Finite Group Databasebeta

← #13121874

Subgroups — #13121874

Order 1664.

552 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#388C211yesmaximal, characteristic, complemented
2#11718655C211yesmaximal, characteristic, complemented
3#11718654C211yesmaximal, characteristic, complemented
4#11718616C211yesmaximal, characteristic
5#11718616C211yesmaximal, characteristic
6#11718616C211yesmaximal, characteristic
7#11718613C211yesmaximal, characteristic, complemented
8#11718610C211yesmaximal, characteristic, complemented
9#11718606C211yesmaximal, characteristic, complemented
10#11718601C211yesmaximal, characteristic, complemented
11#11718601C211yesmaximal, characteristic, complemented
12#11718337C211yesmaximal, characteristic, complemented
13#11718336C211yesmaximal, characteristic, complemented
14#11718331C211yesmaximal, characteristic, complemented
15#11718330C211yesmaximal, characteristic, complemented
16C24×D13C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic, complemented
18C2×C13×C22⋊C4C2211yescharacteristic
19C2×C13×C22⋊C4C2211yescharacteristic
20C2×C13×C22⋊C4C2211yescharacteristic
21C2×C42×C13C2211yescharacteristic, complemented
22C2×C22⋊Dic13C2211yescharacteristic
23C2×C22⋊Dic13C2211yescharacteristic
24C2×C22⋊Dic13C2211yescharacteristic
25C2×#6103C2211yescharacteristic
26C2×#6103C2211yescharacteristic
27C2×#6103C2211yescharacteristic
28C2×#6103C2211yescharacteristic
29C2×#6103C2211yescharacteristic
30C2×#6103C2211yescharacteristic
31C2×#6103C2211yescharacteristic
32C2×#6103C2211yescharacteristic
33C2×#6103C2211yescharacteristic
34C2×#6103C2211yescharacteristic
35C2×#6103C2211yescharacteristic
36C2×#6103C2211yescharacteristic
37C2×C4⋊Dic13C2211yescharacteristic, complemented
38C2×#6101C2211yescharacteristic, complemented
39C2×#6101C2211yescharacteristic, complemented
40C2×#6101C2211yescharacteristic, complemented
41C2×#6101C2211yescharacteristic, complemented
42C2×C4×Dic13C2211yescharacteristic, complemented
43C13×#95C2211yescharacteristic, complemented
44C13×#95C2211yescharacteristic, complemented
45#88071C2211yescharacteristic, complemented
46#88071C2211yescharacteristic, complemented
47#88071C2211yescharacteristic, complemented
48#88071C2211yescharacteristic, complemented
49#88071C2211yescharacteristic, complemented
50#88071C2211yescharacteristic, complemented
51C24×C13C2311yescharacteristic
52C23×D13—22no—
53C23×D13—22no—
54C23×D13—22no—
55C23×D13—41no—
56C23×D13—41no—
57C23×D13—41no—
58C23×D13—41no—
59C23×D13C2311yescharacteristic
60C23×D13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C22×C4×C13C2311yescharacteristic
65C22×C4×C13C2311yescharacteristic
66C22×C4×C13C2311yescharacteristic
67C22×Dic13C2311yescharacteristic
68C22×Dic13C2311yescharacteristic
69C22×Dic13C2311yescharacteristic
70C22×Dic13C2311yescharacteristic
71C22×Dic13C2311yescharacteristic
72C22×Dic13C2311yescharacteristic
73C13×C4⋊C4—41no—
74C13×C22⋊C4—22no—
75C13×C22⋊C4—41no—
76C13×C22⋊C4—41no—
77C42×C13—41no—
78C22⋊Dic13—22no—
79C22⋊Dic13—41no—
80C22⋊Dic13—41no—
81#6103—22no—
82#6103—22no—
83#6103—22no—
84#6103—22no—
85#6103—41no—
86#6103—41no—
87#6103—41no—
88#6103—41no—
89#6103—41no—
90#6103—41no—
91#6103—41no—
