Finite Group Databasebeta

← #13122201

Subgroups — #13122201

Order 1664.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#388C211yesmaximal, characteristic
2#11718640C211yesmaximal, characteristic, complemented
3#11718635C211yesmaximal, characteristic, complemented
4#11718613C211yesmaximal, characteristic
5#11718613C211yesmaximal, characteristic
6#11718608C211yesmaximal, characteristic
7#11718608C211yesmaximal, characteristic
8#11718605C211yesmaximal, characteristic
9#11718605C211yesmaximal, characteristic
10#11718594C211yesmaximal, characteristic, complemented
11#11718594C211yesmaximal, characteristic, complemented
12C13⋊#401C211yesmaximal, characteristic, complemented
13#11718312C211yesmaximal, characteristic, complemented
14#11718307C211yesmaximal, characteristic, complemented
15#11718307C211yesmaximal, characteristic, complemented
16C22×Dic26C2211yescharacteristic
17C22×Dic26C2211yescharacteristic
18C2×C13×C4⋊C4C2211yescharacteristic
19C2×C13×C22⋊C4C2211yescharacteristic
20C2×C13×C22⋊C4C2211yescharacteristic
21C2×C13×C22⋊C4C2211yescharacteristic
22C2×C42×C13C2211yescharacteristic
23C2×C22⋊Dic13C2211yescharacteristic
24C2×C22⋊Dic13C2211yescharacteristic
25C2×C22⋊Dic13C2211yescharacteristic
26C2×C22⋊Dic13C2211yescharacteristic
27C2×#6101C2211yescharacteristic
28C2×#6101C2211yescharacteristic
29C2×#6101C2211yescharacteristic
30C2×#6101C2211yescharacteristic
31C2×C4×Dic13C2211yescharacteristic
32C2×C4×Dic13C2211yescharacteristic
33C13×#95C2211yescharacteristic
34C13×#95C2211yescharacteristic
35#88071C2211yescharacteristic
36#88071C2211yescharacteristic
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×C13C2311yescharacteristic
53C22×C4×C13C2311yescharacteristic
54C22×C4×C13C2311yescharacteristic
55C22×C4×C13C2311yescharacteristic
56C22×C4×C13C2311yescharacteristic
57C22×C4×C13C2311yescharacteristic
58C22×Dic13C2311yescharacteristic
59C22×Dic13C2311yescharacteristic
60C22×Dic13C2311yescharacteristic
61C22×Dic13C2311yescharacteristic
62C22×Dic13C2311yescharacteristic
63C22×Dic13C2311yescharacteristic
64C22×Dic13C2311yescharacteristic
65C22×Dic13C2311yescharacteristic
66C2×Dic26—22no—
67C2×Dic26—22no—
68C2×Dic26—22no—
69C2×Dic26—41no—
70C2×Dic26—41no—
71C2×Dic26—41no—
72C13×C4⋊C4—41no—
73C13×C22⋊C4—22no—
74C13×C22⋊C4—41no—
75C13×C22⋊C4—41no—
76C42×C13—41no—
77C22⋊Dic13—22no—
78C22⋊Dic13—22no—
79C22⋊Dic13—41no—
80C22⋊Dic13—41no—
81#6101—22no—
82#6101—22no—
83#6101—41no—
84#6101—41no—
85C4×Dic13—22no—
86C4×Dic13—41no—
87#2759—131nomaximal, Sylow
88C23×C13—21no—
89C23×C13—21no—
90C23×C13—21no—
91C23×C13—21no—
92C23×C13—21no—
93C23×C13—21no—
94C23×C13—21no—
95C23×C13C2411yescharacteristic
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
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#4112yes—
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—21no—
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#4112yes—
137C2×Dic13#4112yes—
138Dic26—44no—
139Dic26—44no—
140#401—131no—
141#397—131no—
142#397—131no—
143#395—131no—
144#393—131no—
145#393—131no—
146#391—131no—
147#391—131no—
148#391—131no—
149#388—131no—
150#388—131no—
151#388D1311yescharacteristic
152#387—131no—
153#387—131no—
154#383—131no—
155C22×C13—41no—
156C22×C13—41no—
157C22×C13—41no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13C2×#4111yescharacteristic
163C22×C13C2×#4111yescharacteristic
164C22×C13C2×#4111yescharacteristic
165C22×C13H(5,𝔽2)11yescharacteristic
166C22×C13H(5,𝔽2)11yescharacteristic
167C22×C132−1+411yescharacteristic
168C22×C132−1+411yescharacteristic
