Finite Group Databasebeta

← #13123667

Subgroups — #13123667

Order 1664.

506 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88168C211yesmaximal, characteristic
2#11719279C211yesmaximal, characteristic, complemented
3#11719250C211yesmaximal, characteristic, complemented
4C13×#440C211yesmaximal, characteristic, complemented
5SD16×Dic13C211yesmaximal, characteristic, complemented
6C4×#6106C211yesmaximal, characteristic, complemented
7C4×#6104C211yesmaximal, characteristic, complemented
8#11718542C211yesmaximal, characteristic, complemented
9#11718533C211yesmaximal, characteristic, complemented
10#11718478C211yesmaximal, characteristic, complemented
11#11718465C211yesmaximal, characteristic, complemented
12#11718446C211yesmaximal, characteristic, complemented
13D13×#102C211yesmaximal, characteristic, complemented
14#11718372C211yesmaximal, characteristic, complemented
15#11718369C211yesmaximal, characteristic, complemented
16C2×#6131C2211yescharacteristic
17C2×D4×D13C2211yescharacteristic
18C2×C13×SD16C2211yescharacteristic
19C4×Q8×C13C2211yescharacteristic, complemented
20C4×D4×C13C2211yescharacteristic
21Q8×Dic13C2211yescharacteristic, complemented
22C2×#6106C2211yescharacteristic
23D4×Dic13C2211yescharacteristic
24C2×#6104C2211yescharacteristic
25C4×C22⋊D13—21no—
26C2×#6103—21no—
27#88168C418yescomplemented
28C2×D104C2211yescharacteristic
29C2×#6094C2211yescharacteristic
30C2×C8×D13C2211yescharacteristic
31#88147—21no—
32#88147C2211yescharacteristic
33#88147C2211yescharacteristic, complemented
34#88146C2211yescharacteristic
35C4⋊C4×D13—21no—
36C4⋊C4×D13C2211yescharacteristic
37#88135—21no—
38C22⋊C4×D13—21no—
39C4×D52—21no—
40C4×D52C2211yescharacteristic
41C4×D52C2211yescharacteristic, complemented
42#88126—21no—
43#88126C2211yescharacteristic
44C13×#107C2211yescharacteristic, complemented
45C13×#103C2211yescharacteristic, complemented
46C13×#102C2211yescharacteristic
47C13×#97C2211yescharacteristic, complemented
48#88075C2211yescharacteristic, complemented
49#88072C2211yescharacteristic
50#88061C2211yescharacteristic
51#88061C2211yescharacteristic, complemented
52#88057C2211yescharacteristic, complemented
53#88055C2211yescharacteristic, complemented
54C8×Dic13C2211yescharacteristic, complemented
55#88049C2211yescharacteristic
56#88049C2211yescharacteristic, complemented
57#88048C2211yescharacteristic, complemented
58#88047C2211yescharacteristic, complemented
59C4×#1055C2211yescharacteristic, complemented
60C23×D13—21no—
61C2×Q8×C13C2311yescharacteristic
62C2×D4×C13C2311yescharacteristic
63C22×C4×C13—21no—
64C2×C22⋊D13—21no—
65C22×Dic13—21no—
66#6131—22no—
67#6131C2×C414yescomplemented
68D4×D13—22no—
69D4×D13C2×C414yescomplemented
70C2×D52—21no—
71C2×D52C2311yescharacteristic
72C2×D52C2311yescharacteristic
73C2×C4×D13—21no—
74C2×C4×D13—21no—
75C2×C4×D13—21no—
76C2×C4×D13—21no—
77C2×C4×D13—21no—
78C2×C4×D13—21no—
79C2×C4×D13C2311yescharacteristic
80C13×SD16C2×C414yescomplemented
81C2×C8×C13C2311yescharacteristic
82C2×C8×C13C2311yescharacteristic
83C13×C4⋊C4—21no—
84C13×C4⋊C4C2311yescharacteristic
85C13×C4⋊C4C2311yescharacteristic
86C13×C22⋊C4—21no—
87C42×C13—21no—
88C42×C13C2311yescharacteristic
89C22⋊Dic13—21no—
90#6106C2×C414yescomplemented
91#6104C2×C414yescomplemented
92#6103—21no—
93#6103—21no—
94#6103—21no—
95#6103—21no—
96#6103—21no—
97#6103D411yescharacteristic
98#6103D411yescharacteristic
99C4⋊Dic13—21no—
100C4⋊Dic13C2311yescharacteristic
101C4⋊Dic13C2311yescharacteristic
