Finite Group Databasebeta

← #13122452

Subgroups — #13122452

Order 1664.

498 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#388C211yesmaximal, characteristic, complemented
2#11718650C211yesmaximal, characteristic, complemented
3#11718648C211yesmaximal, characteristic, complemented
4#11718622C211yesmaximal, characteristic, complemented
5#11718621C211yesmaximal, characteristic
6#11718620C211yesmaximal, characteristic, complemented
7#11718617C211yesmaximal, characteristic, complemented
8#11718617C211yesmaximal, characteristic, complemented
9#11718613C211yesmaximal, characteristic, complemented
10#11718601C211yesmaximal, characteristic, complemented
11#11718601C211yesmaximal, characteristic, complemented
12#11718326C211yesmaximal, characteristic, complemented
13#11718326C211yesmaximal, characteristic, complemented
14C13⋊#401C211yesmaximal, characteristic, complemented
15#11718321C211yesmaximal, characteristic, complemented
16C22×C22⋊D13C2211yescharacteristic
17C22×C22⋊D13C2211yescharacteristic
18C22×D52C2211yescharacteristic
19C22×C4×D13C2211yescharacteristic
20C22×C4×D13C2211yescharacteristic
21C2×C13×C4⋊C4C2211yescharacteristic
22C2×C13×C22⋊C4C2211yescharacteristic
23C2×C13×C22⋊C4C2211yescharacteristic
24C2×C13×C22⋊C4C2211yescharacteristic
25C2×C42×C13C2211yescharacteristic
26C2×C22⋊Dic13C2211yescharacteristic
27C2×C22⋊Dic13C2211yescharacteristic
28C2×#6103C2211yescharacteristic
29C2×#6103C2211yescharacteristic
30C2×#6103C2211yescharacteristic
31C2×#6103C2211yescharacteristic
32C2×#6103C2211yescharacteristic
33C2×#6103C2211yescharacteristic
34C2×#6103C2211yescharacteristic
35C2×#6103C2211yescharacteristic
36C2×C4⋊Dic13C2211yescharacteristic
37C2×#6101C2211yescharacteristic
38C2×#6101C2211yescharacteristic
39C13×#95C2211yescharacteristic
40C13×#95C2211yescharacteristic
41#88071C2211yescharacteristic
42#88071C2211yescharacteristic
43#88071C2211yescharacteristic
44#88071C2211yescharacteristic
45#88071C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51C24×C13C2311yescharacteristic
52C23×D13C2311yescharacteristic
53C23×D13C2311yescharacteristic
54C22×C4×C13C2311yescharacteristic
55C22×C4×C13C2311yescharacteristic
56C22×C4×C13C2311yescharacteristic
57C22×C4×C13C2311yescharacteristic
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C2×C22⋊D13—22no—
61C2×C22⋊D13—22no—
62C2×C22⋊D13—41no—
63C2×C22⋊D13—41no—
64C2×C22⋊D13—41no—
65C2×C22⋊D13—41no—
66C22×Dic13C2311yescharacteristic
67C22×Dic13C2311yescharacteristic
68C22×Dic13C2311yescharacteristic
69C22×Dic13C2311yescharacteristic
70C22×Dic13C2311yescharacteristic
71C22×Dic13C2311yescharacteristic
72C2×D52—22no—
73C2×D52—22no—
74C2×D52—41no—
75C2×C4×D13—22no—
76C2×C4×D13—41no—
77C2×C4×D13—41no—
78C2×C4×D13—41no—
79C2×C4×D13—41no—
80C2×C4×D13—41no—
81C13×C4⋊C4—41no—
82C13×C22⋊C4—22no—
83C13×C22⋊C4—41no—
84C13×C22⋊C4—41no—
85C42×C13—41no—
86C22⋊Dic13—41no—
87C22⋊Dic13—41no—
88#6103—22no—
89#6103—22no—
90#6103—22no—
91#6103—41no—
92#6103—41no—
93#6103—41no—
94#6103—41no—
95#6103—41no—
96C4⋊Dic13—41no—
97#6101—41no—
98#6101—41no—
