131no—
214#103—131no—
215#103—131no—
216#103—131no—
217#102—131no—
218#102—131no—
219#102—131no—
220#102—131no—
221#97—131no—
222#97—131no—
223C4×C8—131no—
224C4×C8—131no—
225C2×C13—41no—
226C2×C13—81no—
227C2×C13#53211yescharacteristic
228C2×C13#57511yescharacteristic
229C2×C13#57511yescharacteristic
230D13—81no—
231C2×Q8—131no—
232C2×Q8C22×D1311yescharacteristic
233C2×D4—21no—
234C2×D4—131no—
235C2×D4—261no—
236C2×D4C22×D1311yescharacteristic
237C22×C4—21no—
238C22×C4—261no—
239C22×C4C22⋊D1311yescharacteristic
240C22×C4C22⋊D1311yescharacteristic
241C22×C4C22×D1311yescharacteristic
242Q16—262no—
243SD16—262no—
244SD16—262no—
245D8—262no—
246M16—262no—
247M16—262no—
248C2×C8—131no—
249C2×C8—131no—
250C2×C8—131no—
251C2×C8—131no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—131no—
257C4⋊C4—131no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4—261no—
261C4⋊C4—261no—
262C4⋊C4C22×D1311yescharacteristic
263C4⋊C4C22×D1311yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—261no—
270C22⋊C4—261no—
271C22⋊C4—261no—
272C22⋊C4—261no—
273C22⋊C4—261no—
274C42—21no—
275C42—261no—
276C42C22⋊D1311yescharacteristic
277C42C22⋊D1311yescharacteristic
278C42C22×D1311yescharacteristic
279C42C22×D1311yescharacteristic
280C13#318311yescharacteristic, complemented, Sylow
281C23—21no—
282C23—261no—
283C23C2×C22⋊D1311yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—261no—
287Q8—261no—
288D4—21no—
289D4—21no—
290D4—42no—
291D4—261no—
292D4—261no—
293D4—522no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—522no—
306C2×C4C2×C22⋊D1311yescharacteristic
307C2×C4C2×C22⋊D1311yescharacteristic
308C2×C4C2×C22⋊D1311yescharacteristic
309C2×C4C2×C22⋊D1311yescharacteristic
310C2×C4C2×C22⋊D1311yescharacteristic
311C2×C4C23×D1311yescharacteristic
312C8—132no—
313C8—132no—
314C8—261no—
315C8—261no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—521no—
323C22—521no—
324C22—521no—
325C22C22×C22⋊D1311yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—521no—
335C4—521no—
336C4—521no—
337C4#41×D1311yescharacteristic
338C4#41×D1311yescharacteristic
339C2—41no—
340C2—81no—
341C2—1041no—
342C2#1171952711yescharacteristic
343C2#1171952711yescharacteristic
344C2#1171953711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#529C2
socleC22×C13C22×D4
prime radical#11718700C2
hypercenter#529D13
hypocenterC13#3183
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C13×#529C2semidirect
2. #11719184C2semidirect
3. #11718729C2semidirect
4. #11718725C2semidirect
5. #11718720C2semidirect
6. #11718717C2semidirect
7. #11718713C2semidirect
8. #11718710C2semidirect
9. #11718703C2semidirect
11. #11718691C2semidirect
12. #11718687C2semidirect
13. #11718679C2semidirect
14. #11718675C2semidirect
15. C4×#6099C2semidirect
145. #529D13semidirect
280. C13#3183semidirect

Maximal subgroups

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

subgroupindex
C13×#5292
#117191842
#117187292
#117187252
#117187202
#117187172
#117187132
#117187102
#117187032
#117187002
#117186912
#117186872
#117186792
#117186752
C4×#60992
#318313