Finite Group Databasebeta

← #13126982

Subgroups — #13126982

Order 1664.

462 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719263C211yesmaximal, characteristic, complemented
2D4×D52C211yesmaximal, characteristic, complemented
3C13×#442C211yesmaximal, characteristic, complemented
4#11718817C211yesmaximal, characteristic, complemented
5#11718817C211yesmaximal, characteristic, complemented
6#11718676C211yesmaximal, characteristic, complemented
7#11718670C211yesmaximal, characteristic, complemented
8#11718527C211yesmaximal, characteristic, complemented
9#11718524C211yesmaximal, characteristic, complemented
10#11718443C211yesmaximal, characteristic, complemented
11#11718436C211yesmaximal, characteristic, complemented
12#11718431C211yesmaximal, characteristic, complemented
13D13×#102C211yesmaximal, characteristic, complemented
14#11718374C211yesmaximal, characteristic, complemented
15#11718367C211yesmaximal, characteristic, complemented
16C2×D4×D13C2211yescharacteristic
17C2×D4×D13C2211yescharacteristic
18C22×D52—21no—
19C2×C13×D8C2211yescharacteristic
20C4×D4×C13C2211yescharacteristic
21C4×D4×C13C2211yescharacteristic, complemented
22#88192C2211yescharacteristic, complemented
23#88192C2211yescharacteristic, complemented
24C2×#6104C2211yescharacteristic, complemented
25C2×#6104C2211yescharacteristic, complemented
26#88184—21no—
27#88183—21no—
28C4×C22⋊D13—21no—
29C2×#6094C2211yescharacteristic, complemented
30C2×C8×D13C2211yescharacteristic, complemented
31#88149C2211yescharacteristic
32#88149C2211yescharacteristic
33#88146C2211yescharacteristic, complemented
34C4⋊C4×D13C2211yescharacteristic, complemented
35#88138—21no—
36#88136—21no—
37#88136—21no—
38#88133—21no—
39#88128C2211yescharacteristic
40C4×D52C2211yescharacteristic
41#88124C2211yescharacteristic, complemented
42C13×#106C2211yescharacteristic, complemented
43C13×#102C2211yescharacteristic
44C13×#102C2211yescharacteristic, complemented
45C13×#97C2211yescharacteristic, complemented
46#88072C2211yescharacteristic
47#88072C2211yescharacteristic
48#88061C2211yescharacteristic, complemented
49#88061C2211yescharacteristic, complemented
50#88061C2211yescharacteristic, complemented
51#88061C2211yescharacteristic, complemented
52#88060C2211yescharacteristic, complemented
53#88060C2211yescharacteristic, complemented
54#88049C2211yescharacteristic, complemented
55#88049C2211yescharacteristic, complemented
56#88048C2211yescharacteristic, complemented
57#88047C2211yescharacteristic, complemented
58C4⋊#1055C2211yescharacteristic, complemented
59C23×D13—21no—
60C23×D13—21no—
61C2×D4×C13C2311yescharacteristic
62C2×D4×C13C2311yescharacteristic
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C2×C22⋊D13—21no—
66C2×C22⋊D13—21no—
67C2×C22⋊D13—21no—
68C2×C22⋊D13—21no—
69D4×D13—22no—
70D4×D13—22no—
71D4×D13—41no—
72D4×D13—41no—
73C2×D52—21no—
74C2×D52—21no—
75C2×D52—21no—
76C2×D52—21no—
77C2×D52—44no—
78C2×D52D411yescharacteristic
79C2×D52C2311yescharacteristic
80C2×D52C2311yescharacteristic
81C2×C4×D13—21no—
82C2×C4×D13C2311yescharacteristic
83C2×C4×D13C2311yescharacteristic
84C13×D8—22no—
85C2×C8×C13C2311yescharacteristic
86C2×C8×C13C2311yescharacteristic
87C13×C4⋊C4C2311yescharacteristic
88C13×C4⋊C4C2311yescharacteristic
89C13×C22⋊C4—21no—
90C13×C22⋊C4—21no—
91C42×C13C2311yescharacteristic
92C22⋊Dic13—21no—
93C22⋊Dic13—21no—
94#6104—41no—
95#6104—41no—
96#6103—21no—
97#6103—21no—
98#6103—21no—
99#6103D411yescharacteristic
100#6103D411yescharacteristic
101C4⋊Dic13D411yescharacteristic
