Finite Group Databasebeta

← #15757969

Subgroups — #15757969

Order 3328.

768 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117450C211yesmaximal, characteristic
2#13114922C212yesmaximal, complemented
3C2×#11718117C211yesmaximal, characteristic
4#13112715C212yesmaximal, complemented
5C2×C13×#397C211yesmaximal, characteristic
6C22×C13×C4⋊C4C2211yescharacteristic
7C22×C13×C22⋊C4—21no—
8C22×C13×C22⋊C4C2211yescharacteristic
9C22×C22⋊Dic13—21no—
10C13×#397—22no—
11C13×#397C414yescomplemented
12C2×C13×#95—21no—
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—21no—
29C2×C13×C4⋊C4C2×C412yescomplemented
30C2×C13×C22⋊C4—22no—
31C2×C13×C22⋊C4—22no—
32C2×C13×C22⋊C4—24no—
33C2×C13×C22⋊C4—42no—
34C2×C13×C22⋊C4—42no—
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#88071—22no—
48#88071—22no—
49C22⋊#1055—22no—
50C22⋊#1055—22no—
51#9025—131nomaximal, Sylow
52C24×C13—21no—
53C24×C13—21no—
54C24×C13—21no—
55C24×C13—21no—
56C24×C13—42no—
57C24×C13—42no—
58C24×C13C22⋊C412yes—
59C24×C13D812yes—
60C24×C13SD1612yes—
61C24×C13C2×D411yescharacteristic
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—22no—
65C22×C4×C13—22no—
66C22×C4×C13—42no—
67C22×C4×C13—42no—
68C22×C4×C13—42no—
69C22×C4×C13—42no—
70C22×C4×C13—41no—
71C22×C4×C13—41no—
72C22×C4×C13—41no—
73C22×C4×C13—41no—
74C22×C4×C13—41no—
75C22×C4×C13—41no—
76C22×C4×C13—41no—
77C22×C4×C13—41no—
78C22×C4×C13C22⋊C412yes—
79C22×C4×C13C22×C411yescharacteristic
80C22×C4×C13C2×D412yes—
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13#4112yes—
83C22×Dic13—24no—
84C22×Dic13—44no—
85C22×Dic13—82no—
86C22×Dic13—82no—
87C13×C4⋊C4—24no—
88C13×C4⋊C4—42no—
89C13×C22⋊C4—24no—
90C13×C22⋊C4—24no—
91C13×C22⋊C4—48no—
92C22⋊Dic13—44no—
93C22⋊Dic13—42no—
94C22⋊Dic13—42no—
95C4⋊Dic13—44no—
96C4⋊Dic13—82no—
97C2×#1055—44no—
98C2×#1055—42no—
99C2×#397D1311yescharacteristic
100#2315—131no—
101#1823—132no—
102C2×#323—131no—
103#1294—132no—
104C23×C13—22no—
105C23×C13—22no—
106C23×C13—22no—
107C23×C13—22no—
108C23×C13—22no—
109C23×C13—22no—
110C23×C13—22no—
111C23×C13—22no—
112C23×C13—42no—
113C23×C13—42no—
114C23×C13—44no—
115C23×C13—44no—
116C23×C13—42no—
117C23×C13—42no—
118C23×C13—82no—
119C23×C13—82no—
120C23×C13—81no—
121C23×C13—81no—
122C23×C13#10214yes—
123C23×C13C2×C22⋊C411yescharacteristic
124C23×C13#12011yescharacteristic
125C23×C13#12311yescharacteristic
126C23×C13C2×D811yescharacteristic
127C23×C13C2×SD1611yescharacteristic
128C23×C13AGL(1,ℤ/8)11yescharacteristic
129C23×C13#13711yescharacteristic
130C2×C4×C13—24no—
131C2×C4×C13—22no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—42no—
135C2×C4×C13—42no—
136C2×C4×C13—42no—
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—81no—
144C2×C4×C13—82no—
145C2×C4×C13—82no—
146C2×C4×C13—81no—
147C2×C4×C13—81no—
148C2×C4×C13—81no—
149C2×C4×C13—81no—
150C2×C4×C13C4×D412yes—
151C2×C4×C13#12112yes—
152C2×Dic13—44no—
153C2×Dic13—44no—
154C2×Dic13—44no—
155C2×Dic13—88no—
156#1055—82no—
157C22×C4⋊C4C2×D1311yescharacteristic
158C22×C22⋊C4—21no—
159C22×C22⋊C4—261no—
160C22×C22⋊C4C2×D1311yescharacteristic
161C2×C22⋊C8—132no—
162#397—22no—
163#397Dic1314yescomplemented
164#385—264no—
165#380—132no—
166#380—261no—
167C2×#95—21no—
168C2×#95C2×D1311yescharacteristic
169#340—264no—
170#323—262no—
171C22×C13—22no—
172C22×C13—22no—
173C22×C13—22no—
174C22×C13—22no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—24no—
180C22×C13—44no—
181C22×C13—44no—
182C22×C13—44no—
183C22×C13—42no—
184C22×C13—42no—
185C22×C13—82no—
186C22×C13—82no—
187C22×C13—82no—
188C22×C13#38611yescharacteristic
189C22×C13C2×#10211yescharacteristic
190C22×C13#41711yescharacteristic
191C22×C13#44711yescharacteristic
192C22×C13#44811yescharacteristic
193C22×C13#45512yes—
194C22×C13#45812yes—
195C22×C13#48011yescharacteristic
196C22×C13#48111yescharacteristic
197C4×C13—22no—
198C4×C13—22no—
