Finite Group Databasebeta

← D11×#1550 #14722121

Subgroups — D11×#1550 #14722121

Order 2816.

1074 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#533C211yesmaximal, characteristic
2D11×#423C211yesmaximal, characteristic
3C2×D11×C4⋊C8C211yesmaximal, characteristic
4#13067307C211yesmaximal, characteristic, complemented
5#13067306C211yesmaximal, characteristic, complemented
6#13067305C212yesmaximal, complemented
7#13067304C211yesmaximal, characteristic, complemented
8#13067303C212yesmaximal, complemented
9D11×#333C212yesmaximal, complemented
10D11×#332C212yesmaximal, complemented
11C11×#1550C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×M16×D11—21no—
14C22×C8×D11—21no—
15#10623259C2211yescharacteristic
16#10623259C2211yescharacteristic
17D11×C4⋊Q8C2211yescharacteristic
18D11×C4⋊Q8C2211yescharacteristic
19#10623219—21no—
20D11×#125—21no—
21D11×C22⋊Q8—21no—
22D11×C22⋊Q8C412yes—
23#10623153—21no—
24#10623153C412yes—
25#10623109—21no—
26#10623109C412yes—
27C4×Q8×D11—21no—
28C4×Q8×D11C412yes—
29D11×#117—21no—
30#10623048—21no—
31C2×C42×D11C2211yescharacteristic
32#10623001C2211yescharacteristic
33C11×#423C2211yescharacteristic
34C2×C11×C4⋊C8C2211yescharacteristic
35#10622731—21no—
36C2×Dic11⋊C8—21no—
37#10622537C2211yescharacteristic
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39#10622450—21no—
40#10622450C2212yes—
41D11×C4⋊C8—21no—
42D11×C4⋊C8—21no—
43D11×C4⋊C8—21no—
44D11×C4⋊C8C2212yes—
45D11×C4⋊C8C2212yes—
46D11×C4⋊C8C2212yes—
47C11×#333C2212yescomplemented
48C11×#332C2212yescomplemented
49#10622185C2212yescomplemented
50#10622184C2212yescomplemented
51#10622124C2212yescomplemented
52#10622120C2212yescomplemented
53#10622119C2212yescomplemented
54#10622119C2212yescomplemented
55C2×Q8×D11—21no—
56C2×Q8×D11C2×C412yes—
57C22×C4×D11C2×C411yescharacteristic
58C22×C4×D11D411yescharacteristic
59C22×C4×D11D411yescharacteristic
60C2×C11×M16—21no—
61C22×C8×C11—21no—
62C11×C4⋊Q8C2311yescharacteristic
63C11×C4⋊Q8C2311yescharacteristic
64C11×#125—21no—
65C11×C22⋊Q8—21no—
66C11×C22⋊Q8C2×C412yes—
67C4×Q8×C11—21no—
68C4×Q8×C11C2×C412yes—
69C11×#117—21no—
70C2×C42×C11C2311yescharacteristic
71#66999—21no—
72#66999C2×C412yes—
73Q8×Dic11—21no—
74Q8×Dic11C2×C412yes—
75#66997—21no—
76#66997C2×C412yes—
77#66979—21no—
78#66977—21no—
79#66977C2×C412yes—
80C2×C4×Dic11C2×C411yescharacteristic
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11D411yescharacteristic
83C2×#4318—21no—
84C22×C11⋊C8—21no—
85M16×D11—44no—
86C2×#4313—22no—
87C2×C8×D11—22no—
88C2×C8×D11—22no—
89C2×C8×D11—22no—
90C2×C8×D11—44no—
91#66950—21no—
92#66950C2×C412yes—
93#66949—22no—
94#66949—22no—
95#66945—21no—
96#66945—21no—
97C4⋊C4×D11—22no—
98C4⋊C4×D11—22no—
99C4⋊C4×D11—21no—
100C4⋊C4×D11—21no—
101C4⋊C4×D11—21no—
102C4⋊C4×D11C2×C412yes—
103#66943—21no—
104#66943—21no—
105#66942—22no—
106#66942—22no—
107#66941—21no—
108#66941—21no—
109#66941—21no—
110#66941C2×C412yes—
111#66940—22no—
112#66940—22no—
113#66940—21no—
114#66940C2×C412yes—
115C22⋊C4×D11—22no—
116#66931—22no—
117#66931—22no—
