Finite Group Databasebeta

← #14737812

Subgroups — #14737812

Order 2816.

706 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078703C212yesmaximal, complemented
2C2×#10622301C211yesmaximal, characteristic, complemented
3#13068146C214yesmaximal, complemented
4#13068136C212yesmaximal, complemented
5#13068092C212yesmaximal, complemented
6#13067379C211yesmaximal, characteristic, complemented
7#13067311C212yesmaximal, complemented
8C11×#3169C211yesmaximal, characteristic, complemented
9C11×#532C2212yes—
10C22×#4313—21no—
11C2×C4×D44C2211yescharacteristic
12C11×#500C2211yescharacteristic, complemented
13C11×#493C2211yescharacteristic, complemented
14C11×#486C2212yescomplemented
15C11×#466—21no—
16C11×#466—21no—
17C4×C11×D8—21no—
18C4×C11×D8—21no—
19C2×C4×C8×C11C2211yescharacteristic
20C2×(C2×D11)⋊C8—21no—
21#10622697C2214yes—
22#10622685C2214yes—
23#10622649—22no—
24#10622647—22no—
25#10622627—24no—
26#10622539C2212yes—
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28#10622301—21no—
29#10622301—21no—
30#10622301C2212yes—
31#10622301C2212yes—
32#10622184C2214yescomplemented
33#10622182C2214yescomplemented
34#10622096C2212yescomplemented
35#10622095C2212yescomplemented
36C2×C11×#41—22no—
37C22×D44D411yescharacteristic
38C22×C4×D11—21no—
39C2×C11×D8—21no—
40C2×C11×D8—21no—
41C22×C8×C11D411yescharacteristic
42C22×C8×C11D411yescharacteristic
43C11×C4⋊Q8C2312yes—
44C11×#127C2312yes—
45C11×#124—22no—
46C11×#121—22no—
47C11×#121—22no—
48C4×D4×C11—22no—
49C4×D4×C11—22no—
50C2×C42×C11C2311yescharacteristic
51C2×#4323—24no—
52C2×(C2×D11)⋊C4—21no—
53C2×C4⋊Dic11D411yescharacteristic
54C22×C11⋊C8—21no—
55C2×#4313—22no—
56C2×#4313—22no—
57C2×#4313—44no—
58C4×D44—21no—
59C4×D44—21no—
60C4×D44D412yes—
61C4×D44C2312yes—
62C11×#107—21no—
63C11×#107—21no—
64C11×#102—22no—
65C11×#102—22no—
66C4×C8×C11D411yescharacteristic
67C4×C8×C11D411yescharacteristic
68C4×C8×C11C2311yescharacteristic
69C4×C8×C11C2311yescharacteristic
70#66896—24no—
71C22⋊(C11⋊C8)—22no—
72(C2×D11)⋊C8—22no—
73(C2×D11)⋊C8—22no—
74#66873—24no—
75#66872—24no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)C2312yes—
78C4⋊(C11⋊C8)C2314yes—
79#66867—22no—
80#19283—111nomaximal, Sylow
81C23×D11—21no—
82C11×#41—84no—
83C2×Q8×C11—22no—
84C2×D4×C11—22no—
85C2×D4×C11—22no—
86C2×D4×C11—22no—
87C2×D4×C11—42no—
88C22×C4×C11—42no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C22×Dic11—21no—
93C2×D44—21no—
94C2×D44—42no—
95C2×D44C2×D412yes—
96C2×C4×D11—22no—
97C2×C4×D11—22no—
98C2×C4×D11—42no—
99C2×C4×D11—42no—
100C11×D8—42no—
101C11×D8—42no—
102C2×C8×C11—22no—
103C2×C8×C11—41no—
104C2×C8×C11C2×D411yescharacteristic
105C2×C8×C11C2×D411yescharacteristic
106C2×C8×C11C2×D411yescharacteristic
107C2×C8×C11C2×D411yescharacteristic
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C22⋊C4—42no—
111C11×C22⋊C4—42no—
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11#4111yescharacteristic
115C42×C11C2411yescharacteristic
116#4323—48no—
117(C2×D11)⋊C4—22no—
118(C2×D11)⋊C4—22no—
