Finite Group Databasebeta

← #14770241

Subgroups — #14770241

Order 2816.

1182 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623115C211yesmaximal, characteristic
2C2×#10622451C211yesmaximal, characteristic
3#13071516C211yesmaximal, characteristic
4#13069576C211yesmaximal, characteristic, complemented
5#13069567C211yesmaximal, characteristic, complemented
6#13069046C212yesmaximal, complemented
7#13068920C212yesmaximal, complemented
8#13068709C212yesmaximal, complemented
9C4×#66899C211yesmaximal, characteristic, complemented
10#13068334C212yesmaximal, complemented
11C11×#1803C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#66999C2212yes—
14C22×#4313C2212yes—
15#10623115—24no—
16#10623115C418yescomplemented
17C2×#66951—22no—
18C2×#66946—21no—
19C2×#66945C2212yes—
20C2×C4⋊C4×D11C2212yes—
21C2×#66928—21no—
22C2×C4×D44C2211yescharacteristic
23C2×#66922C2211yescharacteristic
24C2×C4×Dic22—21no—
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#103C2212yes—
27C11×#384C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×(C2×D11)⋊C8C2212yes—
31#10622602—22no—
32#10622600C2212yes—
33#10622586—21no—
34C4×C4⋊Dic11C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622451—24no—
37C11×#340C2212yes—
38#10622189C2212yes—
39#10622189C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622167C2211yescharacteristic
43#10622167C2211yescharacteristic
44C22×Q8×C11C2311yescharacteristic
45C22×D44D411yescharacteristic
46C22×C4×D11—22no—
47C22×C4×D11C2312yes—
48C22×Dic22—21no—
49C22×C8×C11C2312yes—
50C4×Q8×C11—22no—
51C4×Q8×C11C2×C414yescomplemented
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C42×C11—21no—
58C2×C42×C11C2311yescharacteristic
59#66999—24no—
60#66999C2×C418yescomplemented
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4D412yes—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11D411yescharacteristic
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2312yes—
69C2×C4⋊Dic11C2311yescharacteristic
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—22no—
72C2×C4×Dic11—22no—
73C2×C4×Dic11—21no—
74C22×C11⋊C8C2311yescharacteristic
75C22×C11⋊C8C2311yescharacteristic
76C2×#4313—24no—
77C2×#4313—24no—
78C2×#4313—42no—
79#66951—216no—
80#66946—44no—
81#66945—24no—
82#66945C2×C418yescomplemented
83C4⋊C4×D11—24no—
84C4⋊C4×D11—42no—
85#66928—28no—
86C4×D44C2×C414yes—
87C4×D44D414yes—
88#66922—22no—
89#66922C2×C414yescomplemented
90C4×Dic22—28no—
91C11×C4⋊C8—22no—
92C11×#103—42no—
93#66899—22no—
94#66899—22no—
95C11⋊#95—21no—
96C11⋊#95—22no—
97(C2×D11)⋊C8—24no—
98C4×C11⋊C8—22no—
99#22504—111nomaximal, Sylow
100C23×D11C2×D412yes—
101C2×Q8×C11—21no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11C22×C412yes—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2411yescharacteristic
113C22×Dic11—21no—
114C22×Dic11—22no—
115C22×Dic11—21no—
116C22×Dic11C2×D412yes—
117C2×D44—22no—
118C2×D44—22no—
119C2×D44C22⋊C414yes—
120C2×C4×D11—22no—
121C2×C4×D11—22no—
122C2×C4×D11—22no—
123C2×C4×D11—22no—
124C2×C4×D11—44no—
125C2×C4×D11—44no—
126C2×C4×D11—82no—
127C2×C4×D11C22×C414yes—
128C2×C4×D11C2×D414yes—
129C2×Dic22—24no—
130C2×Dic22—42no—
131C2×Dic22—42no—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—42no—
140C11×C4⋊C4—81no—
141C11×C4⋊C4C22×C412yes—
142C42×C11—24no—
143C42×C11C22×C412yes—
144C42×C11C2×D412yes—
145(C2×D11)⋊C4—28no—
146(C2×D11)⋊C4—28no—
147(C2×D11)⋊C4—44no—
148(C2×D11)⋊C4C22⋊C418yes—
149C4⋊Dic11—24no—
150C4⋊Dic11—22no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11C22⋊C414yes—
155C4⋊Dic11C22×C414yes—
156C4⋊Dic11#4112yes—
157Dic11⋊C4—28no—
158Dic11⋊C4—44no—
159C4×Dic11—28no—
160C4×Dic11—42no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8—21no—
166C2×C11⋊C8#4112yes—
167#4313—48no—
