Finite Group Databasebeta

← #13119245

Subgroups — #13119245

Order 1664.

412 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 137 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#11718651C212yesmaximal
3#11718648C211yesmaximal, characteristic
4#11718648C211yesmaximal, characteristic
5#11718643C212yesmaximal, complemented
6C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
7#11718634C211yesmaximal, characteristic, complemented
8C4×#6103C211yesmaximal, characteristic
9#11718597C211yesmaximal, characteristic, complemented
10#11718336C212yesmaximal
11#11718312C212yesmaximal, complemented
12C22×C4×D13C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C4⋊C4C2212yes—
16C2×C42×C13C2211yescharacteristic
17C2×#6103C2211yescharacteristic
18C2×#6103C2212yes—
19C2×#6103C2211yescharacteristic
20C2×#6103C2212yes—
21C2×C4⋊Dic13C2211yescharacteristic
22C2×C4⋊Dic13C2211yescharacteristic
23C2×#6101C2212yes—
24C2×C4×Dic13C2212yes—
25C2×C4×Dic13C2211yescharacteristic
26C13×#95C2212yes—
27#88071C2211yescharacteristic
28#88071C2212yes—
29#88071C2212yes—
30#88071C2212yes—
31#88071C2212yes—
32#88071C2212yes—
33#88071C2212yes—
34#88071C2211yescharacteristic
35C23×D13C2311yescharacteristic
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2311yescharacteristic
38C22×C4×C13C2312yes—
39C22×C4×C13C2312yes—
40C22×C4×C13C2311yescharacteristic
41C22×Dic13C2311yescharacteristic
42C22×Dic13C2312yes—
43C22×Dic13C2312yes—
44C22×Dic13C2311yescharacteristic
45C22×Dic13C2311yescharacteristic
46C2×C4×D13—22no—
47C2×C4×D13—22no—
48C2×C4×D13—22no—
49C13×C4⋊C4—22no—
50C13×C4⋊C4—22no—
51C13×C4⋊C4—42no—
52C42×C13—22no—
53#6103—22no—
54#6103—24no—
55#6103—22no—
56#6103—42no—
57C4⋊Dic13—22no—
58C4⋊Dic13—22no—
59#6101—42no—
60C4×Dic13—22no—
61C4×Dic13—24no—
62#2495—131nomaximal, Sylow
63C23×C13C2411yescharacteristic
64C22×D13—21no—
65C22×D13—21no—
66C22×D13—21no—
67C22×D13—21no—
68C22×D13—21no—
69C22×D13—21no—
70C22×D13#4112yes—
71C2×C4×C13—22no—
72C2×C4×C13—21no—
73C2×C4×C13—22no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—21no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13#4112yes—
84C2×C4×C13#4112yes—
85C2×C4×C13#4112yes—
86C2×Dic13—21no—
87C2×Dic13—21no—
88C2×Dic13—22no—
89C2×Dic13—21no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13—21no—
94C2×Dic13—21no—
95C2×Dic13—21no—
96C2×Dic13—21no—
97C2×Dic13—21no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13#4112yes—
101C4×D13—44no—
102#400—132no—
103#397—132no—
104#389—131no—
105#389D1311yescharacteristic, complemented
106#388—132no—
107#383—132no—
108#382—131no—
109#380—131no—
110#380—131no—
111C4×C4⋊C4—131no—
112C4×C22⋊C4—131no—
113C22×C13C2×#4111yescharacteristic
114C22×C13C2×#4111yescharacteristic
115C22×C13C2×#4111yescharacteristic
116C22×C13C2×#4111yescharacteristic
117C22×C13C2×#4111yescharacteristic
118C22×C13H(5,𝔽2)11yescharacteristic
119C22×C132−1+411yescharacteristic
120C2×D13—22no—
121C2×D13—22no—
122C2×D13—22no—
123C2×D13—41no—
124C2×D13—41no—
125C2×D13—41no—
126C2×D13—41no—
127C4×C13—41no—
128C4×C13—42no—
129C4×C13—42no—
130C4×C13—41no—
131C4×C13#12614yes—
