Finite Group Databasebeta

← #13125659

Subgroups — #13125659

Order 1664.

410 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 115 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×C22⋊Q8C211yesmaximal, characteristic
2C2×#88151C211yesmaximal, characteristic
3C13×#483C211yesmaximal, characteristic, complemented
4#11718711C211yesmaximal, characteristic, complemented
5#11718632C211yesmaximal, characteristic, complemented
6#11718529C212yesmaximal, complemented
7#11718523C212yesmaximal, complemented
8#11718477C212yesmaximal, complemented
9#11718469C212yesmaximal, complemented
10#11718400C211yesmaximal, characteristic, complemented
11#11718387C211yesmaximal, characteristic
12C2×Q8×D13C2211yescharacteristic
13C22×C4×D13C2211yescharacteristic
14C22×Dic26C2211yescharacteristic
15C13×C22⋊Q8C2211yescharacteristic
16C2×C13×C4⋊C4C2211yescharacteristic
17#88200C2211yescharacteristic
18C2×#6107C2212yescomplemented
19C2×#6103—21no—
20C2×C4⋊Dic13—21no—
21#88178C2211yescharacteristic
22C2×Dic52C2212yescomplemented
23C2×#6094C2212yes—
24#88151—21no—
25#88151—21no—
26#88151C2212yes—
27#88151C2212yes—
28#88151C2211yescharacteristic
29#88150—21no—
30C4⋊C4×D13—21no—
31C4⋊C4×D13C2211yescharacteristic
32C22⋊C4×D13—21no—
33#88132—21no—
34C13×#106C2212yescomplemented
35C13×#103C2212yescomplemented
36C13×C22⋊C8C2211yescharacteristic
37C22⋊#1055C2211yescharacteristic
38#88060C2212yes—
39#88056C2212yescomplemented
40#88050C2212yescomplemented
41#88050C2212yescomplemented
42#88048C2212yescomplemented
43C23×D13D411yescharacteristic
44C2×Q8×C13C2311yescharacteristic
45C22×C4×C13—21no—
46C22×C4×C13C2311yescharacteristic
47C22×Dic13—21no—
48C22×Dic13D411yescharacteristic
49Q8×D13—42no—
50C2×C4×D13—21no—
51C2×C4×D13—21no—
52C2×C4×D13—42no—
53C2×C4×D13D411yescharacteristic
54C2×C4×D13D411yescharacteristic
55C2×C4×D13C2311yescharacteristic
56C2×C4×D13C2311yescharacteristic
57C2×Dic26—21no—
58C2×Dic26—21no—
59C2×Dic26—42no—
60C2×Dic26C2312yes—
61C2×Dic26C2311yescharacteristic
62C2×C8×C13C2312yes—
63C13×C4⋊C4—21no—
64C13×C4⋊C4—21no—
65C13×C4⋊C4C2312yes—
66C13×C4⋊C4C2311yescharacteristic
67C13×C22⋊C4—21no—
68C22⋊Dic13—21no—
69#6107—42no—
70#6103—21no—
71#6103—21no—
72#6103—22no—
73#6103—22no—
74C4⋊Dic13—21no—
75C4⋊Dic13—22no—
76C4⋊Dic13—22no—
77C4⋊Dic13C2311yescharacteristic
78#6101—21no—
79#6101—21no—
80#6101—21no—
81C2×#1055C2312yes—
82Dic52—42no—
83#6094—42no—
84#3195—131nomaximal, Sylow
85C23×C13C2×D411yescharacteristic
86C22×D13—22no—
87C22×D13—22no—
88C22×D13—41no—
89C22×D13C2×D411yescharacteristic
90C22×D13C2×D411yescharacteristic
91Q8×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—22no—
96C2×C4×C13—42no—
97C2×C4×C13C2×D411yescharacteristic
98C2×C4×C13C2411yescharacteristic
99C2×Dic13—21no—
100C2×Dic13—21no—
101C2×Dic13—22no—
102C2×Dic13—41no—
103C2×Dic13—42no—
104C2×Dic13C2×D411yescharacteristic
105C2×Dic13C2×D411yescharacteristic
106C4×D13—22no—
107C4×D13—22no—
108C4×D13—41no—
109C4×D13—41no—
110C4×D13—42no—
111C4×D13—42no—
112Dic26—22no—
113Dic26—22no—
114Dic26—22no—
115Dic26—42no—
116Dic26—42no—
117C8×C13—22no—
118#1055—22no—
119C2×C22⋊Q8—131no—
120C2×C22⋊Q8—131no—
121#483—131no—
122#483—132no—
123#483D1311yescharacteristic, complemented
124#470—132no—
125#470—132no—
126#451—131no—
127#451—132no—
128#451—131no—
129#407—131no—
130C22×C13—21no—
131C22×C13—21no—
132C22×C13#13712yes—
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—21no—
142C4×C13—41no—
143C4×C13—41no—
144C4×C13—42no—
145C4×C13H(5,𝔽2)12yes—
146Dic13—21no—
