Finite Group Databasebeta

← #13118719

Subgroups — #13118719

Order 1664.

660 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 145 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×#88148C212yesmaximal, complemented
2C2×#88135C212yesmaximal, complemented
3C13×#399C211yesmaximal, characteristic, complemented
4#11718650C212yesmaximal, complemented
5#11718634C212yesmaximal, complemented
6#11718622C212yesmaximal, complemented
7#11718621C211yesmaximal, characteristic
8#11718607C211yesmaximal, characteristic, complemented
9#11718331C212yesmaximal, complemented
10C22×C22⋊D13C2212yes—
11C23×Dic13C2211yescharacteristic
12C22×D52C2211yescharacteristic
13C22×C4×D13C2212yes—
14C2×C13×C4⋊C4C2212yes—
15C2×C13×C4⋊C4C2211yescharacteristic
16C2×C13×C22⋊C4C2212yes—
17C2×C13×C22⋊C4C2211yescharacteristic
18C2×C22⋊Dic13C2211yescharacteristic
19C2×#6103C2212yes—
20C2×#6103C2212yes—
21C2×#6103C2212yes—
22C2×#6103C2212yes—
23C2×C4⋊Dic13C2212yes—
24C2×#6101C2212yes—
25C2×#6101C2212yes—
26C2×C4×Dic13C2212yes—
27#88148—28no—
28#88135—28no—
29C13×#95C2211yescharacteristic
30#88071C2212yes—
31#88071C2211yescharacteristic
32#88071C2212yes—
33C24×C13C2311yescharacteristic
34C23×D13C2312yes—
35C22×C4×C13C2311yescharacteristic
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2312yes—
38C22×C4×C13C2312yes—
39C2×C22⋊D13—24no—
40C2×C22⋊D13—24no—
41C2×C22⋊D13—24no—
42C22×Dic13—24no—
43C22×Dic13—41no—
44C22×Dic13C2312yes—
45C22×Dic13C2312yes—
46C22×Dic13C2312yes—
47C2×D52—24no—
48C2×D52—41no—
49C2×C4×D13—24no—
50C2×C4×D13—24no—
51C2×C4×D13—42no—
52C13×C4⋊C4—24no—
53C13×C4⋊C4—41no—
54C13×C22⋊C4—24no—
55C13×C22⋊C4—41no—
56C22⋊Dic13—22no—
57#6103—24no—
58#6103—24no—
59#6103—24no—
60#6103D418yescomplemented
61C4⋊Dic13—24no—
62#6101—24no—
63#6101—24no—
64C4×Dic13—24no—
65#2455—131nomaximal, Sylow
66C23×C13—22no—
67C23×C13—22no—
68C23×C13—21no—
69C23×C13—21no—
70C23×C13#4112yes—
71C23×C13C2411yescharacteristic
72C22×D13—22no—
73C22×D13—22no—
74C22×D13—22no—
75C22×D13—22no—
76C22×D13—22no—
77C22×D13—22no—
78C22×D13C2×D414yes—
79C2×C4×C13—22no—
80C2×C4×C13—22no—
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—22no—
88C2×C4×C13C2×D414yes—
89C22⋊D13—216no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13—22no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13—44no—
98C2×Dic13C2×D414yes—
99C2×Dic13#4114yes—
100D52—44no—
101C4×D13—48no—
102C2×#123—132no—
103C2×C4×D4—132no—
104#399D1311yescharacteristic, complemented
105#394—132no—
106#392—131no—
107#389—132no—
108#388—132no—
109#385—132no—
110#385—131no—
111C22×C13—24no—
112C22×C13—22no—
113C22×C13—41no—
114C22×C13—42no—
115C22×C13—41no—
116C22×C13C22×D412yes—
117C22×C13C2×#4111yescharacteristic
118C22×C13C2×#4112yes—
119C22×C13H(5,𝔽2)11yescharacteristic
120C22×C132−1+411yescharacteristic
121C2×D13—24no—
122C2×D13—24no—
123C2×D13—24no—
124C2×D13—42no—
125C2×D13—42no—
126C2×D13—42no—
