Finite Group Databasebeta

← #14760449

Subgroups — #14760449

Order 2816.

1066 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622478C211yesmaximal, characteristic
2C2×#10622485C211yesmaximal, characteristic, complemented
3C2×#10622321C211yesmaximal, characteristic, complemented
4#13071307C212yesmaximal, complemented
5#13069492C211yesmaximal, characteristic, complemented
6#13069298C212yesmaximal, complemented
7#13069043C212yesmaximal, complemented
8#13068650C211yesmaximal, characteristic, complemented
9#106×Dic11C211yesmaximal, characteristic, complemented
10#13068440C212yesmaximal, complemented
11C11×#1944C211yesmaximal, characteristic, complemented
12C22×D88C2211yescharacteristic
13C22×#4313C2211yescharacteristic
14C22×C8×D11C2211yescharacteristic
15C2×#66948C2212yes—
16C2×#66946C2212yes—
17C2×#66925C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19C2×C11×#106C2211yescharacteristic
20C2×C11×#97C2211yescharacteristic
21C11×#389C2212yes—
22C2×#66885C2212yes—
23C2×#66881C2211yescharacteristic
24C2×#66879C2211yescharacteristic
25C2×C8×Dic11C2211yescharacteristic
26#10622602—22no—
27#10622601—22no—
28#10622600C2212yes—
29C4⋊C4×Dic11C2212yes—
30C2×#66873C2212yes—
31C2×#66873C2212yes—
32#10622552C2212yes—
33C2×C4×C11⋊C8C2211yescharacteristic
34#10622485—24no—
35#10622478C418yescomplemented
36#10622321—24no—
37#10622282—22no—
38#10622278—22no—
39C11×#340C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C22×D44—22no—
43C22×D44C2312yes—
44C22×C4×D11—22no—
45C22×C4×D11C2311yescharacteristic
46C22×C8×C11C2311yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C4⋊C4C2312yes—
51C2×C42×C11C2311yescharacteristic
52C2×(C2×D11)⋊C4—22no—
53C2×(C2×D11)⋊C4—22no—
54C2×(C2×D11)⋊C4—22no—
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4D411yescharacteristic
58C2×(C2×D11)⋊C4D411yescharacteristic
59C2×C4⋊Dic11C2312yes—
60C2×Dic11⋊C4D411yescharacteristic
61C2×Dic11⋊C4D411yescharacteristic
62C2×C4×Dic11—22no—
63C2×C4×Dic11C2311yescharacteristic
64C22×C11⋊C8C2311yescharacteristic
65C22×C11⋊C8C2311yescharacteristic
66C2×D88—22no—
67C2×D88—22no—
68C2×D88C2×C414yes—
69C2×#4313—22no—
70C2×#4313—22no—
71C2×#4313C2×C414yescomplemented
72C2×C8×D11—22no—
73C2×C8×D11—22no—
74C2×C8×D11—22no—
75#66948—24no—
76#66948C2×C418yescomplemented
77#66946—24no—
78#66946—24no—
79#66925—22no—
80#66925—22no—
81C11×#107—22no—
82C11×#106C2×C414yescomplemented
83C11×#97—22no—
84C11×#95—22no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87#66885—24no—
88#66881—22no—
89#66879—22no—
90C8×Dic11D414yescomplemented
91#66873—24no—
92#66873C2×C418yescomplemented
93C4×C11⋊C8—22no—
94#21536—111nomaximal, Sylow
95C23×D11—22no—
96C23×D11C2×D411yescharacteristic
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2411yescharacteristic
102C22×Dic11—22no—
103C22×Dic11C2×D411yescharacteristic
104C22×Dic11C2×D411yescharacteristic
105C22×Dic11C2×D411yescharacteristic
106C2×D44—28no—
107C2×D44—22no—
108C2×D44—22no—
109C2×D44—22no—
110C2×D44—22no—
111C2×D44—22no—
112C2×D44—82no—
113C2×D44—82no—
114C2×D44C22×C414yes—
115C2×C4×D11—21no—
116C2×C4×D11—21no—
117C2×C4×D11—21no—
118C2×C4×D11—21no—
119C2×C4×D11—44no—
120C2×C4×D11—82no—
121C2×C4×D11—82no—
122C2×C4×D11C22×C412yes—
123C2×C4×D11#4112yes—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11C22×C412yes—
127C2×C8×C11C2×D412yes—
128C2×C8×C11#4112yes—
129C2×C8×C11#4112yes—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—82no—
134C11×C4⋊C4C22×C414yes—
135C42×C11—21no—
136C42×C11—21no—
137(C2×D11)⋊C4—28no—
138(C2×D11)⋊C4—22no—
139(C2×D11)⋊C4—22no—
140(C2×D11)⋊C4—44no—
141(C2×D11)⋊C4—82no—
142(C2×D11)⋊C4—82no—
143(C2×D11)⋊C4—82no—
144C4⋊Dic11—22no—
145C4⋊Dic11—22no—
146Dic11⋊C4—22no—
147Dic11⋊C4—22no—