119C4⋊Dic11—21no—
120C4⋊Dic11C2×D412yes—
121C2×C11⋊C8—24no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—42no—
124#4313—44no—
125#4313—44no—
126#3169D1111yescharacteristic, complemented
127#3109—112no—
128C2×#436—111no—
129#1697—114no—
130#1695—112no—
131#1687—112no—
132#1568—111no—
133#1551—112no—
134C23×C11—42no—
135C23×C11#12111yescharacteristic
136C22×D11—22no—
137C22×D11—42no—
138C22×D11—42no—
139C22×D11—42no—
140Q8×C11—82no—
141D4×C11—42no—
142D4×C11—44no—
143D4×C11—42no—
144D4×C11—82no—
145D4×C11—84no—
146C2×C4×C11—22no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—22no—
150C2×C4×C11—42no—
151C2×C4×C11—84no—
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11C22×D411yescharacteristic
156C2×C4×C11C22×D411yescharacteristic
157C2×C4×C11C2×#4111yescharacteristic
158C2×Dic11—22no—
159C2×Dic11—42no—
160D44—24no—
161D44—42no—
162C4×D11—44no—
163C4×D11—42no—
164C4×D11—42no—
165C8×C11—21no—
166C8×C11—21no—
167C8×C11—21no—
168C8×C11AGL(1,ℤ/8)12yes—
169C11⋊C8—42no—
170C11⋊C8—44no—
171C22×M16—221no—
172#532C2×D1112yes—
173C2×C4×D4—111no—
174#500C2×D1111yescharacteristic, complemented
175#493C2×D1111yescharacteristic, complemented
176#486C2×D1112yescomplemented
177#481—222no—
178#476—114no—
179#466—21no—
180#466—21no—
181#459—114no—
182#447—222no—
183#442—224no—
184C4×D8—21no—
185C4×D8—21no—
186#436—112no—
187#436—112no—
188#436—221no—
189#436—221no—
190#432—112no—
191C2×C4⋊C8—111no—
192C2×C22⋊C8—221no—
193C2×C4×C8C2×D1111yescharacteristic
194#335—112no—
195#334—112no—
196#333—114no—
197#331—114no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—82no—
201C22×C11—82no—
202C22×C11—82no—
203C22×C11#47212yes—
204C22×C11C2×#12111yescharacteristic
205C2×D11—42no—
206C2×D11—42no—
207C2×D11—42no—
208C2×D11—84no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—82no—
214C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
215C4×C11#57512yes—
216C4×C11#57511yescharacteristic
217Dic11—42no—
218C2×#41—22no—
219C22×D4—111no—
220C23×C4—221no—
221C2×D8—21no—
222C2×D8—21no—
223C2×D8—224no—
224C2×M16—222no—
225C2×M16—222no—
226C2×M16—444no—
227C22×C8—221no—
228C22×C8C22⋊D1111yescharacteristic
229C22×C8C22⋊D1111yescharacteristic
230C4⋊Q8C22×D1112yes—
231#127C22×D1112yes—
232#124—22no—
233#121—22no—
234#121—22no—
235C4×D4—22no—
236C4×D4—22no—
237C4×D4—112no—
238C4×D4—112no—
239C4×D4—221no—
240C4×D4—221no—
241C2×C4⋊C4—111no—
242C2×C22⋊C4—221no—
243C2×C42C22×D1111yescharacteristic
244#107—21no—
245#107—21no—
246#106—224no—
247C4⋊C8—112no—
248C4⋊C8—114no—
249C4⋊C8—221no—
250#102—22no—
251#102—22no—
252#102—224no—
253#102—224no—
254C22⋊C8—222no—
255C22⋊C8—222no—
256C22⋊C8—222no—
257#97—222no—
258C4×C8C22⋊D1111yescharacteristic
259C4×C8C22⋊D1111yescharacteristic
260C4×C8C22×D1111yescharacteristic
261C4×C8C22×D1111yescharacteristic
262C2×C11—22no—
263C2×C11—162no—
264C2×C11#303611yescharacteristic
265C2×C11#305411yescharacteristic
266C2×C11C2×#47211yescharacteristic
267D11—82no—
268C24—221no—
269#41—84no—
