Finite Group Databasebeta

← C22×D11×#99 #15617232

Subgroups — C22×D11×#99 #15617232

Order 2816.

7902 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D4×D11C211yesmaximal, characteristic
2C22×C22⋊C4×D11C212yesmaximal, complemented
3C22×#66898C211yesmaximal, characteristic, complemented
4C22×#66870C212yesmaximal, complemented
5C2×D11×#99C2124yesmaximal, direct product factor
6C22×C11×#99C211yesmaximal, characteristic, complemented
7C25×D11C411yescharacteristic, complemented
8C25×D11C2211yescharacteristic
9C23×D4×C11C2211yescharacteristic
10C23×C22⋊D11C411yescharacteristic, complemented
11C23×C22⋊D11C2211yescharacteristic
12C22×D4×D11—22no—
13C22×D4×D11—212no—
14C22×D4×D11—22no—
15C22×D4×D11C4112yescomplemented
16C22×D4×D11C22112yes—
17C23×D44C411yescharacteristic, complemented
18C23×C4×D11—22no—
19C23×C4×D11C411yescharacteristic, complemented
20C22×C11×C22⋊C4C2212yescomplemented
21C22×C22⋊Dic11C2212yescomplemented
22C22×(C2×D11)⋊C4—22no—
23C2×C22⋊C4×D11—212no—
24C2×C22⋊C4×D11C22124yescomplemented
25C2×C11×#99C22112yescomplemented
26C2×#66898C22112yescomplemented
27C2×#66870C22124yescomplemented
28D11×#99C22164yesdirect product factor
29C25×C11C2×C411yescharacteristic, complemented
30C25×C11C2311yescharacteristic
31C24×D11—26no—
32C24×D11—21no—
33C24×D11—21no—
34C24×D11—48no—
35C24×D11—48no—
36C24×D11C2×C411yescharacteristic
37C24×D11C2×C411yescharacteristic
38C24×D11C2×C416yes—
39C24×D11C2×C4112yescomplemented
40C24×D11C2×C411yescharacteristic, complemented
41C24×D11D412yes—
42C24×D11D4112yes—
43C24×D11D412yes—
44C24×D11C2316yes—
45C22×D4×C11—22no—
46C22×D4×C11—26no—
47C22×D4×C11C2×C416yescomplemented
48C22×D4×C11C2316yes—
49C23×C4×C11—22no—
50C23×C4×C11C2×C411yescharacteristic, complemented
51C22×C22⋊D11—22no—
52C22×C22⋊D11—26no—
53C22×C22⋊D11—22no—
54C22×C22⋊D11—26no—
55C22×C22⋊D11C2×C4112yescomplemented
56C22×C22⋊D11C2×C416yescomplemented
57C22×C22⋊D11C2316yes—
58C23×Dic11—22no—
59C23×Dic11C2×C411yescharacteristic, complemented
60C2×D4×D11—224no—
61C2×D4×D11—224no—
62C2×D4×D11—248no—
63C2×D4×D11—224no—
64C2×D4×D11—248no—
65C2×D4×D11—224no—
66C2×D4×D11C2×C4148yescomplemented
67C2×D4×D11C23116yes—
68C22×D44—22no—
69C22×D44—26no—
70C22×D44C2×C4112yescomplemented
71C22×C4×D11—26no—
72C22×C4×D11—21no—
73C22×C4×D11—21no—
74C22×C4×D11—224no—
75C22×C4×D11—416no—
76C22×C4×D11C2×C4112yescomplemented
77C2×C11×C22⋊C4—26no—
78C2×C11×C22⋊C4C23112yescomplemented
79C2×C22⋊Dic11—26no—
80C2×C22⋊Dic11C23112yescomplemented
81C2×(C2×D11)⋊C4—224no—
82C22⋊C4×D11—248no—
83C22⋊C4×D11C23132yescomplemented
