Finite Group Databasebeta

← #15751213

Subgroups — #15751213

Order 3328.

402 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117313C211yesmaximal, characteristic
2#13114979C211yesmaximal, characteristic
3#13112661C212yesmaximal
4#13112658C212yesmaximal
5C13×#1831C211yesmaximal, characteristic
6C2×C4×Dic26C411yescharacteristic
7C2×C13×C4⋊C8—21no—
8C43×C13C2211yescharacteristic
9C4×C4⋊Dic13C411yescharacteristic
10#11718594—21no—
11#11718594—21no—
12#11718593—21no—
13C4×#6101—21no—
14#11718590C411yescharacteristic
15#11718590C2211yescharacteristic
16#11718589C411yescharacteristic
17#11718589C2211yescharacteristic
18C13×#336—21no—
19C13×#336C2212yes—
20#11718116—21no—
21#11718116—21no—
22#11718116C2212yes—
23C22×Dic26C2×C411yescharacteristic
24C22×C8×C13—22no—
25C2×C42×C13C2×C411yescharacteristic
26C2×C42×C13C2×C411yescharacteristic
27C2×C42×C13D411yescharacteristic
28C2×C42×C13D411yescharacteristic
29C2×C42×C13D411yescharacteristic
30C2×C42×C13D411yescharacteristic
31C2×C42×C13C2311yescharacteristic
32C2×C4⋊Dic13C2×C411yescharacteristic
33C2×C4⋊Dic13C2×C411yescharacteristic
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×#6101—21no—
36C2×#6101—21no—
37C2×#6101—21no—
38C2×C4×Dic13—21no—
39C2×C4×Dic13—21no—
40C22×#1055—22no—
41C4×Dic26—22no—
42C4×Dic26—22no—
43C13×C4⋊C8—42no—
44#88071—21no—
45#88071—21no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#7644—131nomaximal, Sylow
52C22×C4×C13C22⋊C411yescharacteristic
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22×C411yescharacteristic
57C22×C4×C13C2×D411yescharacteristic
58C22×C4×C13C2×D411yescharacteristic
59C22×Dic13—21no—
60C22×Dic13—21no—
61C22×Dic13—21no—
62C22×Dic13—21no—
63C2×Dic26—21no—
64C2×Dic26—41no—
65C2×Dic26—41no—
66C2×Dic26M1612yes—
67C2×C8×C13—42no—
68C2×C8×C13—42no—
69C2×C8×C13—42no—
70C42×C13—21no—
71C42×C13—21no—
72C42×C13—22no—
73C42×C13—41no—
74C42×C13—41no—
75C42×C13—41no—
76C42×C13—41no—
77C42×C13SD1612yes—
78C42×C13Q1612yes—
79C4⋊Dic13—21no—
80C4⋊Dic13—41no—
81C4⋊Dic13—41no—
82C4⋊Dic13M1612yes—
83#6101—24no—
84#6101—42no—
85#6101—42no—
86C4×Dic13—24no—
87C4×Dic13—42no—
88C2×#1055—42no—
89C2×#1055—42no—
90C2×#1055—42no—
91#2295—131no—
92#1839—131no—
93#1831D1311yescharacteristic
94#1272—132no—
95#1271—132no—
96C23×C13C2×C22⋊C411yescharacteristic
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—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13#10312yes—
114C2×C4×C13#10312yes—
115C2×C4×C13C2×M1611yescharacteristic
116C2×C4×C13C2×M1611yescharacteristic
117C2×C4×C13C2×SD1611yescharacteristic
118C2×C4×C13C2×Q1611yescharacteristic
119C2×C4×C13#13512yes—
120C2×Dic13—22no—
121C2×Dic13—22no—
122C2×Dic13—41no—
123C2×Dic13—41no—
124C2×Dic13—41no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132Dic26—42no—
133Dic26—42no—
134C8×C13—82no—
135#1055—82no—
136C2×C4×Q8—131no—
137C2×C4⋊C8—21no—
138#391—131no—
139#391—131no—
140#389—131no—
141#389—131no—
142#387—261no—
143#387—261no—
144C4×C4⋊C4—131no—
145C4×C4⋊C4—261no—
146#376—261no—
147C43C2×D1311yescharacteristic
148#336—21no—
149#336—132no—
150#336—261no—
151#336—261no—
152#336C2×D1312yes—
153C22×C13#40711yescharacteristic
154C22×C13#41011yescharacteristic
155C22×C13#41311yescharacteristic
156C22×C13C2×#10311yescharacteristic
157C22×C13#41611yescharacteristic
158C22×C13#42111yescharacteristic
159C22×C13#42111yescharacteristic
160C4×C13—22no—
161C4×C13—21no—
162C4×C13—21no—
163C4×C13—22no—
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—22no—
