Finite Group Databasebeta

← #14719645

Subgroups — #14719645

Order 2816.

1738 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic
2D11×#407C212yesmaximal, complemented
3#13066951C214yesmaximal, complemented
4#13066945C212yesmaximal, complemented
5#13066943C211yesmaximal, characteristic, complemented
6#13066931C214yesmaximal, complemented
7C11×#1462C211yesmaximal, characteristic, complemented
8C23×C22⋊D11C411yescharacteristic
9C24×Dic11C411yescharacteristic
10C23×C4×D11C2211yescharacteristic
11C22×C11×C22⋊C4C2211yescharacteristic
12C22×(C2×D11)⋊C4C411yescharacteristic
13C22×Dic11⋊C4C2211yescharacteristic
14C22×C4×Dic11C411yescharacteristic
15C2×M16×D11—22no—
16C2×(C22⋊D11)⋊C4—22no—
17C2×(C22⋊D11)⋊C4—22no—
18C2×(C22⋊D11)⋊C4—22no—
19C2×(C22⋊D11)⋊C4—22no—
20C2×(C22⋊D11)⋊C4C412yes—
21C2×(C22⋊D11)⋊C4C412yes—
22C2×(C22⋊D11)⋊C4C2212yes—
23C2×(C22⋊D11)⋊C4C2212yes—
24C11×#407C2212yes—
25#10622820C2212yes—
26#10622739—22no—
27#10622339—22no—
28#10622339C2214yescomplemented
29D11×C22⋊C8—22no—
30D11×C22⋊C8C2214yescomplemented
31C11×#323C2214yescomplemented
32#10622163C2214yescomplemented
33#10622107C2218yescomplemented
34C25×C11C2×C411yescharacteristic
35C24×D11C2×C411yescharacteristic
36C23×C4×C11C2×C411yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C22×C22⋊D11—22no—
39C22×C22⋊D11—22no—
40C22×C22⋊D11—28no—
41C22×C22⋊D11C2×C412yes—
42C22×C22⋊D11C2×C412yes—
43C23×Dic11—21no—
44C23×Dic11—21no—
45C23×Dic11—21no—
46C23×Dic11—21no—
47C23×Dic11—44no—
48C23×Dic11C2×C411yescharacteristic
49C23×Dic11C2×C411yescharacteristic
50C23×Dic11C2×C412yes—
51C23×Dic11C2×C412yes—
52C23×Dic11C2×C411yescharacteristic
53C22×C4×D11—44no—
54C22×C4×D11C2×C411yescharacteristic
55C22×C4×D11C2×C411yescharacteristic
56C22×C4×D11D412yes—
57C22×C4×D11D412yes—
58C22×C4×D11D412yes—
59C22×C4×D11D412yes—
60C22×C4×D11C2311yescharacteristic
61C22×C4×D11C2311yescharacteristic
62C2×C11×M16—22no—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4C2×C412yes—
66C2×C11×C22⋊C4C2312yes—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4C2×C412yes—
70C2×(C2×D11)⋊C4C2×C412yes—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4—22no—
73C2×Dic11⋊C4C2×C412yes—
74C2×Dic11⋊C4C2312yes—
75C2×C4×Dic11—21no—
76C2×C4×Dic11—21no—
77C2×C4×Dic11—21no—
78C2×C4×Dic11—21no—
79C2×C4×Dic11C2×C412yes—
80C2×C4×Dic11C2×C412yes—
81C2×#4318—22no—
82M16×D11—48no—
83C2×#4313—24no—
84C2×C8×D11—24no—
85(C22⋊D11)⋊C4—24no—
86(C22⋊D11)⋊C4—24no—
87(C22⋊D11)⋊C4—24no—
88(C22⋊D11)⋊C4—24no—
89(C22⋊D11)⋊C4—24no—
90(C22⋊D11)⋊C4—24no—
91(C22⋊D11)⋊C4—24no—
92(C22⋊D11)⋊C4—24no—
93C11×C22⋊C8—22no—
94C11×C22⋊C8C2314yes—
95C22⋊(C11⋊C8)—22no—
96C22⋊(C11⋊C8)C2314yes—
97(C2×D11)⋊C8—24no—
98(C2×D11)⋊C8—24no—
99#17362—111nomaximal, Sylow
100C24×C11—21no—
101C24×C11—21no—
102C24×C11—24no—
103C24×C11—42no—
104C24×C11—42no—
105C24×C11C22×C411yescharacteristic
106C24×C11C22×C412yes—
107C23×D11—24no—
108C23×D11—42no—
109C23×D11—42no—
110C23×D11C22⋊C412yes—
111C23×D11C22⋊C412yes—
112C23×D11C22×C411yescharacteristic
113C23×D11C22×C411yescharacteristic
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—42no—
117C22×C4×C11—42no—
118C22×C4×C11C22×C412yes—
119C22×C4×C11C22×C411yescharacteristic
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2411yescharacteristic
