Finite Group Databasebeta

← #14660745

Subgroups — #14660745

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×#66901C211yesmaximal, characteristic
3#13071107C211yesmaximal, characteristic
4C2×#10622193C211yesmaximal, characteristic, complemented
5C2×#10622161C211yesmaximal, characteristic, complemented
6C4×C11⋊#95C211yesmaximal, characteristic, complemented
7C22×C11×#104C211yesmaximal, characteristic
8C22×C11×#41C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C42×C11C2211yescharacteristic
11C2×#66979C2211yescharacteristic
12C22×C4×Dic11C2211yescharacteristic
13C22×C4×Dic11C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C2×C11×#104—22no—
16C2×C11×#104—22no—
17C2×C11×#104—22no—
18C2×#66901—22no—
19C2×#66901—22no—
20C2×#66901—22no—
21#10622843C411yescharacteristic, complemented
22#10622843C411yescharacteristic, complemented
23#10622834C411yescharacteristic, complemented
24#10622834C411yescharacteristic, complemented
25#10622833—22no—
26C4×C22⋊Dic11—22no—
27C2×C11⋊#95—22no—
28#10622731—22no—
29#10622731—22no—
30C2×Dic11⋊C8—22no—
31#10622193—22no—
32#10622161—22no—
33C2×C11×#41—21no—
34C2×C11×#41—21no—
35C2×C11×#41—21no—
36C2×C11×#41—21no—
37C2×C11×#41—21no—
38C2×C11×#41—21no—
39C2×C11×#41—21no—
40C2×C11×#41—21no—
41C2×C11×#41—21no—
42C2×C11×#41—21no—
43C2×C11×#41D412yes—
44C2×C11×#41Q812yes—
45C22×Q8×C11C2×C411yescharacteristic
46C22×D4×C11—21no—
47C22×D4×C11C2×C411yescharacteristic
48C23×C4×C11—21no—
49C23×C4×C11—21no—
50C23×C4×C11C2311yescharacteristic
51C23×Dic11—21no—
52C23×Dic11D412yes—
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—
60C2×C42×C11—21no—
61C2×C42×C11—21no—
62C2×C42×C11—21no—
63C2×C42×C11—21no—
64C2×C42×C11—21no—
65C2×C42×C11D412yes—
66C2×C22⋊Dic11—21no—
67C2×C22⋊Dic11—22no—
68C2×C22⋊Dic11—22no—
69#66979—21no—
70#66979—21no—
71#66979—21no—
72#66979—21no—
73C2×C4⋊Dic11C2×C411yescharacteristic
74C2×C4⋊Dic11C2×C411yescharacteristic
75C2×C4×Dic11—21no—
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×#104—28no—
97#66901—28no—
98C11⋊#95—28no—
99C11⋊#95—22no—
100C11⋊#95—22no—
101Dic11⋊C8—28no—
102#11053—111nomaximal, Sylow
103C24×C11—21no—
104C24×C11C2×D411yescharacteristic
105C11×#41—22no—
106C11×#41—22no—
107C11×#41—22no—
108C11×#41—22no—
109C11×#41—22no—
110C11×#41—22no—
111C11×#41—22no—
112C11×#41—22no—
113C11×#41—41no—
114C11×#41—41no—
115C11×#41—41no—
116C11×#41—41no—
117C11×#41—41no—
118C11×#41—41no—
119C11×#41—41no—
120C11×#41—41no—
121C2×Q8×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11C4⋊C412yes—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—41no—
135C2×D4×C11—41no—
136C2×D4×C11—41no—
137C2×D4×C11—41no—
138C2×D4×C11C4⋊C412yes—
139C22×C4×C11—24no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—42no—
145C22×C4×C11—41no—
146C22×C4×C11—41no—
147C22×C4×C11—41no—
148C22×C4×C11—41no—
149C22×C4×C11—41no—
150C22×C4×C11—41no—
151C22×C4×C11C22×C411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×Q811yescharacteristic
159C22×C4×C11#4111yescharacteristic
160C22×C4×C11#4111yescharacteristic
161C22×C4×C11#4111yescharacteristic
162C22×C4×C11#4111yescharacteristic
163C22×C4×C11#4111yescharacteristic
164C22×C4×C11#4111yescharacteristic
165C22×Dic11—24no—
166C22×Dic11—24no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—42no—
173C22×Dic11—42no—
174C22×Dic11—41no—
175C22×Dic11—41no—
