Finite Group Databasebeta

← #13120799

Subgroups — #13120799

Order 1664.

420 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C13×#389C211yesmaximal, characteristic, complemented
2#11718655C212yesmaximal, complemented
3#11718654C212yesmaximal, complemented
4#11718649C211yesmaximal, characteristic
5#11718649C211yesmaximal, characteristic
6#11718646C211yesmaximal, characteristic, complemented
7#11718634C211yesmaximal, characteristic, complemented
8#11718600C211yesmaximal, characteristic
9#11718593C211yesmaximal, characteristic, complemented
10#11718336C212yesmaximal, complemented
11#11718335C212yesmaximal, complemented
12C22×D52C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C4⋊C4C2212yes—
16C2×C42×C13C2211yescharacteristic
17C2×#6103C2212yes—
18C2×#6103C2212yes—
19C2×#6103C2212yes—
20C2×#6103C2212yes—
21C2×#6103C2212yes—
22C2×#6103C2212yes—
23C2×C4⋊Dic13C2211yescharacteristic
24C2×C4⋊Dic13C2212yes—
25C2×#6101C2212yes—
26C2×C4×Dic13C2211yescharacteristic
27C2×C4×Dic13C2211yescharacteristic
28C13×#95C2212yes—
29#88071C2211yescharacteristic
30#88071C2212yes—
31#88071C2211yescharacteristic
32#88071C2212yes—
33#88071C2211yescharacteristic
34#88071C2211yescharacteristic
35C23×D13C2312yes—
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2311yescharacteristic
38C22×C4×C13C2312yes—
39C22×C4×C13C2312yes—
40C22×C4×C13C2311yescharacteristic
41C22×Dic13C2311yescharacteristic
42C22×Dic13C2311yescharacteristic
43C22×Dic13C2311yescharacteristic
44C22×Dic13C2311yescharacteristic
45C22×Dic13C2312yes—
46C2×D52—22no—
47C2×D52—22no—
48C2×D52—22no—
49C13×C4⋊C4—22no—
50C13×C4⋊C4—22no—
51C13×C4⋊C4—42no—
52C42×C13—22no—
53#6103—42no—
54#6103—42no—
55#6103—42no—
56#6103—42no—
57#6103—42no—
58#6103—42no—
59C4⋊Dic13—22no—
60C4⋊Dic13—42no—
61#6101—42no—
62C4×Dic13—22no—
63C4×Dic13—22no—
64#2644—131nomaximal, Sylow
65C23×C13C2411yescharacteristic
66C22×D13—22no—
67C22×D13—22no—
68C22×D13—22no—
69C22×D13—22no—
70C22×D13—22no—
71C22×D13—22no—
72C22×D13—22no—
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13—22no—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13#4112yes—
86C2×C4×C13#4112yes—
87C2×C4×C13#4112yes—
88C2×Dic13—21no—
89C2×Dic13—21no—
90C2×Dic13—21no—
91C2×Dic13—21no—
92C2×Dic13—22no—
93C2×Dic13—21no—
94C2×Dic13—22no—
95C2×Dic13—21no—
96C2×Dic13—22no—
97C2×Dic13—21no—
98C2×Dic13—21no—
99C2×Dic13—21no—
100C2×Dic13—21no—
101C2×Dic13—21no—
102C2×Dic13—21no—
103D52—44no—
104#397—132no—
105#397—132no—
106#397—132no—
107#396—132no—
108#390—131no—
109#390—131no—
110#390—131no—
111#389—131no—
112#389—131no—
113#389D1311yescharacteristic, complemented
114#376—131no—
115C22×C13C2×#4111yescharacteristic
116C22×C13C2×#4111yescharacteristic
117C22×C13C2×#4111yescharacteristic
118C22×C13H(5,𝔽2)11yescharacteristic
119C22×C13H(5,𝔽2)11yescharacteristic
120C22×C13H(5,𝔽2)11yescharacteristic
121C22×C132−1+411yescharacteristic
122C2×D13—42no—
123C2×D13—42no—
124C2×D13—42no—
125C2×D13—42no—
126C2×D13—42no—
127C2×D13—42no—
128C2×D13—42no—
129C4×C13—42no—
130C4×C13—41no—
131C4×C13—42no—
132C4×C13—41no—
133C4×C13#12614yes—
134Dic13—41no—
135Dic13—41no—
136Dic13—42no—
137Dic13—41no—
