Finite Group Databasebeta

← #13124795

Subgroups — #13124795

Order 1664.

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

normal subgroups only

This group has 418 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
1#11719535C211yesmaximal, characteristic
2#11719532C211yesmaximal, characteristic, complemented
3C13×#408C211yesmaximal, characteristic, complemented
4#11718792C211yesmaximal, characteristic, complemented
5#11718782C211yesmaximal, characteristic, complemented
6C2×#88061C211yesmaximal, characteristic, complemented
7#11718767C211yesmaximal, characteristic, complemented
8#11718398C212yesmaximal, complemented
9#11718398C212yesmaximal, complemented
10#11718397C212yesmaximal, complemented
11#11718396C212yesmaximal, complemented
12C2×C13×#41C2211yescharacteristic
13C22×D52C2211yescharacteristic
14C2×C13×M16C2211yescharacteristic
15C22×C8×C13C2211yescharacteristic
16#88201—21no—
17Q8×Dic13—21no—
18#88194—21no—
19#88191—22no—
20D4×Dic13—21no—
21D4×Dic13—22no—
22#88184C2212yes—
23#88184C2212yes—
24#88180C2211yescharacteristic
25#88180C2211yescharacteristic
26#88180C2212yescomplemented
27C2×C4⋊Dic13C2211yescharacteristic
28C2×C4⋊Dic13C2212yescomplemented
29C13×C22⋊C8C2212yescomplemented
30C13×C22⋊C8C2212yescomplemented
31#88061C2212yes—
32#88061C2212yes—
33#88061C2212yes—
34#88061C2212yes—
35#88058C2211yescharacteristic, complemented
36#88058C2211yescharacteristic, complemented
37#88058C2212yescomplemented
38#88057C2211yescharacteristic, complemented
39#88057C2211yescharacteristic, complemented
40#88057C2212yescomplemented
41C23×D13—21no—
42C13×#41—22no—
43C13×#41—22no—
44C2×Q8×C13D411yescharacteristic
45C2×D4×C13D412yes—
46C2×D4×C13D411yescharacteristic
47C22×C4×C13C2312yes—
48C22×C4×C13C2311yescharacteristic
49C2×C22⋊D13—22no—
50C2×C22⋊D13—22no—
51C22×Dic13—21no—
52C22×Dic13—22no—
53C2×D52—22no—
54C2×D52—22no—
55C2×D52—21no—
56C2×D52C2312yes—
57C13×M16—22no—
58C2×C8×C13—22no—
59C2×C8×C13C2311yescharacteristic
60C2×C8×C13C2311yescharacteristic
61C2×C8×C13C2312yes—
62C22⋊Dic13—21no—
63C22⋊Dic13—21no—
64C22⋊Dic13—22no—
65#6103—22no—
66#6103—22no—
67C4⋊Dic13—21no—
68C4⋊Dic13—22no—
69C4⋊Dic13C2312yes—
70C4⋊Dic13C2311yescharacteristic
71C4⋊Dic13C2311yescharacteristic
72C4⋊Dic13C2311yescharacteristic
73C4⋊Dic13C2311yescharacteristic
74C4×Dic13—21no—
75C4×Dic13—21no—
76C4×Dic13—22no—
77#3096—131nomaximal, Sylow
78C23×C13C2×D412yes—
79C23×C13C2×D411yescharacteristic
80C22×D13—22no—
81C22×D13—42no—
82C22×D13—81no—
83C22×D13—81no—
84Q8×C13—22no—
85D4×C13—24no—
86D4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13C2×D412yes—
90C2×C4×C13C2×D411yescharacteristic
91C2×C4×C13#4112yes—
92C2×C4×C13#4112yes—
93C2×C4×C13C2411yescharacteristic
94C22⋊D13—82no—
95C22⋊D13—82no—
96C2×Dic13—21no—
97C2×Dic13—21no—
98C2×Dic13—22no—
99C2×Dic13—21no—
100C2×Dic13—21no—
101C2×Dic13—81no—
102C2×Dic13—82no—
103D52—22no—
104D52—22no—
105D52—42no—
106C8×C13—21no—
107C8×C13—21no—
108C8×C13—22no—
109#535—131no—
110#520—131no—
111#482—132no—
112#482—132no—
113#481—132no—
114#480—132no—
115#428—131no—
116#427—131no—
117#418—131no—
118C2×#102—131no—
119#408D1311yescharacteristic, complemented
120C22×C13—21no—
121C22×C13—21no—
122C22×C13—22no—
123C22×C13—22no—
124C22×C13—22no—
125C22×C13#12312yes—
126C22×C13C22×D411yescharacteristic
127C2×D13—42no—
128C2×D13—42no—
129C2×D13—42no—
130C2×D13—84no—
131C4×C13—22no—
132C4×C13#12312yes—
133C4×C13C2×#4111yescharacteristic
134C4×C13C2×#4111yescharacteristic
135Dic13—41no—
