Finite Group Databasebeta

← #13120464

Subgroups — #13120464

Order 1664.

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

normal subgroups only

This group has 582 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
1C2×#88152C211yesmaximal, characteristic, complemented
2C2×#88147C211yesmaximal, characteristic, complemented
3C13×#398C211yesmaximal, characteristic, complemented
4#11718654C211yesmaximal, characteristic, complemented
5#11718652C211yesmaximal, characteristic, complemented
6#11718650C212yesmaximal, complemented
7#11718649C212yesmaximal, complemented
8#11718332C211yesmaximal, characteristic
9#11718331C212yesmaximal, complemented
10#11718326C212yesmaximal, complemented
11#11718309C211yesmaximal, characteristic, complemented
12C22×D52C2211yescharacteristic
13C22×D52C2212yes—
14C22×C4×D13C2212yes—
15C2×C13×C4⋊C4C2211yescharacteristic
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C4⋊C4C2212yes—
18C2×#6103C2212yes—
19C2×#6103C2211yescharacteristic
20C2×#6103C2211yescharacteristic
21C2×#6103C2211yescharacteristic
22C2×#6103C2212yes—
23C2×#6103C2212yes—
24C2×#6103C2212yes—
25C2×#6103C2212yes—
26C2×C4⋊Dic13C2211yescharacteristic
27C2×#6101C2211yescharacteristic
28C2×C4×Dic13C2212yes—
29C2×C4×Dic13C2211yescharacteristic
30#88152—24no—
31#88147—24no—
32C13×#95C2211yescharacteristic
33C13×#95C2212yes—
34#88071C2212yes—
35#88071C2211yescharacteristic
36#88071C2212yes—
37C23×D13C2311yescharacteristic
38C23×D13C2312yes—
39C22×C4×C13C2312yes—
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2311yescharacteristic
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2312yes—
44C22×Dic13C2312yes—
45C22×Dic13C2311yescharacteristic
46C22×Dic13C2311yescharacteristic
47C22×Dic13C2311yescharacteristic
48C2×D52—24no—
49C2×D52—22no—
50C2×D52—24no—
51C2×D52—24no—
52C2×D52—42no—
53C2×C4×D13—24no—
54C2×C4×D13—42no—
55C2×C4×D13—42no—
56C13×C4⋊C4—22no—
57C13×C4⋊C4—22no—
58C13×C4⋊C4—42no—
59#6103—24no—
60#6103—22no—
61#6103—24no—
62#6103—24no—
63#6103—22no—
64#6103—22no—
65#6103—42no—
66#6103—42no—
67C4⋊Dic13—22no—
68#6101—22no—
69C4×Dic13—24no—
70C4×Dic13D414yescomplemented
71#2603—131nomaximal, Sylow
72C23×C13C2411yescharacteristic
73C22×D13—22no—
74C22×D13—22no—
75C22×D13—22no—
76C22×D13—22no—
77C22×D13—22no—
78C22×D13—22no—
79C22×D13—21no—
80C22×D13—22no—
81C22×D13—22no—
82C22×D13—21no—
83C22×D13—21no—
84C22×D13#4114yes—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—21no—
93C2×C4×C13—22no—
94C2×C4×C13—21no—
95C2×C4×C13—22no—
96C2×C4×C13C2×D412yes—
97C2×C4×C13#4114yes—
98C2×Dic13—22no—
99C2×Dic13—21no—
100C2×Dic13—21no—
101C2×Dic13—21no—
102C2×Dic13—22no—
103C2×Dic13—22no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13C2×D412yes—
107C2×Dic13C2×D412yes—
108D52—28no—
109D52—48no—
110C4×D13—48no—
111C2×#126—131no—
112C2×C4×D4—131no—
113#398D1311yescharacteristic, complemented
114#397—131no—
115#394—131no—
116#392—131no—
117#390—132no—
118#388—132no—
119#386—132no—
120#385—132no—
121#376—131no—
122C22×C13C22×D411yescharacteristic
123C22×C13C2×#4112yes—
124C22×C13C2×#4112yes—
125C22×C13H(5,𝔽2)11yescharacteristic
126C22×C13H(5,𝔽2)11yescharacteristic
127C2×D13—24no—
128C2×D13—24no—
129C2×D13—24no—
130C2×D13—42no—
131C2×D13—42no—
132C2×D13—42no—
133C2×D13—42no—
134C2×D13—41no—
135C2×D13—41no—
136C2×D13—41no—
