Finite Group Databasebeta

← C2×D11×#470 #15620896

Subgroups — C2×D11×#470 #15620896

Order 2816.

2878 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q16×D11C211yesmaximal, characteristic, complemented
2C22×M16×D11C211yesmaximal, characteristic
3C2×D11×C22⋊Q8C212yesmaximal
4C2×#10622481C211yesmaximal, characteristic, complemented
5C2×#10622750C211yesmaximal, characteristic, complemented
6C2×#10622429C212yesmaximal, complemented
7C2×#10622665C212yesmaximal, complemented
8C2×#10622802C211yesmaximal, characteristic, complemented
9D11×#470C2116yesmaximal, direct product factor
10C2×D11×#106C211yesmaximal, characteristic, complemented
11C2×D11×#103C212yesmaximal, complemented
12C2×C11×#470C211yesmaximal, characteristic, complemented
13C22×Q8×D11C2212yes—
14C23×C4×D11C2211yescharacteristic
15C22×C11×Q16C2211yescharacteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C2×C11×C22⋊Q8C2212yes—
18C2×#66999C2212yes—
19C22×#4326C2212yescomplemented
20C2×#66977C2212yes—
21C22×#4318C2211yescharacteristic
22C2×Q16×D11—28no—
23C2×Q16×D11C2218yescomplemented
24C2×M16×D11—28no—
25C2×M16×D11C2218yes—
26C22×Dic44C2211yescharacteristic, complemented
27C22×#4313C2211yescharacteristic
28C22×#4313C2211yescharacteristic
29C22×C8×D11C2211yescharacteristic
30C22×C8×D11C2211yescharacteristic
31D11×C22⋊Q8—28no—
32D11×C22⋊Q8C22116yes—
33C2×#66950C2212yes—
34C2×#66949—22no—
35C2×C4⋊C4×D11—22no—
36C2×C4⋊C4×D11C2212yes—
37C2×C22⋊C4×D11—22no—
38C2×#66931—22no—
39C11×#470C2218yescomplemented
40C2×C11×#106C2211yescharacteristic, complemented
41C2×C11×#103C2212yescomplemented
42C2×#66899C2212yescomplemented
43#10622802C2218yescomplemented
44#10622750C2218yescomplemented
45C2×#66881C2211yescharacteristic, complemented
46C2×#66880C2212yescomplemented
47#10622665C22116yescomplemented
48C2×#66874C2212yescomplemented
49C2×#66872C2212yescomplemented
50#10622481C2218yescomplemented
51D11×#106C2218yescomplemented
52#10622429C22116yescomplemented
53D11×#103C22116yescomplemented
54C24×D11D411yescharacteristic
55C22×Q8×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C23×Dic11D411yescharacteristic
58C2×Q8×D11—24no—
59C2×Q8×D11—28no—
60C2×Q8×D11—28no—
61C2×Q8×D11C2318yes—
62C22×C4×D11—24no—
63C22×C4×D11—24no—
64C22×C4×D11—22no—
65C22×C4×D11—22no—
66C22×C4×D11D411yescharacteristic
67C22×C4×D11D411yescharacteristic
68C22×C4×D11D414yes—
69C22×C4×D11C2311yescharacteristic
70C22×C4×D11C2314yes—
71C22×C4×D11C2311yescharacteristic
72C22×Dic22—22no—
73C22×Dic22C2312yes—
74C2×C11×Q16—24no—
75C2×C11×Q16C2314yescomplemented
76C2×C11×M16—24no—
77C2×C11×M16C2314yes—
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C11×C22⋊Q8—24no—
81C11×C22⋊Q8C2318yes—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C22⋊C4—22no—
85C2×C22⋊Dic11—22no—
86#66999—24no—
87#66999C2318yes—
88C2×#4326—28no—
89C2×#4326C2318yescomplemented
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—22no—
