Finite Group Databasebeta

← #13120465

Subgroups — #13120465

Order 1664.

582 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 141 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×C13×#126C211yesmaximal, characteristic, complemented
2C2×C4×D52C211yesmaximal, characteristic, complemented
3#11718652C211yesmaximal, characteristic, complemented
4#11718651C212yesmaximal, complemented
5#11718650C212yesmaximal, complemented
6#11718644C211yesmaximal, characteristic, complemented
7#11718621C211yesmaximal, characteristic
8#11718618C212yesmaximal, complemented
9#11718617C212yesmaximal, complemented
10#11718614C211yesmaximal, characteristic, complemented
11#11718593C211yesmaximal, characteristic, complemented
12C22×C22⋊D13C2212yes—
13C22×D52C2211yescharacteristic
14C22×C4×D13C2212yes—
15C13×#126—24no—
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
18C2×C13×C4⋊C4C2211yescharacteristic
19C2×C13×C22⋊C4C2211yescharacteristic
20C2×C13×C22⋊C4C2211yescharacteristic
21C2×C13×C22⋊C4C2211yescharacteristic
22C2×C42×C13C2211yescharacteristic
23C2×C22⋊Dic13C2212yes—
24C2×#6103C2212yes—
25C2×#6103C2212yes—
26C2×#6103C2212yes—
27C2×#6103C2212yes—
28C2×C4⋊Dic13C2211yescharacteristic
29C2×#6101C2212yes—
30C2×C4×Dic13C2212yes—
31C4×D52—24no—
32#88071C2211yescharacteristic
33#88071C2212yes—
34#88071C2211yescharacteristic
35#88071C2212yes—
36#88071C2212yes—
37C24×C13C2311yescharacteristic
38C23×D13C2312yes—
39C22×C4×C13C2311yescharacteristic
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2311yescharacteristic
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2311yescharacteristic
44C22×C4×C13C2311yescharacteristic
45C2×C22⋊D13—24no—
46C2×C22⋊D13—24no—
47C2×C22⋊D13—42no—
48C22×Dic13C2312yes—
49C22×Dic13C2312yes—
50C22×Dic13C2312yes—
51C2×D52—24no—
52C2×D52—22no—
53C2×C4×D13—24no—
54C2×C4×D13—42no—
55C2×C4×D13—42no—
56C13×C4⋊C4—22no—
57C13×C4⋊C4—22no—
58C13×C4⋊C4—22no—
59C13×C22⋊C4—22no—
60C13×C22⋊C4—22no—
61C13×C22⋊C4—22no—
62C42×C13D414yescomplemented
63C22⋊Dic13—42no—
64#6103—24no—
65#6103—24no—
66#6103—24no—
67#6103—42no—
68C4⋊Dic13—22no—
69#6101—42no—
70C4×Dic13—24no—
71#2603—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#4114yes—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13C2×D412yes—
97C2×C4×C13C2×D412yes—
98C2×C4×C13C2×D412yes—
99C22⋊D13—48no—
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13—22no—
103C2×Dic13—22no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—22no—
108C2×Dic13#4114yes—
109D52—28no—
110C4×D13—48no—
111C2×#126D1311yescharacteristic, complemented
112C2×C4×D4—131no—
113#398—131no—
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×C13—41no—
123C22×C13—41no—
124C22×C13—41no—
125C22×C13—42no—
126C22×C13—42no—
127C22×C13C22×D411yescharacteristic
128C22×C13C2×#4112yes—
129C22×C13C2×#4112yes—
130C22×C13H(5,𝔽2)11yescharacteristic
131C22×C13H(5,𝔽2)11yescharacteristic
132C2×D13—24no—
133C2×D13—24no—
134C2×D13—24no—
135C2×D13—42no—
136C2×D13—42no—
137C2×D13—42no—
138C2×D13—42no—
139C4×C13—22no—
140C4×C13—22no—
141C4×C13—22no—
142C4×C13—41no—
143C4×C13—41no—
144C4×C13—41no—
145Dic13—24no—
146Dic13—42no—
147Dic13—42no—
148C22×D4—132no—
149C22×D4—131no—
150C23×C4—132no—
151#126—24no—
152C4×D4—264no—
