Finite Group Databasebeta

← #15760694

Subgroups — #15760694

Order 3328.

598 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123860C211yesmaximal, characteristic
2#13114922C212yesmaximal, complemented
3#13114824C211yesmaximal, characteristic
4#13112703C212yesmaximal, complemented
5C13×#2486C211yesmaximal, characteristic
6C2×C13×#123—21no—
7C2×C4×D4×C13C2211yescharacteristic
8C22×C13×C4⋊C4C2211yescharacteristic
9C13×#398C412yescomplemented
10C13×#397C412yescomplemented
11C13×#389—21no—
12C13×#381—21no—
13C13×#380—21no—
14C13×#380C2211yescharacteristic
15C2×#88074—21no—
16#11718873C2212yes—
17C2×C22⋊#1055—21no—
18C2×C22⋊#1055C2212yes—
19D4×#1055—24no—
20#11718586—21no—
21#11718121—24no—
22#11718118—21no—
23C22×D4×C13D411yescharacteristic
24C23×C4×C13—21no—
25C23×C4×C13D411yescharacteristic
26C23×C4×C13C2311yescharacteristic
27C13×#123—42no—
28C13×#123—42no—
29C4×D4×C13—22no—
30C4×D4×C13—22no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4—22no—
33C2×C13×C4⋊C4—22no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4C2×C412yes—
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4C2×C411yescharacteristic
41C2×C13×C22⋊C4D411yescharacteristic
42C2×C42×C13D411yescharacteristic
43C2×C22⋊Dic13—22no—
44C2×C4⋊Dic13—22no—
45C22×#1055—22no—
46C22×#1055D414yes—
47C13×#95—22no—
48C13×#95—22no—
49C13×#95C2×C412yes—
50#88074—42no—
51#88071—22no—
52C22⋊#1055—22no—
53C22⋊#1055—22no—
54C22⋊#1055—22no—
55C4⋊#1055—22no—
56C4×#1055—22no—
57#9470—131nomaximal, Sylow
58C24×C13C22⋊C411yescharacteristic
59C24×C13C2×D411yescharacteristic
60C2×D4×C13—22no—
61C2×D4×C13—22no—
62C2×D4×C13D812yes—
63C2×D4×C13SD1612yes—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—22no—
67C22×C4×C13—22no—
68C22×C4×C13—42no—
69C22×C4×C13—42no—
70C22×C4×C13—42no—
71C22×C4×C13—41no—
72C22×C4×C13—41no—
73C22×C4×C13—42no—
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22×C411yescharacteristic
78C22×C4×C13C2×D412yes—
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13#4112yes—
81C22×Dic13—42no—
82C13×C4⋊C4—22no—
83C13×C4⋊C4—24no—
84C13×C4⋊C4—42no—
85C13×C4⋊C4—44no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—41no—
88C13×C22⋊C4—22no—
89C13×C22⋊C4—22no—
90C13×C22⋊C4—44no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—41no—
93C42×C13—21no—
94C42×C13—21no—
95C22⋊Dic13—42no—
96C22⋊Dic13—42no—
97C4⋊Dic13—44no—
98C2×#1055—24no—
99C2×#1055—44no—
100C2×#1055—82no—
101#2972—131no—
102#2486D1311yescharacteristic
103#1823—132no—
104#1799—131no—
105#1289—132no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13#10212yes—
113C23×C13C2×C22⋊C411yescharacteristic
114C23×C13#12112yes—
115C23×C13C2×D811yescharacteristic
116C23×C13C2×SD1611yescharacteristic
117C23×C13#13512yes—
118D4×C13—24no—
119D4×C13—24no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—24no—
123C2×C4×C13—22no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—41no—
127C2×C4×C13—42no—
128C2×C4×C13—42no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13—42no—
134C2×C4×C13—42no—
135C2×C4×C13—42no—
136C2×C4×C13—42no—
137C2×C4×C13—81no—
138C2×C4×C13—82no—
139C2×C4×C13—82no—
140C2×C4×C13#10212yes—
141C2×C4×C13C4×D412yes—
142C2×C4×C13#12011yescharacteristic
143C2×C4×C13#12311yescharacteristic
144C2×Dic13—82no—
145C2×Dic13—82no—
146C2×Dic13—82no—
147#1055—44no—
148C2×#123—21no—
149C2×C4×D4C2×D1311yescharacteristic
150C22×C4⋊C4C2×D1311yescharacteristic
151C8×D4—264no—
152#431—261no—
153C2×#99—261no—
154C2×C22⋊C8—132no—
155C2×C22⋊C8—261no—
156#398Dic1312yescomplemented
157#397Dic1312yescomplemented
158#389—21no—
159#381—21no—
160#380—21no—
161#380—132no—
162#380C2×D1311yescharacteristic
163#342—261no—
164#340—264no—
165C22×C13—22no—
166C22×C13—21no—
167C22×C13—22no—
168C22×C13—21no—
169C22×C13—22no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13—42no—