84C11×#99C23116yescomplemented
85#66898C23116yescomplemented
86#66870C23132yescomplemented
87C23×#99—111nomaximal, Sylow
88C24×C11—23no—
89C24×C11—21no—
90C24×C11—44no—
91C24×C11—44no—
92C24×C11C22×C411yescharacteristic
93C24×C11C22×C413yes—
94C24×C11C22×C416yescomplemented
95C24×C11C2×D412yes—
96C24×C11C2×D416yes—
97C24×C11C2413yes—
98C23×D11—216no—
99C23×D11—28no—
100C23×D11—23no—
101C23×D11—21no—
102C23×D11—224no—
103C23×D11—212no—
104C23×D11—212no—
105C23×D11—424no—
106C23×D11—448no—
107C23×D11—424no—
108C23×D11—44no—
109C23×D11—48no—
110C23×D11—48no—
111C23×D11—448no—
112C23×D11—448no—
113C23×D11—48no—
114C23×D11—44no—
115C23×D11C22⋊C411yescharacteristic
116C23×D11C22⋊C416yes—
117C23×D11C22⋊C412yes—
118C23×D11C22⋊C4112yes—
119C23×D11C22⋊C416yes—
120C23×D11C22⋊C4124yes—
121C23×D11C22⋊C4112yes—
122C23×D11C22⋊C411yescharacteristic
123C23×D11C22×C416yes—
124C23×D11C22×C416yes—
125C23×D11C22×C4112yes—
126C23×D11C22×C4116yescomplemented
127C23×D11C22×C416yescomplemented
128C23×D11C2×D4112yes—
129C23×D11C2×D4124yes—
130C23×D11C2×D4112yes—
131C23×D11C2414yes—
132C2×D4×C11—212no—
133C2×D4×C11—212no—
134C2×D4×C11—212no—
135C2×D4×C11—212no—
136C2×D4×C11C22×C4112yescomplemented
137C2×D4×C11C2414yes—
138C22×C4×C11—23no—
139C22×C4×C11—21no—
140C22×C4×C11—212no—
141C22×C4×C11—48no—
142C22×C4×C11C22×C416yescomplemented
143C2×C22⋊D11—212no—
144C2×C22⋊D11—212no—
145C2×C22⋊D11—212no—
146C2×C22⋊D11—212no—
147C2×C22⋊D11—224no—
148C2×C22⋊D11—224no—
149C2×C22⋊D11C22×C4116yescomplemented
150C2×C22⋊D11C22×C4112yescomplemented
151C2×C22⋊D11C2414yes—
152C22×Dic11—23no—
153C22×Dic11—21no—
154C22×Dic11—212no—
155C22×Dic11—48no—
156C22×Dic11C22×C416yescomplemented
157D4×D11—296no—
158D4×D11—296no—
159D4×D11—232no—
160D4×D11—232no—
161C2×D44—224no—
162C2×D44—224no—
163C2×D44C22×C4116yescomplemented
164C2×C4×D11—224no—
165C2×C4×D11—212no—
166C2×C4×D11—212no—
167C2×C4×D11—232no—
168C2×C4×D11—496no—
169C2×C4×D11C22×C4116yescomplemented
170C11×C22⋊C4—212no—
171C11×C22⋊C4C2418yescomplemented
172C22⋊Dic11—212no—
173C22⋊Dic11C2418yescomplemented
174(C2×D11)⋊C4—232no—
175C24×D4—111no—
176C23×C22⋊C4—112no—
177C22×#99—1124no—
178C22×#99—111no—
179C22×#99—112no—
180C22×#99D1111yescharacteristic, direct product factor
181C23×C11—28no—
182C23×C11—24no—
183C23×C11—26no—
184C23×C11—26no—
185C23×C11—46no—
186C23×C11—412no—
187C23×C11—46no—
188C23×C11—412no—
189C23×C11—412no—
190C23×C11—44no—
191C23×C11C2×C22⋊C413yes—
192C23×C11C2×C22⋊C416yes—
193C23×C11C2×C22⋊C416yes—
194C23×C11C2×C22⋊C411yescharacteristic
195C23×C11C23×C413yes—
