Finite Group Databasebeta

← #13125536

Subgroups — #13125536

Order 1664.

410 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 119 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, complemented
2#11719396C211yesmaximal, characteristic, complemented
3C13×#501C211yesmaximal, characteristic, complemented
4#11718750C211yesmaximal, characteristic, complemented
5#11718728C211yesmaximal, characteristic, complemented
6#11718550C212yesmaximal, complemented
7#11718544C212yesmaximal, complemented
8#11718530C212yesmaximal, complemented
9#11718525C212yesmaximal, complemented
10#11718373C211yesmaximal, characteristic, complemented
11D13×#97C211yesmaximal, characteristic, complemented
12C2×#6131—21no—
13C13×C4⋊Q8C2211yescharacteristic
14C13×#125C2211yescharacteristic
15#88201—21no—
16C2×D104C2212yes—
17C2×#6095C2212yes—
18C2×C8×D13C2212yes—
19#88152—21no—
20#88151C2211yescharacteristic
21#88149—21no—
22#88149C2212yes—
23#88149C2211yescharacteristic
24#88148—21no—
25#88147—21no—
26#88147—21no—
27#88147C2212yes—
28#88147C2211yescharacteristic
29#88146—21no—
30#88141C2211yescharacteristic
31#88129C2211yescharacteristic
32#88128C2211yescharacteristic
33C42×D13C2211yescharacteristic
34C13×#107C2212yes—
35C13×#106C2212yes—
36C13×#97C2211yescharacteristic
37#88055C2212yes—
38#88050C2212yes—
39#88049C2212yes—
40#88049C2212yes—
41#88049C2212yes—
42#88043C2211yescharacteristic
43C2×Q8×C13—21no—
44#6131—44no—
45C2×D52—21no—
46C2×D52—22no—
47C2×D52—21no—
48C2×D52—21no—
49C2×D52C2312yes—
50C2×D52C2311yescharacteristic
51C2×C4×D13—21no—
52C2×C4×D13—22no—
53C2×C4×D13D411yescharacteristic
54C2×C4×D13D411yescharacteristic
55C2×C4×D13C2311yescharacteristic
56C2×Dic26C2311yescharacteristic
57C2×C8×C13C2312yes—
58C13×C4⋊C4—21no—
59C13×C4⋊C4—21no—
60C13×C4⋊C4—21no—
61C13×C4⋊C4C2311yescharacteristic
62C13×C4⋊C4C2312yes—
63C13×C4⋊C4C2311yescharacteristic
64C42×C13C2311yescharacteristic
65#6103—21no—
66#6103—21no—
67#6103—21no—
68#6103—21no—
69#6103—22no—
70#6103—21no—
71#6103—22no—
72C4⋊Dic13—21no—
73#6101—21no—
74C4×Dic13—21no—
75C4×Dic13D411yescharacteristic
76C4×Dic13D411yescharacteristic
77C4×Dic13C2311yescharacteristic
78C2×#1055C2312yes—
79D104—24no—
80#6095—24no—
81C8×D13—24no—
82#3180—131nomaximal, Sylow
83C22×D13—21no—
84C22×D13—22no—
85C22×D13C2×D411yescharacteristic
86Q8×C13—42no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—22no—
90C2×C4×C13C2×D411yescharacteristic
91C2×C4×C13C2×D411yescharacteristic
92C2×C4×C13C2411yescharacteristic
93C2×Dic13—21no—
94C2×Dic13C2×D411yescharacteristic
95C2×Dic13C2×D411yescharacteristic
96C2×Dic13C2×D411yescharacteristic
97D52—22no—
98D52—22no—
99D52—22no—
100D52—42no—
101D52—42no—
102D52—42no—
103D52—44no—
104C4×D13—22no—
105C4×D13—22no—
106C4×D13—41no—
107C4×D13—42no—
108C4×D13—44no—
109Dic26—22no—
110C8×C13#4114yescomplemented
111#1055—22no—
112#532—131no—
113#529—131no—
114#501D1311yescharacteristic, complemented
115#496—131no—
116#490—131no—
117#489—131no—
118#466—132no—
119#465—132no—
120#442—132no—
121#440—132no—
122C2×#97—131no—
123C22×C13C22×D411yescharacteristic
124C2×D13—21no—
125C2×D13—21no—
126C2×D13—42no—
127C2×D13—41no—
128C2×D13—42no—
129C2×D13—41no—
130C2×D13—41no—
131C2×D13—42no—
132C2×D13AGL(1,ℤ/8)12yes—
133C4×C13—21no—
134C4×C13—21no—
