Finite Group Databasebeta

← #13125686

Subgroups — #13125686

Order 1664.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719313C211yesmaximal, characteristic, complemented
2#11719230C211yesmaximal, characteristic, complemented
3C13×#482C211yesmaximal, characteristic, complemented
4#11718697C211yesmaximal, characteristic, complemented
5#11718657C211yesmaximal, characteristic, complemented
6#11718547C211yesmaximal, characteristic, complemented
7#11718543C211yesmaximal, characteristic, complemented
8#11718525C211yesmaximal, characteristic, complemented
9#11718524C211yesmaximal, characteristic, complemented
10#11718443C211yesmaximal, characteristic, complemented
11#11718442C211yesmaximal, characteristic, complemented
12#11718442C211yesmaximal, characteristic, complemented
13#11718436C211yesmaximal, characteristic, complemented
14#11718392C211yesmaximal, characteristic, complemented
15#11718388C211yesmaximal, characteristic, complemented
16C2×#6129C2211yescharacteristic, complemented
17C2×#6127C2211yescharacteristic
18C22×D52C2211yescharacteristic
19C13×#121C2211yescharacteristic
20C13×#117C2211yescharacteristic
21#88193—21no—
22#88192—21no—
23#88192C2211yescharacteristic, complemented
24C2×#6104C2211yescharacteristic
25C2×#6104C2211yescharacteristic
26#88178C2211yescharacteristic
27C2×#6095C2211yescharacteristic
28C2×#6095C2211yescharacteristic
29C2×#6094C2211yescharacteristic, complemented
30C2×C8×D13C2211yescharacteristic, complemented
31#88151C2211yescharacteristic, complemented
32#88149C2211yescharacteristic
33#88149C2211yescharacteristic
34#88149C2211yescharacteristic
35#88149C2211yescharacteristic
36C4⋊C4×D13C2211yescharacteristic, complemented
37#88138—21no—
38#88136—21no—
39#88136—21no—
40#88132—21no—
41#88129—21no—
42#88128—21no—
43C13×#107C2211yescharacteristic, complemented
44C13×#106C2211yescharacteristic, complemented
45C13×#102C2211yescharacteristic, complemented
46C13×#102C2211yescharacteristic, complemented
47C13×C22⋊C8C2211yescharacteristic
48C22⋊#1055C2211yescharacteristic
49#88061C2211yescharacteristic
50#88061C2211yescharacteristic
51#88060C2211yescharacteristic, complemented
52#88060C2211yescharacteristic, complemented
53#88050C2211yescharacteristic, complemented
54#88050C2211yescharacteristic, complemented
55#88049C2211yescharacteristic
56#88049C2211yescharacteristic
57#88048C2211yescharacteristic, complemented
58#88047C2211yescharacteristic, complemented
59C23×D13—21no—
60C2×D4×C13—21no—
61C2×D4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C2×C22⋊D13—21no—
64C2×C22⋊D13—21no—
65C2×C22⋊D13D411yescharacteristic
66C2×C22⋊D13D411yescharacteristic
67C22×Dic13—21no—
68#6129—41no—
69#6129—41no—
70#6127—41no—
71#6127—41no—
72C2×D52—21no—
73C2×D52—21no—
74C2×D52—21no—
75C2×D52—21no—
76C2×D52—21no—
77C2×D52—41no—
78C2×D52—41no—
79C2×D52D411yescharacteristic
80C2×D52C2311yescharacteristic
81C2×D52C2311yescharacteristic
82C2×C4×D13—21no—
83C2×C4×D13C2311yescharacteristic
84C2×C4×D13C2311yescharacteristic
85C2×Dic26D411yescharacteristic
86C2×Dic26C2311yescharacteristic
87C2×C8×C13C2311yescharacteristic
88C2×C8×C13C2311yescharacteristic
89C13×C4⋊C4C2311yescharacteristic
90C13×C4⋊C4C2311yescharacteristic
91C13×C4⋊C4C2311yescharacteristic
92C13×C22⋊C4—21no—
93C13×C22⋊C4—21no—
94C42×C13—21no—
95C22⋊Dic13—21no—
96C22⋊Dic13—21no—
97#6104—41no—
98#6104—41no—
99#6103—21no—
