Finite Group Databasebeta

← #14660746

Subgroups — #14660746

Order 2816.

1070 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622731C211yesmaximal, characteristic, complemented
2C22×#66869C211yesmaximal, characteristic
3C22×#66889C211yesmaximal, characteristic
4#13071104C211yesmaximal, characteristic
5C2×#10622170C211yesmaximal, characteristic, complemented
6C4×C11⋊#95C211yesmaximal, characteristic, complemented
7C2×C11×#339C211yesmaximal, characteristic, complemented
8C22×#4339C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C2×C11×#117C2211yescharacteristic
11C22×C42×C11C2211yescharacteristic
12C22×C4×Dic11C2211yescharacteristic
13C22×C4×Dic11C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C2×C11⋊#95—22no—
16C2×#66889—22no—
17C2×#66889—22no—
18C2×#66889—22no—
19#10622731—22no—
20#10622731—22no—
21C2×Dic11⋊C8—22no—
22#10622601C411yescharacteristic, complemented
23#10622601C411yescharacteristic, complemented
24#10622587C411yescharacteristic, complemented
25#10622587C411yescharacteristic, complemented
26#10622571—22no—
27C4×(C2×D11)⋊C4—22no—
28C2×#66869—22no—
29C2×#66869—22no—
30C2×#66869—22no—
31C11×#339—22no—
32#10622170—22no—
33C23×C4×C11—21no—
34C23×C4×C11C2311yescharacteristic
35C22×C22⋊D11—21no—
36C23×Dic11—21no—
37C23×Dic11D412yes—
38C2×#4339—21no—
39C2×#4339—21no—
40C2×#4339—21no—
41C2×#4339—21no—
42C2×#4339—21no—
43C2×#4339—21no—
44C2×#4339—21no—
45C2×#4339—21no—
46C2×#4339—21no—
47C2×#4339—21no—
48C2×#4339D412yes—
49C2×#4339Q812yes—
50C22×D44C2×C411yescharacteristic
51C22×C4×D11—21no—
52C22×Dic22C2×C411yescharacteristic
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C2×C11×M16—21no—
56C2×C11×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16D412yes—
59C22×C8×C11—21no—
60C11×#117—21no—
61C11×#117—21no—
62C11×#117—21no—
63C11×#117—21no—
64C2×C11×C4⋊C4C2×C411yescharacteristic
65C2×C11×C4⋊C4C2×C411yescharacteristic
66C2×C11×C22⋊C4—21no—
67C2×C42×C11—21no—
68C2×C42×C11—21no—
69C2×C42×C11—21no—
70C2×C42×C11—21no—
71C2×C42×C11—21no—
72C2×C42×C11—21no—
73C2×C42×C11D412yes—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4—22no—
76C2×C4×Dic11—21no—
77C2×C4×Dic11—21no—
78C2×C4×Dic11—21no—
79C2×C4×Dic11—21no—
80C2×C4×Dic11—21no—
81C2×C4×Dic11—21no—
82C2×C4×Dic11—21no—
83C2×C4×Dic11—21no—
84C2×C4×Dic11—21no—
85C2×C4×Dic11C2×C411yescharacteristic
86C2×C4×Dic11C2×C411yescharacteristic
87C2×C4×Dic11D412yes—
88C2×C4×Dic11D412yes—
89C2×#4318—21no—
90C2×#4318—21no—
91C2×#4318—21no—
92C2×#4318—21no—
93C2×#4318—21no—
94C2×#4318D412yes—
95C22×C11⋊C8—21no—
96C11⋊#95—28no—
97C11⋊#95—22no—
98C11⋊#95—22no—
99#66889—28no—
100Dic11⋊C8—28no—
101#66869—28no—
102#11053—111nomaximal, Sylow
103C24×C11C2×D411yescharacteristic
104C23×D11—21no—
105C22×C4×C11—24no—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—42no—
110C22×C4×C11—41no—
111C22×C4×C11—41no—
112C22×C4×C11C22×C411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×Q811yescharacteristic
120C22×C4×C11#4111yescharacteristic
121C22×C4×C11#4111yescharacteristic
122C22×C4×C11#4111yescharacteristic
