Finite Group Databasebeta

← #13127068

Subgroups — #13127068

Order 1664.

448 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 123 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
1D4×D52C211yesmaximal, characteristic
2#11719247C211yesmaximal, characteristic, complemented
3C13×#436C211yesmaximal, characteristic, complemented
4#11718795C212yesmaximal, complemented
5#11718792C212yesmaximal, complemented
6#11718509C211yesmaximal, characteristic, complemented
7#11718507C211yesmaximal, characteristic, complemented
8#11718398C212yesmaximal, complemented
9#11718392C212yesmaximal, complemented
10#11718355C211yesmaximal, characteristic, complemented
11C4×#6095C211yesmaximal, characteristic, complemented
12C2×D4×D13—21no—
13C22×D52C2212yes—
14C2×C13×M16C2212yescomplemented
15C4×D4×C13C2211yescharacteristic
16#88190—21no—
17#88184C2212yes—
18#88180C2212yescomplemented
19#88178C2212yescomplemented
20C2×#6095C2211yescharacteristic
21C2×#6095C2212yescomplemented
22#88149—21no—
23#88141—21no—
24#88136—22no—
25#88133—22no—
26#88128C2211yescharacteristic
27C4×D52C2211yescharacteristic
28#88123C2211yescharacteristic, complemented
29C4×Dic26C2211yescharacteristic, complemented
30C13×C4⋊C8C2211yescharacteristic, complemented
31C13×C22⋊C8C2212yescomplemented
32C4×C8×C13C2211yescharacteristic, complemented
33#88061C2212yes—
34#88061C2211yescharacteristic
35#88061C2212yescomplemented
36#88061C2212yescomplemented
37#88061C2212yescomplemented
38#88058C2212yescomplemented
39#88057C2211yescharacteristic, complemented
40#88056C2211yescharacteristic, complemented
41C23×D13—22no—
42C2×D4×C13D411yescharacteristic
43C22×C4×C13C2312yes—
44C2×C22⋊D13—22no—
45D4×D13—44no—
46C2×D52—24no—
47C2×D52—21no—
48C2×D52—22no—
49C2×D52—21no—
50C2×D52—42no—
51C2×D52C2312yes—
52C2×D52C2311yescharacteristic
53C2×C4×D13—21no—
54C2×Dic26—21no—
55C2×Dic26C2311yescharacteristic
56C13×M16—42no—
57C2×C8×C13C2311yescharacteristic
58C2×C8×C13C2311yescharacteristic
59C2×C8×C13C2312yes—
60C13×C4⋊C4D411yescharacteristic
61C13×C22⋊C4D412yes—
62C42×C13C2311yescharacteristic
63C22⋊Dic13—22no—
64C22⋊Dic13—22no—
65#6103—21no—
66#6103—22no—
67C4⋊Dic13—21no—
68C4⋊Dic13C2311yescharacteristic
69C4⋊Dic13C2312yes—
70C4⋊Dic13C2311yescharacteristic
71#6101—21no—
72#6101—22no—
73C4×Dic13—21no—
74C4×Dic13—22no—
75#6095—22no—
76#6095—42no—
77#3324—131nomaximal, Sylow
78C23×C13C2×D412yes—
79C22×D13—21no—
80C22×D13—22no—
81C22×D13—44no—
82C22×D13—44no—
83C22×D13—82no—
84D4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13C2×D412yes—
88C2×C4×C13C2×D411yescharacteristic
89C2×C4×C13C2×D411yescharacteristic
90C2×C4×C13C2411yescharacteristic
91C22⋊D13—44no—
92C2×Dic13—21no—
93C2×Dic13—21no—
94C2×Dic13—22no—
95C2×Dic13—21no—
96D52—22no—
97D52—21no—
98D52—22no—
99D52—44no—
100D52—42no—
101D52—81no—
102D52#4112yes—
103C4×D13—42no—
104Dic26—21no—
105Dic26—21no—
106Dic26—42no—
107C8×C13—21no—
108C8×C13—22no—
109C8×C13—21no—
110#556—131no—
111D42—131no—
112#486—131no—
113#482—132no—
114#474—131no—
115#468—132no—
116#460—131no—
117#450—132no—
118C4×SD16—131no—
119#436D1311yescharacteristic, complemented
120#418—132no—
121C22×C13—22no—
122C22×C13—22no—
123C22×C13—22no—
124C22×C13C22×D411yescharacteristic
125C2×D13—22no—
126C2×D13—41no—
127C2×D13—41no—
128C2×D13—42no—
129C2×D13—42no—
130C2×D13—42no—
131C2×D13—88no—
132C4×C13—22no—
133C4×C13—21no—
134C4×C13AGL(1,ℤ/8)12yes—
135C4×C13C2×#4111yescharacteristic
136C4×C13H(5,𝔽2)11yescharacteristic
137Dic13—41no—
138Dic13—42no—
139Dic13—41no—
140Dic13—41no—
141C22×D4—132no—
142C22×D4—261no—
143C2×SD16—131no—
144C2×SD16—132no—
