Finite Group Databasebeta

← C2×D11×#462 #15620571

Subgroups — C2×D11×#462 #15620571

Order 2816.

2790 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q16×D11C212yesmaximal
2C2×D11×C4⋊Q8C211yesmaximal, characteristic
3C2×C4×Q8×D11C211yesmaximal, characteristic
4C2×#10622462C211yesmaximal, characteristic, complemented
5C2×#10622644C211yesmaximal, characteristic, complemented
6C2×#10622406C212yesmaximal, complemented
7C2×#10622795C212yesmaximal, complemented
8C2×#10622703C211yesmaximal, characteristic, complemented
9D11×#462C2116yesmaximal, direct product factor
10C2×D11×C4⋊C8C211yesmaximal, characteristic
11C2×D11×#103C212yesmaximal
12C2×C11×#462C211yesmaximal, characteristic, complemented
13C22×Q8×D11C2212yes—
14C22×Q8×D11C2211yescharacteristic
15C22×C11×Q16C2212yes—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×#66997C2212yes—
20C22×#4326C2212yes—
21C22×#4326C2212yes—
22C2×Q16×D11—216no—
23C2×Q16×D11C22116yes—
24C22×Dic44C2212yes—
25C22×C8×D11C2212yes—
26D11×C4⋊Q8—24no—
27D11×C4⋊Q8C2218yes—
28C4×Q8×D11—24no—
29C4×Q8×D11C2218yes—
30C2×C4⋊C4×D11—21no—
31C2×C4⋊C4×D11—21no—
32C2×C4⋊C4×D11—21no—
33C2×C4⋊C4×D11C2211yescharacteristic
34C2×#66941—21no—
35C2×#66941—21no—
36C2×#66940—21no—
37C2×#66940C2211yescharacteristic
38C2×C42×D11—21no—
39C2×C42×D11C2211yescharacteristic
40C2×#66922C2211yescharacteristic
41C2×C4×Dic22—21no—
42C2×C4×Dic22C2211yescharacteristic
43C11×#462C2218yescomplemented
44C2×C11×C4⋊C8C2211yescharacteristic
45C2×C11×#103C2212yes—
46C2×#66899C2212yes—
47#10622795C22116yescomplemented
48C2×#66880C2212yes—
49C2×Dic11⋊C8C2212yes—
50#10622703C2218yescomplemented
51#10622644C2218yescomplemented
52C2×#66874C2212yes—
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54#10622462C2218yescomplemented
55D11×C4⋊C8C2218yes—
56D11×#103C22116yes—
57#10622406C22116yescomplemented
58C22×Q8×C11C2312yes—
59C22×Q8×C11C2311yescharacteristic
60C2×Q8×D11—22no—
61C2×Q8×D11—24no—
62C2×Q8×D11—24no—
63C2×Q8×D11—28no—
64C2×Q8×D11—28no—
65C2×Q8×D11D418yes—
66C2×Q8×D11C2318yes—
67C2×Q8×D11C2314yes—
68C22×C4×D11—21no—
69C22×C4×D11—21no—
70C22×C4×D11—22no—
71C22×C4×D11D411yescharacteristic
72C22×C4×D11D411yescharacteristic
73C22×C4×D11C2311yescharacteristic
74C22×Dic22—21no—
75C22×Dic22—22no—
76C22×Dic22C2312yes—
77C22×Dic22C2311yescharacteristic
78C2×C11×Q16—28no—
79C2×C11×Q16C2318yes—
80C22×C8×C11C2312yes—
81C11×C4⋊Q8—22no—
82C11×C4⋊Q8C2314yes—
83C4×Q8×C11—22no—
84C4×Q8×C11C2314yes—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C42×C11—21no—
90C2×C42×C11C2311yescharacteristic
91Q8×Dic11—22no—
92Q8×Dic11C2314yes—
93#66997—24no—
94#66997C2318yes—
95C2×#4326—28no—
96C2×#4326—28no—
97C2×#4326C2318yes—
98C2×#4326C2318yes—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11C2311yescharacteristic
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—21no—
106C2×Dic11⋊C4—22no—