102C4⋊Dic13C2311yescharacteristic
103C4⋊Dic13C2311yescharacteristic
104#6101—21no—
105#6101—21no—
106#6101—21no—
107C4×Dic13—21no—
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110#6094—41no—
111C8×D13—41no—
112#3318—131nomaximal, Sylow
113C23×C13—21no—
114C23×C13—21no—
115C22×D13—21no—
116C22×D13—21no—
117C22×D13—42no—
118C22×D13—42no—
119C22×D13—42no—
120C22×D13—42no—
121C22×D13—81no—
122C22×D13—81no—
123C22×D13C2×D411yescharacteristic
124C22×D13C2×D411yescharacteristic
125D4×C13—21no—
126D4×C13—21no—
127D4×C13—21no—
128D4×C13#4112yes—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—42no—
132C2×C4×C13—81no—
133C2×C4×C13C2×D411yescharacteristic
134C2×C4×C13C2×D411yescharacteristic
135C2×C4×C13C2411yescharacteristic
136C22⋊D13—42no—
137C22⋊D13—42no—
138C22⋊D13—42no—
139C22⋊D13—81no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13C2×D411yescharacteristic
143C2×Dic13C2×D411yescharacteristic
144D52—22no—
145D52—21no—
146D52—21no—
147D52—21no—
148D52—21no—
149D52—42no—
150D52—42no—
151D52—42no—
152D52—81no—
153C4×D13—21no—
154C4×D13—21no—
155C4×D13—21no—
156C4×D13—21no—
157C4×D13—81no—
158C8×C13—21no—
159C8×C13—21no—
160#1055—21no—
161#1055—21no—
162#553—131no—
163D42—131no—
164#490—131no—
165#482—131no—
166#481—131no—
167#478—131no—
168#469—131no—
169#466—131no—
170#459—131no—
171#447—131no—
172#447—131no—
173#442D1311yescharacteristic, complemented
174#435—131no—
175#418—131no—
176C2×#102—131no—
177C22×C13—22no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13C22×D411yescharacteristic
184C2×D13—21no—
185C2×D13—21no—
186C2×D13—21no—
187C2×D13—21no—
188C2×D13—21no—
189C2×D13—41no—
190C2×D13—41no—
191C2×D13—41no—
192C2×D13—41no—
193C2×D13—41no—
194C2×D13—41no—
195C2×D13—84no—
196C2×D13—84no—
197C2×D13AGL(1,ℤ/8)12yes—
198C4×C13—21no—
199C4×C13—21no—
200C4×C13—41no—
201C4×C13—41no—
202C4×C13C2×#4111yescharacteristic
203C4×C13H(5,𝔽2)11yescharacteristic
204Dic13—21no—
205Dic13—21no—
206Dic13—41no—
207Dic13—41no—
208C22×D4—131no—
209C22×D4—131no—
210C22×D4—261no—
211C2×D8—131no—
212C2×D8—131no—
213C2×D8C2×D1311yescharacteristic
214C2×M16—131no—
215C22×C8—131no—
216#127—131no—
217#126—261no—
218#125—131no—
219#123—261no—
220#121—131no—
221#121—131no—
222#121—131no—
223#121—131no—
224#121—261no—
225#121—261no—
226#120—261no—
227#120—261no—
228C4×D4—131no—
229C4×D4—261no—
230C4×D4C2×D1311yescharacteristic
231C4×D4C2×D1311yescharacteristic, complemented
232#117—131no—
233C2×C4⋊C4—131no—
234#107—131no—
235#106—131no—
236#106C2×D1311yescharacteristic, complemented
237C4⋊C8—131no—
238#102—131no—
239#102—131no—
240#102—131no—
241#102—131no—
242#102—131no—
243#102—131no—
244#102—131no—
245#102—131no—
246#102C2×D1311yescharacteristic
247#102C2×D1311yescharacteristic, complemented
248C22⋊C8—131no—
249C22⋊C8—131no—
250#97C2×D1311yescharacteristic, complemented
251C2×C13—42no—
252C2×C13—81no—
253C2×C13#54611yescharacteristic
254C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
255C2×C13#57611yescharacteristic
256D13—22no—
257D13—41no—
258D13—81no—
259D13—81no—
260C24—261no—
261C24—261no—
262C2×D4—131no—
263C2×D4—131no—
264C2×D4—131no—
265C2×D4—261no—
266C2×D4—261no—
267C2×D4—261no—
268C2×D4—261no—
269C2×D4—262no—
270C2×D4—262no—
271C2×D4—261no—
272C2×D4—261no—
273C2×D4—261no—
274C2×D4—261no—
275C2×D4—524no—
276C2×D4—521no—
277C2×D4—521no—
278C2×D4C22×D1311yescharacteristic
279C2×D4C22×D1311yescharacteristic
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—131no—
283C22×C4—131no—
284C22×C4—261no—
285D8—22no—
286D8—521no—
287D8—521no—