102#6101—21no—
103#6101D411yescharacteristic
104#6101D411yescharacteristic
105C4×Dic13—21no—
106C4×Dic13—21no—
107C4×Dic13C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110D104C2×C414yescomplemented
111#6094C2×C414yescomplemented
112C8×D13—22no—
113#2946—131nomaximal, Sylow
114C23×C13—21no—
115C22×D13—21no—
116C22×D13—21no—
117C22×D13—24no—
118C22×D13—81no—
119C22×D13—81no—
120C22×D13C2×D411yescharacteristic
121Q8×C13—21no—
122Q8×C13C22×C412yes—
123D4×C13—21no—
124D4×C13C22×C412yes—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—81no—
129C2×C4×C13C2×D411yescharacteristic
130C2×C4×C13C2×D411yescharacteristic
131C2×C4×C13C2411yescharacteristic
132C22⋊D13—24no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—81no—
136C2×Dic13C2×D411yescharacteristic
137C2×Dic13C2×D411yescharacteristic
138C2×Dic13C2×D411yescharacteristic
139D52—24no—
140D52—21no—
141D52—21no—
142D52C22×C412yes—
143D52C22×C412yes—
144C4×D13—24no—
145C4×D13—81no—
146C4×D13—81no—
147C4×D13—81no—
148C4×D13—81no—
149C4×D13—81no—
150C4×D13C22×C412yes—
151C4×D13#4112yes—
152C8×C13—21no—
153C8×C13C22×C412yes—
154#1055—21no—
155#1055C22×C412yes—
156C2×AGL(1,ℤ/8)—131no—
157#520—131no—
158#518—131no—
159#442—131no—
160#442—131no—
161#440—131no—
162#440D1311yescharacteristic, complemented
163C4×SD16—131no—
164C4×SD16—131no—
165C4×D8—131no—
166C4×D8—131no—
167#428—131no—
168#416—131no—
169C2×#102—131no—
170#405—131no—
171C22×C13—22no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13C22×D411yescharacteristic
175C2×D13—21no—
176C2×D13—21no—
177C2×D13—22no—
178C2×D13—22no—
179C2×D13—41no—
180C2×D13—41no—
181C2×D13—41no—
182C2×D13—41no—
183C2×D13—84no—
184C2×D13C4×D412yes—
185C4×C13—22no—
186C4×C13—21no—
187C4×C13—21no—
188C4×C13—41no—
189C4×C13—41no—
190C4×C13C23×C411yescharacteristic
191C4×C13C2×#4111yescharacteristic
192Dic13—21no—
193Dic13—21no—
194Dic13—41no—
195Dic13—41no—
196Dic13C4×D412yes—
197C2×#41—131no—
198C22×D4—131no—
199AGL(1,ℤ/8)—138no—
200C2×SD16—131no—
201C2×SD16C2×D1311yescharacteristic
202C2×D8—131no—
203C2×D8—131no—
204C2×M16—131no—
205C22×C8—131no—
206C4×Q8—131no—
207C4×Q8C2×D1311yescharacteristic, complemented
208C4×D4—131no—
209C4×D4—131no—
210C4×D4—131no—
211C4×D4—131no—
212C4×D4—131no—
213C4×D4—261no—
214C4×D4—261no—
215C4×D4—261no—
216C4×D4—261no—
217C4×D4C2×D1311yescharacteristic
218#117—131no—
219#117—131no—
220#117—261no—
221C2×C4⋊C4—131no—
222C2×C4⋊C4—261no—
223C2×C22⋊C4—261no—
224C2×C22⋊C4—261no—
225#107—131no—
226#107C2×D1311yescharacteristic, complemented
227#106—131no—
228#106—131no—
229#103—131no—
230#103C2×D1311yescharacteristic, complemented
231#102—131no—
232#102—131no—
233#102—131no—
234#102—131no—
235#102—131no—
236#102C2×D1311yescharacteristic
237#97—131no—
238#97C2×D1311yescharacteristic, complemented
239C4×C8—131no—
240C4×C8—131no—
241C2×C13—42no—
242C2×C13C2×C4×D411yescharacteristic
243C2×C13#57611yescharacteristic
244C2×C13#57711yescharacteristic
245D13—22no—
246D13—42no—
247D13—42no—
248C24—261no—
249#41—134no—
250#41—262no—
251C2×Q8C22×D1311yescharacteristic
252C2×D4—134no—
253C2×D4—131no—
254C2×D4—131no—
255C2×D4—261no—
256C2×D4—262no—
257C2×D4—261no—
258C2×D4C22×D1311yescharacteristic
259C22×C4—21no—
260C22×C4—131no—
261C22×C4—261no—
262C22×C4—261no—
263C22×C4—261no—
264C22×C4—261no—
265C22×C4—261no—
266C22×C4—261no—
267C22×C4—261no—
268SD16—134no—
269SD16C4×D1314yescomplemented
270D8—134no—
271D8—134no—
272M16—134no—
273C2×C8—131no—
274C2×C8—131no—
275C2×C8—262no—
