Finite Group Databasebeta

← #14762830

Subgroups — #14762830

Order 2816.

1538 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66950C211yesmaximal, characteristic
2C2×#10622339C211yesmaximal, characteristic
3D11×#380C211yesmaximal, characteristic
4#13069048C214yesmaximal, complemented
5#13068922C214yesmaximal, complemented
6#13068702C211yesmaximal, characteristic, complemented
7#13068552C211yesmaximal, characteristic, complemented
8#13068550C211yesmaximal, characteristic, complemented
9C11×#1823C211yesmaximal, characteristic, complemented
10C23×C4×D11C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×(C2×D11)⋊C4—21no—
14C22×C4⋊Dic11—21no—
15C22×#4313C2212yes—
16C2×#66950—21no—
17C2×#66950—21no—
18C2×#66950—24no—
19C2×#66950C418yescomplemented
20C2×#66950C2212yes—
21C2×#66950C2212yes—
22C2×C4⋊C4×D11C2212yes—
23C2×C22⋊C4×D11—21no—
24C2×C11×C22⋊C8C2211yescharacteristic
25C11×#380C2211yescharacteristic
26#10622825C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×(C2×D11)⋊C8C2212yes—
29C2×#66880C2214yescomplemented
30#10622600C2212yes—
31C2×#66874C2214yescomplemented
32#10622555—21no—
33#10622339—24no—
34#10622280—21no—
35D11×#95—21no—
36C11×#340C2214yescomplemented
37#10622167C2214yescomplemented
38C24×D11D411yescharacteristic
39C23×C4×C11—21no—
40C23×C4×C11C2311yescharacteristic
41C23×Dic11—21no—
42C23×Dic11D411yescharacteristic
43C22×C4×D11—22no—
44C22×C4×D11—44no—
45C22×C4×D11C2×C414yes—
46C22×C4×D11D411yescharacteristic
47C22×C4×D11D411yescharacteristic
48C22×C4×D11D414yes—
49C22×C4×D11C2311yescharacteristic
50C22×C4×D11C2311yescharacteristic
51C22×Dic22—21no—
52C22×Dic22—22no—
53C22×Dic22—44no—
54C22×Dic22C2×C414yescomplemented
55C22×Dic22C2312yes—
56C22×C8×C11C2312yes—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4C2×C414yescomplemented
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C22⋊C4—21no—
63C2×C22⋊Dic11—21no—
64C2×(C2×D11)⋊C4—28no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4—22no—
68C2×C4⋊Dic11—28no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11C2312yes—
72C2×Dic11⋊C4—22no—
73C22×C11⋊C8C2312yes—
74C2×#4313—24no—
75C2×#4313—44no—
76#66950—28no—
77#66950—28no—
78#66950—24no—
79#66950—24no—
80#66950C2×C418yes—
81#66950C2×C418yescomplemented
82C4⋊C4×D11—44no—
83C22⋊C4×D11—44no—
84C11×C22⋊C8—22no—
85C11×#95—21no—
86C11⋊#95—21no—
87C11⋊#95—22no—
88C22⋊(C11⋊C8)—22no—
89(C2×D11)⋊C8—24no—
90#66880—44no—
91#66874—44no—
92#21765—111nomaximal, Sylow
93C24×C11C2×D411yescharacteristic
94C23×D11—22no—
95C23×D11—22no—
96C23×D11—24no—
97C23×D11—42no—
98C23×D11C22⋊C414yes—
99C23×D11C2×D411yescharacteristic
100C23×D11C2×D411yescharacteristic
101C22×C4×C11—24no—
102C22×C4×C11—24no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11C22×C412yes—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2411yescharacteristic
111C22×Dic11—24no—