138Dic13—41no—
139C22×D4—131no—
140C2×C4⋊C4—131no—
141C2×C4⋊C4—132no—
142C2×C4⋊C4—132no—
143C2×C4⋊C4C2×D1311yescharacteristic
144C2×C4⋊C4C2×D1311yescharacteristic
145C2×C4⋊C4C2×D1312yes—
146C2×C22⋊C4—132no—
147C2×C22⋊C4—132no—
148C2×C22⋊C4—132no—
149C2×C22⋊C4—132no—
150C2×C22⋊C4—132no—
151C2×C22⋊C4—132no—
152C2×C42—131no—
153C2×C42—131no—
154C2×C42C2×D1311yescharacteristic
155#95—131no—
156#95—131no—
157#95—131no—
158#95—131no—
159#95—132no—
160#95—132no—
161#95C2×D1312yes—
162C2×C13C2×#12611yescharacteristic
163C2×C13#54011yescharacteristic
164C2×C13#54011yescharacteristic
165C2×C13#54011yescharacteristic
166C2×C13#54211yescharacteristic
167C2×C13#54211yescharacteristic
168C2×C13#54211yescharacteristic
169D13—82no—
170C24—132no—
171C2×D4—262no—
172C2×D4—262no—
173C2×D4—262no—
174C22×C4—131no—
175C22×C4—131no—
176C22×C4—131no—
177C22×C4—131no—
178C22×C4—132no—
179C22×C4C22×D1311yescharacteristic
180C22×C4C22×D1311yescharacteristic
181C22×C4C22×D1312yes—
182C22×C4C22×D1312yes—
183C22×C4C22×D1311yescharacteristic
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4—42no—
187C4⋊C4—262no—
188C4⋊C4—522no—
189C4⋊C4—522no—
190C22⋊C4—522no—
191C22⋊C4—522no—
192C22⋊C4—522no—
193C22⋊C4—522no—
194C22⋊C4—522no—
195C22⋊C4—522no—
196C42—22no—
197C42—262no—
198C42—262no—
199C13#264411yescharacteristic, complemented, Sylow
200C23—262no—
201C23—262no—
202C23—262no—
203C23—262no—
204C23—262no—
205C23—262no—
206C23—262no—
207C23C23×D1311yescharacteristic
208D4—524no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—261no—
222C2×C4—261no—
223C2×C4—261no—
224C2×C4—261no—
225C2×C4—261no—
226C2×C4—261no—
227C2×C4—262no—
228C2×C4—261no—
229C2×C4—261no—
230C2×C4—261no—
231C2×C4—261no—
232C2×C4—262no—
233C2×C4—262no—
234C2×C4—261no—
235C2×C4—261no—
236C2×C4#612712yes—
237C2×C4#612912yes—
238C2×C4#613112yes—
239C22—522no—
240C22—522no—
241C22—522no—
242C22—522no—
243C22—522no—
244C22—522no—
245C22—522no—
246C22C2×#612711yescharacteristic
247C22C2×#612911yescharacteristic
248C22#8825111yescharacteristic
249C22C2×#613111yescharacteristic
250C22#8825411yescharacteristic
251C22#8825611yescharacteristic
252C22#8825611yescharacteristic
253C4—42no—
254C4—41no—
255C4—42no—
256C4—41no—
257C4—521no—
258C4—521no—
259C4—521no—
260C4—521no—
261C4—522no—
262C4#8815214yes—
263C2—1042no—
264C2C2×#8815211yescharacteristic
265C2#1171926711yescharacteristic
266C2#1171928711yescharacteristic
267C2#1171932411yescharacteristic
268C2#1171934811yescharacteristic
269C2#1171940311yescharacteristic
270C2#1171943811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#389C2
prime radicalC22×D52C22
hypercenter#389D13
hypocenterC13#2644
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C13×#389C2semidirect
2. #11718655C2semidirect
3. #11718654C2semidirect
6. #11718646C2semidirect
7. #11718634C2semidirect
9. #11718593C2semidirect
10. #11718336C2semidirect
11. #11718335C2semidirect
113. #389D13semidirect
199. C13#2644semidirect

Maximal subgroups

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

subgroupindex
C13×#3892
#117186552
#117186542
#117186492
#117186462
#117186342
#117186002
#117185932
#117183362
#117183352
#264413