Finite Group Databasebeta

← #14645583

Subgroups — #14645583

Order 2816.

1020 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623165C211yesmaximal, characteristic
2#13068924C211yesmaximal, characteristic, complemented
3#13068921C211yesmaximal, characteristic, complemented
4C2×#10622090C211yesmaximal, characteristic, complemented
5C2×#10622106C211yesmaximal, characteristic
6#13066862C211yesmaximal, characteristic
7C2×C11×#328C211yesmaximal, characteristic, complemented
8C2×C11×C22⋊Q8C2211yescharacteristic
9C2×#66999—21no—
10C22×(C2×D11)⋊C4—21no—
11C22×(C2×D11)⋊C4C2211yescharacteristic
12C22×C4⋊Dic11C2211yescharacteristic
13C2×#66977C2211yescharacteristic
14#10623165—22no—
15#10623165—22no—
16#10623165—22no—
17#10623165C414yescomplemented
18C2×#66950—21no—
19C2×#66949—21no—
20C2×#66949—21no—
21C2×C22⋊C4×D11—21no—
22C2×#66931—21no—
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×#95C2211yescharacteristic
25C2×#66899—21no—
26C2×C11⋊#95—21no—
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×#66880—21no—
29C11×#328—22no—
30#10622189—21no—
31#10622167—21no—
32#10622106—22no—
33#10622090—22no—
34C24×D11D411yescharacteristic
35C22×Q8×C11D411yescharacteristic
36C23×C4×C11—21no—
37C23×C4×C11C2311yescharacteristic
38C23×Dic11—21no—
39C23×Dic11D411yescharacteristic
40C22×C4×D11—21no—
41C22×C4×D11—21no—
42C22×Dic22—21no—
43C22×Dic22D411yescharacteristic
44C22×C8×C11—21no—
45C11×C22⋊Q8—21no—
46C11×C22⋊Q8—21no—
47C11×C22⋊Q8C2×C412yes—
48C11×C22⋊Q8D412yes—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C22⋊C4—21no—
52C2×C22⋊Dic11—21no—
53#66999—24no—
54#66999—24no—
55C2×(C2×D11)⋊C4—21no—
56C2×(C2×D11)⋊C4—21no—
57C2×(C2×D11)⋊C4—21no—
58C2×(C2×D11)⋊C4—21no—
59C2×(C2×D11)⋊C4—21no—
60C2×(C2×D11)⋊C4—21no—
61C2×(C2×D11)⋊C4—42no—
62C2×(C2×D11)⋊C4—42no—
63C2×(C2×D11)⋊C4—42no—
64C2×(C2×D11)⋊C4C2×C412yes—
65C2×(C2×D11)⋊C4D412yes—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—42no—
70C2×C4⋊Dic11D411yescharacteristic
71#66977—21no—
72#66977—21no—
73#66977C2×C412yes—
74#66977D412yes—
75C2×Dic11⋊C4—21no—
76C2×Dic11⋊C4—21no—
77C2×Dic11⋊C4—21no—
78C22×C11⋊C8—21no—
79#66950—24no—
80#66950—24no—
81#66949—24no—
82#66949—24no—
83#66949—24no—
84#66949—24no—
85C22⋊C4×D11—24no—
86C22⋊C4×D11—24no—
87#66931—24no—
88#66931—24no—
89C11×C22⋊C8—21no—
90C11×C22⋊C8—21no—
91C11×#95—21no—
92C11×#95—21no—
93#66899—42no—
94C11⋊#95—42no—
95C22⋊(C11⋊C8)—21no—
96C22⋊(C11⋊C8)—21no—
97#66880—42no—
98#8405—111nomaximal, Sylow
99C24×C11C2×D411yescharacteristic
100C23×D11—21no—
101C23×D11—21no—
102C23×D11—21no—
103C23×D11—21no—
104C23×D11—41no—
105C23×D11—41no—
106C23×D11—41no—
107C23×D11—41no—
108C23×D11C22⋊C412yes—
109C23×D11SD1612yes—
110C23×D11Q1612yes—
111C2×Q8×C11—21no—
112C2×Q8×C11—41no—
113C2×Q8×C11—41no—
114C2×Q8×C11C22⋊C412yescomplemented
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—41no—
119C22×C4×C11—41no—
120C22×C4×C11—41no—
121C22×C4×C11—41no—
122C22×C4×C11—41no—
123C22×C4×C11—41no—
124C22×C4×C11—41no—
125C22×C4×C11—41no—
126C22×C4×C11C22×C411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×Dic11—22no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—41no—
138C22×Dic11—41no—
139C22×Dic11—41no—
140C22×Dic11—41no—
141C22×Dic11—41no—
142C22×Dic11—41no—
143C22×Dic11—41no—
144C22×Dic11—41no—
145C22×Dic11C22⋊C412yes—
