Finite Group Databasebeta

← #15756465

Subgroups — #15756465

Order 3328.

530 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114824C211yesmaximal, characteristic
2#13113154C211yesmaximal, characteristic
3#13112715C212yesmaximal, complemented
4#13112703C212yesmaximal, complemented
5C13×#2349C211yesmaximal, characteristic
6C2×C4×D4×C13—21no—
7C2×C4×D4×C13C2211yescharacteristic
8C13×#389—21no—
9C13×#385—21no—
10C13×#385—21no—
11C13×#382C411yescharacteristic, complemented
12C13×#380C411yescharacteristic, complemented
13C13×#380C2211yescharacteristic
14C4×C13×C4⋊C4C411yescharacteristic, complemented
15C2×C13×#95C411yescharacteristic, complemented
16C2×C13×#95C2211yescharacteristic
17C2×#88074—21no—
18#11718873C2212yes—
19C2×C22⋊#1055C2212yes—
20#11718120—21no—
21#11718118—21no—
22#11718117—21no—
23C22×D4×C13D411yescharacteristic
24C23×C4×C13—21no—
25C23×C4×C13—21no—
26C23×C4×C13C2×C411yescharacteristic
27C23×C4×C13C2311yescharacteristic
28C4×D4×C13—22no—
29C4×D4×C13—22no—
30C4×D4×C13—42no—
31C4×D4×C13—42no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4D411yescharacteristic
40C2×C13×C22⋊C4D411yescharacteristic
41C2×C42×C13—21no—
42C2×C42×C13C2×C411yescharacteristic
43C2×C22⋊Dic13—22no—
44C2×C4⋊Dic13—22no—
45C22×#1055—22no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95C2×C411yescharacteristic
50C13×#95C2×C411yescharacteristic
51C13×#95C2×C411yescharacteristic
52C13×#95C2×C411yescharacteristic
53#88074—42no—
54#88071—22no—
55C22⋊#1055—22no—
56C22⋊#1055—22no—
57#8760—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—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—42no—
71C22×C4×C13—42no—
72C22×C4×C13—42no—
73C22×C4×C13—41no—
74C22×C4×C13—41no—
75C22×C4×C13—81no—
76C22×C4×C13—81no—
77C22×C4×C13—81no—
78C22×C4×C13—81no—
79C22×C4×C13C22⋊C411yescharacteristic
80C22×C4×C13C22⋊C411yescharacteristic
81C22×C4×C13C22⋊C411yescharacteristic
82C22×C4×C13C22×C411yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C22×C4×C13#4112yes—
85C22×C4×C13#4112yes—
86C22×Dic13—42no—
87C13×C4⋊C4—22no—
88C13×C4⋊C4—42no—
89C13×C4⋊C4—42no—
90C13×C4⋊C4—81no—
91C13×C4⋊C4—81no—
92C13×C22⋊C4—22no—
93C13×C22⋊C4—22no—
94C13×C22⋊C4—42no—
95C13×C22⋊C4—41no—
96C13×C22⋊C4—41no—
97C42×C13—21no—
98C42×C13—21no—
99C42×C13—42no—
100C22⋊Dic13—42no—
101C22⋊Dic13—42no—
102C4⋊Dic13—82no—
103C2×#1055—42no—
104C2×#1055—82no—
105#2349D1311yescharacteristic
106#1799—131no—
107#1459—131no—
108#1294—132no—
109#1289—132no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13—41no—
116C23×C13#10212yes—
117C23×C13C2×C22⋊C411yescharacteristic
118C23×C13#12312yes—
119C23×C13C2×D811yescharacteristic
120C23×C13C2×SD1611yescharacteristic
121C23×C13#13712yes—
122D4×C13—24no—
123D4×C13—24no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—22no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—81no—
147C2×C4×C13—81no—
148C2×C4×C13—82no—
149C2×C4×C13—82no—
150C2×C4×C13—84no—
151C2×C4×C13#10212yes—
152C2×C4×C13#11711yescharacteristic
153C2×C4×C13#11711yescharacteristic
154C2×C4×C13#12312yes—
155C2×Dic13—82no—
156C2×Dic13—82no—
157C2×Dic13—82no—
158#1055—82no—
159C2×C4×D4—21no—
160C2×C4×D4C2×D1311yescharacteristic
161C2×#99—261no—
162C2×C22⋊C8—132no—
163#389—21no—
164#385—21no—
165#385—21no—
166#382Dic1311yescharacteristic, complemented
167#380—132no—
168#380Dic1311yescharacteristic, complemented
169#380C2×D1311yescharacteristic
170C4×C4⋊C4Dic1311yescharacteristic, complemented
171C2×#95Dic1311yescharacteristic, complemented
172C2×#95C2×D1311yescharacteristic
173#342—261no—
174#324—261no—
175#323—261no—
176C22×C13—22no—
177C22×C13—21no—
178C22×C13—22no—
179C22×C13—21no—
180C22×C13—22no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13—42no—
184C22×C13—42no—
185C22×C13—42no—
186C22×C13—41no—
187C22×C13—41no—
188C22×C13#38111yescharacteristic
189C22×C13C2×#10211yescharacteristic
190C22×C13#41911yescharacteristic
191C22×C13#48012yes—
