Finite Group Databasebeta

← #15763111

Subgroups — #15763111

Order 3328.

548 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114816C211yesmaximal, characteristic
2#13113063C211yesmaximal, characteristic
3#13112714C212yesmaximal
4#13112714C212yesmaximal
5C13×#2851C211yesmaximal, characteristic
6C2×C13×#125C411yescharacteristic, complemented
7C22×C42×C13C2211yescharacteristic
8C13×#389C411yescharacteristic, complemented
9C13×#389C411yescharacteristic, complemented
10C13×#387—21no—
11C13×#387—21no—
12C13×#385—21no—
13C13×#385—21no—
14C13×#382C411yescharacteristic, complemented
15C13×#380C2211yescharacteristic
16C13×#380C2211yescharacteristic
17C2×#88071—21no—
18C2×#88071—21no—
19C2×#88071C2212yes—
20C2×C22⋊#1055C2212yes—
21C2×C4⋊#1055—21no—
22#11718116—21no—
23C23×C4×C13D411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13C2311yescharacteristic
26C23×Dic13—22no—
27C13×#125—42no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C42×C13—42no—
39C2×C42×C13C2×C411yescharacteristic
40C2×C42×C13C2×C411yescharacteristic
41C2×C42×C13D411yescharacteristic
42C2×C42×C13D411yescharacteristic
43C22×#1055—22no—
44C13×#95—21no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50#88071—22no—
51#88071—42no—
52#88071—42no—
53#88071Q814yes—
54C22⋊#1055—24no—
55C4⋊#1055—42no—
56#9913—131nomaximal, Sylow
57C24×C13C2×D411yescharacteristic
58C22×C4×C13—22no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—22no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—41no—
67C22×C4×C13—41no—
68C22×C4×C13—41no—
69C22×C4×C13—41no—
70C22×C4×C13—41no—
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22×C411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×Q812yes—
78C22×C4×C13#4112yes—
79C22×Dic13—24no—
80C22×Dic13—42no—
81C22×Dic13—42no—
82C22×Dic13—42no—
83C22×Dic13—42no—
84C22×Dic13—42no—
85C22×Dic13—42no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—42no—
91C13×C4⋊C4—42no—
92C13×C4⋊C4—42no—
93C13×C4⋊C4—42no—
94C13×C22⋊C4—42no—
95C13×C22⋊C4—41no—
96C13×C22⋊C4—41no—
97C42×C13—22no—
98C42×C13—22no—
99C42×C13—41no—
100C42×C13—41no—
101C2×#1055—42no—
102C2×#1055—42no—
103C2×#1055—42no—
104#2851D1311yescharacteristic
105#1797—131no—
106#1434—131no—
107#1294—132no—
108#1294—132no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13C2×C22⋊C411yescharacteristic
114C23×C13C22⋊Q812yes—
115C23×C13#13512yes—
116C23×C13AGL(1,ℤ/8)11yescharacteristic
117C23×C13#13711yescharacteristic
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—42no—
134C2×C4×C13—42no—
135C2×C4×C13—44no—
136C2×C4×C13—42no—
137C2×C4×C13—42no—
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—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13#9912yes—
151C2×C4×C13C4×Q812yes—
152C2×C4×C13#12411yescharacteristic
153C2×C4×C13C4⋊Q811yescharacteristic
154C2×Dic13—44no—
155C2×Dic13—44no—
156C2×Dic13—44no—
157C2×Dic13—82no—
158C2×Dic13—82no—
159C2×Dic13—82no—
160C2×Dic13—82no—
161#1055—82no—
162C2×#125Dic1311yescharacteristic, complemented
163C22×C42C2×D1311yescharacteristic
164C2×C4⋊C8—261no—
165C2×C22⋊C8—132no—
166#389Dic1311yescharacteristic, complemented
167#389Dic1311yescharacteristic, complemented
168#387—21no—
169#387—21no—
170#385—21no—
171#385—21no—
172#382Dic1311yescharacteristic, complemented
173#380C2×D1311yescharacteristic
174#380C2×D1311yescharacteristic
175C2×#95—132no—
176C2×#95—261no—
177C2×#95—261no—
178#336—261no—
179C22×C13—22no—
180C22×C13—22no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—22no—
186C22×C13—22no—
187C22×C13#39111yescharacteristic
188C22×C13C2×#9911yescharacteristic
189C22×C13#41011yescharacteristic
190C22×C13#41611yescharacteristic
191C22×C13#41711yescharacteristic
192C22×C13#42111yescharacteristic
193C22×C13#42111yescharacteristic
194C22×C13#47812yes—
195C22×C13#47912yes—
196C4×C13—21no—
197C4×C13—22no—
198C4×C13—21no—
199C4×C13—22no—
200C4×C13—41no—
201C4×C13—41no—
202C4×C13—41no—
