Finite Group Databasebeta

← #13122898

Subgroups — #13122898

Order 1664.

430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C2×#88198C211yesmaximal, characteristic, complemented
2C2×#88133C211yesmaximal, characteristic
3C13×#393C211yesmaximal, characteristic
4#11718890C211yesmaximal, characteristic, complemented
5#11718613C212yesmaximal
6#11718610C212yesmaximal
7#11718608C211yesmaximal, characteristic
8#11718321C212yesmaximal, complemented
9#11718318C212yesmaximal, complemented
10#11718317C211yesmaximal, characteristic, complemented
11#11718312C211yesmaximal, characteristic, complemented
12C22×Q8×C13C2211yescharacteristic
13C22×Dic26C2211yescharacteristic
14C2×C13×C22⋊C4C2211yescharacteristic
15C2×C13×C22⋊C4C2212yes—
16C2×C22⋊Dic13C2211yescharacteristic
17C2×C22⋊Dic13C2211yescharacteristic
18C2×C22⋊Dic13C2212yes—
19#88198—24no—
20C2×C4⋊Dic13C2211yescharacteristic
21C2×C4⋊Dic13C2212yes—
22C2×#6101C2211yescharacteristic
23C2×#6101C2211yescharacteristic
24C2×#6101C2212yes—
25C2×#6101C2212yes—
26C2×#6101C2212yes—
27C2×C4×Dic13C2211yescharacteristic
28#88133—24no—
29C13×#95C2211yescharacteristic
30C13×#95C2212yes—
31#88071C2212yes—
32#88071C2212yes—
33#88071C2211yescharacteristic
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37C24×C13C2311yescharacteristic
38C2×Q8×C13—22no—
39C2×Q8×C13—42no—
40C22×C4×C13C2312yes—
41C22×C4×C13C2311yescharacteristic
42C22×C4×C13C2312yes—
43C22×C4×C13C2311yescharacteristic
44C22×Dic13C2312yes—
45C22×Dic13C2311yescharacteristic
46C22×Dic13C2312yes—
47C22×Dic13C2311yescharacteristic
48C22×Dic13C2311yescharacteristic
49C22×Dic13C2311yescharacteristic
50C2×Dic26—22no—
51C2×Dic26—42no—
52C13×C22⋊C4—22no—
53C13×C22⋊C4—42no—
54C22⋊Dic13—22no—
55C22⋊Dic13—22no—
56C22⋊Dic13—42no—
57C4⋊Dic13—22no—
58C4⋊Dic13—42no—
59#6101—22no—
60#6101—22no—
61#6101—24no—
62#6101—24no—
63#6101—42no—
64C4×Dic13D414yes—
65#2821—131nomaximal, Sylow
66C23×C13—21no—
67C23×C13—22no—
68C23×C13—21no—
69C23×C13—21no—
70C23×C13—22no—
71C23×C13C2411yescharacteristic
72Q8×C13—44no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13—21no—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13C2×D412yes—
83C2×Dic13—21no—
84C2×Dic13—22no—
85C2×Dic13—21no—
86C2×Dic13—21no—
87C2×Dic13—22no—
88C2×Dic13—21no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13—21no—
94C2×Dic13—21no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13C2×D412yes—
98C2×Dic13C2×D412yes—
99Dic26—44no—
100C2×C4⋊Q8—131no—
101C2×#126—131no—
102#400—132no—
103#399—132no—
104#398—132no—
105#397—132no—
106#395—131no—
107#395—131no—
108#393—131no—
109#393D1311yescharacteristic
110#383—131no—
111C22×C13—41no—
112C22×C13—41no—
113C22×C13—41no—
114C22×C13—42no—
115C22×C13—42no—
116C22×C13C22×D411yescharacteristic
117C22×C13H(5,𝔽2)12yes—
118C22×C132−1+411yescharacteristic
119C22×C132−1+411yescharacteristic
120C22×C132−1+412yes—
