Finite Group Databasebeta

← #16779748

Subgroups — #16779748

Order 3328.

786 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719055C211yesmaximal, characteristic
2C2×#11719057C211yesmaximal, characteristic
3#13129709C214yesmaximal
4#13117240C211yesmaximal, characteristic
5C22×C4×#261—21no—
6C2×#88126—21no—
7C2×C42×D13C2211yescharacteristic
8C2×(C2×#261)⋊C4—21no—
9C2×(C2×#261)⋊C4C2212yes—
10C2×#88112—21no—
11C2×#88111C2212yes—
12C2×#88110—21no—
13#11719057—22no—
14#11719057C414yescomplemented
15#11719055—22no—
16#11719055C414yescomplemented
17C4×C13×C4⋊C4C411yescharacteristic, complemented
18#11718648C2212yes—
19#11718637C412yescomplemented
20C4×C4⋊Dic13C411yescharacteristic, complemented
21C4×#6101—21no—
22#11718328—21no—
23#11718311—21no—
24C23×#261—22no—
25C22×C4×D13D411yescharacteristic
26C22×C4×D13D411yescharacteristic
27C22×C4×D13C2311yescharacteristic
28C22×#1057—22no—
29C2×C4×#261—28no—
30C2×C4×#261—24no—
31C2×C13×C4⋊C4C2×C412yes—
32C2×C42×C13—21no—
33C2×C42×C13C2×C411yescharacteristic
34C2×#6103—22no—
35C2×C4⋊Dic13C2×C412yes—
36C2×#6101—22no—
37C2×#6101—22no—
38C2×C4×Dic13—21no—
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42#88126—44no—
43C42×D13C2×C412yes—
44C42×D13C2×C412yes—
45C42×D13D412yes—
46C42×D13Q812yes—
47(C2×#261)⋊C4—24no—
48(C2×#261)⋊C4—22no—
49(C2×#261)⋊C4C2×C414yes—
50#88112—24no—
51#88111—22no—
52#88111C2×C414yes—
53#88110—24no—
54C13×#95—21no—
55#88071—21no—
56#88071—22no—
57#8022—131nomaximal, Sylow
58C23×D13C2×D411yescharacteristic
59C22×#261—28no—
60C22×#261—24no—
61C22×#261—44no—
62C22×#261—42no—
63C22×#261—42no—
64C22×C4×C13—22no—
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22×C411yescharacteristic
68C22×Dic13—22no—
69C22×Dic13C22⋊C411yescharacteristic
70C22×Dic13C22⋊C411yescharacteristic
71C22×Dic13C2×D411yescharacteristic
72C2×C4×D13—22no—
73C2×C4×D13—22no—
74C2×C4×D13—24no—
75C2×C4×D13—42no—
76C2×C4×D13C22⋊C412yes—
77C2×C4×D13C22⋊C412yes—
78C2×C4×D13C4⋊C412yes—
79C2×C4×D13C4⋊C412yes—
80C2×C4×D13C22×C411yescharacteristic
81C2×C4×D13C22×C411yescharacteristic
82C2×C4×D13C2×D411yescharacteristic
83C2×C4×D13C2×Q811yescharacteristic
84C2×#1057—24no—
85C2×#1057—44no—
86C4×#261—216no—
87C13×C4⋊C4—42no—
88C42×C13—42no—
89C42×C13C4212yes—
90C42×C13C4⋊C412yes—
91#6103—44no—
92C4⋊Dic13—42no—
93#6101—44no—
94#6101—44no—
95C4×Dic13—42no—
96C4×Dic13C4212yes—
97C4×Dic13C22⋊C412yes—
98C4×Dic13C22⋊C412yes—
99C4×Dic13C4⋊C412yes—
100C4×Dic13C4⋊C412yes—
101C4×Dic13C4⋊C412yes—
102C2×#432—131no—
103#2285—131no—
104C2×#376—131no—
105#1294—134no—
106C23×C13C2×C22⋊C411yescharacteristic
107C22×D13—22no—
108C22×D13—22no—
109C22×D13C2×C22⋊C411yescharacteristic
110C22×D13C2×C4⋊C411yescharacteristic
111C22×D13AGL(1,ℤ/8)12yes—
112C22×D13#13712yes—
113C2×#261—28no—
114C2×#261—44no—
115C2×#261—48no—
116C2×#261—48no—
117C2×#261—44no—
118C2×C4×C13—22no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—22no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13#9512yes—
126C2×C4×C13#9512yes—
127C2×C4×C13C2×C4211yescharacteristic
128C2×C4×C13C2×C4⋊C411yescharacteristic
129C2×Dic13—22no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—42no—
133C2×Dic13—42no—
134C2×Dic13—42no—
135C2×Dic13#9512yes—
136C2×Dic13#9512yes—
137C2×Dic13#10414yes—
138C2×Dic13C2×C22⋊C411yescharacteristic
139C2×Dic13C2×C4⋊C411yescharacteristic
140C4×D13—24no—
141C4×D13—24no—
142C4×D13—24no—
143C4×D13—24no—
144C4×D13—41no—
145C4×D13—41no—
146C4×D13—41no—
147C4×D13—41no—
148#1057—44no—
149C2×#117—261no—
150C22×C42—131no—
151C22×C42—261no—
152#432—134no—
153#432—262no—
154C2×C4⋊C8—261no—
155C2×C22⋊C8—132no—
156C2×#97—261no—
157#384—132no—
158#382—261no—
159#380—132no—
160#380—261no—
161C4×C4⋊C4—131no—
162C4×C4⋊C4—261no—
163C4×C4⋊C4#26111yescharacteristic, complemented
164#376—134no—
165#376—262no—
166C2×#95—132no—
167C2×#95—261no—
168C22×C13C2×#9511yescharacteristic
