Finite Group Databasebeta

← #15757909

Subgroups — #15757909

Order 3328.

908 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117450C211yesmaximal, characteristic
2#13114771C212yesmaximal, complemented
3C2×#11718117C211yesmaximal, characteristic
4#13112715C212yesmaximal, complemented
5C2×C13×#393C211yesmaximal, characteristic
6C23×Q8×C13C2211yescharacteristic
7C22×C13×C22⋊C4—21no—
8C22×C13×C22⋊C4C2211yescharacteristic
9C22×C22⋊Dic13—21no—
10C13×#393—22no—
11C13×#393C414yescomplemented
12C2×C13×#95—21no—
13C2×C13×#95C2211yescharacteristic
14C2×#88075—24no—
15#11718873—21no—
16#11718873C2212yes—
17C2×C22⋊#1055C2212yes—
18#11718611—24no—
19#11718117—22no—
20C25×C13D411yescharacteristic
21C22×Q8×C13—21no—
22C22×Q8×C13—22no—
23C22×Q8×C13—22no—
24C22×Q8×C13—44no—
25C22×Q8×C13C2×C412yescomplemented
26C23×C4×C13—21no—
27C23×C4×C13—21no—
28C23×C4×C13D411yescharacteristic
29C23×C4×C13C2311yescharacteristic
30C23×Dic13—22no—
31C2×C13×C22⋊C4—22no—
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4—24no—
34C2×C13×C22⋊C4—44no—
35C2×C13×C22⋊C4C2×C412yes—
36C2×C13×C22⋊C4D412yes—
37C2×C22⋊Dic13—22no—
38C2×C22⋊Dic13—22no—
39C2×C22⋊Dic13—42no—
40C2×C22⋊Dic13—42no—
41C2×C4⋊Dic13—22no—
42C2×C4⋊Dic13D414yes—
43C22×#1055—22no—
44C13×#95—24no—
45C13×#95—21no—
46C13×#95C2×C412yescomplemented
47#88075—48no—
48#88071—22no—
49#88071—22no—
50C22⋊#1055—22no—
51C22⋊#1055—22no—
52#9013—131nomaximal, Sylow
53C24×C13—21no—
54C24×C13—21no—
55C24×C13—21no—
56C24×C13—21no—
57C24×C13—42no—
58C24×C13—42no—
59C24×C13C22⋊C412yes—
60C24×C13SD1612yes—
61C24×C13Q1612yes—
62C24×C13C2×D411yescharacteristic
63C2×Q8×C13—28no—
64C2×Q8×C13—24no—
65C2×Q8×C13—44no—
66C2×Q8×C13—44no—
67C2×Q8×C13—44no—
68C2×Q8×C13—48no—
69C2×Q8×C13—42no—
70C22×C4×C13—24no—
71C22×C4×C13—22no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—22no—
75C22×C4×C13—42no—
76C22×C4×C13—42no—
77C22×C4×C13—41no—
78C22×C4×C13—41no—
79C22×C4×C13—42no—
80C22×C4×C13—42no—
81C22×C4×C13—42no—
82C22×C4×C13—41no—
83C22×C4×C13—41no—
84C22×C4×C13C22⋊C412yes—
85C22×C4×C13C22×C411yescharacteristic
86C22×C4×C13C2×D412yes—
87C22×C4×C13C2×D411yescharacteristic
88C22×C4×C13#4112yes—
89C22×Dic13—24no—
90C22×Dic13—44no—
91C22×Dic13—82no—
92C22×Dic13—82no—
93C13×C22⋊C4—24no—
94C13×C22⋊C4—24no—
95C13×C22⋊C4—48no—
96C22⋊Dic13—44no—
97C22⋊Dic13—42no—
98C22⋊Dic13—42no—
99C4⋊Dic13—44no—
100C4⋊Dic13—82no—
101C2×#1055—44no—
102C2×#1055—42no—
103C2×#393D1311yescharacteristic
104#2315—131no—
105#1787—132no—
106C2×#323—131no—
107#1294—132no—
108C23×C13—22no—
109C23×C13—22no—
110C23×C13—22no—
111C23×C13—22no—
112C23×C13—22no—
113C23×C13—22no—
114C23×C13—22no—
115C23×C13—22no—
116C23×C13—42no—
117C23×C13—42no—
118C23×C13—44no—
119C23×C13—44no—
120C23×C13—42no—
121C23×C13—42no—
122C23×C13—82no—
123C23×C13—82no—
124C23×C13—81no—
125C23×C13—81no—
126C23×C13#10314yescomplemented