135C4×C13—42no—
136C4×C13—41no—
137C4×C13—41no—
138C4×C13C2×#4112yes—
139Dic13—21no—
140Dic13—21no—
141Dic13—21no—
142Dic13—41no—
143C2×#41—261no—
144C2×SD16—132no—
145C2×D8—132no—
146C22×C8—132no—
147C4⋊Q8C2×D1311yescharacteristic
148#127—131no—
149#126—261no—
150#125C2×D1311yescharacteristic
151#124—131no—
152#124—261no—
153#123—261no—
154C22⋊Q8—131no—
155#121—131no—
156#121—132no—
157#121—261no—
158C4×Q8—131no—
159C4×D4—131no—
160C4×D4—132no—
161C4×D4—261no—
162C4×D4—261no—
163#117—261no—
164C2×C42—131no—
165#107C2×D1312yes—
166#106C2×D1312yes—
167#103—132no—
168#102—132no—
169#102—132no—
170#102—132no—
171#97—132no—
172#97—131no—
173#97C2×D1311yescharacteristic
174C2×C13#53211yescharacteristic
175C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
176C2×C13#57511yescharacteristic
177D13—22no—
178D13—82no—
179D13—81no—
180#41—524no—
181C2×Q8—21no—
182C2×Q8—131no—
183C2×D4—131no—
184C2×D4—132no—
185C2×D4—261no—
186C2×D4—262no—
187C2×D4—261no—
188C2×D4—261no—
189C22×C4—131no—
190C22×C4—131no—
191C22×C4—131no—
192C22×C4—261no—
193C22×C4—262no—
194SD16—264no—
195D8—264no—
196C2×C8—132no—
197C2×C8—264no—
198C2×C8C22×D1312yes—
199C4⋊C4—21no—
200C4⋊C4—21no—
201C4⋊C4—21no—
202C4⋊C4—261no—
203C4⋊C4—261no—
204C4⋊C4C22×D1311yescharacteristic
205C4⋊C4C22×D1311yescharacteristic
206C4⋊C4C22×D1312yes—
207C22⋊C4—261no—
208C22⋊C4—262no—
209C22⋊C4—261no—
210C22⋊C4—262no—
211C22⋊C4—261no—
212C22⋊C4—261no—
213C22⋊C4—261no—
214C42—131no—
215C42—131no—
216C42—131no—
217C42—261no—
218C42C22×D1311yescharacteristic
219C13#318011yescharacteristic, complemented, Sylow
220C23—131no—
221C23—261no—
222C23—262no—
223Q8—42no—
224Q8—262no—
225D4—262no—
226D4—262no—
227D4—262no—
228D4—522no—
229D4—522no—
230D4—522no—
231D4—524no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—131no—
236C2×C4—131no—
237C2×C4—131no—
238C2×C4—262no—
239C2×C4—262no—
240C2×C4—261no—
241C2×C4—521no—
242C2×C4—522no—
243C2×C4—524no—
244C2×C4D4×D1311yescharacteristic
245C2×C4D4×D1311yescharacteristic
246C2×C4C23×D1311yescharacteristic
247C8—262no—
248C8#613114yescomplemented
249C22—132no—
250C22—261no—
251C22—261no—
252C22—521no—
253C22—522no—
254C22—522no—
255C22—521no—
256C22—521no—
257C22—522no—
258C22C2×D4×D1311yescharacteristic
259C4—21no—
260C4—21no—
261C4—42no—
262C4—41no—
263C4—41no—
264C4—261no—
265C4—261no—
266C4—261no—
267C4—521no—
268C4C2×#613112yes—
269C2—262no—
270C2—1042no—
271C2—1041no—
272C2#1171943011yescharacteristic
273C2D13×AGL(1,ℤ/8)11yescharacteristic
274C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#501C2
socleC22×C13C22×D4
hypercenter#501D13
hypocenterC13#3180
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #11719430C2semidirect
2. #11719396C2semidirect
3. C13×#501C2semidirect
4. #11718750C2semidirect
5. #11718728C2semidirect
6. #11718550C2semidirect
7. #11718544C2semidirect
8. #11718530C2semidirect
9. #11718525C2semidirect
10. #11718373C2semidirect
11. D13×#97C2semidirect
110. C8×C13#41semidirect
114. #501D13semidirect
219. C13#3180semidirect
248. C8#6131semidirect

Maximal subgroups

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

subgroupindex
#117194302
#117193962
C13×#5012
#117187502
#117187282
#117185502
#117185442
#117185302
#117185252
#117183732
D13×#972
#318013