Finite Group Databasebeta

← #13120408

Subgroups — #13120408

Order 1664.

492 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 139 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×Q8×Dic13C211yesmaximal, characteristic, complemented
2C2×#88146C211yesmaximal, characteristic
3C13×#395C211yesmaximal, characteristic, complemented
4#11718892C211yesmaximal, characteristic
5#11718651C212yesmaximal
6#11718644C211yesmaximal, characteristic, complemented
7#11718642C212yesmaximal, complemented
8#11718335C211yesmaximal, characteristic
9#11718329C212yesmaximal
10#11718316C212yesmaximal, complemented
11#11718312C211yesmaximal, characteristic, complemented
12C22×Q8×C13C2211yescharacteristic
13C22×C4×D13C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C4⋊C4C2212yes—
16Q8×Dic13—24no—
17C2×#6103C2211yescharacteristic
18C2×#6103C2211yescharacteristic
19C2×#6103C2212yes—
20C2×#6103C2212yes—
21C2×C4⋊Dic13C2211yescharacteristic
22C2×C4⋊Dic13C2212yes—
23C2×C4⋊Dic13C2211yescharacteristic
24C2×#6101C2212yes—
25C2×C4×Dic13C2211yescharacteristic
26C2×C4×Dic13C2212yes—
27C2×C4×Dic13C2211yescharacteristic
28#88146—24no—
29C13×#95C2211yescharacteristic
30C13×#95C2212yes—
31#88071C2212yes—
32#88071C2212yes—
33#88071C2211yescharacteristic
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37C23×D13C2311yescharacteristic
38C2×Q8×C13—22no—
39C2×Q8×C13—24no—
40C22×C4×C13C2312yes—
41C22×C4×C13C2311yescharacteristic
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2312yes—
44C22×C4×C13C2311yescharacteristic
45C22×Dic13C2312yes—
46C22×Dic13C2311yescharacteristic
47C22×Dic13C2312yes—
48C22×Dic13C2311yescharacteristic
49C22×Dic13C2311yescharacteristic
50C2×C4×D13—22no—
51C2×C4×D13—22no—
52C2×C4×D13—22no—
53C13×C4⋊C4—22no—
54C13×C4⋊C4—24no—
55#6103—24no—
56#6103—22no—
57#6103—24no—
58#6103—22no—
59C4⋊Dic13—22no—
60C4⋊Dic13—22no—
61C4⋊Dic13—24no—
62#6101—24no—
63C4×Dic13—22no—
64C4×Dic13—24no—
65C4×Dic13D414yes—
66#2599—131nomaximal, Sylow
67C23×C13C2411yescharacteristic
68C22×D13—21no—
69C22×D13—22no—
70C22×D13—21no—
71C22×D13—22no—
72C22×D13#4112yes—
73Q8×C13—28no—
74C2×C4×C13—22no—
75C2×C4×C13—21no—
76C2×C4×C13—21no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—21no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13C2×D412yes—
85C2×C4×C13#4114yes—
86C2×C4×C13#4112yes—
87C2×Dic13—21no—
88C2×Dic13—21no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—21no—
92C2×Dic13—22no—
93C2×Dic13—22no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13C2×D412yes—
99C2×Dic13C2×D412yes—
100C4×D13—28no—
101C2×C4×Q8—131no—
102C2×#117—131no—
103#398—131no—
104#397—131no—
105#395D1311yescharacteristic, complemented
106#393—131no—
107#388—132no—
108#387—132no—
109#387—132no—
110#385—132no—
111#383—131no—
112C22×C13C22×D411yescharacteristic
113C22×C13C2×#4112yes—
114C22×C13C2×#4111yescharacteristic
115C22×C13C2×#4111yescharacteristic
116C22×C132−1+412yes—
117C2×D13—22no—
