Finite Group Databasebeta

← #13124313

Subgroups — #13124313

Order 1664.

584 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88168C212yesmaximal, complemented
2D13×#127C211yesmaximal, characteristic, complemented
3C4×#6131C211yesmaximal, characteristic, complemented
4C13×#460C211yesmaximal, characteristic, complemented
5#11718824C212yesmaximal, complemented
6#11718733C211yesmaximal, characteristic, complemented
7#11718688C211yesmaximal, characteristic, complemented
8#11718504C211yesmaximal, characteristic, complemented
9#11718498C211yesmaximal, characteristic, complemented
10#11718447C212yesmaximal, complemented
11#11718431C212yesmaximal, complemented
12C2×#6131C2211yescharacteristic
13C2×D4×D13—21no—
14C2×D4×D13—21no—
15C2×D4×D13C2212yes—
16C2×C13×SD16C2212yescomplemented
17C13×#127C2211yescharacteristic
18C4×Q8×C13C2211yescharacteristic, complemented
19Q8×Dic13C2211yescharacteristic, complemented
20C2×#6106C2212yescomplemented
21#88194—21no—
22#88194—21no—
23#88194C2212yes—
24C2×#6104C2212yescomplemented
25#88168—28no—
26C2×D104C2212yescomplemented
27C2×#6094C2212yes—
28#88147—21no—
29#88147C2211yescharacteristic, complemented
30#88146—21no—
31#88146C2211yescharacteristic
32#88128C2211yescharacteristic
33C4×D52—21no—
34C4×D52C2211yescharacteristic, complemented
35C42×D13—21no—
36C42×D13C2211yescharacteristic
37C13×C4⋊C8C2211yescharacteristic, complemented
38C13×#102C2212yescomplemented
39#88072C2212yescomplemented
40#88061C2212yescomplemented
41#88054C2212yescomplemented
42#88049C2212yescomplemented
43C4⋊#1055C2211yescharacteristic, complemented
44C23×D13—22no—
45C2×Q8×C13C2311yescharacteristic
46C2×D4×C13—21no—
47C2×D4×C13—21no—
48C2×D4×C13C2312yes—
49C2×C22⋊D13—22no—
50C2×C22⋊D13—22no—
51C2×C22⋊D13—22no—
52#6131—22no—
53#6131D414yescomplemented
54D4×D13—24no—
55D4×D13—24no—
56D4×D13—44no—
57D4×D13—44no—
58C2×D52—21no—
59C2×D52—21no—
60C2×D52—21no—
61C2×D52C2312yes—
62C2×D52C2311yescharacteristic
63C2×C4×D13—21no—
64C2×C4×D13—21no—
65C2×C4×D13—21no—
66C2×C4×D13D411yescharacteristic
67C2×C4×D13D411yescharacteristic
68C2×C4×D13C2311yescharacteristic
69C13×SD16—24no—
70C2×C8×C13C2312yes—
71C13×C4⋊C4—21no—
72C13×C4⋊C4C2311yescharacteristic
73C42×C13—21no—
74C42×C13C2311yescharacteristic
75#6106—24no—
76#6104—24no—
77#6103—21no—
78#6103—21no—
79#6103—21no—
80C4⋊Dic13—21no—
81C4⋊Dic13C2311yescharacteristic
82C4×Dic13—21no—
83C4×Dic13—21no—
84C4×Dic13D411yescharacteristic
85C4×Dic13D411yescharacteristic
86C4×Dic13C2311yescharacteristic
87C2×#1055C2312yes—
88D104—24no—
89#6094—24no—
90#3038—131nomaximal, Sylow
91C23×C13—22no—
92C22×D13—21no—
93C22×D13—22no—
94C22×D13—44no—
95C22×D13—44no—
96C22×D13—44no—
97C22×D13C2×D411yescharacteristic
98Q8×C13—21no—
99Q8×C13C2×D412yescomplemented
100D4×C13—22no—
101D4×C13—22no—
