Finite Group Databasebeta

← #15751502

Subgroups — #15751502

Order 3328.

372 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114953C211yesmaximal, characteristic
2#13114585C211yesmaximal, characteristic
3#13112662C212yesmaximal
4#13112659C212yesmaximal
5C13×#2863C211yesmaximal, characteristic
6C13×#391C411yescharacteristic
7C13×#391C411yescharacteristic
8C13×#391C2211yescharacteristic
9C13×#389C411yescharacteristic
10C13×#389C411yescharacteristic
11C13×#389C2211yescharacteristic
12C13×#387—21no—
13C13×#387—21no—
14C13×#387—21no—
15C13×#383—21no—
16C43×C13C2211yescharacteristic
17C2×C4⋊#1055—21no—
18C2×#88043—21no—
19#11718116—21no—
20#11718116—21no—
21#11718116C2212yes—
22#11718116C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C42×C13C2×C411yescharacteristic
31C2×C42×C13C2×C411yescharacteristic
32C2×C42×C13D411yescharacteristic
33C2×C42×C13D411yescharacteristic
34C2×C42×C13D411yescharacteristic
35C2×C42×C13D411yescharacteristic
36C2×C42×C13C2311yescharacteristic
37C22×#1055—22no—
38C22×#1055—22no—
39C13×#95—21no—
40C13×#95—21no—
41C13×#95—21no—
42C13×#95—21no—
43C13×#95—21no—
44C13×#95—21no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C4⋊#1055—42no—
49#88043—24no—
50#7709—131nomaximal, Sylow
51C2×Q8×C13—22no—
52C2×Q8×C13—41no—
53C2×Q8×C13—41no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22×C411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C13×C4⋊C4—22no—
66C13×C4⋊C4—41no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—42no—
69C13×C4⋊C4—42no—
70C13×C4⋊C4—41no—
71C13×C4⋊C4—41no—
72C42×C13—22no—
73C42×C13—22no—
74C42×C13—21no—
75C42×C13—22no—
76C42×C13—21no—
77C42×C13—41no—
78C42×C13—41no—
79C42×C13—41no—
80C2×#1055—24no—
81C2×#1055—42no—
82C2×#1055—42no—
83C2×#1055—42no—
84C2×#1055—42no—
85C2×#1055—42no—
86#2863D1311yescharacteristic
87#1831—131no—
88#1745—131no—
89#1272—132no—
90#1271—132no—
91C23×C13C2×C22⋊C411yescharacteristic
92Q8×C13—82no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
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—41no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13#10412yes—
123C2×C4×C13#13112yes—
124C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C13#13711yescharacteristic
126C2×C4×C13#13712yes—
127#1055—44no—
128#1055—82no—
129C2×C4⋊C8—261no—
130C2×#97—261no—
131#391Dic1311yescharacteristic
132#391Dic1311yescharacteristic
133#391C2×D1311yescharacteristic
134#389Dic1311yescharacteristic
135#389Dic1311yescharacteristic
136#389C2×D1311yescharacteristic
137#387—21no—
138#387—21no—
139#387—21no—
140#383—21no—
141C43C2×D1311yescharacteristic
142#336—132no—
143#336—132no—
144#336—261no—
145#336—261no—
146C22×C13#40811yescharacteristic
147C22×C13#41011yescharacteristic
148C22×C13#41311yescharacteristic
149C22×C13#41711yescharacteristic
150C22×C13#41911yescharacteristic
151C22×C13C2×#10411yescharacteristic
152C22×C13#42111yescharacteristic
153C4×C13—22no—
154C4×C13—22no—
155C4×C13—22no—
156C4×C13—21no—
157C4×C13—21no—
158C4×C13—41no—
159C4×C13—41no—
160C4×C13—41no—
161C4×C13—81no—
162C4×C13—81no—
163C4×C13—81no—
164C4×C13—81no—
165C22×Q8C2×Dic1311yescharacteristic
166C22×C8—262no—
167C22×C8—262no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4C2×Dic1311yescharacteristic
172C2×C4⋊C4C2×Dic1311yescharacteristic
173C2×C4⋊C4C2×Dic1311yescharacteristic
174C2×C42C2×Dic1311yescharacteristic
175C2×C42C2×Dic1311yescharacteristic
176C2×C42C22⋊D1311yescharacteristic
177C2×C42C22⋊D1311yescharacteristic
178C2×C42C22⋊D1311yescharacteristic
179C2×C42C22⋊D1311yescharacteristic
180C2×C42C22×D1311yescharacteristic
181C4⋊C8—522no—
182#97—264no—
183#95—21no—
184#95—21no—
185#95—21no—
186#95—21no—
187#95—21no—
188#95—21no—
189#95—21no—
190#95—21no—
191#95—21no—
192C2×C13#147311yescharacteristic
193C2×C13#148311yescharacteristic
194C2×C13#149711yescharacteristic
195C2×C13#150611yescharacteristic
196C2×C13#151211yescharacteristic
197C2×C13#152911yescharacteristic
198C2×C13#155911yescharacteristic
199C2×Q8—22no—
200C2×Q8—41no—
201C2×Q8—41no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4C22⋊Dic1311yescharacteristic
207C22×C4C22⋊Dic1311yescharacteristic
208C22×C4C22⋊Dic1311yescharacteristic
209C22×C4C22⋊Dic1311yescharacteristic
210C22×C4C22×Dic1311yescharacteristic
211C22×C4C2×C22⋊D1311yescharacteristic
212C22×C4C2×C22⋊D1311yescharacteristic
213C2×C8—264no—
214C2×C8—522no—
215C2×C8—522no—
216C2×C8—522no—
217C2×C8—522no—
218C2×C8—522no—
219C4⋊C4—22no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C42—22no—
227C42—22no—
228C42—22no—
229C42—21no—
230C42—21no—
231C42—41no—
232C42—41no—
233C42—41no—
234C13#770911yescharacteristic, complemented, Sylow
235C23C2×C22⋊Dic1311yescharacteristic
236Q8—82no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4#8807712yes—
267C2×C4#8819612yes—
268C2×C4#8820212yes—
269C2×C4#8820311yescharacteristic
270C2×C4#8820511yescharacteristic
271C8—524no—
272C8—1042no—
273C22#1171888611yescharacteristic
274C22#1171889311yescharacteristic
275C22#1171889511yescharacteristic
276C22C2×#8807711yescharacteristic
277C22#1171889711yescharacteristic
278C22#1171889811yescharacteristic
279C22#1171890111yescharacteristic
280C4—22no—
281C4—21no—
282C4—21no—
283C4—22no—
284C4—22no—
285C4—41no—
286C4—41no—
287C4—41no—
288C4—81no—
289C4—81no—
290C4—81no—
291C4—81no—
292C2#1311320511yescharacteristic
293C2#1311324911yescharacteristic
294C2#1311330911yescharacteristic
295C2#1311334811yescharacteristic
296C2#1311337411yescharacteristic
297C2#1311344311yescharacteristic
298C2#1311356611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2863C2
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2863D13
hypocenterC13#7709
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ #2863

Complements

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

NH ≅ G/Ntype
234. C13#7709semidirect

Maximal subgroups

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

subgroupindex
#131149532
#131145852
#131126622
#131126592
C13×#28632
#770913