121C4×C13—22no—
122C4×C13—42no—
123C4×C13—41no—
124C4×C13—42no—
125Dic13—22no—
126Dic13—22no—
127Dic13—42no—
128Dic13—41no—
129Dic13—41no—
130Dic13—42no—
131C22×Q8—131no—
132C22×Q8C2×D1311yescharacteristic
133C4⋊Q8—264no—
134#126—264no—
135C2×C4⋊C4—131no—
136C2×C4⋊C4—131no—
137C2×C4⋊C4—131no—
138C2×C4⋊C4—132no—
139C2×C4⋊C4—132no—
140C2×C4⋊C4—132no—
141C2×C4⋊C4—132no—
142C2×C22⋊C4—131no—
143C2×C22⋊C4—131no—
144C2×C22⋊C4—132no—
145C2×C22⋊C4C2×D1311yescharacteristic
146C2×C22⋊C4C2×D1312yes—
147C2×C42—131no—
148#95—131no—
149#95—132no—
150#95—132no—
151#95—132no—
152#95—132no—
153#95—132no—
154#95C2×D1311yescharacteristic
155#95C2×D1312yes—
156C2×C13—81no—
157C2×C13#53511yescharacteristic
158C2×C13#53611yescharacteristic
159C2×C13#53611yescharacteristic
160C2×C13#56312yes—
161C2×C13#56312yes—
162C24C22×D1311yescharacteristic
163C2×Q8—22no—
164C2×Q8—42no—
165C2×Q8—262no—
166C2×Q8—522no—
167C22×C4—131no—
168C22×C4—131no—
169C22×C4—132no—
170C22×C4—131no—
171C22×C4—132no—
172C22×C4—131no—
173C22×C4C22×D1312yes—
174C22×C4C22×D1311yescharacteristic
175C22×C4C22×D1312yes—
176C22×C4C22×D1311yescharacteristic
177C4⋊C4—262no—
178C4⋊C4—262no—
179C4⋊C4—264no—
180C4⋊C4—264no—
181C4⋊C4—262no—
182C4⋊C4—522no—
183C4⋊C4—522no—
184C22⋊C4—22no—
185C22⋊C4—42no—
186C22⋊C4—262no—
187C22⋊C4—262no—
188C22⋊C4—522no—
189C42—134no—
190C13#282111yescharacteristic, complemented, Sylow
191C23—21no—
192C23—22no—
193C23—21no—
194C23—21no—
195C23—22no—
196C23C23×D1311yescharacteristic
197Q8—44no—
198Q8—524no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—132no—
209C2×C4—132no—
210C2×C4—261no—
211C2×C4—261no—
212C2×C4—262no—
213C2×C4—261no—
214C2×C4—261no—
215C2×C4—262no—
216C2×C4—262no—
217C2×C4—262no—
218C2×C4—262no—
219C2×C4—262no—
220C2×C4—261no—
221C2×C4—262no—
222C2×C4—261no—
223C2×C4—262no—
224C2×C4D4×D1312yes—
225C22—41no—
226C22—41no—
227C22—42no—
228C22—42no—
229C22—41no—
230C22C2×D4×D1311yescharacteristic
231C22#8825112yes—
232C22#8825411yescharacteristic
233C22#8825711yescharacteristic
234C22#8825712yes—
235C4—22no—
236C4—42no—
237C4—42no—
238C4—41no—
239C4—262no—
240C4—262no—
241C4—521no—
242C4—522no—
243C4—521no—
244C4—522no—
245C2—81no—
246C2#1171929711yescharacteristic
247C2#1171933311yescharacteristic
248C2#1171935112yes—
249C2#1171937712yes—
250C2#1171938011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#393C2
prime radicalC24×C13C23
hypercenter#393D13
hypocenterC13#2821
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#88198C2semidirect
4. #11718890C2semidirect
8. #11718321C2semidirect
9. #11718318C2semidirect
10. #11718317C2semidirect
11. #11718312C2semidirect
190. C13#2821semidirect

Maximal subgroups

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

subgroupindex
C2×#881982
C2×#881332
C13×#3932
#117188902
#117186132
#117186102
#117186082
#117183212
#117183182
#117183172
#117183122
#282113