Finite Group Databasebeta

← #13124523

Subgroups — #13124523

Order 1664.

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

normal subgroups only

This group has 472 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×#536C211yesmaximal, characteristic, complemented
2#11719538C211yesmaximal, characteristic
3C2×#88202C211yesmaximal, characteristic, complemented
4C2×#88196C211yesmaximal, characteristic, complemented
5C2×#88075C211yesmaximal, characteristic, complemented
6#11718713C212yesmaximal, complemented
7#11718712C212yesmaximal, complemented
8#11718710C212yesmaximal, complemented
9#11718709C212yesmaximal, complemented
10#11718663C211yesmaximal, characteristic, complemented
11#11718656C211yesmaximal, characteristic, complemented
12C2×C13×#41C2211yescharacteristic
13C22×Q8×C13C2211yescharacteristic
14C2×#6127C2211yescharacteristic
15C13×C4⋊Q8—21no—
16C13×#124—21no—
17C13×#123—22no—
18C13×C22⋊Q8C2212yes—
19C13×C22⋊Q8C2212yes—
20C13×#117C2211yescharacteristic
21#88202—24no—
22#88200—21no—
23C2×#6107C2212yes—
24#88196—24no—
25C2×#6106C2212yes—
26#88193—22no—
27#88192—21no—
28#88184C2212yes—
29C2×C4⋊Dic13C2211yescharacteristic
30#88178C2212yes—
31C2×#6099C2212yes—
32C2×#6099C2211yescharacteristic
33C22×#1055C2211yescharacteristic
34C22×#1055C2212yes—
35#88075C2212yes—
36#88075C2212yes—
37#88050C2211yescharacteristic
38#88050C2211yescharacteristic
39#88049C2211yescharacteristic
40#88049C2211yescharacteristic
41#88048C2212yes—
42#88047C2212yes—
43C13×#41—22no—
44C13×#41—22no—
45C2×Q8×C13—21no—
46C2×Q8×C13—22no—
47C2×Q8×C13—22no—
48C2×Q8×C13D411yescharacteristic
49C2×Q8×C13C2312yes—
50C2×D4×C13D411yescharacteristic
51C2×D4×C13D412yes—
52C22×C4×C13—21no—
53C22×C4×C13C2312yes—
54C22×C4×C13C2311yescharacteristic
55C2×C22⋊D13—21no—
56C2×C22⋊D13—22no—
57C22×Dic13—21no—
58#6127—22no—
59#6127—22no—
60C2×D52C2311yescharacteristic
61C2×C4×D13—21no—
62C2×Dic26C2311yescharacteristic
63C13×C4⋊C4—22no—
64C13×C4⋊C4—22no—
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#6107—24no—
73#6106—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#3063—131nomaximal, Sylow
86C23×C13C2×D412yes—
87C23×C13C2×D411yescharacteristic
88C22×D13—21no—
89Q8×C13—22no—
90Q8×C13—22no—
91Q8×C13—22no—
92Q8×C13—42no—
93D4×C13—24no—
94D4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—22no—
100C2×C4×C13—42no—
101C2×C4×C13C2×D412yes—
102C2×C4×C13C2×D411yescharacteristic
103C2×C4×C13C2×D412yes—
104C2×C4×C13#4112yes—
105C2×C4×C13C2411yescharacteristic
106C22⋊D13—42no—
107C22⋊D13—82no—
108C2×Dic13—21no—
109C2×Dic13—22no—
110C2×Dic13—81no—
111D52—21no—
112D52—21no—
113C4×D13—42no—
114Dic26—21no—
115Dic26—21no—
116#1055—21no—
117#1055—21no—
118#1055C2×D414yes—
119C2×#137—131no—
120C2×#131—131no—
121#537—131no—
122#536D1311yescharacteristic, complemented
123#470—132no—
124#468—132no—
125#467—132no—
126#465—132no—
127#428—131no—
128#416—131no—
129C2×#103—131no—
130C22×C13—21no—
131C22×C13—21no—
132C22×C13—22no—
133C22×C13—22no—
134C22×C13—22no—
135C22×C13#12112yes—
136C22×C13C22×D411yescharacteristic
137C2×D13—41no—
138C2×D13—41no—
139C2×D13—41no—
140C4×C13—22no—
141C4×C13—42no—
142C4×C13—41no—
143C4×C13—41no—
144C4×C13#12112yes—
145C4×C13C22×D411yescharacteristic
146C4×C13C2×#4111yescharacteristic
147Dic13—41no—