127C23×C13C2×C22⋊C411yescharacteristic
128C23×C13#12011yescharacteristic
129C23×C13#12311yescharacteristic
130C23×C13C2×SD1611yescharacteristic
131C23×C13C2×Q1611yescharacteristic
132C23×C13AGL(1,ℤ/8)11yescharacteristic
133C23×C13#13711yescharacteristic
134Q8×C13—28no—
135Q8×C13—48no—
136Q8×C13—44no—
137C2×C4×C13—24no—
138C2×C4×C13—24no—
139C2×C4×C13—22no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—42no—
143C2×C4×C13—42no—
144C2×C4×C13—44no—
145C2×C4×C13—42no—
146C2×C4×C13—42no—
147C2×C4×C13—44no—
148C2×C4×C13—42no—
149C2×C4×C13—42no—
150C2×C4×C13—42no—
151C2×C4×C13—42no—
152C2×C4×C13—81no—
153C2×C4×C13—82no—
154C2×C4×C13—82no—
155C2×C4×C13C4×D412yes—
156C2×C4×C13#12112yes—
157C2×Dic13—44no—
158C2×Dic13—44no—
159C2×Dic13—44no—
160C2×Dic13—88no—
161#1055—82no—
162C23×Q8C2×D1311yescharacteristic
163C22×C22⋊C4—21no—
164C22×C22⋊C4—261no—
165C22×C22⋊C4C2×D1311yescharacteristic
166C2×#103—264no—
167C2×C22⋊C8—132no—
168#393—22no—
169#393Dic1314yescomplemented
170#385—264no—
171#380—132no—
172#380—261no—
173C2×#95—21no—
174C2×#95C2×D1311yescharacteristic
175#323—262no—
176C22×C13—22no—
177C22×C13—22no—
178C22×C13—22no—
179C22×C13—22no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—24no—
185C22×C13—44no—
186C22×C13—44no—
187C22×C13—44no—
188C22×C13—42no—
189C22×C13—42no—
190C22×C13—82no—
191C22×C13—82no—
192C22×C13—82no—
193C22×C13#38611yescharacteristic
194C22×C13C2×#10311yescharacteristic
195C22×C13#41711yescharacteristic
196C22×C13#45011yescharacteristic
197C22×C13#45111yescharacteristic
198C22×C13#45512yes—
199C22×C13B(4,𝔽2)12yes—
200C22×C13#48311yescharacteristic
201C22×C13#48411yescharacteristic
202C4×C13—22no—
203C4×C13—22no—
204C4×C13—42no—
205C4×C13—44no—
206C4×C13—82no—
207Dic13—84no—
208C25C22⋊D1311yescharacteristic
209C22×Q8—21no—
210C22×Q8—22no—
211C22×Q8—22no—
212C22×Q8—44no—
213C22×Q8C2×Dic1312yescomplemented
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—262no—
217C23×C4C22⋊D1311yescharacteristic
218C23×C4C22×D1311yescharacteristic
219C22×C8—262no—
220C2×C4⋊C4—134no—
221C2×C4⋊C4—262no—
222C2×C22⋊C4—22no—
223C2×C22⋊C4—22no—
224C2×C22⋊C4—24no—
225C2×C22⋊C4—44no—
226C2×C22⋊C4—262no—
227C2×C22⋊C4—262no—
228C2×C22⋊C4—522no—
229C2×C22⋊C4—522no—
230C2×C22⋊C4C2×Dic1312yes—
231C2×C22⋊C4C22⋊D1312yes—
232#103—528no—
233C22⋊C8—262no—
234C22⋊C8—262no—
235#95—24no—
236#95—21no—
237#95—262no—
238#95—262no—
239#95C2×Dic1312yescomplemented
240C2×C13—21no—
241C2×C13—21no—
242C2×C13—21no—
243C2×C13—21no—
244C2×C13—44no—
245C2×C13#160112yes—
246C2×C13#160212yes—
247C2×C13#187211yescharacteristic
248C2×C13#188511yescharacteristic
249C2×C13#188911yescharacteristic
250C24—21no—
251C24—21no—
252C24—21no—
253C24—21no—
254C24—42no—
255C24—42no—
256C24#610612yes—
257C24#610712yes—
258C24C22⋊Dic1312yes—
259C24C2×C22⋊D1311yescharacteristic
260C2×Q8—28no—
261C2×Q8—24no—
262C2×Q8—44no—