136Dic13—42no—
137Dic13—41no—
138Dic13—41no—
139Dic13—41no—
140C2×#41C2×D1311yescharacteristic
141C22×D4—131no—
142C2×M16C2×D1311yescharacteristic
143C22×C8C2×D1311yescharacteristic
144#127—261no—
145#124—261no—
146#121—132no—
147#121—132no—
148#120—262no—
149C4×Q8—261no—
150C4×D4—262no—
151C4×D4—261no—
152#117—131no—
153#117—132no—
154#117—131no—
155C2×C4⋊C4—131no—
156C2×C4⋊C4—132no—
157#107—131no—
158#107—131no—
159#107—132no—
160#106—131no—
161#106—131no—
162#106—132no—
163#102—132no—
164#102—132no—
165#102—132no—
166#102—132no—
167C22⋊C8C2×D1312yescomplemented
168C22⋊C8C2×D1312yescomplemented
169C2×C13—22no—
170C2×C13—42no—
171C2×C13C2×#12311yescharacteristic
172C2×C13#57611yescharacteristic
173C2×C13#57711yescharacteristic
174D13—82no—
175C24—261no—
176#41—22no—
177#41—22no—
178C2×Q8D5211yescharacteristic
179C2×D4—132no—
180C2×D4—262no—
181C2×D4—262no—
182C2×D4—261no—
183C2×D4—262no—
184C2×D4—262no—
185C2×D4D5212yes—
186C2×D4D5211yescharacteristic
187C22×C4—262no—
188C22×C4—261no—
189C22×C4C22×D1312yes—
190C22×C4C22×D1311yescharacteristic
191M16—22no—
192C2×C8—22no—
193C2×C8C22×D1311yescharacteristic
194C2×C8C22×D1312yes—
195C2×C8C22×D1311yescharacteristic
196C4⋊C4—132no—
197C4⋊C4—131no—
198C4⋊C4—131no—
199C4⋊C4—131no—
200C4⋊C4—131no—
201C4⋊C4—262no—
202C4⋊C4—261no—
203C22⋊C4—262no—
204C22⋊C4—261no—
205C22⋊C4—261no—
206C22⋊C4—262no—
207C22⋊C4—262no—
208C42—262no—
209C42—261no—
210C42—261no—
211C13#309611yescharacteristic, complemented, Sylow
212C23—262no—
213C23—522no—
214C23—1041no—
215C23—1041no—
216C23C2×D5212yes—
217C23C2×D5211yescharacteristic
218Q8—22no—
219D4—24no—
220D4—22no—
221D4—262no—
222D4—262no—
223D4—522no—
224D4—1042no—
225D4—1042no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—261no—
229C2×C4—261no—
230C2×C4—261no—
231C2×C4—262no—
232C2×C4—261no—
233C2×C4—1041no—
234C2×C4—1042no—
235C2×C4C2×D5212yes—
236C2×C4C2×D5211yescharacteristic
237C2×C4#612912yes—
238C2×C4#612912yes—
239C2×C4C23×D1311yescharacteristic
240C8—21no—
241C8—21no—
242C8—22no—
243C22—21no—
244C22—21no—
245C22—22no—
246C22—22no—
247C22—22no—
248C22—522no—
249C22—522no—
250C22—522no—
251C22—1044no—
252C22#8814012yes—
253C22C22×D5211yescharacteristic
254C4—22no—
255C4—521no—
256C4—521no—
257C4—522no—
258C4—521no—
259C4—521no—
260C4#8814012yes—
261C4C2×#612911yescharacteristic
262C4C2×#612911yescharacteristic
263C2—22no—
264C2—42no—
265C2—1042no—
266C2C2×#8814011yescharacteristic
267C2#1171945611yescharacteristic
268C2#1171945711yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#408C2
socleC22×C13C22×D4
prime radical#11719535C2
hypercenter#408D13
hypocenterC13#3096
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #11719532C2semidirect
3. C13×#408C2semidirect
4. #11718792C2semidirect
5. #11718782C2semidirect
6. C2×#88061C2semidirect
7. #11718767C2semidirect
8. #11718398C2semidirect
9. #11718398C2semidirect
10. #11718397C2semidirect
11. #11718396C2semidirect
26. #88180C22semidirect
28. C2×C4⋊Dic13C22semidirect
29. C13×C22⋊C8C22semidirect
30. C13×C22⋊C8C22semidirect
35. #88058C22semidirect
36. #88058C22semidirect
37. #88058C22semidirect
38. #88057C22semidirect
39. #88057C22semidirect
40. #88057C22semidirect
119. #408D13semidirect
167. C22⋊C8C2×D13semidirect
168. C22⋊C8C2×D13semidirect
211. C13#3096semidirect

Maximal subgroups

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

subgroupindex
#117195352
#117195322
C13×#4082
#117187922
#117187822
C2×#880612
#117187672
#117183982
#117183972
#117183962
#309613