92C2×C4⋊Dic11—22no—
93C2×C4⋊Dic11C2312yes—
94#66977—24no—
95#66977C2318yes—
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4—22no—
99C2×#4318—24no—
100C2×#4318C2314yes—
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103Q16×D11—232no—
104M16×D11—232no—
105C2×Dic44—24no—
106C2×Dic44C2314yescomplemented
107C2×#4313—24no—
108C2×#4313—24no—
109C2×#4313C2314yes—
110C2×#4313C2314yes—
111C2×C8×D11—24no—
112C2×C8×D11D418yes—
113C2×C8×D11C2314yes—
114C2×C8×D11C2314yes—
115#66950—24no—
116#66950C2318yes—
117#66949—216no—
118C4⋊C4×D11—216no—
119C4⋊C4×D11—24no—
120C4⋊C4×D11C2318yes—
121C22⋊C4×D11—216no—
122#66931—216no—
123C11×#106C2314yescomplemented
124C11×#103C2318yescomplemented
125#66899C2318yescomplemented
126#66881C2314yescomplemented
127#66880C2318yescomplemented
128#66874C2318yescomplemented
129#66872C2318yescomplemented
130C22×#470—111nomaximal, Sylow
131C24×C11C2×D411yescharacteristic
132C23×D11—24no—
133C23×D11—28no—
134C23×D11C2×D414yes—
135C23×D11C2×D411yescharacteristic
136C23×D11C2×D411yescharacteristic
137C2×Q8×C11—22no—
138C2×Q8×C11—24no—
139C2×Q8×C11—24no—
140C2×Q8×C11C2414yes—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2412yes—
148C22×C4×C11C2411yescharacteristic
149C22×Dic11—24no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11C2×D414yes—
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155Q8×D11—216no—
156Q8×D11—216no—
157Q8×D11—416no—
158C2×C4×D11—24no—
159C2×C4×D11—216no—
160C2×C4×D11—28no—
161C2×C4×D11—28no—
162C2×C4×D11—24no—
163C2×C4×D11—28no—
164C2×C4×D11—28no—
165C2×C4×D11—22no—
166C2×C4×D11—22no—
167C2×C4×D11—48no—
168C2×C4×D11—48no—
169C2×C4×D11C2×D414yes—
170C2×C4×D11C2×D414yes—
171C2×C4×D11C2×D414yes—
172C2×C4×D11C2×D412yes—
173C2×C4×D11C2×D412yes—
174C2×C4×D11#4114yes—
175C2×C4×D11C2412yes—
176C2×C4×D11C2412yes—
177C2×Dic22—28no—
178C2×Dic22—24no—
179C2×Dic22—22no—
180C2×Dic22—24no—
181C2×Dic22—48no—
182C2×Dic22C2414yes—
183C11×Q16—28no—
184C11×M16—28no—
185C2×C8×C11—22no—
186C2×C8×C11C2×D414yes—
187C2×C8×C11C2412yes—
188C2×C8×C11C2412yes—
189C11×C4⋊C4—28no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4C2414yes—
192C11×C22⋊C4—28no—
193C22⋊Dic11—28no—
194#4326—216no—
195(C2×D11)⋊C4—28no—
196(C2×D11)⋊C4—28no—
197C4⋊Dic11—28no—
198C4⋊Dic11—22no—
199C4⋊Dic11C2414yes—
200Dic11⋊C4—28no—
201Dic11⋊C4—28no—
202Dic11⋊C4—28no—
203#4318—28no—
204C2×C11⋊C8—22no—
205C2×C11⋊C8C2×D414yes—
206C2×C11⋊C8C2412yes—
207C2×C11⋊C8C2412yes—
208Dic44—28no—
209#4313—28no—
210#4313—28no—
211C8×D11—28no—
212C8×D11C2×D4116yes—
213C23×Q16—111no—
214C23×M16—111no—
215C22×C22⋊Q8—112no—
216C2×#470—1116no—
217C2×#470—111no—
218C2×#470—112no—
219C2×#470—111no—
220C2×#470—111no—
221C2×#470—112no—
222C2×#470D1111yescharacteristic, direct product factor
223C22×#106—111no—
224C22×#103—112no—
225C23×C11—22no—
226C23×C11—24no—
227C23×C11C22×D412yes—
228C23×C11C22×D411yescharacteristic
229C22×D11—22no—
