Finite Group Databasebeta

← #14764002

Subgroups — #14764002

Order 2816.

1258 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622339C211yesmaximal, characteristic
2C22×(C2×D11)⋊C8C211yesmaximal, characteristic
3C4×C22⋊C4×D11C211yesmaximal, characteristic
4#13068800C212yesmaximal, complemented
5#13068797C212yesmaximal, complemented
6#13068796C211yesmaximal, characteristic, complemented
7#13068794C211yesmaximal, characteristic, complemented
8#13068793C211yesmaximal, characteristic, complemented
9#13068595C212yesmaximal, complemented
10#13068593C212yesmaximal, complemented
11C11×#1850C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C23×C11⋊C8C2211yescharacteristic
15C22×#4313C2211yescharacteristic
16C22×#4313C2211yescharacteristic
17C2×C22⋊C4×D11C411yescharacteristic
18C2×C22⋊C4×D11C411yescharacteristic
19C2×C42×D11C2212yes—
20C2×C11×C4⋊C8C2212yescomplemented
21C2×C11×C22⋊C8C2211yescharacteristic
22C4×C11×C22⋊C4C2211yescharacteristic
23C4×C22⋊Dic11C2211yescharacteristic
24C2×C22⋊(C11⋊C8)C2211yescharacteristic
25C2×(C2×D11)⋊C8—24no—
26C2×(C2×D11)⋊C8C2212yes—
27C2×(C2×D11)⋊C8C2211yescharacteristic
28C2×(C2×D11)⋊C8C2212yes—
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2212yescomplemented
31C2×Dic11⋊C8C2212yescomplemented
32C22⋊C4×Dic11C411yescharacteristic
33C22⋊C4×Dic11C411yescharacteristic
34C4×(C2×D11)⋊C4C2212yes—
35C2×C4⋊(C11⋊C8)C2212yescomplemented
36#10622339—24no—
37#10622279C412yes—
38D11×#95C412yes—
39C11×#336C2212yescomplemented
40#10622188C2212yescomplemented
41#10622188C2212yescomplemented
42#10622162C2212yescomplemented
43C24×D11C2×C411yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×Dic11C2×C411yescharacteristic
46C22×C4×D11—42no—
47C22×C4×D11—42no—
48C22×C4×D11C2×C412yes—
49C22×C4×D11C2×C412yes—
50C22×C4×D11C2×C411yescharacteristic
51C22×C4×D11C2×C411yescharacteristic
52C22×C4×D11D414yes—
53C22×C4×D11Q814yes—
54C22×C4×D11C2311yescharacteristic
55C22×C4×D11C2311yescharacteristic
56C22×C8×C11—22no—
57C22×C8×C11—42no—
58C22×C8×C11C2312yes—
59C22×C8×C11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C2×C11×C22⋊C4C2×C411yescharacteristic
62C2×C11×C22⋊C4C2×C411yescharacteristic
63C2×C42×C11C2312yes—
64C2×C22⋊Dic11C2×C411yescharacteristic
65C2×C22⋊Dic11C2×C411yescharacteristic
66C2×(C2×D11)⋊C4C2×C412yes—
67C2×(C2×D11)⋊C4C2×C412yes—
68C2×C4×Dic11C2×C412yes—
69C2×C4×Dic11C2×C412yes—
70C2×C4×Dic11C2312yes—
71C22×C11⋊C8—22no—
72C22×C11⋊C8—42no—
73C22×C11⋊C8C2312yes—
74C22×C11⋊C8C2311yescharacteristic
75C22×C11⋊C8C2311yescharacteristic
76C2×#4313—22no—
77C2×#4313—22no—
78C2×#4313—42no—
79C2×#4313—42no—
80C22⋊C4×D11—24no—
81C22⋊C4×D11—24no—
82C42×D11—42no—
83C42×D11—42no—
84C11×C4⋊C8—42no—
85C11×C22⋊C8—22no—
86C11×#95C2×C412yes—
87C11⋊#95C2×C412yes—
88C11⋊#95C2×C412yes—
89C11⋊#95C2×C412yes—
90C22⋊(C11⋊C8)—22no—
91(C2×D11)⋊C8—24no—
92(C2×D11)⋊C8—24no—
93(C2×D11)⋊C8—22no—
94(C2×D11)⋊C8—22no—
95Dic11⋊C8—42no—
96Dic11⋊C8—42no—
97C4⋊(C11⋊C8)—42no—
98#21932—111nomaximal, Sylow
99C24×C11C22×C411yescharacteristic
100C23×D11—22no—
101C23×D11—22no—
102C23×D11—24no—
103C23×D11—42no—
104C23×D11C4⋊C414yes—
105C23×D11C22×C411yescharacteristic
