Finite Group Databasebeta

← #13125602

Subgroups — #13125602

Order 1664.

472 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719332C211yesmaximal, characteristic, complemented
2D13×#121C211yesmaximal, characteristic, complemented
3C13×#465C211yesmaximal, characteristic, complemented
4#11718833C211yesmaximal, characteristic, complemented
5#11718830C211yesmaximal, characteristic, complemented
6#11718776C211yesmaximal, characteristic, complemented
7C2×#88060C211yesmaximal, characteristic, complemented
8#11718709C211yesmaximal, characteristic, complemented
9#11718699C211yesmaximal, characteristic, complemented
10#11718527C211yesmaximal, characteristic, complemented
11#11718524C211yesmaximal, characteristic, complemented
12#11718472C211yesmaximal, characteristic, complemented
13#11718470C211yesmaximal, characteristic, complemented
14#11718445C211yesmaximal, characteristic, complemented
15#11718434C211yesmaximal, characteristic, complemented
16C2×#6131C2211yescharacteristic, complemented
17C2×D4×D13—21no—
18C2×D4×D13C2211yescharacteristic
19C22×C4×D13C2211yescharacteristic
20C2×C13×SD16C2211yescharacteristic, complemented
21C22×C8×C13C2211yescharacteristic, complemented
22C13×C22⋊Q8C2211yescharacteristic, complemented
23C13×#121C2211yescharacteristic
24#88200C2211yescharacteristic
25C2×#6106C2211yescharacteristic, complemented
26#88193—21no—
27#88192C2211yescharacteristic
28C2×#6104C2211yescharacteristic, complemented
29#88184C2211yescharacteristic
30#88184C2211yescharacteristic, complemented
31C22×#1055C2211yescharacteristic, complemented
32C2×D104C2211yescharacteristic, complemented
33#88149C2211yescharacteristic
34#88149C2211yescharacteristic
35#88148—21no—
36#88147—21no—
37#88146C2211yescharacteristic, complemented
38C4⋊C4×D13C2211yescharacteristic
39#88138—21no—
40#88136—21no—
41#88135—21no—
42C22⋊C4×D13—21no—
43C13×#106C2211yescharacteristic, complemented
44C13×#103C2211yescharacteristic, complemented
45C13×#102C2211yescharacteristic, complemented
46#88075C2211yescharacteristic, complemented
47#88072C2211yescharacteristic, complemented
48#88061C2211yescharacteristic, complemented
49#88061C2211yescharacteristic, complemented
50#88060C2211yescharacteristic
51#88060C2211yescharacteristic
52#88060C2211yescharacteristic, complemented
53#88060C2211yescharacteristic, complemented
54#88058C2211yescharacteristic, complemented
55#88049C2211yescharacteristic, complemented
56#88049C2211yescharacteristic, complemented
57#88048C2211yescharacteristic, complemented
58#88047C2211yescharacteristic, complemented
59C23×D13—21no—
60C23×D13D411yescharacteristic
61C2×Q8×C13C2311yescharacteristic
62C2×D4×C13—21no—
63C2×D4×C13C2311yescharacteristic
64C22×C4×C13C2311yescharacteristic
65C2×C22⋊D13—21no—
66C2×C22⋊D13—21no—
67C2×C22⋊D13—21no—
68C2×C22⋊D13—21no—
69C22×Dic13D411yescharacteristic
70#6131—41no—
71#6131—41no—
72D4×D13—41no—
73D4×D13—41no—
74D4×D13—44no—
75C2×D52—21no—
76C2×D52—21no—
77C2×D52—21no—
78C2×D52C2311yescharacteristic
79C2×D52C2311yescharacteristic
80C2×C4×D13—21no—
81C2×C4×D13—21no—
82C2×C4×D13—41no—
83C2×C4×D13—41no—
84C2×C4×D13D411yescharacteristic
85C2×C4×D13D411yescharacteristic
86C2×C4×D13C2311yescharacteristic
87C2×C4×D13C2311yescharacteristic
88C13×SD16—41no—
89C2×C8×C13—41no—
90C2×C8×C13C2311yescharacteristic
91C2×C8×C13C2311yescharacteristic
92C13×C4⋊C4—21no—
93C13×C4⋊C4C2311yescharacteristic
94C13×C4⋊C4C2311yescharacteristic
95C13×C22⋊C4—21no—
96C13×C22⋊C4—21no—
97C22⋊Dic13—21no—
98#6106—41no—
99#6104—41no—
100#6103—21no—
101#6103—21no—
102#6103—21no—
103#6103—21no—
104#6103—21no—
105#6103—21no—