288M16—521no—
289C2×C8—131no—
290C2×C8—131no—
291C2×C8—521no—
292C2×C8C22×D1311yescharacteristic
293C2×C8C22×D1311yescharacteristic
294C4⋊C4—131no—
295C4⋊C4—131no—
296C4⋊C4—131no—
297C4⋊C4—261no—
298C4⋊C4—261no—
299C4⋊C4—261no—
300C4⋊C4C22×D1311yescharacteristic
301C4⋊C4C22×D1311yescharacteristic
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—131no—
305C22⋊C4—131no—
306C22⋊C4—261no—
307C22⋊C4—261no—
308C22⋊C4—261no—
309C22⋊C4—261no—
310C22⋊C4—261no—
311C42—261no—
312C42C22×D1311yescharacteristic
313C13#331811yescharacteristic, complemented, Sylow
314C23—21no—
315C23—21no—
316C23—131no—
317C23—131no—
318C23—261no—
319C23—261no—
320C23—522no—
321C23—522no—
322C23—522no—
323C23—522no—
324C23—1041no—
325C23—1041no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—262no—
330D4—261no—
331D4—261no—
332D4—261no—
333D4—261no—
334D4—522no—
335D4—522no—
336D4—522no—
337D4—522no—
338D4—522no—
339D4—522no—
340D4—1041no—
341D4—1041no—
342D4#612712yes—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—42no—
346C2×C4—81no—
347C2×C4—131no—
348C2×C4—131no—
349C2×C4—261no—
350C2×C4—261no—
351C2×C4—261no—
352C2×C4—261no—
353C2×C4—261no—
354C2×C4—261no—
355C2×C4—1041no—
356C2×C4D4×D1311yescharacteristic
357C2×C4D4×D1311yescharacteristic
358C2×C4C23×D1311yescharacteristic
359C8—21no—
360C8—21no—
361C8—261no—
362C8—261no—
363C22—22no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—132no—
370C22—261no—
371C22—261no—
372C22—261no—
373C22—261no—
374C22—261no—
375C22—521no—
376C22—521no—
377C22—521no—
378C22—521no—
379C22—521no—
380C22—521no—
381C22—1044no—
382C22—1044no—
383C22C2×D4×D1311yescharacteristic
384C4—21no—
385C4—21no—
386C4—41no—
387C4—41no—
388C4—261no—
389C4—261no—
390C4—521no—
391C4—521no—
392C4C2×#612711yescharacteristic
393C4#8825611yescharacteristic
394C2—42no—
395C2—81no—
396C2—262no—
397C2—521no—
398C2—1041no—
399C2—1041no—
400C2#1171925511yescharacteristic
401C2D13×AGL(1,ℤ/8)11yescharacteristic
402C2#1171947911yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#442C2
socleC22×C13C22×D4
hypercenter#442D13
hypocenterC13#3318
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #11719263C2semidirect
2. D4×D52C2semidirect
3. C13×#442C2semidirect
4. #11718817C2semidirect
5. #11718817C2semidirect
6. #11718676C2semidirect
7. #11718670C2semidirect
8. #11718527C2semidirect
9. #11718524C2semidirect
10. #11718443C2semidirect
11. #11718436C2semidirect
12. #11718431C2semidirect
13. D13×#102C2semidirect
14. #11718374C2semidirect
15. #11718367C2semidirect
21. C4×D4×C13C22semidirect
22. #88192C22semidirect
23. #88192C22semidirect
24. C2×#6104C22semidirect
25. C2×#6104C22semidirect
29. C2×#6094C22semidirect
30. C2×C8×D13C22semidirect
33. #88146C22semidirect
34. C4⋊C4×D13C22semidirect
41. #88124C22semidirect
42. C13×#106C22semidirect
44. C13×#102C22semidirect
45. C13×#97C22semidirect
48. #88061C22semidirect
49. #88061C22semidirect
50. #88061C22semidirect
51. #88061C22semidirect
52. #88060C22semidirect
53. #88060C22semidirect
54. #88049C22semidirect
55. #88049C22semidirect
56. #88048C22semidirect
57. #88047C22semidirect
58. C4⋊#1055C22semidirect
173. #442D13semidirect
231. C4×D4C2×D13semidirect
236. #106C2×D13semidirect
247. #102C2×D13semidirect
250. #97C2×D13semidirect
313. C13#3318semidirect

Maximal subgroups

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

subgroupindex
#117192632
D4×D522
C13×#4422
#117188172
#117186762
#117186702
#117185272
#117185242
#117184432
#117184362
#117184312
D13×#1022
#117183742
#117183672
#331813