102D4×C13—42no—
103D4×C13—42no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13C2×D411yescharacteristic
107C2×C4×C13C2×D411yescharacteristic
108C2×C4×C13C2411yescharacteristic
109C22⋊D13—44no—
110C22⋊D13—44no—
111C22⋊D13—44no—
112C2×Dic13—21no—
113C2×Dic13C2×D411yescharacteristic
114C2×Dic13C2×D411yescharacteristic
115C2×Dic13C2×D411yescharacteristic
116D52—24no—
117D52—22no—
118D52—21no—
119D52—22no—
120D52—42no—
121D52—42no—
122D52C2×D412yescomplemented
123C4×D13—22no—
124C4×D13—24no—
125C4×D13—22no—
126C4×D13—42no—
127C4×D13—42no—
128C4×D13C2×D412yes—
129C4×D13#4112yes—
130C8×C13—22no—
131#1055—22no—
132C2×AGL(1,ℤ/8)—132no—
133C2×#127—131no—
134C4×#41—131no—
135#460—132no—
136#460—131no—
137#460D1311yescharacteristic, complemented
138#459—131no—
139#459—131no—
140#459—132no—
141#423—131no—
142#418—132no—
143C22×C13—42no—
144C22×C13—42no—
145C22×C13—42no—
146C22×C13C22×D411yescharacteristic
147C2×D13—21no—
148C2×D13—21no—
149C2×D13—22no—
150C2×D13—41no—
151C2×D13—41no—
152C2×D13—42no—
153C2×D13—42no—
154C2×D13—42no—
155C2×D13—88no—
156C2×D13#12112yes—
157C4×C13—22no—
158C4×C13—21no—
159C4×C13—41no—
160C4×C13AGL(1,ℤ/8)12yescomplemented
161C4×C13C22×D411yescharacteristic
162C4×C13C2×#4111yescharacteristic
163Dic13—21no—
164Dic13—41no—
165Dic13#12112yes—
166Dic13AGL(1,ℤ/8)12yescomplemented
167C2×#41—131no—
168C22×D4—132no—
169C22×D4—261no—
170C22×D4—261no—
171AGL(1,ℤ/8)—268no—
172C2×SD16—132no—
173C2×SD16C2×D1312yescomplemented
174C2×D8—132no—
175C2×D8—132no—
176C2×M16—132no—
177#127—132no—
178#127—131no—
179#127—261no—
180#127—261no—
181#127C2×D1311yescharacteristic
182C4×Q8—131no—
183C4×Q8C2×D1311yescharacteristic, complemented
184C4×D4—131no—
185C4×D4—131no—
186C4×D4—261no—
187C4×D4—261no—
188#117—131no—
189#117—261no—
190C2×C42—131no—
191C2×C42—261no—
192C4⋊C8—132no—
193C4⋊C8—131no—
194C4⋊C8C2×D1311yescharacteristic, complemented
195#102—132no—
196#102—132no—
197#102—132no—
198#102C2×D1312yescomplemented
199C2×C13—82no—
200C2×C13C2×#12111yescharacteristic
201C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
202C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
203D13—22no—
204D13—42no—
205D13—82no—
206C24—262no—
207#41—134no—
208#41—262no—
209C2×Q8C22×D1311yescharacteristic
210C2×D4—21no—
211C2×D4—21no—
212C2×D4—131no—
213C2×D4—132no—
214C2×D4—261no—
215C2×D4—264no—
216C2×D4—264no—
217C2×D4—262no—
218C2×D4—262no—
219C2×D4—262no—
220C2×D4—261no—
221C2×D4—261no—
222C2×D4—524no—
223C2×D4—524no—
224C2×D4C22×D1312yes—
225C22×C4—131no—
226C22×C4—131no—
227C22×C4—131no—
228C22×C4—261no—
229C22×C4—261no—
230C22×C4—261no—
231SD16—24no—
232SD16—264no—
233D8—264no—
234D8—264no—
235M16—264no—
236C2×C8—132no—
237C2×C8C22×D1312yes—
238C4⋊C4—21no—
239C4⋊C4—131no—
240C4⋊C4—261no—
241C4⋊C4C22×D1311yescharacteristic
242C22⋊C4—261no—
