Finite Group Databasebeta

← #13125889

Subgroups — #13125889

Order 1664.

420 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 109 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
1#11719403C211yesmaximal, characteristic, complemented
2#11719379C211yesmaximal, characteristic, complemented
3C13×#488C211yesmaximal, characteristic, complemented
4#11718728C211yesmaximal, characteristic, complemented
5#11718719C211yesmaximal, characteristic, complemented
6#11718480C212yesmaximal, complemented
7#11718472C212yesmaximal, complemented
8#11718447C212yesmaximal, complemented
9#11718434C212yesmaximal, complemented
10#11718356C211yesmaximal, characteristic, complemented
11#11718351C211yesmaximal, characteristic, complemented
12C2×#6131C2211yescharacteristic
13C2×D4×D13C2211yescharacteristic
14C13×#125C2211yescharacteristic, complemented
15C13×#124C2211yescharacteristic
16#88201C2211yescharacteristic
17C2×#6106C2212yescomplemented
18#88194C2211yescharacteristic
19C2×#6104C2212yes—
20C2×D104C2212yes—
21C2×D104C2212yescomplemented
22#88149—22no—
23#88149C2212yes—
24#88148—22no—
25#88147C2212yescomplemented
26#88138—22no—
27#88136—22no—
28#88128C2211yescharacteristic
29#88128C2211yescharacteristic, complemented
30#88126C2211yescharacteristic
31C13×#103C2212yescomplemented
32C13×#102C2212yes—
33C4×C8×C13C2211yescharacteristic, complemented
34#88060C2212yes—
35#88054C2212yescomplemented
36#88049C2212yes—
37#88049C2212yescomplemented
38#88043C2211yescharacteristic, complemented
39C23×D13—21no—
40C2×Q8×C13C2311yescharacteristic
41C2×D4×C13C2311yescharacteristic
42C2×C22⋊D13—21no—
43C2×C22⋊D13—22no—
44#6131—42no—
45D4×D13—42no—
46C2×D52—21no—
47C2×D52—22no—
48C2×D52—22no—
49C2×D52—22no—
50C2×D52C2311yescharacteristic
51C2×D52C2311yescharacteristic
52C2×D52C2312yes—
53C2×C4×D13—21no—
54C2×C4×D13—22no—
55C2×C4×D13C2311yescharacteristic
56C2×C8×C13C2312yes—
57C13×C4⋊C4—22no—
58C13×C4⋊C4C2312yes—
59C13×C22⋊C4—22no—
60C42×C13C2311yescharacteristic
61#6106—42no—
62#6104—42no—
63#6103—22no—
64#6103—22no—
65#6103—22no—
66#6103D412yes—
67#6101D412yes—
68C4×Dic13C2311yescharacteristic
69C2×#1055C2312yes—
70D104—42no—
71D104—42no—
72#3220—131nomaximal, Sylow
73C23×C13—21no—
74C22×D13—22no—
75C22×D13—21no—
76C22×D13—21no—
77C22×D13—42no—
78C22×D13—82no—
79C22×D13C2×D411yescharacteristic
80Q8×C13—22no—
81D4×C13—22no—
82C2×C4×C13—21no—
83C2×C4×C13—22no—
84C2×C4×C13C2×D412yes—
85C2×C4×C13C2411yescharacteristic
86C22⋊D13—42no—
87C22⋊D13—82no—
88C2×Dic13C2×D412yes—
89C2×Dic13C2×D411yescharacteristic
90D52—22no—
91D52—22no—
92D52—22no—
93D52—22no—
94D52—42no—
95D52—82no—
96D52—82no—
97D52—82no—
98C4×D13—22no—
99C4×D13—42no—
100C4×D13—82no—
101C8×C13—22no—
102#1055—22no—
103#540—131no—
104#535—131no—
105#496—131no—
106#493—131no—
107#490—131no—
108#488D1311yescharacteristic, complemented
109#463—132no—
110#459—132no—
111#449—132no—
112#447—132no—
113#433—131no—
114C22×C13—41no—
115C22×C13—42no—
116C22×C13C22×D411yescharacteristic
117C2×D13—21no—
118C2×D13—22no—
119C2×D13—41no—
120C2×D13—41no—
121C2×D13—42no—
122C2×D13—42no—
123C2×D13—42no—
124C2×D13—42no—
125C2×D13—42no—
126C2×D13—84no—
127C4×C13—22no—
128C4×C13—41no—
129C4×C13—42no—
130C4×C13H(5,𝔽2)12yes—
131Dic13—21no—