169C22×C13#41012yes—
170C22×C13#41811yescharacteristic
171C22×C13#41911yescharacteristic
172C22×C13C2×#10412yes—
173C2×D13—21no—
174C2×D13—21no—
175C2×D13—21no—
176C2×D13—21no—
177C2×D13—24no—
178C2×D13—24no—
179C2×D13#41712yes—
180C2×D13#42812yes—
181#261—48no—
182C4×C13—22no—
183C4×C13—22no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—82no—
187Dic13—22no—
188Dic13—21no—
189Dic13—21no—
190Dic13—82no—
191Dic13#33914yes—
192C23×C4—131no—
193C23×C4—131no—
194C23×C4—131no—
195C23×C4—262no—
196C22×C8—262no—
197#117—524no—
198C2×C4⋊C4—132no—
199C2×C4⋊C4—262no—
200C2×C4⋊C4—262no—
201C2×C4⋊C4C2×#26112yes—
202C2×C22⋊C4—262no—
203C2×C42—21no—
204C2×C42—131no—
205C2×C42—131no—
206C2×C42—131no—
207C2×C42—132no—
208C2×C42—132no—
209C2×C42—132no—
210C2×C42—132no—
211C2×C42—264no—
212C2×C42—268no—
213C2×C42—261no—
214C2×C42C2×#26111yescharacteristic
215C4⋊C8—264no—
216C22⋊C8—134no—
217C22⋊C8—262no—
218#97—264no—
219#95—21no—
220#95—134no—
221#95—262no—
222#95—262no—
223#95—264no—
224#95—261no—
225C2×C13#150512yes—
226C2×C13#150612yes—
227C2×C13C2×#33911yescharacteristic
228C2×C13#173611yescharacteristic
229C2×C13#174011yescharacteristic
230D13—22no—
231D13—22no—
232C24—131no—
233C22×C4—22no—
234C22×C4—131no—
235C22×C4—131no—
236C22×C4—131no—
237C22×C4—132no—
238C22×C4—132no—
239C22×C4—132no—
240C22×C4—132no—
241C22×C4—131no—
242C22×C4—131no—
243C22×C4—131no—
244C22×C4—131no—
245C22×C4—264no—
246C22×C4—262no—
247C22×C4—262no—
248C22×C4—264no—
249C22×C4—268no—
250C22×C4—262no—
251C22×C4—522no—
252C22×C4—522no—
253C22×C4—522no—
254C22×C4—524no—
255C22×C4C22⋊#26111yescharacteristic
256C22×C4C22⋊#26111yescharacteristic
257C22×C4C22×#26111yescharacteristic
258C2×C8—264no—
259C2×C8—524no—
260C4⋊C4—42no—
261C4⋊C4—522no—
262C4⋊C4—524no—
263C4⋊C4—524no—
264C22⋊C4—524no—
265C42—42no—
266C42—132no—
267C42—132no—
268C42—132no—
269C42—132no—
270C42—132no—
271C42—132no—
272C42—2616no—
273C42—522no—
274C42C4×#26112yes—
275C42C4⋊#26112yes—
276C13#802211yescharacteristic, complemented, Sylow
277C23—131no—
278C23—131no—
279C23—132no—
280C23—132no—
281C23—262no—
282C23—262no—
283C23C2×C22⋊#26111yescharacteristic
284C2×C4—22no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—132no—
292C2×C4—134no—
293C2×C4—131no—
294C2×C4—132no—
295C2×C4—131no—
296C2×C4—264no—
297C2×C4—264no—
298C2×C4—264no—
299C2×C4—264no—
300C2×C4—262no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—268no—
304C2×C4—521no—
305C2×C4—521no—
306C2×C4—521no—
307C2×C4—521no—
308C2×C4—524no—
309C2×C4—524no—
310C2×C4—528no—
311C2×C4—528no—
312C2×C4—522no—
313C2×C4—522no—
314C2×C4—522no—
315C2×C4(C2×#261)⋊C412yes—
316C2×C4(C2×#261)⋊C412yes—
317C2×C4C2×C4×#26111yescharacteristic
318C2×C4C2×C4⋊#26111yescharacteristic
319C8—524no—
320C22—132no—
321C22—132no—
322C22—261no—
323C22—261no—
324C22—261no—
325C22—261no—
326C22—264no—
327C22—264no—
328C22#1171911612yes—
329C22C2×(C2×#261)⋊C411yescharacteristic
330C22#1171913811yescharacteristic
331C22#1171915311yescharacteristic
332C22D13⋊#10412yes—
333C4—22no—
334C4—22no—
335C4—21no—
336C4—21no—
337C4—82no—
338C4—134no—
339C4—262no—
340C4—261no—
341C4—261no—
342C4—528no—
343C4—1042no—
344C2—262no—
345C2—262no—
346C2#1313022612yes—
347C2#1313022912yes—
348C2#1313051211yescharacteristic
349C2#1313052311yescharacteristic
350C2#1313053511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC4×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C2×D4
cosocleC22×C4×D13C23
hypercenterC4×C4⋊C4#261
hypocenterC13#8022
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
14. #11719057C4semidirect
16. #11719055C4semidirect
17. C4×C13×C4⋊C4C4semidirect
19. #11718637C4semidirect
20. C4×C4⋊Dic13C4semidirect
163. C4×C4⋊C4#261semidirect
276. C13#8022semidirect

Maximal subgroups

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

subgroupindex
C2×#117190552
C2×#117190572
#131297092
#131172402
#802213