Finite Group Databasebeta

← #15757949

Subgroups — #15757949

Order 3328.

812 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117450C211yesmaximal, characteristic
2#13114926C212yesmaximal, complemented
3C2×#11718117C211yesmaximal, characteristic
4#13112715C212yesmaximal, complemented
5C2×C13×#399C211yesmaximal, characteristic
6C22×C13×C4⋊C4—21no—
7C22×C13×C4⋊C4C2211yescharacteristic
8C22×C13×C22⋊C4—21no—
9C22×C13×C22⋊C4C2211yescharacteristic
10C22×C22⋊Dic13—21no—
11C13×#399—22no—
12C13×#399C414yescomplemented
13C2×C13×#95C2211yescharacteristic
14#11718873—21no—
15#11718873C2212yes—
16C2×C22⋊#1055C2212yes—
17#11718611—24no—
18#11718121—24no—
19#11718117—22no—
20C25×C13D411yescharacteristic
21C23×C4×C13—21no—
22C23×C4×C13—21no—
23C23×C4×C13D411yescharacteristic
24C23×C4×C13C2311yescharacteristic
25C23×Dic13—22no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—24no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—44no—
31C2×C13×C4⋊C4C2×C412yescomplemented
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4—22no—
34C2×C13×C22⋊C4—24no—
35C2×C13×C22⋊C4—44no—
36C2×C13×C22⋊C4C2×C412yes—
37C2×C13×C22⋊C4D412yes—
38C2×C22⋊Dic13—22no—
39C2×C22⋊Dic13—22no—
40C2×C22⋊Dic13—42no—
41C2×C22⋊Dic13—42no—
42C2×C4⋊Dic13—22no—
43C2×C4⋊Dic13D414yes—
44C22×#1055—22no—
45C13×#95—21no—
46C13×#95C2×C412yescomplemented
47#88071—22no—
48#88071—22no—
49C22⋊#1055—22no—
50C22⋊#1055—22no—
51#9021—131nomaximal, Sylow
52C24×C13—21no—
53C24×C13—21no—
54C24×C13—21no—
55C24×C13—21no—
56C24×C13—42no—
57C24×C13—42no—
58C24×C13C22⋊C412yes—
59C24×C13SD1612yes—
60C24×C13Q1612yes—
61C24×C13C2×D411yescharacteristic
62C22×C4×C13—24no—
63C22×C4×C13—22no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—22no—
67C22×C4×C13—42no—
68C22×C4×C13—42no—
69C22×C4×C13—41no—
70C22×C4×C13—41no—
71C22×C4×C13—42no—
72C22×C4×C13—42no—
73C22×C4×C13—42no—
74C22×C4×C13—41no—
75C22×C4×C13—41no—
76C22×C4×C13C22⋊C412yes—
77C22×C4×C13C22×C411yescharacteristic
78C22×C4×C13C2×D412yes—
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13#4112yes—
81C22×Dic13—24no—
82C22×Dic13—44no—
83C22×Dic13—82no—
84C22×Dic13—82no—
85C13×C4⋊C4—24no—
86C13×C4⋊C4—48no—
87C13×C4⋊C4—42no—
88C13×C22⋊C4—24no—
89C13×C22⋊C4—24no—
90C13×C22⋊C4—48no—
91C22⋊Dic13—44no—
92C22⋊Dic13—42no—
93C22⋊Dic13—42no—
94C4⋊Dic13—44no—
95C4⋊Dic13—82no—
96C2×#1055—44no—
97C2×#1055—42no—
98C2×#399D1311yescharacteristic
99#2315—131no—
100#1824—132no—
101C2×#323—131no—
102#1294—132no—
103C23×C13—22no—
104C23×C13—22no—
105C23×C13—22no—
106C23×C13—22no—
107C23×C13—22no—
108C23×C13—22no—
109C23×C13—22no—
110C23×C13—22no—
111C23×C13—42no—
112C23×C13—42no—
113C23×C13—44no—
114C23×C13—44no—
115C23×C13—42no—
116C23×C13—42no—
117C23×C13—82no—
118C23×C13—82no—
119C23×C13—81no—
120C23×C13—81no—
121C23×C13#10314yes—
122C23×C13C2×C22⋊C411yescharacteristic