106C23×D11C22×C411yescharacteristic
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11C22×C412yes—
110C22×C4×C11C22×C411yescharacteristic
111C22×C4×C11C22×C412yes—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×Q812yes—
114C22×C4×C11C2411yescharacteristic
115C22×Dic11—42no—
116C22×Dic11C4⋊C414yes—
117C22×Dic11C22×C412yes—
118C22×Dic11C22×C411yescharacteristic
119C22×Dic11C22×C411yescharacteristic
120C22×Dic11C22×C412yes—
121C2×C4×D11—24no—
122C2×C4×D11—24no—
123C2×C4×D11—24no—
124C2×C4×D11—24no—
125C2×C4×D11—22no—
126C2×C4×D11—22no—
127C2×C4×D11—22no—
128C2×C4×D11—22no—
129C2×C4×D11—42no—
130C2×C4×D11—42no—
131C2×C4×D11—42no—
132C2×C4×D11—42no—
133C2×C4×D11—44no—
134C2×C4×D11—44no—
135C2×C4×D11—48no—
136C2×C4×D11C4⋊C414yes—
137C2×C4×D11C4⋊C414yes—
138C2×C4×D11C2×D412yes—
139C2×C4×D11C2×D412yes—
140C2×C4×D11C2×Q812yes—
141C2×C4×D11C2×Q812yes—
142C2×C8×C11—22no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—44no—
150C11×C22⋊C4—22no—
151C11×C22⋊C4M1614yescomplemented
152C42×C11—22no—
153C42×C11—22no—
154C22⋊Dic11—22no—
155C22⋊Dic11M1614yescomplemented
156(C2×D11)⋊C4—24no—
157(C2×D11)⋊C4—24no—
158C4×Dic11—22no—
159C4×Dic11—22no—
160C4×Dic11—42no—
161C4×Dic11—42no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—44no—
170#4313—44no—
171#4313—44no—
172C2×#407—111no—
173C22×C22⋊C8—111no—
174C2×C4×C22⋊C4—111no—
175#1851—112no—
176#1851—112no—
177#1850—111no—
178#1850—111no—
179#1850—111no—
180#1850D1111yescharacteristic, complemented
181#1797—112no—
182#1797—112no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11C2×C4⋊C412yes—
186C23×C11C2×M1612yes—
187C23×C11C2×M1612yes—
188C23×C11C23×C411yescharacteristic
189C22×D11—22no—
190C22×D11—21no—
191C22×D11—21no—
192C22×D11—22no—
193C22×D11—21no—
194C22×D11—21no—
195C22×D11—22no—
196C22×D11—28no—
197C22×D11—28no—
198C22×D11—44no—
199C22×D11—48no—
200C22×D11—48no—
201C22×D11C2×C4⋊C412yes—
202C22×D11C2×C4⋊C412yes—
203C22×D11#13114yes—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—24no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11C2×C4⋊C412yes—
214C2×C4×C11C2×M1614yes—
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C22×Q811yescharacteristic
217C2×C4×C11H(5,𝔽2)12yes—
218C2×C4×C11H(5,𝔽2)12yes—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—44no—
227C2×Dic11C2×C4⋊C412yes—
228C2×Dic11C2×C4⋊C412yes—
229C2×Dic11C2×M1614yes—
230C4×D11—22no—
231C4×D11—22no—
232C4×D11—22no—
233C4×D11—22no—
234C4×D11—24no—
235C4×D11—24no—
236C4×D11—44no—
237C4×D11—44no—
238C4×D11—48no—
239C4×D11—48no—
240C8×C11—41no—
241C8×C11—41no—
242C8×C11—42no—
243C11⋊C8—41no—
244C11⋊C8—41no—
245C11⋊C8—42no—
246C24×C4—111no—
247C22×M16—111no—
248C22×M16—111no—
249C23×C8—111no—
250C23×C8C2×D1111yescharacteristic
251C22×C22⋊C4—111no—
252C22×C22⋊C4—111no—
253C22×C42—112no—
254C2×C4⋊C8—112no—
255C2×C4⋊C8—112no—
256C2×C4⋊C8—112no—
257C2×C4⋊C8C2×D1112yescomplemented
258#407—224no—
259C2×C22⋊C8—111no—
260C2×C22⋊C8—112no—
261C2×C22⋊C8—111no—
262C2×C22⋊C8—111no—
263C2×C22⋊C8—112no—
264C2×C22⋊C8—224no—
265C2×C22⋊C8C2×D1111yescharacteristic
266C4×C22⋊C4—111no—
267C4×C22⋊C4—111no—
268C4×C22⋊C4—111no—