112C22×Dic11—22no—
113C22×Dic11—22no—
114C22×Dic11—42no—
115C22×Dic11—44no—
116C22×Dic11C22⋊C414yes—
117C22×Dic11C2×D411yescharacteristic
118C22×Dic11C2×D411yescharacteristic
119C2×C4×D11—24no—
120C2×C4×D11—24no—
121C2×C4×D11—42no—
122C2×C4×D11—42no—
123C2×C4×D11—48no—
124C2×C4×D11—48no—
125C2×C4×D11—44no—
126C2×C4×D11—44no—
127C2×C4×D11—44no—
128C2×C4×D11C22⋊C414yes—
129C2×C4×D11C22⋊C414yes—
130C2×C4×D11C22×C412yes—
131C2×C4×D11C22×C412yes—
132C2×C4×D11C2×D412yes—
133C2×C4×D11C2×D412yes—
134C2×Dic22—24no—
135C2×Dic22—22no—
136C2×Dic22—24no—
137C2×Dic22—24no—
138C2×Dic22—48no—
139C2×Dic22—44no—
140C2×Dic22—48no—
141C2×Dic22C22×C414yes—
142C2×C8×C11—22no—
143C2×C8×C11—24no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4C22×C414yes—
148C11×C22⋊C4—42no—
149C22⋊Dic11—42no—
150(C2×D11)⋊C4—28no—
151(C2×D11)⋊C4—28no—
152(C2×D11)⋊C4—44no—
153C4⋊Dic11—28no—
154C4⋊Dic11—28no—
155C4⋊Dic11—24no—
156Dic11⋊C4—44no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—24no—
159#4313—48no—
160C22×C22⋊Q8—111no—
161C2×#407—111no—
162C2×#380—111no—
163#1894—114no—
164#1872—114no—
165#1823—111no—
166#1823D1111yescharacteristic, complemented
167#1787—111no—
168#1787—111no—
169C23×C11—22no—
170C23×C11—22no—
171C23×C11C2×C22⋊C412yes—
172C23×C11AGL(1,ℤ/8)12yes—
173C23×C11#13712yes—
174C23×C11C22×D411yescharacteristic
175C22×D11—22no—
176C22×D11—21no—
177C22×D11—21no—
178C22×D11—22no—
179C22×D11—21no—
180C22×D11—21no—
181C22×D11—22no—
182C22×D11—28no—
183C22×D11—28no—
184C22×D11—44no—
185C22×D11—48no—
186C22×D11—48no—
187C22×D11C2×C22⋊C412yes—
188C22×D11C2×C22⋊C412yes—
189C22×D11#13714yes—
190C2×C4×C11—22no—
191C2×C4×C11—24no—
192C2×C4×C11—24no—
193C2×C4×C11—24no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—48no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11C2×C22⋊C412yes—
201C2×C4×C11C23×C411yescharacteristic
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11H(5,𝔽2)14yes—
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—24no—
207C2×Dic11—44no—
208C2×Dic11—48no—
209C2×Dic11—44no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11C2×C22⋊C412yes—
214C2×Dic11C2×C22⋊C412yes—
215C4×D11—24no—
216C4×D11—24no—
217C4×D11—24no—
218C4×D11—24no—
219C4×D11—44no—
220C4×D11—44no—
221C4×D11—88no—
222Dic22—24no—
223Dic22—24no—
224Dic22—48no—
225Dic22—44no—
226C8×C11—42no—
227C11⋊C8—42no—
228C23×Q8—111no—
229C24×C4—111no—
230C22×M16—112no—
231C2×C22⋊Q8—112no—
232C2×C22⋊Q8—112no—
233C2×C22⋊Q8—118no—
234C2×C22⋊Q8—221no—
235C2×C22⋊Q8—221no—
236C2×C22⋊Q8—224no—
237C22×C4⋊C4—112no—
238C22×C4⋊C4—221no—
239C22×C4⋊C4C2×D1111yescharacteristic
240C22×C22⋊C4—221no—
241C22×C22⋊C4—221no—
242C2×#103—114no—
243C2×#103—114no—
244#407—224no—
245C2×C22⋊C8—111no—
246C2×C22⋊C8—112no—
247C2×C22⋊C8C2×D1111yescharacteristic
248#380—111no—
249#380—112no—
250#380—221no—
251#380—221no—
