Finite Group Databasebeta

← #13120808

Subgroups — #13120808

Order 1664.

436 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#385C211yesmaximal, characteristic
2#11718871C211yesmaximal, characteristic
3C2×#88071C211yesmaximal, characteristic
4#11718645C211yesmaximal, characteristic, complemented
5#11718644C211yesmaximal, characteristic, complemented
6#11718643C211yesmaximal, characteristic, complemented
7#11718641C211yesmaximal, characteristic, complemented
8#11718611C211yesmaximal, characteristic
9#11718607C211yesmaximal, characteristic
10#11718603C211yesmaximal, characteristic
11#11718603C211yesmaximal, characteristic
12#11718320C211yesmaximal, characteristic, complemented
13#11718319C211yesmaximal, characteristic, complemented
14#11718319C211yesmaximal, characteristic, complemented
15#11718318C211yesmaximal, characteristic, complemented
16C23×C4×C13C2211yescharacteristic
17C23×Dic13C2211yescharacteristic
18C23×Dic13C2211yescharacteristic
19C2×C13×C4⋊C4C2211yescharacteristic
20C2×C13×C4⋊C4C2211yescharacteristic
21C2×C13×C22⋊C4C2211yescharacteristic
22C2×C13×C22⋊C4C2211yescharacteristic
23C2×C22⋊Dic13C2211yescharacteristic
24C2×C22⋊Dic13C2211yescharacteristic
25C2×C4⋊Dic13C2211yescharacteristic
26C2×C4⋊Dic13C2211yescharacteristic
27C2×#6101C2211yescharacteristic
28C2×#6101C2211yescharacteristic
29C2×#6101C2211yescharacteristic
30C2×#6101C2211yescharacteristic
31C2×#6101C2211yescharacteristic
32C2×#6101C2211yescharacteristic
33C2×#6101C2211yescharacteristic
34C2×#6101C2211yescharacteristic
35C13×#95C2211yescharacteristic
36C13×#95C2211yescharacteristic
37#88071C2211yescharacteristic
38#88071C2211yescharacteristic
39#88071C2211yescharacteristic
40#88071C2211yescharacteristic
41#88071C2211yescharacteristic
42#88071C2211yescharacteristic
43#88071C2211yescharacteristic
44#88071C2211yescharacteristic
45#88071C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51C24×C13C2311yescharacteristic
52C22×C4×C13—22no—
53C22×C4×C13—41no—
54C22×C4×C13—41no—
55C22×C4×C13C2311yescharacteristic
56C22×C4×C13C2311yescharacteristic
57C22×C4×C13C2311yescharacteristic
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×Dic13—22no—
62C22×Dic13—41no—
63C22×Dic13—41no—
64C22×Dic13—41no—
65C22×Dic13—41no—
66C22×Dic13Q814yes—
67C22×Dic13C2311yescharacteristic
68C22×Dic13C2311yescharacteristic
69C22×Dic13C2311yescharacteristic
70C22×Dic13C2311yescharacteristic
71C22×Dic13C2311yescharacteristic
72C22×Dic13C2311yescharacteristic
73C22×Dic13C2311yescharacteristic
74C22×Dic13C2311yescharacteristic
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C22⋊C4—22no—
78C13×C22⋊C4—22no—
79C22⋊Dic13—22no—
80C22⋊Dic13—22no—
81C4⋊Dic13—41no—
82C4⋊Dic13—41no—
83#6101—41no—
84#6101—41no—
85#6101—41no—
86#6101—41no—
87#6101—41no—
88#6101—41no—
89#6101—41no—
90#6101—41no—
91#2646—131nomaximal, Sylow
92C23×C13—21no—
93C23×C13—21no—
94C23×C13—21no—
95C23×C13—21no—
96C23×C13C2×Q812yes—
97C23×C13#4112yes—
98C23×C13#4112yes—
99C23×C13C2411yescharacteristic
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
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—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—44no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—44no—
142C2×Dic13—44no—
143C2×Dic13C2×Q812yes—
144C2×Dic13C2×Q812yes—
145#400—131no—
146#400—131no—
147#400—131no—
148#400—131no—
149#398—131no—
150#398—131no—
151#398—131no—
152#398—131no—
153#385—131no—
154#385—131no—
155#385—131no—
156#385D1311yescharacteristic
157#380—131no—
158#380—131no—
159C2×#95—131no—
160C22×C13—22no—
161C22×C13—22no—
162C22×C13—22no—
163C22×C13—22no—
164C22×C13—22no—
165C22×C13—22no—
166C22×C13#12514yes—
167C22×C13C22×Q811yescharacteristic
168C22×C13C2×#4111yescharacteristic
169C22×C13C2×#4111yescharacteristic
170C22×C13H(5,𝔽2)11yescharacteristic
171C22×C13H(5,𝔽2)11yescharacteristic
172C22×C13H(5,𝔽2)11yescharacteristic
173C22×C132−1+411yescharacteristic