263C2×Q8—44no—
264C2×Q8—44no—
265C2×Q8—48no—
266C2×Q8—42no—
267C22×C4—24no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—264no—
282C22×C4—524no—
283C22×C4—1042no—
284C22×C4—1042no—
285C22×C4C22⋊Dic1312yes—
286C22×C4D4×D1312yes—
287C22×C4#612912yes—
288C22×C4C22×Dic1311yescharacteristic
289C22×C4C2×C22⋊D1311yescharacteristic
290C2×C8—524no—
291C2×C8—522no—
292C4⋊C4—524no—
293C4⋊C4—1042no—
294C22⋊C4—24no—
295C22⋊C4—24no—
296C22⋊C4—48no—
297C22⋊C4—524no—
298C22⋊C4—522no—
299C22⋊C4—522no—
300C13#901311yescharacteristic, complemented, Sylow
301C23—22no—
302C23—22no—
303C23—22no—
304C23—22no—
305C23—22no—
306C23—22no—
307C23—22no—
308C23—22no—
309C23—42no—
310C23—44no—
311C23—44no—
312C23—42no—
313C23—42no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—82no—
318C23—82no—
319C23#8807514yescomplemented
320C23#8818911yescharacteristic
321C23#8819111yescharacteristic
322C23C2×#610611yescharacteristic
323C23C2×#610711yescharacteristic
324C23#8820311yescharacteristic
325C23#8820511yescharacteristic
326C23C2×C22⋊Dic1311yescharacteristic
327Q8—28no—
328Q8—48no—
329Q8—44no—
330C2×C4—24no—
331C2×C4—24no—
332C2×C4—22no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—44no—
338C2×C4—44no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—81no—
346C2×C4—82no—
347C2×C4—82no—
348C2×C4—524no—
349C2×C4—524no—
350C2×C4—524no—
351C2×C4—1048no—
352C2×C4D4×Dic1312yes—
353C2×C4#8819312yes—
354C8—1042no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—24no—
364C22—44no—
365C22—42no—
366C22—42no—
367C22—44no—
368C22—44no—
369C22—82no—
370C22—82no—
371C22—82no—
372C22#1171869312yes—
373C22#1171870411yescharacteristic
374C22#1171870511yescharacteristic
375C22#1171870711yescharacteristic
376C22#1171871111yescharacteristic
377C22#1171872212yes—
378C22#1171888111yescharacteristic
379C22C2×#8807511yescharacteristic
380C22#1171889311yescharacteristic
381C4—22no—
382C4—22no—
383C4—42no—
384C4—44no—
385C4—82no—
386C4—1044no—
387C2—21no—
388C2—21no—
389C2—21no—
390C2—21no—
391C2—44no—
392C2#1311378712yes—
393C2#1311379212yes—
394C2#1311514411yescharacteristic
395C2#1311522511yescharacteristic
396C2#1311524511yescharacteristic
subgroupG/H
centerC23#88191
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#393C2
socleC23×C13#120
prime radicalC25×C13D4
cosocleC23×C4×C13C23
hypercenterC2×#393D13
hypocenterC13#9013
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
2. #13114771C2semidirect
4. #13112715C2semidirect
11. C13×#393C4semidirect
25. C22×Q8×C13C2×C4semidirect
46. C13×#95C2×C4semidirect
126. C23×C13#103semidirect
169. #393Dic13semidirect
213. C22×Q8C2×Dic13semidirect
239. #95C2×Dic13semidirect
300. C13#9013semidirect
319. C23#88075semidirect

Maximal subgroups

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

subgroupindex
#131174502
#131147712
C2×#117181172
#131127152
C2×C13×#3932
#901313