168C2×#556—111no—
169C2×#436—111no—
170D4×C4⋊C4—111no—
171#1990—111no—
172#1988—111no—
173#1894—112no—
174#1872—112no—
175#1825—112no—
176#1803D1111yescharacteristic, complemented
177C4×#103—111no—
178#1736—112no—
179C23×C11C22×D411yescharacteristic
180C22×D11—22no—
181C22×D11—22no—
182C22×D11—22no—
183C22×D11—22no—
184C22×D11—22no—
185C22×D11—22no—
186C22×D11C2×C22⋊C414yes—
187Q8×C11—22no—
188Q8×C11—22no—
189Q8×C11—41no—
190Q8×C11—41no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11C2×C22⋊C412yes—
203C2×C4×C11C2×C22⋊C412yes—
204C2×C4×C11AGL(1,ℤ/8)12yes—
205C2×C4×C11#13712yes—
206C2×C4×C11C23×C411yescharacteristic
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11H(5,𝔽2)11yescharacteristic
211C2×C4×C112−1+411yescharacteristic
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—24no—
215C2×Dic11—22no—
216C2×Dic11—41no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11C2×C22⋊C414yes—
224D44—28no—
225C4×D11—24no—
226C4×D11—24no—
227C4×D11—24no—
228C4×D11—24no—
229C4×D11—88no—
230Dic22—48no—
231C8×C11—42no—
232C11⋊C8—22no—
233C11⋊C8—41no—
234C22×M16—112no—
235#556—118no—
236#556—224no—
237C2×C4⋊Q8—111no—
238C2×#126—222no—
239C2×#124—221no—
240C2×C22⋊Q8—112no—
241C2×C4×Q8—221no—
242C2×C4×Q8C2×D1111yescharacteristic
243C2×C4×D4—111no—
244C2×C4×D4—221no—
245C2×#117—112no—
246C22×C4⋊C4—112no—
247#436—224no—
248C2×C4⋊C8C2×D1111yescharacteristic
249C2×#103—111no—
250C2×#103—111no—
251C2×#103C2×D1112yes—
252C2×C22⋊C8—112no—
253C2×C4×C8—111no—
254#389—221no—
255#385—222no—
256#384C2×D1111yescharacteristic
257#380—112no—
258C4×C4⋊C4—111no—
259#340—112no—
260#340—112no—
261#340—111no—
262#340—112no—
263#340—112no—
264#340—111no—
265#340C2×D1112yes—
266C22×C11C22×C22⋊C411yescharacteristic
267C22×C11#54611yescharacteristic
268C22×C11#54711yescharacteristic
269C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
270C22×C11C2×#13711yescharacteristic
271C22×C11#57711yescharacteristic
272C22×C11#57811yescharacteristic
273C2×D11—24no—
274C2×D11—24no—
275C2×D11—24no—
276C2×D11—42no—
277C2×D11—42no—
278C2×D11—42no—
279C2×D11—42no—
280C4×C11—22no—
281C4×C11—42no—
282C4×C11—42no—
283C4×C11—82no—
284C4×C11#41714yes—
285C4×C11C4×#4111yescharacteristic
286C4×C11#52011yescharacteristic
287C4×C11#54611yescharacteristic
288C4×C11#54711yescharacteristic
289Dic11—24no—
290Dic11—44no—
291Dic11—42no—
292Dic11—81no—
293C22×Q8—221no—
294C22×Q8C22×D1111yescharacteristic
295C22×D4—111no—
296C23×C4—112no—
297C23×C4—222no—
298C2×M16—224no—
299C2×M16—224no—
300C2×M16—442no—
301C22×C8—111no—
302C22×C8—111no—
303C22×C8C22×D1112yes—
304C4⋊Q8—114no—
305C4⋊Q8—222no—
306#126—2216no—
307#124—228no—
308C22⋊Q8—118no—
309C22⋊Q8—224no—
310C4×Q8—22no—
311C4×Q8—228no—
312C4×Q8C4×D1114yescomplemented
313C4×D4—114no—
314C4×D4—114no—
315C4×D4—444no—
316#117—118no—
317#117—224no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—111no—
322C2×C4⋊C4—111no—
323C2×C4⋊C4—112no—
324C2×C4⋊C4—111no—
325C2×C4⋊C4—224no—
326C2×C4⋊C4—222no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4—222no—
329C2×C4⋊C4—442no—
330C2×C4⋊C4C22×D1112yes—
331C2×C4⋊C4C22×D1111yescharacteristic
332C2×C22⋊C4—112no—
333C2×C22⋊C4—222no—
334C2×C22⋊C4—222no—
335C2×C22⋊C4—222no—
336C2×C42—21no—
337C2×C42—222no—
338C2×C42—221no—
339C2×C42C22×D1111yescharacteristic
340C4⋊C8—22no—
341#103—42no—
342#103—222no—
343#103—222no—
344C22⋊C8—224no—
345C4×C8—222no—
346#95—222no—
347#95—221no—
348C2×C11#233911yescharacteristic
349C2×C11C2×#41711yescharacteristic
350C2×C11#289811yescharacteristic
351C2×C11#332411yescharacteristic
352C2×C11#332811yescharacteristic
353C2×C11#335311yescharacteristic
354C2×C11#335611yescharacteristic
355D11—44no—
356C24—112no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—224no—