123C2×C22⋊D11—216no—
124C2×C22⋊D11—216no—
125C2×C22⋊D11—24no—
126C2×C22⋊D11—24no—
127C2×C22⋊D11—24no—
128C2×C22⋊D11—24no—
129C2×C22⋊D11—24no—
130C2×C22⋊D11M1618yescomplemented
131C22×Dic11—24no—
132C22×Dic11—24no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—42no—
142C22×Dic11—44no—
143C22×Dic11—44no—
144C22×Dic11—44no—
145C22×Dic11—44no—
146C22×Dic11—44no—
147C22×Dic11—44no—
148C22×Dic11C22⋊C411yescharacteristic
149C22×Dic11C22⋊C411yescharacteristic
150C22×Dic11C22⋊C411yescharacteristic
151C22×Dic11C22⋊C411yescharacteristic
152C22×Dic11C22×C411yescharacteristic
153C22×Dic11C22×C411yescharacteristic
154C22×Dic11C22×C412yes—
155C22×Dic11C22×C412yes—
156C2×C4×D11—28no—
157C2×C4×D11—44no—
158C2×C4×D11—42no—
159C2×C4×D11—42no—
160C2×C4×D11—44no—
161C2×C4×D11—44no—
162C2×C4×D11—42no—
163C2×C4×D11—42no—
164C2×C4×D11C22⋊C412yes—
165C2×C4×D11C22⋊C412yes—
166C2×C4×D11C22⋊C412yes—
167C2×C4×D11C22⋊C412yes—
168C2×C4×D11C2×D412yes—
169C2×C4×D11C2×D412yes—
170C2×C4×D11C2×D412yes—
171C2×C4×D11C2×D412yes—
172C11×M16—44no—
173C2×C8×C11—24no—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—24no—
176(C2×D11)⋊C4—24no—
177(C2×D11)⋊C4—24no—
178Dic11⋊C4—24no—
179Dic11⋊C4—24no—
180C4×Dic11—22no—
181C4×Dic11—22no—
182C4×Dic11—22no—
183C4×Dic11—22no—
184#4318—44no—
185C2×C11⋊C8—24no—
186#4313—48no—
187C8×D11—48no—
188C22×C4×D4—111no—
189C2×#407—112no—
190#1465—114no—
191#1463—112no—
192#1462—111no—
193#1462D1111yescharacteristic, complemented
194#1459—114no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—416no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11C2×C22⋊C411yescharacteristic
210C23×C11C2×C22⋊C411yescharacteristic
211C23×C11C2×M1614yescomplemented
212C23×C11C23×C411yescharacteristic
213C22×D11—22no—
214C22×D11—24no—
215C22×D11—24no—
216C22×D11—24no—
217C22×D11—24no—
218C22×D11—42no—
219C22×D11—41no—
220C22×D11—41no—
221C22×D11—42no—
222C22×D11—41no—
223C22×D11—41no—
224C22×D11—416no—
225C22×D11C2×C22⋊C412yes—
226C22×D11C2×C22⋊C412yes—
227C22×D11C2×M1614yes—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—41no—
231C2×C4×C11—42no—
232C2×C4×C11—41no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11C2×C22⋊C412yes—
237C2×C4×C11C22×D412yes—
238C22⋊D11—216no—
239C22⋊D11—216no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—44no—
251C2×Dic11—44no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—44no—
255C2×Dic11—44no—
256C2×Dic11—42no—
257C2×Dic11#9914yes—
258C2×Dic11C2×C22⋊C411yescharacteristic
259C2×Dic11C2×C22⋊C411yescharacteristic
260C2×Dic11C2×C22⋊C411yescharacteristic
261C2×Dic11C2×C22⋊C411yescharacteristic
262C2×Dic11C2×M1614yescomplemented
263C4×D11—24no—
264C4×D11—24no—
265C4×D11—24no—
266C4×D11—24no—
267C4×D11—42no—
268C4×D11—42no—
269C4×D11—42no—
270C4×D11—42no—
271C8×C11—44no—
272C11⋊C8—44no—
273C23×D4—111no—
274C24×C4—111no—
275C24×C4—111no—
276C22×M16—222no—
277C2×C4×D4—112no—
278C2×C4×D4—112no—
279C2×C4×D4—112no—
280C2×C4×D4—112no—
281C2×C4×D4—222no—
282C2×C4×D4—222no—
283C2×C4×D4—222no—
284C2×C4×D4—222no—
285C22×C4⋊C4—111no—
286C22×C22⋊C4—111no—
287C22×C22⋊C4C2×D1111yescharacteristic
288C22×C42—111no—
289#407—112no—
290#407—114no—
291#407—222no—
292#407—222no—
293#407C2×D1112yes—
294C2×C22⋊C8—114no—
