Finite Group Databasebeta

← #14649506

Subgroups — #14649506

Order 2816.

1348 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076898C211yesmaximal, characteristic
2C22×C11⋊#95C211yesmaximal, characteristic, complemented
3C2×#10622108C212yesmaximal, complemented
4#13066496C212yesmaximal, complemented
5C11×#1779C211yesmaximal, characteristic, complemented
6C24×C4×C11C2211yescharacteristic
7C24×Dic11—21no—
8C2×#67006—21no—
9C2×#66983C412yescomplemented
10C2×#66983C2211yescharacteristic
11C2×C11×C22⋊C8—22no—
12C2×C11×C22⋊C8C2212yes—
13#10622826—21no—
14#10622826—22no—
15#10622825C412yescomplemented
16#10622825C2211yescharacteristic
17C2×C11⋊#95—21no—
18C2×C11⋊#95—24no—
19C2×C11⋊#95C2212yes—
20#10622108—24no—
21C25×C11D411yescharacteristic
22C23×C4×C11—22no—
23C23×C4×C11—22no—
24C23×C4×C11—44no—
25C23×C4×C11C2×C412yes—
26C23×C4×C11D411yescharacteristic
27C23×C4×C11D412yes—
28C23×C4×C11C2311yescharacteristic
29C22×C22⋊D11—22no—
30C22×C22⋊D11—21no—
31C23×Dic11—24no—
32C23×Dic11—28no—
33C23×Dic11—22no—
34C23×Dic11—44no—
35C23×Dic11—42no—
36C23×Dic11—42no—
37C22×D44C2×C411yescharacteristic, complemented
38C22×C8×C11—22no—
39#67006—42no—
40#67006—42no—
41C2×C22⋊Dic11—22no—
42C2×C22⋊Dic11—21no—
43#66983—22no—
44#66983—22no—
45#66983—44no—
46C2×(C2×D11)⋊C4—22no—
47C2×(C2×D11)⋊C4—21no—
48C2×C4⋊Dic11C2×C411yescharacteristic, complemented
49C2×C4⋊Dic11C2×C412yescomplemented
50C11×C22⋊C8—22no—
51C11×C22⋊C8—22no—
52C11×C22⋊C8—44no—
53C11⋊#95—24no—
54C11⋊#95—22no—
55C11⋊#95—22no—
56C11⋊#95—21no—
57C11⋊#95D414yescomplemented
58#9147—111nomaximal, Sylow
59C24×C11—24no—
60C24×C11—24no—
61C24×C11—21no—
62C24×C11—21no—
63C24×C11—21no—
64C24×C11—21no—
65C24×C11C22⋊C412yes—
66C24×C11D812yes—
67C24×C11SD1612yes—
68C24×C11C2×D411yescharacteristic
69C23×D11—21no—
70C22×C4×C11—24no—
71C22×C4×C11—24no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—24no—
75C22×C4×C11—24no—
76C22×C4×C11—42no—
77C22×C4×C11—42no—
78C22×C4×C11—42no—
79C22×C4×C11—42no—
80C22×C4×C11—48no—
81C22×C4×C11—48no—
82C22×C4×C11C22⋊C412yes—
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D412yes—
86C22×C4×C11#4112yes—
87C2×C22⋊D11—44no—
88C2×C22⋊D11—44no—
89C2×C22⋊D11—44no—
90C2×C22⋊D11—41no—
91C2×C22⋊D11—41no—
92C2×C22⋊D11—41no—
93C2×C22⋊D11—41no—
94C2×C22⋊D11—41no—
95C2×C22⋊D11—41no—
96C22×Dic11—216no—
97C22×Dic11—28no—
98C22×Dic11—21no—
99C22×Dic11—22no—
100C22×Dic11—24no—
101C22×Dic11—48no—
102C22×Dic11—416no—
103C22×Dic11—416no—
104C22×Dic11—44no—
105C22×Dic11—48no—
106C22×Dic11—42no—
107C22×Dic11—42no—
108C2×D44—22no—
109C2×D44—42no—
110C2×C8×C11—44no—
111C2×C8×C11—42no—
112C22⋊Dic11—44no—
113C22⋊Dic11—41no—
114C22⋊Dic11—41no—
115(C2×D11)⋊C4—44no—
116(C2×D11)⋊C4—42no—
117C4⋊Dic11—22no—
118C4⋊Dic11—42no—
119#2847—111no—
120C22×#95—111no—
121#1779D1111yescharacteristic, complemented
122C2×#327—112no—
123#1294—112no—
124C23×C11—24no—
125C23×C11—24no—
126C23×C11—28no—
127C23×C11—24no—
128C23×C11—24no—
129C23×C11—28no—
130C23×C11—28no—
131C23×C11—28no—
132C23×C11—22no—
133C23×C11—22no—
134C23×C11—22no—
135C23×C11—22no—
136C23×C11—22no—
137C23×C11—22no—
138C23×C11—22no—
139C23×C11—22no—
140C23×C11—22no—
141C23×C11—22no—
142C23×C11#9914yes—
143C23×C11#10214yes—
144C23×C11#10414yes—
145C23×C11C2×C22⋊C411yescharacteristic
146C23×C11#12011yescharacteristic