106C4⋊Dic13C2311yescharacteristic
107C4⋊Dic13C2311yescharacteristic
108#6101—21no—
109#6101—21no—
110C4×Dic13—21no—
111C2×#1055—41no—
112C2×#1055C2311yescharacteristic
113C2×#1055C2311yescharacteristic
114D104—41no—
115#3188—131nomaximal, Sylow
116C23×C13—21no—
117C23×C13C2×D411yescharacteristic
118C22×D13—22no—
119C22×D13—22no—
120C22×D13—21no—
121C22×D13—21no—
122C22×D13—41no—
123C22×D13—42no—
124C22×D13—42no—
125C22×D13—42no—
126C22×D13C2×D411yescharacteristic
127C22×D13C2×D411yescharacteristic
128Q8×C13—21no—
129Q8×C13—21no—
130D4×C13—21no—
131D4×C13—21no—
132D4×C13—42no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13C2×D411yescharacteristic
139C2×C4×C13C2411yescharacteristic
140C22⋊D13—42no—
141C22⋊D13—42no—
142C22⋊D13—42no—
143C22⋊D13—42no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—41no—
147C2×Dic13C2×D411yescharacteristic
148C2×Dic13C2×D411yescharacteristic
149D52—21no—
150D52—21no—
151D52—21no—
152D52—21no—
153D52—42no—
154D52—42no—
155D52—42no—
156C4×D13—21no—
157C4×D13—21no—
158C4×D13—21no—
159C4×D13—21no—
160C4×D13—41no—
161C4×D13—41no—
162C4×D13—42no—
163C4×D13—42no—
164C8×C13—21no—
165C8×C13—21no—
166#1055—21no—
167#1055—21no—
168#525—131no—
169C2×#121—131no—
170#484—131no—
171#482—131no—
172#482—131no—
173#481—131no—
174#466—131no—
175#466—131no—
176#465—131no—
177#465D1311yescharacteristic, complemented
178#450—131no—
179#449—131no—
180#449—131no—
181#447—131no—
182C2×C22⋊C8—131no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—41no—
186C22×C13—41no—
187C22×C13—41no—
188C22×C13AGL(1,ℤ/8)12yes—
189C22×C13C22×D411yescharacteristic
190C2×D13—21no—
191C2×D13—21no—
192C2×D13—21no—
193C2×D13—21no—
194C2×D13—21no—
195C2×D13—44no—
196C2×D13—41no—
197C2×D13—41no—
198C2×D13—41no—
199C2×D13—41no—
200C2×D13—41no—
201C2×D13—41no—
202C2×D13—84no—
203C2×D13#13512yes—
204C4×C13—21no—
205C4×C13—41no—
206C4×C13—41no—
207C4×C13—41no—
208C4×C13H(5,𝔽2)11yescharacteristic
209C4×C13H(5,𝔽2)11yescharacteristic
210Dic13—21no—
211Dic13—21no—
212Dic13—41no—
213Dic13—41no—
214C2×#41—131no—
215C22×D4—131no—
216C22×D4—261no—
217C23×C4—131no—
218C2×SD16—131no—
219C2×SD16C2×D1311yescharacteristic, complemented
220C2×D8—131no—
221C2×D8—131no—
222C22×C8—131no—
223C22×C8C2×D1311yescharacteristic, complemented
224#123—261no—
225C22⋊Q8—131no—
226C22⋊Q8C2×D1311yescharacteristic, complemented
227#121—131no—
228#121—131no—
229#121—131no—
230#121—131no—
231#121—131no—
232#121—261no—
233#121—261no—
234#121C2×D1311yescharacteristic
235#120—261no—
236C4×D4—261no—
237C4×D4—261no—
238#117—131no—
239C2×C4⋊C4—131no—
240C2×C22⋊C4—261no—
241#107—131no—
242#107—131no—
243#106—131no—
244#106C2×D1311yescharacteristic, complemented
245#103—131no—
246#103C2×D1311yescharacteristic, complemented
247#102—131no—
248#102—131no—
249#102—131no—
250#102—131no—
251#102—131no—
252#102C2×D1311yescharacteristic, complemented
253C22⋊C8—131no—
254C22⋊C8—131no—
255C22⋊C8—131no—
256C22⋊C8—131no—
257C2×C13—22no—
258C2×C13—81no—
259C2×C13#53411yescharacteristic
260C2×C13C2×#13511yescharacteristic
261C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
262D13—22no—
263D13—41no—
264D13—81no—
265D13—81no—
266C24—131no—
267C24—261no—
268#41—521no—
269#41—521no—
270C2×Q8C22×D1311yescharacteristic
271C2×D4—21no—
272C2×D4—131no—
273C2×D4—131no—
274C2×D4—261no—
275C2×D4—261no—
276C2×D4—261no—
277C2×D4—261no—
278C2×D4—261no—
279C2×D4—261no—
280C2×D4—261no—
281C2×D4—521no—
282C2×D4—521no—
283C2×D4—524no—
284C2×D4C22×D1311yescharacteristic
285C22×C4—131no—
286C22×C4—131no—
287C22×C4—131no—
288C22×C4—131no—
289C22×C4—131no—
290C22×C4—261no—
291C22×C4—261no—
292C22×C4—521no—
