Finite Group Databasebeta

← #14660271

Subgroups — #14660271

Order 2816.

1778 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66983C211yesmaximal, characteristic
2C22×#66887C212yesmaximal, complemented
3C2×#10622820C211yesmaximal, characteristic, complemented
4C2×#10622192C212yesmaximal, complemented
5C2×C11×#407C211yesmaximal, characteristic, complemented
6C24×C4×C11C2211yescharacteristic
7C23×C22⋊D11C412yes—
8C23×D44C2211yescharacteristic
9C22×C11×M16C2212yes—
10C2×#66983—22no—
11C2×#66983—22no—
12C2×#66983—24no—
13C2×#66983—24no—
14C22×(C2×D11)⋊C4C412yes—
15C22×C4⋊Dic11C2211yescharacteristic
16C22×#4318C2212yes—
17C11×#407—24no—
18C2×C11×C22⋊C8—22no—
19#10622820—24no—
20C2×C22⋊(C11⋊C8)—22no—
21C2×#66887—24no—
22C2×#66887—24no—
23C2×#66887—24no—
24#10622192—24no—
25C25×C11C2×C411yescharacteristic
26C24×D11C2×C412yes—
27C23×C4×C11—22no—
28C23×C4×C11—22no—
29C23×C4×C11—22no—
30C23×C4×C11—22no—
31C23×C4×C11—22no—
32C23×C4×C11—22no—
33C23×C4×C11C2×C411yescharacteristic
34C23×C4×C11D412yes—
35C23×C4×C11D412yes—
36C23×C4×C11C2311yescharacteristic
37C22×C22⋊D11—24no—
38C22×C22⋊D11—24no—
39C22×C22⋊D11—24no—
40C22×C22⋊D11—48no—
41C23×Dic11C2×C412yes—
42C22×D44—22no—
43C22×D44—22no—
44C22×D44—21no—
45C22×D44—22no—
46C22×D44—21no—
47C22×D44—22no—
48C22×D44—22no—
49C22×D44D414yes—
50C2×C11×M16—22no—
51C2×C11×M16—22no—
52C2×C11×M16—22no—
53C2×C11×M16—22no—
54C2×C11×M16—22no—
55C2×C11×M16D414yescomplemented
56C22×C8×C11—22no—
57#66983—216no—
58#66983—216no—
59C2×(C2×D11)⋊C4—24no—
60C2×(C2×D11)⋊C4—24no—
61C2×(C2×D11)⋊C4—24no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11D414yes—
66C2×#4318—22no—
67C2×#4318—22no—
68C2×#4318—22no—
69C2×#4318—22no—
70C2×#4318—22no—
71C2×#4318D414yescomplemented
72C22×C11⋊C8—22no—
73C11×C22⋊C8—28no—
74C22⋊(C11⋊C8)—28no—
75#66887—216no—
76#10967—111nomaximal, Sylow
77C24×C11—24no—
78C24×C11—21no—
79C24×C11—21no—
80C24×C11—22no—
81C24×C11—22no—
82C24×C11—42no—
83C24×C11C22⋊C412yes—
84C24×C11C22×C411yescharacteristic
85C23×D11—22no—
86C23×D11—22no—
87C23×D11—24no—
88C23×D11—24no—
89C23×D11—44no—
90C23×D11—44no—
91C23×D11C22⋊C414yes—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—24no—
99C22×C4×C11—24no—
100C22×C4×C11—24no—
101C22×C4×C11—24no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—42no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11—42no—
112C22×C4×C11C22⋊C412yes—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D412yes—
119C22×C4×C11#4112yes—
120C22×C4×C11#4112yes—
121C2×C22⋊D11—216no—
122C2×C22⋊D11—416no—
123C2×C22⋊D11—48no—
124C2×C22⋊D11—416no—
125C2×C22⋊D11—48no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—44no—
129C22×Dic11C22⋊C414yes—
130C2×D44—24no—
131C2×D44—24no—
132C2×D44—24no—