176C22×Dic11C22⋊C412yes—
177C22×Dic11C22⋊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—
185C42×C11—22no—
186C42×C11—22no—
187C42×C11—41no—
188C42×C11—41no—
189C22⋊Dic11—44no—
190C22⋊Dic11—44no—
191C22⋊Dic11—41no—
192C22⋊Dic11—41no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—22no—
202C4×Dic11—22no—
203C4×Dic11—22no—
204C4×Dic11—22no—
205C4×Dic11—41no—
206C4×Dic11—41no—
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×#104D1111yescharacteristic
219#2297—111no—
220C2×#339—111no—
221C2×#339—111no—
222C4×#95—111no—
223C23×C11—22no—
224C23×C11—22no—
225C23×C11—22no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—42no—
229C23×C11—42no—
230C23×C11C2×C22⋊C411yescharacteristic
231C23×C11#12111yescharacteristic
232C23×C11#12111yescharacteristic
233C23×C11#12111yescharacteristic
234C23×C11#12111yescharacteristic
235C23×C11#12111yescharacteristic
236C23×C11C22⋊Q811yescharacteristic
237Q8×C11—22no—
238Q8×C11—22no—
239Q8×C11—41no—
240Q8×C11—41no—
241D4×C11—22no—
242D4×C11—22no—
243D4×C11—42no—
244D4×C11—42no—
245D4×C11—42no—
246D4×C11—42no—
247D4×C11—41no—
248D4×C11—41no—
249C2×C4×C11—24no—
250C2×C4×C11—22no—
251C2×C4×C11—44no—
252C2×C4×C11—44no—
253C2×C4×C11—42no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11C2×C4⋊C411yescharacteristic
262C2×C4×C11#11711yescharacteristic
263C2×C4×C11C4×D411yescharacteristic
264C2×C4×C11C4×D411yescharacteristic
265C2×C4×C11C4×D411yescharacteristic
266C2×C4×C11C4×D411yescharacteristic
267C2×C4×C11#12011yescharacteristic
268C2×C4×C11#12011yescharacteristic
269C2×C4×C11#12011yescharacteristic
270C2×C4×C11#12111yescharacteristic
271C2×C4×C11#12111yescharacteristic
272C2×C4×C11#12111yescharacteristic
273C2×C4×C11C22⋊Q811yescharacteristic
274C2×C4×C11C22⋊Q811yescharacteristic
275C2×C4×C11C22⋊Q811yescharacteristic
276C2×C4×C11C22⋊Q811yescharacteristic
277C2×C4×C11C22⋊Q811yescharacteristic
278C2×C4×C11#12311yescharacteristic
279C2×C4×C11#12311yescharacteristic
280C2×C4×C11#12311yescharacteristic
281C2×C4×C11#12311yescharacteristic
282C2×C4×C11#12311yescharacteristic
283C2×C4×C11#12411yescharacteristic
284C2×C4×C11#12411yescharacteristic
285C2×C4×C11#12411yescharacteristic
286C2×C4×C11#12611yescharacteristic
287C2×C4×C11#12611yescharacteristic
288C2×C4×C11#12711yescharacteristic
289C2×Dic11—22no—
290C2×Dic11—22no—
291C2×Dic11—24no—
292C2×Dic11—22no—
293C2×Dic11—22no—
294C2×Dic11—22no—
295C2×Dic11—44no—
296C2×Dic11—44no—
297C2×Dic11—44no—
298C2×Dic11—44no—
299C2×Dic11—42no—
300C2×Dic11—42no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—42no—
304C2×Dic11—42no—
305C2×Dic11#10414yescomplemented
306C8×C11—42no—
307C11⋊C8—42no—
308C22×#41C2×D1111yescharacteristic
309C22×M16—111no—
310C22×M16C2×D1111yescharacteristic
311C2×#117—111no—
312C22×C42—111no—
313C22×C42—111no—
314C22×C42C2×D1111yescharacteristic
315#423—222no—
316#423—222no—
317C2×C4⋊C8—222no—
318C2×#104—22no—
319C2×#104—22no—
320C2×#104—22no—
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—222no—
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—44no—
342C22×C11—42no—
343C22×C11—82no—
344C22×C11—81no—
345C22×C11—81no—
346C22×C11#38011yescharacteristic
347C22×C11#38611yescharacteristic
348C22×C11#39011yescharacteristic
349C22×C11#39411yescharacteristic
350C22×C11#39411yescharacteristic
351C22×C11#39611yescharacteristic
