Finite Group Databasebeta

← #15872375

Subgroups — #15872375

Order 3328.

990 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719224C211yesmaximal, characteristic
2#13117437C212yesmaximal
3#13115819C218yesmaximal
4#13114913C211yesmaximal, characteristic
5#13114911C212yesmaximal
6C13×#1820C211yesmaximal, characteristic
7C2×C13×#117C2211yescharacteristic
8C2×#88180C2211yescharacteristic
9C22×C4⋊Dic13C2211yescharacteristic
10#11719224—24no—
11#11719224—24no—
12C2×#88144C412yescomplemented
13C2×#88142C412yescomplemented
14C2×#88132C2214yes—
15C2×#88124C412yescomplemented
16C2×#88123C412yescomplemented
17C13×#381C2212yes—
18#11718872C2212yes—
19#11718603C2214yes—
20C22⋊C4×Dic13C2214yes—
21#11718315—24no—
22#11718314—24no—
23C13×#342C2214yes—
24#11718119C2218yes—
25#11718118C2214yes—
26C23×C4×C13C2311yescharacteristic
27C23×Dic13C2312yes—
28C22×Dic26C2×C414yes—
29C13×#117—22no—
30C13×#117—22no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C22⋊C4C2314yes—
34C2×C13×C22⋊C4C2312yes—
35C2×C42×C13C2×C412yes—
36C2×C22⋊Dic13C2314yes—
37C2×C22⋊Dic13C2312yes—
38#88180—22no—
39#88180—22no—
40C2×C4⋊Dic13C2×C411yescharacteristic
41C2×C4⋊Dic13C2×C414yes—
42C2×C4⋊Dic13C2×C411yescharacteristic
43C2×C4⋊Dic13C2×C412yes—
44C2×C4⋊Dic13C2×C412yes—
45C2×C4⋊Dic13D414yes—
46C2×C4⋊Dic13D414yes—
47C2×#6101—24no—
48C2×#6101C2×C414yes—
49C2×#6101C2×C414yes—
50C2×C4×Dic13—24no—
51C2×C4×Dic13C2×C412yes—
52#88144—28no—
53#88142—28no—
54#88132—28no—
55#88132—28no—
56#88124—24no—
57#88124—24no—
58#88123—24no—
59#88123—24no—
60C13×#95—22no—
61C13×#95—22no—
62#88071—22no—
63#88071—22no—
64#88071—24no—
65#88071—24no—
66#21828—131nomaximal, Sylow
67C24×C13C2411yescharacteristic
68C22×C4×C13—24no—
69C22×C4×C13—24no—
70C22×C4×C13C22×C411yescharacteristic
71C22×C4×C13C22×C411yescharacteristic
72C22×C4×C13C22×C412yes—
73C22×C4×C13C22×C412yes—
74C22×C4×C13C2×D412yes—
75C22×C4×C13C2×D412yes—
76C22×Dic13—24no—
77C22×Dic13—82no—
78C22×Dic13C22×C412yes—
79C22×Dic13C22×C412yes—
80C22×Dic13C22×C414yes—
81C22×Dic13C2×D414yes—
82C22×Dic13C2×D414yes—
83C2×Dic26—28no—
84C2×Dic26—84no—
85C13×C4⋊C4—22no—
86C13×C4⋊C4—22no—
87C13×C22⋊C4—24no—
88C13×C22⋊C4—28no—
89C42×C13—22no—
90C42×C13—22no—
91C22⋊Dic13—24no—
92C22⋊Dic13—28no—
93C4⋊Dic13—21no—
94C4⋊Dic13—21no—
95C4⋊Dic13—21no—
96C4⋊Dic13—21no—
97C4⋊Dic13—28no—
98C4⋊Dic13C22⋊C414yes—
99C4⋊Dic13C22⋊C414yes—
100C4⋊Dic13C22⋊C418yes—
101#6101—28no—
102#6101—28no—
103#6101—84no—
104C4×Dic13—24no—
105C4×Dic13—84no—
106C2×#544—131no—
107#2313—132no—
108#1996—138no—
109#1820—132no—
110#1820—131no—
111#1820D1311yescharacteristic
112C23×C13—41no—
113C23×C13—41no—
114C23×C13C23×C411yescharacteristic
115C23×C13C22×D412yes—
116C23×C132−1+414yes—
117C2×C4×C13—22no—
118C2×C4×C13—22no—
119C2×C4×C13—24no—
120C2×C4×C13—24no—
121C2×C4×C13—22no—
122C2×C4×C13—22no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—44no—
126C2×C4×C13—44no—
127C2×C4×C13—44no—
128C2×C4×C13C2×C22⋊C412yes—
129C2×C4×C13C2×C22⋊C411yescharacteristic
130C2×C4×C13C2×C22⋊C411yescharacteristic
131C2×Dic13—22no—
132C2×Dic13—22no—
133C2×Dic13—44no—
134C2×Dic13—44no—
135C2×Dic13—44no—
136C2×Dic13—42no—
137C2×Dic13—42no—
138C2×Dic13—44no—
139C2×Dic13—44no—
140C2×Dic13—44no—
141C2×Dic13C2×C22⋊C418yes—
142Dic26—88no—
143#544—264no—
144#544—264no—
145C2×C4⋊Q8—132no—
146C2×C4⋊Q8—132no—
147C2×#125—132no—
148C2×#125—132no—
149C2×C22⋊Q8—134no—
150C2×#117—131no—
151C2×#117C2×D1311yescharacteristic
152C22×C4⋊C4—131no—
153#387—264no—
154#387—264no—
155#381—132no—
156#381C2×D1312yes—
157#380—134no—
158C4×C22⋊C4—134no—
159#342—134no—
160#342—138no—
161#342C2×D1314yes—