196C23×C11C23×C413yes—
197C23×C11C23×C414yescomplemented
198C23×C11C22×D416yes—
199C23×C11C22×D416yes—
200C23×C11C2511yescharacteristic
201C22×D11—24no—
202C22×D11—28no—
203C22×D11—248no—
204C22×D11—224no—
205C22×D11—224no—
206C22×D11—248no—
207C22×D11—26no—
208C22×D11—26no—
209C22×D11—216no—
210C22×D11—216no—
211C22×D11—448no—
212C22×D11—424no—
213C22×D11—448no—
214C22×D11—48no—
215C22×D11—424no—
216C22×D11—412no—
217C22×D11—412no—
218C22×D11—424no—
219C22×D11—448no—
220C22×D11—496no—
221C22×D11—432no—
222C22×D11—412no—
223C22×D11—44no—
224C22×D11—448no—
225C22×D11—412no—
226C22×D11#9918yesdirect product factor
227C22×D11C2×C22⋊C416yes—
228C22×D11C2×C22⋊C4112yes—
229C22×D11C2×C22⋊C4112yes—
230C22×D11C2×C22⋊C4124yes—
231C22×D11C2×C22⋊C4112yes—
232C22×D11C2×C22⋊C4124yes—
233C22×D11C2×C22⋊C416yes—
234C22×D11C23×C414yes—
235C22×D11C23×C414yes—
236C22×D11C23×C414yescomplemented
237C22×D11C22×D418yes—
238C22×D11C22×D418yes—
239D4×C11—224no—
240D4×C11—28no—
241C2×C4×C11—26no—
242C2×C4×C11—26no—
243C2×C4×C11—28no—
244C2×C4×C11—424no—
245C2×C4×C11C23×C414yescomplemented
246C22⋊D11—224no—
247C22⋊D11—28no—
248C22⋊D11—232no—
249C2×Dic11—26no—
250C2×Dic11—26no—
251C2×Dic11—28no—
252C2×Dic11—424no—
253C2×Dic11C23×C414yescomplemented
254D44—232no—
255C4×D11—216no—
256C4×D11—216no—
257C4×D11—464no—
258C26—111no—
259C26—111no—
260C23×D4—111no—
261C23×D4—111no—
262C23×D4—1112no—
263C23×D4—1112no—
264C23×D4—111no—
265C23×D4—222no—
266C23×D4—2212no—
267C23×D4—222no—
268C23×D4C2×D1111yescharacteristic
269C24×C4—111no—
270C24×C4—222no—
271C22×C22⋊C4—112no—
272C22×C22⋊C4—1124no—
273C22×C22⋊C4—2212no—
274C22×C22⋊C4—222no—
275C22×C22⋊C4C2×D1112yescomplemented
276C2×#99—1112no—
277C2×#99—1124no—
278C2×#99—1164no—
279C2×#99C2×D11112yesdirect product factor
280C22×C11—212no—
281C22×C11—26no—
282C22×C11—26no—
283C22×C11—212no—
284C22×C11—24no—
285C22×C11—46no—
286C22×C11—43no—
287C22×C11—46no—
288C22×C11—41no—
289C22×C11—44no—
290C22×C11—412no—
291C22×C11—412no—
292C22×C11C2×#9914yescomplemented
293C22×C11C22×C22⋊C413yes—
294C22×C11C22×C22⋊C416yes—
295C22×C11C22×C22⋊C413yes—
296C22×C11C24×C411yescharacteristic
297C22×C11C23×D412yes—
298C2×D11—212no—
299C2×D11—224no—
300C2×D11—224no—
301C2×D11—28no—
302C2×D11—248no—
303C2×D11—216no—
304C2×D11—24no—
305C2×D11—424no—
306C2×D11—412no—
307C2×D11—44no—
308C2×D11—48no—
309C2×D11—432no—
310C2×D11—412no—
311C2×D11—412no—
312C2×D11—432no—
313C2×D11—44no—
314C2×D11C2×#99124yesdirect product factor
315C2×D11C22×C22⋊C414yes—
316C2×D11C22×C22⋊C418yes—
317C2×D11C22×C22⋊C414yes—