133C2×D44—24no—
134C2×D44—24no—
135C2×D44—24no—
136C2×D44—41no—
137C2×D44—41no—
138C2×D44—42no—
139C2×D44—42no—
140C2×D44—42no—
141C2×D44—42no—
142C2×D44—41no—
143C2×D44—41no—
144C2×D44—42no—
145C2×D44—42no—
146C11×M16—24no—
147C11×M16—24no—
148C11×M16—42no—
149C11×M16—42no—
150C2×C8×C11—24no—
151C2×C8×C11—42no—
152C2×C8×C11—42no—
153(C2×D11)⋊C4—216no—
154C4⋊Dic11—24no—
155C4⋊Dic11—24no—
156#4318—24no—
157#4318—24no—
158#4318—42no—
159#4318—42no—
160C2×C11⋊C8—24no—
161C2×C11⋊C8—42no—
162C2×C11⋊C8—42no—
163C22×#121—111no—
164C22×#100—112no—
165C2×#407—111no—
166C2×#407D1111yescharacteristic, complemented
167C2×#343—112no—
168C23×C11—22no—
169C23×C11—22no—
170C23×C11—24no—
171C23×C11—24no—
172C23×C11—22no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—22no—
177C23×C11—22no—
178C23×C11—48no—
179C23×C11—48no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11#10014yescomplemented
185C23×C11C2×C22⋊C411yescharacteristic
186C23×C11C2×C22⋊C411yescharacteristic
187C23×C11C2×C22⋊C411yescharacteristic
188C23×C11C4×D412yes—
189C23×C11C4×D412yes—
190C22×D11—24no—
191C22×D11—28no—
192C22×D11—44no—
193C22×D11—44no—
194C22×D11—42no—
195C22×D11—42no—
196C22×D11—44no—
197C22×D11—44no—
198C22×D11—44no—
199C22×D11—44no—
200C22×D11—44no—
201C22×D11—88no—
202C22×D11—88no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—44no—
209C2×C4×C11—44no—
210C2×C4×C11—44no—
211C2×C4×C11—44no—
212C2×C4×C11#12011yescharacteristic
213C2×C4×C11#12012yes—
214C2×C4×C11#12012yes—
215C2×C4×C11#12012yes—
216C2×C4×C11#12011yescharacteristic
217C2×C4×C11#12112yes—
218C2×C4×C11#12112yes—
219C2×C4×C11#12112yes—
220C2×C4×C11#12112yes—
221C2×C4×C11#12112yes—
222C2×C4×C11#12112yes—
223C2×C4×C11#12312yes—
224C2×C4×C11#12311yescharacteristic
225C2×C4×C11#12311yescharacteristic
226C2×C4×C11#12412yes—
227C2×C4×C11#12712yes—
228C22⋊D11—432no—
229C2×Dic11—24no—
230C2×Dic11—44no—
231C2×Dic11—44no—
232C2×Dic11—44no—
233D44—44no—
234D44—44no—
235D44—44no—
236D44—44no—
237C8×C11—44no—
238C11⋊C8—44no—
239C23×D4—112no—
240C23×D4—111no—
241C24×C4C2×D1111yescharacteristic
242C22×M16—112no—
243C22×M16C2×D1112yes—
244C2×#121—224no—
245C2×#121—224no—
246C2×#121—222no—
247C2×#121—222no—
248C22×C4⋊C4—111no—
249C22×C22⋊C4—112no—
250C2×#100—224no—
251C2×#100—224no—
252C2×#100—224no—
253#407—24no—
254#407—224no—
255C2×C22⋊C8—22no—
256C2×C22⋊C8—222no—
257#343—224no—
258C22×C11—24no—
259C22×C11—24no—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—24no—
265C22×C11—24no—
266C22×C11—24no—
267C22×C11—48no—
268C22×C11—48no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11#37911yescharacteristic
274C22×C11#38612yes—
275C22×C11#38611yescharacteristic
276C22×C11#38611yescharacteristic
277C22×C11#39012yes—
278C22×C11C2×#10012yes—