199C4×C13—42no—
200C4×C13—82no—
201C4×C13—82no—
202Dic13—84no—
203C25C22⋊D1311yescharacteristic
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—262no—
207C23×C4C22⋊D1311yescharacteristic
208C23×C4C22×D1311yescharacteristic
209C22×C8—262no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—134no—
214C2×C4⋊C4—262no—
215C2×C4⋊C4C2×Dic1312yescomplemented
216C2×C22⋊C4—22no—
217C2×C22⋊C4—22no—
218C2×C22⋊C4—24no—
219C2×C22⋊C4—42no—
220C2×C22⋊C4—42no—
221C2×C22⋊C4—262no—
222C2×C22⋊C4—262no—
223C2×C22⋊C4—522no—
224C2×C22⋊C4—522no—
225C2×C22⋊C4C2×Dic1312yes—
226C2×C22⋊C4C22⋊D1312yes—
227C22⋊C8—262no—
228C22⋊C8—262no—
229#95—24no—
230#95—21no—
231#95—262no—
232#95—262no—
233#95C2×Dic1312yescomplemented
234C2×C13—21no—
235C2×C13—21no—
236C2×C13—21no—
237C2×C13—21no—
238C2×C13—44no—
239C2×C13#160712yes—
240C2×C13#160812yes—
241C2×C13#187411yescharacteristic
242C2×C13#188511yescharacteristic
243C2×C13#189011yescharacteristic
244C24—21no—
245C24—21no—
246C24—21no—
247C24—21no—
248C24—42no—
249C24—42no—
250C24#610412yes—
251C24#610512yes—
252C24C22⋊Dic1312yes—
253C24C2×C22⋊D1311yescharacteristic
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—264no—
271C22×C4—524no—
272C22×C4—1042no—
273C22×C4—1042no—
274C22×C4C22⋊Dic1312yes—
275C22×C4D4×D1312yes—
276C22×C4#612912yes—
277C22×C4C22×Dic1311yescharacteristic
278C22×C4C2×C22⋊D1311yescharacteristic
279C2×C8—524no—
280C2×C8—522no—
281C4⋊C4—24no—
282C4⋊C4—42no—
283C4⋊C4—524no—
284C4⋊C4—1042no—
285C22⋊C4—24no—
286C22⋊C4—24no—
287C22⋊C4—48no—
288C22⋊C4—524no—
289C22⋊C4—522no—
290C22⋊C4—522no—
291C13#902511yescharacteristic, complemented, Sylow
292C23—22no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—22no—
297C23—22no—
298C23—22no—
299C23—22no—
300C23—44no—
301C23—44no—
302C23—42no—
303C23—42no—
304C23—42no—
305C23—42no—
306C23—81no—
307C23—81no—
308C23—82no—
309C23—82no—
310C23#8807214yes—
311C23C2×#610411yescharacteristic
312C23C2×#610511yescharacteristic
313C23#8818911yescharacteristic
314C23#8819111yescharacteristic
315C23#8820311yescharacteristic
316C23#8820511yescharacteristic
317C23C2×C22⋊Dic1311yescharacteristic
318C2×C4—24no—
319C2×C4—22no—
320C2×C4—42no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—81no—
332C2×C4—82no—
333C2×C4—82no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—524no—
339C2×C4—524no—
340C2×C4—524no—
341C2×C4—1048no—
342C2×C4D4×Dic1312yes—
343C2×C4#8819312yes—
344C8—1042no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—22no—
350C22—22no—
351C22—22no—
352C22—22no—
353C22—24no—
354C22—44no—
355C22—42no—
356C22—42no—
357C22—44no—
358C22—44no—
359C22—82no—
360C22—82no—
361C22—82no—
362C22#1171869411yescharacteristic
363C22#1171869511yescharacteristic
364C22#1171869711yescharacteristic
365C22#1171870111yescharacteristic
366C22#1171871412yes—
367C22#1171872212yes—
368C22C2×#8807211yescharacteristic
369C22#1171888111yescharacteristic
370C22#1171889311yescharacteristic
371C4—22no—
372C4—22no—
373C4—42no—
374C4—82no—
375C4—82no—
376C4—1044no—
377C2—21no—
378C2—21no—
379C2—21no—
380C2—21no—
381C2—44no—
382C2#1311382112yes—
383C2#1311382612yes—
384C2#1311515411yescharacteristic
385C2#1311522511yescharacteristic
386C2#1311525011yescharacteristic
subgroupG/H
centerC23#88191
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#397C2
socleC23×C13#120
prime radicalC25×C13D4
cosocleC23×C4×C13C23
hypercenterC2×#397D13
hypocenterC13#9025
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
2. #13114922C2semidirect
4. #13112715C2semidirect
11. C13×#397C4semidirect
29. C2×C13×C4⋊C4C2×C4semidirect
46. C13×#95C2×C4semidirect
163. #397Dic13semidirect
215. C2×C4⋊C4C2×Dic13semidirect
233. #95C2×Dic13semidirect
291. C13#9025semidirect

Maximal subgroups

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

subgroupindex
#131174502
#131149222
C2×#117181172
#131127152
C2×C13×#3972
#902513