Finite Group Databasebeta

← #14780621

Subgroups — #14780621

Order 2816.

2170 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67004C211yesmaximal, characteristic, complemented
2C2×#10623359C211yesmaximal, characteristic
3C22×#66950C211yesmaximal, characteristic, complemented
4C2×#10622733C211yesmaximal, characteristic, complemented
5C2×#10622739C211yesmaximal, characteristic, complemented
6#13069625C214yesmaximal, complemented
7#13069620C214yesmaximal, complemented
8#13068335C211yesmaximal, characteristic, complemented
9C2×C11×#417C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C23×C4×D11C2211yescharacteristic
12C23×Dic22C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15#10623359—24no—
16#10623359—24no—
17C2×#67004—24no—
18C2×#67004—24no—
19C2×#67004—24no—
20C2×#66999C2212yes—
21C22×#4326C2212yescomplemented
22C2×#66991C2212yes—
23C2×#66990—21no—
24C2×#66988—21no—
25C22×#4324C2212yescomplemented
26C2×C4×C22⋊D11—22no—
27C22×(C2×D11)⋊C4—21no—
28C2×#66979C2211yescharacteristic
29C22×C4⋊Dic11—21no—
30C22×#4318C2211yescharacteristic
31C2×#66950—22no—
32C2×#66950—24no—
33C2×#66950—24no—
34C2×#66950C2214yes—
35C11×#417—24no—
36C2×C11×#103C2212yescomplemented
37C2×C11×#102C2212yescomplemented
38#10622739—24no—
39#10622733—24no—
40C2×(C2×D11)⋊C8C2214yes—
41C2×#66880C2214yescomplemented
42#10622167C2214yescomplemented
43C24×D11D411yescharacteristic
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41D414yes—
50C22×Q8×C11C2311yescharacteristic
51C22×D4×C11—21no—
52C22×D4×C11C2311yescharacteristic
53C23×C4×C11—21no—
54C23×C4×C11—21no—
55C23×C4×C11C2311yescharacteristic
56C22×C22⋊D11—22no—
57C23×Dic11—21no—
58C23×Dic11D411yescharacteristic
59C22×C4×D11—22no—
60C22×C4×D11—22no—
61C22×C4×D11—22no—
62C22×C4×D11—22no—
63C22×C4×D11—22no—
64C22×C4×D11—22no—
65C22×C4×D11D412yes—
66C22×C4×D11C2312yes—
67C22×Dic22—22no—
68C22×Dic22—22no—
69C22×Dic22—22no—
70C22×Dic22—22no—
71C22×Dic22—21no—
72C22×Dic22—22no—
73C22×Dic22D414yescomplemented
74C22×Dic22C2312yes—
75C2×C11×M16—22no—
76C2×C11×M16—22no—
77C2×C11×M16—22no—
78C22×C8×C11C2312yes—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4D414yescomplemented
82C2×C11×C4⋊C4C2312yes—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—22no—
85#67004—232no—
86#66999—24no—
87#66999—24no—
88C2×#4326—24no—
89C2×#4326—24no—
90C2×#4326—24no—
91#66991—24no—
92#66991—24no—
93#66990—28no—
94#66988—28no—
95C2×#4324—24no—
96C2×#4324—24no—
97C2×#4324—24no—
98C4×C22⋊D11—216no—
99C2×(C2×D11)⋊C4—28no—
100C2×(C2×D11)⋊C4—24no—
101C2×(C2×D11)⋊C4—22no—
102#66979—22no—
103#66979D414yes—
104C2×C4⋊Dic11—28no—
105C2×C4⋊Dic11—24no—
106C2×C4⋊Dic11C2312yes—
107C2×Dic11⋊C4—22no—
108C2×C4×Dic11—21no—
109C2×#4318—22no—
110C2×#4318—22no—
111C2×#4318D414yescomplemented
112C22×C11⋊C8C2312yes—
113#66950—216no—
114#66950—28no—
115#66950—28no—
