Finite Group Databasebeta

← #14757385

Subgroups — #14757385

Order 2816.

1718 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623359C211yesmaximal, characteristic
2C2×#10622715C211yesmaximal, characteristic, complemented
3C2×#10622847C211yesmaximal, characteristic, complemented
4C2×#10622739C211yesmaximal, characteristic, complemented
5C22×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
6C2×#10622735C211yesmaximal, characteristic, complemented
7#13069412C214yesmaximal, complemented
8#13069408C214yesmaximal, complemented
9C2×C11×#408C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C23×C4×D11C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14#10623359—24no—
15#10623359—24no—
16C2×#66999C412yes—
17C2×#66991C412yes—
18C2×#66990C412yes—
19C2×#66988C412yes—
20C2×C4×C22⋊D11C2214yes—
21C2×#66979C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C23×C11⋊C8C2211yescharacteristic
24C11×#408—24no—
25C2×C11×C22⋊C8C2214yescomplemented
26#10622847—24no—
27C2×C22⋊(C11⋊C8)C2212yescomplemented
28C2×C22⋊(C11⋊C8)C2212yescomplemented
29#10622739—24no—
30#10622735—24no—
31C2×(C2×D11)⋊C8—24no—
32C2×(C2×D11)⋊C8C2212yes—
33C2×(C2×D11)⋊C8C2212yes—
34C2×(C2×D11)⋊C8C2214yes—
35#10622715—24no—
36C2×#66879C2212yescomplemented
37C2×Dic11⋊C8C2214yescomplemented
38C2×C8×Dic11C2212yescomplemented
39C24×D11C2×C411yescharacteristic
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C22×Q8×C11C2×C411yescharacteristic
47C22×D4×C11C2×C412yes—
48C22×D4×C11C2×C411yescharacteristic
49C23×C4×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C22×C22⋊D11C2×C414yes—
52C23×Dic11C2×C411yescharacteristic
53C22×C4×D11—22no—
54C22×C4×D11—22no—
55C22×C4×D11—22no—
56C22×C4×D11—22no—
57C22×C4×D11—22no—
58C22×C4×D11—22no—
59C22×C4×D11C2×C412yes—
60C22×C4×D11C2312yes—
61C2×C11×M16—22no—
62C2×C11×M16—22no—
63C2×C11×M16D414yescomplemented
64C22×C8×C11—22no—
65C22×C8×C11—22no—
66C22×C8×C11—22no—
67C22×C8×C11C2312yes—
68C22×C8×C11C2312yes—
69C2×C22⋊Dic11C2×C414yes—
70C2×C22⋊Dic11C2×C412yes—
71#66999—28no—
72#66991—28no—
73#66990—28no—
74#66988—28no—
75C4×C22⋊D11—28no—
76C4×C22⋊D11—28no—
77C2×(C2×D11)⋊C4C2×C414yes—
78#66979D414yes—
79#66979D414yes—
80C2×C4⋊Dic11C2×C412yes—
81C2×Dic11⋊C4C2×C414yes—
82C2×C4×Dic11C2312yes—
83C2×#4318—22no—
84C2×#4318—22no—
85C2×#4318—22no—
86C22×C11⋊C8—22no—
87C22×C11⋊C8—22no—
88C22×C11⋊C8D414yescomplemented
89C22×C11⋊C8C2312yes—
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C11×C22⋊C8—28no—
93C22⋊(C11⋊C8)—24no—
94C22⋊(C11⋊C8)—24no—
95(C2×D11)⋊C8—28no—
96(C2×D11)⋊C8—24no—
97(C2×D11)⋊C8—24no—
98#66879—24no—
99Dic11⋊C8—28no—
100C8×Dic11—24no—
101#21191—111nomaximal, Sylow
102C24×C11C22×C412yes—
103C24×C11C22×C411yescharacteristic
104C23×D11—22no—
105C23×D11—24no—
106C23×D11—22no—
107C23×D11—22no—
108C23×D11—42no—
109C23×D11C22×C412yes—
110C11×#41—44no—
111C11×#41—44no—
112C11×#41—44no—
113C11×#41—44no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×D4×C11—24no—
118C2×D4×C11—24no—