123C22×C4×C11#4111yescharacteristic
124C22×C4×C11#4111yescharacteristic
125C22×C4×C11#4111yescharacteristic
126C2×C22⋊D11—22no—
127C2×C22⋊D11—22no—
128C2×C22⋊D11—41no—
129C2×C22⋊D11—41no—
130C2×C22⋊D11—41no—
131C2×C22⋊D11—41no—
132C22×Dic11—24no—
133C22×Dic11—24no—
134C22×Dic11—21no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—42no—
139C22×Dic11—42no—
140C22×Dic11—41no—
141C22×Dic11—41no—
142C22×Dic11C22⋊C412yes—
143C22×Dic11C22⋊C412yes—
144#4339—22no—
145#4339—22no—
146#4339—22no—
147#4339—22no—
148#4339—22no—
149#4339—22no—
150#4339—22no—
151#4339—22no—
152#4339—41no—
153#4339—41no—
154#4339—41no—
155#4339—41no—
156#4339—41no—
157#4339—41no—
158#4339—41no—
159#4339—41no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44C4⋊C412yes—
166C2×C4×D11—22no—
167C2×C4×D11—22no—
168C2×C4×D11—41no—
169C2×C4×D11—41no—
170C2×C4×D11—41no—
171C2×C4×D11—41no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22—21no—
177C2×Dic22C4⋊C412yes—
178C11×M16—22no—
179C11×M16—22no—
180C11×M16—41no—
181C11×M16—41no—
182C2×C8×C11—22no—
183C2×C8×C11—41no—
184C2×C8×C11—41no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C22⋊C4—41no—
190C11×C22⋊C4—41no—
191C42×C11—22no—
192C42×C11—22no—
193C42×C11—41no—
194C42×C11—41no—
195C42×C11—41no—
196C42×C11—41no—
197(C2×D11)⋊C4—44no—
198(C2×D11)⋊C4—44no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C4×Dic11—22no—
204C4×Dic11—22no—
205C4×Dic11—22no—
206C4×Dic11—22no—
207C4×Dic11—41no—
208C4×Dic11—41no—
209#4318—22no—
210#4318—22no—
211#4318—41no—
212#4318—41no—
213C2×C11⋊C8—22no—
214C2×C11⋊C8—41no—
215C2×C11⋊C8—41no—
216C2×#423—111no—
217C22×#104—111no—
218C22×#104—111no—
219#2297—111no—
220C2×#339—111no—
221C2×#339D1111yescharacteristic, complemented
222C4×#95—111no—
223C23×C11—22no—
224C23×C11—22no—
225C23×C11C2×C22⋊C411yescharacteristic
226C23×C11#12111yescharacteristic
227C23×C11#12111yescharacteristic
228C23×C11#12111yescharacteristic
229C23×C11#12111yescharacteristic
230C23×C11#12111yescharacteristic
231C23×C11C22⋊Q811yescharacteristic
232C22×D11—22no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—42no—
236C22×D11—42no—
237C2×C4×C11—24no—
238C2×C4×C11—44no—
239C2×C4×C11—44no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11C2×C4⋊C411yescharacteristic
247C2×C4×C11#11711yescharacteristic
248C2×C4×C11C4×D411yescharacteristic
249C2×C4×C11C4×D411yescharacteristic
250C2×C4×C11C4×D411yescharacteristic
251C2×C4×C11C4×D411yescharacteristic
252C2×C4×C11#12011yescharacteristic
253C2×C4×C11#12011yescharacteristic
254C2×C4×C11#12011yescharacteristic
255C2×C4×C11#12111yescharacteristic
256C2×C4×C11#12111yescharacteristic
257C2×C4×C11#12111yescharacteristic
258C2×C4×C11C22⋊Q811yescharacteristic
259C2×C4×C11C22⋊Q811yescharacteristic
260C2×C4×C11C22⋊Q811yescharacteristic
261C2×C4×C11C22⋊Q811yescharacteristic
262C2×C4×C11C22⋊Q811yescharacteristic
263C2×C4×C11#12311yescharacteristic
264C2×C4×C11#12311yescharacteristic
265C2×C4×C11#12311yescharacteristic
266C2×C4×C11#12311yescharacteristic
267C2×C4×C11#12311yescharacteristic
268C2×C4×C11#12411yescharacteristic