318C4×C11—24no—
319C4×C11—48no—
320Dic11—24no—
321Dic11—48no—
322C25—111no—
323C25—112no—
324C25—116no—
325C25—111no—
326C25—1112no—
327C25—112no—
328C25—116no—
329C25—111no—
330C25—1112no—
331C25—226no—
332C25—221no—
333C25—221no—
334C25—448no—
335C25—448no—
336C25C4×D1111yescharacteristic, complemented
337C25C22×D1111yescharacteristic
338C22×D4—26no—
339C22×D4—22no—
340C22×D4—116no—
341C22×D4—1112no—
342C22×D4—116no—
343C22×D4—1148no—
344C22×D4—1116no—
345C22×D4—1112no—
346C22×D4—226no—
347C22×D4—222no—
348C22×D4—2224no—
349C22×D4—2224no—
350C22×D4—2248no—
351C22×D4—2224no—
352C22×D4—2224no—
353C22×D4—2248no—
354C22×D4—226no—
355C22×D4—222no—
356C22×D4—226no—
357C22×D4—222no—
358C22×D4C4×D1116yescomplemented
359C22×D4C22×D1116yes—
360C23×C4—22no—
361C23×C4—111no—
362C23×C4—1112no—
363C23×C4—226no—
364C23×C4—221no—
365C23×C4—221no—
366C23×C4—2224no—
367C23×C4—222no—
368C23×C4—4416no—
369C23×C4C4×D1111yescharacteristic, complemented
370C2×C22⋊C4—26no—
371C2×C22⋊C4—1112no—
372C2×C22⋊C4—1132no—
373C2×C22⋊C4—2248no—
374C2×C22⋊C4—2224no—
375C2×C22⋊C4—226no—
376C2×C22⋊C4C22×D11112yescomplemented
377#99—1116no—
378#99—1132no—
379#99C22×D11116yesdirect product factor
380C2×C11—22no—
381C2×C11—23no—
382C2×C11—21no—
383C2×C11—26no—
384C2×C11—44no—
385C2×C11C22×#9916yescomplemented
386C2×C11C23×C22⋊C411yescharacteristic
387D11—24no—
388D11—28no—
389D11—44no—
390D11C22×#9918yesdirect product factor
391C24—23no—
392C24—21no—
393C24—44no—
394C24—44no—
395C24—111no—
396C24—116no—
397C24—1112no—
398C24—111no—
399C24—112no—
400C24—116no—
401C24—1112no—
402C24—1124no—
403C24—1112no—
404C24—116no—
405C24—1112no—
406C24—116no—
407C24—1124no—
408C24—1112no—
409C24—114no—
410C24—116no—
411C24—1116no—
412C24—2216no—
413C24—228no—
414C24—2212no—
415C24—2224no—
416C24—2212no—
417C24—223no—
418C24—221no—
419C24—448no—
420C24—444no—
421C24—444no—
422C24—448no—
423C24—4424no—
424C24—4448no—
425C24—4424no—
426C24—4448no—
427C24—4448no—
428C24—448no—
429C24C2×C4×D1111yescharacteristic
430C24C2×C4×D1113yes—
431C24C2×C4×D1116yescomplemented
432C24D4×D1112yes—
433C24D4×D1116yes—
434C24C23×D1113yes—
435C2×D4—212no—
436C2×D4—212no—
437C2×D4—212no—
438C2×D4—212no—
439C2×D4—1112no—
440C2×D4—1116no—
441C2×D4—114no—
442C2×D4—1116no—
443C2×D4—2224no—
444C2×D4—2224no—
445C2×D4—2296no—
446C2×D4—2296no—
447C2×D4—2232no—
448C2×D4—2232no—
449C2×D4—2224no—
450C2×D4—2224no—
451C2×D4—2212no—
452C2×D4—2212no—
453C2×D4—2212no—
454C2×D4—2212no—
455C2×D4C2×C4×D11112yescomplemented
456C2×D4C23×D1114yes—
457C22×C4—23no—
458C22×C4—21no—
459C22×C4—212no—
