Finite Group Databasebeta

← #13122159

Subgroups — #13122159

Order 1664.

484 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#380C211yesmaximal, characteristic, complemented
2#11718874C211yesmaximal, characteristic, complemented
3#11718874C211yesmaximal, characteristic, complemented
4#11718652C211yesmaximal, characteristic, complemented
5#11718651C211yesmaximal, characteristic, complemented
6#11718651C211yesmaximal, characteristic, complemented
7#11718645C211yesmaximal, characteristic, complemented
8#11718622C211yesmaximal, characteristic, complemented
9#11718621C211yesmaximal, characteristic
10#11718618C211yesmaximal, characteristic, complemented
11#11718605C211yesmaximal, characteristic, complemented
12#11718335C211yesmaximal, characteristic, complemented
13#11718333C211yesmaximal, characteristic, complemented
14#11718330C211yesmaximal, characteristic, complemented
15#11718312C211yesmaximal, characteristic, complemented
16C23×C4×C13C2211yescharacteristic
17C22×C22⋊D13C2211yescharacteristic
18C22×C22⋊D13C2211yescharacteristic
19C22×D52C2211yescharacteristic
20C2×C13×C4⋊C4C2211yescharacteristic
21C2×C13×C4⋊C4C2211yescharacteristic
22C2×C13×C22⋊C4C2211yescharacteristic
23C2×C13×C22⋊C4C2211yescharacteristic
24C2×C22⋊Dic13C2211yescharacteristic
25C2×C22⋊Dic13C2211yescharacteristic
26C2×#6103C2211yescharacteristic
27C2×#6103C2211yescharacteristic
28C2×#6103C2211yescharacteristic
29C2×#6103C2211yescharacteristic
30C2×#6103C2211yescharacteristic
31C2×#6103C2211yescharacteristic
32C2×#6103C2211yescharacteristic
33C2×#6103C2211yescharacteristic
34C2×#6103C2211yescharacteristic
35C2×#6103C2211yescharacteristic
36C2×C4⋊Dic13C2211yescharacteristic
37C2×#6101C2211yescharacteristic
38C2×#6101C2211yescharacteristic
39C2×C4×Dic13C2211yescharacteristic
40C2×C4×Dic13C2211yescharacteristic
41C13×#95C2211yescharacteristic
42C13×#95C2211yescharacteristic
43#88071C2211yescharacteristic
44#88071C2211yescharacteristic
45#88071C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51C24×C13C2311yescharacteristic
52C23×D13C2311yescharacteristic
53C23×D13C2311yescharacteristic
54C22×C4×C13—22no—
55C22×C4×C13—41no—
56C22×C4×C13—41no—
57C22×C4×C13C2311yescharacteristic
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C2×C22⋊D13—22no—
64C2×C22⋊D13—22no—
65C2×C22⋊D13—22no—
66C2×C22⋊D13—41no—
67C2×C22⋊D13—41no—
68C2×C22⋊D13—41no—
69C22×Dic13C2311yescharacteristic
70C22×Dic13C2311yescharacteristic
71C22×Dic13C2311yescharacteristic
72C22×Dic13C2311yescharacteristic
73C22×Dic13C2311yescharacteristic
74C22×Dic13C2311yescharacteristic
75C2×D52—41no—
76C2×D52—41no—
77C2×D52—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C13×C22⋊C4—41no—
81C13×C22⋊C4—41no—
82C22⋊Dic13—22no—
83C22⋊Dic13—41no—
84#6103—22no—
85#6103—22no—
86#6103—22no—
87#6103—41no—
88#6103—41no—
89#6103—41no—
90#6103—41no—
91#6103—41no—
92#6103—41no—
93#6103—41no—
94C4⋊Dic13—41no—
95#6101—41no—
96#6101—41no—
97C4×Dic13—22no—
98C4×Dic13—41no—
99#2756—131nomaximal, Sylow
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13#4112yes—
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—21no—
121C22×D13—21no—
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—44no—
140C2×C4×C13#4112yes—
141C22⋊D13—44no—
142C22⋊D13—44no—
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—
160C2×Dic13#4112yes—
161D52—44no—
162#398—131no—
163#397—131no—
164#394—131no—
165#394—131no—
166#394—131no—
167#392—131no—
168#390—131no—
169#388—131no—
170#388—131no—
171#388—131no—
172#388—131no—
173#386—131no—
174#386—131no—
175#383—131no—
176#380D1311yescharacteristic, complemented
177C22×C13—22no—
178C22×C13—22no—
179C22×C13—22no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13C2×#4111yescharacteristic
185C22×C13C2×#4111yescharacteristic
186C22×C13C2×#4111yescharacteristic
187C22×C13H(5,𝔽2)11yescharacteristic
188C22×C13H(5,𝔽2)11yescharacteristic
189C22×C13H(5,𝔽2)11yescharacteristic
190C22×C13H(5,𝔽2)11yescharacteristic
191C2×D13—41no—
192C2×D13—41no—
193C2×D13—41no—
194C2×D13—41no—
195C2×D13—41no—
196C2×D13—41no—
197C2×D13—41no—
198C2×D13—41no—
199C2×D13—41no—
200C2×D13—41no—
201C2×D13—41no—
202C2×D13—41no—
203C2×D13—41no—
204C2×D13—41no—
205C4×C13—22no—