167C4×C13—41no—
168C4×C13—41no—
169Dic13—42no—
170Dic13—42no—
171Dic13—81no—
172Dic13—81no—
173C22×Q8—131no—
174C22×C8—22no—
175C22×C8—262no—
176C4×Q8—262no—
177C4×Q8—262no—
178C2×C4⋊C4—131no—
179C2×C4⋊C4—131no—
180C2×C4⋊C4—131no—
181C2×C4⋊C4—261no—
182C2×C4⋊C4—261no—
183C2×C4⋊C4—261no—
184C2×C42—261no—
185C2×C42—261no—
186C2×C42C4×D1311yescharacteristic
187C2×C42C4×D1311yescharacteristic
188C2×C42D5211yescharacteristic
189C2×C42D5211yescharacteristic
190C2×C42C22⋊D1311yescharacteristic
191C2×C42C22⋊D1311yescharacteristic
192C2×C42C22×D1311yescharacteristic
193C4⋊C8—42no—
194#95—261no—
195#95—261no—
196#95—261no—
197#95—261no—
198#95—261no—
199#95—261no—
200#95—261no—
201C2×C13#146411yescharacteristic
202C2×C13#148711yescharacteristic
203C2×C13#148811yescharacteristic
204C2×C13#151811yescharacteristic
205C2×C13#152111yescharacteristic
206C2×C13#153511yescharacteristic
207C2×C13#154211yescharacteristic
208C2×Q8—132no—
209C2×Q8—261no—
210C2×Q8—521no—
211C2×Q8—521no—
212C22×C4—261no—
213C22×C4—261no—
214C22×C4—261no—
215C22×C4—261no—
216C22×C4#610311yescharacteristic
217C22×C4#610311yescharacteristic
218C22×C4#610311yescharacteristic
219C22×C4#610311yescharacteristic
220C22×C4C2×C4×D1311yescharacteristic
221C22×C4C2×D5211yescharacteristic
222C22×C4C2×C22⋊D1311yescharacteristic
223C2×C8—42no—
224C2×C8—42no—
225C2×C8—42no—
226C2×C8—522no—
227C2×C8—522no—
228C2×C8—522no—
229C4⋊C4—132no—
230C4⋊C4—264no—
231C4⋊C4—261no—
232C4⋊C4—521no—
233C4⋊C4—521no—
234C4⋊C4—522no—
235C4⋊C4—522no—
236C42—22no—
237C42—21no—
238C42—21no—
239C42—41no—
240C42—41no—
241C42—41no—
242C42—41no—
243C42—264no—
244C42—522no—
245C42#610512yes—
246C42#610712yes—
247C13#764411yescharacteristic, complemented, Sylow
248C23C2×#610311yescharacteristic
249Q8—522no—
250Q8—522no—
251C2×C4—21no—
252C2×C4—21no—
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—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—262no—
268C2×C4—262no—
269C2×C4—521no—
270C2×C4—521no—
271C2×C4—521no—
272C2×C4—521no—
273C2×C4—521no—
274C2×C4—521no—
275C2×C4—521no—
276C2×C4—521no—
277C2×C4—521no—
278C2×C4—521no—
279C2×C4#8805012yes—
280C2×C4#8805012yes—
281C2×C4#8815812yes—
282C2×C4M16×D1311yescharacteristic
283C2×C4M16×D1311yescharacteristic
284C2×C4C2×#610511yescharacteristic
285C2×C4C2×#610711yescharacteristic
286C8—82no—
287C8—1042no—
288C22C2×#8805011yescharacteristic
289C22#1171866611yescharacteristic
290C22#1171866711yescharacteristic
291C22#1171877411yescharacteristic
292C22#1171878711yescharacteristic
293C22#1171879311yescharacteristic
294C22#1171880011yescharacteristic
295C4—21no—
296C4—21no—
297C4—22no—
298C4—21no—
299C4—21no—
300C4—22no—
301C4—22no—
302C4—41no—
303C4—41no—
304C4—522no—
305C4—522no—
306C4—1041no—
307C4—1041no—
308C2#1311316811yescharacteristic
309C2#1311326411yescharacteristic
310C2#1311327111yescharacteristic
311C2#1311339911yescharacteristic
312C2#1311341411yescharacteristic
313C2#1311346811yescharacteristic
314C2#1311349411yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1831C2
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1831D13
hypocenterC13#7644
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ #1831

Complements

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

NH ≅ G/Ntype
247. C13#7644semidirect

Maximal subgroups

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

subgroupindex
#131173132
#131149792
#131126612
#131126582
C13×#18312
#764413