118#66930—22no—
119#66925—22no—
120C42×D11—22no—
121C42×D11C2×C411yescharacteristic
122C42×D11C2×C411yescharacteristic
123C42×D11D411yescharacteristic
124C42×D11D411yescharacteristic
125C42×D11D411yescharacteristic
126C42×D11D411yescharacteristic
127C42×D11C2311yescharacteristic
128C42×D11C2311yescharacteristic
129#66923—21no—
130#66922C2311yescharacteristic
131#66922C2311yescharacteristic
132C4×Dic22—21no—
133C4×Dic22—22no—
134C4×Dic22—22no—
135C4×Dic22C2×C412yes—
136C11×C4⋊C8—21no—
137C11×C4⋊C8—21no—
138C11×C4⋊C8C2312yes—
139C11×C4⋊C8C2312yes—
140Dic11⋊C8—22no—
141Dic11⋊C8—22no—
142Dic11⋊C8—22no—
143Dic11⋊C8—22no—
144C4⋊(C11⋊C8)—21no—
145C4⋊(C11⋊C8)—21no—
146C4⋊(C11⋊C8)C2312yes—
147C4⋊(C11⋊C8)C2312yes—
148C2×#1550—111nomaximal, Sylow
149C23×D11C22⋊C411yescharacteristic
150C2×Q8×C11—21no—
151C2×Q8×C11C22×C412yes—
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×Dic11C22⋊C411yescharacteristic
156C22×Dic11C22⋊C411yescharacteristic
157C22×Dic11C22⋊C411yescharacteristic
158Q8×D11—44no—
159Q8×D11—42no—
160Q8×D11—42no—
161C2×C4×D11—22no—
162C2×C4×D11—22no—
163C2×C4×D11—22no—
164C2×C4×D11—22no—
165C2×C4×D11—42no—
166C2×C4×D11C22⋊C411yescharacteristic
167C2×C4×D11C22⋊C411yescharacteristic
168C2×C4×D11C22⋊C411yescharacteristic
169C2×C4×D11C22⋊C411yescharacteristic
170C2×C4×D11C22⋊C411yescharacteristic
171C2×C4×D11C22⋊C411yescharacteristic
172C2×C4×D11SD1614yes—
173C2×C4×D11Q1614yes—
174C2×C4×D11C22×C411yescharacteristic
175C2×C4×D11C22×C411yescharacteristic
176C2×C4×D11C2×D411yescharacteristic
177C2×C4×D11C2×D411yescharacteristic
178C2×C4×D11C2×D411yescharacteristic
179C2×C4×D11C2×D411yescharacteristic
180C2×Dic22—22no—
181C2×Dic22—22no—
182C2×Dic22—21no—
183C2×Dic22C22×C412yes—
184C11×M16—42no—
185C2×C8×C11—22no—
186C2×C8×C11—22no—
187C2×C8×C11—42no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4C22×C412yes—
194C11×C22⋊C4—22no—
195C42×C11—22no—
196C42×C11C22×C411yescharacteristic
197C42×C11C2×D411yescharacteristic
198C42×C11C2×D411yescharacteristic
199C42×C11C2411yescharacteristic
200C22⋊Dic11—22no—
201(C2×D11)⋊C4—22no—
202(C2×D11)⋊C4—22no—
203C4⋊Dic11—22no—
204C4⋊Dic11—22no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11C22×C412yes—
209Dic11⋊C4—22no—
210Dic11⋊C4—22no—
211Dic11⋊C4—22no—
212Dic11⋊C4—22no—
213Dic11⋊C4—22no—
214Dic11⋊C4—22no—
215Dic11⋊C4—22no—
216Dic11⋊C4—22no—
217C4×Dic11—22no—
218C4×Dic11—22no—
219C4×Dic11—22no—
220C4×Dic11C22⋊C411yescharacteristic
221C4×Dic11C22⋊C411yescharacteristic
222C4×Dic11C22⋊C411yescharacteristic
223C4×Dic11C22⋊C411yescharacteristic
224C4×Dic11C22⋊C411yescharacteristic
225C4×Dic11C22⋊C411yescharacteristic
226C4×Dic11C22×C411yescharacteristic
227C4×Dic11C22×C411yescharacteristic
228C4×Dic11C2×D411yescharacteristic
229C4×Dic11C2×D411yescharacteristic
230C4×Dic11C2×D411yescharacteristic
231C4×Dic11C2×D411yescharacteristic
232#4318—42no—
233C2×C11⋊C8—22no—
234C2×C11⋊C8—22no—
235C2×C11⋊C8—42no—
236#4313—44no—
237C8×D11—44no—
238C8×D11—44no—
239C8×D11—44no—
240C2×#533—111no—
241C2×#423—111no—
242C22×C4⋊C8—111no—