107C2×Dic11⋊C4—22no—
108C2×C4×Dic11—21no—
109C2×C4×Dic11—21no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11D411yescharacteristic
112C2×C4×Dic11D411yescharacteristic
113C2×C4×Dic11C2311yescharacteristic
114C22×C11⋊C8C2312yes—
115Q16×D11—264no—
116C2×Dic44—28no—
117C2×Dic44C2318yes—
118C2×C8×D11—28no—
119C2×C8×D11C2318yes—
120C4⋊C4×D11—28no—
121C4⋊C4×D11—28no—
122C4⋊C4×D11—28no—
123C4⋊C4×D11—22no—
124C4⋊C4×D11C2314yes—
125#66941—28no—
126#66941—28no—
127#66940—28no—
128#66940—22no—
129#66940C2314yes—
130C42×D11—28no—
131C42×D11D414yes—
132C42×D11C2314yes—
133#66922—22no—
134#66922C2314yes—
135C4×Dic22—22no—
136C4×Dic22—28no—
137C4×Dic22C2314yes—
138C11×C4⋊C8C2314yes—
139C11×#103C2318yes—
140#66899C2318yes—
141#66880C2318yes—
142Dic11⋊C8C2318yes—
143#66874C2318yes—
144C4⋊(C11⋊C8)C2314yes—
145C22×#462—111nomaximal, Sylow
146C23×D11C2×D411yescharacteristic
147C2×Q8×C11—21no—
148C2×Q8×C11—22no—
149C2×Q8×C11—22no—
150C2×Q8×C11—24no—
151C2×Q8×C11—24no—
152C2×Q8×C11C2×D414yes—
153C2×Q8×C11C2414yes—
154C2×Q8×C11C2412yes—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—22no—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2411yescharacteristic
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—22no—
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167Q8×D11—216no—
168Q8×D11—28no—
169Q8×D11—216no—
170Q8×D11—216no—
171Q8×D11—416no—
172Q8×D11C2×D4116yes—
173C2×C4×D11—28no—
174C2×C4×D11—24no—
175C2×C4×D11—24no—
176C2×C4×D11—24no—
177C2×C4×D11—28no—
178C2×C4×D11—48no—
179C2×C4×D11—44no—
180C2×C4×D11Q1618yescomplemented
181C2×C4×D11C2×D414yes—
182C2×C4×D11C2×D414yes—
183C2×C4×D11C2×D412yes—
184C2×C4×D11C2×D414yes—
185C2×C4×D11#4114yes—
186C2×C4×D11C2412yes—
187C2×Dic22—28no—
188C2×Dic22—24no—
189C2×Dic22—28no—
190C2×Dic22—21no—
191C2×Dic22—24no—
192C2×Dic22—22no—
193C2×Dic22—22no—
194C2×Dic22—24no—
195C2×Dic22—48no—
196C2×Dic22C2×D414yes—
197C2×Dic22C2414yes—
198C2×Dic22C2412yes—
199C11×Q16—216no—
200C2×C8×C11—24no—
201C2×C8×C11C2414yes—
202C11×C4⋊C4—24no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—24no—
205C11×C4⋊C4—24no—
206C11×C4⋊C4C2412yes—
207C42×C11—24no—
208C42×C11C2×D412yes—
209C42×C11C2412yes—
210#4326—216no—
211#4326—216no—
212C4⋊Dic11—24no—
213C4⋊Dic11—21no—
214C4⋊Dic11—24no—
215C4⋊Dic11—24no—
216C4⋊Dic11C2412yes—
217Dic11⋊C4—24no—
218Dic11⋊C4—24no—
219Dic11⋊C4—28no—
220Dic11⋊C4—28no—
221Dic11⋊C4—24no—
222C4×Dic11—24no—
223C4×Dic11—24no—
224C4×Dic11—24no—
225C4×Dic11C2×D414yes—
226C4×Dic11C2×D412yes—
227C4×Dic11C2×D414yes—
228C4×Dic11C2412yes—
229C2×C11⋊C8—24no—
230C2×C11⋊C8C2414yes—
231Dic44—216no—
232C8×D11—216no—
233C23×Q16—112no—
234C22×C4⋊Q8—111no—
235C22×C4×Q8—111no—
236C2×#462—1116no—
237C2×#462—111no—
238C2×#462—112no—
239C2×#462—112no—
240C2×#462—111no—
241C2×#462—111no—
242C2×#462D1111yescharacteristic, direct product factor
