Finite Group Databasebeta

← #13124512

Subgroups — #13124512

Order 1664.

504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#535C211yesmaximal, characteristic, complemented
2#11719538C211yesmaximal, characteristic, complemented
3C2×#88202C211yesmaximal, characteristic, complemented
4C2×#88186C211yesmaximal, characteristic, complemented
5C2×#88072C211yesmaximal, characteristic, complemented
6#11718703C212yesmaximal, complemented
7#11718702C212yesmaximal, complemented
8#11718700C212yesmaximal, complemented
9#11718699C212yesmaximal, complemented
10#11718663C211yesmaximal, characteristic, complemented
11#11718656C211yesmaximal, characteristic, complemented
12C2×C13×#41C2211yescharacteristic
13C22×D4×C13C2211yescharacteristic
14C2×#6127C2211yescharacteristic
15C13×#127—21no—
16C13×#124—21no—
17C13×#121C2212yes—
18C13×#121C2212yes—
19C13×#120—22no—
20C13×#117C2211yescharacteristic
21#88202—24no—
22#88200—21no—
23#88193—22no—
24#88192—21no—
25C2×#6105C2212yes—
26#88186—24no—
27C2×#6104C2212yes—
28#88184C2212yescomplemented
29C2×C4⋊Dic13C2211yescharacteristic
30#88178C2212yescomplemented
31C2×#6099C2211yescharacteristic
32C2×#6099C2212yescomplemented
33C22×#1055C2211yescharacteristic
34C22×#1055C2212yescomplemented
35#88072C2212yes—
36#88072C2212yes—
37#88050C2211yescharacteristic, complemented
38#88050C2211yescharacteristic, complemented
39#88049C2211yescharacteristic, complemented
40#88049C2211yescharacteristic, complemented
41#88048C2212yescomplemented
42#88047C2212yescomplemented
43C24×C13—21no—
44C13×#41—22no—
45C13×#41—22no—
46C2×Q8×C13D411yescharacteristic
47C2×D4×C13—22no—
48C2×D4×C13—22no—
49C2×D4×C13—22no—
50C2×D4×C13—21no—
51C2×D4×C13—22no—
52C2×D4×C13D411yescharacteristic
53C2×D4×C13D412yes—
54C2×D4×C13C2312yes—
55C22×C4×C13C2312yes—
56C22×C4×C13C2311yescharacteristic
57C2×C22⋊D13—21no—
58C2×C22⋊D13—22no—
59C22×Dic13—21no—
60#6127—22no—
61#6127—22no—
62C2×D52C2311yescharacteristic
63C2×C4×D13—21no—
64C2×Dic26C2311yescharacteristic
65C13×C4⋊C4C2311yescharacteristic
66C13×C4⋊C4C2311yescharacteristic
67C13×C22⋊C4—21no—
68C13×C22⋊C4—22no—
69C13×C22⋊C4—22no—
70C42×C13—21no—
71C22⋊Dic13—22no—
72#6105—24no—
73#6104—24no—
74#6103—22no—
75C4⋊Dic13—21no—
76C4⋊Dic13C2312yes—
77#6101—22no—
78#6099—24no—
79#6099D414yescomplemented
80C2×#1055—22no—
81C2×#1055—24no—
82C2×#1055C2311yescharacteristic
83C2×#1055C2311yescharacteristic
84C2×#1055C2312yes—
85#3062—131nomaximal, Sylow
86C23×C13—22no—
87C23×C13—42no—
88C23×C13—81no—
89C23×C13—81no—
90C23×C13C2×D412yes—
91C23×C13C2×D411yescharacteristic
92C22×D13—21no—
93Q8×C13—22no—
94D4×C13—24no—
95D4×C13—22no—
96D4×C13—22no—
97D4×C13—22no—
98D4×C13—42no—
99D4×C13—82no—
100D4×C13—82no—
101C2×C4×C13—22no—
102C2×C4×C13—22no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13C2×D412yes—
106C2×C4×C13C2×D411yescharacteristic
107C2×C4×C13C2×D412yes—
108C2×C4×C13#4112yes—
109C2×C4×C13C2411yescharacteristic
110C22⋊D13—42no—
111C22⋊D13—82no—
112C2×Dic13—21no—
113C2×Dic13—22no—
114C2×Dic13—81no—
115D52—21no—
116D52—21no—
117C4×D13—42no—
118Dic26—21no—
119Dic26—21no—
120#1055—21no—
121#1055—21no—
122#1055C2×D414yes—
123C2×AGL(1,ℤ/8)—131no—
124C2×#131—131no—
125#537—131no—
126#535D1311yescharacteristic, complemented
127#469—132no—
128#468—132no—
129#466—132no—
130#465—132no—
131#428—131no—
132#416—131no—
133C2×#102—131no—
134C22×C13—21no—
135C22×C13—21no—
136C22×C13—22no—
137C22×C13—22no—
138C22×C13—22no—
139C22×C13—42no—
140C22×C13—42no—
141C22×C13—42no—
142C22×C13—84no—
143C22×C13#12112yes—
144C22×C13C22×D411yescharacteristic
145C2×D13—41no—
146C2×D13—41no—
147C2×D13—41no—
148C4×C13—22no—
149C4×C13—41no—
150C4×C13—41no—
151C4×C13#12112yes—
152C4×C13C22×D411yescharacteristic
