Finite Group Databasebeta

← #14719649

Subgroups — #14719649

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×#66946C211yesmaximal, characteristic
2D11×#407C212yesmaximal, complemented
3#13066953C214yesmaximal, complemented
4#13066946C211yesmaximal, characteristic, complemented
5#13066942C212yesmaximal, complemented
6#13066933C214yesmaximal, complemented
7C11×#1463C211yesmaximal, characteristic, complemented
8C23×D44C411yescharacteristic
9C23×C4×D11C411yescharacteristic
10C23×C4×D11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×(C2×D11)⋊C4C411yescharacteristic
13C22×(C2×D11)⋊C4C2211yescharacteristic
14C22×C4×Dic11C411yescharacteristic
15C2×M16×D11—22no—
16C2×#66946—22no—
17C2×#66946—22no—
18C2×#66946—22no—
19C2×#66946—22no—
20C2×#66946C412yes—
21C2×#66946C412yes—
22C2×#66946C2212yes—
23C2×#66946C2212yes—
24C11×#407C2212yes—
25#10622820C2212yes—
26#10622739—22no—
27#10622339—22no—
28#10622339C2214yescomplemented
29D11×C22⋊C8—22no—
30D11×C22⋊C8C2214yescomplemented
31C11×#324C2214yescomplemented
32#10622166C2214yescomplemented
33#10622106C2218yescomplemented
34C24×D11C2×C411yescharacteristic
35C24×D11C2×C411yescharacteristic
36C23×C4×C11C2×C411yescharacteristic
37C23×C4×C11C2×C411yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C23×Dic11C2×C411yescharacteristic
40C23×Dic11C2×C411yescharacteristic
41C22×D44—22no—
42C22×D44—22no—
43C22×D44—28no—
44C22×D44C2×C412yes—
45C22×D44C2×C412yes—
46C22×C4×D11—21no—
47C22×C4×D11—21no—
48C22×C4×D11—21no—
49C22×C4×D11—21no—
50C22×C4×D11—44no—
51C22×C4×D11—44no—
52C22×C4×D11C2×C412yes—
53C22×C4×D11C2×C412yes—
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×C4⋊C4—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4C2×C412yes—
66C2×C11×C4⋊C4C2312yes—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4C2×C412yes—
72C2×(C2×D11)⋊C4C2×C412yes—
73C2×(C2×D11)⋊C4C2×C412yes—
74C2×(C2×D11)⋊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#66946—24no—
86#66946—24no—
87#66946—24no—
88#66946—24no—
89#66946—24no—
90#66946—24no—
91#66946—24no—
92#66946—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×C11C22×C411yescharacteristic
101C23×D11—21no—
102C23×D11—21no—
103C23×D11—24no—
104C23×D11—24no—
105C23×D11—42no—
106C23×D11—42no—
107C23×D11—42no—
108C23×D11—42no—
109C23×D11C22⋊C412yes—
110C23×D11C22⋊C412yes—
111C23×D11C22×C411yescharacteristic
112C23×D11C22×C412yes—
113C23×D11C22×C411yescharacteristic
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—24no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11C22×C412yes—
122C22×C4×C11C22×C412yes—
123C22×C4×C11C22×C411yescharacteristic
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2411yescharacteristic
127C22×Dic11—24no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—42no—
131C22×Dic11C22⋊C411yescharacteristic
132C22×Dic11C22⋊C411yescharacteristic
133C22×Dic11C22⋊C411yescharacteristic
134C22×Dic11C22⋊C411yescharacteristic
135C22×Dic11C22×C411yescharacteristic
136C22×Dic11C22×C411yescharacteristic
137C22×Dic11C22×C412yes—
138C2×D44—216no—
139C2×D44—216no—
140C2×D44—24no—
141C2×D44—24no—
142C2×D44—24no—
143C2×D44—24no—
144C2×D44—24no—
145C2×D44M1618yescomplemented
146C2×C4×D11—28no—
147C2×C4×D11—22no—
148C2×C4×D11—22no—
149C2×C4×D11—22no—
150C2×C4×D11—22no—
151C2×C4×D11—44no—
152C2×C4×D11—42no—
153C2×C4×D11—42no—
154C2×C4×D11—44no—
155C2×C4×D11—44no—
156C2×C4×D11—42no—
157C2×C4×D11—42no—
158C2×C4×D11—44no—
159C2×C4×D11—44no—
160C2×C4×D11—44no—
161C2×C4×D11—44no—
162C2×C4×D11—44no—
163C2×C4×D11—44no—