100#6103—21no—
101#6103—21no—
102#6103—21no—
103#6103—21no—
104C4⋊Dic13—21no—
105C4⋊Dic13C2311yescharacteristic
106#6101—21no—
107#6101—21no—
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110#6095—41no—
111#6095—41no—
112#6094—41no—
113C8×D13—41no—
114#3198—131nomaximal, Sylow
115C23×C13—21no—
116C23×C13C2×D411yescharacteristic
117C22×D13—21no—
118C22×D13—21no—
119C22×D13—42no—
120C22×D13—81no—
121C22×D13—81no—
122C22×D13C2×D411yescharacteristic
123C22×D13C2×D411yescharacteristic
124D4×C13—21no—
125D4×C13—21no—
126D4×C13—81no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13C2×D411yescharacteristic
133C2×C4×C13C2411yescharacteristic
134C22⋊D13—41no—
135C22⋊D13—41no—
136C22⋊D13—42no—
137C22⋊D13—81no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—42no—
141C2×Dic13C2×D411yescharacteristic
142C2×Dic13C2×D411yescharacteristic
143D52—21no—
144D52—21no—
145D52—21no—
146D52—21no—
147D52—41no—
148D52—42no—
149D52—81no—
150D52—81no—
151D52—81no—
152D52—81no—
153C4×D13—21no—
154C4×D13—21no—
155C4×D13—21no—
156C4×D13—21no—
157C4×D13—81no—
158Dic26—21no—
159Dic26—21no—
160Dic26—41no—
161C8×C13—21no—
162C8×C13—21no—
163#1055—21no—
164#1055—21no—
165#537—131no—
166#535—131no—
167#485—131no—
168#482D1311yescharacteristic, complemented
169#481—131no—
170#480—131no—
171#469—131no—
172#468—131no—
173#466—131no—
174#465—131no—
175#450—131no—
176#449—131no—
177#449—131no—
178#447—131no—
179#408—131no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—41no—
186C22×C13C22×D411yescharacteristic
187C2×D13—21no—
188C2×D13—21no—
189C2×D13—21no—
190C2×D13—21no—
191C2×D13—21no—
192C2×D13—21no—
193C2×D13—41no—
194C2×D13—41no—
195C2×D13—41no—
196C2×D13—41no—
197C2×D13—41no—
198C2×D13—41no—
199C2×D13—84no—
200C4×C13—21no—
201C4×C13—41no—
202C4×C13—41no—
203C4×C13—41no—
204C4×C13H(5,𝔽2)11yescharacteristic
205C4×C13H(5,𝔽2)11yescharacteristic
206Dic13—21no—
207Dic13—21no—
208Dic13—41no—
209Dic13—41no—
210C2×#41—131no—
211C2×#41—131no—
212C22×D4—131no—
213C2×SD16—131no—
214C2×SD16—131no—
215C2×D8—131no—
216C2×D8—131no—
217C2×M16—131no—
218C22×C8—131no—
219#127—261no—
220#124—261no—
221C22⋊Q8—131no—
222C22⋊Q8—131no—
223C22⋊Q8—261no—
224#121—131no—
225#121—131no—
226#121—131no—
227#121—131no—
228#121—131no—
229#121—261no—
230#121—261no—
231#121—261no—
232#121C2×D1311yescharacteristic
233#120—261no—
234#120—261no—
235#117C2×D1311yescharacteristic
236C2×C4⋊C4—131no—
237#107—131no—
238#107C2×D1311yescharacteristic, complemented
239#106—131no—
240#106C2×D1311yescharacteristic, complemented
241#103—131no—
242#103—131no—
243#102—131no—
244#102—131no—
245#102—131no—
246#102—131no—
247#102C2×D1311yescharacteristic, complemented
248#102C2×D1311yescharacteristic, complemented
249C22⋊C8—131no—
250C22⋊C8—131no—
251C22⋊C8—131no—
252C22⋊C8C2×D1311yescharacteristic
253C2×C13—41no—
254C2×C13—81no—
255C2×C13#53411yescharacteristic
256C2×C13#57611yescharacteristic
257C2×C13#57711yescharacteristic
258D13—41no—
259D13—41no—
260D13—81no—
261D13—81no—
262C24—261no—
263#41—521no—
264#41—521no—
265#41—521no—
266#41—521no—
267C2×Q8—131no—
268C2×Q8—131no—
269C2×D4—21no—
270C2×D4—131no—
271C2×D4—131no—
272C2×D4—131no—
273C2×D4—131no—
274C2×D4—131no—
275C2×D4—261no—
276C2×D4—261no—
277C2×D4—261no—
278C2×D4—261no—
279C2×D4—261no—
280C2×D4—261no—
281C2×D4—261no—
282C2×D4—521no—
283C2×D4—521no—
284C2×D4C22×D1311yescharacteristic