153C4×C13C2×#4111yescharacteristic
154Dic13—41no—
155Dic13—42no—
156C2×#41—131no—
157C2×#41C2×D1311yescharacteristic
158C22×D4C2×D1311yescharacteristic
159AGL(1,ℤ/8)—264no—
160C2×SD16—132no—
161C2×D8—132no—
162#131—264no—
163C2×M16—131no—
164C2×M16—132no—
165C22×C8—131no—
166C22×C8—132no—
167#127—21no—
168#124—21no—
169C22⋊Q8—132no—
170C22⋊Q8—261no—
171#121—132no—
172#121—261no—
173#121—262no—
174#121C2×D1312yes—
175#121C2×D1312yes—
176#120—22no—
177#117C2×D1311yescharacteristic
178C2×C4⋊C4—131no—
179#107—132no—
180#106—132no—
181#103—131no—
182#103—131no—
183#102—132no—
184#102—132no—
185#102—131no—
186#102—131no—
187C2×C13—22no—
188C2×C13—42no—
189C2×C13—82no—
190C2×C13C2×#12111yescharacteristic
191C2×C13#57611yescharacteristic
192C2×C13#57711yescharacteristic
193D13—81no—
194C24—21no—
195#41—22no—
196#41—22no—
197#41—262no—
198#41—262no—
199C2×Q8—131no—
200C2×Q8C22⋊D1311yescharacteristic
201C2×D4—22no—
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—22no—
205C2×D4—21no—
206C2×D4—131no—
207C2×D4—261no—
208C2×D4—262no—
209C2×D4C22⋊D1312yes—
210C2×D4C22⋊D1311yescharacteristic
211C2×D4C22×D1312yes—
212C22×C4—261no—
213C22×C4—261no—
214C22×C4C22×D1312yes—
215C22×C4C22×D1311yescharacteristic
216SD16—264no—
217D8—264no—
218M16—134no—
219M16—264no—
220C2×C8—132no—
221C2×C8—131no—
222C2×C8—131no—
223C2×C8—264no—
224C2×C8—262no—
225C4⋊C4—132no—
226C4⋊C4—261no—
227C4⋊C4—262no—
228C4⋊C4C22×D1311yescharacteristic
229C4⋊C4C22×D1311yescharacteristic
230C22⋊C4—21no—
231C22⋊C4—22no—
232C22⋊C4—22no—
233C22⋊C4—262no—
234C22⋊C4—262no—
235C42—21no—
236C13#306211yescharacteristic, complemented, Sylow
237C23—22no—
238C23—42no—
239C23—81no—
240C23—81no—
241C23—261no—
242C23C2×C22⋊D1312yes—
243C23C2×C22⋊D1311yescharacteristic
244Q8—22no—
245Q8—261no—
246Q8—261no—
247D4—24no—
248D4—22no—
249D4—22no—
250D4—22no—
251D4—42no—
252D4—82no—
253D4—82no—
254D4—261no—
255D4—261no—
256D4—522no—
257D4—1042no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—262no—
263C2×C4—261no—
264C2×C4—522no—
265C2×C4—1041no—
266C2×C4D4×D1312yes—
267C2×C4#612912yes—
268C2×C4C2×C22⋊D1312yes—
269C2×C4C2×C22⋊D1311yescharacteristic
270C2×C4C23×D1311yescharacteristic
271C8—134no—
272C8—261no—
273C8—261no—
274C22—21no—
275C22—21no—
276C22—22no—
277C22—22no—
278C22—22no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—84no—
283C22—521no—
284C22—521no—
285C22—521no—
286C22#8819312yes—
287C22C22×C22⋊D1311yescharacteristic
288C4—22no—
289C4—41no—
290C4—41no—
291C4—521no—
292C4—522no—
293C4#8819312yes—
294C4C2×D4×D1311yescharacteristic
295C4C2×#612911yescharacteristic
296C2—22no—
297C2—42no—
298C2—82no—
299C2—1041no—
300C2C2×#8819311yescharacteristic
301C2#1171954011yescharacteristic
302C2#1171954111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#535C2
socleC22×C13C22×D4
hypercenter#535D13
hypocenterC13#3062
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C13×#535C2semidirect
2. #11719538C2semidirect
3. C2×#88202C2semidirect
4. C2×#88186C2semidirect
5. C2×#88072C2semidirect
6. #11718703C2semidirect
7. #11718702C2semidirect
8. #11718700C2semidirect
9. #11718699C2semidirect
10. #11718663C2semidirect
11. #11718656C2semidirect
28. #88184C22semidirect
30. #88178C22semidirect
32. C2×#6099C22semidirect
34. C22×#1055C22semidirect
37. #88050C22semidirect
38. #88050C22semidirect
39. #88049C22semidirect
40. #88049C22semidirect
41. #88048C22semidirect
42. #88047C22semidirect
79. #6099D4semidirect
126. #535D13semidirect
236. C13#3062semidirect

Maximal subgroups

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

subgroupindex
C13×#5352
#117195382
C2×#882022
C2×#881862
C2×#880722
#117187032
#117187022
#117187002
#117186992
#117186632
#117186562
#306213