123C23×C13#12011yescharacteristic
124C23×C13#12311yescharacteristic
125C23×C13C2×SD1611yescharacteristic
126C23×C13C2×Q1611yescharacteristic
127C23×C13AGL(1,ℤ/8)11yescharacteristic
128C23×C13#13711yescharacteristic
129C2×C4×C13—24no—
130C2×C4×C13—24no—
131C2×C4×C13—22no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—42no—
135C2×C4×C13—44no—
136C2×C4×C13—44no—
137C2×C4×C13—42no—
138C2×C4×C13—42no—
139C2×C4×C13—42no—
140C2×C4×C13—42no—
141C2×C4×C13—42no—
142C2×C4×C13—42no—
143C2×C4×C13—42no—
144C2×C4×C13—81no—
145C2×C4×C13—82no—
146C2×C4×C13—82no—
147C2×C4×C13C4×D412yes—
148C2×C4×C13#12112yes—
149C2×Dic13—44no—
150C2×Dic13—44no—
151C2×Dic13—44no—
152C2×Dic13—88no—
153#1055—82no—
154C22×C4⋊C4—21no—
155C22×C4⋊C4C2×D1311yescharacteristic
156C22×C22⋊C4—21no—
157C22×C22⋊C4—261no—
158C22×C22⋊C4C2×D1311yescharacteristic
159C2×C22⋊C8—132no—
160#399—22no—
161#399Dic1314yescomplemented
162#385—264no—
163#380—132no—
164#380—261no—
165C2×#95C2×D1311yescharacteristic
166#340—264no—
167#323—262no—
168C22×C13—22no—
169C22×C13—22no—
170C22×C13—22no—
171C22×C13—22no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—24no—
177C22×C13—44no—
178C22×C13—44no—
179C22×C13—44no—
180C22×C13—42no—
181C22×C13—42no—
182C22×C13—82no—
183C22×C13—82no—
184C22×C13—82no—
185C22×C13#38611yescharacteristic
186C22×C13C2×#10311yescharacteristic
187C22×C13#41711yescharacteristic
188C22×C13#45011yescharacteristic
189C22×C13#45111yescharacteristic
190C22×C13#45312yes—
191C22×C13#45812yes—
192C22×C13#48311yescharacteristic
193C22×C13#48411yescharacteristic
194C4×C13—22no—
195C4×C13—22no—
196C4×C13—44no—
197C4×C13—42no—
198C4×C13—82no—
199Dic13—84no—
200C25C22⋊D1311yescharacteristic
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—262no—
204C23×C4C22⋊D1311yescharacteristic
205C23×C4C22×D1311yescharacteristic
206C22×C8—262no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—24no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—44no—
212C2×C4⋊C4—134no—
213C2×C4⋊C4—262no—
214C2×C4⋊C4C2×Dic1312yescomplemented
215C2×C22⋊C4—22no—
216C2×C22⋊C4—22no—
217C2×C22⋊C4—24no—
218C2×C22⋊C4—44no—
219C2×C22⋊C4—262no—
220C2×C22⋊C4—262no—
221C2×C22⋊C4—522no—
222C2×C22⋊C4—522no—
223C2×C22⋊C4C2×Dic1312yes—
224C2×C22⋊C4C22⋊D1312yes—
225C22⋊C8—262no—
226C22⋊C8—262no—
227#95—21no—
228#95—262no—
229#95—262no—
230#95C2×Dic1312yescomplemented
231C2×C13—21no—
232C2×C13—21no—
233C2×C13—21no—
234C2×C13—21no—
235C2×C13—44no—
236C2×C13#161312yes—
237C2×C13#161412yes—
238C2×C13#187211yescharacteristic
239C2×C13#188711yescharacteristic
240C2×C13#189011yescharacteristic
241C24—21no—
242C24—21no—
243C24—21no—
244C24—21no—
245C24—42no—
246C24—42no—
247C24#610612yes—
248C24#610712yes—
249C24C22⋊Dic1312yes—
250C24C2×C22⋊D1311yescharacteristic
251C22×C4—24no—
252C22×C4—21no—
253C22×C4—22no—
254C22×C4—21no—