243C22×C4⋊C8—111no—
244C22×#103—112no—
245C23×C11C22×D411yescharacteristic
246C22×D11#12114yes—
247C22×D11C2×Q1614yes—
248C22×D11#13714yes—
249C22×D11C22×D412yes—
250Q8×C11—24no—
251Q8×C11—22no—
252Q8×C11—24no—
253Q8×C11—24no—
254Q8×C11—44no—
255Q8×C11C22×D414yes—
256C2×C4×C11—24no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—24no—
261C2×C4×C11—44no—
262C2×C4×C11—42no—
263C2×C4×C11C2×Q1614yescomplemented
264C2×C4×C11C22×D412yes—
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C22×D412yes—
267C2×C4×C11C22×D412yes—
268C2×C4×C11C2×#4112yes—
269C2×C4×C11C2511yescharacteristic
270C2×Dic11—24no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—24no—
275C2×Dic11—44no—
276C2×Dic11—42no—
277C2×Dic11#12114yes—
278C2×Dic11C2×Q1614yescomplemented
279C2×Dic11C22×D412yes—
280C2×Dic11C22×D412yes—
281C2×Dic11C22×D412yes—
282C4×D11—216no—
283C4×D11—28no—
284C4×D11—416no—
285C4×D11—48no—
286C4×D11#12118yes—
287C4×D11C2×Q16116yescomplemented
288C4×D11C22×D414yes—
289C4×D11C2×#4114yes—
290Dic22—24no—
291Dic22—22no—
292Dic22—216no—
293Dic22—24no—
294Dic22—24no—
295Dic22—44no—
296Dic22—416no—
297Dic22C22×D414yes—
298C8×C11—24no—
299C11⋊C8—24no—
300C23×Q8—111no—
301C23×Q8—112no—
302C22×Q16—112no—
303C22×Q16—112no—
304C22×Q16—1116no—
305C22×Q16—112no—
306C22×Q16—2216no—
307C22×Q16C2×D1112yes—
308C23×C8—112no—
309C2×C4⋊Q8—112no—
310C2×C4⋊Q8—118no—
311C2×C4⋊Q8—111no—
312C2×C4⋊Q8—221no—
313C2×C4⋊Q8—221no—
314C2×C4⋊Q8—224no—
315C2×C4⋊Q8C2×D1111yescharacteristic
316C2×C4×Q8—111no—
317C2×C4×Q8—118no—
318C2×C4×Q8—111no—
319C2×C4×Q8—111no—
320C2×C4×Q8—221no—
321C2×C4×Q8—221no—
322C2×C4×Q8—224no—
323C2×C4×Q8C2×D1111yescharacteristic
324C22×C4⋊C4—111no—
325C22×C4⋊C4—221no—
326C22×C4⋊C4—221no—
327C22×C4⋊C4—221no—
328C22×C42—111no—
329C22×C42—221no—
330#462—1116no—
331#462—118no—
332#462—118no—
333#462—118no—
334#462—1116no—
335#462C2×D1118yesdirect product factor
336C2×C4⋊C8—112no—
337C2×C4⋊C8—111no—
338C2×C4⋊C8—118no—
339C2×C4⋊C8C2×D1111yescharacteristic
340C2×#103—112no—
341C2×#103—112no—
342C2×#103—112no—
343C2×#103—1116no—
344C2×#103C2×D1112yes—
345C22×C11C2×#12112yes—
346C22×C11C22×Q1612yes—
347C22×C11C2×#13712yes—
348C22×C11C23×D411yescharacteristic
349C2×D11#462116yesdirect product factor
350C2×D11C2×#12114yes—
351C2×D11C22×Q1614yes—
352C2×D11C2×#13714yes—
353C4×C11—24no—
354C4×C11—22no—
355C4×C11—44no—
356C4×C11—42no—
357C4×C11C2×#12112yes—
358C4×C11C22×Q1614yescomplemented
359C4×C11C23×D411yescharacteristic
360C4×C11C22×#4111yescharacteristic
361Dic11—24no—
362Dic11—22no—
363Dic11—44no—
364Dic11—42no—
365Dic11C2×#12114yes—
366Dic11C22×Q1614yescomplemented
367C22×Q8—118no—
368C22×Q8—114no—
369C22×Q8—118no—
370C22×Q8—111no—
371C22×Q8—112no—
372C22×Q8—221no—
373C22×Q8—222no—
374C22×Q8—222no—
375C22×Q8—224no—
376C22×Q8—224no—
377C22×Q8—228no—
378C22×Q8—228no—
379C22×Q8C22×D1112yes—