132Dic13—22no—
133C2×#41—131no—
134C22×D4—131no—
135C2×SD16—132no—
136C2×D8—132no—
137C2×D8—132no—
138C2×D8—132no—
139#127—131no—
140#127—131no—
141#127—131no—
142#125C2×D1311yescharacteristic, complemented
143#124—131no—
144#124C2×D1311yescharacteristic
145#123—262no—
146#121—132no—
147#121—262no—
148#121—262no—
149#120—262no—
150C4×D4—132no—
151#117—131no—
152C4⋊C8—132no—
153#103C2×D1312yescomplemented
154#102—132no—
155#102—132no—
156#102C2×D1312yes—
157C22⋊C8—132no—
158#97—131no—
159C4×C8C2×D1311yescharacteristic, complemented
160C2×C13—81no—
161C2×C13#53511yescharacteristic
162C2×C13#57612yes—
163D13—41no—
164D13—81no—
165D13—82no—
166D13—81no—
167C24—261no—
168#41—522no—
169C2×Q8C22×D1311yescharacteristic
170C2×D4—131no—
171C2×D4—131no—
172C2×D4—132no—
173C2×D4—261no—
174C2×D4—262no—
175C2×D4—261no—
176C2×D4—262no—
177C2×D4—262no—
178C2×D4—262no—
179C2×D4—522no—
180C2×D4C22×D1311yescharacteristic
181C22×C4—131no—
182C22×C4—261no—
183C22×C4—262no—
184SD16—522no—
185D8—522no—
186D8—522no—
187D8—522no—
188C2×C8—132no—
189C2×C8C22×D1312yes—
190C4⋊C4—22no—
191C4⋊C4—132no—
192C4⋊C4C22×D1312yes—
193C22⋊C4—22no—
194C22⋊C4—132no—
195C22⋊C4—262no—
196C22⋊C4—262no—
197C22⋊C4—262no—
198C42—131no—
199C42C22×D1311yescharacteristic
200C13#322011yescharacteristic, complemented, Sylow
201C23—21no—
202C23—131no—
203C23—262no—
204C23—261no—
205C23—261no—
206C23—522no—
207C23—1042no—
208Q8—22no—
209D4—22no—
210D4—262no—
211D4—262no—
212D4—262no—
213D4—262no—
214D4—522no—
215D4—522no—
216D4—1042no—
217D4—1042no—
218D4—1042no—
219D4—1042no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—132no—
223C2×C4—131no—
224C2×C4—262no—
225C2×C4—522no—
226C2×C4—1042no—
227C2×C4D4×D1312yes—
228C2×C4C23×D1311yescharacteristic
229C8—22no—
230C8—262no—
231C22—42no—
232C22—41no—
233C22—262no—
234C22—261no—
235C22—522no—
236C22—522no—
237C22—522no—
238C22—522no—
239C22—521no—
240C22—521no—
241C22—522no—
242C22—1044no—
243C22C2×D4×D1311yescharacteristic
244C4—22no—
245C4—42no—
246C4—41no—
247C4—262no—
248C4—261no—
249C4#8825612yes—
250C2—81no—
251C2—521no—
252C2—1041no—
253C2—1042no—
254C2—1041no—
255C2#1171937911yescharacteristic
256C2#1171947412yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#488C2
socleC22×C13C22×D4
hypercenter#488D13
hypocenterC13#3220
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #11719403C2semidirect
2. #11719379C2semidirect
3. C13×#488C2semidirect
4. #11718728C2semidirect
5. #11718719C2semidirect
6. #11718480C2semidirect
7. #11718472C2semidirect
8. #11718447C2semidirect
9. #11718434C2semidirect
10. #11718356C2semidirect
11. #11718351C2semidirect
14. C13×#125C22semidirect
17. C2×#6106C22semidirect
21. C2×D104C22semidirect
25. #88147C22semidirect
29. #88128C22semidirect
31. C13×#103C22semidirect
33. C4×C8×C13C22semidirect
35. #88054C22semidirect
37. #88049C22semidirect
38. #88043C22semidirect
108. #488D13semidirect
142. #125C2×D13semidirect
153. #103C2×D13semidirect
159. C4×C8C2×D13semidirect
200. C13#3220semidirect

Maximal subgroups

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

subgroupindex
#117194032
#117193792
C13×#4882
#117187282
#117187192
#117184802
#117184722
#117184472
#117184342
#117183562
#117183512
#322013