116C11×#103—24no—
117C11×#102—24no—
118(C2×D11)⋊C8—28no—
119#66880—28no—
120#23392—111nomaximal, Sylow
121C24×C11—21no—
122C24×C11C2×D411yescharacteristic
123C23×D11—22no—
124C23×D11—24no—
125C23×D11—22no—
126C23×D11—22no—
127C23×D11—42no—
128C23×D11C2×D412yes—
129C11×#41—28no—
130C11×#41—28no—
131C11×#41—44no—
132C11×#41—44no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11C2×D412yes—
139C2×D4×C11—24no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—42no—
146C2×D4×C11—42no—
147C2×D4×C11C2×D412yes—
148C22×C4×C11—24no—
149C22×C4×C11—21no—
150C22×C4×C11—22no—
151C22×C4×C11—24no—
152C22×C4×C11—44no—
153C22×C4×C11—42no—
154C22×C4×C11—42no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11#4112yes—
162C22×C4×C11C2411yescharacteristic
163C2×C22⋊D11—28no—
164C2×C22⋊D11—44no—
165C2×C22⋊D11—44no—
166C22×Dic11—22no—
167C22×Dic11—24no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—42no—
173C22×Dic11—42no—
174C22×Dic11C2×D412yes—
175C2×C4×D11—24no—
176C2×C4×D11—24no—
177C2×C4×D11—24no—
178C2×C4×D11—22no—
179C2×C4×D11—22no—
180C2×C4×D11—22no—
181C2×C4×D11—22no—
182C2×C4×D11—22no—
183C2×C4×D11—22no—
184C2×C4×D11—44no—
185C2×C4×D11—44no—
186C2×C4×D11—44no—
187C2×C4×D11—44no—
188C2×Dic22—28no—
189C2×Dic22—24no—
190C2×Dic22—28no—
191C2×Dic22—22no—
192C2×Dic22—22no—
193C2×Dic22—22no—
194C2×Dic22—22no—
195C2×Dic22—22no—
196C2×Dic22—42no—
197C2×Dic22—42no—
198C2×Dic22—44no—
199C2×Dic22—44no—
200C2×Dic22C2×D414yes—
201C11×M16—44no—
202C2×C8×C11—22no—
203C2×C8×C11—22no—
204C2×C8×C11—22no—
205C11×C4⋊C4—24no—
206C11×C4⋊C4—22no—
207C11×C4⋊C4C2×D414yes—
208C22⋊Dic11—28no—
209C22⋊Dic11—24no—
210#4326—216no—
211#4324—216no—
212(C2×D11)⋊C4—216no—
213(C2×D11)⋊C4—28no—
214C4⋊Dic11—216no—
215C4⋊Dic11—22no—
216C4⋊Dic11C2×D414yes—
217Dic11⋊C4—28no—
218C4×Dic11—24no—
219#4318—28no—
220C2×C11⋊C8—22no—
221C2×C11⋊C8—22no—
222C2×C11⋊C8C2×D414yes—
223C22×#137—111no—
224C2×#525—111no—
225C22×C22⋊Q8—111no—
226C2×#417D1111yescharacteristic, complemented
227C2×#419—111no—
228C2×#407—111no—
229#2001—114no—
230#2000—114no—
231#1736—111no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—22no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—42no—
238C23×C11—42no—
239C23×C11#12012yes—
240C23×C11#12012yes—
241C23×C11#12112yes—
242C23×C11C22×D411yescharacteristic
243C22×D11—28no—
244C22×D11—22no—
245C22×D11—22no—
246C22×D11—22no—
247C22×D11—22no—
248C22×D11—22no—
249C22×D11—22no—
250C22×D11—48no—
251C22×D11—48no—
252C22×D11—44no—
253C22×D11—44no—
254C22×D11#13714yescomplemented
255Q8×C11—22no—
256Q8×C11—22no—
257Q8×C11—41no—
258Q8×C11—41no—
259D4×C11—22no—
260D4×C11—22no—
261D4×C11—48no—
262D4×C11—41no—
263D4×C11—41no—
264C2×C4×C11—22no—
265C2×C4×C11—24no—
266C2×C4×C11—48no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—44no—
270C2×C4×C11—48no—
271C2×C4×C11#12014yes—