269C2×C4×C11#12411yescharacteristic
270C2×C4×C11#12411yescharacteristic
271C2×C4×C11#12611yescharacteristic
272C2×C4×C11#12611yescharacteristic
273C2×C4×C11#12711yescharacteristic
274C22⋊D11—42no—
275C22⋊D11—42no—
276C22⋊D11—42no—
277C22⋊D11—42no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—24no—
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—44no—
286C2×Dic11—44no—
287C2×Dic11—44no—
288C2×Dic11—44no—
289C2×Dic11—42no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—42no—
293C2×Dic11#10414yescomplemented
294D44—22no—
295D44—22no—
296D44—41no—
297D44—41no—
298C4×D11—42no—
299C4×D11—42no—
300C4×D11—42no—
301C4×D11—42no—
302Dic22—22no—
303Dic22—22no—
304Dic22—41no—
305Dic22—41no—
306C8×C11—42no—
307C11⋊C8—42no—
308C22×#41—111no—
309C22×M16—111no—
310C22×M16C2×D1111yescharacteristic
311C2×#117C2×D1111yescharacteristic
312C22×C42—111no—
313C22×C42—111no—
314C22×C42C2×D1111yescharacteristic
315#423—222no—
316#423—222no—
317C2×C4⋊C8—222no—
318C2×#104—222no—
319C2×#104—222no—
320C2×#104—222no—
321C2×#104—222no—
322C2×#104—222no—
323C2×#104—222no—
324#391—111no—
325#391—111no—
326#390—111no—
327#390—111no—
328#386—222no—
329C4×C22⋊C4—222no—
330C2×#95—222no—
331#339—22no—
332#339—222no—
333C22×C11—22no—
334C22×C11—22no—
335C22×C11—22no—
336C22×C11—22no—
337C22×C11—21no—
338C22×C11—21no—
339C22×C11—21no—
340C22×C11—21no—
341C22×C11#38011yescharacteristic
342C22×C11#38611yescharacteristic
343C22×C11#39011yescharacteristic
344C22×C11#39411yescharacteristic
345C22×C11#39411yescharacteristic
346C22×C11#39611yescharacteristic
347C22×C11#39611yescharacteristic
348C22×C11C2×#10412yes—
349C22×C11#42112yes—
350C2×D11—44no—
351C2×D11—42no—
352C2×D11—82no—
353C2×D11—81no—
354C2×D11—81no—
355C4×C11—44no—
356C4×C11—81no—
357C4×C11—81no—
358C4×C11#38511yescharacteristic
359C4×C11#38511yescharacteristic
360C4×C11#38811yescharacteristic
361C4×C11#38811yescharacteristic
362C4×C11#39211yescharacteristic
363C4×C11#39311yescharacteristic
364C4×C11#39711yescharacteristic
365C4×C11#39911yescharacteristic
366Dic11—24no—
367Dic11—44no—
368Dic11—42no—
369Dic11—42no—
370C2×#41—112no—
371C2×#41—112no—
372C2×#41—221no—
373C2×#41—221no—
374C2×#41—221no—
375C2×#41—221no—
376C2×#41—221no—
377C2×#41—221no—
378C2×#41—221no—
379C2×#41—221no—
380C2×#41—221no—
381C2×#41—221no—
382C22×Q8—111no—
383C22×D4—111no—
384C22×D4—221no—
385C23×C4—21no—
386C23×C4—112no—
387C23×C4—221no—
388C23×C4—221no—
389C23×C4C22×D1111yescharacteristic
390C2×M16—21no—
391C2×M16—21no—
392C2×M16—21no—
393C2×M16—21no—
394C2×M16—21no—
395C2×M16—112no—
396C2×M16—221no—
397C2×M16—221no—
398C2×M16—221no—
399C2×M16—221no—
400C2×M16—221no—
401C2×M16D4412yes—
402C22×C8—21no—
403C22×C8—221no—
404#117—21no—
405#117—21no—
406#117—21no—
407#117—21no—
408C2×C4⋊C4C4×D1111yescharacteristic
409C2×C4⋊C4C4×D1111yescharacteristic
410C2×C22⋊C4—21no—
411C2×C22⋊C4—222no—
412C2×C22⋊C4—222no—
413C2×C42—21no—
414C2×C42—21no—
415C2×C42—21no—
416C2×C42—21no—
417C2×C42—21no—
418C2×C42—21no—
419C2×C42—111no—
420C2×C42—111no—
421C2×C42—112no—
422C2×C42—112no—
423C2×C42—221no—
