Finite Group Databasebeta

← #13118712

Subgroups — #13118712

Order 1664.

660 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 149 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×#88189C212yesmaximal, complemented
2C2×D4×Dic13C212yesmaximal, complemented
3C13×#392C211yesmaximal, characteristic
4#11718883C212yesmaximal, complemented
5#11718611C212yesmaximal, complemented
6#11718610C211yesmaximal, characteristic, complemented
7#11718607C211yesmaximal, characteristic, complemented
8#11718606C212yesmaximal, complemented
9#11718308C212yesmaximal, complemented
10C22×D4×C13C2212yes—
11C22×D4×C13C2211yescharacteristic
12C23×Dic13C2211yescharacteristic
13C23×Dic13C2212yes—
14C2×C13×C22⋊C4C2212yes—
15C2×C13×C22⋊C4C2211yescharacteristic
16C2×C22⋊Dic13C2212yes—
17C2×C22⋊Dic13C2212yes—
18C2×C22⋊Dic13C2212yes—
19C2×C22⋊Dic13C2211yescharacteristic
20C2×C22⋊Dic13C2212yes—
21#88189—28no—
22D4×Dic13—28no—
23C2×C4⋊Dic13C2212yes—
24C2×C4⋊Dic13C2211yescharacteristic
25C2×#6101C2212yes—
26C2×#6101C2212yes—
27C2×#6101C2212yes—
28C2×C4×Dic13C2212yes—
29C13×#95C2211yescharacteristic
30#88071C2212yes—
31#88071C2211yescharacteristic
32#88071C2212yes—
33C24×C13C2312yes—
34C24×C13C2311yescharacteristic
35C2×D4×C13—24no—
36C2×D4×C13—24no—
37C2×D4×C13—24no—
38C2×D4×C13—24no—
39C2×D4×C13—41no—
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2311yescharacteristic
42C22×C4×C13C2312yes—
43C22×Dic13—24no—
44C22×Dic13—24no—
45C22×Dic13—24no—
46C22×Dic13—41no—
47C22×Dic13—42no—
48C22×Dic13C2312yes—
49C22×Dic13C2312yes—
50C22×Dic13C2312yes—
51C22×Dic13C2312yes—
52C13×C22⋊C4—24no—
53C13×C22⋊C4—41no—
54C22⋊Dic13—24no—
55C22⋊Dic13—22no—
56C22⋊Dic13—24no—
57C22⋊Dic13—24no—
58C22⋊Dic13D418yescomplemented
59C4⋊Dic13—24no—
60C4⋊Dic13—41no—
61#6101—24no—
62#6101—24no—
63#6101—24no—
64C4×Dic13—24no—
65#2455—131nomaximal, Sylow
66C23×C13—22no—
67C23×C13—22no—
68C23×C13—22no—
69C23×C13—22no—
70C23×C13—22no—
71C23×C13—22no—
72C23×C13—21no—
73C23×C13—22no—
74C23×C13—21no—
75C23×C13—22no—
76C23×C13C2×D414yes—
77C23×C13#4112yes—
78C23×C13C2411yescharacteristic
79D4×C13—216no—
80D4×C13—44no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13#4114yes—
88C2×Dic13—22no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13—22no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—44no—
99C2×Dic13—48no—
100C2×Dic13C2×D414yes—
101C2×Dic13C2×D414yes—
102C2×#123—132no—
103C2×C4×D4—132no—
104#399—131no—
105#394—132no—
106#392D1311yescharacteristic
107#389—132no—
108#388—132no—
109#385—131no—
110#385—132no—
111C22×C13—24no—
112C22×C13—24no—
113C22×C13—22no—
114C22×C13—24no—
115C22×C13—24no—
116C22×C13—42no—
117C22×C13—42no—
118C22×C13—41no—
119C22×C13—42no—
120C22×C13—42no—
121C22×C13—42no—
122C22×C13—41no—
123C22×C13C22×D412yes—
124C22×C13C2×#4111yescharacteristic
125C22×C13C2×#4112yes—
126C22×C13H(5,𝔽2)11yescharacteristic
127C22×C132−1+411yescharacteristic
128C4×C13—24no—
129C4×C13—41no—
130C4×C13—41no—
131Dic13—24no—
132Dic13—24no—
133Dic13—42no—