272C2×C4×C11#12012yes—
273C2×C4×C11#12012yes—
274C2×C4×C11#12114yes—
275C2×C4×C11#12112yes—
276C2×C4×C11#12114yes—
277C2×C4×C11#12714yes—
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C22×D411yescharacteristic
281C2×C4×C11C22×D411yescharacteristic
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C22⋊D11—416no—
285C2×Dic11—24no—
286C2×Dic11—22no—
287C2×Dic11—22no—
288C2×Dic11—24no—
289C2×Dic11—22no—
290C2×Dic11—42no—
291C2×Dic11—42no—
292C2×Dic11—42no—
293C2×Dic11—42no—
294C2×Dic11—48no—
295C2×Dic11—44no—
296C4×D11—42no—
297C4×D11—42no—
298C4×D11—42no—
299C4×D11—42no—
300C4×D11—48no—
301Dic22—24no—
302Dic22—24no—
303Dic22—42no—
304Dic22—42no—
305Dic22—48no—
306C8×C11—42no—
307C11⋊C8—24no—
308C22×#41C2×D1111yescharacteristic
309C23×Q8—111no—
310C24×C4—111no—
311C2×#137—224no—
312C2×#137—224no—
313C2×#137—224no—
314C22×Q16—112no—
315C22×SD16—112no—
316C22×M16—111no—
317C22×M16C2×D1111yescharacteristic
318#525—224no—
319#525—224no—
320C2×#123—221no—
321C2×C22⋊Q8—112no—
322C2×C22⋊Q8—114no—
323C2×C22⋊Q8—222no—
324C2×C22⋊Q8—224no—
325C2×C22⋊Q8—224no—
326C2×#121—112no—
327C2×#120—221no—
328C2×C4×D4—222no—
329C2×#117—111no—
330C22×C4⋊C4—221no—
331C22×C4⋊C4C2×D1111yescharacteristic
332C22×C22⋊C4—221no—
333#419—224no—
334#417—24no—
335C2×#103—114no—
336C2×#103C2×D1112yescomplemented
337C2×#102C2×D1112yescomplemented
338#407—224no—
339C2×C22⋊C8—114no—
340#340—114no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—24no—
344C22×C11—24no—
345C22×C11—42no—
346C22×C11—44no—
347C22×C11—81no—
348C22×C11—81no—
349C22×C11—82no—
350C22×C11#39214yes—
351C22×C11C2×#12011yescharacteristic
352C22×C11C2×#12011yescharacteristic
353C22×C11C2×#12111yescharacteristic
354C22×C11C2×#13712yes—
355C22×C11#57512yes—
356C2×D11—24no—
357C2×D11—24no—
358C2×D11—24no—
359C2×D11—416no—
360C2×D11—42no—
361C2×D11—42no—
362C2×D11—42no—
363C2×D11—42no—
364C4×C11—42no—
365C4×C11—44no—
366C4×C11#39214yes—
367C4×C11C2×#12011yescharacteristic
368C4×C11C2×#12111yescharacteristic
369C4×C11C2×#12111yescharacteristic
370C4×C11C2×#12711yescharacteristic
371Dic11—44no—
372Dic11—42no—
373Dic11—44no—
374C25—111no—
375C2×#41—22no—
376C2×#41—22no—
377C2×#41—22no—
378C2×#41—22no—
379C2×#41—22no—
380C2×#41D4414yes—
381C22×Q8—114no—
382C22×Q8—112no—
383C22×Q8—221no—
384C22×Q8—222no—
385C22×Q8—222no—
386C22×Q8—222no—
387C22×Q8—222no—
388C22×Q8—222no—
389C22×Q8C22×D1111yescharacteristic
390C22×D4—21no—
391C22×D4—222no—
392C22×D4C22×D1111yescharacteristic
393C23×C4—21no—
394C23×C4—21no—
395C23×C4—111no—
396C23×C4—112no—
397C23×C4—112no—
398C23×C4—221no—
399C23×C4—222no—
400C23×C4—222no—
401C23×C4—222no—
402C23×C4—222no—
403C23×C4—222no—
404C23×C4—222no—
405C23×C4C22×D1111yescharacteristic
406#137—2232no—
407C2×Q16—224no—
408C2×Q16—224no—
409C2×Q16—224no—
410C2×SD16—224no—
411C2×SD16—224no—
412C2×SD16—224no—