230C22×D11—24no—
231C22×D11—28no—
232C22×D11—216no—
233C22×D11—416no—
234C22×D11#12114yes—
235C22×D11#13718yes—
236C22×D11C22×D412yes—
237C22×D11C22×D412yes—
238Q8×C11—24no—
239Q8×C11—24no—
240Q8×C11—44no—
241C2×C4×C11—22no—
242C2×C4×C11—24no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—44no—
248C2×C4×C11—44no—
249C2×C4×C11C22×D412yes—
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D412yes—
252C2×C4×C11C2×#4112yes—
253C2×C4×C11C2511yescharacteristic
254C2×Dic11—22no—
255C2×Dic11—28no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—44no—
259C2×Dic11—44no—
260C2×Dic11#12114yes—
261C2×Dic11C22×D412yes—
262C2×Dic11C22×D412yes—
263C4×D11—28no—
264C4×D11—24no—
265C4×D11—22no—
266C4×D11—22no—
267C4×D11—28no—
268C4×D11—416no—
269C4×D11—416no—
270C4×D11#12118yes—
271C4×D11C22×D414yes—
272C4×D11C2×#4114yes—
273Dic22—24no—
274Dic22—24no—
275Dic22—44no—
276Dic22—416no—
277C8×C11—22no—
278C8×C11C22×D414yes—
279C11⋊C8—22no—
280C11⋊C8C22×D414yes—
281C23×Q8—112no—
282C24×C4—111no—
283C22×Q16—112no—
284C22×Q16—118no—
285C22×Q16—111no—
286C22×Q16—228no—
287C22×Q16C2×D1111yescharacteristic, complemented
288C22×M16—111no—
289C22×M16—118no—
290C22×M16—111no—
291C22×M16—111no—
292C22×M16—228no—
293C22×M16C2×D1111yescharacteristic
294C23×C8—111no—
295C23×C8—111no—
296C2×C22⋊Q8—112no—
297C2×C22⋊Q8—112no—
298C2×C22⋊Q8—1116no—
299C2×C22⋊Q8—112no—
300C2×C22⋊Q8—222no—
301C2×C22⋊Q8—222no—
302C2×C22⋊Q8—228no—
303C2×C22⋊Q8C2×D1112yes—
304C22×C4⋊C4—112no—
305C22×C4⋊C4—222no—
306C22×C22⋊C4—222no—
307#470—118no—
308#470—118no—
309#470—1116no—
310#470—118no—
311#470—1116no—
312#470C2×D1118yesdirect product factor
313C2×#106—111no—
314C2×#106—112no—
315C2×#106—118no—
316C2×#106C2×D1111yescharacteristic, complemented
317C2×#103—112no—
318C2×#103—112no—
319C2×#103—112no—
320C2×#103—1116no—
321C2×#103C2×D1112yescomplemented
322C22×C11—22no—
323C22×C11—24no—
324C22×C11—44no—
325C22×C11C2×#12112yes—
326C22×C11C2×#13714yes—
327C22×C11C23×D411yescharacteristic
328C2×D11—22no—
329C2×D11—24no—
330C2×D11—44no—
331C2×D11—416no—
332C2×D11#470116yesdirect product factor
333C2×D11C2×#12114yes—
334C2×D11C2×#13718yes—
335C4×C11—22no—
336C4×C11—44no—
337C4×C11—44no—
338C4×C11C2×#12112yes—
339C4×C11C23×D411yescharacteristic
340C4×C11C22×#4111yescharacteristic
341Dic11—22no—
342Dic11—44no—
343Dic11—44no—
344Dic11C2×#12114yes—
345C25—111no—
346C22×Q8—118no—
347C22×Q8—112no—
348C22×Q8—222no—
349C22×Q8—224no—
350C22×Q8—228no—
351C22×Q8—228no—
352C22×Q8C22×D1112yes—
353C23×C4—111no—
354C23×C4—111no—
355C23×C4—111no—
356C23×C4—111no—
357C23×C4—114no—
358C23×C4—114no—
359C23×C4—111no—
360C23×C4—224no—
361C23×C4—224no—
362C23×C4—222no—
363C23×C4—222no—
364C23×C4C22×D1111yescharacteristic
365C2×Q16—24no—
366C2×Q16—118no—
367C2×Q16—114no—
368C2×Q16—2232no—
369C2×Q16—228no—
370C2×Q16—224no—
371C2×Q16C22×D1114yescomplemented
372C2×M16—24no—
373C2×M16—114no—
