Finite Group Databasebeta

← #13125770

Subgroups — #13125770

Order 1664.

438 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 117 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#11719421C211yesmaximal, characteristic, complemented
3C13×#486C211yesmaximal, characteristic, complemented
4#11718754C211yesmaximal, characteristic, complemented
5#11718734C211yesmaximal, characteristic, complemented
6#11718448C214yesmaximal, complemented
7#11718442C214yesmaximal, complemented
8#11718354C211yesmaximal, characteristic, complemented
9#11718346C211yesmaximal, characteristic, complemented
10C2×#6131—21no—
11C2×#6129C2212yes—
12C13×C4⋊Q8C2211yescharacteristic
13C13×#127C2211yescharacteristic
14#88201—21no—
15#88192—21no—
16#88192—21no—
17#88190C2212yes—
18D4×Dic13—21no—
19D4×Dic13—21no—
20C2×#6104C2214yes—
21C2×#6095C2214yes—
22#88149—21no—
23#88149C2212yes—
24#88147—21no—
25#88147C2212yes—
26#88128C2211yescharacteristic
27C42×D13C2211yescharacteristic
28#88123C2211yescharacteristic
29C13×#102C2214yes—
30C4×C8×C13C2211yescharacteristic
31#88060C2212yes—
32#88054C2212yes—
33#88050C2214yes—
34C4×#1055C2211yescharacteristic
35C2×Q8×C13—21no—
36C2×D4×C13—21no—
37C2×D4×C13—21no—
38C2×D4×C13C2312yes—
39C2×C22⋊D13—22no—
40C22×Dic13—22no—
41#6131—44no—
42#6129—44no—
43C2×D52—22no—
44C2×D52—21no—
45C2×D52—21no—
46C2×D52C2312yes—
47C2×C4×D13—22no—
48C2×C4×D13D411yescharacteristic
49C2×C4×D13D411yescharacteristic
50C2×C4×D13C2311yescharacteristic
51C2×Dic26C2312yes—
52C2×C8×C13C2312yes—
53C13×C4⋊C4—21no—
54C13×C4⋊C4C2312yes—
55C42×C13C2311yescharacteristic
56C22⋊Dic13—22no—
57C22⋊Dic13—22no—
58#6104—44no—
59#6103—22no—
60#6103—22no—
61C4⋊Dic13—21no—
62C4⋊Dic13—21no—
63C4×Dic13D411yescharacteristic
64C4×Dic13D411yescharacteristic
65C4×Dic13C2311yescharacteristic
66C2×#1055C2312yes—
67#6095—44no—
68#3207—131nomaximal, Sylow
69C23×C13—22no—
70C22×D13—22no—
71C22×D13C2×D411yescharacteristic
72Q8×C13—42no—
73D4×C13—24no—
74D4×C13—42no—
75D4×C13—42no—
76C2×C4×C13—22no—
77C2×C4×C13C2×D411yescharacteristic
78C2×C4×C13C2×D411yescharacteristic
79C2×C4×C13C2411yescharacteristic
80C22⋊D13—44no—
81C2×Dic13—22no—
82C2×Dic13—44no—
83C2×Dic13C2×D411yescharacteristic
84C2×Dic13C2×D411yescharacteristic
85C2×Dic13C2×D411yescharacteristic
86D52—24no—
87D52—44no—
88D52—42no—
89D52—42no—
90C4×D13—22no—
91C4×D13—22no—
92C4×D13—22no—
93C4×D13—44no—
94Dic26—24no—
95C8×C13—22no—
96#1055—22no—
97#532—131no—
98#532—131no—
99#493—131no—
100#492—131no—
101#487—131no—
102#486D1311yescharacteristic, complemented
103#463—134no—
104#449—134no—
105#431—131no—
106C22×C13—42no—
107C22×C13—42no—
108C22×C13—42no—
109C22×C13C22×D411yescharacteristic
110C2×D13—21no—
111C2×D13—21no—
112C2×D13—21no—
113C2×D13—42no—
114C2×D13—42no—
115C2×D13—42no—
116C4×C13—42no—
117C4×C13#13512yes—
118C4×C13AGL(1,ℤ/8)12yes—