146C2×C4×D11—24no—
147C2×C4×D11—24no—
148C2×C4×D11—81no—
149C2×C4×D11—81no—
150C2×C4×D11—81no—
151C2×C4×D11—81no—
152C2×Dic22—24no—
153C2×Dic22—21no—
154C2×Dic22—41no—
155C2×Dic22—41no—
156C2×Dic22—81no—
157C2×Dic22—81no—
158C2×Dic22C22⋊C412yescomplemented
159C2×C8×C11—41no—
160C2×C8×C11—41no—
161C2×C8×C11—41no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4C22⋊C412yescomplemented
166C11×C22⋊C4—22no—
167C11×C22⋊C4—22no—
168C22⋊Dic11—22no—
169C22⋊Dic11—22no—
170(C2×D11)⋊C4—24no—
171(C2×D11)⋊C4—24no—
172(C2×D11)⋊C4—22no—
173(C2×D11)⋊C4—22no—
174(C2×D11)⋊C4—22no—
175(C2×D11)⋊C4—22no—
176(C2×D11)⋊C4—48no—
177C4⋊Dic11—24no—
178C4⋊Dic11—22no—
179C4⋊Dic11—22no—
180C4⋊Dic11—21no—
181C4⋊Dic11—41no—
182C4⋊Dic11—41no—
183C4⋊Dic11C22⋊C412yescomplemented
184Dic11⋊C4—24no—
185Dic11⋊C4—24no—
186Dic11⋊C4—22no—
187Dic11⋊C4—22no—
188C2×C11⋊C8—41no—
189C2×C11⋊C8—41no—
190C2×C11⋊C8—41no—
191C2×#543—111no—
192#1872—111no—
193#1872—111no—
194C2×#328—111no—
195C2×#328D1111yescharacteristic, complemented
196C2×#323—111no—
197#1439—111no—
198C23×C11—21no—
199C23×C11—21no—
200C23×C11—21no—
201C23×C11—21no—
202C23×C11C2×C22⋊C411yescharacteristic
203C23×C11#12011yescharacteristic
204C23×C11#12011yescharacteristic
205C23×C11C2×SD1611yescharacteristic
206C23×C11C2×Q1611yescharacteristic
207C23×C11#13711yescharacteristic
208C23×C11#13711yescharacteristic
209C22×D11—22no—
210C22×D11—22no—
211C22×D11—22no—
212C22×D11—22no—
213C22×D11—22no—
214C22×D11—22no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—41no—
218C22×D11—41no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11—42no—
224C22×D11—42no—
225C22×D11—81no—
226C22×D11—81no—
227C22×D11—81no—
228C22×D11—81no—
229C22×D11—81no—
230C22×D11—81no—
231C22×D11#10314yescomplemented
232Q8×C11—42no—
233Q8×C11—81no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—81no—
252C2×C4×C11—81no—
253C2×C4×C11—81no—
254C2×C4×C11—81no—
255C2×C4×C11C2×C22⋊C411yescharacteristic
256C2×C4×C11C2×C22⋊C411yescharacteristic
257C2×C4×C11#12011yescharacteristic
258C2×C4×C11#12011yescharacteristic
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—81no—
273C2×Dic11—81no—
274C2×Dic11—81no—
275C2×Dic11—81no—
276C2×Dic11—81no—
277C4×D11—84no—
278C4×D11—84no—
279Dic22—42no—
280Dic22—81no—
281Dic22—84no—
282C8×C11—81no—
283C11⋊C8—81no—
284#543—114no—
285#543—222no—
286#543—222no—
287#543—222no—
288C2×C22⋊Q8—111no—
289C2×C22⋊Q8—221no—
290C2×C22⋊Q8—221no—
291C2×C22⋊Q8—221no—
292C2×C22⋊Q8—221no—
293C2×C22⋊Q8—221no—
294C2×C22⋊Q8C2×D1111yescharacteristic
295C22×C4⋊C4—111no—
296C22×C22⋊C4—111no—
297C22×C22⋊C4—221no—
298C22×C22⋊C4—221no—
299C2×#103—221no—
300C2×#103—221no—
301C2×C22⋊C8—111no—
302C2×C22⋊C8C2×D1111yescharacteristic
303C2×#95—221no—
304C2×#95C2×D1111yescharacteristic
305#340—221no—
306#340—221no—
307#328—22no—
308#328—222no—
309#323—222no—
310C22×C11—21no—
311C22×C11—21no—
312C22×C11—21no—
313C22×C11—21no—
314C22×C11—21no—
315C22×C11—21no—
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11#37911yescharacteristic
323C22×C11C2×#10311yescharacteristic
324C22×C11#41911yescharacteristic
325C22×C11#44811yescharacteristic
326C22×C11#44811yescharacteristic
327C22×C11#45111yescharacteristic
328C22×C11#45111yescharacteristic
329C22×C11#45311yescharacteristic
330C22×C11#45511yescharacteristic