269C4×C22⋊C4—112no—
270C4×C22⋊C4—112no—
271C4×C22⋊C4C2×D1111yescharacteristic
272C2×#95—112no—
273#336—112no—
274#336—112no—
275#336—112no—
276#336C2×D1112yescomplemented
277C22×C11—22no—
278C22×C11—22no—
279C22×C11—24no—
280C22×C11—24no—
281C22×C11#42314yes—
282C22×C11C22×C4⋊C411yescharacteristic
283C22×C11#51812yes—
284C22×C11C22×M1611yescharacteristic
285C22×C11C22×M1611yescharacteristic
286C22×C11C2×#13112yes—
287C2×D11—22no—
288C2×D11—22no—
289C2×D11—24no—
290C2×D11—24no—
291C2×D11—22no—
292C2×D11—22no—
293C2×D11—22no—
294C2×D11—416no—
295C2×D11—42no—
296C2×D11—42no—
297C2×D11#42414yes—
298C4×C11—22no—
299C4×C11—24no—
300C4×C11—42no—
301C4×C11#53411yescharacteristic
302C4×C11#53411yescharacteristic
303C4×C11#54312yes—
304Dic11—22no—
305Dic11—22no—
306Dic11—24no—
307Dic11—42no—
308C25—111no—
309C23×C4—111no—
310C23×C4—111no—
311C23×C4—111no—
312C23×C4—111no—
313C23×C4—111no—
314C23×C4—114no—
315C23×C4—114no—
316C23×C4—112no—
317C23×C4—112no—
318C23×C4—442no—
319C23×C4—442no—
320C23×C4C22×D1111yescharacteristic
321C2×M16—222no—
322C2×M16—222no—
323C2×M16—442no—
324C2×M16—442no—
325C22×C8—22no—
326C22×C8—42no—
327C22×C8—112no—
328C22×C8—111no—
329C22×C8—111no—
330C22×C8—222no—
331C22×C8—442no—
332C22×C8C22×D1112yes—
333C22×C8C22×D1111yescharacteristic
334C22×C8C22×D1111yescharacteristic
335C2×C22⋊C4—111no—
336C2×C22⋊C4—111no—
337C2×C22⋊C4—112no—
338C2×C22⋊C4—112no—
339C2×C22⋊C4—224no—
340C2×C22⋊C4—224no—
341C2×C22⋊C4C4×D1111yescharacteristic
342C2×C22⋊C4C4×D1111yescharacteristic
343C2×C42—112no—
344C2×C42—112no—
345C2×C42—112no—
346C2×C42—442no—
347C2×C42—442no—
348C2×C42C22×D1112yes—
349C4⋊C8—42no—
350C4⋊C8—442no—
351C4⋊C8—442no—
352C4⋊C8—442no—
353C22⋊C8—22no—
354C22⋊C8—224no—
355C22⋊C8—224no—
356C22⋊C8—222no—
357C22⋊C8—222no—
358C22⋊C8—222no—
359#95—112no—
360#95—112no—
361#95—112no—
362#95C4×D1112yes—
363C2×C11—24no—
364C2×C11#231511yescharacteristic
365C2×C11C2×#42311yescharacteristic
366C2×C11C2×#42411yescharacteristic
367C2×C11#297412yes—
368C2×C11#297412yes—
369D11—24no—
370D11—42no—
371C24—111no—
372C24—111no—
373C24—114no—
374C24—224no—
375C24—222no—
376C24—222no—
377C24—442no—
378C24C2×C4×D1111yescharacteristic
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—111no—
382C22×C4—112no—
383C22×C4—111no—
384C22×C4—114no—
385C22×C4—112no—
386C22×C4—112no—
387C22×C4—112no—
388C22×C4—112no—
389C22×C4—114no—
390C22×C4—114no—
391C22×C4—112no—
392C22×C4—224no—
393C22×C4—224no—
394C22×C4—224no—
395C22×C4—222no—
396C22×C4—222no—
397C22×C4—222no—
398C22×C4—222no—
399C22×C4—224no—
400C22×C4—444no—
401C22×C4—448no—
402C22×C4—444no—
403C22×C4—442no—
404C22×C4—442no—
405C22×C4—442no—
406C22×C4—442no—
407C22×C4—442no—
408C22×C4C2×C4×D1112yes—
409C22×C4C2×C4×D1111yescharacteristic
410C22×C4C2×C4×D1112yes—
411C22×C4D4×D1112yes—
412C22×C4Q8×D1112yes—
413C22×C4C23×D1111yescharacteristic
414M16—444no—
415M16—444no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—22no—
419C2×C8—22no—
420C2×C8—22no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—44no—
424C2×C8—222no—
425C2×C8—221no—
426C2×C8—221no—
427C2×C8—222no—
428C2×C8—222no—
429C2×C8—222no—
