Finite Group Databasebeta

← #13126436

Subgroups — #13126436

Order 1664.

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

normal subgroups only

This group has 546 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
1C13×#547C211yesmaximal, characteristic, complemented
2C2×#88203C212yesmaximal, complemented
3D4×D52C211yesmaximal, characteristic, complemented
4#11718899C212yesmaximal, complemented
5#11718746C211yesmaximal, characteristic, complemented
6#11718744C211yesmaximal, characteristic, complemented
7#11718710C212yesmaximal, complemented
8#11718707C212yesmaximal, complemented
9#11718676C211yesmaximal, characteristic, complemented
10C4×#6104C211yesmaximal, characteristic, complemented
11#11718673C211yesmaximal, characteristic, complemented
12C2×C13×#41C2212yescomplemented
13C2×D4×D13—21no—
14C22×D52C2212yes—
15C13×C4⋊Q8C2211yescharacteristic, complemented
16C13×#123—22no—
17C13×C22⋊Q8C2212yescomplemented
18C13×#121—21no—
19C4×D4×C13C2211yescharacteristic
20C4×D4×C13C2211yescharacteristic, complemented
21C2×C13×C4⋊C4—21no—
22#88203—28no—
23C2×#6106C2212yes—
24C2×#6106C2212yescomplemented
25C2×#6106C2212yescomplemented
26C2×#6104C2211yescharacteristic
27C2×#6104C2212yescomplemented
28#88184C2212yes—
29C2×#6099C2212yescomplemented
30#88149—21no—
31#88136—22no—
32#88128C2211yescharacteristic
33C4×D52C2211yescharacteristic
34#88075C2212yescomplemented
35#88072C2211yescharacteristic, complemented
36C22⋊#1055C2212yescomplemented
37#88049C2211yescharacteristic
38#88049C2212yescomplemented
39#88047C2211yescharacteristic, complemented
40C4⋊#1055C2211yescharacteristic, complemented
41C4×#1055C2211yescharacteristic, complemented
42C23×D13—22no—
43C13×#41—24no—
44C13×#41—42no—
45C2×Q8×C13C2312yes—
46C2×D4×C13—22no—
47C2×D4×C13D411yescharacteristic
48C2×D4×C13C2311yescharacteristic
49C22×C4×C13—21no—
50C22×C4×C13—22no—
51C22×C4×C13C2312yes—
52C2×C22⋊D13—22no—
53D4×D13—44no—
54C2×D52—24no—
55C2×D52—21no—
56C2×D52—22no—
57C2×D52—21no—
58C2×D52—42no—
59C2×D52C2312yes—
60C2×D52C2311yescharacteristic
61C2×C4×D13—21no—
62C13×C4⋊C4—21no—
63C13×C4⋊C4—22no—
64C13×C4⋊C4—21no—
65C13×C4⋊C4D411yescharacteristic
66C13×C4⋊C4C2311yescharacteristic
67C13×C22⋊C4—22no—
68C13×C22⋊C4—21no—
69C13×C22⋊C4D412yes—
70C42×C13C2311yescharacteristic
71#6106—24no—
72#6106—24no—
73#6106—42no—
74#6104—24no—
75#6104D414yescomplemented
76#6103—21no—
77#6103—22no—
78C4⋊Dic13C2311yescharacteristic
79#6099—24no—
80C2×#1055C2311yescharacteristic
81C2×#1055C2312yes—
82C2×#1055C2311yescharacteristic
83#3272—131nomaximal, Sylow
84C23×C13—21no—
85C23×C13C2×D412yes—
86C22×D13—21no—
87C22×D13—22no—
88C22×D13—44no—
89C22×D13—44no—
90C22×D13—82no—
91Q8×C13—22no—
92Q8×C13—22no—
93D4×C13—22no—
94D4×C13—21no—
95D4×C13—44no—
96D4×C13C2×D412yescomplemented
97C2×C4×C13—22no—
98C2×C4×C13—22no—
99C2×C4×C13—21no—
100C2×C4×C13—22no—
101C2×C4×C13—44no—
102C2×C4×C13—42no—
103C2×C4×C13C2×D411yescharacteristic
104C2×C4×C13C2×D412yes—
105C2×C4×C13C2×D411yescharacteristic
106C2×C4×C13C2411yescharacteristic
107C22⋊D13—44no—
108C2×Dic13—21no—
109D52—22no—
110D52—21no—
111D52—22no—
112D52—44no—
113D52—42no—
114D52—81no—
115D52C2×D412yes—
116C4×D13—42no—
117#1055—22no—
118#1055—21no—
119#1055C2×D412yescomplemented
120C2×AGL(1,ℤ/8)—132no—
121#547D1311yescharacteristic, complemented
122D42—131no—
123#492—131no—
124#468—132no—
125#461—131no—
126#459—131no—
127#450—132no—
128#449—132no—
129C4×D8—131no—
130#436—131no—
131C22×C13—22no—
132C22×C13—22no—
133C22×C13—22no—
134C22×C13—22no—
135C22×C13—41no—
136C22×C13—41no—
137C22×C13C22×D411yescharacteristic
138C2×D13—22no—
139C2×D13—41no—
140C2×D13—41no—
141C2×D13—42no—
142C2×D13—42no—
143C2×D13—42no—
144C2×D13—88no—
145C4×C13—22no—
146C4×C13—21no—
147C4×C13—42no—
148C4×C13—41no—
149C4×C13AGL(1,ℤ/8)12yescomplemented
150C4×C13C22×D411yescharacteristic
151C4×C13H(5,𝔽2)11yescharacteristic
152Dic13—41no—
153C2×#41C2×D1312yescomplemented
154C22×D4—132no—
155C22×D4—261no—
156AGL(1,ℤ/8)—268no—