92#6103—41no—
93C4⋊Dic13—41no—
94#6101—41no—
95#6101—41no—
96#6101—41no—
97#6101—41no—
98C4×Dic13—41no—
99#2735—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—44no—
121C22×D13—44no—
122C22×D13—44no—
123C22×D13—44no—
124C22×D13—44no—
125C22×D13—44no—
126C22×D13—44no—
127C22×D13#4112yes—
128C22×D13#4112yes—
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—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—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—21no—
161C2×Dic13—21no—
162C2×Dic13—21no—
163C2×Dic13—21no—
164C2×Dic13—21no—
165#399—131no—
166#397—131no—
167#397—131no—
168#397—131no—
169#396—131no—
170#396—131no—
171#388—131no—
172#388—131no—
173#388—131no—
174#388—131no—
175#388—131no—
176#388D1311yescharacteristic, complemented
177#379—131no—
178#379—131no—
179#379—131no—
180C22×C13—22no—
181C22×C13—22no—
182C22×C13—22no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—41no—
186C22×C13—41no—
187C22×C13C2×#4111yescharacteristic
188C22×C13C2×#4111yescharacteristic
189C22×C13C2×#4111yescharacteristic
190C22×C13H(5,𝔽2)11yescharacteristic
191C22×C13H(5,𝔽2)11yescharacteristic
192C22×C13H(5,𝔽2)11yescharacteristic
193C22×C13H(5,𝔽2)11yescharacteristic
194C2×D13—22no—
195C2×D13—22no—
196C2×D13—22no—
197C2×D13—22no—
198C2×D13—22no—
199C2×D13—22no—
200C2×D13—416no—
201C2×D13—41no—
202C2×D13—41no—
203C2×D13—41no—
204C2×D13—41no—
205C2×D13—41no—
206C2×D13—41no—
207C2×D13—41no—
208C2×D13—41no—
209C4×C13—41no—
210C4×C13—41no—
211C4×C13—41no—
212C4×C13—41no—
213C4×C13—41no—
214C4×C13—41no—
215Dic13—41no—
216Dic13—41no—
217Dic13—41no—
218Dic13—41no—
219Dic13—41no—
220Dic13—41no—
221C25—131no—
222C2×C4⋊C4—131no—
223C2×C4⋊C4—131no—
224C2×C4⋊C4—131no—
225C2×C4⋊C4—131no—
226C2×C4⋊C4—131no—
227C2×C4⋊C4C2×D1311yescharacteristic, complemented
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⋊C4—131no—
239C2×C22⋊C4—131no—
240C2×C22⋊C4—131no—
241C2×C22⋊C4—131no—
242C2×C22⋊C4—131no—
243C2×C22⋊C4C2×D1311yescharacteristic
244C2×C22⋊C4C2×D1311yescharacteristic
245C2×C22⋊C4C2×D1311yescharacteristic
246C2×C42—131no—
247C2×C42C2×D1311yescharacteristic, complemented
248#95—131no—
249#95—131no—
250#95—131no—
251#95—131no—
252#95—131no—
253#95—131no—
254#95C2×D1311yescharacteristic, complemented
255#95C2×D1311yescharacteristic, complemented
256C2×C13—42no—
257C2×C13#53811yescharacteristic
258C2×C13#53811yescharacteristic
259C2×C13#53811yescharacteristic
260C2×C13#55111yescharacteristic
261C2×C13#55111yescharacteristic
262C2×C13#55111yescharacteristic
263C2×C13#56011yescharacteristic
264D13—42no—
265D13—42no—
266C24—131no—
267C24—131no—
268C24—262no—
269C24—262no—
270C24—262no—
271C24—521no—
272C24—521no—
273C24—521no—
274C24—521no—
275C24C22×D1311yescharacteristic
276C22×C4—131no—
277C22×C4—131no—
278C22×C4—131no—
279C22×C4—131no—
280C22×C4—131no—
281C22×C4—131no—
282C22×C4C22×D1311yescharacteristic
283C22×C4C22×D1311yescharacteristic
284C22×C4C22×D1311yescharacteristic
285C22×C4C22×D1311yescharacteristic
286C22×C4C22×D1311yescharacteristic
287C22×C4C22×D1311yescharacteristic
288C4⋊C4—41no—
289C4⋊C4—521no—
290C4⋊C4—521no—
291C4⋊C4—521no—
292C4⋊C4—521no—
293C4⋊C4—521no—
294C22⋊C4—22no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—262no—
