Finite Group Databasebeta

← #13127080

Subgroups — #13127080

Order 1664.

460 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 117 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#11719268C211yesmaximal, characteristic, complemented
2D4×D52C211yesmaximal, characteristic, complemented
3C4×C13×D8C211yesmaximal, characteristic, complemented
4#11718817C212yesmaximal, complemented
5#11718676C211yesmaximal, characteristic, complemented
6#11718669C211yesmaximal, characteristic, complemented
7#11718546C212yesmaximal, complemented
8#11718443C212yesmaximal, complemented
9#11718431C212yesmaximal, complemented
10#11718355C211yesmaximal, characteristic, complemented
11#11718349C211yesmaximal, characteristic, complemented
12C2×D4×D13C2212yes—
13C22×D52—21no—
14C2×C13×D8C2211yescharacteristic
15C4×D4×C13C2211yescharacteristic
16C4×D4×C13C2211yescharacteristic, complemented
17#88192C2212yescomplemented
18C2×#6104C2212yescomplemented
19#88184—21no—
20#88184—21no—
21#88180—21no—
22C2×#6094C2212yescomplemented
23#88149C2212yes—
24#88146C2212yescomplemented
25#88139—22no—
26#88136—22no—
27#88128C2211yescharacteristic
28C4×D52C2211yescharacteristic
29#88123C2211yescharacteristic, complemented
30C13×#107C2211yescharacteristic, complemented
31C13×#102C2211yescharacteristic
32C13×#102C2211yescharacteristic, complemented
33C4×C8×C13C2211yescharacteristic, complemented
34#88072C2212yes—
35#88061C2212yescomplemented
36#88061C2212yescomplemented
37#88060C2212yescomplemented
38#88049C2212yescomplemented
39#88048C2212yescomplemented
40C4⋊#1055C2211yescharacteristic, complemented
41C23×D13—22no—
42C2×D4×C13C2311yescharacteristic
43C2×D4×C13C2311yescharacteristic
44C22×C4×C13—21no—
45C22×C4×C13—21no—
46C2×C22⋊D13—22no—
47C2×C22⋊D13—22no—
48D4×D13—24no—
49D4×D13—42no—
50C2×D52—22no—
51C2×D52—21no—
52C2×D52—21no—
53C2×D52—44no—
54C2×D52D411yescharacteristic
55C2×D52C2312yes—
56C2×C4×D13C2312yes—
57C2×Dic26—21no—
58C13×D8—22no—
59C2×C8×C13C2311yescharacteristic
60C2×C8×C13C2311yescharacteristic
61C13×C4⋊C4C2311yescharacteristic
62C13×C4⋊C4C2311yescharacteristic
63C13×C22⋊C4—21no—
64C13×C22⋊C4—21no—
65C42×C13C2311yescharacteristic
66C22⋊Dic13—22no—
67#6104—42no—
68#6103—22no—
69#6103—22no—
70#6103D412yes—
71C4⋊Dic13—21no—
72C4⋊Dic13D411yescharacteristic
73C4⋊Dic13C2312yes—
74C4×Dic13—22no—
75C2×#1055C2312yes—
76#6094—42no—
77#3325—131nomaximal, Sylow
78C23×C13—21no—
79C23×C13—21no—
80C22×D13—22no—
81C22×D13—44no—
82C22×D13—44no—
83C22×D13—82no—
84C22×D13C2×D412yes—
85D4×C13—21no—
86D4×C13—21no—
87D4×C13—21no—
88D4×C13#4112yes—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—42no—
92C2×C4×C13—42no—
93C2×C4×C13C2×D411yescharacteristic
94C2×C4×C13C2×D411yescharacteristic
95C2×C4×C13C2411yescharacteristic
96C22⋊D13—44no—
97C22⋊D13—82no—
98C2×Dic13—22no—
99C2×Dic13C2×D412yes—
100D52—22no—
101D52—22no—
102D52—22no—
103D52—44no—
104D52—42no—
105D52—81no—
106C4×D13—22no—
107C4×D13—22no—
108Dic26—81no—
109C8×C13—21no—
110C8×C13—21no—
111#1055—22no—
112#555—131no—
113D42—131no—
114#486—131no—
115#482—132no—
116#476—131no—
117#469—132no—
118#459—131no—
119#447—132no—
120C4×D8D1311yescharacteristic, complemented
121#436—131no—
122#418—132no—
123C22×C13—22no—
124C22×C13—41no—
125C22×C13—41no—
126C22×C13—41no—
127C22×C13—41no—
128C22×C13—41no—
129C22×C13C22×D411yescharacteristic
130C2×D13—22no—
131C2×D13—22no—
132C2×D13—22no—
133C2×D13—42no—
134C2×D13—42no—
135C2×D13—42no—
136C2×D13—88no—
137C4×C13—21no—
138C4×C13—41no—
139C4×C13—41no—
140C4×C13AGL(1,ℤ/8)12yes—
141C4×C13C2×#4111yescharacteristic
142C4×C13H(5,𝔽2)11yescharacteristic
143Dic13—22no—
144Dic13—42no—
145C22×D4—132no—
146C22×D4—261no—
147C2×D8—132no—
148C2×D8C2×D1311yescharacteristic
149C2×M16—132no—
