Finite Group Databasebeta

← #14755014

Subgroups — #14755014

Order 2816.

1934 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66950C211yesmaximal, characteristic
2C2×D11×#117C211yesmaximal, characteristic
3C2×#10622733C211yesmaximal, characteristic, complemented
4C2×#10622617C211yesmaximal, characteristic, complemented
5C2×#10622739C211yesmaximal, characteristic
6#13068927C214yesmaximal, complemented
7#13068922C214yesmaximal, complemented
8#13068335C211yesmaximal, characteristic, complemented
9C11×#1736C211yesmaximal, characteristic, complemented
10C23×C4×D11C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×(C2×D11)⋊C4—21no—
16C2×#66979C2211yescharacteristic
17C22×C4⋊Dic11—21no—
18C22×#4318C2211yescharacteristic
19D11×#117—24no—
20D11×#117—24no—
21C2×#66950—21no—
22C2×#66950—21no—
23C2×#66950—24no—
24C2×#66950C418yescomplemented
25C2×#66950C2212yes—
26C2×#66950C2212yes—
27C2×#66945C2212yes—
28C2×C4⋊C4×D11C2212yes—
29C2×C22⋊C4×D11—21no—
30C2×#66930—21no—
31C2×#66925—21no—
32C2×C42×D11—21no—
33#10622739—24no—
34#10622733—24no—
35C2×(C2×D11)⋊C8C2212yes—
36C2×(C2×D11)⋊C8C2212yes—
37C2×#66880C2214yescomplemented
38#10622617—24no—
39C2×#66874C2214yescomplemented
40C11×#340C2214yescomplemented
41#10622167C2214yescomplemented
42C24×D11D411yescharacteristic
43C23×C4×C11—21no—
44C23×C4×C11C2311yescharacteristic
45C23×Dic11—21no—
46C23×Dic11D411yescharacteristic
47C22×C4×D11—22no—
48C22×C4×D11—22no—
49C22×C4×D11—22no—
50C22×C4×D11—22no—
51C22×C4×D11—22no—
52C22×C4×D11C2×C414yes—
53C22×C4×D11D411yescharacteristic
54C22×C4×D11D411yescharacteristic
55C22×C4×D11D414yes—
56C22×C4×D11C2311yescharacteristic
57C22×C4×D11C2311yescharacteristic
58C22×Dic22—22no—
59C22×Dic22—22no—
60C22×Dic22—22no—
61C22×Dic22—22no—
62C22×Dic22—21no—
63C22×Dic22—22no—
64C22×Dic22C2×C414yescomplemented
65C22×Dic22C2312yes—
66C2×C11×M16—22no—
67C2×C11×M16—22no—
68C2×C11×M16—22no—
69C22×C8×C11C2312yes—
70C11×#117—22no—
71C11×#117D414yes—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4C2×C414yescomplemented
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C22⋊C4—21no—
78C2×C42×C11—21no—
79C2×C22⋊Dic11—21no—
80C2×(C2×D11)⋊C4—28no—
81C2×(C2×D11)⋊C4—22no—
82C2×(C2×D11)⋊C4—22no—
83C2×(C2×D11)⋊C4—22no—
84#66979—22no—
85#66979D414yes—
86C2×C4⋊Dic11—28no—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11C2312yes—
90C2×Dic11⋊C4—22no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—22no—
93C2×#4318—22no—
94C2×#4318—22no—
95C2×#4318—22no—
96C22×C11⋊C8C2312yes—
97#66950—28no—
98#66950—28no—
99#66950—24no—
100#66950—24no—
101#66950C2×C418yes—
102#66950C2×C418yescomplemented
103#66945—24no—
104#66945—24no—
105C4⋊C4×D11—24no—
106C4⋊C4×D11—24no—
107C22⋊C4×D11—28no—
108#66930—28no—
109#66925—28no—
110C42×D11—28no—
111(C2×D11)⋊C8—24no—
112(C2×D11)⋊C8—24no—
113#66880—28no—
114#66874—28no—
115#20911—111nomaximal, Sylow
116C24×C11C2×D411yescharacteristic
117C23×D11—22no—
118C23×D11—22no—
119C23×D11—24no—
120C23×D11—42no—
121C23×D11C22⋊C414yes—
122C23×D11C2×D411yescharacteristic
123C23×D11C2×D411yescharacteristic
124C22×C4×C11—24no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—44no—
128C22×C4×C11C22×C412yes—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11#4112yes—
134C22×C4×C11#4112yes—
135C22×C4×C11C2411yescharacteristic
136C22×Dic11—24no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—42no—
142C22×Dic11—42no—