331C22×C11B(4,𝔽2)11yescharacteristic
332C22×C11#45811yescharacteristic
333C2×D11—24no—
334C2×D11—42no—
335C2×D11—42no—
336C2×D11—42no—
337C2×D11—42no—
338C2×D11—42no—
339C2×D11—42no—
340C2×D11—44no—
341C2×D11—82no—
342C2×D11—82no—
343C2×D11—82no—
344C4×C11—21no—
345C4×C11—21no—
346C4×C11—21no—
347C4×C11—21no—
348C4×C11—42no—
349C4×C11—42no—
350C4×C11—82no—
351Dic11—42no—
352Dic11—42no—
353Dic11—42no—
354Dic11—82no—
355C25—111no—
356C22×Q8—111no—
357C22×Q8—221no—
358C22×Q8D4411yescharacteristic
359C23×C4—21no—
360C23×C4—111no—
361C23×C4—221no—
362C23×C4—221no—
363C23×C4—221no—
364C23×C4C22×D1111yescharacteristic
365C22×C8—21no—
366C22×C8—221no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8—112no—
370C22⋊Q8—112no—
371C22⋊Q8—224no—
372C22⋊Q8—224no—
373C22⋊Q8—224no—
374C22⋊Q8—224no—
375C22⋊Q8—224no—
376C22⋊Q8—224no—
377C22⋊Q8—224no—
378C22⋊Q8—224no—
379C22⋊Q8—224no—
380C22⋊Q8—221no—
381C22⋊Q8—221no—
382C22⋊Q8—224no—
383C22⋊Q8C4×D1112yes—
384C22⋊Q8C22⋊D1112yes—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—442no—
394C2×C4⋊C4D4411yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—112no—
397C2×C22⋊C4—112no—
398C2×C22⋊C4—224no—
399C2×C22⋊C4—224no—
400C2×C22⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C22⋊C4—221no—
403C2×C22⋊C4—221no—
404C2×C22⋊C4—221no—
405C2×C22⋊C4—221no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4—442no—
408C2×C22⋊C4—442no—
409C2×C22⋊C4—442no—
410#103—442no—
411#103—442no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—221no—
415C22⋊C8—221no—
416#95—21no—
417#95—21no—
418#95—442no—
419C2×C11—21no—
420C2×C11—21no—
421C2×C11—21no—
422C2×C11—21no—
423C2×C11#159611yescharacteristic
424C2×C11#160211yescharacteristic
425C2×C11#160811yescharacteristic
426C2×C11#161411yescharacteristic
427C2×C11#178711yescharacteristic
428C2×C11#179011yescharacteristic
429C2×C11#179211yescharacteristic
430D11—44no—
431C24—112no—
432C24—112no—
433C24—112no—
434C24—221no—
435C24—221no—
436C24—221no—
437C24—221no—
438C24—441no—
439C24—441no—
440C24—441no—
441C24—441no—
442C24D4×D1111yescharacteristic
443C2×Q8—21no—
444C2×Q8—41no—
445C2×Q8—41no—
446C2×Q8—112no—
447C2×Q8—224no—
448C2×Q8—221no—
449C2×Q8—441no—
450C2×Q8—441no—
451C2×Q8—881no—
452C2×Q8—881no—
453C2×Q8(C2×D11)⋊C412yescomplemented
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—112no—
466C22×C4—224no—
467C22×C4—224no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—222no—
473C22×C4—441no—
474C22×C4—441no—
475C22×C4—441no—
476C22×C4—441no—
477C22×C4—441no—
478C22×C4—441no—
479C22×C4—441no—
480C22×C4—441no—
481C22×C4—881no—
482C22×C4—881no—
483C22×C4—881no—
484C22×C4—881no—
485C22×C4C2×C4×D1111yescharacteristic
486C22×C4C2×D4411yescharacteristic
487C22×C4D4×D1111yescharacteristic
488C22×C4D4×D1111yescharacteristic
489C22×C4D4×D1111yescharacteristic
490C22×C4C2×C22⋊D1111yescharacteristic
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—441no—
495C2×C8—441no—
496C2×C8—441no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—22no—
500C4⋊C4—112no—
501C4⋊C4—224no—
502C4⋊C4—224no—
503C4⋊C4—224no—
504C4⋊C4—222no—
505C4⋊C4—222no—
506C4⋊C4—222no—
507C4⋊C4—222no—
508C4⋊C4—221no—
509C4⋊C4—441no—
510C4⋊C4—441no—
511C4⋊C4(C2×D11)⋊C412yescomplemented
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—224no—