157C2×SD16—132no—
158C2×SD16—132no—
159C2×SD16—132no—
160C2×D8—131no—
161C2×D8—132no—
162C2×M16—132no—
163C4⋊Q8C2×D1311yescharacteristic, complemented
164#127—131no—
165#123—22no—
166C22⋊Q8C2×D1312yescomplemented
167#121—21no—
168#121—132no—
169#121—261no—
170#120—262no—
171C4×D4—131no—
172C4×D4C2×D1311yescharacteristic
173C4×D4C2×D1311yescharacteristic, complemented
174C2×C4⋊C4—21no—
175#107—131no—
176C4⋊C8—131no—
177#103—132no—
178#102—131no—
179#102—131no—
180#102—132no—
181C22⋊C8—132no—
182C4×C8—131no—
183C2×C13—42no—
184C2×C13—42no—
185C2×C13D4211yescharacteristic
186C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
187C2×C13#57711yescharacteristic
188D13—42no—
189D13—82no—
190C24—262no—
191#41—24no—
192#41—42no—
193C2×Q8C22×D1312yes—
194C2×D4—22no—
195C2×D4—131no—
196C2×D4—132no—
197C2×D4—264no—
198C2×D4—262no—
199C2×D4—262no—
200C2×D4—261no—
201C2×D4—261no—
202C2×D4—522no—
203C2×D4—524no—
204C2×D4C22⋊D1311yescharacteristic
205C2×D4C22×D1311yescharacteristic
206C22×C4—21no—
207C22×C4—22no—
208C22×C4—261no—
209C22×C4C22×D1312yes—
210SD16—264no—
211SD16—264no—
212SD16—522no—
213D8—134no—
214D8—264no—
215M16—264no—
216C2×C8—131no—
217C2×C8—131no—
218C2×C8—132no—
219C4⋊C4—21no—
220C4⋊C4—22no—
221C4⋊C4—21no—
222C4⋊C4—131no—
223C4⋊C4C22⋊D1311yescharacteristic
224C4⋊C4C22×D1311yescharacteristic
225C22⋊C4—22no—
226C22⋊C4—21no—
227C22⋊C4—261no—
228C22⋊C4—262no—
229C22⋊C4C22⋊D1312yes—
230C42C22×D1311yescharacteristic
231C13#327211yescharacteristic, complemented, Sylow
232C23—21no—
233C23—261no—
234C23—262no—
235C23—524no—
236C23—524no—
237C23—1042no—
238C23C2×C22⋊D1312yes—
239Q8—22no—
240Q8—22no—
241D4—22no—
242D4—21no—
243D4—44no—
244D4—132no—
245D4—262no—
246D4—261no—
247D4—262no—
248D4—524no—
249D4—524no—
250D4—522no—
251D4—1041no—
252D4D4×D1312yescomplemented
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—44no—
258C2×C4—42no—
259C2×C4—261no—
260C2×C4—522no—
261C2×C4C2×C22⋊D1311yescharacteristic
262C2×C4C2×C22⋊D1312yes—
263C2×C4C2×C22⋊D1311yescharacteristic
264C2×C4C23×D1311yescharacteristic
265C8—132no—
266C8—262no—
267C8—261no—
268C22—22no—
269C22—22no—
270C22—22no—
271C22—22no—
272C22—41no—
273C22—41no—
274C22—262no—
275C22—521no—
276C22—521no—
277C22—522no—
278C22—522no—
279C22—522no—
280C22—1048no—
281C22C22×C22⋊D1311yescharacteristic
282C4—22no—
283C4—21no—
284C4—42no—
285C4—41no—
286C4—521no—
287C4#8820312yescomplemented
288C4C2×D4×D1311yescharacteristic
289C4#8825111yescharacteristic
290C2—42no—
291C2—42no—
292C2—522no—
293C2—1042no—
294C2D4×C22⋊D1311yescharacteristic
295C2C2×#8820311yescharacteristic
296C2#1171954211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#547C2
socleC22×C13C22×D4
hypercenter#547D13
hypocenterC13#3272
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C13×#547C2semidirect
2. C2×#88203C2semidirect
3. D4×D52C2semidirect
4. #11718899C2semidirect
5. #11718746C2semidirect
6. #11718744C2semidirect
7. #11718710C2semidirect
8. #11718707C2semidirect
9. #11718676C2semidirect
10. C4×#6104C2semidirect
11. #11718673C2semidirect
12. C2×C13×#41C22semidirect
15. C13×C4⋊Q8C22semidirect
17. C13×C22⋊Q8C22semidirect
20. C4×D4×C13C22semidirect
24. C2×#6106C22semidirect
25. C2×#6106C22semidirect
27. C2×#6104C22semidirect
29. C2×#6099C22semidirect
34. #88075C22semidirect
35. #88072C22semidirect
36. C22⋊#1055C22semidirect
38. #88049C22semidirect
39. #88047C22semidirect
40. C4⋊#1055C22semidirect
41. C4×#1055C22semidirect
75. #6104D4semidirect
96. D4×C13C2×D4semidirect
119. #1055C2×D4semidirect
121. #547D13semidirect
149. C4×C13AGL(1,ℤ/8)semidirect
153. C2×#41C2×D13semidirect
163. C4⋊Q8C2×D13semidirect
166. C22⋊Q8C2×D13semidirect
173. C4×D4C2×D13semidirect
231. C13#3272semidirect
252. D4D4×D13semidirect
287. C4#88203semidirect

Maximal subgroups

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

subgroupindex
C13×#5472
C2×#882032
D4×D522
#117188992
#117187462
#117187442
#117187102
#117187072
#117186762
C4×#61042
#117186732
#327213