148C4×Dic11—82no—
149C4×Dic11C2×D412yes—
150C4×Dic11#4112yes—
151C2×C11⋊C8—21no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8C22×C412yes—
156C2×C11⋊C8C2×D412yes—
157D88—28no—
158#4313—28no—
159C8×D11—28no—
160C2×#469—111no—
161C2×C4×D8—111no—
162C2×#405—111no—
163#2324—112no—
164#1972—111no—
165#1944D1111yescharacteristic, complemented
166#1934—112no—
167#1893—112no—
168#1809—111no—
169C4×#106—111no—
170#1762—112no—
171C23×C11C22×D411yescharacteristic
172C22×D11—21no—
173C22×D11—21no—
174C22×D11—22no—
175C22×D11—22no—
176C22×D11—24no—
177C22×D11—42no—
178C22×D11—42no—
179C22×D11—42no—
180C22×D11—42no—
181C22×D11—42no—
182C22×D11—42no—
183C22×D11C4×D412yes—
184C2×C4×C11—24no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11C23×C411yescharacteristic
195C2×C4×C11C22×D411yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×Dic11—21no—
201C2×Dic11—21no—
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11C4×D412yes—
208C2×Dic11#12112yes—
209C2×Dic11#12112yes—
210D44—24no—
211D44—24no—
212D44—42no—
213D44—42no—
214D44—88no—
215C4×D11—22no—
216C4×D11—22no—
217C4×D11—22no—
218C4×D11—22no—
219C4×D11—88no—
220C8×C11—22no—
221C8×C11C4×D414yes—
222C11⋊C8—22no—
223C11⋊C8—22no—
224C22×D8—111no—
225C22×M16—111no—
226C23×C8—111no—
227C2×#121—112no—
228C2×C4×D4—112no—
229C2×#117—111no—
230#469—118no—
231C4×D8—224no—
232C2×#107C2×D1111yescharacteristic
233C2×#106—111no—
234C2×#106C2×D1111yescharacteristic
235C2×#102—112no—
236C2×#102—112no—
237C2×#102—112no—
238#405—224no—
239C2×#97—111no—
240C2×#97C2×D1111yescharacteristic
241C2×C4×C8—111no—
242C2×C4×C8—111no—
243#390—112no—
244#390—222no—
245#389C2×D1112yes—
246#388—222no—
247#386—222no—
248#385—222no—
249#380—112no—
250C4×C4⋊C4—112no—
251#340—112no—
252#340—112no—
253#340C2×D1112yes—
254C22×C11C2×C4×D411yescharacteristic
255C22×C11C2×#12111yescharacteristic
256C22×C11#53211yescharacteristic
257C22×C11#57612yes—
258C22×C11#57712yes—
259C2×D11—24no—
260C2×D11—22no—
261C2×D11—42no—
262C2×D11—41no—
263C2×D11—41no—
264C2×D11—44no—
265C2×D11—44no—
266C2×D11—44no—
267C2×D11—82no—
268C2×D11—82no—
269C2×D11—82no—
270C2×D11—82no—
271C4×C11—44no—
272C4×C11—41no—
273C4×C11—41no—
274C4×C11—82no—
275C4×C11C2×C4×D411yescharacteristic
276C4×C11C4×#4111yescharacteristic
277C4×C11#52511yescharacteristic
278C4×C11#52911yescharacteristic
279Dic11—22no—
280Dic11—22no—
281Dic11—22no—
282Dic11—82no—
283C22×D4—112no—
284C22×D4—222no—
285C23×C4—111no—
286C23×C4—222no—
287C2×D8—114no—
288C2×D8—222no—
289C2×D8—222no—
290C2×M16—114no—
291C2×M16—222no—
292C2×M16—222no—
293C22×C8—111no—
294C22×C8—111no—
295C22×C8—222no—
296C22×C8—222no—
297C22×C8—222no—
298C22×C8C22×D1111yescharacteristic
299C22×C8C22×D1111yescharacteristic
300#121—118no—
301#121—224no—
302C4×D4—224no—
303C4×D4—224no—
304#117—222no—
305#117—222no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—111no—
308C2×C4⋊C4—111no—
309C2×C4⋊C4—112no—
310C2×C4⋊C4C22×D1112yes—
311C2×C4⋊C4C22×D1112yes—
312C2×C22⋊C4—111no—
313C2×C22⋊C4—111no—
314C2×C22⋊C4—222no—
315C2×C22⋊C4—222no—
316C2×C22⋊C4—222no—
317C2×C22⋊C4—222no—
318C2×C22⋊C4—222no—
319C2×C42—111no—
320C2×C42—222no—
321C2×C42C22×D1111yescharacteristic
322#107—22no—
323#106—222no—
324#106C4×D1114yescomplemented
325#102—118no—
326#102—224no—
327#102—224no—
328#97—22no—
329#97—222no—
330C4×C8—114no—
331C4×C8—222no—
332#95—22no—
333#95—222no—
334#95—222no—
335C2×C11C4×#12111yescharacteristic
336C2×C11#294612yes—
337C2×C11#305811yescharacteristic
338C2×C11#306011yescharacteristic
339C2×C11#317912yes—
340D11—42no—
341D11—84no—
342C24—111no—
343C24—222no—
344C2×D4—114no—
345C2×D4—228no—
346C2×D4—222no—
347C2×D4—222no—
348C2×D4—222no—
349C2×D4—222no—
350C2×D4—222no—
