Finite Group Databasebeta

← #13124661

Subgroups — #13124661

Order 1664.

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

normal subgroups only

This group has 398 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×#544C211yesmaximal, characteristic, complemented
2#11719226C211yesmaximal, characteristic
3#11718748C212yesmaximal, complemented
4#11718745C212yesmaximal, complemented
5#11718727C212yesmaximal, complemented
6#11718727C212yesmaximal, complemented
7#11718662C211yesmaximal, characteristic
8#11718660C211yesmaximal, characteristic, complemented
9#11718659C211yesmaximal, characteristic, complemented
10C2×#88049C211yesmaximal, characteristic
11#11718625C211yesmaximal, characteristic, complemented
12C22×D52C2211yescharacteristic
13C13×C4⋊Q8—21no—
14C13×C4⋊Q8C2212yescomplemented
15C13×#125—21no—
16C13×#125C2212yescomplemented
17C13×C22⋊Q8—22no—
18C13×#117C2211yescharacteristic
19C13×#117C2211yescharacteristic
20C2×C13×C4⋊C4C2211yescharacteristic
21#88180C2211yescharacteristic
22C2×#6099C2211yescharacteristic
23C22×#1055C2211yescharacteristic
24#88147—21no—
25#88147—21no—
26C22⋊C4×D13—22no—
27C4×D52C2212yes—
28C4×D52C2212yes—
29#88049C2212yes—
30#88049C2212yes—
31#88049C2212yes—
32#88049C2212yes—
33#88048C2211yescharacteristic, complemented
34#88048C2211yescharacteristic, complemented
35#88048C2212yescomplemented
36#88047C2211yescharacteristic, complemented
37#88047C2211yescharacteristic, complemented
38#88047C2212yescomplemented
39C4⋊#1055C2212yescomplemented
40C4⋊#1055C2212yescomplemented
41C23×D13—21no—
42C2×Q8×C13—22no—
43C22×C4×C13—21no—
44C22×C4×C13C2311yescharacteristic
45C2×D52—21no—
46C2×D52—22no—
47C2×D52Q814yescomplemented
48C2×D52C2312yes—
49C2×C4×D13—22no—
50C2×C4×D13—22no—
51C13×C4⋊C4—21no—
52C13×C4⋊C4—22no—
53C13×C4⋊C4—22no—
54C13×C4⋊C4—22no—
55C13×C4⋊C4D411yescharacteristic
56C13×C4⋊C4D411yescharacteristic
57C13×C4⋊C4C2312yes—
58C13×C4⋊C4C2311yescharacteristic
59C13×C4⋊C4C2311yescharacteristic
60C13×C22⋊C4—21no—
61C13×C22⋊C4D412yes—
62C42×C13—21no—
63C42×C13C2312yes—
64C22⋊Dic13—21no—
65#6103—22no—
66#6103—22no—
67C4⋊Dic13C2311yescharacteristic
68C4⋊Dic13C2311yescharacteristic
69C4×Dic13—21no—
70#6099—22no—
71C2×#1055—22no—
72C2×#1055C2311yescharacteristic
73C2×#1055C2311yescharacteristic
74C2×#1055C2312yes—
75#3081—131nomaximal, Sylow
76C23×C13C2×D411yescharacteristic
77C22×D13—22no—
78C22×D13—24no—
79C22×D13—81no—
80C22×D13—81no—
81Q8×C13—82no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—22no—
85C2×C4×C13—81no—
86C2×C4×C13C2×D412yes—
87C2×C4×C13C2×D412yes—
88C2×C4×C13C2×D411yescharacteristic
89C2×C4×C13C2×Q812yes—
90C2×C4×C13#4112yes—
91C2×C4×C13C2411yescharacteristic
92C2×Dic13—21no—
93C2×Dic13—21no—
94D52—24no—
95D52—22no—
96D52C2×Q814yes—
97C4×D13—82no—
98C4×D13—82no—
99#1055—21no—
100#1055—21no—
101#1055—22no—
102#544D1311yescharacteristic, complemented
103#518—131no—
104#478—132no—
105#478—132no—
106#476—132no—
107#474—132no—
108#428—131no—
109#427—131no—
110#424—131no—
111#418—131no—
112C2×#102—131no—
113C22×C13—21no—
114C22×C13—21no—
115C22×C13C22⋊Q812yes—
116C22×C13C22×D411yescharacteristic
117C2×D13—24no—
118C2×D13—42no—
119C2×D13—42no—
120C2×D13—84no—
121C4×C13—22no—
122C4×C13—22no—
123C4×C13—42no—
124C4×C13—41no—
125C4×C13—41no—
126C4×C13C22⋊Q812yes—
127C4×C13C22×Q811yescharacteristic
128C4×C13C2×#4111yescharacteristic
129Dic13—41no—