255C22×C4—22no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—264no—
266C22×C4—524no—
267C22×C4—1042no—
268C22×C4—1042no—
269C22×C4C22⋊Dic1312yes—
270C22×C4D4×D1312yes—
271C22×C4#612912yes—
272C22×C4C22×Dic1311yescharacteristic
273C22×C4C2×C22⋊D1311yescharacteristic
274C2×C8—524no—
275C2×C8—522no—
276C4⋊C4—24no—
277C4⋊C4—48no—
278C4⋊C4—42no—
279C4⋊C4—524no—
280C4⋊C4—1042no—
281C22⋊C4—24no—
282C22⋊C4—24no—
283C22⋊C4—48no—
284C22⋊C4—524no—
285C22⋊C4—522no—
286C22⋊C4—522no—
287C13#902111yescharacteristic, complemented, Sylow
288C23—22no—
289C23—22no—
290C23—22no—
291C23—22no—
292C23—22no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—42no—
297C23—44no—
298C23—44no—
299C23—42no—
300C23—42no—
301C23—42no—
302C23—82no—
303C23—81no—
304C23—81no—
305C23—82no—
306C23#8807514yes—
307C23#8818911yescharacteristic
308C23#8819111yescharacteristic
309C23C2×#610611yescharacteristic
310C23C2×#610711yescharacteristic
311C23#8820311yescharacteristic
312C23#8820511yescharacteristic
313C23C2×C22⋊Dic1311yescharacteristic
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—22no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—44no—
321C2×C4—42no—
322C2×C4—44no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—81no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—524no—
333C2×C4—524no—
334C2×C4—524no—
335C2×C4—1048no—
336C2×C4D4×Dic1312yes—
337C2×C4#8819312yes—
338C8—1042no—
339C22—22no—
340C22—22no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—22no—
346C22—22no—
347C22—24no—
348C22—44no—
349C22—44no—
350C22—42no—
351C22—42no—
352C22—44no—
353C22—82no—
354C22—82no—
355C22—82no—
356C22#1171870411yescharacteristic
357C22#1171870511yescharacteristic
358C22#1171870711yescharacteristic
359C22#1171871111yescharacteristic
360C22#1171871412yes—
361C22#1171873812yes—
362C22#1171888111yescharacteristic
363C22C2×#8807511yescharacteristic
364C22#1171889311yescharacteristic
365C4—22no—
366C4—22no—
367C4—44no—
368C4—42no—
369C4—82no—
370C4—1044no—
371C2—21no—
372C2—21no—
373C2—21no—
374C2—21no—
375C2—44no—
376C2#1311385512yes—
377C2#1311386012yes—
378C2#1311514411yescharacteristic
379C2#1311523511yescharacteristic
380C2#1311525011yescharacteristic
subgroupG/H
centerC23#88191
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#399C2
socleC23×C13#120
prime radicalC25×C13D4
cosocleC23×C4×C13C23
hypercenterC2×#399D13
hypocenterC13#9021
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
2. #13114926C2semidirect
4. #13112715C2semidirect
12. C13×#399C4semidirect
31. C2×C13×C4⋊C4C2×C4semidirect
46. C13×#95C2×C4semidirect
161. #399Dic13semidirect
214. C2×C4⋊C4C2×Dic13semidirect
230. #95C2×Dic13semidirect
287. C13#9021semidirect

Maximal subgroups

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

subgroupindex
#131174502
#131149262
C2×#117181172
#131127152
C2×C13×#3992
#902113