174C4×C13—41no—
175C4×C13—41no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13—41no—
180Dic13—22no—
181Dic13—22no—
182Dic13—41no—
183Dic13—41no—
184Dic13—41no—
185Dic13—41no—
186Dic13—41no—
187Dic13—41no—
188C23×C4—131no—
189C23×C4—131no—
190C23×C4C2×D1311yescharacteristic
191C2×C4⋊C4—131no—
192C2×C4⋊C4—131no—
193C2×C4⋊C4—131no—
194C2×C4⋊C4—131no—
195C2×C4⋊C4—131no—
196C2×C4⋊C4—131no—
197C2×C4⋊C4—131no—
198C2×C4⋊C4—131no—
199C2×C4⋊C4—131no—
200C2×C4⋊C4—131no—
201C2×C4⋊C4C2×D1311yescharacteristic
202C2×C4⋊C4C2×D1311yescharacteristic
203C2×C22⋊C4—131no—
204C2×C22⋊C4—131no—
205C2×C22⋊C4C2×D1311yescharacteristic
206C2×C22⋊C4C2×D1311yescharacteristic
207#95—131no—
208#95—131no—
209#95—131no—
210#95—131no—
211#95—131no—
212#95—131no—
213#95—131no—
214#95—131no—
215#95—131no—
216#95—131no—
217#95—131no—
218#95—131no—
219#95—131no—
220#95—131no—
221#95C2×D1311yescharacteristic
222#95C2×D1311yescharacteristic
223C2×C13—24no—
224C2×C13C2×#12511yescharacteristic
225C2×C13#53811yescharacteristic
226C2×C13#53811yescharacteristic
227C2×C13#53911yescharacteristic
228C2×C13#53911yescharacteristic
229C2×C13#54311yescharacteristic
230C2×C13#54411yescharacteristic
231C24C22×D1311yescharacteristic
232C22×C4—22no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—131no—
236C22×C4—131no—
237C22×C4—134no—
238C22×C4—131no—
239C22×C4—131no—
240C22×C4—131no—
241C22×C4—131no—
242C22×C4—131no—
243C22×C4—131no—
244C22×C4—262no—
245C22×C4—521no—
246C22×C4—521no—
247C22×C4—521no—
248C22×C4—521no—
249C22×C4C22×D1311yescharacteristic
250C22×C4C22×D1311yescharacteristic
251C22×C4C22×D1311yescharacteristic
252C22×C4C22×D1311yescharacteristic
253C22×C4C22×D1311yescharacteristic
254C22×C4C22×D1311yescharacteristic
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—521no—
258C4⋊C4—521no—
259C4⋊C4—521no—
260C4⋊C4—521no—
261C4⋊C4—521no—
262C4⋊C4—521no—
263C4⋊C4—521no—
264C4⋊C4—521no—
265C4⋊C4—521no—
266C4⋊C4—521no—
267C22⋊C4—22no—
268C22⋊C4—22no—
269C22⋊C4—262no—
270C22⋊C4—262no—
271C13#264611yescharacteristic, complemented, Sylow
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23#612712yes—
277C23#612912yes—
278C23Q8×D1312yes—
279C23C23×D1311yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—44no—
299C2×C4—132no—
300C2×C4—132no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—261no—
310C2×C4—261no—
311C2×C4—261no—
312C2×C4—261no—
313C2×C4—261no—
314C2×C4—261no—
315C2×C4—261no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—261no—
322C2×C4—261no—
323C2×C4—524no—
324C2×C4—524no—
325C22—22no—
326C22—22no—
327C22—22no—
328C22—22no—
329C22—22no—
330C22—22no—
331C22#8814314yes—
332C22C2×#612711yescharacteristic
333C22C2×#612911yescharacteristic
334C22#8825111yescharacteristic
335C22#8825111yescharacteristic
336C22C2×Q8×D1311yescharacteristic
337C22#8825611yescharacteristic
338C22#8825711yescharacteristic
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—262no—
346C4—262no—
347C4—521no—
348C4—521no—
349C4—521no—
350C4—521no—
351C4—521no—
352C4—521no—
353C2—24no—
354C2C2×#8814311yescharacteristic
355C2#1171926511yescharacteristic
356C2#1171926911yescharacteristic
357C2#1171929811yescharacteristic
358C2#1171932811yescharacteristic
359C2#1171933911yescharacteristic
360C2#1171937011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#385C2
prime radicalC24×C13C23
hypercenter#385D13
hypocenterC13#2646
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
4. #11718645C2semidirect
5. #11718644C2semidirect
6. #11718643C2semidirect
7. #11718641C2semidirect
12. #11718320C2semidirect
13. #11718319C2semidirect
14. #11718319C2semidirect
15. #11718318C2semidirect
271. C13#2646semidirect

Maximal subgroups

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

subgroupindex
C13×#3852
#117188712
C2×#880712
#117186452
#117186442
#117186432
#117186412
#117186112
#117186072
#117186032
#117183202
#117183192
#117183182
#264613