150C4⋊Q8—131no—
151#127—131no—
152#124—262no—
153#121—132no—
154#121—132no—
155#121—261no—
156#121—261no—
157#120—262no—
158C4×D4—131no—
159C4×D4C2×D1311yescharacteristic
160C4×D4C2×D1311yescharacteristic, complemented
161#117—132no—
162#117—261no—
163#107C2×D1311yescharacteristic, complemented
164#106—132no—
165C4⋊C8—131no—
166#102—132no—
167#102—132no—
168#102—132no—
169#102—132no—
170#102C2×D1311yescharacteristic
171#102C2×D1311yescharacteristic, complemented
172C22⋊C8—132no—
173C4×C8C2×D1311yescharacteristic, complemented
174C2×C13—42no—
175C2×C13—81no—
176C2×C13#54611yescharacteristic
177C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
178C2×C13#57611yescharacteristic
179D13—42no—
180D13—82no—
181C24—262no—
182C2×Q8—261no—
183C2×D4—131no—
184C2×D4—132no—
185C2×D4—262no—
186C2×D4—262no—
187C2×D4—264no—
188C2×D4—262no—
189C2×D4—261no—
190C2×D4—261no—
191C2×D4—524no—
192C2×D4—522no—
193C2×D4C22×D1311yescharacteristic
194C2×D4C22×D1311yescharacteristic
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—132no—
198D8—22no—
199D8—522no—
200M16—522no—
201C2×C8—132no—
202C2×C8C22×D1311yescharacteristic
203C2×C8C22×D1311yescharacteristic
204C4⋊C4—131no—
205C4⋊C4—132no—
206C4⋊C4—261no—
207C4⋊C4C22×D1311yescharacteristic
208C4⋊C4C22×D1311yescharacteristic
209C22⋊C4—21no—
210C22⋊C4—21no—
211C22⋊C4—132no—
212C22⋊C4—262no—
213C22⋊C4—262no—
214C22⋊C4—262no—
215C42—262no—
216C42C22×D1311yescharacteristic
217C13#332511yescharacteristic, complemented, Sylow
218C23—21no—
219C23—21no—
220C23—132no—
221C23—262no—
222C23—524no—
223C23—524no—
224C23—1042no—
225Q8—1041no—
226D4—21no—
227D4—21no—
228D4—21no—
229D4—262no—
230D4—262no—
231D4—262no—
232D4—524no—
233D4—524no—
234D4—522no—
235D4—1041no—
236D4—1042no—
237D4#612712yes—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—132no—
243C2×C4—262no—
244C2×C4—262no—
245C2×C4—262no—
246C2×C4D4×D1311yescharacteristic
247C2×C4D4×D1311yescharacteristic
248C2×C4C23×D1311yescharacteristic
249C8—21no—
250C8—21no—
251C8—262no—
252C22—22no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—41no—
257C22—41no—
258C22—262no—
259C22—262no—
260C22—262no—
261C22—522no—
262C22—522no—
263C22—522no—
264C22—1048no—
265C22C2×D4×D1311yescharacteristic
266C4—21no—
267C4—41no—
268C4—41no—
269C4—262no—
270C4—522no—
271C4#8816512yes—
272C4C2×#612711yescharacteristic
273C4#8825611yescharacteristic
274C2—42no—
275C2—81no—
276C2—522no—
277C2—1042no—
278C2#1171925511yescharacteristic
279C2C2×#8816511yescharacteristic
280C2#1171947411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC4×C13×D8C2
socleC22×C13C22×D4
hypercenterC4×D8D13
hypocenterC13#3325
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #11719268C2semidirect
2. D4×D52C2semidirect
3. C4×C13×D8C2semidirect
4. #11718817C2semidirect
5. #11718676C2semidirect
6. #11718669C2semidirect
7. #11718546C2semidirect
8. #11718443C2semidirect
9. #11718431C2semidirect
10. #11718355C2semidirect
11. #11718349C2semidirect
16. C4×D4×C13C22semidirect
17. #88192C22semidirect
18. C2×#6104C22semidirect
22. C2×#6094C22semidirect
24. #88146C22semidirect
29. #88123C22semidirect
30. C13×#107C22semidirect
32. C13×#102C22semidirect
33. C4×C8×C13C22semidirect
35. #88061C22semidirect
36. #88061C22semidirect
37. #88060C22semidirect
38. #88049C22semidirect
39. #88048C22semidirect
40. C4⋊#1055C22semidirect
120. C4×D8D13semidirect
160. C4×D4C2×D13semidirect
163. #107C2×D13semidirect
171. #102C2×D13semidirect
173. C4×C8C2×D13semidirect
217. C13#3325semidirect

Maximal subgroups

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

subgroupindex
#117192682
D4×D522
C4×C13×D82
#117188172
#117186762
#117186692
#117185462
#117184432
#117184312
#117183552
#117183492
#332513