Finite Group Databasebeta

← #13120529

Subgroups — #13120529

Order 1664.

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

normal subgroups only

This group has 476 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×#88146C211yesmaximal, characteristic
2C2×#88144C211yesmaximal, characteristic, complemented
3C13×#398C211yesmaximal, characteristic, complemented
4#11718654C211yesmaximal, characteristic
5#11718650C212yesmaximal
6#11718647C211yesmaximal, characteristic, complemented
7#11718646C212yesmaximal, complemented
8#11718338C211yesmaximal, characteristic
9#11718331C212yesmaximal
10#11718315C212yesmaximal, complemented
11#11718309C211yesmaximal, characteristic, complemented
12C22×C4×D13C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C4⋊C4C2212yes—
16C2×#6103C2211yescharacteristic
17C2×#6103C2211yescharacteristic
18C2×#6103C2212yes—
19C2×#6103C2212yes—
20C2×C4⋊Dic13C2212yes—
21C2×C4⋊Dic13C2211yescharacteristic
22C2×C4⋊Dic13C2211yescharacteristic
23C2×C4⋊Dic13C2212yes—
24C2×#6101C2212yes—
25C2×C4×Dic13C2211yescharacteristic
26C2×C4×Dic13C2212yes—
27C2×C4×Dic13C2211yescharacteristic
28#88146—24no—
29#88144—24no—
30C13×#95C2211yescharacteristic
31C13×#95C2212yes—
32#88071C2212yes—
33#88071C2211yescharacteristic
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37C23×D13C2311yescharacteristic
38C22×C4×C13C2311yescharacteristic
39C22×C4×C13C2312yes—
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2311yescharacteristic
42C22×C4×C13C2312yes—
43C22×Dic13C2312yes—
44C22×Dic13C2311yescharacteristic
45C22×Dic13C2312yes—
46C22×Dic13C2311yescharacteristic
47C22×Dic13C2311yescharacteristic
48C2×C4×D13—22no—
49C2×C4×D13—22no—
50C2×C4×D13—22no—
51C13×C4⋊C4—22no—
52C13×C4⋊C4—22no—
53C13×C4⋊C4—24no—
54#6103—24no—
55#6103—22no—
56#6103—24no—
57#6103—22no—
58C4⋊Dic13—22no—
59C4⋊Dic13—24no—
60C4⋊Dic13—24no—
61C4⋊Dic13—22no—
62#6101—24no—
63C4×Dic13—24no—
64C4×Dic13—22no—
65C4×Dic13D414yes—
66#2611—131nomaximal, Sylow
67C23×C13C2411yescharacteristic
68C22×D13—21no—
69C22×D13—22no—
70C22×D13—21no—
71C22×D13—22no—
72C22×D13#4112yes—
73C2×C4×C13—21no—
74C2×C4×C13—22no—
75C2×C4×C13—21no—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—21no—
79C2×C4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13C2×D412yes—
84C2×C4×C13#4112yes—
85C2×C4×C13#4114yes—
86C2×Dic13—22no—
87C2×Dic13—21no—
88C2×Dic13—21no—
89C2×Dic13—21no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13—22no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13C2×D412yes—
98C2×Dic13C2×D412yes—
99C4×D13—28no—
100C2×#125—131no—
101C2×#117—131no—
102#400—131no—
103#399—131no—
104#398D1311yescharacteristic, complemented
105#397—131no—
106#389—132no—
107#388—132no—
108#387—132no—
109#385—132no—
110#376—131no—
111C22×C13C22×D411yescharacteristic
112C22×C13C2×#4111yescharacteristic
113C22×C13C2×#4112yes—
114C22×C13C2×#4111yescharacteristic
115C22×C132−1+412yes—
116C2×D13—22no—
117C2×D13—24no—
118C2×D13—41no—
119C2×D13—41no—
120C2×D13—42no—
121C4×C13—22no—
122C4×C13—22no—
123C4×C13—24no—
124C4×C13—42no—
125C4×C13—41no—
126Dic13—22no—
127Dic13—22no—
128Dic13—41no—
129Dic13—42no—
130Dic13—42no—
131C23×C4—131no—
132#125—264no—
133#117—264no—
134C2×C4⋊C4—131no—
135C2×C4⋊C4—132no—
136C2×C4⋊C4—132no—
137C2×C4⋊C4—131no—
138C2×C4⋊C4—132no—
139C2×C4⋊C4C2×D1311yescharacteristic
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—131no—
151#95—132no—
152#95—132no—
153#95—132no—
154#95C2×D1311yescharacteristic
155#95C2×D1312yes—
156C2×C13#52511yescharacteristic
157C2×C13#53211yescharacteristic
158C2×C13#53611yescharacteristic
159C2×C13#55212yes—
160C2×C13#55212yes—
161D13—42no—
162C24—131no—
163C22×C4—131no—
164C22×C4—131no—
165C22×C4—132no—
166C22×C4—131no—
167C22×C4—132no—
168C22×C4—262no—
169C22×C4—262no—
170C22×C4—262no—
171C22×C4C22×D1311yescharacteristic
172C22×C4C22×D1312yes—
173C22×C4C22×D1311yescharacteristic
174C22×C4C22×D1311yescharacteristic
175C22×C4C22×D1312yes—
176C4⋊C4—22no—
177C4⋊C4—22no—
178C4⋊C4—24no—
179C4⋊C4—262no—
180C4⋊C4—264no—
181C4⋊C4—264no—
182C4⋊C4—262no—
183C4⋊C4—264no—
184C22⋊C4—262no—
185C22⋊C4—264no—
186C22⋊C4—262no—
187C22⋊C4—264no—
188C42—134no—
189C42—262no—
190C42—264no—
191C13#261111yescharacteristic, complemented, Sylow
192C23—132no—
193C23—261no—
194C23—261no—
195C23—262no—
196C23—262no—
197C23C23×D1311yescharacteristic
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—132no—
209C2×C4—132no—
210C2×C4—268no—
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—262no—
221C2×C4—262no—
222C2×C4D4×D1312yes—
223C2×C4#612912yes—
224C2×C4#613114yes—
225C22—262no—
226C22—264no—
227C22—521no—
228C22—522no—
229C22—521no—
230C22C2×D4×D1311yescharacteristic
231C22C2×#612911yescharacteristic
232C22C2×#613112yes—
233C22#41×D1311yescharacteristic
234C22#8825712yes—
235C4—22no—
236C4—24no—
237C4—22no—
238C4—42no—
239C4—41no—
240C4—262no—
241C4—262no—
242C4—521no—
243C4—522no—
244C4—522no—
245C2—522no—
246C2#1171931111yescharacteristic
247C2#1171934712yes—
248C2#1171935311yescharacteristic
249C2#1171939912yes—
250C2#1171943011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#398C2
prime radicalC23×D13C23
hypercenter#398D13
hypocenterC13#2611
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
2. C2×#88144C2semidirect
3. C13×#398C2semidirect
6. #11718647C2semidirect
7. #11718646C2semidirect
10. #11718315C2semidirect
11. #11718309C2semidirect
104. #398D13semidirect
191. C13#2611semidirect

Maximal subgroups

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

subgroupindex
C2×#881462
C2×#881442
C13×#3982
#117186542
#117186502
#117186472
#117186462
#117183382
#117183312
#117183152
#117183092
#261113