Finite Group Databasebeta

← #13125648

Subgroups — #13125648

Order 1664.

466 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#11719533C211yesmaximal, characteristic, complemented
2D13×#121C211yesmaximal, characteristic, complemented
3C13×#449C211yesmaximal, characteristic, complemented
4#11718899C211yesmaximal, characteristic, complemented
5#11718835C211yesmaximal, characteristic, complemented
6#11718830C211yesmaximal, characteristic, complemented
7#11718820C211yesmaximal, characteristic, complemented
8#11718817C211yesmaximal, characteristic, complemented
9#11718696C211yesmaximal, characteristic, complemented
10#11718473C211yesmaximal, characteristic, complemented
11#11718466C211yesmaximal, characteristic, complemented
12#11718443C211yesmaximal, characteristic, complemented
13#11718435C211yesmaximal, characteristic, complemented
14#11718398C211yesmaximal, characteristic, complemented
15#11718387C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic, complemented
17C2×D4×D13—21no—
18C2×D4×D13C2211yescharacteristic
19C22×C4×D13C2211yescharacteristic
20C2×C13×SD16C2211yescharacteristic, complemented
21C2×C13×D8C2211yescharacteristic, complemented
22C13×#121C2211yescharacteristic
23#88200C2211yescharacteristic
24#88200C2211yescharacteristic, complemented
25C2×#6106C2211yescharacteristic, complemented
26#88193—21no—
27#88192C2211yescharacteristic
28#88192C2211yescharacteristic
29#88192C2211yescharacteristic, complemented
30#88191—21no—
31#88189—21no—
32C2×#6104C2211yescharacteristic, complemented
33#88184C2211yescharacteristic
34C4×C22⋊D13—21no—
35C4×C22⋊D13—21no—
36#88180C2211yescharacteristic, complemented
37C2×#6094C2211yescharacteristic, complemented
38C2×#6094C2211yescharacteristic, complemented
39#88149C2211yescharacteristic
40C4⋊C4×D13C2211yescharacteristic
41#88138—21no—
42C22⋊C4×D13—21no—
43C13×#103C2211yescharacteristic, complemented
44C13×#102C2211yescharacteristic, complemented
45C13×C22⋊C8C2211yescharacteristic, complemented
46#88075C2211yescharacteristic, complemented
47#88072C2211yescharacteristic, complemented
48#88072C2211yescharacteristic, complemented
49#88072C2211yescharacteristic, complemented
50C22⋊#1055C2211yescharacteristic, complemented
51#88061C2211yescharacteristic, complemented
52#88061C2211yescharacteristic, complemented
53#88060C2211yescharacteristic
54#88060C2211yescharacteristic
55#88058C2211yescharacteristic, complemented
56#88057C2211yescharacteristic, complemented
57#88048C2211yescharacteristic, complemented
58#88047C2211yescharacteristic, complemented
59C23×D13—21no—
60C23×D13D411yescharacteristic
61C13×#41—41no—
62C13×#41—41no—
63C2×Q8×C13C2311yescharacteristic
64C2×D4×C13—21no—
65C2×D4×C13—21no—
66C2×D4×C13C2311yescharacteristic
67C2×D4×C13C2311yescharacteristic
68C22×C4×C13—21no—
69C22×C4×C13C2311yescharacteristic
70C2×C22⋊D13—21no—
71C2×C22⋊D13—21no—
72C2×C22⋊D13—21no—
73C2×C22⋊D13—21no—
74C2×C22⋊D13—21no—
75C22×Dic13D411yescharacteristic
76D4×D13—41no—
77D4×D13—41no—
78D4×D13—44no—
79C2×D52—21no—
80C2×D52C2311yescharacteristic
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—
89C13×D8—41no—
90C2×C8×C13C2311yescharacteristic
91C2×C8×C13C2311yescharacteristic
92C13×C4⋊C4C2311yescharacteristic
93C13×C22⋊C4—21no—
94C22⋊Dic13—21no—