293C22×C4—521no—
294C22×C4C22×D1311yescharacteristic
295SD16—41no—
296SD16—521no—
297D8—521no—
298D8—521no—
299C2×C8—41no—
300C2×C8—131no—
301C2×C8—131no—
302C2×C8—521no—
303C2×C8C22×D1311yescharacteristic
304C2×C8C22×D1311yescharacteristic
305C4⋊C4—21no—
306C4⋊C4—131no—
307C4⋊C4—131no—
308C4⋊C4—261no—
309C4⋊C4—261no—
310C4⋊C4C22×D1311yescharacteristic
311C4⋊C4C22×D1311yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—261no—
315C22⋊C4—261no—
316C22⋊C4—261no—
317C22⋊C4—261no—
318C22⋊C4—261no—
319C22⋊C4—261no—
320C22⋊C4—261no—
321C42—261no—
322C13#318811yescharacteristic, complemented, Sylow
323C23—21no—
324C23—131no—
325C23—131no—
326C23—262no—
327C23—262no—
328C23—261no—
329C23—261no—
330C23—521no—
331C23—522no—
332C23—522no—
333C23—522no—
334C23D4×D1311yescharacteristic
335Q8—21no—
336Q8—21no—
337D4—21no—
338D4—21no—
339D4—42no—
340D4—261no—
341D4—261no—
342D4—261no—
343D4—261no—
344D4—522no—
345D4—522no—
346D4—522no—
347D4—522no—
348D4—522no—
349D4—522no—
350D4—522no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—131no—
357C2×C4—131no—
358C2×C4—261no—
359C2×C4—261no—
360C2×C4—261no—
361C2×C4—261no—
362C2×C4—261no—
363C2×C4—261no—
364C2×C4—521no—
365C2×C4—521no—
366C2×C4—522no—
367C2×C4—522no—
368C2×C4—521no—
369C2×C4D4×D1311yescharacteristic
370C2×C4C23×D1311yescharacteristic
371C8—21no—
372C8—21no—
373C8—261no—
374C8—261no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—132no—
381C22—261no—
382C22—261no—
383C22—261no—
384C22—261no—
385C22—261no—
386C22—524no—
387C22—521no—
388C22—521no—
389C22—521no—
390C22—521no—
391C22—521no—
392C22—521no—
393C22—1044no—
394C22#8816812yes—
395C22C2×D4×D1311yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—41no—
400C4—261no—
401C4—261no—
402C4—521no—
403C4—521no—
404C4#8825111yescharacteristic
405C4#8825611yescharacteristic
406C2—22no—
407C2—81no—
408C2—262no—
409C2—521no—
410C2—1041no—
411C2—1041no—
412C2#1171931011yescharacteristic
413C2C2×#8816811yescharacteristic
414C2D13×#13511yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#465C2
socleC22×C13C22×D4
hypercenter#465D13
hypocenterC13#3188
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #11719332C2semidirect
2. D13×#121C2semidirect
3. C13×#465C2semidirect
4. #11718833C2semidirect
5. #11718830C2semidirect
6. #11718776C2semidirect
7. C2×#88060C2semidirect
8. #11718709C2semidirect
9. #11718699C2semidirect
10. #11718527C2semidirect
11. #11718524C2semidirect
12. #11718472C2semidirect
13. #11718470C2semidirect
14. #11718445C2semidirect
15. #11718434C2semidirect
16. C2×#6131C22semidirect
20. C2×C13×SD16C22semidirect
21. C22×C8×C13C22semidirect
22. C13×C22⋊Q8C22semidirect
25. C2×#6106C22semidirect
28. C2×#6104C22semidirect
30. #88184C22semidirect
31. C22×#1055C22semidirect
32. C2×D104C22semidirect
37. #88146C22semidirect
43. C13×#106C22semidirect
44. C13×#103C22semidirect
45. C13×#102C22semidirect
46. #88075C22semidirect
47. #88072C22semidirect
48. #88061C22semidirect
49. #88061C22semidirect
52. #88060C22semidirect
53. #88060C22semidirect
54. #88058C22semidirect
55. #88049C22semidirect
56. #88049C22semidirect
57. #88048C22semidirect
58. #88047C22semidirect
177. #465D13semidirect
219. C2×SD16C2×D13semidirect
223. C22×C8C2×D13semidirect
226. C22⋊Q8C2×D13semidirect
244. #106C2×D13semidirect
246. #103C2×D13semidirect
252. #102C2×D13semidirect
322. C13#3188semidirect

Maximal subgroups

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

subgroupindex
#117193322
D13×#1212
C13×#4652
#117188332
#117188302
#117187762
C2×#880602
#117187092
#117186992
#117185272
#117185242
#117184722
#117184702
#117184452
#117184342
#318813