119C2×D4×C11—24no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11C22×C412yes—
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D412yes—
135C22×C4×C11#4112yes—
136C22×C4×C11#4112yes—
137C22×C4×C11C2411yescharacteristic
138C2×C22⋊D11—28no—
139C2×C22⋊D11—28no—
140C2×C22⋊D11—44no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11C22×C412yes—
145C22×Dic11C22×C414yes—
146C2×C4×D11—24no—
147C2×C4×D11—24no—
148C2×C4×D11—24no—
149C2×C4×D11—22no—
150C2×C4×D11—22no—
151C2×C4×D11—22no—
152C2×C4×D11—22no—
153C2×C4×D11—22no—
154C2×C4×D11—22no—
155C2×C4×D11—44no—
156C2×C4×D11—44no—
157C2×C4×D11—44no—
158C2×C4×D11—44no—
159C11×M16—28no—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11—44no—
166C2×C8×C11C2×D414yes—
167C22⋊Dic11—28no—
168C22⋊Dic11C22⋊C418yes—
169(C2×D11)⋊C4—28no—
170C4⋊Dic11C22⋊C418yes—
171Dic11⋊C4—28no—
172C4×Dic11C2×D414yes—
173C4×Dic11C2×D414yes—
174#4318—44no—
175C2×C11⋊C8—28no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—21no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8C2×D412yes—
184C2×C11⋊C8C2×D412yes—
185C2×#525—111no—
186C2×#424—111no—
187C2×#408—111no—
188C2×#408D1111yescharacteristic, complemented
189C2×#407—111no—
190C22×C22⋊C8—111no—
191C2×#405—111no—
192#1955—114no—
193#1954—114no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11C2×C22⋊C412yes—
202C23×C11C4×D412yes—
203C23×C11C4×D412yes—
204C23×C11C23×C411yescharacteristic
205C22×D11—28no—
206C22×D11—22no—
207C22×D11—22no—
208C22×D11—22no—
209C22×D11—22no—
210C22×D11—22no—
211C22×D11—22no—
212C22×D11—48no—
213C22×D11—48no—
214C22×D11—44no—
215C22×D11—44no—
216C22×D11#13114yes—
217Q8×C11—44no—
218D4×C11—48no—
219D4×C11—44no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11C2×C22⋊C412yes—
228C2×C4×C11C4×D412yes—
229C2×C4×C11C4×D412yes—
230C2×C4×C11#12114yes—
231C2×C4×C11#12114yes—
232C2×C4×C11#12414yes—
233C2×C4×C11#12714yes—
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C22⋊D11—416no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—44no—
247C2×Dic11C2×C22⋊C418yes—
248C4×D11—42no—
249C4×D11—42no—
250C4×D11—42no—
251C4×D11—42no—
252C4×D11—48no—
253C8×C11—24no—
254C8×C11—42no—
255C11⋊C8—22no—
256C11⋊C8—22no—
257C11⋊C8—42no—
258C22×#41C2×D1111yescharacteristic
259C24×C4—111no—
260C22×M16—111no—
261C22×M16C2×D1111yescharacteristic
262C23×C8—111no—
263C23×C8C2×D1111yescharacteristic
264#525—224no—
265#525—224no—
266C2×#123—112no—
267C2×C22⋊Q8—112no—
268C2×#121—112no—
269C2×#120—112no—
270C2×C4×D4—114no—
271C2×#117—111no—
272#424—224no—
273C2×C4⋊C8—114no—
274#408—24no—
275#408—224no—
276#407—224no—
277C2×C22⋊C8—112no—
278C2×C22⋊C8—112no—
279C2×C22⋊C8—112no—
280C2×C22⋊C8—112no—
281C2×C22⋊C8—114no—
282C2×C22⋊C8—224no—
283C2×C22⋊C8C2×D1114yescomplemented
284#405—224no—
285C2×#97—112no—
286C2×C4×C8—112no—
287C22×C11—24no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—24no—
291C22×C11—44no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—44no—
295C22×C11—42no—
296C22×C11#39014yes—
297C22×C11C22×C22⋊C411yescharacteristic