276C2×C8C22×D1311yescharacteristic
277C2×C8C22×D1311yescharacteristic
278C4⋊C4—21no—
279C4⋊C4—131no—
280C4⋊C4—131no—
281C4⋊C4—131no—
282C4⋊C4—131no—
283C4⋊C4—261no—
284C4⋊C4—261no—
285C4⋊C4C22×D1311yescharacteristic
286C4⋊C4C22×D1311yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—131no—
289C22⋊C4—131no—
290C22⋊C4—261no—
291C22⋊C4—261no—
292C22⋊C4—261no—
293C22⋊C4—261no—
294C22⋊C4—261no—
295C22⋊C4—261no—
296C42—21no—
297C42—131no—
298C42—261no—
299C42—261no—
300C42C22×D1311yescharacteristic
301C13#294611yescharacteristic, complemented, Sylow
302C23—21no—
303C23—131no—
304C23—264no—
305C23—261no—
306C23—261no—
307C23—1041no—
308C23—1041no—
309Q8—21no—
310Q8C2×C4×D1312yes—
311D4—21no—
312D4—132no—
313D4—132no—
314D4—264no—
315D4—264no—
316D4—261no—
317D4—261no—
318D4C2×C4×D1312yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—81no—
323C2×C4—131no—
324C2×C4—132no—
325C2×C4—132no—
326C2×C4—131no—
327C2×C4—131no—
328C2×C4—264no—
329C2×C4—261no—
330C2×C4—261no—
331C2×C4—1041no—
332C2×C4—1041no—
333C2×C4—1041no—
334C2×C4—1041no—
335C2×C4—1041no—
336C2×C4—1041no—
337C2×C4D4×D1311yescharacteristic
338C2×C4D4×D1311yescharacteristic
339C2×C4C23×D1311yescharacteristic
340C8—21no—
341C8—132no—
342C8—261no—
343C8C2×C4×D1312yes—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—132no—
348C22—261no—
349C22—261no—
350C22—262no—
351C22—262no—
352C22—521no—
353C22—521no—
354C22—521no—
355C22—521no—
356C22—1044no—
357C22C2×D4×D1311yescharacteristic
358C4—21no—
359C4—21no—
360C4—22no—
361C4—41no—
362C4—41no—
363C4—132no—
364C4—261no—
365C4—261no—
366C4—521no—
367C4—521no—
368C4C22×C4×D1311yescharacteristic
369C4#41×D1311yescharacteristic
370C2—42no—
371C2—262no—
372C2—522no—
373C2—522no—
374C2C4×D4×D1311yescharacteristic
375C2#1171947911yescharacteristic
376C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutatorC4×C13C23×C4
FrattiniC2×C4C23×D13
FittingC13×#440C2
socleC22×C13C22×D4
prime radicalC2×#88168C2
cosocleC2×C4×C13C24
hypercenter#440D13
hypocenterC13#2946
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. #11719279C2semidirect
3. #11719250C2semidirect
4. C13×#440C2semidirect
5. SD16×Dic13C2semidirect
6. C4×#6106C2semidirect
7. C4×#6104C2semidirect
8. #11718542C2semidirect
9. #11718533C2semidirect
10. #11718478C2semidirect
11. #11718465C2semidirect
12. #11718446C2semidirect
13. D13×#102C2semidirect
14. #11718372C2semidirect
15. #11718369C2semidirect
19. C4×Q8×C13C22semidirect
21. Q8×Dic13C22semidirect
27. #88168C4semidirect
33. #88147C22semidirect
41. C4×D52C22semidirect
44. C13×#107C22semidirect
45. C13×#103C22semidirect
47. C13×#97C22semidirect
48. #88075C22semidirect
51. #88061C22semidirect
52. #88057C22semidirect
53. #88055C22semidirect
54. C8×Dic13C22semidirect
56. #88049C22semidirect
57. #88048C22semidirect
58. #88047C22semidirect
59. C4×#1055C22semidirect
67. #6131C2×C4semidirect
69. D4×D13C2×C4semidirect
80. C13×SD16C2×C4semidirect
90. #6106C2×C4semidirect
91. #6104C2×C4semidirect
110. D104C2×C4semidirect
111. #6094C2×C4semidirect
162. #440D13semidirect
207. C4×Q8C2×D13semidirect
226. #107C2×D13semidirect
230. #103C2×D13semidirect
238. #97C2×D13semidirect
269. SD16C4×D13semidirect
301. C13#2946semidirect

Maximal subgroups

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

subgroupindex
C2×#881682
#117192792
#117192502
C13×#4402
SD16×Dic132
C4×#61062
C4×#61042
#117185422
#117185332
#117184782
#117184652
#117184462
D13×#1022
#117183722
#117183692
#294613