Finite Group Databasebeta

← #13120797

Subgroups — #13120797

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×#390C211yesmaximal, characteristic
2#11718882C211yesmaximal, characteristic
3#11718882C211yesmaximal, characteristic
4#11718646C211yesmaximal, characteristic, complemented
5#11718634C211yesmaximal, characteristic, complemented
6#11718614C212yesmaximal, complemented
7#11718613C212yesmaximal, complemented
8#11718613C212yesmaximal, complemented
9#11718609C212yesmaximal, complemented
10#11718593C211yesmaximal, characteristic, complemented
11#11718589C211yesmaximal, characteristic, complemented
12C22×D4×C13C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C22⋊C4C2212yes—
15C2×C13×C22⋊C4C2212yes—
16C2×C42×C13C2211yescharacteristic
17C2×C22⋊Dic13C2212yes—
18C2×C22⋊Dic13C2212yes—
19C2×C22⋊Dic13C2212yes—
20C2×C22⋊Dic13C2212yes—
21C2×C4⋊Dic13C2211yescharacteristic
22C2×C4⋊Dic13C2211yescharacteristic
23C2×C4⋊Dic13C2212yes—
24C2×#6101C2212yes—
25C2×#6101C2212yes—
26C2×C4×Dic13C2211yescharacteristic
27C2×C4×Dic13C2211yescharacteristic
28#88071C2212yes—
29#88071C2211yescharacteristic
30#88071C2211yescharacteristic
31#88071C2211yescharacteristic
32#88071C2211yescharacteristic
33#88071C2212yes—
34#88071C2212yes—
35C24×C13C2312yes—
36C2×D4×C13—22no—
37C2×D4×C13—22no—
38C2×D4×C13—22no—
39C22×C4×C13C2311yescharacteristic
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2312yes—
42C22×C4×C13C2311yescharacteristic
43C22×Dic13C2311yescharacteristic
44C22×Dic13C2311yescharacteristic
45C22×Dic13C2311yescharacteristic
46C22×Dic13C2311yescharacteristic
47C22×Dic13C2312yes—
48C22×Dic13C2312yes—
49C13×C4⋊C4—22no—
50C13×C22⋊C4—42no—
51C13×C22⋊C4—42no—
52C42×C13—22no—
53C22⋊Dic13—42no—
54C22⋊Dic13—42no—
55C22⋊Dic13—42no—
56C22⋊Dic13—42no—
57C4⋊Dic13—22no—
58C4⋊Dic13—22no—
59C4⋊Dic13—42no—
60#6101—42no—
61#6101—42no—
62C4×Dic13—22no—
63C4×Dic13—22no—
64#2644—131nomaximal, Sylow
65C23×C13—22no—
66C23×C13—22no—
67C23×C13—22no—
68C23×C13—22no—
69C23×C13—22no—
70C23×C13—22no—
71C23×C13—22no—
72C23×C13C2411yescharacteristic
73D4×C13—44no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—22no—
77C2×C4×C13—21no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—21no—
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—21no—
89C2×Dic13—21no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—21no—
93C2×Dic13—22no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—21no—
97C2×Dic13—22no—
98C2×Dic13—21no—
99C2×Dic13—21no—
100C2×Dic13—21no—
101C2×Dic13—21no—
102C2×Dic13—21no—
103C2×Dic13—21no—
104#397—132no—
105#397—132no—
106#397—132no—
107#396—132no—
108#390—131no—
109#390—131no—
110#390D1311yescharacteristic
111#389—131no—
112#389—131no—
113#389—131no—
114#376—131no—
115C22×C13—42no—
116C22×C13—42no—
117C22×C13—42no—
118C22×C13—42no—
119C22×C13—42no—
120C22×C13—42no—
121C22×C13—42no—
122C22×C13C2×#4111yescharacteristic
123C22×C13C2×#4111yescharacteristic
124C22×C13C2×#4111yescharacteristic
125C22×C13H(5,𝔽2)11yescharacteristic
126C22×C13H(5,𝔽2)11yescharacteristic
127C22×C13H(5,𝔽2)11yescharacteristic