145C2×M16C2×D1312yescomplemented
146C4⋊Q8—131no—
147#127—131no—
148#126—262no—
149#124—261no—
150C22⋊Q8—132no—
151#121—132no—
152#121—261no—
153#120—262no—
154C4×Q8—131no—
155C4×Q8—261no—
156C4×D4—131no—
157C4×D4C2×D1311yescharacteristic
158#117—132no—
159#107—132no—
160#106—131no—
161C4⋊C8C2×D1311yescharacteristic, complemented
162#103—131no—
163#102—131no—
164#102—132no—
165#102—132no—
166#102—132no—
167#102—132no—
168C22⋊C8C2×D1312yescomplemented
169C4×C8C2×D1311yescharacteristic, complemented
170C2×C13—42no—
171C2×C13#54611yescharacteristic
172C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
173C2×C13#57711yescharacteristic
174D13—42no—
175D13—82no—
176C24—262no—
177C2×Q8—131no—
178C2×Q8—261no—
179C2×D4—131no—
180C2×D4—132no—
181C2×D4—264no—
182C2×D4—262no—
183C2×D4—262no—
184C2×D4—261no—
185C2×D4—261no—
186C2×D4—522no—
187C2×D4—524no—
188C2×D4D5211yescharacteristic
189C22×C4—261no—
190C22×C4C22×D1312yes—
191SD16—262no—
192SD16—522no—
193M16—42no—
194C2×C8C22×D1311yescharacteristic
195C2×C8C22×D1311yescharacteristic
196C2×C8C22×D1312yes—
197C4⋊C4—131no—
198C4⋊C4—132no—
199C4⋊C4—131no—
200C4⋊C4—261no—
201C4⋊C4—262no—
202C4⋊C4—261no—
203C4⋊C4D5211yescharacteristic
204C22⋊C4—262no—
205C22⋊C4—262no—
206C22⋊C4—261no—
207C22⋊C4—262no—
208C22⋊C4D5212yes—
209C42—262no—
210C42—261no—
211C42C22×D1311yescharacteristic
212C13#332411yescharacteristic, complemented, Sylow
213C23—261no—
214C23—262no—
215C23—524no—
216C23—524no—
217C23—1042no—
218C23C2×D5212yes—
219Q8—261no—
220Q8—261no—
221Q8—522no—
222D4—22no—
223D4—132no—
224D4—261no—
225D4—262no—
226D4—262no—
227D4—524no—
228D4—524no—
229D4—522no—
230D4—1041no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—261no—
234C2×C4—262no—
235C2×C4—261no—
236C2×C4—261no—
237C2×C4—522no—
238C2×C4C2×D5212yes—
239C2×C4C2×D5211yescharacteristic
240C2×C4C2×D5211yescharacteristic
241C2×C4C23×D1311yescharacteristic
242C8—21no—
243C8—22no—
244C8—21no—
245C22—22no—
246C22—22no—
247C22—22no—
248C22—262no—
249C22—521no—
250C22—521no—
251C22—522no—
252C22—522no—
253C22—522no—
254C22—1048no—
255C22C22×D5211yescharacteristic
256C4—21no—
257C4—22no—
258C4—521no—
259C4—522no—
260C4—521no—
261C4—521no—
262C4#8816212yes—
263C4#8825111yescharacteristic
264C4#41×D1311yescharacteristic
265C2—42no—
266C2—522no—
267C2—1042no—
268C2#1171925911yescharacteristic
269C2C2×#8816211yescharacteristic
270C2#1171945611yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#436C2
socleC22×C13C22×D4
prime radicalD4×D52C2
hypercenter#436D13
hypocenterC13#3324
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
2. #11719247C2semidirect
3. C13×#436C2semidirect
4. #11718795C2semidirect
5. #11718792C2semidirect
6. #11718509C2semidirect
7. #11718507C2semidirect
8. #11718398C2semidirect
9. #11718392C2semidirect
10. #11718355C2semidirect
11. C4×#6095C2semidirect
14. C2×C13×M16C22semidirect
18. #88180C22semidirect
19. #88178C22semidirect
21. C2×#6095C22semidirect
28. #88123C22semidirect
29. C4×Dic26C22semidirect
30. C13×C4⋊C8C22semidirect
31. C13×C22⋊C8C22semidirect
32. C4×C8×C13C22semidirect
35. #88061C22semidirect
36. #88061C22semidirect
37. #88061C22semidirect
38. #88058C22semidirect
39. #88057C22semidirect
40. #88056C22semidirect
119. #436D13semidirect
145. C2×M16C2×D13semidirect
161. C4⋊C8C2×D13semidirect
168. C22⋊C8C2×D13semidirect
169. C4×C8C2×D13semidirect
212. C13#3324semidirect

Maximal subgroups

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

subgroupindex
D4×D522
#117192472
C13×#4362
#117187952
#117187922
#117185092
#117185072
#117183982
#117183922
#117183552
C4×#60952
#332413