147C23×C11#12311yescharacteristic
148C23×C11C2×D811yescharacteristic
149C23×C11C2×SD1611yescharacteristic
150C23×C11AGL(1,ℤ/8)11yescharacteristic
151C23×C11#13711yescharacteristic
152C22×D11—41no—
153C22×D11—42no—
154C22×D11—41no—
155C22×D11—41no—
156C22×D11—42no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—48no—
165C2×C4×C11—48no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11C4×D412yes—
169C2×C4×C11#12112yes—
170C22⋊D11—88no—
171C22⋊D11—81no—
172C22⋊D11—81no—
173C22⋊D11—81no—
174C22⋊D11—81no—
175C2×Dic11—28no—
176C2×Dic11—432no—
177C2×Dic11—44no—
178C2×Dic11—48no—
179C2×Dic11—48no—
180C2×Dic11—44no—
181C2×Dic11—41no—
182C2×Dic11—42no—
183C2×Dic11—41no—
184C2×Dic11—42no—
185C2×Dic11—41no—
186C2×Dic11—42no—
187D44—82no—
188C8×C11—82no—
189C24×C4—221no—
190C24×C4C2×D1111yescharacteristic
191C2×#121—111no—
192C2×#121—112no—
193C2×#120—221no—
194C2×C22⋊C8—22no—
195C2×C22⋊C8C2×D1112yes—
196#386—221no—
197#386—222no—
198#380—111no—
199#380—112no—
200C2×#95—112no—
201C2×#95—224no—
202C2×#95—221no—
203#327—224no—
204C22×C11—28no—
205C22×C11—28no—
206C22×C11—28no—
207C22×C11—28no—
208C22×C11—24no—
209C22×C11—24no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—24no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—24no—
216C22×C11—22no—
217C22×C11—22no—
218C22×C11—24no—
219C22×C11—24no—
220C22×C11—22no—
221C22×C11—22no—
222C22×C11#32718yescomplemented
223C22×C11#38611yescharacteristic
224C22×C11C2×#9912yes—
225C22×C11C2×#10211yescharacteristic
226C22×C11#41711yescharacteristic
227C22×C11C2×#10412yes—
228C22×C11#44711yescharacteristic
229C22×C11#44811yescharacteristic
230C22×C11#48011yescharacteristic
231C22×C11#48111yescharacteristic
232C2×D11—81no—
233C2×D11—81no—
234C2×D11—81no—
235C2×D11—82no—
236C2×D11—82no—
237C4×C11—22no—
238C4×C11—22no—
239C4×C11—42no—
240Dic11—48no—
241Dic11—81no—
242Dic11—82no—
243C25D4411yescharacteristic
244C22×D4—111no—
245C22×D4—222no—
246C22×D4—221no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—44no—
250C23×C4—224no—
251C23×C4—228no—
252C23×C4—222no—
253C23×C4—444no—
254C23×C4—442no—
255C23×C4—442no—
256C23×C4C4×D1112yes—
257C23×C4D4411yescharacteristic
258C23×C4C22⋊D1112yes—
259C23×C4C22×D1111yescharacteristic
260C22×C8—22no—
261#121—222no—
262#121—222no—
263#121—444no—
264#120—442no—
265#120—442no—
266C2×C4⋊C4—111no—
267C2×C4⋊C4—112no—
268C2×C22⋊C4—222no—
269C2×C22⋊C4—221no—
270C2×C22⋊C4—222no—
271C2×C22⋊C4—221no—
272C22⋊C8—22no—
273C22⋊C8—22no—
274C22⋊C8—44no—
275#95—114no—
276#95—224no—
277#95—222no—
278#95—222no—
279#95—221no—
280C2×C11—21no—
281C2×C11—28no—
282C2×C11—21no—
283C2×C11—21no—
284C2×C11—21no—
285C2×C11C2×#32712yes—
286C2×C11#150412yes—
287C2×C11#187411yescharacteristic
288C2×C11#189611yescharacteristic
289C2×C11#189811yescharacteristic
290D11—161no—
291C24—24no—
292C24—24no—
293C24—21no—
294C24—21no—
295C24—21no—
296C24—21no—
297C24—221no—
298C24#431412yes—
299C24D8812yes—
300C24(C2×D11)⋊C412yes—
301C24C2×D4411yescharacteristic
302C2×D4—222no—
303C2×D4—442no—
304C2×D4—444no—
305C2×D4—444no—
306C2×D4—444no—
307C2×D4—441no—
308C2×D4—441no—
309C2×D4—441no—
310C2×D4—441no—
311C2×D4—441no—
312C2×D4—441no—
313C22×C4—24no—
314C22×C4—24no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—24no—
318C22×C4—24no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—48no—