363C2×Q8—442no—
364C2×Q8—442no—
365C2×Q8C2×C4×D1112yes—
366C2×D4—114no—
367C2×D4—222no—
368C2×D4—222no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—112no—
373C22×C4—114no—
374C22×C4—114no—
375C22×C4—222no—
376C22×C4—222no—
377C22×C4—222no—
378C22×C4—222no—
379C22×C4—221no—
380C22×C4—222no—
381C22×C4—221no—
382C22×C4—444no—
383C22×C4—444no—
384C22×C4—882no—
385C22×C4D4×D1111yescharacteristic
386C22×C4D4×D1111yescharacteristic
387C22×C4C23×D1111yescharacteristic
388M16—448no—
389C2×C8—22no—
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—112no—
393C2×C8—221no—
394C2×C8—221no—
395C2×C8—221no—
396C2×C8—221no—
397C2×C8—221no—
398C4⋊C4—24no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—42no—
403C4⋊C4—81no—
404C4⋊C4—114no—
405C4⋊C4—114no—
406C4⋊C4—112no—
407C4⋊C4—228no—
408C4⋊C4—224no—
409C4⋊C4—222no—
410C4⋊C4—221no—
411C4⋊C4—221no—
412C4⋊C4—221no—
413C4⋊C4—444no—
414C4⋊C4C2×C4×D1112yes—
415C22⋊C4—118no—
416C22⋊C4—228no—
417C22⋊C4—228no—
418C22⋊C4—444no—
419C42—24no—
420C42—228no—
421C42—442no—
422C42C2×C4×D1112yes—
423C42D4×D1112yes—
424C11#2250411yescharacteristic, complemented, Sylow
425C23—114no—
426C23—222no—
427C23—222no—
428C23—222no—
429C23—222no—
430C23—222no—
431C23—222no—
432C23C2×D4×D1111yescharacteristic
433Q8—22no—
434Q8—22no—
435Q8—41no—
436Q8—41no—
437Q8—448no—
438D4—228no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—114no—
451C2×C4—222no—
452C2×C4—222no—
453C2×C4—224no—
454C2×C4—224no—
455C2×C4—224no—
456C2×C4—224no—
457C2×C4—224no—
458C2×C4—222no—
459C2×C4—441no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4—441no—
463C2×C4—441no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—888no—
467C2×C4C22⋊C4×D1112yes—
468C2×C4C22⋊C4×D1112yes—
469C2×C4#6696712yes—
470C2×C4#6697112yes—
471C2×C4C22×C4×D1111yescharacteristic
472C2×C4C2×D4×D1111yescharacteristic
473C2×C4#6703711yescharacteristic
474C2×C4#6704011yescharacteristic
475C2×C4#41×D1111yescharacteristic
476C2×C4#41×D1111yescharacteristic
477C8—42no—
478C8—222no—
479C8—441no—
480C22—224no—
481C22—224no—
482C22—224no—
483C22—442no—
484C22—442no—
485C22—442no—
486C22—442no—
487C22C2×C22⋊C4×D1111yescharacteristic
488C22#1062314311yescharacteristic
489C22#1062316211yescharacteristic
490C22C2×#6696711yescharacteristic
491C22C2×#6697111yescharacteristic
492C22#1062330611yescharacteristic
493C22#1062331011yescharacteristic
494C4—22no—
495C4—42no—
496C4—42no—
497C4—82no—
498C4—224no—
499C4—442no—
500C4—444no—
501C4—881no—
502C4#1062241614yes—
503C4#1062303511yescharacteristic
504C4#1062305311yescharacteristic
505C4#1062314311yescharacteristic
506C4#1062316211yescharacteristic
507C2—444no—
508C2#1307144411yescharacteristic
509C2C2×#1062241611yescharacteristic
510C2#1307714711yescharacteristic
511C2#1308085011yescharacteristic
512C2#1308090211yescharacteristic
513C2#1308120311yescharacteristic
514C2#1308123411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1803C2
socleC23×C11C22×D4
prime radicalC22×D44D4
cosocleC22×C4×C11C24
hypercenter#1803D11
hypocenterC11#22504
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
4. #13069576C2semidirect
5. #13069567C2semidirect
6. #13069046C2semidirect
7. #13068920C2semidirect
8. #13068709C2semidirect
9. C4×#66899C2semidirect
10. #13068334C2semidirect
11. C11×#1803C2semidirect
16. #10623115C4semidirect
51. C4×Q8×C11C2×C4semidirect
60. #66999C2×C4semidirect
82. #66945C2×C4semidirect
89. #66922C2×C4semidirect
176. #1803D11semidirect
312. C4×Q8C4×D11semidirect
424. C11#22504semidirect

Maximal subgroups

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

subgroupindex
C2×#106231152
C2×#106224512
#130715162
#130695762
#130695672
#130690462
#130689202
#130687092
C4×#668992
#130683342
C11×#18032
#2250411