143C22×Dic11C22⋊C414yes—
144C22×Dic11C2×D411yescharacteristic
145C22×Dic11C2×D411yescharacteristic
146C2×C4×D11—28no—
147C2×C4×D11—28no—
148C2×C4×D11—28no—
149C2×C4×D11—22no—
150C2×C4×D11—22no—
151C2×C4×D11—28no—
152C2×C4×D11—28no—
153C2×C4×D11—22no—
154C2×C4×D11—22no—
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—44no—
164C2×C4×D11—44no—
165C2×C4×D11C22⋊C414yes—
166C2×C4×D11C22⋊C414yes—
167C2×C4×D11C22×C412yes—
168C2×C4×D11C22×C412yes—
169C2×C4×D11C2×D412yes—
170C2×C4×D11C2×D412yes—
171C2×Dic22—24no—
172C2×Dic22—28no—
173C2×Dic22—28no—
174C2×Dic22—22no—
175C2×Dic22—22no—
176C2×Dic22—22no—
177C2×Dic22—22no—
178C2×Dic22—22no—
179C2×Dic22—42no—
180C2×Dic22—44no—
181C2×Dic22—44no—
182C2×Dic22—42no—
183C2×Dic22C22×C414yes—
184C11×M16—44no—
185C2×C8×C11—22no—
186C2×C8×C11—22no—
187C2×C8×C11—22no—
188C11×C4⋊C4—24no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4C22×C414yes—
192C11×C4⋊C4C2×D414yes—
193C11×C22⋊C4—24no—
194C42×C11—24no—
195C22⋊Dic11—24no—
196(C2×D11)⋊C4—28no—
197(C2×D11)⋊C4—28no—
198(C2×D11)⋊C4—28no—
199C4⋊Dic11—28no—
200C4⋊Dic11—28no—
201C4⋊Dic11—22no—
202C4⋊Dic11C2×D414yes—
203Dic11⋊C4—28no—
204C4×Dic11—28no—
205C4×Dic11—24no—
206#4318—44no—
207C2×C11⋊C8—22no—
208C2×C11⋊C8—22no—
209C2×C11⋊C8—22no—
210C22×C22⋊Q8—111no—
211C22×#117—111no—
212C2×#419—111no—
213C2×#419—111no—
214C2×#407—111no—
215#1873—114no—
216#1872—114no—
217#1736—111no—
218#1736D1111yescharacteristic, complemented
219C23×C11—22no—
220C23×C11—22no—
221C23×C11C2×C22⋊C412yes—
222C23×C11#12012yes—
223C23×C11#12312yes—
224C23×C11C22×D411yescharacteristic
225C22×D11—21no—
226C22×D11—21no—
227C22×D11—22no—
228C22×D11—21no—
229C22×D11—21no—
230C22×D11—22no—
231C22×D11—22no—
232C22×D11—28no—
233C22×D11—28no—
234C22×D11—44no—
235C22×D11—48no—
236C22×D11—48no—
237C22×D11C2×C22⋊C412yes—
238C22×D11C2×C22⋊C412yes—
239C22×D11#13714yes—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—48no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—44no—
246C2×C4×C11C2×C22⋊C412yes—
247C2×C4×C11C4×D414yes—
248C2×C4×C11C4×D414yes—
249C2×C4×C11#12012yes—
250C2×C4×C11#12114yes—
251C2×C4×C11#12114yes—
252C2×C4×C11#12312yes—
253C2×C4×C11C23×C411yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—28no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11—48no—
271C2×Dic11C2×C22⋊C412yes—
272C2×Dic11C2×C22⋊C412yes—
273C4×D11—22no—
274C4×D11—22no—
275C4×D11—22no—
276C4×D11—22no—
277C4×D11—22no—
278C4×D11—22no—
279C4×D11—22no—
280C4×D11—22no—
281C4×D11—28no—
282C4×D11—28no—
283C4×D11—416no—
284Dic22—24no—
285Dic22—24no—
286Dic22—42no—
287Dic22—42no—
288Dic22—48no—
289C8×C11—42no—
290C11⋊C8—42no—
291C23×Q8—111no—
292C24×C4—111no—
293C22×M16—111no—
294C22×M16C2×D1111yescharacteristic
295C2×C22⋊Q8—112no—
296C2×C22⋊Q8—112no—
297C2×C22⋊Q8—118no—
298C2×C22⋊Q8—221no—
299C2×C22⋊Q8—224no—
300C2×C22⋊Q8—221no—
301C2×#117—111no—
302C2×#117—112no—
303C2×#117—221no—
304C2×#117—221no—
305C2×#117—224no—
306C2×#117—224no—
307C2×#117C2×D1111yescharacteristic
308C22×C4⋊C4—112no—
309C22×C4⋊C4—221no—
310C22×C4⋊C4C2×D1111yescharacteristic
311C22×C22⋊C4—221no—
312C22×C22⋊C4—221no—
313C22×C42—221no—
314#419—224no—
315#419—224no—
316C2×#103—114no—
317C2×#103—114no—
318#407—224no—
319C2×C22⋊C8—112no—
320C2×C22⋊C8—112no—
321#340—114no—
322#340C2×D1114yescomplemented
323C22×C11—24no—
324C22×C11—22no—
325C22×C11—22no—
326C22×C11—24no—
327C22×C11#38614yes—