430C2×C8—222no—
431C2×C8—444no—
432C22⋊C4—22no—
433C22⋊C4—114no—
434C22⋊C4—224no—
435C22⋊C4—222no—
436C22⋊C4—224no—
437C22⋊C4#431314yescomplemented
438C42—22no—
439C42—22no—
440C42—222no—
441C42—222no—
442C42—442no—
443C42—442no—
444C11#2193211yescharacteristic, complemented, Sylow
445C23—22no—
446C23—22no—
447C23—114no—
448C23—112no—
449C23—112no—
450C23—228no—
451C23—221no—
452C23—221no—
453C23—222no—
454C23—221no—
455C23—221no—
456C23—222no—
457C23—222no—
458C23—228no—
459C23—444no—
460C23—448no—
461C23—448no—
462C23C4⋊C4×D1112yes—
463C23C2×#431312yes—
464C23M16×D1112yes—
465C23C22×C4×D1111yescharacteristic
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—24no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—114no—
476C2×C4—112no—
477C2×C4—112no—
478C2×C4—222no—
479C2×C4—222no—
480C2×C4—222no—
481C2×C4—222no—
482C2×C4—222no—
483C2×C4—222no—
484C2×C4—224no—
485C2×C4—224no—
486C2×C4—222no—
487C2×C4—222no—
488C2×C4—222no—
489C2×C4—222no—
490C2×C4—222no—
491C2×C4—444no—
492C2×C4—444no—
493C2×C4—448no—
494C2×C4—448no—
495C2×C4—444no—
496C2×C4C4⋊C4×D1112yes—
497C2×C4C2×#431314yes—
498C2×C4C2×D4×D1111yescharacteristic
499C2×C4#6703712yes—
500C2×C4C2×Q8×D1111yescharacteristic
501C2×C4#6704212yes—
502C8—42no—
503C8—41no—
504C8—41no—
505C8—441no—
506C8—442no—
507C8—441no—
508C22—22no—
509C22—24no—
510C22—24no—
511C22—22no—
512C22—114no—
513C22—222no—
514C22—224no—
515C22—224no—
516C22—222no—
517C22—222no—
518C22—222no—
519C22—222no—
520C22—4416no—
521C22—442no—
522C22—442no—
523C22#1062245014yes—
524C22C2×C4⋊C4×D1111yescharacteristic
525C22#1062307612yes—
526C22C22×#431311yescharacteristic
527C22C2×M16×D1111yescharacteristic
528C22D11×#13112yes—
529C4—22no—
530C4—24no—
531C4—42no—
532C4—222no—
533C4—222no—
534C4—224no—
535C4—442no—
536C4#1062312011yescharacteristic
537C4#1062316512yes—
538C4#1062318411yescharacteristic
539C2—24no—
540C2—224no—
541C2—442no—
542C2#1307122711yescharacteristic
543C2C2×#1062245011yescharacteristic
544C2D11×#42411yescharacteristic
545C2#1307764612yes—
546C2#1307764912yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1850C2
prime radicalC24×D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1850D11
hypocenterC11#21932
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
4. #13068800C2semidirect
5. #13068797C2semidirect
6. #13068796C2semidirect
7. #13068794C2semidirect
8. #13068793C2semidirect
9. #13068595C2semidirect
10. #13068593C2semidirect
11. C11×#1850C2semidirect
20. C2×C11×C4⋊C8C22semidirect
30. C2×Dic11⋊C8C22semidirect
31. C2×Dic11⋊C8C22semidirect
35. C2×C4⋊(C11⋊C8)C22semidirect
39. C11×#336C22semidirect
40. #10622188C22semidirect
41. #10622188C22semidirect
42. #10622162C22semidirect
151. C11×C22⋊C4M16semidirect
155. C22⋊Dic11M16semidirect
180. #1850D11semidirect
257. C2×C4⋊C8C2×D11semidirect
276. #336C2×D11semidirect
437. C22⋊C4#4313semidirect
444. C11#21932semidirect

Maximal subgroups

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

subgroupindex
C2×#106223392
C22×(C2×D11)⋊C82
C4×C22⋊C4×D112
#130688002
#130687972
#130687962
#130687942
#130687932
#130685952
#130685932
C11×#18502
#2193211