252#380C2×D1111yescharacteristic
253C2×#95—221no—
254#340—114no—
255#340C2×D1114yescomplemented
256C22×C11—22no—
257C22×C11—22no—
258C22×C11—24no—
259C22×C11—24no—
260C22×C11#41714yes—
261C22×C11C22×C22⋊C411yescharacteristic
262C22×C11#53412yes—
263C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
264C22×C11C2×#13711yescharacteristic
265C22×C11C2×#13712yes—
266C2×D11—22no—
267C2×D11—22no—
268C2×D11—24no—
269C2×D11—24no—
270C2×D11—22no—
271C2×D11—22no—
272C2×D11—22no—
273C2×D11—416no—
274C2×D11—42no—
275C2×D11—42no—
276C2×D11#41914yes—
277C4×C11—22no—
278C4×C11—44no—
279C4×C11—82no—
280C4×C11#51812yes—
281C4×C11#53412yes—
282Dic11—22no—
283Dic11—22no—
284Dic11—44no—
285Dic11—82no—
286C25—111no—
287C22×Q8—114no—
288C22×Q8—112no—
289C22×Q8—222no—
290C22×Q8—221no—
291C22×Q8—444no—
292C23×C4—21no—
293C23×C4—111no—
294C23×C4—111no—
295C23×C4—111no—
296C23×C4—114no—
297C23×C4—111no—
298C23×C4—111no—
299C23×C4—114no—
300C23×C4—222no—
301C23×C4—221no—
302C23×C4—444no—
303C23×C4C22×D1111yescharacteristic
304C2×M16—224no—
305C2×M16—444no—
306C22×C8—112no—
307C22×C8C22×D1112yes—
308C22⋊Q8—118no—
309C22⋊Q8—118no—
310C22⋊Q8—228no—
311C22⋊Q8—228no—
312C22⋊Q8—224no—
313C22⋊Q8—224no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—112no—
317C2×C4⋊C4—228no—
318C2×C4⋊C4—222no—
319C2×C4⋊C4—222no—
320C2×C4⋊C4—222no—
321C2×C4⋊C4—444no—
322C2×C4⋊C4C4×D1114yescomplemented
323C2×C4⋊C4C22×D1112yes—
324C2×C4⋊C4C22×D1112yes—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—228no—
327C2×C22⋊C4—222no—
328C2×C22⋊C4—222no—
329C2×C22⋊C4—222no—
330C2×C22⋊C4—221no—
331C2×C22⋊C4—444no—
332#103—444no—
333#103—444no—
334C22⋊C8—22no—
335C22⋊C8—224no—
336C22⋊C8—222no—
337#95—21no—
338#95—222no—
339#95—221no—
340C2×C11—24no—
341C2×C11#230811yescharacteristic
342C2×C11C2×#41911yescharacteristic
343C2×C11C2×#41711yescharacteristic
344C2×C11#319312yes—
345C2×C11#319512yes—
346D11—24no—
347D11—42no—
348C24—111no—
349C24—111no—
350C24—114no—
351C24—224no—
352C24—222no—
353C24—222no—
354C24—442no—
355C24D4×D1111yescharacteristic
356C2×Q8—114no—
357C2×Q8—224no—
358C2×Q8—222no—
359C2×Q8—224no—
360C2×Q8—224no—
361C2×Q8—448no—
362C2×Q8—444no—
363C2×Q8—448no—
364C22×C4—24no—
365C22×C4—24no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—42no—
369C22×C4—42no—
370C22×C4—111no—
371C22×C4—111no—
372C22×C4—114no—
373C22×C4—112no—
374C22×C4—112no—
375C22×C4—112no—
376C22×C4—112no—
377C22×C4—114no—
378C22×C4—114no—
379C22×C4—224no—
380C22×C4—224no—
381C22×C4—224no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—448no—
385C22×C4—448no—
386C22×C4—442no—
387C22×C4—442no—
388C22×C4—444no—
389C22×C4—444no—
390C22×C4—444no—
391C22×C4—442no—
392C22×C4—444no—
393C22×C4C2×C4×D1112yes—
394C22×C4D4×D1111yescharacteristic
395C22×C4D4×D1112yes—
396C22×C4C23×D1111yescharacteristic
397M16—448no—
398C2×C8—22no—
399C2×C8—24no—
400C2×C8—222no—
