Finite Group Databasebeta

← #15762999

Subgroups — #15762999

Order 3328.

598 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114598C211yesmaximal, characteristic
2#13113066C211yesmaximal, characteristic
3#13112714C212yesmaximal
4#13112714C212yesmaximal
5C13×#2851C211yesmaximal, characteristic
6C2×C13×#125C411yescharacteristic, complemented
7C22×C42×C13C2211yescharacteristic
8C22×C4⋊Dic13—21no—
9C13×#389C411yescharacteristic, complemented
10C13×#389C411yescharacteristic, complemented
11C13×#387—21no—
12C13×#387—21no—
13C13×#385—21no—
14C13×#385—21no—
15C13×#382C411yescharacteristic, complemented
16C13×#380C2211yescharacteristic
17C13×#380C2211yescharacteristic
18C2×#88071—21no—
19C2×#88071C2212yes—
20C2×C22⋊#1055C2212yes—
21C2×#88043—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
43C2×C4⋊Dic13—24no—
44C2×C4⋊Dic13—42no—
45C2×C4⋊Dic13—42no—
46C22×#1055—22no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53#88071—24no—
54#88071—42no—
55C22⋊#1055—22no—
56C22⋊#1055Q814yes—
57#88043—42no—
58#9887—131nomaximal, Sylow
59C24×C13C2×D411yescharacteristic
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—22no—
63C22×C4×C13—22no—
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—41no—
71C22×C4×C13—41no—
72C22×C4×C13—41no—
73C22×C4×C13—41no—
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C22×C411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13C2×Q812yes—
81C22×C4×C13#4112yes—
82C22×Dic13—24no—
83C22×Dic13—42no—
84C22×Dic13—42no—
85C22×Dic13—42no—
86C22×Dic13—42no—
87C22×Dic13—42no—
88C22×Dic13—42no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—42no—
94C13×C4⋊C4—42no—
95C13×C4⋊C4—42no—
96C13×C4⋊C4—42no—
97C13×C22⋊C4—41no—
98C13×C22⋊C4—41no—
99C13×C22⋊C4—41no—
100C13×C22⋊C4—41no—
101C42×C13—22no—
102C42×C13—22no—
103C42×C13—41no—
104C42×C13—41no—
105C4⋊Dic13—48no—
106C2×#1055—24no—
107C2×#1055—42no—
108C2×#1055—42no—
109#2851D1311yescharacteristic
110#1749—131no—
111C4⋊#95—131no—
112#1294—132no—
113#1294—132no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—21no—
118C23×C13C2×C22⋊C411yescharacteristic
119C23×C13#12411yescharacteristic
120C23×C13C4⋊Q811yescharacteristic
121C23×C13AGL(1,ℤ/8)11yescharacteristic
122C23×C13AGL(1,ℤ/8)11yescharacteristic
123C23×C13#13711yescharacteristic
124C23×C13#13711yescharacteristic
125C2×C4×C13—24no—
126C2×C4×C13—24no—
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—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—42no—
142C2×C4×C13—42no—
143C2×C4×C13—42no—
144C2×C4×C13—42no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13#9912yes—
158C2×C4×C13#10412yes—
159C2×C4×C13C4×Q812yes—
160C2×C4×C13C22⋊Q812yes—
161C2×Dic13—44no—
162C2×Dic13—44no—
163C2×Dic13—44no—
164C2×Dic13—82no—
165C2×Dic13—82no—
166C2×Dic13—82no—
167C2×Dic13—82no—
168#1055—44no—
169C2×#125Dic1311yescharacteristic, complemented
170C22×C4⋊C4—261no—
171C22×C42C2×D1311yescharacteristic
172C2×C22⋊C8—132no—
173C2×#97—261no—
174#389Dic1311yescharacteristic, complemented
175#389Dic1311yescharacteristic, complemented
176#387—21no—
177#387—21no—
178#385—21no—
179#385—21no—
180#382Dic1311yescharacteristic, complemented
181#380C2×D1311yescharacteristic
182#380C2×D1311yescharacteristic
183C2×#95—132no—
184C2×#95—261no—
185#336—261no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—21no—
198C22×C13#39111yescharacteristic
199C22×C13C2×#9911yescharacteristic
200C22×C13#41011yescharacteristic
201C22×C13#41711yescharacteristic
202C22×C13#41711yescharacteristic
203C22×C13C2×#10411yescharacteristic
204C22×C13#42111yescharacteristic
205C22×C13#49011yescharacteristic
206C22×C13#49111yescharacteristic
207C22×C13#50111yescharacteristic
208C22×C13#50111yescharacteristic
209C4×C13—22no—
210C4×C13—22no—
211C4×C13—22no—
