Finite Group Databasebeta

← #13124782

Subgroups — #13124782

Order 1664.

410 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C2×#88200C211yesmaximal, characteristic
2D13×#117C211yesmaximal, characteristic
3C13×#419C211yesmaximal, characteristic, complemented
4#11718886C211yesmaximal, characteristic, complemented
5#11718787C211yesmaximal, characteristic
6#11718782C211yesmaximal, characteristic, complemented
7#11718656C211yesmaximal, characteristic, complemented
8#11718476C212yesmaximal, complemented
9#11718475C212yesmaximal, complemented
10#11718470C212yesmaximal, complemented
11#11718466C212yesmaximal, complemented
12C22×Q8×C13C2211yescharacteristic
13C22×C4×D13C2211yescharacteristic
14C2×C13×M16C2211yescharacteristic
15C13×#117C2211yescharacteristic
16#88200—21no—
17#88200—21no—
18#88200C2212yes—
19#88200C2212yes—
20C2×#6103—21no—
21#88180C2211yescharacteristic
22C2×C4⋊Dic13C2211yescharacteristic
23C2×#6101—21no—
24C2×#6099C2211yescharacteristic
25#88146C2211yescharacteristic
26#88146C2211yescharacteristic
27C4⋊C4×D13C2211yescharacteristic
28C4⋊C4×D13C2211yescharacteristic
29C22⋊C4×D13—21no—
30#88131—21no—
31#88126—21no—
32C42×D13—21no—
33C13×#103C2212yescomplemented
34C13×#103C2212yescomplemented
35#88075C2212yescomplemented
36#88075C2212yescomplemented
37#88060C2212yes—
38#88060C2212yes—
39#88058C2212yescomplemented
40#88057C2212yescomplemented
41#88048C2212yescomplemented
42#88047C2212yescomplemented
43C23×D13D411yescharacteristic
44C2×Q8×C13—21no—
45C2×Q8×C13—22no—
46C2×Q8×C13—22no—
47C2×Q8×C13C2312yes—
48C22×C4×C13—21no—
49C22×C4×C13C2311yescharacteristic
50C22×Dic13—21no—
51C22×Dic13D411yescharacteristic
52C2×C4×D13—22no—
53C2×C4×D13—22no—
54C2×C4×D13—21no—
55C2×C4×D13—21no—
56C2×C4×D13D411yescharacteristic
57C2×C4×D13D411yescharacteristic
58C2×C4×D13C2311yescharacteristic
59C2×C4×D13C2311yescharacteristic
60C13×M16—22no—
61C2×C8×C13C2312yes—
62C13×C4⋊C4C2311yescharacteristic
63C13×C4⋊C4C2311yescharacteristic
64C13×C22⋊C4—21no—
65C42×C13—21no—
66C22⋊Dic13—21no—
67#6103—21no—
68#6103—21no—
69#6103—22no—
70#6103—22no—
71C4⋊Dic13—21no—
72C4⋊Dic13C2311yescharacteristic
73C4⋊Dic13C2311yescharacteristic
74C4⋊Dic13C2312yes—
75#6101—21no—
76#6101—21no—
77#6101—22no—
78#6101—22no—
79C4×Dic13—21no—
80C4×Dic13—21no—
81C4×Dic13—21no—
82#6099—22no—
83C2×#1055C2312yes—
84#3095—131nomaximal, Sylow
85C23×C13C2×D411yescharacteristic
86C22×D13—22no—
87C22×D13—22no—
88C22×D13—41no—
89C22×D13C2×D411yescharacteristic
90C22×D13C2×D411yescharacteristic
91Q8×C13—22no—
92Q8×C13—22no—
93Q8×C13—42no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—22no—
97C2×C4×C13—42no—
98C2×C4×C13C2×D411yescharacteristic
99C2×C4×C13#4112yes—
100C2×C4×C13#4112yes—
101C2×C4×C13C2411yescharacteristic
102C2×Dic13—22no—
103C2×Dic13—21no—
104C2×Dic13—21no—
105C2×Dic13—22no—
106C2×Dic13—42no—
107C2×Dic13C2×D411yescharacteristic
108C2×Dic13C2×D411yescharacteristic
109C4×D13—22no—
110C4×D13—22no—
111C4×D13—21no—
112C4×D13—21no—
113C4×D13—21no—
114C4×D13—21no—
115C4×D13—42no—
116C4×D13—42no—
117C8×C13—22no—
118#1055—22no—
119C2×C22⋊Q8—131no—
120C2×#117—131no—
121#485—132no—
122#485—132no—
123#484—132no—
124#483—132no—
125#428—131no—
126#428—131no—
127#419—131no—
128#419D1311yescharacteristic, complemented
129#407—131no—
130C22×C13—21no—
131C22×C13—21no—
132C22×C13#12312yes—
133C22×C13C22×D411yescharacteristic
134C2×D13—21no—
135C2×D13—21no—
136C2×D13—21no—
137C2×D13—21no—
138C2×D13—21no—
139C2×D13—44no—
140C2×D13#13712yes—
141C4×C13—42no—
142C4×C13—41no—
143C4×C13—41no—
144C4×C13#12312yes—
145C4×C13C2×#4111yescharacteristic