99#2778—131nomaximal, Sylow
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13C2411yescharacteristic
108C22×D13—21no—
109C22×D13—21no—
110C22×D13—21no—
111C22×D13—21no—
112C22×D13—21no—
113C22×D13—21no—
114C22×D13—21no—
115C22×D13—21no—
116C22×D13—21no—
117C22×D13—21no—
118C22×D13—21no—
119C22×D13—21no—
120C22×D13#4112yes—
121C22×D13#4112yes—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13#4112yes—
140C22⋊D13—44no—
141C22⋊D13—44no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—21no—
147C2×Dic13—21no—
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—21no—
152C2×Dic13—21no—
153C2×Dic13—21no—
154C2×Dic13—21no—
155C2×Dic13—21no—
156C2×Dic13—21no—
157C2×Dic13—21no—
158C2×Dic13—21no—
159C2×Dic13—21no—
160D52—44no—
161C4×D13—44no—
162C4×D13—44no—
163#401—131no—
164#400—131no—
165#397—131no—
166#394—131no—
167#394—131no—
168#392—131no—
169#388—131no—
170#388—131no—
171#388D1311yescharacteristic, complemented
172#386—131no—
173#386—131no—
174#386—131no—
175#386—131no—
176#385—131no—
177#380—131no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13C2×#4111yescharacteristic
186C22×C13C2×#4111yescharacteristic
187C22×C13C2×#4111yescharacteristic
188C22×C13H(5,𝔽2)11yescharacteristic
189C22×C13H(5,𝔽2)11yescharacteristic
190C22×C13H(5,𝔽2)11yescharacteristic
191C22×C13H(5,𝔽2)11yescharacteristic
192C2×D13—22no—
193C2×D13—22no—
194C2×D13—22no—
195C2×D13—22no—
196C2×D13—22no—
197C2×D13—22no—
198C2×D13—41no—
199C2×D13—41no—
200C2×D13—41no—
201C2×D13—41no—
202C2×D13—41no—
203C2×D13—41no—
204C2×D13—41no—
205C2×D13—41no—
206C4×C13—22no—
207C4×C13—41no—
208C4×C13—41no—
209C4×C13—41no—
210C4×C13—41no—
211C4×C13—41no—
212Dic13—41no—
213Dic13—41no—
214Dic13—41no—
215Dic13—41no—
216Dic13—41no—
217Dic13—41no—
218C22×D4—131no—
219C22×D4—131no—
220C22×D4—131no—
221C23×C4—131no—
222C23×C4—131no—
223C2×C4⋊C4—131no—
224C2×C4⋊C4—131no—
225C2×C4⋊C4—131no—
226C2×C4⋊C4C2×D1311yescharacteristic
227C2×C22⋊C4—131no—
228C2×C22⋊C4—131no—
229C2×C22⋊C4—131no—
230C2×C22⋊C4—131no—
231C2×C22⋊C4—131no—
232C2×C22⋊C4—131no—
233C2×C22⋊C4—131no—
234C2×C22⋊C4—131no—
235C2×C22⋊C4—131no—
236C2×C22⋊C4—131no—
237C2×C22⋊C4C2×D1311yescharacteristic
238C2×C22⋊C4C2×D1311yescharacteristic
239C2×C22⋊C4C2×D1311yescharacteristic
240C2×C42C2×D1311yescharacteristic
241#95—131no—
242#95—131no—
243#95—131no—
244#95—131no—
245#95—131no—
246#95—131no—
247#95—131no—
248#95—131no—
249#95—131no—
250#95—131no—
251#95C2×D1311yescharacteristic
252#95C2×D1311yescharacteristic
253C2×C13—81no—
254C2×C13#53811yescharacteristic
255C2×C13#53811yescharacteristic
256C2×C13#53811yescharacteristic
257C2×C13#55111yescharacteristic
258C2×C13#55311yescharacteristic
259C2×C13#55311yescharacteristic
260C2×C13#56011yescharacteristic
261D13—42no—
262D13—42no—
263C24—131no—
264C24—131no—
265C24C22×D1311yescharacteristic
266C2×D4—262no—
267C2×D4—262no—
268C2×D4—262no—
269C2×D4—262no—
270C2×D4—521no—
271C2×D4—521no—
272C2×D4—521no—
273C2×D4—521no—
274C2×D4—521no—
275C22×C4—131no—
276C22×C4—131no—
277C22×C4—131no—
278C22×C4—131no—
279C22×C4—131no—
280C22×C4—131no—
281C22×C4—262no—