460C22×C4—48no—
461C22×C4—116no—
462C22×C4—1116no—
463C22×C4—2212no—
464C22×C4—2224no—
465C22×C4—2212no—
466C22×C4—2232no—
467C22×C4—223no—
468C22×C4—221no—
469C22×C4—2212no—
470C22×C4—4496no—
471C22×C4—448no—
472C22×C4C2×C4×D1116yescomplemented
473C22⋊C4—212no—
474C22⋊C4—118no—
475C22⋊C4—2232no—
476C22⋊C4—2212no—
477C22⋊C4C23×D1118yescomplemented
478C11C23×#9911yescharacteristic, complemented, Sylow
479C23—28no—
480C23—24no—
481C23—26no—
482C23—26no—
483C23—46no—
484C23—412no—
485C23—46no—
486C23—412no—
487C23—412no—
488C23—44no—
489C23—116no—
490C23—118no—
491C23—1112no—
492C23—116no—
493C23—1124no—
494C23—1112no—
495C23—114no—
496C23—118no—
497C23—1124no—
498C23—1112no—
499C23—114no—
500C23—118no—
501C23—114no—
502C23—2248no—
503C23—2248no—
504C23—2224no—
505C23—2224no—
506C23—2216no—
507C23—2216no—
508C23—228no—
509C23—224no—
510C23—226no—
511C23—226no—
512C23—4424no—
513C23—4412no—
514C23—4412no—
515C23—4424no—
516C23—4412no—
517C23—4412no—
518C23—4448no—
519C23—4448no—
520C23—4424no—
521C23—4448no—
522C23—448no—
523C23—4432no—
524C23—4496no—
525C23—4448no—
526C23—444no—
527C23C22⋊C4×D1113yes—
528C23C22⋊C4×D1116yes—
529C23C22⋊C4×D1116yes—
530C23C22⋊C4×D1111yescharacteristic
531C23C22×C4×D1113yes—
532C23C22×C4×D1113yes—
533C23C22×C4×D1114yescomplemented
534C23C2×D4×D1116yes—
535C23C2×D4×D1116yes—
536C23C24×D1111yescharacteristic
537D4—224no—
538D4—28no—
539D4—2232no—
540D4—2232no—
541D4—2224no—
542D4—228no—
543C2×C4—26no—
544C2×C4—26no—
545C2×C4—28no—
546C2×C4—424no—
547C2×C4—114no—
548C2×C4—2216no—
549C2×C4—2216no—
550C2×C4—226no—
551C2×C4—226no—
552C2×C4—228no—
553C2×C4—4464no—
554C2×C4—4424no—
555C2×C4C22×C4×D1114yescomplemented
556C22—212no—
557C22—26no—
558C22—26no—
559C22—212no—
560C22—24no—
561C22—46no—
562C22—43no—
563C22—46no—
564C22—41no—
565C22—44no—
566C22—412no—
567C22—412no—
568C22—1124no—
569C22—114no—
570C22—114no—
571C22—118no—
572C22—2216no—
573C22—2224no—
574C22—228no—
575C22—2248no—
576C22—2212no—
577C22—2224no—
578C22—224no—
579C22—448no—
580C22—4412no—
581C22—444no—
582C22—4424no—
583C22—444no—
584C22—4412no—
585C22—4432no—
586C22—4432no—
587C22—4412no—
588C22D11×#9914yesdirect product factor
589C22C2×C22⋊C4×D1113yes—
590C22C2×C22⋊C4×D1116yes—
591C22C2×C22⋊C4×D1113yes—
592C22C23×C4×D1111yescharacteristic
593C22C22×D4×D1112yes—
594C4—24no—
595C4—48no—
596C4—224no—
597C4—448no—
598C2—22no—
599C2—23no—
600C2—21no—
601C2—26no—
602C2—44no—
603C2—118no—
604C2—224no—
605C2—228no—
606C2—444no—
607C2C2×D11×#9916yesdirect product factor