285C22×C4—131no—
286C22×C4—131no—
287C22×C4—261no—
288C22×C4—261no—
289C22×C4C22×D1311yescharacteristic
290SD16—521no—
291SD16—521no—
292D8—521no—
293D8—521no—
294M16—521no—
295C2×C8—131no—
296C2×C8—131no—
297C2×C8—521no—
298C2×C8C22×D1311yescharacteristic
299C2×C8C22×D1311yescharacteristic
300C4⋊C4—131no—
301C4⋊C4—261no—
302C4⋊C4—261no—
303C4⋊C4—261no—
304C4⋊C4C22×D1311yescharacteristic
305C4⋊C4C22×D1311yescharacteristic
306C4⋊C4C22×D1311yescharacteristic
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—261no—
310C22⋊C4—261no—
311C22⋊C4—261no—
312C22⋊C4—261no—
313C22⋊C4—261no—
314C22⋊C4—261no—
315C22⋊C4—261no—
316C42—21no—
317C13#319811yescharacteristic, complemented, Sylow
318C23—21no—
319C23—131no—
320C23—131no—
321C23—261no—
322C23—261no—
323C23—522no—
324C23—1041no—
325C23—1041no—
326C23D4×D1311yescharacteristic
327Q8—261no—
328Q8—261no—
329Q8—521no—
330D4—21no—
331D4—21no—
332D4—81no—
333D4—261no—
334D4—261no—
335D4—261no—
336D4—261no—
337D4—521no—
338D4—522no—
339D4—521no—
340D4—521no—
341D4—522no—
342D4—1041no—
343D4—1041no—
344D4—1041no—
345D4—1041no—
346D4—1041no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—131no—
353C2×C4—131no—
354C2×C4—261no—
355C2×C4—261no—
356C2×C4—261no—
357C2×C4—261no—
358C2×C4—261no—
359C2×C4—261no—
360C2×C4—522no—
361C2×C4—1041no—
362C2×C4D4×D1311yescharacteristic
363C2×C4C23×D1311yescharacteristic
364C8—21no—
365C8—21no—
366C8—261no—
367C8—261no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—261no—
375C22—261no—
376C22—261no—
377C22—261no—
378C22—261no—
379C22—261no—
380C22—521no—
381C22—521no—
382C22—521no—
383C22—521no—
384C22—521no—
385C22—521no—
386C22—1044no—
387C22C2×D4×D1311yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—261no—
393C4—261no—
394C4—521no—
395C4—521no—
396C4#8825611yescharacteristic
397C4#8825611yescharacteristic
398C2—41no—
399C2—81no—
400C2—521no—
401C2—521no—
402C2—1041no—
403C2—1041no—
404C2#1171935811yescharacteristic
405C2#1171947511yescharacteristic
406C2#1171947911yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#482C2
socleC22×C13C22×D4
hypercenter#482D13
hypocenterC13#3198
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #11719313C2semidirect
2. #11719230C2semidirect
3. C13×#482C2semidirect
4. #11718697C2semidirect
5. #11718657C2semidirect
6. #11718547C2semidirect
7. #11718543C2semidirect
8. #11718525C2semidirect
9. #11718524C2semidirect
10. #11718443C2semidirect
11. #11718442C2semidirect
12. #11718442C2semidirect
13. #11718436C2semidirect
14. #11718392C2semidirect
15. #11718388C2semidirect
16. C2×#6129C22semidirect
23. #88192C22semidirect
29. C2×#6094C22semidirect
30. C2×C8×D13C22semidirect
31. #88151C22semidirect
36. C4⋊C4×D13C22semidirect
43. C13×#107C22semidirect
44. C13×#106C22semidirect
45. C13×#102C22semidirect
46. C13×#102C22semidirect
51. #88060C22semidirect
52. #88060C22semidirect
53. #88050C22semidirect
54. #88050C22semidirect
57. #88048C22semidirect
58. #88047C22semidirect
168. #482D13semidirect
238. #107C2×D13semidirect
240. #106C2×D13semidirect
247. #102C2×D13semidirect
248. #102C2×D13semidirect
317. C13#3198semidirect

Maximal subgroups

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

subgroupindex
#117193132
#117192302
C13×#4822
#117186972
#117186572
#117185472
#117185432
#117185252
#117185242
#117184432
#117184422
#117184362
#117183922
#117183882
#319813