282C22×C4—521no—
283C22×C4—521no—
284C22×C4—521no—
285C22×C4—521no—
286C22×C4—521no—
287C22×C4C22×D1311yescharacteristic
288C22×C4C22×D1311yescharacteristic
289C22×C4C22×D1311yescharacteristic
290C22×C4C22×D1311yescharacteristic
291C22×C4C22×D1311yescharacteristic
292C22×C4C22×D1311yescharacteristic
293C4⋊C4—41no—
294C4⋊C4—521no—
295C4⋊C4—521no—
296C4⋊C4—521no—
297C22⋊C4—22no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—262no—
301C22⋊C4—262no—
302C22⋊C4—262no—
303C22⋊C4—521no—
304C22⋊C4—521no—
305C22⋊C4—521no—
306C22⋊C4—521no—
307C22⋊C4—521no—
308C22⋊C4—521no—
309C22⋊C4—521no—
310C42—41no—
311C13#277811yescharacteristic, complemented, Sylow
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—132no—
320C23—132no—
321C23—261no—
322C23—261no—
323C23—261no—
324C23—261no—
325C23—261no—
326C23—261no—
327C23—261no—
328C23—261no—
329C23—261no—
330C23—261no—
331C23—261no—
332C23—261no—
333C23C23×D1311yescharacteristic
334D4—524no—
335D4—524no—
336D4—524no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—261no—
355C2×C4—261no—
356C2×C4—261no—
357C2×C4—261no—
358C2×C4—261no—
359C2×C4—261no—
360C2×C4—261no—
361C2×C4—261no—
362C2×C4—261no—
363C2×C4—261no—
364C2×C4—261no—
365C2×C4—261no—
366C2×C4—261no—
367C2×C4—261no—
368C2×C4—261no—
369C2×C4—261no—
370C2×C4—261no—
371C2×C4—261no—
372C2×C4—524no—
373C2×C4—524no—
374C2×C4#612712yes—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—262no—
383C22—262no—
384C22—262no—
385C22—262no—
386C22—262no—
387C22—262no—
388C22—521no—
389C22—521no—
390C22—521no—
391C22—521no—
392C22—521no—
393C22—521no—
394C22—521no—
395C22—521no—
396C22C2×#612711yescharacteristic
397C22#8825111yescharacteristic
398C22#8825111yescharacteristic
399C22#41×D1311yescharacteristic
400C22#41×D1311yescharacteristic
401C22#8825611yescharacteristic
402C22#8825611yescharacteristic
403C4—22no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4—41no—
408C4—41no—
409C4—521no—
410C4—521no—
411C4—521no—
412C4—521no—
413C4—521no—
414C4—521no—
415C2—81no—
416C2—522no—
417C2—522no—
418C2#1171923511yescharacteristic
419C2#1171926311yescharacteristic
420C2#1171926511yescharacteristic
421C2#1171932511yescharacteristic
422C2#1171936211yescharacteristic
423C2#1171938411yescharacteristic
424C2#1171940911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#388C2
prime radical#11718621C2
hypercenter#388D13
hypocenterC13#2778
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C13×#388C2semidirect
2. #11718650C2semidirect
3. #11718648C2semidirect
4. #11718622C2semidirect
6. #11718620C2semidirect
7. #11718617C2semidirect
8. #11718617C2semidirect
9. #11718613C2semidirect
10. #11718601C2semidirect
11. #11718601C2semidirect
12. #11718326C2semidirect
13. #11718326C2semidirect
14. C13⋊#401C2semidirect
15. #11718321C2semidirect
171. #388D13semidirect
311. C13#2778semidirect

Maximal subgroups

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

subgroupindex
C13×#3882
#117186502
#117186482
#117186222
#117186212
#117186202
#117186172
#117186132
#117186012
#117183262
C13⋊#4012
#117183212
#277813