413C2×M16—22no—
414C2×M16—22no—
415C2×M16—22no—
416C2×M16—114no—
417C2×M16—222no—
418C2×M16—222no—
419C22×C8—112no—
420C22×C8C22×D1112yes—
421#123—228no—
422C22⋊Q8—228no—
423C22⋊Q8—2216no—
424C22⋊Q8—224no—
425C22⋊Q8—224no—
426C22⋊Q8—228no—
427#121—224no—
428#121—224no—
429#120—228no—
430C4×D4—2216no—
431#117—114no—
432#117—222no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—112no—
436C2×C4⋊C4—224no—
437C2×C4⋊C4—222no—
438C2×C4⋊C4—228no—
439C2×C4⋊C4C22⋊D1114yescomplemented
440C2×C4⋊C4C22×D1112yes—
441C2×C22⋊C4—224no—
442C2×C22⋊C4—222no—
443C2×C22⋊C4—228no—
444C2×C22⋊C4—222no—
445C2×C22⋊C4—221no—
446C2×C42—221no—
447#103—24no—
448#103—228no—
449#102—24no—
450C22⋊C8—228no—
451C2×C11—24no—
452C2×C11—82no—
453C2×C11C2×#39211yescharacteristic
454C2×C11#300411yescharacteristic
455C2×C11#300511yescharacteristic
456C2×C11#300712yes—
457C2×C11#305612yes—
458D11—44no—
459C24—21no—
460C24—112no—
461C24—224no—
462C24—222no—
463C24—222no—
464C24—222no—
465C24—442no—
466C24D4×D1111yescharacteristic
467#41—28no—
468#41—28no—
469#41—44no—
470#41—44no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—114no—
477C2×Q8—224no—
478C2×Q8—222no—
479C2×Q8—228no—
480C2×Q8—228no—
481C2×Q8—222no—
482C2×Q8—222no—
483C2×Q8—222no—
484C2×Q8—222no—
485C2×Q8—442no—
486C2×Q8—442no—
487C2×Q8—444no—
488C2×Q8—444no—
489C2×Q8C2×D4412yes—
490C2×D4—24no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—228no—
499C2×D4—444no—
500C2×D4—444no—
501C2×D4C2×D4412yes—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—24no—
506C22×C4—44no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—112no—
510C22×C4—222no—
511C22×C4—222no—
512C22×C4—224no—
513C22×C4—222no—
514C22×C4—222no—
515C22×C4—222no—
516C22×C4—224no—
517C22×C4—224no—
518C22×C4—224no—
519C22×C4—222no—
520C22×C4—222no—
521C22×C4—222no—
522C22×C4—222no—
523C22×C4—222no—
524C22×C4—222no—
525C22×C4—442no—
526C22×C4—442no—
527C22×C4—444no—
528C22×C4—444no—
529C22×C4—444no—
530C22×C4—444no—
531C22×C4C2×D4412yes—
532C22×C4#433912yes—
533C22×C4D4×D1111yescharacteristic
534C22×C4D4×D1112yes—
535C22×C4D4×D1112yes—
536C22×C4D4×D1112yes—
537C22×C4C2×C22⋊D1112yes—
538C22×C4C23×D1111yescharacteristic
539Q16—2216no—
540SD16—2216no—
541M16—44no—
542M16—228no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—114no—
547C2×C8—222no—
548C2×C8—222no—
549C4⋊C4—24no—
550C4⋊C4—22no—
551C4⋊C4—114no—
552C4⋊C4—2216no—
553C4⋊C4—228no—
554C4⋊C4—222no—
555C4⋊C4C2×C22⋊D1114yes—
556C22⋊C4—2216no—
557C22⋊C4—228no—
558C22⋊C4—228no—
559C22⋊C4—224no—
560C42—224no—
561C11#2339211yescharacteristic, complemented, Sylow
562C23—22no—
563C23—22no—
564C23—22no—
565C23—41no—
566C23—42no—
567C23—42no—
568C23—41no—
569C23—114no—
570C23—228no—
571C23—222no—
572C23—222no—
573C23—222no—
574C23—222no—
575C23—222no—
576C23—222no—
577C23—448no—
578C23—448no—
579C23—444no—