401C2×C8—224no—
402C4⋊C4—24no—
403C4⋊C4—22no—
404C4⋊C4—24no—
405C4⋊C4—228no—
406C4⋊C4—228no—
407C4⋊C4—224no—
408C4⋊C4—444no—
409C4⋊C4C2×C4×D1114yes—
410C22⋊C4—42no—
411C22⋊C4—228no—
412C22⋊C4—228no—
413C22⋊C4—444no—
414C22⋊C4—442no—
415C11#2176511yescharacteristic, complemented, Sylow
416C23—22no—
417C23—22no—
418C23—112no—
419C23—114no—
420C23—112no—
421C23—228no—
422C23—221no—
423C23—221no—
424C23—222no—
425C23—221no—
426C23—221no—
427C23—222no—
428C23—228no—
429C23—222no—
430C23—444no—
431C23—448no—
432C23—448no—
433C23C22⋊C4×D1112yes—
434C23#6696412yes—
435C23#6696812yes—
436C23C2×D4×D1111yescharacteristic
437Q8—224no—
438Q8—224no—
439Q8—448no—
440Q8—444no—
441C2×C4—22no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—48no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—112no—
452C2×C4—112no—
453C2×C4—222no—
454C2×C4—222no—
455C2×C4—224no—
456C2×C4—224no—
457C2×C4—224no—
458C2×C4—224no—
459C2×C4—224no—
460C2×C4—444no—
461C2×C4—444no—
462C2×C4—444no—
463C2×C4—448no—
464C2×C4—444no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4—442no—
468C2×C4—888no—
469C2×C4C22⋊C4×D1112yes—
470C2×C4C22×C4×D1111yescharacteristic
471C2×C4C2×D4×D1111yescharacteristic
472C2×C4#6704214yes—
473C8—42no—
474C8—442no—
475C22—22no—
476C22—22no—
477C22—24no—
478C22—24no—
479C22—114no—
480C22—222no—
481C22—224no—
482C22—222no—
483C22—224no—
484C22—222no—
485C22—222no—
486C22—222no—
487C22—4416no—
488C22—442no—
489C22—442no—
490C22#1062238414yes—
491C22C2×C22⋊C4×D1111yescharacteristic
492C22#1062318412yes—
493C22C2×#6696411yescharacteristic
494C22C2×#6696811yescharacteristic
495C22D11×#13712yes—
496C4—22no—
497C4—44no—
498C4—82no—
499C4—222no—
500C4—222no—
501C4—444no—
502C4—882no—
503C4#1062305212yes—
504C4#1062318412yes—
505C2—24no—
506C2—224no—
507C2—442no—
508C2#1307119311yescharacteristic
509C2D11×#41911yescharacteristic
510C2C2×#1062238411yescharacteristic
511C2#1307942412yes—
512C2#1307943912yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1823C2
socleC23×C11C22×D4
prime radicalC24×D11D4
cosocleC22×C4×C11C24
hypercenter#1823D11
hypocenterC11#21765
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
4. #13069048C2semidirect
5. #13068922C2semidirect
6. #13068702C2semidirect
7. #13068552C2semidirect
8. #13068550C2semidirect
9. C11×#1823C2semidirect
19. C2×#66950C4semidirect
29. C2×#66880C22semidirect
31. C2×#66874C22semidirect
36. C11×#340C22semidirect
37. #10622167C22semidirect
54. C22×Dic22C2×C4semidirect
59. C2×C11×C4⋊C4C2×C4semidirect
81. #66950C2×C4semidirect
166. #1823D11semidirect
255. #340C2×D11semidirect
322. C2×C4⋊C4C4×D11semidirect
415. C11#21765semidirect

Maximal subgroups

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

subgroupindex
C22×#669502
C2×#106223392
D11×#3802
#130690482
#130689222
#130687022
#130685522
#130685502
C11×#18232
#2176511