270C2×Q8—22no—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4—22no—
274C2×D4—42no—
275C2×D4—112no—
276C2×D4—221no—
277C2×D4—442no—
278C22×C4—42no—
279C22×C4—221no—
280C22×C4—222no—
281C22×C4—222no—
282C22×C4—442no—
283C22×C4—442no—
284C22×C4D4×D1111yescharacteristic
285C22×C4#434111yescharacteristic
286C22×C4C2×C22⋊D1111yescharacteristic
287D8—42no—
288D8—42no—
289D8—448no—
290M16—444no—
291M16—444no—
292C2×C8—22no—
293C2×C8—41no—
294C2×C8—224no—
295C2×C8—222no—
296C2×C8—442no—
297C2×C8C2×C22⋊D1111yescharacteristic
298C2×C8C2×C22⋊D1111yescharacteristic
299C2×C8C2×C22⋊D1111yescharacteristic
300C2×C8C2×C22⋊D1111yescharacteristic
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—112no—
304C4⋊C4—221no—
305C22⋊C4—42no—
306C22⋊C4—42no—
307C22⋊C4—222no—
308C22⋊C4—222no—
309C42D4×D1111yescharacteristic
310C42#434111yescharacteristic
311C42C2×C22⋊D1111yescharacteristic
312C42C23×D1111yescharacteristic
313C11#1928311yescharacteristic, complemented, Sylow
314C23—42no—
315C23—222no—
316C23—442no—
317C23—442no—
318C23—442no—
319C23#6699111yescharacteristic
320Q8—82no—
321D4—44no—
322D4—42no—
323D4—42no—
324D4—82no—
325D4—84no—
326D4—224no—
327D4—442no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—42no—
333C2×C4—84no—
334C2×C4—222no—
335C2×C4—444no—
336C2×C4—442no—
337C2×C4—442no—
338C2×C4—442no—
339C2×C4#6699111yescharacteristic
340C2×C4#6699111yescharacteristic
341C2×C4#6699111yescharacteristic
342C2×C4C2×D4×D1111yescharacteristic
343C2×C4C2×#434111yescharacteristic
344C2×C4C22×C22⋊D1111yescharacteristic
345C8—21no—
346C8—21no—
347C8—21no—
348C8—444no—
349C8—442no—
350C8#6700212yes—
351C22—21no—
352C22—21no—
353C22—82no—
354C22—82no—
355C22—82no—
356C22—442no—
357C22—442no—
358C22—442no—
359C22—884no—
360C22#1062277312yes—
361C22C2×#6699111yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—442no—
368C4#1062329912yes—
369C4C2×#6700211yescharacteristic
370C4#1062335311yescharacteristic
371C2—22no—
372C2—162no—
373C2—882no—
374C2#1307807611yescharacteristic
375C2#1307822111yescharacteristic
376C2C2×#1062277311yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3169C2
socleC22×C11C2×#121
hypercenter#3169D11
hypocenterC11#19283
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3169

Complements

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

NH ≅ G/Ntype
1. #13078703C2semidirect
2. C2×#10622301C2semidirect
3. #13068146C2semidirect
4. #13068136C2semidirect
5. #13068092C2semidirect
6. #13067379C2semidirect
7. #13067311C2semidirect
8. C11×#3169C2semidirect
12. C11×#500C22semidirect
13. C11×#493C22semidirect
14. C11×#486C22semidirect
32. #10622184C22semidirect
33. #10622182C22semidirect
34. #10622096C22semidirect
35. #10622095C22semidirect
126. #3169D11semidirect
174. #500C2×D11semidirect
175. #493C2×D11semidirect
176. #486C2×D11semidirect
313. C11#19283semidirect

Maximal subgroups

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

subgroupindex
#130787032
C2×#106223012
#130681462
#130681362
#130680922
#130673792
#130673112
C11×#31692
#1928311