206C4×C13—41no—
207C4×C13—41no—
208C4×C13—41no—
209C4×C13—41no—
210C4×C13—41no—
211Dic13—22no—
212Dic13—41no—
213Dic13—41no—
214Dic13—41no—
215Dic13—41no—
216Dic13—41no—
217C22×D4—131no—
218C22×D4—131no—
219C22×D4—131no—
220C23×C4C2×D1311yescharacteristic
221C2×C4⋊C4—131no—
222C2×C4⋊C4—131no—
223C2×C4⋊C4—131no—
224C2×C4⋊C4C2×D1311yescharacteristic
225C2×C4⋊C4C2×D1311yescharacteristic
226C2×C22⋊C4—131no—
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⋊C4—131no—
238C2×C22⋊C4C2×D1311yescharacteristic
239C2×C22⋊C4C2×D1311yescharacteristic
240C2×C42—131no—
241C2×C42—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#95C2×D1311yescharacteristic
251#95C2×D1311yescharacteristic
252C2×C13—42no—
253C2×C13#53811yescharacteristic
254C2×C13#53811yescharacteristic
255C2×C13#54011yescharacteristic
256C2×C13#55111yescharacteristic
257C2×C13#55311yescharacteristic
258C2×C13#55511yescharacteristic
259C2×C13#56011yescharacteristic
260D13—81no—
261D13—81no—
262C24—131no—
263C24—131no—
264C24C22×D1311yescharacteristic
265C2×D4—262no—
266C2×D4—262no—
267C2×D4—262no—
268C2×D4—521no—
269C2×D4—521no—
270C2×D4—521no—
271C2×D4—521no—
272C2×D4—521no—
273C2×D4—521no—
274C22×C4—22no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—131no—
278C22×C4—131no—
279C22×C4—131no—
280C22×C4—131no—
281C22×C4—131no—
282C22×C4—131no—
283C22×C4C22×D1311yescharacteristic
284C22×C4C22×D1311yescharacteristic
285C22×C4C22×D1311yescharacteristic
286C22×C4C22×D1311yescharacteristic
287C22×C4C22×D1311yescharacteristic
288C22×C4C22×D1311yescharacteristic
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—521no—
292C4⋊C4—521no—
293C4⋊C4—521no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—262no—
297C22⋊C4—262no—
298C22⋊C4—262no—
299C22⋊C4—262no—
300C22⋊C4—521no—
301C22⋊C4—521no—
302C22⋊C4—521no—
303C22⋊C4—521no—
304C22⋊C4—521no—
305C22⋊C4—521no—
306C22⋊C4—521no—
307C22⋊C4—521no—
308C42—262no—
309C42—521no—
310C13#275611yescharacteristic, complemented, Sylow
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—261no—
318C23—261no—
319C23—261no—
320C23—261no—
321C23—261no—
322C23—261no—
323C23—261no—
324C23—261no—
325C23—261no—
326C23—261no—
327C23—261no—
328C23—261no—
329C23—261no—
330C23—261no—
331C23#613112yes—
332C23C23×D1311yescharacteristic
333D4—524no—
334D4—524no—
335D4—524no—
336C2×C4—21no—
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—44no—
354C2×C4—132no—
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#612712yes—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—521no—
381C22—521no—
382C22—521no—
383C22—521no—
384C22—521no—
385C22—521no—
386C22—521no—
387C22—521no—
388C22—521no—
389C22—521no—
390C22—521no—
391C22—521no—
392C22—521no—
393C22—521no—
394C22C2×#612711yescharacteristic
395C22#8825111yescharacteristic
396C22#8825111yescharacteristic
397C22#8825111yescharacteristic
398C22C2×#613111yescharacteristic
399C22#41×D1311yescharacteristic
400C22#8825611yescharacteristic
401C4—22no—
402C4—41no—
403C4—41no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4—262no—
408C4—521no—
409C4—521no—
410C4—521no—
411C4—521no—
412C4—521no—
413C2—42no—
414C2—1041no—
415C2—1041no—
416C2#1171919911yescharacteristic
417C2#1171921911yescharacteristic
418C2#1171923711yescharacteristic
419C2#1171932011yescharacteristic
420C2#1171932511yescharacteristic
421C2#1171934211yescharacteristic
422C2#1171934911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#380C2
prime radical#11718621C2
hypercenter#380D13
hypocenterC13#2756
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C13×#380C2semidirect
2. #11718874C2semidirect
3. #11718874C2semidirect
4. #11718652C2semidirect
5. #11718651C2semidirect
6. #11718651C2semidirect
7. #11718645C2semidirect
8. #11718622C2semidirect
10. #11718618C2semidirect
11. #11718605C2semidirect
12. #11718335C2semidirect
13. #11718333C2semidirect
14. #11718330C2semidirect
15. #11718312C2semidirect
176. #380D13semidirect
310. C13#2756semidirect

Maximal subgroups

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

subgroupindex
C13×#3802
#117188742
#117186522
#117186512
#117186452
#117186222
#117186212
#117186182
#117186052
#117183352
#117183332
#117183302
#117183122
#275613