Finite Group Databasebeta

← #13126151

Subgroups — #13126151

Order 1664.

392 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 121 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#11719430C211yesmaximal, characteristic
2#11719283C211yesmaximal, characteristic, complemented
3C13×#475C211yesmaximal, characteristic, complemented
4#11718755C211yesmaximal, characteristic, complemented
5#11718688C211yesmaximal, characteristic, complemented
6#11718531C212yesmaximal, complemented
7#11718525C212yesmaximal, complemented
8#11718509C211yesmaximal, characteristic, complemented
9D13×C4⋊C8C211yesmaximal, characteristic, complemented
10#11718479C212yesmaximal, complemented
11#11718468C212yesmaximal, complemented
12C2×#6131—21no—
13C13×C4⋊Q8C2211yescharacteristic
14C4×Q8×C13C2211yescharacteristic
15#88201—21no—
16#88200C2211yescharacteristic
17#88198C2211yescharacteristic
18C2×#6106C2212yes—
19C2×#6095C2212yes—
20C2×C8×D13C2212yes—
21#88151C2211yescharacteristic
22#88150—21no—
23#88149—21no—
24#88149C2212yes—
25#88147—21no—
26#88147C2212yes—
27#88143—21no—
28#88142C2211yescharacteristic
29#88128C2211yescharacteristic
30#88126—21no—
31C42×D13C2211yescharacteristic
32C4×Dic26—21no—
33C4×Dic26C2211yescharacteristic
34C13×#106C2212yes—
35C13×C4⋊C8C2211yescharacteristic
36C13×#103C2212yes—
37#88061C2212yes—
38#88054C2212yes—
39#88050C2212yes—
40#88049C2212yes—
41#88048C2212yes—
42C4⋊#1055C2211yescharacteristic
43C2×Q8×C13—21no—
44C2×Q8×C13C2311yescharacteristic
45#6131—44no—
46C2×D52—22no—
47C2×D52—21no—
48C2×D52—21no—
49C2×D52C2312yes—
50C2×C4×D13—22no—
51C2×C4×D13D411yescharacteristic
52C2×C4×D13D411yescharacteristic
53C2×C4×D13C2311yescharacteristic
54C2×Dic26—21no—
55C2×Dic26C2311yescharacteristic
56C2×C8×C13C2312yes—
57C13×C4⋊C4—21no—
58C13×C4⋊C4—21no—
59C13×C4⋊C4C2312yes—
60C13×C4⋊C4C2311yescharacteristic
61C42×C13—21no—
62C42×C13C2311yescharacteristic
63#6106—42no—
64#6103—21no—
65#6103—21no—
66#6103—22no—
67#6103—22no—
68C4⋊Dic13—21no—
69C4⋊Dic13C2311yescharacteristic
70#6101—21no—
71#6101—21no—
72#6101—21no—
73#6101—21no—
74#6101—21no—
75C4×Dic13—21no—
76C4×Dic13D411yescharacteristic
77C4×Dic13D411yescharacteristic
78C4×Dic13C2311yescharacteristic
79C2×#1055C2312yes—
80#6095—42no—
81C8×D13—42no—
82#3246—131nomaximal, Sylow
83C22×D13—22no—
84C22×D13C2×D411yescharacteristic
85Q8×C13—21no—
86Q8×C13—21no—
87Q8×C13—42no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—22no—
91C2×C4×C13C2×D411yescharacteristic
92C2×C4×C13C2×D411yescharacteristic
93C2×C4×C13C2411yescharacteristic
94C2×Dic13—21no—
95C2×Dic13—21no—
96C2×Dic13C2×D411yescharacteristic
97C2×Dic13C2×D411yescharacteristic
98C2×Dic13C2×D411yescharacteristic
99D52—22no—
100D52—22no—
101D52—42no—
102D52—44no—
103D52—42no—
104C4×D13—21no—
105C4×D13—21no—
106C4×D13—41no—
107C4×D13—44no—
108C4×D13SD1614yescomplemented
109Dic26—21no—
110Dic26—21no—
111Dic26—42no—
112C8×C13—22no—
113#1055—22no—
114#533—131no—
115#532—131no—
116#476—132no—
117#475—131no—
118#475D1311yescharacteristic, complemented
119#465—132no—
120#465—132no—
121#461—132no—
122#460—131no—
123#460—131no—
124C2×C4⋊C8—131no—
125C22×C13C22×D411yescharacteristic
126C2×D13—21no—
127C2×D13—21no—
128C2×D13—42no—
129C2×D13—42no—
130C2×D13—42no—
131C2×D13C2×SD1612yes—
132C4×C13—21no—
133C4×C13—41no—
134C4×C13—42no—