146C4×C13C2×#4111yescharacteristic
147Dic13—21no—
148Dic13—21no—
149Dic13—41no—
150Dic13—41no—
151Dic13—42no—
152C22×Q8C2×D1311yescharacteristic
153C23×C4—131no—
154C2×M16—131no—
155C2×M16C2×D1311yescharacteristic
156C22⋊Q8—132no—
157C22⋊Q8—132no—
158C22⋊Q8—261no—
159C22⋊Q8—261no—
160#117—131no—
161#117—131no—
162#117—131no—
163#117—261no—
164#117—261no—
165#117C2×D1311yescharacteristic
166C2×C4⋊C4—131no—
167C2×C4⋊C4—131no—
168C2×C4⋊C4—131no—
169C2×C4⋊C4—261no—
170C2×C22⋊C4—261no—
171C2×C22⋊C4—261no—
172C2×C42—261no—
173#107—132no—
174#107—132no—
175#106—132no—
176#106—132no—
177#103—132no—
178#103—132no—
179#103C2×D1312yescomplemented
180#103C2×D1312yescomplemented
181C22⋊C8—132no—
182C22⋊C8—132no—
183C2×C13—22no—
184C2×C13C2×#12311yescharacteristic
185C2×C13C2×#13711yescharacteristic
186C2×C13#57511yescharacteristic
187D13—22no—
188D13—41no—
189C24—131no—
190C2×Q8—21no—
191C2×Q8—22no—
192C2×Q8—22no—
193C2×Q8C22×D1312yes—
194C22×C4—21no—
195C22×C4—131no—
196C22×C4—131no—
197C22×C4—131no—
198C22×C4—131no—
199C22×C4—131no—
200C22×C4—261no—
201C22×C4—261no—
202C22×C4—262no—
203C22×C4—262no—
204C22×C4—261no—
205C22×C4C22×D1311yescharacteristic
206M16—22no—
207M16—262no—
208C2×C8—132no—
209C2×C8C22×D1312yes—
210C4⋊C4—131no—
211C4⋊C4—131no—
212C4⋊C4—132no—
213C4⋊C4—261no—
214C4⋊C4—261no—
215C4⋊C4—262no—
216C4⋊C4—262no—
217C4⋊C4—261no—
218C4⋊C4C22×D1311yescharacteristic
219C4⋊C4C22×D1311yescharacteristic
220C22⋊C4—21no—
221C22⋊C4—261no—
222C22⋊C4—261no—
223C22⋊C4—262no—
224C22⋊C4—262no—
225C22⋊C4—261no—
226C42—21no—
227C42—261no—
228C42—261no—
229C42—261no—
230C13#309511yescharacteristic, complemented, Sylow
231C23—131no—
232C23—131no—
233C23—262no—
234C23—262no—
235C23—521no—
236C23D4×D1311yescharacteristic
237Q8—22no—
238Q8—22no—
239Q8—42no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—42no—
244C2×C4—131no—
245C2×C4—131no—
246C2×C4—262no—
247C2×C4—262no—
248C2×C4—262no—
249C2×C4—261no—
250C2×C4—261no—
251C2×C4—261no—
252C2×C4—261no—
253C2×C4—261no—
254C2×C4—261no—
255C2×C4—262no—
256C2×C4—522no—
257C2×C4—522no—
258C2×C4—522no—
259C2×C4#612712yes—
260C2×C4D4×D1311yescharacteristic
261C2×C4#612912yes—
262C2×C4C23×D1311yescharacteristic
263C8—22no—
264C8—262no—
265C22—21no—
266C22—21no—
267C22—132no—
268C22—261no—
269C22—261no—
270C22—261no—
271C22—261no—
272C22—261no—
273C22—524no—
274C22#8813712yes—
275C22C2×D4×D1311yescharacteristic
276C4—42no—
277C4—41no—
278C4—41no—
279C4—261no—
280C4—261no—
281C4—521no—
282C4—521no—
283C4—522no—
284C4#8813712yes—
285C4C2×#612711yescharacteristic
286C4C2×#612911yescharacteristic
287C2—22no—
288C2—262no—
289C2—521no—
290C2C2×#8813711yescharacteristic
291C2D13×#13711yescharacteristic
292C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#419C2
socleC22×C13C22×D4
prime radicalC23×D13D4
hypercenter#419D13
hypocenterC13#3095
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. C13×#419C2semidirect
4. #11718886C2semidirect
6. #11718782C2semidirect
7. #11718656C2semidirect
8. #11718476C2semidirect
9. #11718475C2semidirect
10. #11718470C2semidirect
11. #11718466C2semidirect
33. C13×#103C22semidirect
34. C13×#103C22semidirect
35. #88075C22semidirect
36. #88075C22semidirect
39. #88058C22semidirect
40. #88057C22semidirect
41. #88048C22semidirect
42. #88047C22semidirect
128. #419D13semidirect
179. #103C2×D13semidirect
180. #103C2×D13semidirect
230. C13#3095semidirect

Maximal subgroups

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

subgroupindex
C2×#882002
D13×#1172
C13×#4192
#117188862
#117187872
#117187822
#117186562
#117184762
#117184752
#117184702
#117184662
#309513