95C22⋊Dic13—21no—
96C22⋊Dic13—21no—
97C22⋊Dic13—21no—
98#6106—41no—
99#6104—41no—
100#6103—21no—
101#6103—21no—
102#6103—21no—
103#6103—21no—
104C4⋊Dic13C2311yescharacteristic
105C4⋊Dic13C2311yescharacteristic
106C4⋊Dic13C2311yescharacteristic
107#6101—21no—
108#6101—21no—
109#6101—21no—
110C4×Dic13—21no—
111C2×#1055C2311yescharacteristic
112C2×#1055C2311yescharacteristic
113#6094—41no—
114#6094—41no—
115#3194—131nomaximal, Sylow
116C23×C13—21no—
117C23×C13—21no—
118C23×C13C2×D411yescharacteristic
119C22×D13—22no—
120C22×D13—21no—
121C22×D13—41no—
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—21no—
133D4×C13—21no—
134D4×C13—42no—
135D4×C13—42no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—42no—
141C2×C4×C13C2×D411yescharacteristic
142C2×C4×C13C2411yescharacteristic
143C22⋊D13—42no—
144C22⋊D13—42no—
145C22⋊D13—42no—
146C22⋊D13—42no—
147C22⋊D13—42no—
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—41no—
152C2×Dic13C2×D411yescharacteristic
153C2×Dic13C2×D411yescharacteristic
154D52—21no—
155D52—21no—
156D52—42no—
157C4×D13—21no—
158C4×D13—21no—
159C4×D13—21no—
160C4×D13—21no—
161C4×D13—41no—
162C4×D13—41no—
163C4×D13—42no—
164C8×C13—21no—
165C8×C13—21no—
166#1055—21no—
167#1055—21no—
168#525—131no—
169C2×#121—131no—
170#483—131no—
171#482—131no—
172#482—131no—
173#480—131no—
174#469—131no—
175#469—131no—
176#468—131no—
177#468—131no—
178#450—131no—
179#449—131no—
180#449D1311yescharacteristic, complemented
181#447—131no—
182#407—131no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—41no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—41no—
191C22×C13—41no—
192C22×C13C22×D411yescharacteristic
193C2×D13—21no—
194C2×D13—21no—
195C2×D13—21no—
196C2×D13—21no—
197C2×D13—21no—
198C2×D13—44no—
199C2×D13—41no—
200C2×D13—41no—
201C2×D13—41no—
202C2×D13—84no—
203C2×D13AGL(1,ℤ/8)12yes—
204C4×C13—21no—
205C4×C13—41no—
206C4×C13—41no—
207C4×C13H(5,𝔽2)11yescharacteristic
208C4×C13H(5,𝔽2)11yescharacteristic
209Dic13—21no—
210Dic13—21no—
211Dic13—41no—
212Dic13—41no—
213Dic13—41no—
214C2×#41C2×D1311yescharacteristic, complemented
215C22×D4—131no—
216C22×D4—261no—
217C23×C4—131no—
218C2×SD16—131no—
219C2×SD16C2×D1311yescharacteristic, complemented
220C2×D8—131no—
221C2×D8C2×D1311yescharacteristic, complemented
222C2×M16—131no—
223C2×M16—131no—
224#123—261no—
225C22⋊Q8—131no—
226C22⋊Q8—131no—
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#106—131no—
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⋊C8C2×D1311yescharacteristic, complemented
257C2×C13—41no—
258C2×C13—81no—
259C2×C13—81no—
260C2×C13#53411yescharacteristic
261C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
262C2×C13#57511yescharacteristic
263D13—22no—
264D13—41no—
265D13—81no—
266C24—131no—
267C24—261no—
268#41—41no—
269#41—41no—
270C2×Q8C22×D1311yescharacteristic
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—131no—
274C2×D4—261no—
275C2×D4—261no—
276C2×D4—261no—
277C2×D4—261no—
278C2×D4—261no—
279C2×D4—261no—
280C2×D4—521no—
281C2×D4—521no—
282C2×D4—524no—
283C2×D4C22×D1311yescharacteristic
284C2×D4C22×D1311yescharacteristic
285C22×C4—21no—
286C22×C4—131no—
287C22×C4—131no—
288C22×C4—131no—
289C22×C4—131no—
290C22×C4—131no—
291C22×C4—261no—
292C22×C4—521no—
293C22×C4—521no—