424C2×C42—221no—
425C2×C42—221no—
426C2×C42—221no—
427C2×C42—221no—
428C2×C42—221no—
429C2×C42—221no—
430C2×C42—221no—
431C2×C42—221no—
432C2×C42C22⋊D1112yes—
433C4⋊C8—228no—
434#104—228no—
435#104—228no—
436#95—222no—
437#95—222no—
438#95—228no—
439C2×C11—21no—
440C2×C11—21no—
441C2×C11—21no—
442C2×C11—21no—
443C2×C11#143911yescharacteristic
444C2×C11#180612yes—
445C2×C11#187112yes—
446C2×C11#196211yescharacteristic
447C2×C11#196311yescharacteristic
448D11—82no—
449C24—221no—
450C24D4×D1111yescharacteristic
451#41—222no—
452#41—222no—
453#41—222no—
454#41—222no—
455#41—222no—
456#41—222no—
457#41—222no—
458#41—222no—
459#41—441no—
460#41—441no—
461#41—441no—
462#41—441no—
463#41—441no—
464#41—441no—
465#41—441no—
466#41—441no—
467C2×Q8—112no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×Q8—221no—
471C2×Q8—221no—
472C2×Q8—221no—
473C2×D4—112no—
474C2×D4—222no—
475C2×D4—222no—
476C2×D4—221no—
477C2×D4—221no—
478C2×D4—221no—
479C2×D4—221no—
480C2×D4—221no—
481C2×D4—441no—
482C2×D4—441no—
483C2×D4—441no—
484C2×D4—441no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—42no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—112no—
493C22×C4—112no—
494C22×C4—224no—
495C22×C4—224no—
496C22×C4—221no—
497C22×C4—222no—
498C22×C4—222no—
499C22×C4—222no—
500C22×C4—222no—
501C22×C4—222no—
502C22×C4—442no—
503C22×C4—442no—
504C22×C4—441no—
505C22×C4—441no—
506C22×C4—441no—
507C22×C4—441no—
508C22×C4—441no—
509C22×C4—441no—
510C22×C4C2×C4×D1111yescharacteristic
511C22×C4C2×D4411yescharacteristic
512C22×C4#433911yescharacteristic
513C22×C4#433911yescharacteristic
514C22×C4#433911yescharacteristic
515C22×C4#433911yescharacteristic
516C22×C4D4×D1111yescharacteristic
517C22×C4D4×D1111yescharacteristic
518C22×C4D4×D1111yescharacteristic
519C22×C4D4×D1111yescharacteristic
520C22×C4#434111yescharacteristic
521C22×C4Q8×D1111yescharacteristic
522C22×C4#434311yescharacteristic
523C22×C4C2×C22⋊D1111yescharacteristic
524M16—22no—
525M16—22no—
526M16—41no—
527M16—41no—
528M16—222no—
529M16—222no—
530M16—441no—
531M16—441no—
532C2×C8—22no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—222no—
536C2×C8—441no—
537C2×C8—441no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C22⋊C4—41no—
543C22⋊C4—41no—
544C22⋊C4—444no—
545C22⋊C4—444no—
546C42—22no—
547C42—22no—
548C42—41no—
549C42—41no—
550C42—41no—
551C42—41no—
552C42—221no—
553C42—221no—
554C42—222no—
555C42—221no—
556C42—221no—
557C42—222no—
558C42—222no—
559C42—222no—
560C42—441no—
561C42—441no—
562C11#1105311yescharacteristic, complemented, Sylow
563C23—22no—
564C23—22no—
565C23—222no—
566C23—441no—
567C23—441no—
568C23—442no—
569C23—442no—
570C23C22⋊C4×D1111yescharacteristic
571C23#6693711yescharacteristic
572C23#6693711yescharacteristic
573C23#6693711yescharacteristic
574C23#6694811yescharacteristic
575C23#6694911yescharacteristic
576C23#6699211yescharacteristic
577Q8—222no—
578Q8—222no—
579Q8—441no—
580Q8—441no—
581D4—222no—
582D4—222no—
583D4—442no—
584D4—442no—
585D4—442no—
586D4—442no—
587D4—441no—
588D4—441no—
589C2×C4—24no—
590C2×C4—44no—
