Finite Group Databasebeta

← #15751212

Subgroups — #15751212

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#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×C13—22no—
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#7644—131nomaximal, Sylow
52C2×Q8×C13—21no—
53C2×Q8×C13—41no—
54C2×Q8×C13—41no—
55C2×Q8×C13M1612yes—
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—42no—
73C13×C4⋊C4M1612yes—
74C42×C13—24no—
75C42×C13—21no—
76C42×C13—21no—
77C42×C13—22no—
78C42×C13—41no—
79C42×C13—41no—
80C42×C13—41no—
81C42×C13—41no—
82C42×C13—42no—
83C42×C13SD1612yes—
84C42×C13Q1612yes—
85C2×#1055—42no—
86C2×#1055—42no—
87C2×#1055—42no—
88C2×#1055—42no—
89C2×#1055—42no—
90C2×#1055—42no—
91#2295D1311yescharacteristic
92#1839—131no—
93#1831—131no—
94#1272—132no—
95#1271—132no—
96C23×C13C2×C22⋊C411yescharacteristic
97Q8×C13—42no—
98Q8×C13—42no—
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—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—41no—
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#10312yes—
128C2×C4×C13#10312yes—
129C2×C4×C13C2×M1611yescharacteristic
130C2×C4×C13C2×M1611yescharacteristic
131C2×C4×C13C2×SD1611yescharacteristic
132C2×C4×C13C2×Q1611yescharacteristic
133C2×C4×C13#13512yes—
134#1055—82no—
135#1055—82no—
136C2×C4×Q8Dic1311yescharacteristic
137C2×C4⋊C8—261no—
138#391Dic1311yescharacteristic
139#391C2×D1311yescharacteristic
140#389Dic1311yescharacteristic
141#389C2×D1311yescharacteristic
142#387—21no—
143#387—21no—
144C4×C4⋊C4—21no—
145C4×C4⋊C4Dic1311yescharacteristic
146#376—21no—
147C43C2×D1311yescharacteristic
148#336—132no—
149#336—132no—
150#336—261no—
151#336—261no—
152#336—261no—
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—42no—
168C4×C13—41no—
169C4×C13—42no—
170C4×C13—41no—
171C4×C13—81no—
172C4×C13—81no—
173C22×Q8C2×Dic1311yescharacteristic
174C22×C8—262no—
175C22×C8—262no—
176C4×Q8—22no—
177C4×Q8—22no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4C2×Dic1311yescharacteristic
182C2×C4⋊C4C2×Dic1311yescharacteristic
183C2×C4⋊C4C2×Dic1311yescharacteristic
184C2×C42—21no—
185C2×C42—21no—
186C2×C42C2×Dic1311yescharacteristic
187C2×C42C2×Dic1311yescharacteristic
188C2×C42C22⋊D1311yescharacteristic
189C2×C42C22⋊D1311yescharacteristic
190C2×C42C22⋊D1311yescharacteristic
191C2×C42C22⋊D1311yescharacteristic
192C2×C42C22×D1311yescharacteristic
193C4⋊C8—522no—
194#95—21no—
195#95—21no—
196#95—21no—
197#95—21no—
198#95—21no—
199#95—21no—
200#95—21no—
201C2×C13#146411yescharacteristic
202C2×C13#148711yescharacteristic
203C2×C13#148811yescharacteristic
204C2×C13#151811yescharacteristic
205C2×C13#152111yescharacteristic
206C2×C13#153511yescharacteristic
207C2×C13#154211yescharacteristic
208C2×Q8—21no—
209C2×Q8—41no—
210C2×Q8—41no—
211C2×Q8#609912yes—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4C22⋊Dic1311yescharacteristic
217C22×C4C22⋊Dic1311yescharacteristic
218C22×C4C22⋊Dic1311yescharacteristic
219C22×C4C22⋊Dic1311yescharacteristic
220C22×C4C22×Dic1311yescharacteristic
221C22×C4C2×C22⋊D1311yescharacteristic
222C22×C4C2×C22⋊D1311yescharacteristic
223C2×C8—522no—
224C2×C8—522no—
225C2×C8—522no—
226C2×C8—522no—
227C2×C8—522no—
228C2×C8—522no—
229C4⋊C4—24no—
230C4⋊C4—21no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—42no—
234C4⋊C4—42no—
235C4⋊C4#609912yes—
236C42—24no—
237C42—21no—
238C42—21no—
239C42—22no—
240C42—41no—
241C42—41no—
242C42—41no—
243C42—41no—
244C42—42no—
245C42#610612yes—
246C42#610712yes—
247C13#764411yescharacteristic, complemented, Sylow
248C23C2×C22⋊Dic1311yescharacteristic
249Q8—42no—
250Q8—42no—
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—22no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—41no—
270C2×C4—41no—
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#8807512yes—
280C2×C4#8807512yes—
281C2×C4C2×#609911yescharacteristic
282C2×C4C2×#609911yescharacteristic
283C2×C4C2×#610611yescharacteristic
284C2×C4C2×#610711yescharacteristic
285C2×C4#8820412yes—
286C8—1042no—
287C8—1042no—
288C22#1171886811yescharacteristic
289C22C2×#8807511yescharacteristic
290C22#1171889411yescharacteristic
291C22#1171889711yescharacteristic
292C22#1171889711yescharacteristic
293C22#1171889811yescharacteristic
294C22#1171890111yescharacteristic
295C4—21no—
296C4—21no—
297C4—22no—
298C4—21no—
299C4—21no—
300C4—22no—
301C4—22no—
302C4—42no—
303C4—41no—
304C4—41no—
305C4—42no—
306C4—81no—
307C4—81no—
308C2#1311317011yescharacteristic
309C2#1311326511yescharacteristic
310C2#1311327011yescharacteristic
311C2#1311340011yescharacteristic
312C2#1311341311yescharacteristic
313C2#1311346711yescharacteristic
314C2#1311349311yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2295C2
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2295D13
hypocenterC13#7644
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ #2295

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
#131149792
#131149532
#131126622
#131126592
C13×#22952
#764413