119C4×C13H(5,𝔽2)12yes—
120Dic13—21no—
121Dic13—21no—
122Dic13—21no—
123Dic13—42no—
124C2×#41—132no—
125C2×#41—261no—
126C2×SD16—134no—
127C2×D8—134no—
128C4⋊Q8—131no—
129C4⋊Q8C2×D1311yescharacteristic
130#127—131no—
131#127C2×D1311yescharacteristic
132#124—132no—
133#124—261no—
134#121—132no—
135#121—261no—
136#121—261no—
137#121—261no—
138C4×D4—132no—
139C4×D4—261no—
140C4×D4—261no—
141C4×D4—261no—
142C2×C42—131no—
143C4⋊C8—132no—
144#103—134no—
145#102C2×D1314yes—
146C22⋊C8—132no—
147C4×C8—131no—
148C4×C8C2×D1311yescharacteristic
149C2×C13—82no—
150C2×C13#53511yescharacteristic
151C2×C13C2×#13511yescharacteristic
152C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
153D13—41no—
154D13—82no—
155#41—524no—
156#41—524no—
157C2×Q8—21no—
158C2×Q8—132no—
159C2×D4—21no—
160C2×D4—21no—
161C2×D4—132no—
162C2×D4—262no—
163C2×D4—262no—
164C2×D4—261no—
165C2×D4—261no—
166C2×D4C22×D1312yes—
167C22×C4—131no—
168C22×C4—131no—
169C22×C4—131no—
170C22×C4—262no—
171C22×C4—262no—
172SD16—524no—
173D8—524no—
174C2×C8—132no—
175C2×C8C22×D1312yes—
176C4⋊C4—21no—
177C4⋊C4—261no—
178C4⋊C4—261no—
179C4⋊C4C22×D1312yes—
180C22⋊C4—262no—
181C22⋊C4—262no—
182C22⋊C4—262no—
183C22⋊C4—262no—
184C42—131no—
185C42—131no—
186C42—131no—
187C42C22×D1311yescharacteristic
188C13#320711yescharacteristic, complemented, Sylow
189C23—22no—
190C23—131no—
191C23—262no—
192Q8—42no—
193Q8—264no—
194D4—24no—
195D4—42no—
196D4—42no—
197D4—264no—
198D4—524no—
199D4—524no—
200D4—522no—
201D4—522no—
202C2×C4—22no—
203C2×C4—131no—
204C2×C4—131no—
205C2×C4—131no—
206C2×C4—262no—
207C2×C4—262no—
208C2×C4—262no—
209C2×C4—262no—
210C2×C4—524no—
211C2×C4—524no—
212C2×C4D4×D1311yescharacteristic
213C2×C4D4×D1311yescharacteristic
214C2×C4C23×D1311yescharacteristic
215C8—22no—
216C8—262no—
217C22—42no—
218C22—42no—
219C22—42no—
220C22—261no—
221C22—261no—
222C22—261no—
223C22—522no—
224C22—522no—
225C22—522no—
226C22C2×D4×D1311yescharacteristic
227C4—42no—
228C4—261no—
229C4—261no—
230C4—261no—
231C4—522no—
232C4#8816512yes—
233C4#8817012yes—
234C4#8825612yes—
235C2—82no—
236C2—521no—
237C2—1042no—
238C2#1171937911yescharacteristic
239C2C2×#8816511yescharacteristic
240C2C2×#8817011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#486C2
socleC22×C13C22×D4
hypercenter#486D13
hypocenterC13#3207
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #11719430C2semidirect
2. #11719421C2semidirect
3. C13×#486C2semidirect
4. #11718754C2semidirect
5. #11718734C2semidirect
6. #11718448C2semidirect
7. #11718442C2semidirect
8. #11718354C2semidirect
9. #11718346C2semidirect
102. #486D13semidirect
188. C13#3207semidirect

Maximal subgroups

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

subgroupindex
#117194302
#117194212
C13×#4862
#117187542
#117187342
#117184482
#117184422
#117183542
#117183462
#320713