134Dic13—42no—
135C22×D4C2×D1312yes—
136C22×D4C2×D1311yescharacteristic
137C23×C4—131no—
138C23×C4—132no—
139#123—268no—
140C4×D4—268no—
141C2×C4⋊C4—132no—
142C2×C4⋊C4—132no—
143C2×C4⋊C4—132no—
144C2×C4⋊C4—132no—
145C2×C4⋊C4—131no—
146C2×C22⋊C4—132no—
147C2×C22⋊C4—132no—
148C2×C22⋊C4—132no—
149C2×C22⋊C4—132no—
150C2×C22⋊C4—131no—
151C2×C22⋊C4C2×D1312yes—
152C2×C22⋊C4C2×D1311yescharacteristic
153C2×C42—132no—
154#95—132no—
155#95—132no—
156#95—131no—
157#95C2×D1311yescharacteristic
158C2×C13—44no—
159C2×C13—42no—
160C2×C13#52512yes—
161C2×C13#53911yescharacteristic
162C2×C13D4211yescharacteristic
163C2×C13#54712yes—
164C2×C13#55911yescharacteristic
165C24C22×D1312yes—
166C24C22×D1311yescharacteristic
167C2×D4—24no—
168C2×D4—24no—
169C2×D4—24no—
170C2×D4—24no—
171C2×D4—41no—
172C22×C4—132no—
173C22×C4—132no—
174C22×C4—132no—
175C22×C4—132no—
176C22×C4—264no—
177C22×C4—264no—
178C22×C4—264no—
179C22×C4—521no—
180C22×C4—522no—
181C22×C4C22×D1311yescharacteristic
182C22×C4C22×D1311yescharacteristic
183C22×C4C22×D1312yes—
184C4⋊C4—264no—
185C4⋊C4—264no—
186C4⋊C4—264no—
187C4⋊C4—264no—
188C4⋊C4—521no—
189C22⋊C4—24no—
190C22⋊C4—41no—
191C22⋊C4—138no—
192C22⋊C4—264no—
193C22⋊C4—264no—
194C22⋊C4—264no—
195C22⋊C4—262no—
196C42—264no—
197C13#245511yescharacteristic, complemented, Sylow
198C23—22no—
199C23—22no—
200C23—22no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—21no—
205C23—22no—
206C23—21no—
207C23—22no—
208C23D4×D1314yes—
209C23#612912yes—
210C23C23×D1311yescharacteristic
211D4—216no—
212D4—44no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—134no—
220C2×C4—134no—
221C2×C4—262no—
222C2×C4—262no—
223C2×C4—262no—
224C2×C4—262no—
225C2×C4—262no—
226C2×C4—262no—
227C2×C4—262no—
228C2×C4—262no—
229C2×C4—262no—
230C2×C4—262no—
231C2×C4—524no—
232C2×C4—528no—
233C2×C4#612914yes—
234C22—24no—
235C22—24no—
236C22—24no—
237C22—22no—
238C22—24no—
239C22—42no—
240C22—41no—
241C22—42no—
242C22—42no—
243C22—42no—
244C22—42no—
245C22—41no—
246C22C2×D4×D1312yes—
247C22C2×#612911yescharacteristic
248C22C2×#612912yes—
249C22#8825111yescharacteristic
250C22#8825711yescharacteristic
251C4—24no—
252C4—41no—
253C4—41no—
254C4—264no—
255C4—264no—
256C4—522no—
257C4—522no—
258C2—44no—
259C2—42no—
260C2#1171929112yes—
261C2#1171929511yescharacteristic
262C2#1171930711yescharacteristic
263C2#1171931612yes—
264C2#1171941811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
Fitting, prime radicalC13×#392C2
hypercenter#392D13
hypocenterC13#2455
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#88189C2semidirect
2. C2×D4×Dic13C2semidirect
4. #11718883C2semidirect
5. #11718611C2semidirect
6. #11718610C2semidirect
7. #11718607C2semidirect
8. #11718606C2semidirect
9. #11718308C2semidirect
58. C22⋊Dic13D4semidirect
197. C13#2455semidirect

Maximal subgroups

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

subgroupindex
C2×#881892
C2×D4×Dic132
C13×#3922
#117188832
#117186112
#117186102
#117186072
#117186062
#117183082
#245513