608C2C22×C22⋊C4×D1111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC22×C11×#99C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D4×D11C2
cosocleC23×C11C25
hypercenterC22×#99D11
hypocenterC11C23×#99
LCSG ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C25 ◁ C22×#99

Complements

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

NH ≅ G/Ntype
2. C22×C22⋊C4×D11C2semidirect
3. C22×#66898C2semidirect
4. C22×#66870C2semidirect
5. C2×D11×#99C2direct (N × H)
6. C22×C11×#99C2semidirect
7. C25×D11C4semidirect
10. C23×C22⋊D11C4semidirect
15. C22×D4×D11C4semidirect
17. C23×D44C4semidirect
19. C23×C4×D11C4semidirect
20. C22×C11×C22⋊C4C22semidirect
21. C22×C22⋊Dic11C22semidirect
24. C2×C22⋊C4×D11C22semidirect
25. C2×C11×#99C22semidirect
26. C2×#66898C22semidirect
27. C2×#66870C22semidirect
28. D11×#99C22direct (N × H)
29. C25×C11C2×C4semidirect
39. C24×D11C2×C4semidirect
40. C24×D11C2×C4semidirect
47. C22×D4×C11C2×C4semidirect
50. C23×C4×C11C2×C4semidirect
55. C22×C22⋊D11C2×C4semidirect
56. C22×C22⋊D11C2×C4semidirect
59. C23×Dic11C2×C4semidirect
66. C2×D4×D11C2×C4semidirect
70. C22×D44C2×C4semidirect
76. C22×C4×D11C2×C4semidirect
78. C2×C11×C22⋊C4C23semidirect
80. C2×C22⋊Dic11C23semidirect
83. C22⋊C4×D11C23semidirect
84. C11×#99C23semidirect
85. #66898C23semidirect
86. #66870C23semidirect
94. C24×C11C22×C4semidirect
126. C23×D11C22×C4semidirect
127. C23×D11C22×C4semidirect
136. C2×D4×C11C22×C4semidirect
142. C22×C4×C11C22×C4semidirect
149. C2×C22⋊D11C22×C4semidirect
150. C2×C22⋊D11C22×C4semidirect
156. C22×Dic11C22×C4semidirect
163. C2×D44C22×C4semidirect
169. C2×C4×D11C22×C4semidirect
171. C11×C22⋊C4C24semidirect
173. C22⋊Dic11C24semidirect
180. C22×#99D11direct (N × H)
197. C23×C11C23×C4semidirect
226. C22×D11#99direct (N × H)
236. C22×D11C23×C4semidirect
245. C2×C4×C11C23×C4semidirect
253. C2×Dic11C23×C4semidirect
275. C22×C22⋊C4C2×D11semidirect
279. C2×#99C2×D11direct (N × H)
292. C22×C11C2×#99semidirect
314. C2×D11C2×#99direct (N × H)
336. C25C4×D11semidirect
358. C22×D4C4×D11semidirect
369. C23×C4C4×D11semidirect
376. C2×C22⋊C4C22×D11semidirect
379. #99C22×D11direct (N × H)
385. C2×C11C22×#99semidirect
390. D11C22×#99direct (N × H)
431. C24C2×C4×D11semidirect
455. C2×D4C2×C4×D11semidirect
472. C22×C4C2×C4×D11semidirect
477. C22⋊C4C23×D11semidirect
478. C11C23×#99semidirect
533. C23C22×C4×D11semidirect
555. C2×C4C22×C4×D11semidirect
588. C22D11×#99direct (N × H)
607. C2C2×D11×#99direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D4×D112
C22×C22⋊C4×D112
C22×#668982
C22×#668702
C2×D11×#992
C22×C11×#992
C23×#9911