243#1550—111no—
244#1550—111no—
245#1550—112no—
246#1550—112no—
247#1550—111no—
248#1550D1111yescharacteristic, direct product factor
249C2×#333—112no—
250C2×#332—112no—
251C23×C11C2×C22⋊C411yescharacteristic
252C22×D11—22no—
253C22×D11—22no—
254C22×D11#10314yes—
255C22×D11C2×C22⋊C411yescharacteristic
256C22×D11C2×C22⋊C411yescharacteristic
257Q8×C11—42no—
258Q8×C11—41no—
259Q8×C11—41no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—41no—
265C2×C4×C11C2×C22⋊C411yescharacteristic
266C2×C4×C11C2×C22⋊C411yescharacteristic
267C2×C4×C11C2×C22⋊C411yescharacteristic
268C2×C4×C11C2×SD1612yes—
269C2×C4×C11C2×Q1612yes—
270C2×C4×C11C23×C411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—41no—
277C2×Dic11#10314yes—
278C2×Dic11C2×C22⋊C411yescharacteristic
279C2×Dic11C2×C22⋊C411yescharacteristic
280C2×Dic11C2×C22⋊C411yescharacteristic
281C2×Dic11C2×C22⋊C411yescharacteristic
282C2×Dic11C2×C22⋊C411yescharacteristic
283C2×Dic11C2×C22⋊C411yescharacteristic
284C4×D11—22no—
285C4×D11—22no—
286C4×D11—22no—
287C4×D11—21no—
288C4×D11—21no—
289C4×D11—22no—
290C4×D11—41no—
291C4×D11—41no—
292C4×D11—44no—
293C4×D11—44no—
294C4×D11#10314yes—
295C4×D11#10314yes—
296C4×D11C2×SD1612yes—
297C4×D11C2×SD1612yes—
298C4×D11C2×Q1612yes—
299C4×D11C2×Q1612yes—
300C4×D11AGL(1,ℤ/8)12yes—
301C4×D11#13712yes—
302Dic22—44no—
303Dic22—41no—
304Dic22—41no—
305Dic22—44no—
306Dic22—42no—
307C8×C11—42no—
308C8×C11—42no—
309C11⋊C8—42no—
310C11⋊C8—42no—
311C22×M16—221no—
312C23×C8—221no—
313#533—111no—
314#533—111no—
315#533—112no—
316#533—112no—
317#533—111no—
318#533—221no—
319#533—221no—
320#533—221no—
321#533—221no—
322#533C2×D1111yescharacteristic
323C2×C4⋊Q8—111no—
324C2×C4⋊Q8—111no—
325C2×#125—221no—
326C2×C22⋊Q8—112no—
327C2×C22⋊Q8—221no—
328C2×C4×Q8—112no—
329C2×C4×Q8—221no—
330C2×#117—221no—
331C22×C42—111no—
332#423—111no—
333#423—112no—
334#423—221no—
335#423—221no—
336#423C2×D1111yescharacteristic
337C2×C4⋊C8—111no—
338C2×C4⋊C8—112no—
339C2×C4⋊C8—112no—
340C2×C4⋊C8—112no—
341C2×C4⋊C8—221no—
342C2×C4⋊C8—221no—
343C2×C4⋊C8—221no—
344C2×C4⋊C8—221no—
345C2×C4⋊C8C2×D1111yescharacteristic
346#333—112no—
347#333—112no—
348#333—112no—
349#333C2×D1112yescomplemented
350#332—112no—
351#332—112no—
352#332—112no—
353#332C2×D1112yescomplemented
354C22×C11—21no—
355C22×C11—21no—
356C22×C11C2×#10312yes—
357C22×C11C22×C22⋊C411yescharacteristic
358C2×D11—21no—
359C2×D11—21no—
360C2×D11—28no—
361C2×D11#41312yes—
362C2×D11C2×#10312yes—
363C2×D11C2×#10312yes—
364C2×D11#41712yes—
365C4×C11—21no—
366C4×C11—21no—
367C4×C11—21no—
368C4×C11—42no—
369C4×C11—42no—
370C4×C11C2×#10312yes—
371C4×C11C22×SD1611yescharacteristic
372C4×C11C22×Q1611yescharacteristic
373C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
374C4×C11C2×#13711yescharacteristic
375Dic11—21no—
376Dic11—21no—
377Dic11—21no—
378Dic11—42no—
379Dic11—42no—
380Dic11C2×#10312yes—
381Dic11C2×#10312yes—
382Dic11#41712yes—
383C22×Q8—112no—
384C22×Q8—221no—
385C23×C4—111no—
386C23×C4—111no—
387C23×C4—111no—
388C2×M16—21no—
389C2×M16—222no—