212C4×C13—22no—
213C4×C13—41no—
214C4×C13—41no—
215C4×C13—81no—
216C4×C13—81no—
217C4×C13—81no—
218C4×C13—81no—
219Dic13—84no—
220C23×C4—262no—
221C23×C4C22⋊D1311yescharacteristic
222C23×C4C22⋊D1311yescharacteristic
223C23×C4C22×D1311yescharacteristic
224C22×C8—262no—
225#125—42no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—264no—
231C2×C4⋊C4—522no—
232C2×C4⋊C4—522no—
233C2×C4⋊C4C2×Dic1311yescharacteristic
234C2×C4⋊C4C2×Dic1311yescharacteristic
235C2×C4⋊C4C2×Dic1311yescharacteristic
236C2×C4⋊C4C2×Dic1311yescharacteristic
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C42—42no—
240C2×C42C2×Dic1311yescharacteristic
241C2×C42C2×Dic1311yescharacteristic
242C2×C42C22⋊D1311yescharacteristic
243C2×C42C22⋊D1311yescharacteristic
244C22⋊C8—134no—
245C22⋊C8—262no—
246#97—522no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—264no—
254#95—522no—
255C2×C13—21no—
256C2×C13—21no—
257C2×C13—21no—
258C2×C13—21no—
259C2×C13#150411yescharacteristic
260C2×C13#150911yescharacteristic
261C2×C13#151211yescharacteristic
262C2×C13#151311yescharacteristic
263C2×C13#198611yescharacteristic
264C2×C13#199211yescharacteristic
265C2×C13#199611yescharacteristic
266C24C2×C22⋊D1311yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—264no—
282C22×C4—522no—
283C22×C4—522no—
284C22×C4—522no—
285C22×C4—522no—
286C22×C4—522no—
287C22×C4—522no—
288C22×C4C22⋊Dic1311yescharacteristic
289C22×C4C22⋊Dic1311yescharacteristic
290C22×C4C22⋊Dic1311yescharacteristic
291C22×C4C22⋊Dic1311yescharacteristic
292C22×C4Q8×D1312yes—
293C22×C4#613112yes—
294C22×C4C22×Dic1311yescharacteristic
295C22×C4C2×C22⋊D1311yescharacteristic
296C2×C8—264no—
297C2×C8—522no—
298C2×C8—522no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4—42no—
307C4⋊C4—528no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C42—22no—
313C42—22no—
314C42—41no—
315C42—41no—
316C13#988711yescharacteristic, complemented, Sylow
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23#8819811yescharacteristic
322C23#8820111yescharacteristic
323C23#8820311yescharacteristic
324C23#8820311yescharacteristic
325C23#8820511yescharacteristic
326C23#8820511yescharacteristic
327C23C2×C22⋊Dic1311yescharacteristic
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—524no—
361C2×C4—524no—
362C2×C4—524no—
363C2×C4—1042no—
364C2×C4—1042no—
365C2×C4—1042no—
366C2×C4—1042no—
367C2×C4#8807412yes—
368C2×C4#8807712yes—
369C2×C4Q8×Dic1312yes—
370C2×C4#8820012yes—
371C8—524no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22#1171872611yescharacteristic
385C22#1171872611yescharacteristic
386C22#1171872811yescharacteristic
387C22#1171873011yescharacteristic
388C22C2×#8807411yescharacteristic
389C22#1171889111yescharacteristic
390C22#1171889311yescharacteristic
391C22#1171889311yescharacteristic
392C22C2×#8807711yescharacteristic
393C22#1171889711yescharacteristic
394C22#1171890111yescharacteristic
395C4—22no—
396C4—22no—
397C4—22no—
398C4—22no—
399C4—41no—
400C4—41no—
401C4—81no—
402C4—81no—
403C4—81no—
404C4—81no—
405C4—1044no—
406C2—21no—
407C2—21no—
408C2—21no—
409C2—21no—
410C2#1311334011yescharacteristic
411C2#1311336111yescharacteristic
412C2#1311337411yescharacteristic
413C2#1311337911yescharacteristic
414C2#1311578111yescharacteristic
415C2#1311580611yescharacteristic
416C2#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#9887
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
9. C13×#389C4semidirect
10. C13×#389C4semidirect
15. C13×#382C4semidirect
169. C2×#125Dic13semidirect
174. #389Dic13semidirect
175. #389Dic13semidirect
180. #382Dic13semidirect
316. C13#9887semidirect

Maximal subgroups

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

subgroupindex
#131145982
#131130662
#131127142
C13×#28512
#988713