148Dic13—42no—
149C2×#41—131no—
150C2×#41C2×D1311yescharacteristic
151C22×Q8C2×D1311yescharacteristic
152#137—264no—
153C2×Q16—132no—
154C2×SD16—132no—
155#131—264no—
156C2×M16—131no—
157C2×M16—132no—
158C22×C8—131no—
159C22×C8—132no—
160C4⋊Q8—21no—
161#124—21no—
162#123—22no—
163C22⋊Q8—132no—
164C22⋊Q8—261no—
165C22⋊Q8C2×D1312yes—
166C22⋊Q8C2×D1312yes—
167#121—132no—
168#121—261no—
169#121—262no—
170#117C2×D1311yescharacteristic
171C2×C4⋊C4—131no—
172#107—132no—
173#106—132no—
174#103—132no—
175#103—132no—
176#103—131no—
177#103—131no—
178#102—131no—
179#102—131no—
180C2×C13—22no—
181C2×C13—42no—
182C2×C13C2×#12111yescharacteristic
183C2×C13#57711yescharacteristic
184C2×C13#57811yescharacteristic
185D13—81no—
186#41—22no—
187#41—22no—
188#41—262no—
189#41—262no—
190C2×Q8—21no—
191C2×Q8—22no—
192C2×Q8—22no—
193C2×Q8—131no—
194C2×Q8C22⋊D1311yescharacteristic
195C2×Q8C22×D1312yes—
196C2×D4—131no—
197C2×D4—261no—
198C2×D4—262no—
199C2×D4C22⋊D1312yes—
200C2×D4C22⋊D1311yescharacteristic
201C22×C4—21no—
202C22×C4—261no—
203C22×C4—261no—
204C22×C4C22×D1312yes—
205C22×C4C22×D1311yescharacteristic
206Q16—264no—
207SD16—264no—
208M16—134no—
209M16—264no—
210C2×C8—132no—
211C2×C8—131no—
212C2×C8—131no—
213C2×C8—264no—
214C2×C8—262no—
215C4⋊C4—22no—
216C4⋊C4—22no—
217C4⋊C4—132no—
218C4⋊C4—261no—
219C4⋊C4—262no—
220C4⋊C4C22×D1311yescharacteristic
221C4⋊C4C22×D1311yescharacteristic
222C22⋊C4—21no—
223C22⋊C4—22no—
224C22⋊C4—22no—
225C22⋊C4—262no—
226C22⋊C4—262no—
227C42—21no—
228C13#306311yescharacteristic, complemented, Sylow
229C23—261no—
230C23C2×C22⋊D1312yes—
231C23C2×C22⋊D1311yescharacteristic
232Q8—22no—
233Q8—22no—
234Q8—22no—
235Q8—42no—
236Q8—261no—
237Q8—261no—
238D4—24no—
239D4—22no—
240D4—261no—
241D4—261no—
242D4—522no—
243D4—1042no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—42no—
250C2×C4—262no—
251C2×C4—261no—
252C2×C4—522no—
253C2×C4—1041no—
254C2×C4D4×D1312yes—
255C2×C4#612912yes—
256C2×C4C2×C22⋊D1312yes—
257C2×C4C2×C22⋊D1311yescharacteristic
258C2×C4C23×D1311yescharacteristic
259C8—134no—
260C8—261no—
261C8—261no—
262C22—21no—
263C22—21no—
264C22—22no—
265C22—22no—
266C22—22no—
267C22—521no—
268C22—521no—
269C22—521no—
270C22#8819312yes—
271C22C22×C22⋊D1311yescharacteristic
272C4—22no—
273C4—42no—
274C4—41no—
275C4—41no—
276C4—521no—
277C4—522no—
278C4#8819312yes—
279C4C2×D4×D1311yescharacteristic
280C4C2×#612911yescharacteristic
281C2—22no—
282C2—42no—
283C2—1041no—
284C2C2×#8819311yescharacteristic
285C2#1171954211yescharacteristic
286C2#1171954311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#536C2
socleC22×C13C22×D4
prime radical#11719538C2
hypercenter#536D13
hypocenterC13#3063
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C13×#536C2semidirect
3. C2×#88202C2semidirect
4. C2×#88196C2semidirect
5. C2×#88075C2semidirect
6. #11718713C2semidirect
7. #11718712C2semidirect
8. #11718710C2semidirect
9. #11718709C2semidirect
10. #11718663C2semidirect
11. #11718656C2semidirect
79. #6099D4semidirect
122. #536D13semidirect
228. C13#3063semidirect

Maximal subgroups

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

subgroupindex
C13×#5362
#117195382
C2×#882022
C2×#881962
C2×#880752
#117187132
#117187122
#117187102
#117187092
#117186632
#117186562
#306313