351C2×D4—882no—
352C2×D4—882no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—111no—
356C22×C4—111no—
357C22×C4—111no—
358C22×C4—112no—
359C22×C4—112no—
360C22×C4—221no—
361C22×C4—221no—
362C22×C4—221no—
363C22×C4—221no—
364C22×C4—222no—
365C22×C4—444no—
366C22×C4—882no—
367C22×C4—882no—
368C22×C4D4×D1111yescharacteristic
369C22×C4D4×D1111yescharacteristic
370C22×C4C23×D1111yescharacteristic
371D8—228no—
372M16—228no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8—112no—
376C2×C8—112no—
377C2×C8—228no—
378C2×C8—221no—
379C2×C8—221no—
380C2×C8—221no—
381C2×C8—221no—
382C2×C8C2×C4×D1112yes—
383C2×C8D4×D1112yes—
384C2×C8#434312yes—
385C2×C8#434312yes—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—82no—
390C4⋊C4—222no—
391C4⋊C4—222no—
392C4⋊C4—222no—
393C4⋊C4—222no—
394C4⋊C4C2×C4×D1114yes—
395C22⋊C4—222no—
396C22⋊C4—222no—
397C22⋊C4—228no—
398C22⋊C4—444no—
399C22⋊C4—882no—
400C22⋊C4—882no—
401C22⋊C4—882no—
402C42—21no—
403C42—21no—
404C42—112no—
405C42—112no—
406C42—882no—
407C11#2153611yescharacteristic, complemented, Sylow
408C23—112no—
409C23—221no—
410C23—222no—
411C23—222no—
412C23—221no—
413C23—224no—
414C23—442no—
415C23—442no—
416C23—442no—
417C23—442no—
418C23—442no—
419C23—442no—
420C23C2×D4×D1111yescharacteristic
421D4—224no—
422D4—224no—
423D4—442no—
424D4—442no—
425D4—888no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—24no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—112no—
437C2×C4—112no—
438C2×C4—112no—
439C2×C4—221no—
440C2×C4—222no—
441C2×C4—222no—
442C2×C4—221no—
443C2×C4—222no—
444C2×C4—222no—
445C2×C4—222no—
446C2×C4—222no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—888no—
451C2×C4C22×C4×D1111yescharacteristic
452C2×C4C2×D4×D1111yescharacteristic
453C2×C4C2×#434311yescharacteristic
454C2×C4C2×#434311yescharacteristic
455C2×C4#41×D1111yescharacteristic
456C2×C4#41×D1111yescharacteristic
457C8—22no—
458C8—222no—
459C8—222no—
460C8#6694614yes—
461C22—222no—
462C22—224no—
463C22—441no—
464C22—442no—
465C22—441no—
466C22—444no—
467C22—444no—
468C22—444no—
469C22—882no—
470C22—882no—
471C22—882no—
472C22—882no—
473C22C4×D4×D1111yescharacteristic
474C22D11×#12111yescharacteristic
475C22#1062325611yescharacteristic
476C22#1062330512yes—
477C22#1062330912yes—
478C4—41no—
479C4—44no—
480C4—41no—
481C4—82no—
482C4—222no—
483C4—222no—
484C4—222no—
485C4—882no—
486C4C2×#6694611yescharacteristic
487C4C4×#434311yescharacteristic
488C4#1062315811yescharacteristic
489C4#1062322211yescharacteristic
490C2—442no—
491C2—884no—
492C2#1307112411yescharacteristic
493C2#1307744712yes—
494C2#1307826211yescharacteristic
495C2#1307828011yescharacteristic
496C2#1307930412yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1944C2
socleC23×C11C22×D4
prime radicalC2×#10622478C2
cosocleC22×C4×C11C24
hypercenter#1944D11
hypocenterC11#21536
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1944

Complements

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

NH ≅ G/Ntype
2. C2×#10622485C2semidirect
3. C2×#10622321C2semidirect
4. #13071307C2semidirect
5. #13069492C2semidirect
6. #13069298C2semidirect
7. #13069043C2semidirect
8. #13068650C2semidirect
9. #106×Dic11C2semidirect
10. #13068440C2semidirect
11. C11×#1944C2semidirect
35. #10622478C4semidirect
71. C2×#4313C2×C4semidirect
76. #66948C2×C4semidirect
82. C11×#106C2×C4semidirect
90. C8×Dic11D4semidirect
92. #66873C2×C4semidirect
165. #1944D11semidirect
324. #106C4×D11semidirect
407. C11#21536semidirect

Maximal subgroups

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

subgroupindex
C2×#106224782
C2×#106224852
C2×#106223212
#130713072
#130694922
#130692982
#130690432
#130686502
#106×Dic112
#130684402
C11×#19442
#2153611