128C22×C132−1+411yescharacteristic
129C4×C13—42no—
130C4×C13—41no—
131C4×C13—41no—
132C4×C13#12614yes—
133Dic13—41no—
134Dic13—41no—
135Dic13—42no—
136Dic13—42no—
137Dic13—41no—
138Dic13—41no—
139C22×D4C2×D1311yescharacteristic
140C2×C4⋊C4—131no—
141C2×C4⋊C4—131no—
142C2×C4⋊C4—132no—
143C2×C4⋊C4—132no—
144C2×C4⋊C4—132no—
145C2×C4⋊C4C2×D1311yescharacteristic
146C2×C22⋊C4—132no—
147C2×C22⋊C4—132no—
148C2×C22⋊C4—132no—
149C2×C22⋊C4—132no—
150C2×C22⋊C4C2×D1312yes—
151C2×C22⋊C4C2×D1312yes—
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#95—132no—
162C2×C13—82no—
163C2×C13C2×#12611yescharacteristic
164C2×C13#54011yescharacteristic
165C2×C13#54011yescharacteristic
166C2×C13#54011yescharacteristic
167C2×C13#54211yescharacteristic
168C2×C13#54211yescharacteristic
169C2×C13#54211yescharacteristic
170C24C22×D1312yes—
171C2×D4—22no—
172C2×D4—22no—
173C2×D4—22no—
174C22×C4—131no—
175C22×C4—131no—
176C22×C4—131no—
177C22×C4—131no—
178C22×C4—132no—
179C22×C4—132no—
180C22×C4C22×D1311yescharacteristic
181C22×C4C22×D1311yescharacteristic
182C22×C4C22×D1312yes—
183C22×C4C22×D1311yescharacteristic
184C4⋊C4—22no—
185C4⋊C4—262no—
186C4⋊C4—262no—
187C4⋊C4—522no—
188C4⋊C4—522no—
189C4⋊C4—522no—
190C22⋊C4—42no—
191C22⋊C4—42no—
192C22⋊C4—522no—
193C22⋊C4—522no—
194C22⋊C4—522no—
195C22⋊C4—522no—
196C42—22no—
197C42—262no—
198C42—262no—
199C13#264411yescharacteristic, complemented, Sylow
200C23—22no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23C23×D1311yescharacteristic
208D4—44no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—261no—
219C2×C4—261no—
220C2×C4—262no—
221C2×C4—261no—
222C2×C4—261no—
223C2×C4—262no—
224C2×C4—261no—
225C2×C4—261no—
226C2×C4—262no—
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#612912yes—
239C22—42no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—42no—
244C22—42no—
245C22—42no—
246C22C2×#612711yescharacteristic
247C22C2×#612911yescharacteristic
248C22C2×#612911yescharacteristic
249C22#8825111yescharacteristic
250C22#8825111yescharacteristic
251C22#8825611yescharacteristic
252C22#8825711yescharacteristic
253C4—42no—
254C4—41no—
255C4—41no—
256C4—521no—
257C4—521no—
258C4—521no—
259C4—522no—
260C4—522no—
261C4—521no—
262C4#8813314yes—
263C2—82no—
264C2C2×#8813311yescharacteristic
265C2#1171926611yescharacteristic
266C2#1171926711yescharacteristic
267C2#1171930811yescharacteristic
268C2#1171932411yescharacteristic
269C2#1171938711yescharacteristic
270C2#1171942411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#390C2
prime radicalC22×D4×C13C22
hypercenter#390D13
hypocenterC13#2644
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
4. #11718646C2semidirect
5. #11718634C2semidirect
6. #11718614C2semidirect
7. #11718613C2semidirect
8. #11718613C2semidirect
9. #11718609C2semidirect
10. #11718593C2semidirect
11. #11718589C2semidirect
199. C13#2644semidirect

Maximal subgroups

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

subgroupindex
C13×#3902
#117188822
#117186462
#117186342
#117186142
#117186132
#117186092
#117185932
#117185892
#264413