Finite Group Databasebeta

← #13117502

Subgroups — #13117502

Order 1664.

632 conjugacy classes of subgroups.

The subgroup lattice has 290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88183C211yesmaximal, characteristic
2C22×C4⋊Dic13C211yesmaximal, characteristic, complemented
3C2×#88135C211yesmaximal, characteristic
4C13×#381C211yesmaximal, characteristic, complemented
5#11718619C211yesmaximal, characteristic
6#11718607C211yesmaximal, characteristic, complemented
7C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
8#11718331C212yesmaximal, complemented
9#11718329C212yesmaximal, complemented
10#11718316C212yesmaximal, complemented
11#11718308C212yesmaximal, complemented
12C23×C4×C13C2211yescharacteristic
13C22×C22⋊D13C2211yescharacteristic
14C23×Dic13C2211yescharacteristic
15C23×Dic13C2211yescharacteristic
16C22×C4×D13C2211yescharacteristic
17C2×C13×C22⋊C4C2211yescharacteristic
18C2×C13×C22⋊C4C2211yescharacteristic
19C2×C22⋊Dic13C2211yescharacteristic
20#88183C418yescomplemented
21C2×#6103C2211yescharacteristic
22C2×#6103C2212yes—
23C2×#6103C2212yes—
24C2×C4⋊Dic13—24no—
25C2×C4⋊Dic13C2212yes—
26C2×C4⋊Dic13C2212yes—
27C2×#6101C2211yescharacteristic
28C2×#6101C2212yes—
29C2×#6101C2212yes—
30C2×C4×Dic13C2211yescharacteristic
31C2×C4×Dic13C2212yes—
32#88135—24no—
33C13×#95C2212yes—
34C13×#95C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37#88071C2212yes—
38C24×C13C2311yescharacteristic
39C23×D13C2311yescharacteristic
40C22×C4×C13—22no—
41C22×C4×C13—22no—
42C22×C4×C13C2×C414yescomplemented
43C22×C4×C13C2311yescharacteristic
44C22×C4×C13C2312yes—
45C22×C4×C13C2311yescharacteristic
46C22×C4×C13C2312yes—
47C2×C22⋊D13—22no—
48C2×C22⋊D13—22no—
49C2×C22⋊D13C2×C414yes—
50C22×Dic13—22no—
51C22×Dic13—42no—
52C22×Dic13—42no—
53C22×Dic13D414yes—
54C22×Dic13C2312yes—
55C22×Dic13C2311yescharacteristic
56C22×Dic13C2312yes—
57C22×Dic13C2311yescharacteristic
58C22×Dic13C2311yescharacteristic
59C2×C4×D13—22no—
60C2×C4×D13—42no—
61C13×C22⋊C4—22no—
62C13×C22⋊C4—22no—
63C22⋊Dic13C2×C414yescomplemented
64#6103—22no—
65#6103—42no—
66#6103C2×C418yescomplemented
67C4⋊Dic13—24no—
68C4⋊Dic13—24no—
69#6101—22no—
70#6101—42no—
71#6101C2×C418yescomplemented
72C4×Dic13—22no—
73C4×Dic13—42no—
74#2322—131nomaximal, Sylow
75C23×C13—22no—
76C23×C13—22no—
77C23×C13C22×C412yes—
78C23×C13C2×D412yes—
79C23×C13#4112yes—
80C23×C13C2411yescharacteristic
81C22×D13—21no—
82C22×D13—21no—
83C22×D13—22no—
84C22×D13—22no—
85C22×D13C22×C412yes—
86C2×C4×C13—28no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13C22×C414yes—
97C22⋊D13—28no—
98C2×Dic13—21no—
99C2×Dic13—21no—
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13—22no—
103C2×Dic13—22no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—44no—
108C2×Dic13—44no—
109C2×Dic13C22×C412yes—
110C2×Dic13C22×C414yes—
111C2×Dic13C2×D412yes—
112C2×Dic13C2×D412yes—
113C4×D13—44no—
114C2×#123—131no—
115C2×C4×D4—131no—
116C22×C4⋊C4—131no—
117#389—132no—
118#388—132no—
119#387—132no—
120#386—131no—
121#385—131no—
122#385—132no—
123#381D1311yescharacteristic, complemented
124C4×C22⋊C4—131no—
125C22×C13—24no—
126C22×C13—22no—
127C22×C13—22no—
128C22×C13—24no—
129C22×C13C4×D414yes—
130C22×C13C23×C411yescharacteristic
131C22×C13C22×D411yescharacteristic
132C22×C13C2×#4111yescharacteristic
133C22×C13H(5,𝔽2)12yes—
134C22×C132−1+412yes—
135C2×D13—22no—
136C2×D13—24no—
137C2×D13—41no—
138C2×D13—41no—
139C2×D13—42no—
140C4×C13—24no—
141C4×C13—41no—
142C4×C13—41no—
143C4×C13—42no—