130Dic13—41no—
131C22×D4—131no—
132C2×M16—131no—
133C22×C8—131no—
134C4⋊Q8—21no—
135C4⋊Q8C2×D1312yescomplemented
136#125—21no—
137#125C2×D1312yescomplemented
138C22⋊Q8—22no—
139C4×D4—132no—
140C4×D4—132no—
141C4×D4—261no—
142C4×D4—261no—
143#117—131no—
144#117C2×D1311yescharacteristic
145#117C2×D1311yescharacteristic
146C2×C4⋊C4C2×D1311yescharacteristic
147C2×C22⋊C4—262no—
148#107—131no—
149#107—131no—
150#107—132no—
151#106—131no—
152#106—131no—
153#106—132no—
154C4⋊C8—132no—
155C4⋊C8—132no—
156#102—132no—
157#102—132no—
158#102—132no—
159#102—132no—
160C2×C13—22no—
161C2×C13C2×C22⋊Q811yescharacteristic
162C2×C13#57611yescharacteristic
163C2×C13#57711yescharacteristic
164D13—44no—
165C24—261no—
166C2×Q8—22no—
167C2×D4—134no—
168C2×D4—132no—
169C2×D4—262no—
170C2×D4—261no—
171C22×C4—21no—
172C22×C4—262no—
173C22×C4—262no—
174C22×C4C22×D1311yescharacteristic
175M16—262no—
176C2×C8—131no—
177C2×C8—132no—
178C2×C8—131no—
179C2×C8—262no—
180C4⋊C4—21no—
181C4⋊C4—22no—
182C4⋊C4—22no—
183C4⋊C4—22no—
184C4⋊C4—131no—
185C4⋊C4—131no—
186C4⋊C4C22⋊D1311yescharacteristic
187C4⋊C4C22⋊D1311yescharacteristic
188C4⋊C4C22×D1312yes—
189C4⋊C4C22×D1311yescharacteristic
190C4⋊C4C22×D1311yescharacteristic
191C22⋊C4—21no—
192C22⋊C4—261no—
193C22⋊C4—262no—
194C22⋊C4—262no—
195C22⋊C4C22⋊D1312yes—
196C42—21no—
197C42—261no—
198C42C22×D1312yes—
199C13#308111yescharacteristic, complemented, Sylow
200C23—262no—
201C23—264no—
202C23—1041no—
203C23—1041no—
204C23C2×C22⋊D1311yescharacteristic
205Q8—82no—
206D4—134no—
207D4—264no—
208D4—262no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—81no—
213C2×C4—261no—
214C2×C4—261no—
215C2×C4—1042no—
216C2×C4—1042no—
217C2×C4Q8×D1312yes—
218C2×C4#613112yes—
219C2×C4C2×C22⋊D1312yes—
220C2×C4C2×C22⋊D1312yes—
221C2×C4C2×C22⋊D1311yescharacteristic
222C2×C4C23×D1311yescharacteristic
223C8—261no—
224C8—261no—
225C8—262no—
226C22—21no—
227C22—21no—
228C22—264no—
229C22—522no—
230C22—522no—
231C22—1044no—
232C22#8820012yes—
233C22C22×C22⋊D1311yescharacteristic
234C4—22no—
235C4—22no—
236C4—42no—
237C4—41no—
238C4—41no—
239C4—521no—
240C4—521no—
241C4#8820012yes—
242C4C2×Q8×D1311yescharacteristic
243C4C2×#613111yescharacteristic
244C2—22no—
245C2—524no—
246C2C2×#8820011yescharacteristic
247C2#1171954011yescharacteristic
248C2#1171954211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#544C2
socleC22×C13C22×D4
prime radicalC22×D52C22
hypercenter#544D13
hypocenterC13#3081
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #544

Complements

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

NH ≅ G/Ntype
1. C13×#544C2semidirect
3. #11718748C2semidirect
4. #11718745C2semidirect
5. #11718727C2semidirect
6. #11718727C2semidirect
8. #11718660C2semidirect
9. #11718659C2semidirect
11. #11718625C2semidirect
14. C13×C4⋊Q8C22semidirect
16. C13×#125C22semidirect
33. #88048C22semidirect
34. #88048C22semidirect
35. #88048C22semidirect
36. #88047C22semidirect
37. #88047C22semidirect
38. #88047C22semidirect
39. C4⋊#1055C22semidirect
40. C4⋊#1055C22semidirect
47. C2×D52Q8semidirect
102. #544D13semidirect
135. C4⋊Q8C2×D13semidirect
137. #125C2×D13semidirect
199. C13#3081semidirect

Maximal subgroups

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

subgroupindex
C13×#5442
#117192262
#117187482
#117187452
#117187272
#117186622
#117186602
#117186592
C2×#880492
#117186252
#308113