279C22×C11#41312yes—
280C2×D11—44no—
281C2×D11—44no—
282C2×D11—44no—
283C2×D11—88no—
284C2×D11—84no—
285C2×D11—84no—
286C2×D11—88no—
287C4×C11—42no—
288C4×C11#39212yes—
289C4×C11#39212yes—
290C4×C11#39412yes—
291C4×C11#39412yes—
292Dic11—44no—
293C25—112no—
294C25C4×D1111yescharacteristic
295C22×D4—114no—
296C22×D4—224no—
297C22×D4—224no—
298C22×D4—224no—
299C22×D4—221no—
300C22×D4—222no—
301C22×D4—222no—
302C22×D4—222no—
303C22×D4—222no—
304C22×D4—221no—
305C22×D4—222no—
306C22×D4—448no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—112no—
314C23×C4C4×D1111yescharacteristic
315C23×C4D4412yes—
316C23×C4C22⋊D1112yes—
317C23×C4C22×D1111yescharacteristic
318C2×M16—22no—
319C2×M16—22no—
320C2×M16—22no—
321C2×M16—22no—
322C2×M16—22no—
323C2×M16—114no—
324C2×M16—222no—
325C2×M16—222no—
326C2×M16—222no—
327C2×M16—222no—
328C2×M16—222no—
329C2×M16C22⋊D1114yescomplemented
330C22×C8—22no—
331C22×C8—222no—
332#121—2216no—
333#121—2216no—
334C2×C4⋊C4—114no—
335C2×C4⋊C4—221no—
336C2×C4⋊C4—222no—
337C2×C4⋊C4—221no—
338C2×C22⋊C4—224no—
339C2×C22⋊C4—224no—
340C2×C22⋊C4—224no—
341#100—2216no—
342C22⋊C8—28no—
343C22⋊C8—228no—
344C2×C11—22no—
345C2×C11—22no—
346C2×C11—44no—
347C2×C11#143811yescharacteristic
348C2×C11#178311yescharacteristic
349C2×C11#178511yescharacteristic
350C2×C11#190012yes—
351C2×C11#190012yes—
352D11—84no—
353C24—24no—
354C24—21no—
355C24—21no—
356C24—22no—
357C24—22no—
358C24—42no—
359C24—114no—
360C24—222no—
361C24—222no—
362C24—224no—
363C24—224no—
364C24—444no—
365C24—444no—
366C24(C2×D11)⋊C412yes—
367C24C2×C4×D1111yescharacteristic
368C2×D4—2216no—
369C2×D4—224no—
370C2×D4—224no—
371C2×D4—224no—
372C2×D4—224no—
373C2×D4—224no—
374C2×D4—224no—
375C2×D4—4416no—
376C2×D4—448no—
377C2×D4—4416no—
378C2×D4—448no—
379C2×D4—441no—
380C2×D4—442no—
381C2×D4—442no—
382C2×D4—441no—
383C2×D4—441no—
384C2×D4—442no—
385C2×D4—442no—
386C2×D4—442no—
387C2×D4—442no—
388C2×D4—441no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—24no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—24no—
400C22×C4—22no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—42no—
407C22×C4—42no—
408C22×C4—42no—
409C22×C4—114no—
410C22×C4—222no—
411C22×C4—222no—
412C22×C4—444no—
413C22×C4(C2×D11)⋊C412yes—
414C22×C4C2×D4411yescharacteristic
415C22×C4#433912yes—
416C22×C4D4×D1112yes—
417C22×C4D4×D1112yes—
418C22×C4D4×D1112yes—
419C22×C4#434112yes—
420C22×C4C2×C22⋊D1111yescharacteristic
421C22×C4C2×C22⋊D1112yes—
422M16—24no—
423M16—24no—
424M16—42no—
425M16—42no—
426M16—224no—
427M16—224no—
428M16—442no—
429M16—442no—
430C2×C8—24no—
431C2×C8—42no—
432C2×C8—42no—
433C2×C8—224no—
434C2×C8—442no—
435C2×C8—442no—
436C4⋊C4—224no—
437C4⋊C4—224no—
438C22⋊C4—2216no—