374C2×M16—114no—
375C2×M16—114no—
376C2×M16—224no—
377C2×M16—2232no—
378C2×M16—224no—
379C2×M16—224no—
380C2×M16C22×D1114yes—
381C22×C8—111no—
382C22×C8—118no—
383C22×C8—114no—
384C22×C8—111no—
385C22×C8—114no—
386C22×C8—224no—
387C22×C8C22×D1111yescharacteristic
388C22×C8C22×D1111yescharacteristic
389C22⋊Q8—24no—
390C22⋊Q8—118no—
391C22⋊Q8—118no—
392C22⋊Q8—118no—
393C22⋊Q8—2216no—
394C22⋊Q8—2216no—
395C22⋊Q8—224no—
396C22⋊Q8—224no—
397C22⋊Q8—224no—
398C22⋊Q8C22×D1118yes—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—112no—
401C2×C4⋊C4—118no—
402C2×C4⋊C4—224no—
403C2×C4⋊C4—2216no—
404C2×C4⋊C4—222no—
405C2×C4⋊C4—222no—
406C2×C4⋊C4—222no—
407C2×C4⋊C4—222no—
408C2×C4⋊C4C22×D1112yes—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—2216no—
411C2×C22⋊C4—222no—
412C2×C22⋊C4—222no—
413C2×C22⋊C4—222no—
414#106—114no—
415#106—118no—
416#106C22×D1114yescomplemented
417#103—118no—
418#103—118no—
419#103—118no—
420#103C22×D1118yescomplemented
421C2×C11—42no—
422C2×C11C2×#47014yescomplemented
423C2×C11C22×#12111yescharacteristic
424C2×C11C22×#13712yes—
425D11—42no—
426D11C2×#47018yesdirect product factor
427C24—111no—
428C24—114no—
429C24—111no—
430C24—224no—
431C24—228no—
432C24D4×D1111yescharacteristic
433C2×Q8—22no—
434C2×Q8—24no—
435C2×Q8—24no—
436C2×Q8—114no—
437C2×Q8—228no—
438C2×Q8—2216no—
439C2×Q8—2216no—
440C2×Q8—222no—
441C2×Q8—224no—
442C2×Q8—224no—
443C2×Q8—448no—
444C2×Q8—4416no—
445C2×Q8C23×D1114yes—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—111no—
451C22×C4—112no—
452C22×C4—114no—
453C22×C4—114no—
454C22×C4—112no—
455C22×C4—114no—
456C22×C4—111no—
457C22×C4—114no—
458C22×C4—114no—
459C22×C4—112no—
460C22×C4—112no—
461C22×C4—228no—
462C22×C4—224no—
463C22×C4—2216no—
464C22×C4—228no—
465C22×C4—224no—
466C22×C4—228no—
467C22×C4—228no—
468C22×C4—224no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—448no—
474C22×C4—448no—
475C22×C4D4×D1112yes—
476C22×C4D4×D1111yescharacteristic
477C22×C4C23×D1112yes—
478C22×C4C23×D1111yescharacteristic
479Q16—28no—
480Q16—2216no—
481Q16—228no—
482M16—28no—
483M16—228no—
484M16—228no—
485M16—228no—
486C2×C8—22no—
487C2×C8—114no—
488C2×C8—112no—
489C2×C8—1116no—
490C2×C8—112no—
491C2×C8—228no—
492C2×C8—222no—
493C2×C8D4×D1114yes—
494C2×C8C23×D1112yes—
495C2×C8C23×D1112yes—
496C4⋊C4—28no—
497C4⋊C4—22no—
498C4⋊C4—114no—
499C4⋊C4—228no—
500C4⋊C4—228no—
501C4⋊C4—228no—
502C4⋊C4—222no—
503C4⋊C4—228no—
504C4⋊C4C23×D1114yes—
505C22⋊C4—28no—
506C22⋊C4—228no—
507C22⋊C4—228no—
508C22⋊C4—228no—
509C11C22×#47011yescharacteristic, complemented, Sylow
510C23—24no—
511C23—22no—
512C23—118no—
513C23—114no—
514C23—112no—
515C23—112no—
516C23—228no—
517C23—2216no—
518C23—224no—
519C23—222no—
520C23—4416no—
521C23C2×D4×D1112yes—
522C23C2×D4×D1111yescharacteristic
523Q8—24no—
524Q8—24no—
525Q8—44no—
526Q8—224no—
527Q8—224no—
528Q8—4416no—
529Q8—444no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—114no—