173C22×C13—42no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—81no—
177C22×C13#38611yescharacteristic
178C22×C13C2×#10211yescharacteristic
179C22×C13#41611yescharacteristic
180C22×C13#46512yes—
181C22×C13#46612yes—
182C4×C13—21no—
183C4×C13—22no—
184C4×C13—22no—
185C4×C13—41no—
186C4×C13—41no—
187C4×C13—82no—
188C4×C13—82no—
189C4×C13#45812yes—
190Dic13—162no—
191C22×D4C22⋊D1311yescharacteristic
192C23×C4—21no—
193C23×C4C22⋊D1311yescharacteristic
194C23×C4C22×D1311yescharacteristic
195C22×C8—134no—
196C22×C8—262no—
197#123—42no—
198#123—42no—
199C4×D4—22no—
200C4×D4—22no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—262no—
207C2×C4⋊C4C2×Dic1312yes—
208C2×C4⋊C4C2×Dic1311yescharacteristic
209C2×C22⋊C4—22no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—262no—
212C2×C22⋊C4C2×Dic1311yescharacteristic
213C2×C22⋊C4C22⋊D1311yescharacteristic
214C2×C42C22⋊D1311yescharacteristic
215C4⋊C8—262no—
216#99—522no—
217C22⋊C8—262no—
218C22⋊C8—262no—
219C22⋊C8—262no—
220C4×C8—262no—
221#95—22no—
222#95—22no—
223#95—262no—
224#95C2×Dic1312yes—
225C2×C13—22no—
226C2×C13—21no—
227C2×C13—21no—
228C2×C13—22no—
229C2×C13—42no—
230C2×C13#189011yescharacteristic
231C2×C13#189311yescharacteristic
232C2×C13#190911yescharacteristic
233C24C22⋊Dic1311yescharacteristic
234C24C2×C22⋊D1311yescharacteristic
235C2×D4—22no—
236C2×D4—22no—
237C2×D4#610412yes—
238C2×D4#610512yes—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—522no—
250C22×C4C22⋊Dic1311yescharacteristic
251C22×C4C22⋊Dic1311yescharacteristic
252C22×C4C22⋊Dic1311yescharacteristic
253C22×C4D4×D1312yes—
254C22×C4#612912yes—
255C22×C4C22×Dic1311yescharacteristic
256C22×C4C2×C22⋊D1311yescharacteristic
257C2×C8—264no—
258C2×C8—524no—
259C2×C8—1042no—
260C4⋊C4—22no—
261C4⋊C4—24no—
262C4⋊C4—42no—
263C4⋊C4—44no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—524no—
267C22⋊C4—22no—
268C22⋊C4—22no—
269C22⋊C4—44no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—522no—
273C22⋊C4—522no—
274C42—21no—
275C42—21no—
276C13#947011yescharacteristic, complemented, Sylow
277C23—21no—
278C23—21no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23#8807212yes—
284C23C2×#610411yescharacteristic
285C23C2×#610511yescharacteristic
286C23#8819312yes—
287C23#8820412yes—
288C23C2×C22⋊Dic1311yescharacteristic
289D4—24no—
290D4—24no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—24no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—81no—
309C2×C4—82no—
310C2×C4—82no—
311C2×C4—1042no—
312C2×C4—1042no—
313C2×C4—1042no—
314C2×C4#8807212yes—
315C2×C4D4×Dic1312yes—
316C2×C4#8818911yescharacteristic
317C2×C4#8819111yescharacteristic
318C8—524no—
319C22—21no—
320C22—22no—
321C22—21no—
322C22—22no—
323C22—22no—
324C22—41no—
325C22—41no—
326C22—42no—
327C22—42no—
328C22—41no—
329C22—41no—
330C22—81no—
331C22#1171869912yes—
332C22#1171870212yes—
333C22C2×#8807211yescharacteristic
334C22#1171888111yescharacteristic
335C22#1171889411yescharacteristic
336C4—21no—
337C4—22no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—82no—
342C4—82no—
343C4—2082no—
344C4#1171871412yes—
345C2—21no—
346C2—22no—
347C2—21no—
348C2—22no—
349C2—42no—
350C2#1311525011yescharacteristic
351C2#1311526511yescharacteristic
352C2#1311535911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2486C2
socleC22×C13#386
prime radicalC22×D4×C13D4
cosocleC23×C4×C13C23
hypercenter#2486D13
hypocenterC13#9470
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2486

Complements

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

NH ≅ G/Ntype
2. #13114922C2semidirect
4. #13112703C2semidirect
9. C13×#398C4semidirect
10. C13×#397C4semidirect
156. #398Dic13semidirect
157. #397Dic13semidirect
276. C13#9470semidirect

Maximal subgroups

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

subgroupindex
#131238602
#131149222
#131148242
#131127032
C13×#24862
#947013