203C4×C13—81no—
204C4×C13—81no—
205C4×C13—81no—
206C4×C13—81no—
207Dic13—84no—
208C23×C4—262no—
209C23×C4C22⋊D1311yescharacteristic
210C23×C4C22⋊D1311yescharacteristic
211C23×C4C22×D1311yescharacteristic
212C22×C8—262no—
213#125—42no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4C2×Dic1311yescharacteristic
219C2×C4⋊C4C2×Dic1311yescharacteristic
220C2×C4⋊C4C2×Dic1311yescharacteristic
221C2×C4⋊C4C2×Dic1311yescharacteristic
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C42—42no—
225C2×C42C2×Dic1311yescharacteristic
226C2×C42C2×Dic1311yescharacteristic
227C2×C42C22⋊D1311yescharacteristic
228C2×C42C22⋊D1311yescharacteristic
229C4⋊C8—522no—
230C22⋊C8—264no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—21no—
237#95—134no—
238#95—262no—
239#95—522no—
240#95—522no—
241C2×C13—22no—
242C2×C13—22no—
243C2×C13#151211yescharacteristic
244C2×C13#151311yescharacteristic
245C2×C13#151611yescharacteristic
246C2×C13#152111yescharacteristic
247C2×C13#198911yescharacteristic
248C2×C13#199511yescharacteristic
249C2×C13#199611yescharacteristic
250C24C2×C22⋊D1311yescharacteristic
251C22×C4—21no—
252C22×C4—22no—
253C22×C4—21no—
254C22×C4—22no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—264no—
265C22×C4—522no—
266C22×C4—522no—
267C22×C4—522no—
268C22×C4—522no—
269C22×C4—522no—
270C22×C4—522no—
271C22×C4C22⋊Dic1311yescharacteristic
272C22×C4C22⋊Dic1311yescharacteristic
273C22×C4C22⋊Dic1311yescharacteristic
274C22×C4C22⋊Dic1311yescharacteristic
275C22×C4Q8×D1312yes—
276C22×C4#613112yes—
277C22×C4C22×Dic1311yescharacteristic
278C22×C4C2×C22⋊D1311yescharacteristic
279C2×C8—522no—
280C2×C8—522no—
281C2×C8—522no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—42no—
287C4⋊C4—42no—
288C4⋊C4—42no—
289C4⋊C4—42no—
290C22⋊C4—41no—
291C22⋊C4—42no—
292C22⋊C4—41no—
293C42—22no—
294C42—22no—
295C42—41no—
296C42—41no—
297C13#991311yescharacteristic, complemented, Sylow
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23#8820012yes—
303C23#8820311yescharacteristic
304C23#8820412yes—
305C23#8820511yescharacteristic
306C23C2×C22⋊Dic1311yescharacteristic
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—44no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—524no—
340C2×C4—524no—
341C2×C4—524no—
342C2×C4—1042no—
343C2×C4—1042no—
344C2×C4—1042no—
345C2×C4—1042no—
346C2×C4#8807412yes—
347C2×C4#8819811yescharacteristic
348C2×C4Q8×Dic1312yes—
349C2×C4#8820111yescharacteristic
350C8—1042no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—22no—
356C22—22no—
357C22—22no—
358C22—22no—
359C22#1171872412yes—
360C22#1171872712yes—
361C22C2×#8807411yescharacteristic
362C22#1171889111yescharacteristic
363C22#1171889311yescharacteristic
364C22#1171889411yescharacteristic
365C22#1171889711yescharacteristic
366C22#1171889711yescharacteristic
367C22#1171890111yescharacteristic
368C4—22no—
369C4—21no—
370C4—21no—
371C4—22no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—81no—
376C4—81no—
377C4—81no—
378C4—81no—
379C4—1044no—
380C2—22no—
381C2—22no—
382C2#1311337411yescharacteristic
383C2#1311337911yescharacteristic
384C2#1311339211yescharacteristic
385C2#1311341311yescharacteristic
386C2#1311579411yescharacteristic
387C2#1311581811yescharacteristic
388C2#1311582211yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2851C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#2851D13
hypocenterC13#9913
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2851

Complements

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

NH ≅ G/Ntype
6. C2×C13×#125C4semidirect
8. C13×#389C4semidirect
9. C13×#389C4semidirect
14. C13×#382C4semidirect
162. C2×#125Dic13semidirect
166. #389Dic13semidirect
167. #389Dic13semidirect
172. #382Dic13semidirect
297. C13#9913semidirect

Maximal subgroups

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

subgroupindex
#131148162
#131130632
#131127142
C13×#28512
#991313