298C22×C11C2×C4×D411yescharacteristic
299C22×C11C2×C4×D411yescharacteristic
300C22×C11C2×#13112yes—
301C22×C11#56812yes—
302C2×D11—24no—
303C2×D11—24no—
304C2×D11—24no—
305C2×D11—416no—
306C2×D11—42no—
307C2×D11—42no—
308C2×D11—42no—
309C2×D11—42no—
310C4×C11—42no—
311C4×C11#39014yes—
312C4×C11C2×#12111yescharacteristic
313C4×C11C2×#12111yescharacteristic
314C4×C11C2×#12411yescharacteristic
315C4×C11C2×#12711yescharacteristic
316Dic11—28no—
317Dic11—42no—
318C25—111no—
319C2×#41—22no—
320C2×#41—22no—
321C2×#41—22no—
322C2×#41—22no—
323C2×#41—22no—
324C2×#41—22no—
325C22×Q8C4×D1111yescharacteristic
326C22×D4—114no—
327C22×D4C4×D1112yes—
328C22×D4C4×D1111yescharacteristic
329C23×C4—111no—
330C23×C4—112no—
331C23×C4—112no—
332C23×C4—222no—
333C23×C4—222no—
334C23×C4—222no—
335C23×C4—222no—
336C23×C4—222no—
337C23×C4—222no—
338C23×C4C22×D1112yes—
339C23×C4C22×D1111yescharacteristic
340C2×M16—22no—
341C2×M16—22no—
342C2×M16—222no—
343C2×M16—222no—
344C2×M16—222no—
345C2×M16C22⋊D1114yescomplemented
346C22×C8—22no—
347C22×C8—22no—
348C22×C8—22no—
349C22×C8—114no—
350C22×C8—111no—
351C22×C8—111no—
352C22×C8—112no—
353C22×C8—222no—
354C22×C8—222no—
355C22×C8C22×D1112yes—
356C22×C8C22×D1112yes—
357#123—228no—
358C22⋊Q8—228no—
359#121—228no—
360#120—228no—
361C4×D4—228no—
362C4×D4—228no—
363#117—114no—
364#117—114no—
365C2×C4⋊C4—112no—
366C2×C4⋊C4—114no—
367C2×C22⋊C4—112no—
368C2×C22⋊C4—114no—
369C2×C22⋊C4—114no—
370C2×C42—112no—
371C4⋊C8—228no—
372C22⋊C8—28no—
373C22⋊C8—224no—
374C22⋊C8—224no—
375C22⋊C8—224no—
376C22⋊C8—224no—
377C22⋊C8—228no—
378#97—224no—
379C4×C8—224no—
380C2×C11—24no—
381C2×C11—82no—
382C2×C11C2×#39011yescharacteristic
383C2×C11#288012yes—
384C2×C11#292911yescharacteristic
385C2×C11#293011yescharacteristic
386C2×C11#293312yes—
387D11—44no—
388C24—112no—
389C24—224no—
390C24—222no—
391C24—222no—
392C24—222no—
393C24—442no—
394C24C2×C4×D1112yes—
395C24C2×C4×D1111yescharacteristic
396#41—44no—
397#41—44no—
398#41—44no—
399#41—44no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×D4—24no—
404C2×D4—24no—
405C2×D4—24no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—228no—
410C2×D4—228no—
411C2×D4—444no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—114no—
419C22×C4—112no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—224no—
424C22×C4—224no—
425C22×C4—224no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—444no—
433C22×C4—444no—
434C22×C4—444no—
435C22×C4—444no—
436C22×C4C2×C4×D1112yes—
437C22×C4C2×C4×D1111yescharacteristic
438C22×C4#433912yes—
439C22×C4D4×D1112yes—
440C22×C4D4×D1112yes—
441C22×C4D4×D1112yes—
442C22×C4#434112yes—
443C22×C4C2×C22⋊D1112yes—
444C22×C4C23×D1111yescharacteristic
445M16—28no—
446M16—444no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—44no—
453C2×C8—112no—
454C2×C8—112no—
455C2×C8—228no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—222no—
461C2×C8—222no—
462C2×C8—222no—
463C2×C8C2×C22⋊D1114yes—
464C4⋊C4—118no—
465C4⋊C4—228no—
466C22⋊C4—118no—
467C22⋊C4—228no—