135C4×C13—41no—
136C4×C13C2×SD1612yes—
137C4×C13H(5,𝔽2)11yescharacteristic
138C4×C132−1+411yescharacteristic
139Dic13—21no—
140Dic13—21no—
141Dic13—41no—
142Dic13—41no—
143Dic13C2×SD1612yes—
144C2×#41—261no—
145C2×SD16—132no—
146C2×SD16—132no—
147C22×C8—132no—
148C4⋊Q8—131no—
149C4⋊Q8—131no—
150C4⋊Q8C2×D1311yescharacteristic
151#127—131no—
152#125—261no—
153#124—261no—
154C22⋊Q8—131no—
155C22⋊Q8—131no—
156C22⋊Q8—261no—
157#121—132no—
158#121—261no—
159C4×Q8—131no—
160C4×Q8—261no—
161C4×Q8C2×D1311yescharacteristic
162C4×D4—132no—
163C4×D4—261no—
164#117—261no—
165C2×C42—131no—
166#106—132no—
167#106C2×D1312yes—
168C4⋊C8—132no—
169C4⋊C8—131no—
170C4⋊C8C2×D1311yescharacteristic
171#103—132no—
172#103C2×D1312yes—
173#102—132no—
174#102—132no—
175C2×C13#53711yescharacteristic
176C2×C13C22×SD1611yescharacteristic
177C2×C13#57511yescharacteristic
178D13—22no—
179D13—82no—
180#41—524no—
181C2×Q8—21no—
182C2×Q8—131no—
183C2×Q8—261no—
184C2×Q8C22×D1311yescharacteristic
185C2×D4—132no—
186C2×D4—262no—
187C2×D4—261no—
188C2×D4—261no—
189C22×C4—131no—
190C22×C4—131no—
191C22×C4—131no—
192C22×C4—262no—
193SD16—522no—
194SD16—522no—
195C2×C8—132no—
196C2×C8—522no—
197C2×C8C22×D1312yes—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—131no—
201C4⋊C4—261no—
202C4⋊C4—261no—
203C4⋊C4—261no—
204C4⋊C4—261no—
205C4⋊C4—261no—
206C4⋊C4—261no—
207C4⋊C4C22×D1311yescharacteristic
208C4⋊C4C22×D1312yes—
209C22⋊C4—262no—
210C22⋊C4—262no—
211C22⋊C4—261no—
212C22⋊C4—261no—
213C42—21no—
214C42—131no—
215C42—131no—
216C42—131no—
217C42—261no—
218C42C22×D1311yescharacteristic
219C13#324611yescharacteristic, complemented, Sylow
220C23—131no—
221C23—262no—
222Q8—21no—
223Q8—21no—
224Q8—42no—
225Q8—261no—
226Q8—261no—
227Q8—522no—
228D4—262no—
229D4—262no—
230D4—522no—
231D4—524no—
232D4—522no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—131no—
237C2×C4—134no—
238C2×C4—131no—
239C2×C4—131no—
240C2×C4—261no—
241C2×C4—261no—
242C2×C4—261no—
243C2×C4—261no—
244C2×C4—521no—
245C2×C4—524no—
246C2×C4D4×D1311yescharacteristic
247C2×C4D4×D1311yescharacteristic
248C2×C4C23×D1311yescharacteristic
249C8—22no—
250C8—262no—
251C22—132no—
252C22—261no—
253C22—261no—
254C22—522no—
255C22—522no—
256C22—522no—
257C22C2×D4×D1311yescharacteristic
258C4—21no—
259C4—42no—
260C4—41no—
261C4—41no—
262C4—132no—
263C4—261no—
264C4—261no—
265C4—521no—
266C4—521no—
267C4SD16×D1312yes—
268C4#8825411yescharacteristic
269C4#8825611yescharacteristic
270C2—262no—
271C2—1042no—
272C2#1171933411yescharacteristic
273C2C2×SD16×D1311yescharacteristic
274C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#475C2
socleC22×C13C22×D4
prime radical#11719430C2
hypercenter#475D13
hypocenterC13#3246
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #11719283C2semidirect
3. C13×#475C2semidirect
4. #11718755C2semidirect
5. #11718688C2semidirect
6. #11718531C2semidirect
7. #11718525C2semidirect
8. #11718509C2semidirect
9. D13×C4⋊C8C2semidirect
10. #11718479C2semidirect
11. #11718468C2semidirect
108. C4×D13SD16semidirect
118. #475D13semidirect
219. C13#3246semidirect

Maximal subgroups

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

subgroupindex
#117194302
#117192832
C13×#4752
#117187552
#117186882
#117185312
#117185252
#117185092
D13×C4⋊C82
#117184792
#117184682
#324613