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×C4⋊C4—24no—
175C11×C4⋊C4—24no—
176(C2×D11)⋊C4—24no—
177(C2×D11)⋊C4—24no—
178(C2×D11)⋊C4—24no—
179(C2×D11)⋊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—111no—
192#1463D1111yescharacteristic, complemented
193#1462—112no—
194#1459—114no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11C2×C22⋊C411yescharacteristic
199C23×C11C2×C22⋊C411yescharacteristic
200C23×C11C23×C411yescharacteristic
201C22×D11—24no—
202C22×D11—24no—
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—22no—
206C22×D11—24no—
207C22×D11—24no—
208C22×D11—24no—
209C22×D11—24no—
210C22×D11—42no—
211C22×D11—41no—
212C22×D11—41no—
213C22×D11—42no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—42no—
217C22×D11—416no—
218C22×D11—416no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11—42no—
224C22×D11C2×C22⋊C412yes—
225C22×D11C2×C22⋊C412yes—
226C22×D11C2×M1614yes—
227C22×D11C2×M1614yescomplemented
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—41no—
235C2×C4×C11—42no—
236C2×C4×C11—41no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11C2×C22⋊C412yes—
241C2×C4×C11C2×M1614yescomplemented
242C2×C4×C11C22×D412yes—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11#9914yes—
253C2×Dic11C2×C22⋊C411yescharacteristic
254C2×Dic11C2×C22⋊C411yescharacteristic
255C2×Dic11C2×C22⋊C411yescharacteristic
256C2×Dic11C2×C22⋊C411yescharacteristic
257D44—216no—
258D44—216no—
259C4×D11—24no—
260C4×D11—24no—
261C4×D11—24no—
262C4×D11—24no—
263C4×D11—42no—
264C4×D11—42no—
265C4×D11—42no—
266C4×D11—42no—
267C4×D11—44no—
268C4×D11—44no—
269C4×D11—44no—
270C4×D11—44no—
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⋊C4C2×D1111yescharacteristic
286C22×C22⋊C4—111no—
287C22×C22⋊C4—111no—
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—114no—
297#324C2×D1114yescomplemented
298#323—118no—
299C22×C11—28no—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—21no—
303C22×C11—21no—
304C22×C11—21no—
305C22×C11—21no—
306C22×C11C2×#9912yes—
307C22×C11#41312yes—
308C22×C11C22×C22⋊C411yescharacteristic
309C22×C11C22×M1612yes—
310C2×D11—22no—
311C2×D11—22no—
312C2×D11—22no—
313C2×D11—24no—
314C2×D11—22no—
315C2×D11—22no—
316C2×D11—44no—
317C2×D11—48no—
318C2×D11—48no—
319C2×D11—44no—
320C2×D11—44no—
321C2×D11—48no—
322C2×D11—48no—
323C2×D11—42no—
324C2×D11—42no—
325C2×D11—44no—
326C2×D11#40714yes—
327C4×C11—24no—
328C4×C11—22no—
329C4×C11—22no—
330C4×C11—42no—
331Dic11—21no—
332Dic11—21no—
333Dic11—42no—
334Dic11C2×#9912yes—
335Dic11C2×#9912yes—
336C25—111no—
337C25—111no—
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—112no—
354C23×C4—112no—
355C23×C4—221no—
356C23×C4—221no—
357C23×C4—221no—
358C23×C4—221no—
359C23×C4—444no—
360C23×C4—444no—
361C23×C4C4×D1111yescharacteristic
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—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4C4×D1112yes—
380C2×C4⋊C4C22×D1112yes—
381C2×C22⋊C4—112no—
382C2×C22⋊C4—112no—
383C2×C22⋊C4—112no—
384C2×C22⋊C4—112no—
385C2×C22⋊C4—222no—
386C2×C22⋊C4—222no—
387C2×C22⋊C4—222no—
388C2×C22⋊C4—222no—
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×C11C2×#40711yescharacteristic
405C2×C11C22×#9911yescharacteristic
406C2×C11C2×#41311yescharacteristic
407D11—24no—
408D11—42no—
409D11—44no—
410C24—111no—
411C24—112no—
412C24—112no—
413C24—111no—
414C24—112no—
415C24—224no—
416C24—224no—
417C24—221no—
418C24—221no—
419C24—442no—
420C24—442no—
421C24—442no—
422C24—442no—
423C24C2×C4×D1111yescharacteristic