132Dic13—22no—
133Dic13—41no—
134Dic13—42no—
135Dic13—42no—
136Dic13—41no—
137C23×C4—131no—
138C2×C4⋊C4—131no—
139C2×C4⋊C4—131no—
140C2×C4⋊C4—132no—
141C2×C4⋊C4C2×D1311yescharacteristic
142C2×C4⋊C4C2×D1311yescharacteristic
143C2×C4⋊C4C2×D1312yes—
144C2×C22⋊C4—131no—
145C2×C22⋊C4—131no—
146C2×C22⋊C4—132no—
147C2×C22⋊C4—132no—
148C2×C42—131no—
149C2×C42—132no—
150C2×C42C2×D1311yescharacteristic
151#95—131no—
152#95—131no—
153#95—132no—
154#95—132no—
155#95—132no—
156#95—132no—
157#95—132no—
158#95—132no—
159#95C2×D1312yes—
160C2×C13C2×#12611yescharacteristic
161C2×C13#52911yescharacteristic
162C2×C13#54211yescharacteristic
163C2×C13#55211yescharacteristic
164C2×C13#55211yescharacteristic
165C2×C13#55311yescharacteristic
166C2×C13#55511yescharacteristic
167D13—42no—
168C24—131no—
169C22×C4—131no—
170C22×C4—131no—
171C22×C4—132no—
172C22×C4—132no—
173C22×C4—131no—
174C22×C4—262no—
175C22×C4—262no—
176C22×C4—262no—
177C22×C4C22×D1311yescharacteristic
178C22×C4C22×D1311yescharacteristic
179C22×C4C22×D1312yes—
180C22×C4C22×D1312yes—
181C22×C4C22×D1311yescharacteristic
182C4⋊C4—22no—
183C4⋊C4—22no—
184C4⋊C4—42no—
185C4⋊C4—262no—
186C4⋊C4—262no—
187C4⋊C4—522no—
188C22⋊C4—262no—
189C22⋊C4—262no—
190C22⋊C4—264no—
191C22⋊C4—522no—
192C42—22no—
193C42—264no—
194C42—262no—
195C13#249511yescharacteristic, complemented, Sylow
196C23—132no—
197C23—261no—
198C23—261no—
199C23—261no—
200C23—261no—
201C23—261no—
202C23—261no—
203C23C23×D1311yescharacteristic
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—132no—
217C2×C4—261no—
218C2×C4—261no—
219C2×C4—261no—
220C2×C4—261no—
221C2×C4—261no—
222C2×C4—262no—
223C2×C4—261no—
224C2×C4—262no—
225C2×C4—262no—
226C2×C4—261no—
227C2×C4—262no—
228C2×C4—262no—
229C2×C4—261no—
230C2×C4—262no—
231C2×C4—524no—
232C2×C4#612712yes—
233C2×C4#612912yes—
234C2×C4#613112yes—
235C22—262no—
236C22—262no—
237C22—262no—
238C22—521no—
239C22—521no—
240C22—521no—
241C22—521no—
242C22C2×#612711yescharacteristic
243C22C2×#612911yescharacteristic
244C22#8825111yescharacteristic
245C22C2×#613111yescharacteristic
246C22#8825411yescharacteristic
247C22#41×D1311yescharacteristic
248C22#41×D1311yescharacteristic
249C4—42no—
250C4—41no—
251C4—42no—
252C4—41no—
253C4—262no—
254C4—522no—
255C4—521no—
256C4—521no—
257C4—522no—
258C4#8815214yes—
259C2—522no—
260C2C2×#8815211yescharacteristic
261C2#1171926311yescharacteristic
262C2#1171928611yescharacteristic
263C2#1171932111yescharacteristic
264C2#1171934411yescharacteristic
265C2#1171939611yescharacteristic
266C2#1171943811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#389C2
prime radicalC23×D13C23
hypercenter#389D13
hypocenterC13#2495
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C13×#389C2semidirect
5. #11718643C2semidirect
6. C4⋊C4×Dic13C2semidirect
7. #11718634C2semidirect
9. #11718597C2semidirect
11. #11718312C2semidirect
105. #389D13semidirect
195. C13#2495semidirect

Maximal subgroups

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

subgroupindex
C13×#3892
#117186512
#117186482
#117186432
C4⋊C4×Dic132
#117186342
C4×#61032
#117185972
#117183362
#117183122
#249513