539C2×C4—112no—
540C2×C4—118no—
541C2×C4—114no—
542C2×C4—114no—
543C2×C4—112no—
544C2×C4—228no—
545C2×C4—228no—
546C2×C4—228no—
547C2×C4—222no—
548C2×C4—224no—
549C2×C4—222no—
550C2×C4—222no—
551C2×C4—224no—
552C2×C4—224no—
553C2×C4—4416no—
554C2×C4—4416no—
555C2×C4—444no—
556C2×C4—444no—
557C2×C4C2×D4×D1112yes—
558C2×C4C2×D4×D1111yescharacteristic
559C2×C4C2×D4×D1112yes—
560C2×C4#41×D1112yes—
561C2×C4C24×D1111yescharacteristic
562C8—22no—
563C8—114no—
564C8—222no—
565C8C2×D4×D1114yes—
566C22—24no—
567C22—22no—
568C22—44no—
569C22—1116no—
570C22—118no—
571C22—114no—
572C22—224no—
573C22—222no—
574C22—4416no—
575C22—444no—
576C22D11×#12112yes—
577C22D11×#13714yes—
578C22C22×D4×D1111yescharacteristic
579C4—22no—
580C4—44no—
581C4—44no—
582C4—114no—
583C4—222no—
584C4—444no—
585C4—444no—
586C4D11×#12112yes—
587C4C22×D4×D1111yescharacteristic
588C4C2×#41×D1111yescharacteristic
589C2—42no—
590C2—118no—
591C2—442no—
592C2D11×#47014yesdirect product factor
593C2C2×D11×#12111yescharacteristic
594C2C2×D11×#13712yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#470C2
socleC23×C11C22×D4
prime radicalC24×D11D4
hypercenterC2×#470D11
hypocenterC11C22×#470
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
1. C22×Q16×D11C2semidirect
4. C2×#10622481C2semidirect
5. C2×#10622750C2semidirect
6. C2×#10622429C2semidirect
7. C2×#10622665C2semidirect
8. C2×#10622802C2semidirect
9. D11×#470C2direct (N × H)
10. C2×D11×#106C2semidirect
11. C2×D11×#103C2semidirect
12. C2×C11×#470C2semidirect
15. C22×C11×Q16C22semidirect
19. C22×#4326C22semidirect
23. C2×Q16×D11C22semidirect
26. C22×Dic44C22semidirect
39. C11×#470C22semidirect
40. C2×C11×#106C22semidirect
41. C2×C11×#103C22semidirect
42. C2×#66899C22semidirect
43. #10622802C22semidirect
44. #10622750C22semidirect
45. C2×#66881C22semidirect
46. C2×#66880C22semidirect
47. #10622665C22semidirect
48. C2×#66874C22semidirect
49. C2×#66872C22semidirect
50. #10622481C22semidirect
51. D11×#106C22semidirect
52. #10622429C22semidirect
53. D11×#103C22semidirect
75. C2×C11×Q16C23semidirect
89. C2×#4326C23semidirect
106. C2×Dic44C23semidirect
123. C11×#106C23semidirect
124. C11×#103C23semidirect
125. #66899C23semidirect
126. #66881C23semidirect
127. #66880C23semidirect
128. #66874C23semidirect
129. #66872C23semidirect
222. C2×#470D11direct (N × H)
287. C22×Q16C2×D11semidirect
312. #470C2×D11direct (N × H)
316. C2×#106C2×D11semidirect
321. C2×#103C2×D11semidirect
332. C2×D11#470direct (N × H)
371. C2×Q16C22×D11semidirect
416. #106C22×D11semidirect
420. #103C22×D11semidirect
422. C2×C11C2×#470semidirect
426. D11C2×#470direct (N × H)
509. C11C22×#470semidirect
592. C2D11×#470direct (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
C22×M16×D112
C2×D11×C22⋊Q82
C2×#106224812
C2×#106227502
C2×#106224292
C2×#106226652
C2×#106228022
D11×#4702
C2×D11×#1062
C2×D11×#1032
C2×C11×#4702
C22×#47011