118C2×D13—24no—
119C2×D13—41no—
120C2×D13—41no—
121C2×D13—42no—
122C4×C13—22no—
123C4×C13—22no—
124C4×C13—24no—
125C4×C13—41no—
126C4×C13—42no—
127Dic13—22no—
128Dic13—22no—
129Dic13—42no—
130Dic13—41no—
131Dic13—42no—
132C22×Q8C2×D1311yescharacteristic
133C23×C4—131no—
134C4×Q8—264no—
135#117—264no—
136C2×C4⋊C4—131no—
137C2×C4⋊C4—132no—
138C2×C4⋊C4—131no—
139C2×C4⋊C4—132no—
140C2×C4⋊C4C2×D1311yescharacteristic
141C2×C4⋊C4C2×D1312yes—
142C2×C22⋊C4—131no—
143C2×C22⋊C4—131no—
144C2×C22⋊C4—132no—
145C2×C22⋊C4—132no—
146C2×C42—131no—
147C2×C42—131no—
148C2×C42—132no—
149#95—132no—
150#95—132no—
151#95—131no—
152#95—132no—
153#95—132no—
154#95—132no—
155#95C2×D1311yescharacteristic
156#95C2×D1312yes—
157C2×C13#52511yescharacteristic
158C2×C13#52511yescharacteristic
159C2×C13#53611yescharacteristic
160C2×C13#55212yes—
161C2×C13#55612yes—
162D13—42no—
163C24—131no—
164C2×Q8—22no—
165C2×Q8—24no—
166C22×C4—131no—
167C22×C4—131no—
168C22×C4—132no—
169C22×C4—131no—
170C22×C4—132no—
171C22×C4—262no—
172C22×C4—262no—
173C22×C4—262no—
174C22×C4C22×D1312yes—
175C22×C4C22×D1311yescharacteristic
176C22×C4C22×D1311yescharacteristic
177C22×C4C22×D1312yes—
178C22×C4C22×D1311yescharacteristic
179C4⋊C4—22no—
180C4⋊C4—24no—
181C4⋊C4—262no—
182C4⋊C4—264no—
183C4⋊C4—262no—
184C4⋊C4—264no—
185C22⋊C4—262no—
186C22⋊C4—264no—
187C22⋊C4—262no—
188C22⋊C4—264no—
189C42—134no—
190C42—262no—
191C42—264no—
192C13#259911yescharacteristic, complemented, Sylow
193C23—132no—
194C23—261no—
195C23—262no—
196C23—261no—
197C23—262no—
198C23C23×D1311yescharacteristic
199Q8—28no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—132no—
211C2×C4—132no—
212C2×C4—268no—
213C2×C4—261no—
214C2×C4—262no—
215C2×C4—261no—
216C2×C4—261no—
217C2×C4—262no—
218C2×C4—262no—
219C2×C4—262no—
220C2×C4—262no—
221C2×C4—262no—
222C2×C4—262no—
223C2×C4—262no—
224C2×C4D4×D1312yes—
225C2×C4#612914yes—
226C2×C4#613112yes—
227C22—262no—
228C22—264no—
229C22—521no—
230C22—522no—
231C22—521no—
232C22C2×D4×D1311yescharacteristic
233C22C2×#612912yes—
234C22C2×#613111yescharacteristic
235C22#8825412yes—
236C22#41×D1311yescharacteristic
237C4—22no—
238C4—24no—
239C4—22no—
240C4—41no—
241C4—42no—
242C4—262no—
243C4—262no—
244C4—521no—
245C4—522no—
246C4—522no—
247C2—522no—
248C2#1171929111yescharacteristic
249C2#1171933211yescharacteristic
250C2#1171934412yes—
251C2#1171942911yescharacteristic
252C2#1171943712yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#395C2
prime radicalC23×D13C23
hypercenter#395D13
hypocenterC13#2599
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic13C2semidirect
3. C13×#395C2semidirect
6. #11718644C2semidirect
7. #11718642C2semidirect
10. #11718316C2semidirect
11. #11718312C2semidirect
105. #395D13semidirect
192. C13#2599semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic132
C2×#881462
C13×#3952
#117188922
#117186512
#117186442
#117186422
#117183352
#117183292
#117183162
#117183122
#259913