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—24no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—111no—
440C22×C4—111no—
441C22×C4—111no—
442C22×C4—111no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—112no—
446C22×C4—112no—
447C22×C4—112no—
448C22×C4—112no—
449C22×C4—112no—
450C22×C4—112no—
451C22×C4—112no—
452C22×C4—112no—
453C22×C4—112no—
454C22×C4—228no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—222no—
458C22×C4—222no—
459C22×C4—224no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—444no—
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—442no—
476C22×C4C2×C4×D1112yes—
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—24no—
489C4⋊C4—24no—
490C22⋊C4—224no—
491C22⋊C4—224no—
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—112no—
503C23—114no—
504C23—112no—
505C23—114no—
506C23—224no—
507C23—224no—
508C23—224no—
509C23—224no—
510C23—222no—
511C23—222no—
512C23—222no—
513C23—224no—
514C23—224no—
515C23—442no—
516C23—441no—
517C23—441no—
518C23—442no—
519C23—441no—
520C23—441no—
521C23—442no—
522C23—442no—
523C23—442no—
524C23—4416no—
525C23—4416no—
526C23—442no—
527C23—442no—
528C23—442no—
529C23C22⋊C4×D1111yescharacteristic
530C23C22⋊C4×D1111yescharacteristic
531C23C22×C4×D1111yescharacteristic
532D4—2216no—
533D4—2216no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—22no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—111no—
547C2×C4—111no—
548C2×C4—114no—
549C2×C4—111no—
550C2×C4—111no—
551C2×C4—224no—
552C2×C4—224no—
553C2×C4—224no—
554C2×C4—224no—
555C2×C4—222no—
556C2×C4—222no—
557C2×C4—222no—
558C2×C4—222no—
559C2×C4—222no—
560C2×C4—222no—
561C2×C4—442no—
562C2×C4—442no—
563C2×C4—442no—
564C2×C4—442no—
565C2×C4—444no—
566C2×C4—444no—
567C2×C4—444no—
568C2×C4—444no—
569C2×C4—442no—
570C2×C4—442no—
571C2×C4—442no—
572C2×C4C22⋊C4×D1112yes—
573C2×C4M16×D1114yescomplemented
574C2×C4C2×D4×D1112yes—
575C8—44no—
576C8—444no—
577C22—28no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—114no—
585C22—222no—
586C22—222no—
587C22—222no—
588C22—224no—
589C22—222no—
590C22—222no—
591C22—444no—
592C22—448no—
593C22—448no—
594C22—444no—
595C22—444no—
596C22—444no—
597C22—448no—
598C22—448no—
599C22—442no—
600C22—442no—
601C22D11×#9912yes—
602C22#1062236412yes—
603C22C2×C22⋊C4×D1111yescharacteristic
604C22C2×M16×D1112yes—
605C4—24no—
606C4—22no—
607C4—22no—
608C4—42no—
609C4—112no—
610C4—112no—
611C4—221no—
612C4—221no—
613C4—442no—
614C2—22no—
615C2—22no—
616C2—22no—
617C2—224no—
618C2—442no—
619C2—444no—
620C2D11×#40711yescharacteristic
621C2C2×D11×#9911yescharacteristic
622C2C2×#1062236411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1463C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D44C4
cosocleC22×C4×C11C24
hypercenter#1463D11
hypocenterC11#17362
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
2. D11×#407C2semidirect
3. #13066953C2semidirect
4. #13066946C2semidirect
5. #13066942C2semidirect
6. #13066933C2semidirect
7. C11×#1463C2semidirect
28. #10622339C22semidirect
30. D11×C22⋊C8C22semidirect
31. C11×#324C22semidirect
32. #10622166C22semidirect
33. #10622106C22semidirect
145. C2×D44M16semidirect
192. #1463D11semidirect
227. C22×D11C2×M16semidirect
241. C2×C4×C11C2×M16semidirect
297. #324C2×D11semidirect
498. C11#17362semidirect
573. C2×C4M16×D11semidirect

Maximal subgroups

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

subgroupindex
C22×#669462
D11×#4072
#130669532
#130669462
#130669422
#130669332
C11×#14632
#1736211