Finite Group Databasebeta

← #15751012

Subgroups — #15751012

Order 3328.

406 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114979C211yesmaximal, characteristic
2#13114953C211yesmaximal, characteristic
3#13112662C212yesmaximal
4#13112659C212yesmaximal
5C13×#2295C211yesmaximal, characteristic
6C2×C4×Q8×C13C411yescharacteristic
7C13×#391C411yescharacteristic
8C13×#391C2211yescharacteristic
9C13×#389C411yescharacteristic
10C13×#389C2211yescharacteristic
11C13×#387—21no—
12C13×#387—21no—
13C4×C13×C4⋊C4—21no—
14C4×C13×C4⋊C4C411yescharacteristic
15C13×#376—21no—
16C43×C13C2211yescharacteristic
17C2×C4⋊#1055—21no—
18#11718116—21no—
19#11718116—21no—
20#11718116—21no—
21#11718116C2212yes—
22#11718116C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C4×Q8×C13—22no—
25C4×Q8×C13C814yescomplemented
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C42×C13—21no—
33C2×C42×C13—21no—
34C2×C42×C13C2×C411yescharacteristic
35C2×C42×C13C2×C411yescharacteristic
36C2×C42×C13D411yescharacteristic
37C2×C42×C13D411yescharacteristic
38C2×C42×C13D411yescharacteristic
39C2×C42×C13D411yescharacteristic
40C2×C42×C13C2311yescharacteristic
41C22×#1055—22no—
42C22×#1055—22no—
43C13×#95—21no—
44C13×#95—21no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C4⋊#1055—42no—
51#7596—131nomaximal, Sylow
52C2×Q8×C13—21no—
53C2×Q8×C13—41no—
54C2×Q8×C13—41no—
55C2×Q8×C13C2×C812yes—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22×C411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C13×C4⋊C4—24no—
68C13×C4⋊C4—21no—
69C13×C4⋊C4—41no—
70C13×C4⋊C4—41no—
71C13×C4⋊C4—42no—
72C13×C4⋊C4—41no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4C2×C812yes—
75C42×C13—24no—
76C42×C13—21no—
77C42×C13—22no—
78C42×C13—21no—
79C42×C13—41no—
80C42×C13—41no—
81C42×C13—41no—
82C42×C13—41no—
83C42×C13—42no—
84C42×C13C2×C812yes—
85C42×C13M1612yes—
86C2×#1055—42no—
87C2×#1055—42no—
88C2×#1055—42no—
89C2×#1055—42no—
90C2×#1055—42no—
91C2×#1055—42no—
92#2295D1311yescharacteristic
93#1839—131no—
94#1831—131no—
95#1272—132no—
96#1271—132no—
97C23×C13C2×C22⋊C411yescharacteristic
98Q8×C13—42no—
99Q8×C13—42no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—22no—
111C2×C4×C13—22no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13C22⋊C812yes—
129C2×C4×C13C22⋊C812yes—
130C2×C4×C13C22×C811yescharacteristic
131C2×C4×C13C2×M1611yescharacteristic
132C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C13#13711yescharacteristic
134C2×C4×C13#13712yes—
135#1055—82no—
136#1055—82no—
137C2×C4×Q8Dic1311yescharacteristic
138C2×C4⋊C8—261no—
139#391Dic1311yescharacteristic
140#391C2×D1311yescharacteristic
141#389Dic1311yescharacteristic
142#389C2×D1311yescharacteristic
143#387—21no—
144#387—21no—
145C4×C4⋊C4—21no—
146C4×C4⋊C4Dic1311yescharacteristic
147#376—21no—
148C43C2×D1311yescharacteristic
149#336—132no—
150#336—132no—
151#336—261no—
152#336—261no—
153#336—261no—
154C22×C13C2×C22⋊C811yescharacteristic
155C22×C13#41011yescharacteristic
156C22×C13#41311yescharacteristic
157C22×C13#41711yescharacteristic
158C22×C13#41911yescharacteristic
159C22×C13#42111yescharacteristic
160C22×C13#42111yescharacteristic
161C4×C13—21no—
162C4×C13—21no—
163C4×C13—22no—
164C4×C13—22no—
165C4×C13—21no—
166C4×C13—21no—
167C4×C13—22no—
168C4×C13—41no—
169C4×C13—42no—
170C4×C13—42no—