515C22⋊C4—224no—
516C22⋊C4—222no—
517C22⋊C4—222no—
518C22⋊C4—222no—
519C22⋊C4—222no—
520C22⋊C4—222no—
521C22⋊C4—222no—
522C22⋊C4—448no—
523C11#840511yescharacteristic, complemented, Sylow
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—114no—
529C23—222no—
530C23—222no—
531C23—222no—
532C23—222no—
533C23—222no—
534C23—222no—
535C23—442no—
536C23—442no—
537C23—442no—
538C23—442no—
539C23—442no—
540C23—442no—
541C23—441no—
542C23—441no—
543C23—441no—
544C23—441no—
545C23—881no—
546C23—881no—
547C23—881no—
548C23—881no—
549C23—881no—
550C23—881no—
551C23C22⋊C4×D1111yescharacteristic
552C23#6693511yescharacteristic
553C23SD16×D1111yescharacteristic
554C23#6696811yescharacteristic
555C23Q16×D1111yescharacteristic
556C23#6697111yescharacteristic
557C23#6699011yescharacteristic
558Q8—42no—
559Q8—81no—
560Q8—442no—
561Q8—881no—
562Q8—884no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—81no—
581C2×C4—81no—
582C2×C4—81no—
583C2×C4—81no—
584C2×C4—222no—
585C2×C4—222no—
586C2×C4—222no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—442no—
594C2×C4—442no—
595C2×C4—442no—
596C2×C4—442no—
597C2×C4—884no—
598C2×C4—884no—
599C2×C4—881no—
600C2×C4—881no—
601C2×C4—881no—
602C2×C4—881no—
603C2×C4—881no—
604C2×C4C22⋊C4×D1111yescharacteristic
605C2×C4#6693511yescharacteristic
606C2×C4C2×(C2×D11)⋊C411yescharacteristic
607C2×C4#6699011yescharacteristic
608C8—81no—
609C8—881no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—21no—
620C22—21no—
621C22—21no—
622C22—224no—
623C22—444no—
624C22—442no—
625C22—442no—
626C22—442no—
627C22—442no—
628C22—442no—
629C22—442no—
630C22—882no—
631C22—882no—
632C22—882no—
633C22#1062235411yescharacteristic
634C22#1062235511yescharacteristic
635C22D11×#10311yescharacteristic
636C22#1062241511yescharacteristic
637C22#1062241911yescharacteristic
638C22#1062242111yescharacteristic
639C22#1062243511yescharacteristic
640C22#1062243811yescharacteristic
641C22#1062256811yescharacteristic
642C22#1062278311yescharacteristic
643C22#1062279911yescharacteristic
644C4—21no—
645C4—21no—
646C4—21no—
647C4—21no—
648C4—42no—
649C4—42no—
650C4—82no—
651C4—442no—
652C4—442no—
653C4—442no—
654C4—882no—
655C2—21no—
656C2—21no—
657C2—21no—
658C2—21no—
659C2—444no—
660C2#1306754011yescharacteristic
661C2#1306757411yescharacteristic
662C2#1306760811yescharacteristic
663C2#1306764211yescharacteristic
664C2#1306854911yescharacteristic
665C2#1306856211yescharacteristic
666C2#1306857111yescharacteristic
subgroupG/H
centerC23#66935
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#328C2
socleC23×C11#120
prime radicalC24×D11D4
cosocleC23×C4×C11C23
hypercenterC2×#328D11
hypocenterC11#8405
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
2. #13068924C2semidirect
3. #13068921C2semidirect
4. C2×#10622090C2semidirect
7. C2×C11×#328C2semidirect
17. #10623165C4semidirect
114. C2×Q8×C11C22⋊C4semidirect
158. C2×Dic22C22⋊C4semidirect
165. C11×C4⋊C4C22⋊C4semidirect
183. C4⋊Dic11C22⋊C4semidirect
195. C2×#328D11semidirect
231. C22×D11#103semidirect
453. C2×Q8(C2×D11)⋊C4semidirect
511. C4⋊C4(C2×D11)⋊C4semidirect
523. C11#8405semidirect

Maximal subgroups

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

subgroupindex
C2×#106231652
#130689242
#130689212
C2×#106220902
C2×#106221062
#130668622
C2×C11×#3282
#840511