468C22⋊C4—228no—
469C42—114no—
470C42—114no—
471C11#2119111yescharacteristic, complemented, Sylow
472C23—22no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—24no—
477C23—24no—
478C23—22no—
479C23—114no—
480C23—228no—
481C23—222no—
482C23—222no—
483C23—222no—
484C23—222no—
485C23—222no—
486C23—222no—
487C23—448no—
488C23—448no—
489C23—444no—
490C23—444no—
491C23C22⋊C4×D1112yes—
492C23(C22⋊D11)⋊C412yes—
493C23C4×C22⋊D1112yes—
494C23C22×C4×D1111yescharacteristic
495Q8—44no—
496D4—48no—
497D4—44no—
498D4—4416no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—118no—
507C2×C4—224no—
508C2×C4—224no—
509C2×C4—222no—
510C2×C4—222no—
511C2×C4—222no—
512C2×C4—444no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—448no—
518C2×C4C22⋊C4×D1112yes—
519C2×C4(C22⋊D11)⋊C412yes—
520C2×C4#6693714yes—
521C2×C4#6693814yes—
522C2×C4C4×C22⋊D1112yes—
523C2×C4#6699214yes—
524C2×C4#6699314yes—
525C2×C4C2×#433911yescharacteristic
526C2×C4C2×D4×D1111yescharacteristic
527C2×C4C2×D4×D1111yescharacteristic
528C2×C4C2×D4×D1111yescharacteristic
529C2×C4C2×#434111yescharacteristic
530C2×C4C22×C22⋊D1111yescharacteristic
531C8—24no—
532C8—42no—
533C8—222no—
534C8—222no—
535C8—442no—
536C22—22no—
537C22—24no—
538C22—22no—
539C22—24no—
540C22—42no—
541C22—44no—
542C22—42no—
543C22—44no—
544C22—42no—
545C22—224no—
546C22—224no—
547C22—224no—
548C22—4416no—
549C22—442no—
550C22—442no—
551C22—442no—
552C22—442no—
553C22#1062257014yes—
554C22C2×C22⋊C4×D1111yescharacteristic
555C22C2×(C22⋊D11)⋊C411yescharacteristic
556C22D11×#13112yes—
557C22#1062328112yes—
558C22C2×C4×C22⋊D1111yescharacteristic
559C4—42no—
560C4—228no—
561C4—442no—
562C4#1062257014yes—
563C4C2×#6693711yescharacteristic
564C4C2×#6693811yescharacteristic
565C4C2×#6699211yescharacteristic
566C4C2×#6699311yescharacteristic
567C2—24no—
568C2—82no—
569C2—444no—
570C2C2×#1062257011yescharacteristic
571C2#1307706412yes—
572C2#1307731311yescharacteristic
573C2#1307732211yescharacteristic
574C2#1307733812yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC2×C11×#408C2
prime radicalC2×#10623359C2
cosocleC22×C4×C11C24
hypercenterC2×#408D11
hypocenterC11#21191
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
2. C2×#10622715C2semidirect
3. C2×#10622847C2semidirect
4. C2×#10622739C2semidirect
5. C22×(C2×D11)⋊C8C2semidirect
6. C2×#10622735C2semidirect
7. #13069412C2semidirect
8. #13069408C2semidirect
9. C2×C11×#408C2semidirect
25. C2×C11×C22⋊C8C22semidirect
27. C2×C22⋊(C11⋊C8)C22semidirect
28. C2×C22⋊(C11⋊C8)C22semidirect
36. C2×#66879C22semidirect
37. C2×Dic11⋊C8C22semidirect
38. C2×C8×Dic11C22semidirect
63. C2×C11×M16D4semidirect
88. C22×C11⋊C8D4semidirect
188. C2×#408D11semidirect
283. C2×C22⋊C8C2×D11semidirect
345. C2×M16C22⋊D11semidirect
471. C11#21191semidirect

Maximal subgroups

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

subgroupindex
C2×#106233592
C2×#106227152
C2×#106228472
C2×#106227392
C22×(C2×D11)⋊C82
C2×#106227352
#130694122
#130694082
C2×C11×#4082
#2119111