153C2×C4⋊C4—131no—
154C2×C4⋊C4—132no—
155C2×C4⋊C4C2×D1311yescharacteristic
156C2×C4⋊C4C2×D1311yescharacteristic
157C2×C4⋊C4C2×D1311yescharacteristic
158C2×C22⋊C4—132no—
159C2×C22⋊C4—132no—
160C2×C22⋊C4—132no—
161C2×C22⋊C4—132no—
162C2×C22⋊C4—132no—
163C2×C22⋊C4C2×D1311yescharacteristic
164C2×C22⋊C4C2×D1311yescharacteristic
165C2×C22⋊C4C2×D1311yescharacteristic
166C2×C42—132no—
167C2×C42C2×D1311yescharacteristic
168#95—132no—
169#95—131no—
170#95—131no—
171#95—132no—
172#95—132no—
173C2×C13—81no—
174C2×C13#52511yescharacteristic
175C2×C13#53211yescharacteristic
176C2×C13#53511yescharacteristic
177C2×C13#55112yes—
178C2×C13#55312yes—
179D13—44no—
180C24—132no—
181C24C22×D1311yescharacteristic
182C2×D4—264no—
183C2×D4—264no—
184C2×D4—264no—
185C2×D4—262no—
186C2×D4—522no—
187C22×C4—132no—
188C22×C4—132no—
189C22×C4—132no—
190C22×C4—264no—
191C22×C4—522no—
192C22×C4—522no—
193C22×C4C22×D1311yescharacteristic
194C22×C4C22×D1311yescharacteristic
195C22×C4C22×D1311yescharacteristic
196C22×C4C22×D1311yescharacteristic
197C22×C4C22×D1311yescharacteristic
198C22×C4C22×D1311yescharacteristic
199C4⋊C4—22no—
200C4⋊C4—22no—
201C4⋊C4—22no—
202C4⋊C4—262no—
203C4⋊C4—522no—
204C22⋊C4—22no—
205C22⋊C4—22no—
206C22⋊C4—22no—
207C22⋊C4—264no—
208C22⋊C4—264no—
209C22⋊C4—264no—
210C22⋊C4—522no—
211C22⋊C4—522no—
212C42—264no—
213C42C22⋊D1314yescomplemented
214C13#260311yescharacteristic, complemented, Sylow
215C23—22no—
216C23—22no—
217C23—21no—
218C23—21no—
219C23—21no—
220C23—134no—
221C23—262no—
222C23—262no—
223C23—262no—
224C23—262no—
225C23—262no—
226C23—262no—
227C23C23×D1311yescharacteristic
228D4—268no—
229D4—528no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—134no—
242C2×C4—262no—
243C2×C4—262no—
244C2×C4—262no—
245C2×C4—262no—
246C2×C4—262no—
247C2×C4—262no—
248C2×C4—262no—
249C2×C4—262no—
250C2×C4—528no—
251C2×C4C2×C22⋊D1312yes—
252C2×C4C2×C22⋊D1312yes—
253C2×C4C2×C22⋊D1312yes—
254C22—41no—
255C22—41no—
256C22—41no—
257C22—42no—
258C22—42no—
259C22—264no—
260C22—264no—
261C22—264no—
262C22—522no—
263C22—522no—
264C22—522no—
265C22—522no—
266C22#41×D1312yes—
267C22#41×D1312yes—
268C22#8825611yescharacteristic
269C22#8825611yescharacteristic
270C22C22×C22⋊D1311yescharacteristic
271C4—22no—
272C4—22no—
273C4—22no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—264no—
278C4—522no—
279C4—522no—
280C2—81no—
281C2—524no—
282C2#1171941012yes—
283C2#1171941412yes—
284C2#1171953311yescharacteristic
285C2#1171953511yescharacteristic
286C2#1171953711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×#126C2
prime radical#11718621C2
hypercenterC2×#126D13
hypocenterC13#2603
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. C2×C13×#126C2semidirect
2. C2×C4×D52C2semidirect
3. #11718652C2semidirect
4. #11718651C2semidirect
5. #11718650C2semidirect
6. #11718644C2semidirect
8. #11718618C2semidirect
9. #11718617C2semidirect
10. #11718614C2semidirect
11. #11718593C2semidirect
62. C42×C13D4semidirect
111. C2×#126D13semidirect
213. C42C22⋊D13semidirect
214. C13#2603semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1262
C2×C4×D522
#117186522
#117186512
#117186502
#117186442
#117186212
#117186182
#117186172
#117186142
#117185932
#260313