294C22×C4C22×D1311yescharacteristic
295SD16—41no—
296SD16—521no—
297D8—41no—
298D8—521no—
299M16—521no—
300M16—521no—
301C2×C8—131no—
302C2×C8—131no—
303C2×C8C22×D1311yescharacteristic
304C2×C8C22×D1311yescharacteristic
305C4⋊C4—131no—
306C4⋊C4—131no—
307C4⋊C4—131no—
308C4⋊C4—261no—
309C4⋊C4—261no—
310C4⋊C4—261no—
311C4⋊C4C22×D1311yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—261no—
314C22⋊C4—261no—
315C22⋊C4—261no—
316C22⋊C4—261no—
317C22⋊C4—261no—
318C22⋊C4—261no—
319C22⋊C4—261no—
320C22⋊C4—261no—
321C42—261no—
322C13#319411yescharacteristic, complemented, Sylow
323C23—21no—
324C23—21no—
325C23—131no—
326C23—131no—
327C23—262no—
328C23—261no—
329C23—521no—
330C23—521no—
331C23—522no—
332C23—522no—
333C23—522no—
334C23D4×D1311yescharacteristic
335Q8—21no—
336Q8—21no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—42no—
343D4—261no—
344D4—261no—
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—42no—
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—261no—
365C2×C4—521no—
366C2×C4—521no—
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—21no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—132no—
385C22—261no—
386C22—261no—
387C22—261no—
388C22—261no—
389C22—261no—
390C22—524no—
391C22—521no—
392C22—521no—
393C22—521no—
394C22—1044no—
395C22C2×D4×D1311yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—261no—
400C4—261no—
401C4—521no—
402C4—521no—
403C4—521no—
404C4#8825111yescharacteristic
405C4#8825111yescharacteristic
406C2—41no—
407C2—81no—
408C2—81no—
409C2—262no—
410C2—521no—
411C2—1041no—
412C2#1171929411yescharacteristic
413C2#1171947311yescharacteristic
414C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#449C2
socleC22×C13C22×D4
hypercenter#449D13
hypocenterC13#3194
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #11719533C2semidirect
2. D13×#121C2semidirect
3. C13×#449C2semidirect
4. #11718899C2semidirect
5. #11718835C2semidirect
6. #11718830C2semidirect
7. #11718820C2semidirect
8. #11718817C2semidirect
9. #11718696C2semidirect
10. #11718473C2semidirect
11. #11718466C2semidirect
12. #11718443C2semidirect
13. #11718435C2semidirect
14. #11718398C2semidirect
15. #11718387C2semidirect
16. C2×C13×#41C22semidirect
20. C2×C13×SD16C22semidirect
21. C2×C13×D8C22semidirect
24. #88200C22semidirect
25. C2×#6106C22semidirect
29. #88192C22semidirect
32. C2×#6104C22semidirect
36. #88180C22semidirect
37. C2×#6094C22semidirect
38. C2×#6094C22semidirect
43. C13×#103C22semidirect
44. C13×#102C22semidirect
45. C13×C22⋊C8C22semidirect
46. #88075C22semidirect
47. #88072C22semidirect
48. #88072C22semidirect
49. #88072C22semidirect
50. C22⋊#1055C22semidirect
51. #88061C22semidirect
52. #88061C22semidirect
55. #88058C22semidirect
56. #88057C22semidirect
57. #88048C22semidirect
58. #88047C22semidirect
180. #449D13semidirect
214. C2×#41C2×D13semidirect
219. C2×SD16C2×D13semidirect
221. C2×D8C2×D13semidirect
246. #103C2×D13semidirect
252. #102C2×D13semidirect
256. C22⋊C8C2×D13semidirect
322. C13#3194semidirect

Maximal subgroups

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

subgroupindex
#117195332
D13×#1212
C13×#4492
#117188992
#117188352
#117188302
#117188202
#117188172
#117186962
#117184732
#117184662
#117184432
#117184352
#117183982
#117183872
#319413