328C22×C11C22×C22⋊C411yescharacteristic
329C22×C11C2×#12011yescharacteristic
330C22×C11C2×#12311yescharacteristic
331C22×C11C2×#13712yes—
332C22×C11#57512yes—
333C2×D11—24no—
334C2×D11—22no—
335C2×D11—24no—
336C2×D11—22no—
337C2×D11—22no—
338C2×D11—22no—
339C2×D11—22no—
340C2×D11—416no—
341C2×D11—42no—
342C2×D11—42no—
343C2×D11#41914yescomplemented
344C4×C11—44no—
345C4×C11—44no—
346C4×C11#38614yes—
347C4×C11C2×C4×D411yescharacteristic
348C4×C11C2×C4×D411yescharacteristic
349C4×C11C2×#12111yescharacteristic
350C4×C11C2×#12111yescharacteristic
351Dic11—22no—
352Dic11—22no—
353Dic11—44no—
354Dic11—44no—
355C25—111no—
356C22×Q8—114no—
357C22×Q8—112no—
358C22×Q8—222no—
359C22×Q8—221no—
360C22×Q8—222no—
361C22×Q8—222no—
362C22×Q8—222no—
363C22×Q8—222no—
364C23×C4—21no—
365C23×C4—111no—
366C23×C4—114no—
367C23×C4—111no—
368C23×C4—114no—
369C23×C4—111no—
370C23×C4—111no—
371C23×C4—111no—
372C23×C4—222no—
373C23×C4—222no—
374C23×C4—222no—
375C23×C4—222no—
376C23×C4—222no—
377C23×C4—221no—
378C23×C4C22×D1111yescharacteristic
379C2×M16—22no—
380C2×M16—22no—
381C2×M16—22no—
382C2×M16—222no—
383C2×M16—222no—
384C2×M16—222no—
385C22×C8—112no—
386C22×C8C22×D1112yes—
387C22⋊Q8—118no—
388C22⋊Q8—118no—
389C22⋊Q8—228no—
390C22⋊Q8—228no—
391C22⋊Q8—224no—
392C22⋊Q8—224no—
393#117—22no—
394#117—114no—
395#117—228no—
396#117—228no—
397#117—224no—
398#117—222no—
399#117—224no—
400#117D4414yes—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—112no—
404C2×C4⋊C4—224no—
405C2×C4⋊C4—222no—
406C2×C4⋊C4—228no—
407C2×C4⋊C4—222no—
408C2×C4⋊C4—222no—
409C2×C4⋊C4—224no—
410C2×C4⋊C4C4×D1114yescomplemented
411C2×C4⋊C4C22×D1112yes—
412C2×C4⋊C4C22×D1112yes—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—228no—
415C2×C22⋊C4—222no—
416C2×C22⋊C4—228no—
417C2×C22⋊C4—222no—
418C2×C22⋊C4—222no—
419C2×C22⋊C4—221no—
420C2×C42—21no—
421C2×C42—228no—
422C2×C42—222no—
423C2×C42—221no—
424#103—228no—
425#103—228no—
426C22⋊C8—224no—
427C22⋊C8—224no—
428C2×C11—24no—
429C2×C11C2×#38611yescharacteristic
430C2×C11C2×#41911yescharacteristic
431C2×C11#289611yescharacteristic
432C2×C11#300712yes—
433C2×C11#309512yes—
434D11—24no—
435D11—42no—
436C24—111no—
437C24—111no—
438C24—114no—
439C24—224no—
440C24—222no—
441C24—222no—
442C24—442no—
443C24D4×D1111yescharacteristic
444C2×Q8—114no—
445C2×Q8—224no—
446C2×Q8—222no—
447C2×Q8—228no—
448C2×Q8—228no—
449C2×Q8—222no—
450C2×Q8—222no—
451C2×Q8—222no—
452C2×Q8—222no—
453C2×Q8—442no—
454C2×Q8—444no—
455C2×Q8—442no—
456C2×Q8—444no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—44no—
461C22×C4—114no—
462C22×C4—111no—
463C22×C4—111no—
464C22×C4—114no—
465C22×C4—114no—
466C22×C4—112no—
467C22×C4—112no—
468C22×C4—112no—
469C22×C4—112no—
470C22×C4—228no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—228no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—228no—
477C22×C4—228no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—228no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—224no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4—444no—
493C22×C4—444no—
494C22×C4—442no—
495C22×C4—442no—
496C22×C4C2×C4×D1112yes—
497C22×C4C2×D4412yes—
498C22×C4#433912yes—
499C22×C4D4×D1111yescharacteristic
500C22×C4D4×D1112yes—
501C22×C4D4×D1112yes—
502C22×C4#434312yes—
503C22×C4C23×D1111yescharacteristic
504M16—44no—
505M16—444no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—222no—