390C2×M16—221no—
391C2×M16—444no—
392C22×C8—21no—
393C22×C8—222no—
394C22×C8—222no—
395C22×C8—222no—
396C22×C8—221no—
397C22×C8—444no—
398C4⋊Q8—112no—
399C4⋊Q8—112no—
400C4⋊Q8—111no—
401C4⋊Q8—111no—
402C4⋊Q8—221no—
403C4⋊Q8—221no—
404C4⋊Q8—221no—
405C4⋊Q8—221no—
406C4⋊Q8C22×D1111yescharacteristic
407C4⋊Q8C22×D1111yescharacteristic
408#125—21no—
409#125—222no—
410#125—222no—
411#125—221no—
412#125—221no—
413#125—221no—
414C22⋊Q8—21no—
415C22⋊Q8—112no—
416C22⋊Q8—112no—
417C22⋊Q8—112no—
418C22⋊Q8—222no—
419C22⋊Q8—222no—
420C22⋊Q8—222no—
421C22⋊Q8—222no—
422C22⋊Q8—221no—
423C22⋊Q8—221no—
424C22⋊Q8—221no—
425C22⋊Q8C4×D1112yes—
426C4×Q8—21no—
427C4×Q8—112no—
428C4×Q8—112no—
429C4×Q8—112no—
430C4×Q8—222no—
431C4×Q8—222no—
432C4×Q8—222no—
433C4×Q8—222no—
434C4×Q8—221no—
435C4×Q8—221no—
436C4×Q8—221no—
437C4×Q8C4×D1112yes—
438#117—21no—
439#117—222no—
440#117—222no—
441#117—221no—
442#117—221no—
443#117—221no—
444C2×C4⋊C4—112no—
445C2×C4⋊C4—221no—
446C2×C4⋊C4—221no—
447C2×C4⋊C4—222no—
448C2×C4⋊C4—222no—
449C2×C4⋊C4—221no—
450C2×C22⋊C4—222no—
451C2×C42—111no—
452C2×C42—111no—
453C2×C42—111no—
454C2×C42—111no—
455C2×C42—111no—
456C2×C42—111no—
457C2×C42—111no—
458C2×C42—111no—
459C2×C42—111no—
460C2×C42—111no—
461C2×C42—111no—
462C2×C42—222no—
463C2×C42C22×D1111yescharacteristic
464C4⋊C8—21no—
465C4⋊C8—21no—
466C4⋊C8—112no—
467C4⋊C8—112no—
468C4⋊C8—222no—
469C4⋊C8—222no—
470C4⋊C8—222no—
471C4⋊C8—222no—
472C4⋊C8—221no—
473C4⋊C8—221no—
474C4⋊C8C22×D1112yes—
475C4⋊C8C22×D1112yes—
476C2×C11—22no—
477C2×C11C2×#41311yescharacteristic
478C2×C11C22×#10311yescharacteristic
479C2×C11C2×#41711yescharacteristic
480D11—22no—
481D11#155014yesdirect product factor
482C24—111no—
483C2×Q8—21no—
484C2×Q8—112no—
485C2×Q8—222no—
486C2×Q8—222no—
487C2×Q8—221no—
488C2×Q8—442no—
489C2×Q8—442no—
490C2×Q8—444no—
491C2×Q8C2×C4×D1112yes—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—111no—
495C22×C4—114no—
496C22×C4—114no—
497C22×C4—111no—
498C22×C4—111no—
499C22×C4—111no—
500C22×C4—111no—
501C22×C4—111no—
502C22×C4—111no—
503C22×C4—111no—
504C22×C4—111no—
505C22×C4—111no—
506C22×C4—111no—
507C22×C4—111no—
508C22×C4—111no—
509C22×C4—222no—
510C22×C4—222no—
511C22×C4—222no—
512C22×C4—222no—
513C22×C4—442no—
514C22×C4C2×C4×D1111yescharacteristic
515C22×C4D4×D1111yescharacteristic
516C22×C4D4×D1111yescharacteristic
517M16—42no—
518M16—444no—
519M16—442no—
520C2×C8—22no—
521C2×C8—22no—
522C2×C8—42no—
523C2×C8—222no—
524C2×C8—222no—
525C2×C8—444no—
526C2×C8—444no—
527C2×C8—444no—
528C2×C8—442no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—112no—
535C4⋊C4—222no—
536C4⋊C4—222no—
537C4⋊C4—222no—
538C4⋊C4—222no—
539C4⋊C4—222no—
540C4⋊C4—222no—
541C4⋊C4—222no—
542C4⋊C4—222no—
543C4⋊C4—222no—
544C4⋊C4—222no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4C2×C4×D1112yes—
549C22⋊C4—22no—
550C22⋊C4—222no—
551C22⋊C4—222no—
552C22⋊C4—222no—
553C42—22no—
554C42—111no—
555C42—111no—
556C42—111no—
557C42—111no—
558C42—111no—
559C42—111no—
560C42—111no—
561C42—111no—
562C42—111no—
563C42—111no—
