Finite Group Databasebeta

← #13120982

Subgroups — #13120982

Order 1664.

534 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 129 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×#88201C211yesmaximal, characteristic, complemented
2C2×#88133C211yesmaximal, characteristic, complemented
3C13×#393C211yesmaximal, characteristic, complemented
4#11718890C211yesmaximal, characteristic, complemented
5#11718621C211yesmaximal, characteristic
6#11718620C212yesmaximal, complemented
7#11718618C212yesmaximal, complemented
8#11718337C212yesmaximal, complemented
9#11718333C211yesmaximal, characteristic, complemented
10#11718331C212yesmaximal, complemented
11#11718310C211yesmaximal, characteristic, complemented
12C22×Q8×C13C2211yescharacteristic
13C22×C22⋊D13C2212yes—
14C22×D52C2211yescharacteristic
15C2×C13×C22⋊C4C2211yescharacteristic
16C2×C13×C22⋊C4C2212yes—
17C2×C22⋊Dic13C2211yescharacteristic
18C2×C22⋊Dic13C2211yescharacteristic
19#88201—24no—
20C2×#6103C2212yes—
21C2×#6103C2212yes—
22C2×#6103C2212yes—
23C2×#6103C2212yes—
24C2×#6103C2212yes—
25C2×C4⋊Dic13C2211yescharacteristic
26C2×#6101C2211yescharacteristic
27C2×#6101C2211yescharacteristic
28C2×#6101C2212yes—
29C2×#6101C2212yes—
30C2×C4×Dic13C2212yes—
31C2×C4×Dic13C2211yescharacteristic
32#88133—24no—
33C13×#95C2211yescharacteristic
34C13×#95C2212yes—
35#88071C2211yescharacteristic
36#88071C2212yes—
37C24×C13C2311yescharacteristic
38C23×D13C2312yes—
39C2×Q8×C13—22no—
40C2×Q8×C13—42no—
41C22×C4×C13C2312yes—
42C22×C4×C13C2312yes—
43C22×C4×C13C2311yescharacteristic
44C22×C4×C13C2311yescharacteristic
45C2×C22⋊D13—24no—
46C2×C22⋊D13—42no—
47C2×C22⋊D13—42no—
48C22×Dic13C2311yescharacteristic
49C22×Dic13C2311yescharacteristic
50C22×Dic13C2311yescharacteristic
51C22×Dic13C2311yescharacteristic
52C22×Dic13C2312yes—
53C2×D52—22no—
54C2×D52—42no—
55C13×C22⋊C4—22no—
56C13×C22⋊C4—42no—
57C22⋊Dic13—22no—
58C22⋊Dic13—22no—
59#6103—24no—
60#6103—24no—
61#6103—24no—
62#6103—42no—
63#6103—42no—
64C4⋊Dic13—22no—
65#6101—22no—
66#6101—22no—
67#6101—24no—
68#6101—42no—
69C4×Dic13—42no—
70C4×Dic13D414yescomplemented
71#2662—131nomaximal, Sylow
72C23×C13—21no—
73C23×C13—22no—
74C23×C13—22no—
75C23×C13—21no—
76C23×C13—21no—
77C23×C13C2411yescharacteristic
78C22×D13—22no—
79C22×D13—22no—
80C22×D13—22no—
81C22×D13—22no—
82C22×D13—22no—
83C22×D13—22no—
84C22×D13—22no—
85Q8×C13—44no—
86C2×C4×C13—22no—
87C2×C4×C13—21no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13C2×D412yes—
96C22⋊D13—48no—
97C2×Dic13—22no—
98C2×Dic13—21no—
99C2×Dic13—22no—
100C2×Dic13—22no—
101C2×Dic13—21no—
102C2×Dic13—21no—
103C2×Dic13—21no—
104C2×Dic13—22no—
105C2×Dic13—21no—
106C2×Dic13—21no—
107C2×Dic13C2×D412yes—
108C2×Dic13C2×D412yes—
109C2×Dic13#4114yes—
110D52—44no—
111C2×#126—131no—
112C2×#124—131no—
113#396—132no—
114#395—131no—
115#394—132no—
116#394—131no—
117#393D1311yescharacteristic, complemented
118#392—131no—
119#390—132no—
120#388—132no—
121C4×C4⋊C4—131no—
122C22×C13—41no—
123C22×C13—41no—
124C22×C13—41no—
125C22×C13—42no—
126C22×C13—42no—
127C22×C13C22×D411yescharacteristic
128C22×C13C2×#4112yes—
129C22×C13H(5,𝔽2)12yes—
130C22×C13H(5,𝔽2)11yescharacteristic
131C22×C132−1+411yescharacteristic
132C2×D13—42no—
133C2×D13—42no—
134C2×D13—42no—
135C2×D13—42no—
136C2×D13—42no—
137C2×D13—42no—
138C2×D13—42no—