510C2×C8—222no—
511C2×C8—222no—
512C4⋊C4—24no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—114no—
516C4⋊C4—228no—
517C4⋊C4—228no—
518C4⋊C4—228no—
519C4⋊C4—222no—
520C4⋊C4C2×C4×D1114yes—
521C4⋊C4C2×D4414yes—
522C22⋊C4—24no—
523C22⋊C4—228no—
524C22⋊C4—228no—
525C22⋊C4—228no—
526C22⋊C4—224no—
527C42—24no—
528C42—228no—
529C42—224no—
530C11#2091111yescharacteristic, complemented, Sylow
531C23—22no—
532C23—22no—
533C23—112no—
534C23—114no—
535C23—112no—
536C23—228no—
537C23—221no—
538C23—221no—
539C23—222no—
540C23—221no—
541C23—221no—
542C23—228no—
543C23—222no—
544C23—222no—
545C23—444no—
546C23—448no—
547C23—448no—
548C23C22⋊C4×D1112yes—
549C23#6693512yes—
550C23#6694712yes—
551C23C2×D4×D1111yescharacteristic
552Q8—224no—
553Q8—224no—
554Q8—442no—
555Q8—442no—
556Q8—448no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—48no—
560C2×C4—44no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—112no—
564C2×C4—112no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—228no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—222no—
577C2×C4—222no—
578C2×C4—228no—
579C2×C4—228no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—4416no—
583C2×C4—442no—
584C2×C4—442no—
585C2×C4—448no—
586C2×C4—442no—
587C2×C4—442no—
588C2×C4C4×D4414yes—
589C2×C4C22⋊C4×D1112yes—
590C2×C4#6693512yes—
591C2×C4#6693714yes—
592C2×C4#6694614yes—
593C2×C4#6694712yes—
594C2×C4#6694814yes—
595C2×C4C22×C4×D1111yescharacteristic
596C2×C4C22×D4411yescharacteristic
597C2×C4C2×#433911yescharacteristic
598C2×C4C2×D4×D1111yescharacteristic
599C2×C4C2×D4×D1111yescharacteristic
600C2×C4C2×#434311yescharacteristic
601C8—42no—
602C8—442no—
603C22—24no—
604C22—24no—
605C22—22no—
606C22—22no—
607C22—114no—
608C22—224no—
609C22—224no—
610C22—222no—
611C22—222no—
612C22—222no—
613C22—222no—
614C22—222no—
615C22—4416no—
616C22—442no—
617C22—442no—
618C22#1062227814yes—
619C22C2×C22⋊C4×D1111yescharacteristic
620C22C2×#6693511yescharacteristic
621C22C2×#6694711yescharacteristic
622C22#1062330412yes—
623C22D11×#13712yes—
624C4—44no—
625C4—44no—
626C4—222no—
627C4—222no—
628C4—444no—
629C4—444no—
630C4#1062227814yes—
631C4C2×C4×D4411yescharacteristic
632C4C2×#6693711yescharacteristic
633C4C2×#6694611yescharacteristic
634C4C2×#6694811yescharacteristic
635C2—24no—
636C2—224no—
637C2—442no—
638C2C2×#1062227811yescharacteristic
639C2D11×#41911yescharacteristic
640C2#1307713011yescharacteristic
641C2#1307787712yes—
642C2#1307856612yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1736C2
socleC23×C11C22×D4
prime radicalC24×D11D4
cosocleC22×C4×C11C24
hypercenter#1736D11
hypocenterC11#20911
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
3. C2×#10622733C2semidirect
4. C2×#10622617C2semidirect
6. #13068927C2semidirect
7. #13068922C2semidirect
8. #13068335C2semidirect
9. C11×#1736C2semidirect
24. C2×#66950C4semidirect
37. C2×#66880C22semidirect
39. C2×#66874C22semidirect
40. C11×#340C22semidirect
41. #10622167C22semidirect
64. C22×Dic22C2×C4semidirect
74. C2×C11×C4⋊C4C2×C4semidirect
102. #66950C2×C4semidirect
218. #1736D11semidirect
322. #340C2×D11semidirect
343. C2×D11#419semidirect
410. C2×C4⋊C4C4×D11semidirect
530. C11#20911semidirect

Maximal subgroups

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

subgroupindex
C22×#669502
C2×D11×#1172
C2×#106227332
C2×#106226172
C2×#106227392
#130689272
#130689222
#130683352
C11×#17362
#2091111