564C42—111no—
565C42—111no—
566C42—222no—
567C42—222no—
568C42—222no—
569C42C2×C4×D1111yescharacteristic
570C42D4×D1111yescharacteristic
571C42D4×D1111yescharacteristic
572C42C23×D1111yescharacteristic
573C11C2×#155011yescharacteristic, complemented, Sylow
574C23—111no—
575C23—111no—
576C23—114no—
577C23—222no—
578C23—222no—
579C23C22⋊C4×D1111yescharacteristic
580Q8—42no—
581Q8—41no—
582Q8—41no—
583Q8—442no—
584Q8—444no—
585Q8—444no—
586Q8—441no—
587Q8—441no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—41no—
593C2×C4—111no—
594C2×C4—111no—
595C2×C4—111no—
596C2×C4—114no—
597C2×C4—112no—
598C2×C4—112no—
599C2×C4—112no—
600C2×C4—112no—
601C2×C4—112no—
602C2×C4—112no—
603C2×C4—114no—
604C2×C4—114no—
605C2×C4—111no—
606C2×C4—111no—
607C2×C4—111no—
608C2×C4—222no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—221no—
614C2×C4—221no—
615C2×C4—222no—
616C2×C4—222no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—444no—
620C2×C4—444no—
621C2×C4—441no—
622C2×C4C22⋊C4×D1111yescharacteristic
623C2×C4C22⋊C4×D1111yescharacteristic
624C2×C4C22⋊C4×D1111yescharacteristic
625C2×C4SD16×D1112yes—
626C2×C4Q16×D1112yes—
627C2×C4C22×C4×D1111yescharacteristic
628C2×C4C2×D4×D1111yescharacteristic
629C2×C4C2×D4×D1111yescharacteristic
630C8—42no—
631C8—42no—
632C8—442no—
633C8—442no—
634C22—21no—
635C22—21no—
636C22—112no—
637C22—112no—
638C22—112no—
639C22—112no—
640C22—228no—
641C22—221no—
642C22—221no—
643C22D11×#10312yes—
644C22C2×C22⋊C4×D1111yescharacteristic
645C4—21no—
646C4—21no—
647C4—21no—
648C4—42no—
649C4—42no—
650C4—112no—
651C4—112no—
652C4—112no—
653C4—221no—
654C4—221no—
655C4—221no—
656C4—442no—
657C4—442no—
658C4D11×#10312yes—
659C4C2×SD16×D1111yescharacteristic
660C4C2×Q16×D1111yescharacteristic
661C4D11×AGL(1,ℤ/8)11yescharacteristic
662C4D11×#13711yescharacteristic
663C2—22no—
664C2—114no—
665C2—222no—
666C2D11×#41311yescharacteristic
667C2C2×D11×#10311yescharacteristic
668C2D11×#41711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1550C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC42×C11C24
hypercenter#1550D11
hypocenterC11C2×#1550
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1550

Complements

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

NH ≅ G/Ntype
4. #13067307C2semidirect
5. #13067306C2semidirect
6. #13067305C2semidirect
7. #13067304C2semidirect
8. #13067303C2semidirect
9. D11×#333C2semidirect
10. D11×#332C2semidirect
11. C11×#1550C2semidirect
47. C11×#333C22semidirect
48. C11×#332C22semidirect
49. #10622185C22semidirect
50. #10622184C22semidirect
51. #10622124C22semidirect
52. #10622120C22semidirect
53. #10622119C22semidirect
54. #10622119C22semidirect
248. #1550D11direct (N × H)
349. #333C2×D11semidirect
353. #332C2×D11semidirect
481. D11#1550direct (N × H)
573. C11C2×#1550semidirect

Maximal subgroups

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

subgroupindex
D11×#5332
D11×#4232
C2×D11×C4⋊C82
#130673072
#130673062
#130673052
#130673042
#130673032
D11×#3332
D11×#3322
C11×#15502
C2×#155011