243C22⋊C4—261no—
244C22⋊C4—261no—
245C42—21no—
246C42—131no—
247C42—131no—
248C42—131no—
249C42—261no—
250C42—261no—
251C42C22×D1311yescharacteristic
252C13#303811yescharacteristic, complemented, Sylow
253C23—22no—
254C23—131no—
255C23—261no—
256C23—262no—
257C23—524no—
258C23—524no—
259C23—524no—
260Q8—21no—
261Q8D4×D1312yescomplemented
262D4—22no—
263D4—22no—
264D4—42no—
265D4—42no—
266D4—132no—
267D4—264no—
268D4—262no—
269D4—261no—
270D4—262no—
271D4—522no—
272D4—524no—
273D4—524no—
274D4—524no—
275D4—522no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—131no—
279C2×C4—131no—
280C2×C4—132no—
281C2×C4—132no—
282C2×C4—131no—
283C2×C4—262no—
284C2×C4—264no—
285C2×C4—262no—
286C2×C4—261no—
287C2×C4—522no—
288C2×C4—522no—
289C2×C4D4×D1311yescharacteristic
290C2×C4D4×D1311yescharacteristic
291C2×C4C23×D1311yescharacteristic
292C8—22no—
293C8—262no—
294C22—42no—
295C22—42no—
296C22—42no—
297C22—132no—
298C22—261no—
299C22—261no—
300C22—262no—
301C22—521no—
302C22—521no—
303C22—522no—
304C22—522no—
305C22—522no—
306C22—1048no—
307C22C2×D4×D1311yescharacteristic
308C4—21no—
309C4—22no—
310C4—41no—
311C4—132no—
312C4—132no—
313C4—261no—
314C4—521no—
315C4#8816812yescomplemented
316C4C2×D4×D1311yescharacteristic
317C4#41×D1311yescharacteristic
318C2—82no—
319C2—262no—
320C2—522no—
321C2—1042no—
322C2D13×#12111yescharacteristic
323C2C2×#8816811yescharacteristic
324C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#460C2
socleC22×C13C22×D4
hypercenter#460D13
hypocenterC13#3038
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. C2×#88168C2semidirect
2. D13×#127C2semidirect
3. C4×#6131C2semidirect
4. C13×#460C2semidirect
5. #11718824C2semidirect
6. #11718733C2semidirect
7. #11718688C2semidirect
8. #11718504C2semidirect
9. #11718498C2semidirect
10. #11718447C2semidirect
11. #11718431C2semidirect
16. C2×C13×SD16C22semidirect
18. C4×Q8×C13C22semidirect
19. Q8×Dic13C22semidirect
20. C2×#6106C22semidirect
24. C2×#6104C22semidirect
26. C2×D104C22semidirect
29. #88147C22semidirect
34. C4×D52C22semidirect
37. C13×C4⋊C8C22semidirect
38. C13×#102C22semidirect
39. #88072C22semidirect
40. #88061C22semidirect
41. #88054C22semidirect
42. #88049C22semidirect
43. C4⋊#1055C22semidirect
53. #6131D4semidirect
99. Q8×C13C2×D4semidirect
122. D52C2×D4semidirect
137. #460D13semidirect
160. C4×C13AGL(1,ℤ/8)semidirect
166. Dic13AGL(1,ℤ/8)semidirect
173. C2×SD16C2×D13semidirect
183. C4×Q8C2×D13semidirect
194. C4⋊C8C2×D13semidirect
198. #102C2×D13semidirect
252. C13#3038semidirect
261. Q8D4×D13semidirect
315. C4#88168semidirect

Maximal subgroups

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

subgroupindex
C2×#881682
D13×#1272
C4×#61312
C13×#4602
#117188242
#117187332
#117186882
#117185042
#117184982
#117184472
#117184312
#303813