380C22×Q8C22×D1111yescharacteristic
381C23×C4—111no—
382C23×C4—111no—
383C23×C4—111no—
384C23×C4—221no—
385C23×C4—221no—
386C23×C4—222no—
387C2×Q16—28no—
388C2×Q16—118no—
389C2×Q16—118no—
390C2×Q16—118no—
391C2×Q16—228no—
392C2×Q16—2264no—
393C2×Q16—228no—
394C2×Q16—228no—
395C2×Q16C22×D1118yes—
396C22×C8—112no—
397C22×C8—118no—
398C22×C8—228no—
399C22×C8C22×D1112yes—
400C4⋊Q8—22no—
401C4⋊Q8—118no—
402C4⋊Q8—114no—
403C4⋊Q8—228no—
404C4⋊Q8—228no—
405C4⋊Q8—224no—
406C4⋊Q8—222no—
407C4⋊Q8C22×D1114yes—
408C4×Q8—22no—
409C4×Q8—114no—
410C4×Q8—114no—
411C4×Q8—114no—
412C4×Q8—228no—
413C4×Q8—228no—
414C4×Q8—222no—
415C4×Q8—222no—
416C4×Q8—222no—
417C4×Q8C22×D1114yes—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—114no—
423C2×C4⋊C4—222no—
424C2×C4⋊C4—228no—
425C2×C4⋊C4—228no—
426C2×C4⋊C4—228no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—222no—
431C2×C4⋊C4—222no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4C22×D1111yescharacteristic
436C2×C42—21no—
437C2×C42—111no—
438C2×C42—111no—
439C2×C42—111no—
440C2×C42—114no—
441C2×C42—114no—
442C2×C42—228no—
443C2×C42—221no—
444C2×C42—221no—
445C2×C42—221no—
446C2×C42C22×D1111yescharacteristic
447C4⋊C8—118no—
448C4⋊C8—114no—
449C4⋊C8C22×D1114yes—
450#103—118no—
451#103—118no—
452#103—118no—
453#103C22×D1118yes—
454C2×C11C2×#46214yescomplemented
455C2×C11C22×#12111yescharacteristic
456C2×C11C23×Q1611yescharacteristic
457C2×C11C22×#13711yescharacteristic
458D11C2×#46218yesdirect product factor
459C24—111no—
460C2×Q8—21no—
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—24no—
464C2×Q8—24no—
465C2×Q8—1116no—
466C2×Q8—114no—
467C2×Q8—112no—
468C2×Q8—114no—
469C2×Q8—224no—
470C2×Q8—228no—
471C2×Q8—228no—
472C2×Q8—2216no—
473C2×Q8—228no—
474C2×Q8—2216no—
475C2×Q8—2216no—
476C2×Q8—221no—
477C2×Q8—222no—
478C2×Q8—222no—
479C2×Q8—224no—
480C2×Q8—224no—
481C2×Q8—448no—
482C2×Q8—4416no—
483C2×Q8D4×D1114yes—
484C2×Q8C23×D1114yes—
485C2×Q8C23×D1112yes—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—118no—
492C22×C4—114no—
493C22×C4—112no—
494C22×C4—114no—
495C22×C4—114no—
496C22×C4—112no—
497C22×C4—111no—
498C22×C4—114no—
499C22×C4—224no—
500C22×C4—224no—
501C22×C4—228no—
502C22×C4—224no—
503C22×C4—228no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—222no—
507C22×C4—448no—
508C22×C4—444no—
509C22×C4D4×D1111yescharacteristic
510C22×C4D4×D1111yescharacteristic
511C22×C4C23×D1111yescharacteristic
512Q16—216no—
513Q16—2216no—
514Q16—2216no—
515Q16—2216no—
516C2×C8—24no—
517C2×C8—114no—
518C2×C8—2216no—
519C2×C8—224no—
520C2×C8C23×D1114yes—
521C4⋊C4—24no—
522C4⋊C4—24no—
523C4⋊C4—24no—
524C4⋊C4—21no—
525C4⋊C4—112no—
526C4⋊C4—224no—
527C4⋊C4—224no—
528C4⋊C4—224no—
529C4⋊C4—228no—
530C4⋊C4—228no—
531C4⋊C4—221no—
532C4⋊C4—224no—
533C4⋊C4—224no—
534C4⋊C4—224no—
535C4⋊C4C23×D1112yes—
536C42—24no—
537C42—114no—
538C42—112no—
539C42—114no—