192C22×C13#48312yes—
193C4×C13—22no—
194C4×C13—22no—
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—42no—
198C4×C13—41no—
199C4×C13—41no—
200C4×C13—81no—
201C4×C13—81no—
202C4×C13—81no—
203Dic13—162no—
204C22×D4C22⋊D1311yescharacteristic
205C23×C4—21no—
206C23×C4—21no—
207C23×C4C2×Dic1311yescharacteristic
208C23×C4C22×D1311yescharacteristic
209C22×C8—262no—
210C4×D4—22no—
211C4×D4—22no—
212C4×D4—42no—
213C4×D4—42no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—262no—
219C2×C4⋊C4C22⋊D1311yescharacteristic
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—262no—
223C2×C22⋊C4C22⋊D1311yescharacteristic
224C2×C22⋊C4C22⋊D1311yescharacteristic
225C2×C42—21no—
226C2×C42C2×Dic1311yescharacteristic
227#99—522no—
228C22⋊C8—262no—
229C22⋊C8—262no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—262no—
234#95C2×Dic1311yescharacteristic
235#95C2×Dic1311yescharacteristic
236#95C2×Dic1311yescharacteristic
237#95C2×Dic1311yescharacteristic
238C2×C13—22no—
239C2×C13—21no—
240C2×C13—21no—
241C2×C13—22no—
242C2×C13—42no—
243C2×C13#182311yescharacteristic
244C2×C13#182711yescharacteristic
245C2×C13#182811yescharacteristic
246C24C22⋊Dic1311yescharacteristic
247C24C2×C22⋊D1311yescharacteristic
248C2×D4—22no—
249C2×D4—22no—
250C2×D4#610412yes—
251C2×D4#610512yes—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—81no—
264C22×C4—81no—
265C22×C4—81no—
266C22×C4—81no—
267C22×C4—522no—
268C22×C4C22⋊Dic1311yescharacteristic
269C22×C4C22⋊Dic1311yescharacteristic
270C22×C4C22⋊Dic1311yescharacteristic
271C22×C4#612712yes—
272C22×C4#612712yes—
273C22×C4C22×Dic1311yescharacteristic
274C22×C4C2×C22⋊D1311yescharacteristic
275C2×C8—522no—
276C2×C8—1042no—
277C4⋊C4—22no—
278C4⋊C4—42no—
279C4⋊C4—42no—
280C4⋊C4—81no—
281C4⋊C4—81no—
282C4⋊C4—1042no—
283C22⋊C4—22no—
284C22⋊C4—22no—
285C22⋊C4—42no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—522no—
289C22⋊C4—522no—
290C42—21no—
291C42—21no—
292C42—42no—
293C13#876011yescharacteristic, complemented, Sylow
294C23—21no—
295C23—21no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23#8807212yes—
301C23#8818312yes—
302C23C2×#610411yescharacteristic
303C23C2×#610511yescharacteristic
304C23#8819612yes—
305C23C2×C22⋊Dic1311yescharacteristic
306D4—24no—
307D4—24no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—82no—
333C2×C4—82no—
334C2×C4—84no—
335C2×C4—1042no—
336C2×C4—1042no—
337C2×C4—1042no—
338C2×C4#8807212yes—
339C2×C4#8818011yescharacteristic
340C2×C4#8818011yescharacteristic
341C2×C4#8818312yes—
342C8—1042no—
343C22—21no—
344C22—22no—
345C22—21no—
346C22—22no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—42no—
351C22—42no—
352C22—42no—
353C22—41no—
354C22—41no—
355C22#1171862812yes—
356C22#1171863212yes—
357C22#1171887211yescharacteristic
358C22C2×#8807211yescharacteristic
359C22#1171888611yescharacteristic
360C4—22no—
361C4—22no—
362C4—21no—
363C4—21no—
364C4—42no—
365C4—41no—
366C4—41no—
367C4—81no—
368C4—81no—
369C4—81no—
370C4—2082no—
371C2—21no—
372C2—22no—
373C2—21no—
374C2—22no—
375C2—42no—
376C2#1311492211yescharacteristic
377C2#1311494011yescharacteristic
378C2#1311494411yescharacteristic
subgroupG/H
centerC22#11718872
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2349C2
socleC22×C13#381
prime radicalC22×D4×C13D4
cosocleC23×C4×C13C23
hypercenter#2349D13
hypocenterC13#8760
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2349

Complements

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

NH ≅ G/Ntype
3. #13112715C2semidirect
4. #13112703C2semidirect
11. C13×#382C4semidirect
12. C13×#380C4semidirect
14. C4×C13×C4⋊C4C4semidirect
15. C2×C13×#95C4semidirect
166. #382Dic13semidirect
168. #380Dic13semidirect
170. C4×C4⋊C4Dic13semidirect
171. C2×#95Dic13semidirect
293. C13#8760semidirect

Maximal subgroups

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

subgroupindex
#131148242
#131131542
#131127152
#131127032
C13×#23492
#876013