Finite Group Databasebeta

← #13119400

Subgroups — #13119400

Order 1664.

482 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#386C211yesmaximal, characteristic
2#11718881C211yesmaximal, characteristic
3#11718881C211yesmaximal, characteristic
4#11718873C211yesmaximal, characteristic, complemented
5C2×#88071C211yesmaximal, characteristic, complemented
6#11718614C211yesmaximal, characteristic, complemented
7#11718613C211yesmaximal, characteristic, complemented
8#11718612C211yesmaximal, characteristic, complemented
9#11718607C211yesmaximal, characteristic, complemented
10#11718606C211yesmaximal, characteristic, complemented
11C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
12C13⋊#401C211yesmaximal, characteristic, complemented
13#11718321C211yesmaximal, characteristic, complemented
14#11718314C211yesmaximal, characteristic, complemented
15#11718312C211yesmaximal, characteristic, complemented
16C22×D4×C13C2211yescharacteristic
17C23×C4×C13C2211yescharacteristic
18C23×Dic13C2211yescharacteristic
19C23×Dic13C2211yescharacteristic
20C2×C13×C22⋊C4C2211yescharacteristic
21C2×C13×C22⋊C4C2211yescharacteristic
22C2×C13×C22⋊C4C2211yescharacteristic
23C2×C22⋊Dic13C2211yescharacteristic
24C2×C22⋊Dic13C2211yescharacteristic
25C2×C22⋊Dic13C2211yescharacteristic
26C2×C22⋊Dic13C2211yescharacteristic
27C2×C22⋊Dic13C2211yescharacteristic
28C2×C22⋊Dic13C2211yescharacteristic
29C2×C4⋊Dic13C2211yescharacteristic
30C2×C4⋊Dic13C2211yescharacteristic
31C2×#6101C2211yescharacteristic
32C2×#6101C2211yescharacteristic
33C2×C4×Dic13C2211yescharacteristic
34C2×C4×Dic13C2211yescharacteristic
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
52C24×C13C2311yescharacteristic
53C2×D4×C13—22no—
54C2×D4×C13—22no—
55C2×D4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13—22no—
58C22×C4×C13—41no—
59C22×C4×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C22×Dic13—22no—
65C22×Dic13—22no—
66C22×Dic13—22no—
67C22×Dic13—41no—
68C22×Dic13—41no—
69C22×Dic13—41no—
70C22×Dic13C2311yescharacteristic
71C22×Dic13C2311yescharacteristic
72C22×Dic13C2311yescharacteristic
73C22×Dic13C2311yescharacteristic
74C22×Dic13C2311yescharacteristic
75C22×Dic13C2311yescharacteristic
76C22×Dic13C2311yescharacteristic
77C22×Dic13C2311yescharacteristic
78C13×C22⋊C4—22no—
79C13×C22⋊C4—22no—
80C13×C22⋊C4—41no—
81C22⋊Dic13—22no—
82C22⋊Dic13—22no—
83C22⋊Dic13—22no—
84C22⋊Dic13—41no—
85C22⋊Dic13—41no—
86C22⋊Dic13—41no—
87C4⋊Dic13—22no—
88C4⋊Dic13—41no—
89#6101—41no—
90#6101—41no—
91C4×Dic13—22no—
92C4×Dic13—41no—
93#2510—131nomaximal, Sylow
94C23×C13—21no—
95C23×C13—21no—
96C23×C13—21no—
97C23×C13—21no—
98C23×C13—21no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13#4112yes—
106C23×C13#4112yes—
107C23×C13#4112yes—
108C23×C13C2411yescharacteristic
109D4×C13—44no—
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—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—44no—
125C2×C4×C13#4112yes—
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—21no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—21no—
147C2×Dic13—21no—
148C2×Dic13—21no—
149C2×Dic13—44no—
150C2×Dic13—44no—
151C2×Dic13#4112yes—
152#401—131no—
153#400—131no—
154#397—131no—
155#397—131no—
156#388—131no—
157#388—131no—
158#387—131no—
159#386—131no—
160#386—131no—
161#386D1311yescharacteristic
162#385—131no—
163#383—131no—
164#380—131no—
165C4×C22⋊C4—131no—
166C2×#95—131no—
167C22×C13—22no—
168C22×C13—22no—
169C22×C13—22no—
170C22×C13—22no—
171C22×C13—22no—
172C22×C13—22no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13#12614yes—
181C22×C13C2×#4111yescharacteristic
182C22×C13C2×#4111yescharacteristic
183C22×C13C2×#4111yescharacteristic
184C22×C13C2×#4111yescharacteristic
185C22×C13C2×#4111yescharacteristic
186C22×C13H(5,𝔽2)11yescharacteristic
187C22×C13H(5,𝔽2)11yescharacteristic
188C4×C13—22no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13—41no—
192C4×C13—41no—
193Dic13—22no—
194Dic13—41no—
195Dic13—41no—
196Dic13—41no—
197Dic13—41no—
198Dic13—41no—
199Dic13—41no—
200Dic13—41no—