352C22×C11#39611yescharacteristic
353C22×C11C2×#10412yes—
354C22×C11#42112yes—
355C4×C11—44no—
356C4×C11—42no—
357C4×C11#38511yescharacteristic
358C4×C11#38511yescharacteristic
359C4×C11#38811yescharacteristic
360C4×C11#38811yescharacteristic
361C4×C11#39211yescharacteristic
362C4×C11#39311yescharacteristic
363C4×C11#39711yescharacteristic
364C4×C11#39911yescharacteristic
365Dic11—24no—
366Dic11—44no—
367Dic11—42no—
368Dic11—81no—
369Dic11—81no—
370C2×#41—21no—
371C2×#41—21no—
372C2×#41—21no—
373C2×#41—21no—
374C2×#41—21no—
375C2×#41—21no—
376C2×#41—21no—
377C2×#41—21no—
378C2×#41—21no—
379C2×#41—21no—
380C2×#41Dic2212yes—
381C2×#41C22⋊D1112yes—
382C22×Q8C4×D1111yescharacteristic
383C22×D4—21no—
384C22×D4C4×D1111yescharacteristic
385C23×C4—21no—
386C23×C4—21no—
387C23×C4—112no—
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×M16C22⋊D1112yes—
402C22×C8—21no—
403C22×C8—221no—
404#117—221no—
405#117—221no—
406#117—221no—
407#117—221no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C22⋊C4—222no—
411C2×C22⋊C4—222no—
412C2×C22⋊C4—221no—
413C2×C42—21no—
414C2×C42—21no—
415C2×C42—21no—
416C2×C42—21no—
417C2×C42—21no—
418C2×C42—111no—
419C2×C42—111no—
420C2×C42—112no—
421C2×C42—112no—
422C2×C42—221no—
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—28no—
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—82no—
444C2×C11#143911yescharacteristic
445C2×C11#180612yes—
446C2×C11#187112yes—
447C2×C11#196211yescharacteristic
448C2×C11#196311yescharacteristic
449C24—21no—
450C24D4×D1111yescharacteristic
451#41—22no—
452#41—22no—
453#41—22no—
454#41—22no—
455#41—22no—
456#41—22no—
457#41—22no—
458#41—22no—
459#41—41no—
460#41—41no—
461#41—41no—
462#41—41no—
463#41—41no—
464#41—41no—
465#41—41no—
466#41—41no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8Dic11⋊C412yes—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4Dic11⋊C412yes—
485C22×C4—24no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—42no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—112no—
498C22×C4—112no—
499C22×C4—224no—
500C22×C4—224no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4—222no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—442no—
507C22×C4—442no—
508C22×C4—441no—
509C22×C4—441no—
510C22×C4C2×Dic2211yescharacteristic
511C22×C4C2×C4×D1111yescharacteristic
512C22×C4#433911yescharacteristic
513C22×C4#433911yescharacteristic
514C22×C4D4×D1111yescharacteristic
515C22×C4D4×D1111yescharacteristic
516C22×C4D4×D1111yescharacteristic
517C22×C4#434111yescharacteristic
518C22×C4#434111yescharacteristic
519C22×C4#434111yescharacteristic
520C22×C4#434111yescharacteristic
521C22×C4C2×C22⋊D1111yescharacteristic
522C22×C4C2×C22⋊D1111yescharacteristic
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—221no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C22⋊C4—444no—
543C22⋊C4—444no—
544C22⋊C4—441no—
545C22⋊C4—441no—
546C42—22no—
547C42—22no—
548C42—41no—
549C42—41no—
550C42—221no—
551C42—221no—
552C42—222no—
553C42—221no—
554C42—221no—
555C42—222no—
556C42—222no—
557C42—222no—
558C42—441no—
559C42—441no—
560C42—441no—
561C42—441no—
562C11#1105311yescharacteristic, complemented, Sylow
563C23—22no—
564C23—22no—
565C23—22no—
566C23—41no—
567C23—41no—
568C23—42no—
569C23—42no—
570C23#6693111yescharacteristic
571C23C22⋊C4×D1111yescharacteristic
