Finite Group Databasebeta

← #13124786

Subgroups — #13124786

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
1D13×#117C211yesmaximal, characteristic
2C2×#88151C211yesmaximal, characteristic
3C13×#428C211yesmaximal, characteristic, complemented
4#11718787C211yesmaximal, characteristic
5#11718781C211yesmaximal, characteristic, complemented
6#11718665C211yesmaximal, characteristic, complemented
7#11718625C211yesmaximal, characteristic, complemented
8#11718549C212yesmaximal, complemented
9#11718545C212yesmaximal, complemented
10#11718528C212yesmaximal, complemented
11#11718523C212yesmaximal, complemented
12C22×C4×D13C2211yescharacteristic
13C22×Dic26C2211yescharacteristic
14C2×C13×M16C2211yescharacteristic
15C13×#117C2211yescharacteristic
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×#6103—21no—
18#88180C2211yescharacteristic
19C2×C4⋊Dic13—21no—
20C2×#6099C2211yescharacteristic
21#88151—21no—
22#88151—21no—
23#88151C2212yes—
24#88151C2212yes—
25#88146C2211yescharacteristic
26#88146C2211yescharacteristic
27C4⋊C4×D13C2211yescharacteristic
28C4⋊C4×D13C2211yescharacteristic
29C22⋊C4×D13—21no—
30#88131—21no—
31#88126—21no—
32C42×D13—21no—
33C13×#107C2212yescomplemented
34C13×#106C2212yescomplemented
35#88060C2212yes—
36#88060C2212yes—
37#88056C2212yescomplemented
38#88056C2212yescomplemented
39#88050C2212yescomplemented
40#88050C2212yescomplemented
41#88048C2212yescomplemented
42#88047C2212yescomplemented
43C23×D13D411yescharacteristic
44C22×C4×C13—21no—
45C22×C4×C13C2311yescharacteristic
46C22×Dic13—21no—
47C22×Dic13D411yescharacteristic
48C2×C4×D13—22no—
49C2×C4×D13—22no—
50C2×C4×D13—21no—
51C2×C4×D13—21no—
52C2×C4×D13D411yescharacteristic
53C2×C4×D13D411yescharacteristic
54C2×C4×D13C2311yescharacteristic
55C2×C4×D13C2311yescharacteristic
56C2×Dic26—22no—
57C2×Dic26—22no—
58C2×Dic26—21no—
59C2×Dic26C2312yes—
60C13×M16—22no—
61C2×C8×C13C2312yes—
62C13×C4⋊C4—21no—
63C13×C4⋊C4C2311yescharacteristic
64C13×C4⋊C4C2312yes—
65C13×C4⋊C4C2311yescharacteristic
66C13×C22⋊C4—21no—
67C42×C13—21no—
68C22⋊Dic13—21no—
69#6103—21no—
70#6103—21no—
71#6103—22no—
72#6103—22no—
73C4⋊Dic13—22no—
74C4⋊Dic13—22no—
75C4⋊Dic13C2311yescharacteristic
76C4⋊Dic13C2311yescharacteristic
77#6101—21no—
78#6101—21no—
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
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—22no—
94C2×C4×C13—42no—
95C2×C4×C13C2×D411yescharacteristic
96C2×C4×C13#4112yes—
97C2×C4×C13#4112yes—
98C2×C4×C13C2411yescharacteristic
99C2×Dic13—22no—
100C2×Dic13—21no—
101C2×Dic13—21no—
102C2×Dic13—22no—
103C2×Dic13—42no—
104C2×Dic13C2×D411yescharacteristic
105C2×Dic13C2×D411yescharacteristic
106C4×D13—22no—
107C4×D13—22no—
108C4×D13—21no—
109C4×D13—21no—
110C4×D13—21no—
111C4×D13—21no—
112C4×D13—42no—
113C4×D13—42no—
114Dic26—22no—
115Dic26—22no—
116Dic26—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#428D1311yescharacteristic, complemented
127#419—131no—
128#419—131no—
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—41no—
142C4×C13—41no—
143C4×C13—42no—
144C4×C13#12312yes—
145C4×C13C2×#4111yescharacteristic
146C4×C13C2×#4111yescharacteristic
147Dic13—21no—
148Dic13—21no—
149Dic13—42no—
150Dic13—41no—
151Dic13—41no—
152C22×Q8—131no—
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—261no—
169C2×C4⋊C4C2×D1311yescharacteristic
170C2×C22⋊C4—261no—
171C2×C22⋊C4—261no—
172C2×C42—261no—
173#107—132no—
174#107C2×D1312yescomplemented
175#106—132no—
176#106C2×D1312yescomplemented
177#103—132no—
178#103—132no—
179#103—132no—
180#103—132no—
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—132no—
191C2×Q8—261no—
192C2×Q8—262no—
193C2×Q8—262no—
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—21no—
211C4⋊C4—131no—
212C4⋊C4—131no—
213C4⋊C4—261no—
214C4⋊C4—261no—
215C4⋊C4—262no—
216C4⋊C4—262no—
217C4⋊C4C22×D1311yescharacteristic
218C4⋊C4C22×D1311yescharacteristic
219C4⋊C4C22×D1312yes—
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—262no—
238Q8—262no—
239Q8—522no—
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#613112yes—
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#8814812yes—
275C22C2×D4×D1311yescharacteristic
276C4—42no—
277C4—41no—
278C4—41no—
279C4—261no—
280C4—261no—
281C4—522no—
282C4—521no—
283C4—521no—
284C4#8814812yes—
285C4C2×#612711yescharacteristic
286C4C2×#613111yescharacteristic
287C2—22no—
288C2—262no—
289C2—521no—
290C2C2×#8814811yescharacteristic
291C2#1171947811yescharacteristic
292C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#428C2
socleC22×C13C22×D4
prime radicalC23×D13D4
hypercenter#428D13
hypocenterC13#3095
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
3. C13×#428C2semidirect
5. #11718781C2semidirect
6. #11718665C2semidirect
7. #11718625C2semidirect
8. #11718549C2semidirect
9. #11718545C2semidirect
10. #11718528C2semidirect
11. #11718523C2semidirect
33. C13×#107C22semidirect
34. C13×#106C22semidirect
37. #88056C22semidirect
38. #88056C22semidirect
39. #88050C22semidirect
40. #88050C22semidirect
41. #88048C22semidirect
42. #88047C22semidirect
126. #428D13semidirect
174. #107C2×D13semidirect
176. #106C2×D13semidirect
230. C13#3095semidirect

Maximal subgroups

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

subgroupindex
D13×#1172
C2×#881512
C13×#4282
#117187872
#117187812
#117186652
#117186252
#117185492
#117185452
#117185282
#117185232
#309513