295C2×C22⋊C8—222no—
296#324—118no—
297#323—114no—
298#323C2×D1114yescomplemented
299C22×C11—28no—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—21no—
303C22×C11—21no—
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—24no—
307C22×C11—44no—
308C22×C11—44no—
309C22×C11—48no—
310C22×C11—48no—
311C22×C11—42no—
312C22×C11—42no—
313C22×C11C2×#9912yes—
314C22×C11#41312yes—
315C22×C11C22×C22⋊C411yescharacteristic
316C22×C11C22×M1612yes—
317C2×D11—22no—
318C2×D11—22no—
319C2×D11—22no—
320C2×D11—22no—
321C2×D11—22no—
322C2×D11—44no—
323C2×D11—48no—
324C2×D11—48no—
325C2×D11—44no—
326C2×D11#40714yes—
327C4×C11—22no—
328C4×C11—22no—
329C4×C11—42no—
330Dic11—24no—
331Dic11—21no—
332Dic11—21no—
333Dic11—42no—
334Dic11C2×#9912yes—
335Dic11C2×#9912yes—
336C25—111no—
337C25C4×D1111yescharacteristic
338C22×D4—112no—
339C22×D4—112no—
340C22×D4—228no—
341C22×D4—222no—
342C22×D4—222no—
343C23×C4—111no—
344C23×C4—112no—
345C23×C4—111no—
346C23×C4—111no—
347C23×C4—112no—
348C23×C4—112no—
349C23×C4—112no—
350C23×C4—111no—
351C23×C4—111no—
352C23×C4—111no—
353C23×C4—111no—
354C23×C4—112no—
355C23×C4—112no—
356C23×C4—221no—
357C23×C4—221no—
358C23×C4—221no—
359C23×C4—221no—
360C23×C4—444no—
361C23×C4—444no—
362C23×C4C4×D1111yescharacteristic
363C23×C4C22×D1111yescharacteristic
364C2×M16—22no—
365C2×M16—224no—
366C2×M16—222no—
367C2×M16—448no—
368C22×C8—224no—
369C4×D4—224no—
370C4×D4—224no—
371C4×D4—224no—
372C4×D4—224no—
373C4×D4—224no—
374C4×D4—224no—
375C4×D4—224no—
376C4×D4—224no—
377C2×C4⋊C4—112no—
378C2×C4⋊C4—112no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4—222no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—112no—
384C2×C22⋊C4—112no—
385C2×C22⋊C4—222no—
386C2×C22⋊C4—222no—
387C2×C22⋊C4C4×D1112yes—
388C2×C22⋊C4C22×D1112yes—
389C2×C42—112no—
390C2×C42—112no—
391C2×C42—221no—
392C2×C42—221no—
393C2×C42—221no—
394C2×C42—221no—
395C22⋊C8—22no—
396C22⋊C8—114no—
397C22⋊C8—224no—
398C22⋊C8—224no—
399C22⋊C8—222no—
400C22⋊C8C22×D1114yes—
401C2×C11—22no—
402C2×C11—22no—
403C2×C11—22no—
404C2×C11—44no—
405C2×C11C2×#40711yescharacteristic
406C2×C11C22×#9911yescharacteristic
407C2×C11C2×#41311yescharacteristic
408D11—24no—
409D11—42no—
410C24—21no—
411C24—21no—
412C24—24no—
413C24—42no—
414C24—42no—
415C24—111no—
416C24—112no—
417C24—112no—
418C24—111no—
419C24—224no—
420C24—442no—
421C24—442no—
422C24C2×C4×D1111yescharacteristic
423C24C2×C4×D1112yes—
424C2×D4—118no—
425C2×D4—224no—
426C2×D4—224no—
427C2×D4—224no—
428C2×D4—224no—
429C2×D4—2216no—
430C2×D4—2216no—
431C2×D4—224no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—111no—
437C22×C4—111no—
438C22×C4—111no—
439C22×C4—111no—
440C22×C4—112no—
441C22×C4—111no—
442C22×C4—111no—
443C22×C4—112no—
444C22×C4—112no—
445C22×C4—112no—
446C22×C4—112no—
447C22×C4—112no—
448C22×C4—112no—
449C22×C4—112no—
450C22×C4—112no—
451C22×C4—112no—
452C22×C4—228no—
453C22×C4—224no—
454C22×C4—224no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—222no—
458C22×C4—222no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—444no—
464C22×C4—442no—
465C22×C4—442no—
466C22×C4—444no—
467C22×C4—444no—
468C22×C4—442no—
469C22×C4—442no—
470C22×C4—444no—
471C22×C4—444no—
472C22×C4—444no—
473C22×C4—444no—
474C22×C4—444no—
475C22×C4—444no—