127C2×D13—42no—
128C4×C13—24no—
129C4×C13—42no—
130C4×C13—41no—
131C4×C13—41no—
132Dic13—24no—
133Dic13—24no—
134Dic13—42no—
135C22×D4—132no—
136C22×D4—131no—
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⋊C4C2×D1312yes—
145C2×C4⋊C4C2×D1311yescharacteristic
146C2×C22⋊C4—132no—
147C2×C22⋊C4—131no—
148C2×C22⋊C4—132no—
149C2×C22⋊C4—132no—
150C2×C22⋊C4—132no—
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—42no—
159C2×C13#52512yes—
160C2×C13#53911yescharacteristic
161C2×C13D4211yescharacteristic
162C2×C13#54712yes—
163C2×C13#55911yescharacteristic
164D13—44no—
165C24—132no—
166C24C22×D1311yescharacteristic
167C2×D4—264no—
168C2×D4—264no—
169C2×D4—264no—
170C2×D4—264no—
171C2×D4—521no—
172C22×C4—132no—
173C22×C4—132no—
174C22×C4—132no—
175C22×C4—264no—
176C22×C4—264no—
177C22×C4—264no—
178C22×C4—522no—
179C22×C4—521no—
180C22×C4C22×D1311yescharacteristic
181C22×C4C22×D1312yes—
182C22×C4C22×D1311yescharacteristic
183C22×C4C22×D1312yes—
184C4⋊C4—24no—
185C4⋊C4—41no—
186C4⋊C4—264no—
187C4⋊C4—264no—
188C4⋊C4—264no—
189C22⋊C4—24no—
190C22⋊C4—41no—
191C22⋊C4—138no—
192C22⋊C4—264no—
193C22⋊C4—264no—
194C22⋊C4—262no—
195C22⋊C4—264no—
196C42—264no—
197C13#245511yescharacteristic, complemented, Sylow
198C23—22no—
199C23—21no—
200C23—22no—
201C23—21no—
202C23—134no—
203C23—262no—
204C23—262no—
205C23—262no—
206C23—262no—
207C23—262no—
208C23—262no—
209C23#613112yes—
210C23C23×D1311yescharacteristic
211D4—2616no—
212D4—524no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—134no—
223C2×C4—134no—
224C2×C4—262no—
225C2×C4—262no—
226C2×C4—262no—
227C2×C4—262no—
228C2×C4—262no—
229C2×C4—262no—
230C2×C4—262no—
231C2×C4—528no—
232C2×C4—524no—
233C2×C4D4×D1314yes—
234C22—24no—
235C22—22no—
236C22—42no—
237C22—41no—
238C22—41no—
239C22—264no—
240C22—264no—
241C22—264no—
242C22—522no—
243C22—522no—
244C22—522no—
245C22—522no—
246C22C2×D4×D1312yes—
247C22#8825111yescharacteristic
248C22C2×#613111yescharacteristic
249C22#41×D1312yes—
250C22#8825711yescharacteristic
251C4—24no—
252C4—41no—
253C4—42no—
254C4—41no—
255C4—264no—
256C4—264no—
257C4—522no—
258C2—42no—
259C2—524no—
260C2#1171933212yes—
261C2#1171935011yescharacteristic
262C2#1171936012yes—
263C2#1171936911yescharacteristic
264C2#1171942211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#399C2
prime radical#11718621C2
hypercenter#399D13
hypocenterC13#2455
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#88148C2semidirect
2. C2×#88135C2semidirect
3. C13×#399C2semidirect
4. #11718650C2semidirect
5. #11718634C2semidirect
6. #11718622C2semidirect
8. #11718607C2semidirect
9. #11718331C2semidirect
60. #6103D4semidirect
104. #399D13semidirect
197. C13#2455semidirect

Maximal subgroups

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

subgroupindex
C2×#881482
C2×#881352
C13×#3992
#117186502
#117186342
#117186222
#117186212
#117186072
#117183312
#245513