324C22×C4—48no—
325C22×C4—2216no—
326C22×C4—228no—
327C22×C4—224no—
328C22×C4—221no—
329C22×C4—222no—
330C22×C4—448no—
331C22×C4—4416no—
332C22×C4—444no—
333C22×C4—4416no—
334C22×C4—448no—
335C22×C4—442no—
336C22×C4—442no—
337C22×C4(C2×D11)⋊C412yes—
338C22×C4C2×C4×D1111yescharacteristic
339C22×C4D4×D1112yes—
340C22×C4#434112yes—
341C22×C4C2×C22⋊D1111yescharacteristic
342C2×C8—44no—
343C2×C8—42no—
344C4⋊C4—222no—
345C4⋊C4—442no—
346C22⋊C4—444no—
347C22⋊C4—444no—
348C22⋊C4—441no—
349C22⋊C4—441no—
350C22⋊C4—442no—
351C11#914711yescharacteristic, complemented, Sylow
352C23—24no—
353C23—24no—
354C23—24no—
355C23—28no—
356C23—24no—
357C23—28no—
358C23—22no—
359C23—22no—
360C23—22no—
361C23—22no—
362C23—22no—
363C23—22no—
364C23—22no—
365C23—22no—
366C23—22no—
367C23—22no—
368C23—28no—
369C23—28no—
370C23—441no—
371C23—441no—
372C23—442no—
373C23—442no—
374C23—441no—
375C23#6687014yes—
376C23#6688514yes—
377C23#6688914yes—
378C23#6693511yescharacteristic
379C23#6693911yescharacteristic
380C23C2×#431411yescharacteristic
381C23C2×D8811yescharacteristic
382C23#6696111yescharacteristic
383C23#6696211yescharacteristic
384C23C2×(C2×D11)⋊C411yescharacteristic
385D4—882no—
386D4—881no—
387D4—881no—
388D4—881no—
389D4—881no—
390D4—888no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—48no—
399C2×C4—48no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—228no—
403C2×C4—4432no—
404C2×C4—444no—
405C2×C4—448no—
406C2×C4—448no—
407C2×C4—444no—
408C2×C4—442no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4—442no—
412C2×C4—442no—
413C2×C4—441no—
414C2×C4(C22⋊D11)⋊C412yes—
415C2×C4#6699212yes—
416C8—82no—
417C22—28no—
418C22—28no—
419C22—28no—
420C22—28no—
421C22—21no—
422C22—24no—
423C22—21no—
424C22—21no—
425C22—24no—
426C22—21no—
427C22—22no—
428C22—24no—
429C22—22no—
430C22—22no—
431C22—24no—
432C22—24no—
433C22—22no—
434C22—24no—
435C22—881no—
436C22—881no—
437C22—882no—
438C22—882no—
439C22—881no—
440C22#1062210818yescomplemented
441C22#1062234511yescharacteristic
442C22#1062234811yescharacteristic
443C22#1062234911yescharacteristic
444C22#1062235111yescharacteristic
445C22C2×#6687012yes—
446C22#1062257111yescharacteristic
447C22C2×#6688511yescharacteristic
448C22#1062274611yescharacteristic
449C22C2×#6688912yes—
450C4—22no—
451C4—22no—
452C4—42no—
453C4—448no—
454C4—882no—
455C4—881no—
456C2—21no—
457C2—21no—
458C2—21no—
459C2—21no—
460C2—28no—
461C2—1761no—
462C2C2×#1062210812yes—
463C2#1306712112yes—
464C2#1306893111yescharacteristic
465C2#1306905711yescharacteristic
466C2#1306906711yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1779C2
socleC23×C11C2×C22⋊C4
prime radical#13076898C2
cosocleC23×C4×C11C23
hypercenter#1779D11
hypocenterC11#9147
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
2. C22×C11⋊#95C2semidirect
3. C2×#10622108C2semidirect
4. #13066496C2semidirect
5. C11×#1779C2semidirect
9. C2×#66983C4semidirect
15. #10622825C4semidirect
37. C22×D44C2×C4semidirect
48. C2×C4⋊Dic11C2×C4semidirect
49. C2×C4⋊Dic11C2×C4semidirect
57. C11⋊#95D4semidirect
121. #1779D11semidirect
222. C22×C11#327semidirect
351. C11#9147semidirect
440. C22#10622108semidirect

Maximal subgroups

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

subgroupindex
#130768982
C22×C11⋊#952
C2×#106221082
#130664962
C11×#17792
#914711