476C22×C4—442no—
477C22×C4C2×C4×D1112yes—
478C22×C4C2×C4×D1111yescharacteristic
479C22×C4D4×D1112yes—
480C22×C4D4×D1112yes—
481C22×C4C23×D1111yescharacteristic
482M16—44no—
483M16—448no—
484M16—444no—
485C2×C8—24no—
486C2×C8—224no—
487C2×C8—448no—
488C4⋊C4—224no—
489C4⋊C4—224no—
490C22⋊C4—24no—
491C22⋊C4—24no—
492C22⋊C4—224no—
493C22⋊C4—224no—
494C42—222no—
495C42—222no—
496C42—222no—
497C42—222no—
498C11#1736211yescharacteristic, complemented, Sylow
499C23—22no—
500C23—22no—
501C23—22no—
502C23—24no—
503C23—24no—
504C23—22no—
505C23—22no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—416no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—112no—
514C23—114no—
515C23—112no—
516C23—224no—
517C23—224no—
518C23—222no—
519C23—224no—
520C23—224no—
521C23—442no—
522C23—441no—
523C23—441no—
524C23—442no—
525C23—441no—
526C23—441no—
527C23—4416no—
528C23C22⋊C4×D1111yescharacteristic
529C23C22⋊C4×D1111yescharacteristic
530C23M16×D1114yescomplemented
531C23C22×C4×D1111yescharacteristic
532D4—2216no—
533D4—2216no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—111no—
543C2×C4—111no—
544C2×C4—114no—
545C2×C4—111no—
546C2×C4—111no—
547C2×C4—114no—
548C2×C4—224no—
549C2×C4—224no—
550C2×C4—224no—
551C2×C4—224no—
552C2×C4—222no—
553C2×C4—222no—
554C2×C4—222no—
555C2×C4—222no—
556C2×C4—224no—
557C2×C4—224no—
558C2×C4—222no—
559C2×C4—222no—
560C2×C4—222no—
561C2×C4—222no—
562C2×C4—442no—
563C2×C4—442no—
564C2×C4—442no—
565C2×C4—442no—
566C2×C4—444no—
567C2×C4—444no—
568C2×C4—444no—
569C2×C4—444no—
570C2×C4—442no—
571C2×C4—442no—
572C2×C4—442no—
573C2×C4C22⋊C4×D1112yes—
574C2×C4C2×D4×D1112yes—
575C8—44no—
576C8—444no—
577C22—28no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—24no—
585C22—44no—
586C22—44no—
587C22—48no—
588C22—48no—
589C22—42no—
590C22—42no—
591C22—114no—
592C22—222no—
593C22—222no—
594C22—222no—
595C22—222no—
596C22—222no—
597C22—444no—
598C22—448no—
599C22—448no—
600C22—444no—
601C22D11×#9912yes—
602C22#1062235812yes—
603C22C2×C22⋊C4×D1111yescharacteristic
604C22C2×M16×D1112yes—
605C4—22no—
606C4—22no—
607C4—42no—
608C4—112no—
609C4—112no—
610C4—224no—
611C4—221no—
612C4—221no—
613C4—442no—
614C2—22no—
615C2—22no—
616C2—22no—
617C2—44no—
618C2—224no—
619C2—442no—
620C2D11×#40711yescharacteristic
621C2C2×D11×#9911yescharacteristic
622C2C2×#1062235811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1462C2
socleC22×C11C22×C22⋊C4
prime radicalC23×C22⋊D11C4
cosocleC22×C4×C11C24
hypercenter#1462D11
hypocenterC11#17362
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1462

Complements

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

NH ≅ G/Ntype
2. D11×#407C2semidirect
3. #13066951C2semidirect
4. #13066945C2semidirect
5. #13066943C2semidirect
6. #13066931C2semidirect
7. C11×#1462C2semidirect
28. #10622339C22semidirect
30. D11×C22⋊C8C22semidirect
31. C11×#323C22semidirect
32. #10622163C22semidirect
33. #10622107C22semidirect
130. C2×C22⋊D11M16semidirect
193. #1462D11semidirect
211. C23×C11C2×M16semidirect
262. C2×Dic11C2×M16semidirect
298. #323C2×D11semidirect
498. C11#17362semidirect
530. C23M16×D11semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D11)⋊C42
D11×#4072
#130669512
#130669452
#130669432
#130669312
C11×#14622
#1736211