147Dic13—21no—
148Dic13—41no—
149Dic13—42no—
150Dic13—41no—
151C22×Q8—131no—
152C22×Q8—131no—
153C23×C4—131no—
154C2×Q16—132no—
155C2×Q16—132no—
156C2×M16—132no—
157C22⋊Q8—131no—
158C22⋊Q8—131no—
159C22⋊Q8—132no—
160C22⋊Q8—131no—
161C22⋊Q8—132no—
162C22⋊Q8—261no—
163C22⋊Q8—261no—
164C22⋊Q8—261no—
165C22⋊Q8—261no—
166C22⋊Q8C2×D1311yescharacteristic
167C2×C4⋊C4—131no—
168C2×C4⋊C4—261no—
169C2×C4⋊C4—261no—
170C2×C4⋊C4C2×D1311yescharacteristic
171C2×C22⋊C4—261no—
172C2×C22⋊C4—261no—
173#106—132no—
174#106C2×D1312yescomplemented
175#103—132no—
176#103—132no—
177#103—132no—
178#103C2×D1312yescomplemented
179C22⋊C8—131no—
180C22⋊C8—132no—
181C22⋊C8C2×D1311yescharacteristic
182C2×C13—22no—
183C2×C13#53411yescharacteristic
184C2×C13C2×#13711yescharacteristic
185C2×C13C2×#13711yescharacteristic
186D13—22no—
187D13—41no—
188C24—131no—
189C2×Q8—132no—
190C2×Q8—131no—
191C2×Q8—261no—
192C2×Q8—261no—
193C2×Q8—522no—
194C2×Q8—522no—
195C2×Q8C22×D1311yescharacteristic
196C22×C4—21no—
197C22×C4—131no—
198C22×C4—131no—
199C22×C4—131no—
200C22×C4—131no—
201C22×C4—131no—
202C22×C4—261no—
203C22×C4—261no—
204C22×C4—261no—
205C22×C4—522no—
206C22×C4C22×D1311yescharacteristic
207Q16—522no—
208Q16—522no—
209M16—522no—
210C2×C8—132no—
211C2×C8C22×D1312yes—
212C4⋊C4—21no—
213C4⋊C4—21no—
214C4⋊C4—131no—
215C4⋊C4—261no—
216C4⋊C4—261no—
217C4⋊C4—261no—
218C4⋊C4—262no—
219C4⋊C4—262no—
220C4⋊C4—261no—
221C4⋊C4C22×D1311yescharacteristic
222C4⋊C4C22×D1312yes—
223C22⋊C4—21no—
224C22⋊C4—261no—
225C22⋊C4—261no—
226C22⋊C4—262no—
227C22⋊C4—262no—
228C22⋊C4—261no—
229C13#319511yescharacteristic, complemented, Sylow
230C23—131no—
231C23—131no—
232C23—262no—
233C23—262no—
234C23—521no—
235C23D4×D1311yescharacteristic
236Q8—22no—
237Q8—262no—
238Q8—262no—
239Q8—262no—
240Q8—522no—
241Q8—522no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—42no—
247C2×C4—131no—
248C2×C4—131no—
249C2×C4—262no—
250C2×C4—262no—
251C2×C4—261no—
252C2×C4—262no—
253C2×C4—261no—
254C2×C4—521no—
255C2×C4—521no—
256C2×C4—522no—
257C2×C4—522no—
258C2×C4—521no—
259C2×C4—522no—
260C2×C4D4×D1311yescharacteristic
261C2×C4C23×D1311yescharacteristic
262C8—22no—
263C8—262no—
264C22—21no—
265C22—21no—
266C22—132no—
267C22—261no—
268C22—261no—
269C22—261no—
270C22—261no—
271C22—261no—
272C22—524no—
273C22#8816912yes—
274C22C2×D4×D1311yescharacteristic
275C4—21no—
276C4—42no—
277C4—41no—
278C4—41no—
279C4—261no—
280C4—261no—
281C4—521no—
282C4—521no—
283C4—522no—
284C4#8825612yes—
285C2—22no—
286C2—262no—
287C2—521no—
288C2#1171935811yescharacteristic
289C2C2×#8816911yescharacteristic
290C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#483C2
socleC22×C13C22×D4
prime radicalC23×D13D4
hypercenter#483D13
hypocenterC13#3195
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. C13×#483C2semidirect
4. #11718711C2semidirect
5. #11718632C2semidirect
6. #11718529C2semidirect
7. #11718523C2semidirect
8. #11718477C2semidirect
9. #11718469C2semidirect
10. #11718400C2semidirect
18. C2×#6107C22semidirect
22. C2×Dic52C22semidirect
34. C13×#106C22semidirect
35. C13×#103C22semidirect
39. #88056C22semidirect
40. #88050C22semidirect
41. #88050C22semidirect
42. #88048C22semidirect
123. #483D13semidirect
174. #106C2×D13semidirect
178. #103C2×D13semidirect
229. C13#3195semidirect

Maximal subgroups

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

subgroupindex
D13×C22⋊Q82
C2×#881512
C13×#4832
#117187112
#117186322
#117185292
#117185232
#117184772
#117184692
#117184002
#117183872
#319513