169C4×C13—22no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13—41no—
175Dic13—22no—
176Dic13—22no—
177Dic13—41no—
178Dic13—41no—
179Dic13—41no—
180Dic13—41no—
181Dic13—41no—
182Dic13—41no—
183C22×Q8—131no—
184C22×Q8—131no—
185C2×C4⋊C4—131no—
186C2×C4⋊C4—131no—
187C2×C4⋊C4—131no—
188C2×C4⋊C4—131no—
189C2×C4⋊C4C2×D1311yescharacteristic
190C2×C22⋊C4—131no—
191C2×C22⋊C4—131no—
192C2×C22⋊C4—131no—
193C2×C22⋊C4—131no—
194C2×C22⋊C4C2×D1311yescharacteristic
195C2×C22⋊C4C2×D1311yescharacteristic
196C2×C22⋊C4C2×D1311yescharacteristic
197C2×C42—131no—
198C2×C42—131no—
199C2×C42C2×D1311yescharacteristic
200#95—131no—
201#95—131no—
202#95—131no—
203#95—131no—
204#95—131no—
205#95—131no—
206#95—131no—
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#95C2×D1311yescharacteristic
217#95C2×D1311yescharacteristic
218C2×C13—81no—
219C2×C13#53811yescharacteristic
220C2×C13#54211yescharacteristic
221C2×C13#54211yescharacteristic
222C2×C13#55111yescharacteristic
223C2×C13#55611yescharacteristic
224C2×C13#55611yescharacteristic
225C2×C13#56311yescharacteristic
226C24C22×D1311yescharacteristic
227C2×Q8—262no—
228C2×Q8—262no—
229C2×Q8—262no—
230C2×Q8—521no—
231C2×Q8—521no—
232C2×Q8—521no—
233C22×C4—131no—
234C22×C4—131no—
235C22×C4—131no—
236C22×C4—131no—
237C22×C4—131no—
238C22×C4—131no—
239C22×C4—131no—
240C22×C4—131no—
241C22×C4C22×D1311yescharacteristic
242C22×C4C22×D1311yescharacteristic
243C22×C4C22×D1311yescharacteristic
244C22×C4C22×D1311yescharacteristic
245C22×C4C22×D1311yescharacteristic
246C22×C4C22×D1311yescharacteristic
247C4⋊C4—41no—
248C4⋊C4—262no—
249C4⋊C4—262no—
250C4⋊C4—521no—
251C4⋊C4—521no—
252C22⋊C4—22no—
253C22⋊C4—41no—
254C22⋊C4—41no—
255C22⋊C4—262no—
256C22⋊C4—262no—
257C22⋊C4—521no—
258C22⋊C4—521no—
259C42—41no—
260C42—262no—
261C42—521no—
262C13#275911yescharacteristic, complemented, Sylow
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23—21no—
270C23C23×D1311yescharacteristic
271Q8—524no—
272Q8—524no—
273C2×C4—21no—
274C2×C4—21no—
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—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—132no—
291C2×C4—132no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
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#612712yes—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22C2×#612711yescharacteristic
323C22#8825111yescharacteristic
324C22#8825111yescharacteristic
325C22#41×D1311yescharacteristic
326C22#41×D1311yescharacteristic
327C22#8825711yescharacteristic
328C22#8825711yescharacteristic
329C4—22no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—262no—
336C4—262no—
337C4—521no—
338C4—521no—
339C4—521no—
340C4—521no—
341C4—521no—
342C4—521no—
343C2—81no—
344C2#1171923811yescharacteristic
345C2#1171926111yescharacteristic
346C2#1171926611yescharacteristic
347C2#1171931811yescharacteristic
348C2#1171936711yescharacteristic
349C2#1171937711yescharacteristic
350C2#1171940711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#388C2
prime radicalC24×C13C23
hypercenter#388D13
hypocenterC13#2759
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #11718640C2semidirect
3. #11718635C2semidirect
10. #11718594C2semidirect
11. #11718594C2semidirect
12. C13⋊#401C2semidirect
13. #11718312C2semidirect
14. #11718307C2semidirect
15. #11718307C2semidirect
262. C13#2759semidirect

Maximal subgroups

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

subgroupindex
C13×#3882
#117186402
#117186352
#117186132
#117186082
#117186052
#117185942
C13⋊#4012
#117183122
#117183072
#275913