137C2×D13—42no—
138C2×D13—42no—
139C4×C13—22no—
140C4×C13—24no—
141C4×C13—41no—
142C4×C13—42no—
143C4×C13—41no—
144Dic13—22no—
145Dic13—22no—
146Dic13—41no—
147Dic13—42no—
148C22×D4—131no—
149C22×D4—132no—
150C23×C4—132no—
151#126—264no—
152C4×D4—264no—
153C2×C4⋊C4—131no—
154C2×C4⋊C4—131no—
155C2×C4⋊C4C2×D1311yescharacteristic
156C2×C4⋊C4C2×D1311yescharacteristic
157C2×C4⋊C4C2×D1312yes—
158C2×C22⋊C4—132no—
159C2×C22⋊C4—131no—
160C2×C22⋊C4—131no—
161C2×C22⋊C4—131no—
162C2×C22⋊C4—132no—
163C2×C22⋊C4—132no—
164C2×C22⋊C4—132no—
165C2×C22⋊C4—132no—
166C2×C42—131no—
167C2×C42—132no—
168#95—132no—
169#95—131no—
170#95—132no—
171#95C2×D1311yescharacteristic
172#95C2×D1312yes—
173C2×C13#52511yescharacteristic
174C2×C13#53211yescharacteristic
175C2×C13#53511yescharacteristic
176C2×C13#55112yes—
177C2×C13#55312yes—
178D13—44no—
179D13—81no—
180C24—132no—
181C24—131no—
182C2×D4—264no—
183C2×D4—264no—
184C2×D4—262no—
185C2×D4—264no—
186C2×D4—522no—
187C22×C4—131no—
188C22×C4—131no—
189C22×C4—132no—
190C22×C4—131no—
191C22×C4—264no—
192C22×C4—522no—
193C22×C4—522no—
194C22×C4C22×D1312yes—
195C22×C4C22×D1311yescharacteristic
196C22×C4C22×D1311yescharacteristic
197C22×C4C22×D1311yescharacteristic
198C22×C4C22×D1312yes—
199C4⋊C4—22no—
200C4⋊C4—22no—
201C4⋊C4—42no—
202C4⋊C4—262no—
203C4⋊C4—262no—
204C22⋊C4—264no—
205C22⋊C4—262no—
206C22⋊C4—262no—
207C22⋊C4—264no—
208C22⋊C4—262no—
209C22⋊C4—264no—
210C22⋊C4—522no—
211C22⋊C4—522no—
212C42—134no—
213C42—264no—
214C13#260311yescharacteristic, complemented, Sylow
215C23—134no—
216C23—262no—
217C23—262no—
218C23—262no—
219C23—262no—
220C23—262no—
221C23—262no—
222C23—261no—
223C23—261no—
224C23—262no—
225C23—262no—
226C23—261no—
227C23C23×D1311yescharacteristic
228D4—268no—
229D4—528no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—132no—
242C2×C4—132no—
243C2×C4—261no—
244C2×C4—262no—
245C2×C4—261no—
246C2×C4—261no—
247C2×C4—262no—
248C2×C4—262no—
249C2×C4—262no—
250C2×C4—262no—
251C2×C4—528no—
252C2×C4D4×D1312yes—
253C2×C4#613114yes—
254C22—264no—
255C22—264no—
256C22—264no—
257C22—522no—
258C22—522no—
259C22—522no—
260C22—522no—
261C22—521no—
262C22—521no—
263C22—522no—
264C22—521no—
265C22—522no—
266C22C2×D4×D1311yescharacteristic
267C22#8825111yescharacteristic
268C22C2×#613112yes—
269C22#41×D1312yes—
270C22#8825611yescharacteristic
271C4—24no—
272C4—22no—
273C4—41no—
274C4—42no—
275C4—41no—
276C4—262no—
277C4—262no—
278C4—521no—
279C4—522no—
280C2—524no—
281C2—1041no—
282C2#1171931211yescharacteristic
283C2#1171934212yes—
284C2#1171936111yescharacteristic
285C2#1171940012yes—
286C2#1171943011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#398C2
prime radical#11718332C2
hypercenter#398D13
hypocenterC13#2603
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#88152C2semidirect
2. C2×#88147C2semidirect
3. C13×#398C2semidirect
4. #11718654C2semidirect
5. #11718652C2semidirect
6. #11718650C2semidirect
7. #11718649C2semidirect
9. #11718331C2semidirect
10. #11718326C2semidirect
11. #11718309C2semidirect
70. C4×Dic13D4semidirect
113. #398D13semidirect
214. C13#2603semidirect

Maximal subgroups

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

subgroupindex
C2×#881522
C2×#881472
C13×#3982
#117186542
#117186522
#117186502
#117186492
#117183322
#117183312
#117183262
#117183092
#260313