201C22×D4C2×D1311yescharacteristic
202C23×C4—131no—
203C23×C4—131no—
204C23×C4C2×D1311yescharacteristic
205C2×C4⋊C4—131no—
206C2×C4⋊C4—131no—
207C2×C4⋊C4—131no—
208C2×C4⋊C4—131no—
209C2×C22⋊C4—131no—
210C2×C22⋊C4—131no—
211C2×C22⋊C4—131no—
212C2×C22⋊C4—131no—
213C2×C22⋊C4—131no—
214C2×C22⋊C4—131no—
215C2×C22⋊C4C2×D1311yescharacteristic
216C2×C22⋊C4C2×D1311yescharacteristic
217C2×C22⋊C4C2×D1311yescharacteristic
218C2×C42—131no—
219C2×C42—131no—
220#95—131no—
221#95—131no—
222#95—131no—
223#95—131no—
224#95—131no—
225#95—131no—
226#95—131no—
227#95—131no—
228#95—131no—
229#95—131no—
230#95—131no—
231#95—131no—
232#95—131no—
233#95—131no—
234#95C2×D1311yescharacteristic
235#95C2×D1311yescharacteristic
236C2×C13—24no—
237C2×C13—81no—
238C2×C13C2×#12611yescharacteristic
239C2×C13#52911yescharacteristic
240C2×C13#53811yescharacteristic
241C2×C13#55111yescharacteristic
242C2×C13#55111yescharacteristic
243C2×C13#55311yescharacteristic
244C2×C13#55311yescharacteristic
245C24C22×D1311yescharacteristic
246C24C22×D1311yescharacteristic
247C2×D4—22no—
248C2×D4—22no—
249C2×D4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—41no—
253C22×C4—131no—
254C22×C4—131no—
255C22×C4—131no—
256C22×C4—131no—
257C22×C4—131no—
258C22×C4—131no—
259C22×C4—131no—
260C22×C4—131no—
261C22×C4—262no—
262C22×C4—262no—
263C22×C4—262no—
264C22×C4—521no—
265C22×C4—521no—
266C22×C4—521no—
267C22×C4C22×D1311yescharacteristic
268C22×C4C22×D1311yescharacteristic
269C22×C4C22×D1311yescharacteristic
270C22×C4C22×D1311yescharacteristic
271C22×C4C22×D1311yescharacteristic
272C4⋊C4—262no—
273C4⋊C4—521no—
274C4⋊C4—521no—
275C4⋊C4—521no—
276C22⋊C4—22no—
277C22⋊C4—22no—
278C22⋊C4—41no—
279C22⋊C4—262no—
280C22⋊C4—262no—
281C22⋊C4—262no—
282C22⋊C4—521no—
283C22⋊C4—521no—
284C22⋊C4—521no—
285C42—262no—
286C42—521no—
287C13#251011yescharacteristic, complemented, Sylow
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23#612712yes—
300C23#612912yes—
301C23#612912yes—
302C23C23×D1311yescharacteristic
303D4—44no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—44no—
319C2×C4—132no—
320C2×C4—261no—
321C2×C4—261no—
322C2×C4—261no—
323C2×C4—261no—
324C2×C4—261no—
325C2×C4—261no—
326C2×C4—261no—
327C2×C4—261no—
328C2×C4—261no—
329C2×C4—261no—
330C2×C4—261no—
331C2×C4—261no—
332C2×C4—261no—
333C2×C4—261no—
334C2×C4—261no—
335C2×C4—261no—
336C2×C4—261no—
337C2×C4—261no—
338C2×C4—261no—
339C2×C4—261no—
340C2×C4—261no—
341C2×C4—261no—
342C2×C4—261no—
343C2×C4—524no—
344C2×C4—524no—
345C2×C4#612912yes—
346C22—22no—
347C22—22no—
348C22—22no—
349C22—22no—
350C22—22no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22#8813314yes—
360C22C2×#612711yescharacteristic
361C22C2×#612911yescharacteristic
362C22C2×#612911yescharacteristic
363C22C2×#612911yescharacteristic
364C22#8825111yescharacteristic
365C22#41×D1311yescharacteristic
366C22#8825611yescharacteristic
367C4—22no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—262no—
373C4—521no—
374C4—521no—
375C4—521no—
376C4—521no—
377C4—521no—
378C4—521no—
379C4—521no—
380C2—24no—
381C2—81no—
382C2C2×#8813311yescharacteristic
383C2#1171924511yescharacteristic
384C2#1171927011yescharacteristic
385C2#1171929211yescharacteristic
386C2#1171930511yescharacteristic
387C2#1171932211yescharacteristic
388C2#1171936311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#386C2
prime radicalC22×D4×C13C22
hypercenter#386D13
hypocenterC13#2510
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
4. #11718873C2semidirect
5. C2×#88071C2semidirect
6. #11718614C2semidirect
7. #11718613C2semidirect
8. #11718612C2semidirect
9. #11718607C2semidirect
10. #11718606C2semidirect
11. C22⋊C4×Dic13C2semidirect
12. C13⋊#401C2semidirect
13. #11718321C2semidirect
14. #11718314C2semidirect
15. #11718312C2semidirect
287. C13#2510semidirect

Maximal subgroups

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

subgroupindex
C13×#3862
#117188812
#117188732
C2×#880712
#117186142
#117186132
#117186122
#117186072
#117186062
C22⋊C4×Dic132
C13⋊#4012
#117183212
#117183142
#117183122
#251013