439C11#1096711yescharacteristic, complemented, Sylow
440C23—22no—
441C23—22no—
442C23—24no—
443C23—24no—
444C23—22no—
445C23—22no—
446C23—22no—
447C23—22no—
448C23—22no—
449C23—22no—
450C23—48no—
451C23—48no—
452C23—42no—
453C23—42no—
454C23—42no—
455C23—42no—
456C23—224no—
457C23—228no—
458C23—444no—
459C23—444no—
460C23—444no—
461C23—444no—
462C23—444no—
463C23—444no—
464C23—444no—
465C23—442no—
466C23—442no—
467C23—888no—
468C23—888no—
469C23#6688714yescomplemented
470C23C22⋊C4×D1111yescharacteristic
471C23C22⋊C4×D1111yescharacteristic
472C23(C22⋊D11)⋊C412yes—
473C23C2×(C2×D11)⋊C411yescharacteristic
474C23C4×C22⋊D1112yes—
475D4—4432no—
476D4—444no—
477D4—444no—
478D4—444no—
479D4—444no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—44no—
486C2×C4—44no—
487C2×C4—44no—
488C2×C4—44no—
489C2×C4—224no—
490C2×C4—444no—
491C2×C4—444no—
492C2×C4—444no—
493C2×C4#6693511yescharacteristic
494C2×C4#6693512yes—
495C2×C4#6693612yes—
496C2×C4#6693712yes—
497C2×C4#6693712yes—
498C2×C4#6693812yes—
499C2×C4#6693911yescharacteristic
500C2×C4#6698211yescharacteristic
501C2×C4#6698312yes—
502C2×C4#6699012yes—
503C2×C4#6699012yes—
504C2×C4#6699112yes—
505C2×C4#6699212yes—
506C2×C4#6699212yes—
507C2×C4#6699312yes—
508C2×C4#6700611yescharacteristic
509C8—44no—
510C8—444no—
511C22—24no—
512C22—24no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—24no—
518C22—24no—
519C22—24no—
520C22—48no—
521C22—48no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—444no—
527C22—444no—
528C22—444no—
529C22—888no—
530C22—888no—
531C22—884no—
532C22—884no—
533C22#1062256811yescharacteristic
534C22#1062256912yes—
535C22#1062257012yes—
536C22#1062257111yescharacteristic
537C22C2×#6688712yes—
538C22#1062274512yes—
539C22#1062282611yescharacteristic
540C4—42no—
541C4—444no—
542C4#1062257212yes—
543C4#1062257312yes—
544C4#1062257412yes—
545C4#1062283612yes—
546C2—22no—
547C2—22no—
548C2—44no—
549C2—884no—
550C2#1306685511yescharacteristic
551C2#1306853611yescharacteristic
552C2#1306854211yescharacteristic
553C2#1306907712yes—
554C2#1306907912yes—
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#407C2
socleC23×C11C2×C22⋊C4
prime radicalC22×#66983C2
cosocleC23×C4×C11C23
hypercenterC2×#407D11
hypocenterC11#10967
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C22×#66887C2semidirect
3. C2×#10622820C2semidirect
4. C2×#10622192C2semidirect
5. C2×C11×#407C2semidirect
55. C2×C11×M16D4semidirect
71. C2×#4318D4semidirect
166. C2×#407D11semidirect
184. C23×C11#100semidirect
329. C2×M16C22⋊D11semidirect
439. C11#10967semidirect
469. C23#66887semidirect

Maximal subgroups

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

subgroupindex
C22×#669832
C22×#668872
C2×#106228202
C2×#106221922
C2×C11×#4072
#1096711