591C2×C4—44no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—114no—
599C2×C4—222no—
600C2×C4—222no—
601C2×C4—224no—
602C2×C4—222no—
603C2×C4—222no—
604C2×C4—222no—
605C2×C4—222no—
606C2×C4—444no—
607C2×C4—444no—
608C2×C4—444no—
609C2×C4—444no—
610C2×C4—442no—
611C2×C4—441no—
612C2×C4—442no—
613C2×C4—441no—
614C2×C4—442no—
615C2×C4—442no—
616C2×C4—442no—
617C2×C4—442no—
618C2×C4#6692511yescharacteristic
619C2×C4C4×D4411yescharacteristic
620C2×C4#6692811yescharacteristic
621C2×C4#6692911yescharacteristic
622C2×C4(C22⋊D11)⋊C411yescharacteristic
623C2×C4#6693511yescharacteristic
624C2×C4#6693511yescharacteristic
625C2×C4#6693611yescharacteristic
626C2×C4#6693711yescharacteristic
627C2×C4#6693711yescharacteristic
628C2×C4#6693811yescharacteristic
629C2×C4#6693811yescharacteristic
630C2×C4C4⋊C4×D1111yescharacteristic
631C2×C4#6694611yescharacteristic
632C2×C4#6694711yescharacteristic
633C2×C4#6694711yescharacteristic
634C2×C4#6694711yescharacteristic
635C2×C4#6694911yescharacteristic
636C2×C4#6694911yescharacteristic
637C2×C4#6694911yescharacteristic
638C2×C4#6695011yescharacteristic
639C2×C4#6695111yescharacteristic
640C2×C4C4×C22⋊D1111yescharacteristic
641C2×C4#6698211yescharacteristic
642C2×C4#6698311yescharacteristic
643C2×C4#6699011yescharacteristic
644C2×C4#6699311yescharacteristic
645C2×C4#6699911yescharacteristic
646C8—42no—
647C8—442no—
648C22—22no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—444no—
657C22—442no—
658C22—882no—
659C22—881no—
660C22—881no—
661C22#1062227811yescharacteristic
662C22#1062228011yescharacteristic
663C22#1062228511yescharacteristic
664C22#1062228911yescharacteristic
665C22D11×#10412yes—
666C22#1062243412yes—
667C22#1062257011yescharacteristic
668C22#1062257211yescharacteristic
669C22#1062260711yescharacteristic
670C4—44no—
671C4—81no—
672C4—81no—
673C4—224no—
674C4—444no—
675C4—442no—
676C4—442no—
677C4#1062228111yescharacteristic
678C4#1062228211yescharacteristic
679C4#1062228611yescharacteristic
680C4#1062228811yescharacteristic
681C4#1062255311yescharacteristic
682C4#1062257311yescharacteristic
683C4#1062260211yescharacteristic
684C4#1062260511yescharacteristic
685C2—21no—
686C2—21no—
687C2—21no—
688C2—21no—
689C2—882no—
690C2#1306686011yescharacteristic
691C2#1306863512yes—
692C2#1306891712yes—
693C2#1306944211yescharacteristic
694C2#1306944611yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#339C2
socleC23×C11C2×C22⋊C4
prime radicalC22×#4339C22
cosocleC23×C4×C11C23
hypercenterC2×#339D11
hypocenterC11#11053
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
1. C2×#10622731C2semidirect
5. C2×#10622170C2semidirect
6. C4×C11⋊#95C2semidirect
7. C2×C11×#339C2semidirect
22. #10622601C4semidirect
23. #10622601C4semidirect
24. #10622587C4semidirect
25. #10622587C4semidirect
221. C2×#339D11semidirect
293. C2×Dic11#104semidirect
562. C11#11053semidirect

Maximal subgroups

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

subgroupindex
C2×#106227312
C22×#668692
C22×#668892
#130711042
C2×#106221702
C4×C11⋊#952
C2×C11×#3392
#1105311