171C4×C13—41no—
172C4×C13—81no—
173C4×C13—81no—
174C22×Q8C2×Dic1311yescharacteristic
175C22×C8—262no—
176C22×C8—262no—
177C4×Q8—22no—
178C4×Q8#105514yescomplemented
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4C2×Dic1311yescharacteristic
183C2×C4⋊C4C2×Dic1311yescharacteristic
184C2×C4⋊C4C2×Dic1311yescharacteristic
185C2×C42—21no—
186C2×C42—21no—
187C2×C42C2×Dic1311yescharacteristic
188C2×C42C2×Dic1311yescharacteristic
189C2×C42C22⋊D1311yescharacteristic
190C2×C42C22⋊D1311yescharacteristic
191C2×C42C22⋊D1311yescharacteristic
192C2×C42C22⋊D1311yescharacteristic
193C2×C42C22×D1311yescharacteristic
194C4⋊C8—522no—
195#95—21no—
196#95—21no—
197#95—21no—
198#95—21no—
199#95—21no—
200#95—21no—
201#95—21no—
202C2×C13#145811yescharacteristic
203C2×C13#147711yescharacteristic
204C2×C13#147911yescharacteristic
205C2×C13#151211yescharacteristic
206C2×C13#151511yescharacteristic
207C2×C13#153511yescharacteristic
208C2×C13#155911yescharacteristic
209C2×Q8—21no—
210C2×Q8—41no—
211C2×Q8—41no—
212C2×Q8C2×#105512yes—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4C22⋊Dic1311yescharacteristic
218C22×C4C22⋊Dic1311yescharacteristic
219C22×C4C22⋊Dic1311yescharacteristic
220C22×C4C22⋊Dic1311yescharacteristic
221C22×C4C22×Dic1311yescharacteristic
222C22×C4C2×C22⋊D1311yescharacteristic
223C22×C4C2×C22⋊D1311yescharacteristic
224C2×C8—522no—
225C2×C8—522no—
226C2×C8—522no—
227C2×C8—522no—
228C2×C8—522no—
229C2×C8—522no—
230C4⋊C4—24no—
231C4⋊C4—21no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—42no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4C2×#105512yes—
238C42—24no—
239C42—22no—
240C42—21no—
241C42—21no—
242C42—41no—
243C42—41no—
244C42—41no—
245C42—41no—
246C42—42no—
247C42C2×#105512yes—
248C42#609912yes—
249C13#759611yescharacteristic, complemented, Sylow
250C23C2×C22⋊Dic1311yescharacteristic
251Q8—42no—
252Q8—42no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4C22⋊#105512yes—
282C2×C4C22⋊#105512yes—
283C2×C4C22×#105511yescharacteristic
284C2×C4C2×#609911yescharacteristic
285C2×C4#8819612yes—
286C2×C4#8820311yescharacteristic
287C2×C4#8820511yescharacteristic
288C8—1042no—
289C8—1042no—
290C22C2×C22⋊#105511yescharacteristic
291C22#1171888611yescharacteristic
292C22#1171889311yescharacteristic
293C22#1171889711yescharacteristic
294C22#1171889711yescharacteristic
295C22#1171889811yescharacteristic
296C22#1171890111yescharacteristic
297C4—21no—
298C4—21no—
299C4—22no—
300C4—21no—
301C4—21no—
302C4—22no—
303C4—22no—
304C4—42no—
305C4—41no—
306C4—42no—
307C4—41no—
308C4—81no—
309C4—81no—
310C2#1311315011yescharacteristic
311C2#1311322311yescharacteristic
312C2#1311323111yescharacteristic
313C2#1311337411yescharacteristic
314C2#1311338711yescharacteristic
315C2#1311346711yescharacteristic
316C2#1311356611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#2295C2
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2295D13
hypocenterC13#7596
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ #2295

Complements

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

NH ≅ G/Ntype
25. C4×Q8×C13C8semidirect
178. C4×Q8#1055semidirect
249. C13#7596semidirect

Maximal subgroups

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

subgroupindex
#131149792
#131149532
#131126622
#131126592
C13×#22952
#759613