139C4×C13—22no—
140C4×C13—41no—
141C4×C13—42no—
142C4×C13—42no—
143Dic13—22no—
144Dic13—22no—
145Dic13—24no—
146Dic13—41no—
147Dic13—41no—
148C22×Q8C2×D1311yescharacteristic
149C22×D4—132no—
150C22×D4—131no—
151#126—264no—
152#124—264no—
153C2×C4⋊C4—131no—
154C2×C4⋊C4—131no—
155C2×C4⋊C4—131no—
156C2×C4⋊C4—132no—
157C2×C4⋊C4—132no—
158C2×C22⋊C4—131no—
159C2×C22⋊C4—131no—
160C2×C22⋊C4—132no—
161C2×C22⋊C4—132no—
162C2×C22⋊C4—132no—
163C2×C22⋊C4—132no—
164C2×C22⋊C4—132no—
165C2×C22⋊C4C2×D1311yescharacteristic
166C2×C22⋊C4C2×D1312yes—
167C2×C42—131no—
168C2×C42—132no—
169#95—131no—
170#95—132no—
171#95C2×D1311yescharacteristic
172#95C2×D1312yes—
173C2×C13—81no—
174C2×C13#53211yescharacteristic
175C2×C13#53511yescharacteristic
176C2×C13#53711yescharacteristic
177C2×C13#53812yes—
178C2×C13#54212yes—
179D13—82no—
180C24—132no—
181C24C22×D1311yescharacteristic
182C2×Q8—22no—
183C2×Q8—42no—
184C2×D4—264no—
185C2×D4—262no—
186C2×D4—522no—
187C2×D4—522no—
188C2×D4—522no—
189C22×C4—132no—
190C22×C4—131no—
191C22×C4—131no—
192C22×C4—131no—
193C22×C4—131no—
194C22×C4C22×D1312yes—
195C22×C4C22×D1312yes—
196C22×C4C22×D1311yescharacteristic
197C22×C4C22×D1311yescharacteristic
198C4⋊C4—262no—
199C4⋊C4—262no—
200C4⋊C4—264no—
201C4⋊C4—262no—
202C4⋊C4—522no—
203C22⋊C4—22no—
204C22⋊C4—42no—
205C22⋊C4—264no—
206C22⋊C4—264no—
207C22⋊C4—264no—
208C22⋊C4—262no—
209C22⋊C4—262no—
210C22⋊C4—522no—
211C22⋊C4—522no—
212C42—134no—
213C42—522no—
214C13#266211yescharacteristic, complemented, Sylow
215C23—21no—
216C23—22no—
217C23—21no—
218C23—22no—
219C23—21no—
220C23—262no—
221C23—262no—
222C23—262no—
223C23—262no—
224C23—262no—
225C23—262no—
226C23—262no—
227C23C23×D1311yescharacteristic
228Q8—44no—
229D4—524no—
230D4—528no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—132no—
241C2×C4—132no—
242C2×C4—134no—
243C2×C4—262no—
244C2×C4—261no—
245C2×C4—262no—
246C2×C4—261no—
247C2×C4—262no—
248C2×C4—261no—
249C2×C4—261no—
250C2×C4—262no—
251C2×C4—261no—
252C2×C4—261no—
253C2×C4D4×D1312yes—
254C22—41no—
255C22—41no—
256C22—42no—
257C22—41no—
258C22—42no—
259C22—522no—
260C22—522no—
261C22—522no—
262C22—522no—
263C22—522no—
264C22—522no—
265C22—522no—
266C22C2×D4×D1311yescharacteristic
267C22#8825112yes—
268C22#8825411yescharacteristic
269C22#41×D1312yes—
270C22#8825611yescharacteristic
271C4—22no—
272C4—42no—
273C4—41no—
274C4—42no—
275C4—262no—
276C4—262no—
277C4—264no—
278C4—521no—
279C4—521no—
280C2—81no—
281C2—1042no—
282C2#1171929711yescharacteristic
283C2#1171933411yescharacteristic
284C2#1171934512yes—
285C2#1171937311yescharacteristic
286C2#1171938312yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#393C2
prime radical#11718621C2
hypercenter#393D13
hypocenterC13#2662
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#88201C2semidirect
2. C2×#88133C2semidirect
3. C13×#393C2semidirect
4. #11718890C2semidirect
6. #11718620C2semidirect
7. #11718618C2semidirect
8. #11718337C2semidirect
9. #11718333C2semidirect
10. #11718331C2semidirect
11. #11718310C2semidirect
70. C4×Dic13D4semidirect
117. #393D13semidirect
214. C13#2662semidirect

Maximal subgroups

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

subgroupindex
C2×#882012
C2×#881332
C13×#3932
#117188902
#117186212
#117186202
#117186182
#117183372
#117183332
#117183312
#117183102
#266213