540C42—112no—
541C42—224no—
542C42—224no—
543C42—224no—
544C42D4×D1112yes—
545C42C23×D1112yes—
546C11C22×#46211yescharacteristic, complemented, Sylow
547C23—114no—
548C23—114no—
549C23—114no—
550C23—112no—
551C23C2×D4×D1111yescharacteristic
552Q8—24no—
553Q8—22no—
554Q8—24no—
555Q8—24no—
556Q8—44no—
557Q8—114no—
558Q8—2216no—
559Q8—224no—
560Q8—222no—
561Q8—224no—
562Q8—224no—
563Q8—4416no—
564Q8—444no—
565Q8C2×D4×D1114yes—
566C2×C4—22no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—42no—
572C2×C4—44no—
573C2×C4—114no—
574C2×C4—114no—
575C2×C4—112no—
576C2×C4—112no—
577C2×C4—1116no—
578C2×C4—118no—
579C2×C4—114no—
580C2×C4—114no—
581C2×C4—112no—
582C2×C4—228no—
583C2×C4—2216no—
584C2×C4—222no—
585C2×C4—224no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—224no—
589C2×C4—4416no—
590C2×C4—448no—
591C2×C4—442no—
592C2×C4—444no—
593C2×C4Q16×D1114yescomplemented
594C2×C4C2×D4×D1112yes—
595C2×C4C2×D4×D1112yes—
596C2×C4C2×D4×D1111yescharacteristic
597C2×C4C2×D4×D1112yes—
598C2×C4#41×D1112yes—
599C2×C4C24×D1111yescharacteristic
600C8—24no—
601C8—224no—
602C22—1116no—
603C22—114no—
604C22—114no—
605C22—114no—
606C22D11×#12112yes—
607C22C2×Q16×D1112yes—
608C22D11×#13712yes—
609C22C22×D4×D1111yescharacteristic
610C4—22no—
611C4—24no—
612C4—42no—
613C4—44no—
614C4—114no—
615C4—114no—
616C4—222no—
617C4—224no—
618C4—442no—
619C4—444no—
620C4D11×#12112yes—
621C4C2×Q16×D1114yescomplemented
622C4C22×D4×D1111yescharacteristic
623C4C2×#41×D1111yescharacteristic
624C2—118no—
625C2D11×#46214yesdirect product factor
626C2C2×D11×#12111yescharacteristic
627C2C22×Q16×D1111yescharacteristic
628C2C2×D11×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#462C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenterC2×#462D11
hypocenterC11C22×#462
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
4. C2×#10622462C2semidirect
5. C2×#10622644C2semidirect
6. C2×#10622406C2semidirect
7. C2×#10622795C2semidirect
8. C2×#10622703C2semidirect
9. D11×#462C2direct (N × H)
12. C2×C11×#462C2semidirect
43. C11×#462C22semidirect
47. #10622795C22semidirect
50. #10622703C22semidirect
51. #10622644C22semidirect
54. #10622462C22semidirect
57. #10622406C22semidirect
180. C2×C4×D11Q16semidirect
242. C2×#462D11direct (N × H)
263. C2×C4×C11C2×Q16semidirect
278. C2×Dic11C2×Q16semidirect
287. C4×D11C2×Q16semidirect
335. #462C2×D11direct (N × H)
349. C2×D11#462direct (N × H)
358. C4×C11C22×Q16semidirect
366. Dic11C22×Q16semidirect
454. C2×C11C2×#462semidirect
458. D11C2×#462direct (N × H)
546. C11C22×#462semidirect
593. C2×C4Q16×D11semidirect
621. C4C2×Q16×D11semidirect
625. C2D11×#462direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q16×D112
C2×D11×C4⋊Q82
C2×C4×Q8×D112
C2×#106224622
C2×#106226442
C2×#106224062
C2×#106227952
C2×#106227032
D11×#4622
C2×D11×C4⋊C82
C2×D11×#1032
C2×C11×#4622
C22×#46211