298C22⋊C4—262no—
299C22⋊C4—262no—
300C22⋊C4—262no—
301C22⋊C4—262no—
302C22⋊C4—521no—
303C22⋊C4—521no—
304C22⋊C4—521no—
305C22⋊C4—521no—
306C22⋊C4—521no—
307C22⋊C4—521no—
308C22⋊C4—521no—
309C22⋊C4—521no—
310C22⋊C4—521no—
311C22⋊C4—521no—
312C42—41no—
313C42—521no—
314C13#273511yescharacteristic, complemented, Sylow
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—132no—
322C23—132no—
323C23—261no—
324C23—261no—
325C23—261no—
326C23—261no—
327C23—261no—
328C23—261no—
329C23—261no—
330C23—261no—
331C23—261no—
332C23—261no—
333C23—261no—
334C23—261no—
335C23—524no—
336C23—524no—
337C23—524no—
338C23—524no—
339C23—524no—
340C23—524no—
341C23—524no—
342C23#612712yes—
343C23C23×D1311yescharacteristic
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—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
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—261no—
373C2×C4—261no—
374C2×C4—261no—
375C2×C4—261no—
376C2×C4—261no—
377C2×C4—261no—
378C2×C4—261no—
379C2×C4—261no—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—262no—
388C22—262no—
389C22—262no—
390C22—262no—
391C22—262no—
392C22—262no—
393C22—5216no—
394C22—521no—
395C22—521no—
396C22—521no—
397C22—521no—
398C22—521no—
399C22—521no—
400C22—521no—
401C22—521no—
402C22C2×#612711yescharacteristic
403C22#8825111yescharacteristic
404C22#8825111yescharacteristic
405C22#41×D1311yescharacteristic
406C22#41×D1311yescharacteristic
407C22#8825611yescharacteristic
408C22#8825611yescharacteristic
409C4—41no—
410C4—41no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—521no—
416C4—521no—
417C4—521no—
418C4—521no—
419C4—521no—
420C4—521no—
421C2—42no—
422C2—522no—
423C2—522no—
424C2#1171923211yescharacteristic
425C2#1171926111yescharacteristic
426C2#1171926511yescharacteristic
427C2#1171931811yescharacteristic
428C2#1171937111yescharacteristic
429C2#1171938311yescharacteristic
430C2#1171941011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#388C2
prime radicalC24×D13C22
hypercenter#388D13
hypocenterC13#2735
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. #11718655C2semidirect
3. #11718654C2semidirect
7. #11718613C2semidirect
8. #11718610C2semidirect
9. #11718606C2semidirect
10. #11718601C2semidirect
11. #11718601C2semidirect
12. #11718337C2semidirect
13. #11718336C2semidirect
14. #11718331C2semidirect
15. #11718330C2semidirect
17. C2×C13×C4⋊C4C22semidirect
21. C2×C42×C13C22semidirect
37. C2×C4⋊Dic13C22semidirect
38. C2×#6101C22semidirect
39. C2×#6101C22semidirect
40. C2×#6101C22semidirect
41. C2×#6101C22semidirect
42. C2×C4×Dic13C22semidirect
43. C13×#95C22semidirect
44. C13×#95C22semidirect
45. #88071C22semidirect
46. #88071C22semidirect
47. #88071C22semidirect
48. #88071C22semidirect
49. #88071C22semidirect
50. #88071C22semidirect
176. #388D13semidirect
227. C2×C4⋊C4C2×D13semidirect
247. C2×C42C2×D13semidirect
254. #95C2×D13semidirect
255. #95C2×D13semidirect
314. C13#2735semidirect

Maximal subgroups

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

subgroupindex
C13×#3882
#117186552
#117186542
#117186162
#117186132
#117186102
#117186062
#117186012
#117183372
#117183362
#117183312
#117183302
#273513