144Dic13—22no—
145Dic13—24no—
146Dic13—22no—
147Dic13—22no—
148Dic13—42no—
149C22×D4—131no—
150C23×C4—131no—
151C23×C4—131no—
152C23×C4—131no—
153C23×C4C2×D1311yescharacteristic
154#123—138no—
155C4×D4—264no—
156C2×C4⋊C4—132no—
157C2×C4⋊C4—132no—
158C2×C4⋊C4—132no—
159C2×C4⋊C4—131no—
160C2×C4⋊C4—132no—
161C2×C4⋊C4—264no—
162C2×C22⋊C4—131no—
163C2×C22⋊C4—132no—
164C2×C22⋊C4—131no—
165C2×C22⋊C4—132no—
166C2×C22⋊C4C2×D1311yescharacteristic
167C2×C22⋊C4C2×D1311yescharacteristic
168C2×C42—131no—
169C2×C42—132no—
170#95—132no—
171#95—132no—
172#95—132no—
173#95C2×D1312yes—
174#95C2×D1312yes—
175C2×C13—24no—
176C2×C13C2×C4×D411yescharacteristic
177C2×C13#52012yes—
178C2×C13#53411yescharacteristic
179C2×C13#53611yescharacteristic
180C2×C13#53912yes—
181D13—42no—
182C24—131no—
183C24C22×D1311yescharacteristic
184C2×D4—134no—
185C2×D4—262no—
186C2×D4—262no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—132no—
190C22×C4—131no—
191C22×C4—131no—
192C22×C4—131no—
193C22×C4—134no—
194C22×C4—132no—
195C22×C4—262no—
196C22×C4—262no—
197C22×C4—522no—
198C22×C4—522no—
199C22×C4—522no—
200C22×C4C4×D1314yescomplemented
201C22×C4C22×D1311yescharacteristic
202C22×C4C22×D1312yes—
203C22×C4C22×D1311yescharacteristic
204C22×C4C22×D1312yes—
205C4⋊C4—138no—
206C4⋊C4—264no—
207C4⋊C4—264no—
208C4⋊C4—262no—
209C4⋊C4—522no—
210C22⋊C4—22no—
211C22⋊C4—22no—
212C22⋊C4—134no—
213C22⋊C4—138no—
214C22⋊C4—262no—
215C22⋊C4—522no—
216C42—262no—
217C42—522no—
218C13#232211yescharacteristic, complemented, Sylow
219C23—22no—
220C23—22no—
221C23—132no—
222C23—261no—
223C23—261no—
224C23—262no—
225C23—262no—
226C23C2×C4×D1312yes—
227C23D4×D1312yes—
228C23#612912yes—
229C23C23×D1311yescharacteristic
230D4—268no—
231C2×C4—28no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—134no—
242C2×C4—132no—
243C2×C4—132no—
244C2×C4—132no—
245C2×C4—261no—
246C2×C4—261no—
247C2×C4—262no—
248C2×C4—262no—
249C2×C4—262no—
250C2×C4—262no—
251C2×C4—262no—
252C2×C4—262no—
253C2×C4—262no—
254C2×C4—524no—
255C2×C4—524no—
256C2×C4—524no—
257C2×C4C2×C4×D1314yes—
258C22—24no—
259C22—22no—
260C22—22no—
261C22—24no—
262C22—262no—
263C22—264no—
264C22—521no—
265C22—521no—
266C22—522no—
267C22#8813514yes—
268C22C22×C4×D1311yescharacteristic
269C22C2×D4×D1311yescharacteristic
270C22C2×#612911yescharacteristic
271C22#8825612yes—
272C22#8825712yes—
273C4—24no—
274C4—41no—
275C4—41no—
276C4—42no—
277C4—262no—
278C4—264no—
279C4—262no—
280C4—262no—
281C4—522no—
282C2—24no—
283C2—522no—
284C2C2×#8813511yescharacteristic
285C2#1171922812yes—
286C2#1171935311yescharacteristic
287C2#1171935811yescharacteristic
288C2#1171937012yes—
subgroupG/H
center, FrattiniC23C23×D13
commutatorC22×C13C23×C4
FittingC13×#381C2
socle, cosocleC23×C13C24
prime radicalC22×C22⋊D13C22
hypercenter#381D13
hypocenterC13#2322
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊Dic13C2semidirect
4. C13×#381C2semidirect
6. #11718607C2semidirect
7. C22⋊C4×Dic13C2semidirect
8. #11718331C2semidirect
9. #11718329C2semidirect
10. #11718316C2semidirect
11. #11718308C2semidirect
20. #88183C4semidirect
42. C22×C4×C13C2×C4semidirect
63. C22⋊Dic13C2×C4semidirect
66. #6103C2×C4semidirect
71. #6101C2×C4semidirect
123. #381D13semidirect
200. C22×C4C4×D13semidirect
218. C13#2322semidirect

Maximal subgroups

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

subgroupindex
C2×#881832
C22×C4⋊Dic132
C2×#881352
C13×#3812
#117186192
#117186072
C22⋊C4×Dic132
#117183312
#117183292
#117183162
#117183082
#232213