572C23#6693711yescharacteristic
573C23#6693711yescharacteristic
574C23#6699111yescharacteristic
575C23#6699211yescharacteristic
576C23#6699211yescharacteristic
577Q8—22no—
578Q8—22no—
579Q8—41no—
580Q8—41no—
581D4—22no—
582D4—22no—
583D4—42no—
584D4—42no—
585D4—42no—
586D4—42no—
587D4—41no—
588D4—41no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—44no—
592C2×C4—44no—
593C2×C4—42no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—114no—
602C2×C4—222no—
603C2×C4—222no—
604C2×C4—224no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—222no—
608C2×C4—444no—
609C2×C4—444no—
610C2×C4—444no—
611C2×C4—444no—
612C2×C4—442no—
613C2×C4—442no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—442no—
617C2×C4—442no—
618C2×C4#6693011yescharacteristic
619C2×C4#6693111yescharacteristic
620C2×C4#6693111yescharacteristic
621C2×C4#6693111yescharacteristic
622C2×C4#6693211yescharacteristic
623C2×C4#6693211yescharacteristic
624C2×C4(C22⋊D11)⋊C411yescharacteristic
625C2×C4(C22⋊D11)⋊C411yescharacteristic
626C2×C4#6693611yescharacteristic
627C2×C4#6693611yescharacteristic
628C2×C4#6693811yescharacteristic
629C2×C4#6693811yescharacteristic
630C2×C4C2×Dic11⋊C411yescharacteristic
631C2×C4#6697711yescharacteristic
632C2×C4#6697711yescharacteristic
633C2×C4C4×C22⋊D1111yescharacteristic
634C2×C4C4×C22⋊D1111yescharacteristic
635C2×C4#6698211yescharacteristic
636C2×C4#6698811yescharacteristic
637C2×C4#6698811yescharacteristic
638C2×C4#6698911yescharacteristic
639C2×C4#6699011yescharacteristic
640C2×C4#6699011yescharacteristic
641C2×C4#6699111yescharacteristic
642C2×C4#6699211yescharacteristic
643C2×C4#6699211yescharacteristic
644C2×C4#6699311yescharacteristic
645C2×C4#6700611yescharacteristic
646C8—42no—
647C8—442no—
648C22—22no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—44no—
657C22—42no—
658C22—82no—
659C22—81no—
660C22—81no—
661C22D11×#10412yes—
662C22#1062243412yes—
663C22#1062255511yescharacteristic
664C22#1062256111yescharacteristic
665C22#1062256111yescharacteristic
666C22#1062256911yescharacteristic
667C22#1062257011yescharacteristic
668C22#1062257211yescharacteristic
669C22#1062283511yescharacteristic
670C4—44no—
671C4—42no—
672C4—224no—
673C4—444no—
674C4—442no—
675C4—881no—
676C4—881no—
677C4#1062255711yescharacteristic
678C4#1062255811yescharacteristic
679C4#1062255911yescharacteristic
680C4#1062256011yescharacteristic
681C4#1062256211yescharacteristic
682C4#1062256511yescharacteristic
683C4#1062282311yescharacteristic
684C4#1062283611yescharacteristic
685C2—21no—
686C2—21no—
687C2—21no—
688C2—21no—
689C2—82no—
690C2#1306685911yescharacteristic
691C2#1306863412yes—
692C2#1306891512yes—
693C2#1306944211yescharacteristic
694C2#1306944611yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC22×C11×#104C2
socleC23×C11C2×C22⋊C4
prime radicalC22×C11×#41C22
cosocleC23×C4×C11C23
hypercenterC22×#104D11
hypocenterC11#11053
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
1. C2×#10622731C2semidirect
4. C2×#10622193C2semidirect
5. C2×#10622161C2semidirect
6. C4×C11⋊#95C2semidirect
21. #10622843C4semidirect
22. #10622843C4semidirect
23. #10622834C4semidirect
24. #10622834C4semidirect
305. 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×#669012
#130711072
C2×#106221932
C2×#106221612
C4×C11⋊#952
C22×C11×#1042
#1105311