162C22×C13—21no—
163C22×C13—22no—
164C22×C13—21no—
165C22×C13—22no—
166C22×C13—44no—
167C22×C13C22×C22⋊C411yescharacteristic
168C22×C13#51912yes—
169C22×C13#53614yes—
170C4×C13—22no—
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—42no—
174C4×C13—42no—
175C4×C13—84no—
176Dic13—28no—
177Dic13—42no—
178Dic13—42no—
179Dic13—84no—
180C22×Q8—134no—
181C23×C4—132no—
182C23×C4C22×D1311yescharacteristic
183C4⋊Q8—264no—
184C4⋊Q8—264no—
185C4⋊Q8—268no—
186#125—264no—
187#125—264no—
188#125—268no—
189C22⋊Q8—268no—
190C22⋊Q8—268no—
191#117—22no—
192#117—22no—
193#117—262no—
194#117—262no—
195C2×C4⋊C4—132no—
196C2×C4⋊C4—132no—
197C2×C4⋊C4—134no—
198C2×C4⋊C4—134no—
199C2×C4⋊C4—131no—
200C2×C4⋊C4—131no—
201C2×C4⋊C4—134no—
202C2×C4⋊C4—134no—
203C2×C4⋊C4—134no—
204C2×C4⋊C4—264no—
205C2×C4⋊C4C4×D1311yescharacteristic
206C2×C4⋊C4C4×D1311yescharacteristic
207C2×C22⋊C4—132no—
208C2×C22⋊C4—134no—
209C2×C22⋊C4C22×D1314yes—
210C2×C22⋊C4C22×D1312yes—
211C2×C42—132no—
212C2×C42—264no—
213C2×C42C4×D1312yes—
214#95—22no—
215#95—22no—
216#95—264no—
217#95—264no—
218#95—262no—
219#95—262no—
220C2×C13—24no—
221C2×C13—22no—
222C2×C13#231011yescharacteristic
223C2×C13#288311yescharacteristic
224C2×C13#288411yescharacteristic
225C24C23×D1311yescharacteristic
226C2×Q8—268no—
227C2×Q8—1044no—
228C22×C4—24no—
229C22×C4—24no—
230C22×C4—134no—
231C22×C4—134no—
232C22×C4—134no—
233C22×C4—132no—
234C22×C4—132no—
235C22×C4—264no—
236C22×C4—1042no—
237C22×C4C2×C4×D1311yescharacteristic
238C22×C4C2×C4×D1311yescharacteristic
239C22×C4C2×C4×D1312yes—
240C22×C4C2×C4×D1312yes—
241C22×C4D4×D1312yes—
242C22×C4D4×D1312yes—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—134no—
246C4⋊C4—134no—
247C4⋊C4—138no—
248C4⋊C4—268no—
249C4⋊C4—268no—
250C4⋊C4—268no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—1044no—
256C22⋊C4—24no—
257C22⋊C4—28no—
258C22⋊C4—264no—
259C22⋊C4—268no—
260C42—22no—
261C42—22no—
262C42—264no—
263C42—1044no—
264C13#2182811yescharacteristic, complemented, Sylow
265C23—41no—
266C23—41no—
267C23C22×C4×D1311yescharacteristic
268C23C2×D4×D1312yes—
269C23#8825714yes—
270Q8—1048no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—24no—
274C2×C4—24no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—44no—
280C2×C4—44no—
281C2×C4—44no—
282C2×C4—138no—
283C2×C4—262no—
284C2×C4—262no—
285C2×C4—524no—
286C2×C4—524no—
287C2×C4—524no—
288C2×C4—522no—
289C2×C4—522no—
290C2×C4—524no—
291C2×C4—524no—
292C2×C4—524no—
293C2×C4C22⋊C4×D1311yescharacteristic
294C2×C4C22⋊C4×D1311yescharacteristic
295C2×C4C22⋊C4×D1312yes—
296C22—21no—
297C22—22no—
298C22—21no—
299C22—22no—
300C22—44no—
301C22C2×C22⋊C4×D1311yescharacteristic
302C22#1171922112yes—
303C22#1171935314yes—
304C4—21no—
305C4—21no—
306C4—22no—
307C4—42no—
308C4—42no—
309C4—84no—
310C4—268no—
311C4—522no—
312C4—522no—
313C4—1044no—
314C2—24no—
315C2—22no—
316C2#1311742111yescharacteristic
317C2#1312329511yescharacteristic
318C2#1312329811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D13
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingC13×#1820C2
socleC22×C13C22×C22⋊C4
prime radical, cosocleC24×C13C24
hypercenter#1820D13
hypocenterC13#21828
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1820

Complements

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

NH ≅ G/Ntype
12. C2×#88144C4semidirect
13. C2×#88142C4semidirect
15. C2×#88124C4semidirect
16. C2×#88123C4semidirect
264. C13#21828semidirect

Maximal subgroups

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

subgroupindex
C2×#117192242
#131174372
#131158192
#131149132
#131149112
C13×#18202
#2182813