580C23—444no—
581C23#6693512yes—
582C23#6693712yes—
583C23#6699012yes—
584C23C2×D4×D1111yescharacteristic
585Q8—22no—
586Q8—22no—
587Q8—41no—
588Q8—41no—
589Q8—224no—
590Q8—224no—
591Q8—442no—
592Q8—442no—
593Q8—448no—
594D4—22no—
595D4—22no—
596D4—48no—
597D4—41no—
598D4—41no—
599D4—4416no—
600C2×C4—22no—
601C2×C4—24no—
602C2×C4—48no—
603C2×C4—41no—
604C2×C4—44no—
605C2×C4—41no—
606C2×C4—48no—
607C2×C4—224no—
608C2×C4—222no—
609C2×C4—222no—
610C2×C4—224no—
611C2×C4—222no—
612C2×C4—442no—
613C2×C4—442no—
614C2×C4—442no—
615C2×C4—442no—
616C2×C4—444no—
617C2×C4—448no—
618C2×C4—442no—
619C2×C4—442no—
620C2×C4—442no—
621C2×C4—442no—
622C2×C4—448no—
623C2×C4#6693514yes—
624C2×C4#6693512yes—
625C2×C4#6693714yes—
626C2×C4#6693712yes—
627C2×C4#6698314yes—
628C2×C4#6699012yes—
629C2×C4#6699314yes—
630C2×C4C22×D4411yescharacteristic
631C2×C4C2×#433911yescharacteristic
632C2×C4C2×D4×D1111yescharacteristic
633C2×C4C2×D4×D1111yescharacteristic
634C2×C4C2×D4×D1111yescharacteristic
635C2×C4C22×C22⋊D1111yescharacteristic
636C8—42no—
637C8—224no—
638C22—22no—
639C22—22no—
640C22—24no—
641C22—24no—
642C22—44no—
643C22—42no—
644C22—81no—
645C22—81no—
646C22—82no—
647C22—224no—
648C22—224no—
649C22—224no—
650C22—4416no—
651C22—442no—
652C22—442no—
653C22—442no—
654C22—442no—
655C22#1062257314yes—
656C22C2×#6693511yescharacteristic
657C22C2×#6693711yescharacteristic
658C22#1062330412yes—
659C22D11×#13712yes—
660C22C2×#6699011yescharacteristic
661C4—44no—
662C4—42no—
663C4—444no—
664C4—442no—
665C4—444no—
666C4#1062257314yes—
667C4C2×#6693511yescharacteristic
668C4C2×#6693711yescharacteristic
669C4C2×#6698311yescharacteristic
670C4C2×#6699311yescharacteristic
671C2—24no—
672C2—82no—
673C2—444no—
674C2C2×#1062257311yescharacteristic
675C2#1307784811yescharacteristic
676C2#1307785511yescharacteristic
677C2#1307787712yes—
678C2#1307824912yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#417C2
socleC23×C11C22×D4
prime radicalC2×#10623359C2
hypercenterC2×#417D11
hypocenterC11#23392
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C22×#67004C2semidirect
3. C22×#66950C2semidirect
4. C2×#10622733C2semidirect
5. C2×#10622739C2semidirect
6. #13069625C2semidirect
7. #13069620C2semidirect
8. #13068335C2semidirect
9. C2×C11×#417C2semidirect
21. C22×#4326C22semidirect
25. C22×#4324C22semidirect
36. C2×C11×#103C22semidirect
37. C2×C11×#102C22semidirect
41. C2×#66880C22semidirect
42. #10622167C22semidirect
73. C22×Dic22D4semidirect
81. C2×C11×C4⋊C4D4semidirect
111. C2×#4318D4semidirect
226. C2×#417D11semidirect
254. C22×D11#137semidirect
336. C2×#103C2×D11semidirect
337. C2×#102C2×D11semidirect
439. C2×C4⋊C4C22⋊D11semidirect
561. C11#23392semidirect

Maximal subgroups

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

subgroupindex
C22×#670042
C2×#106233592
C22×#669502
C2×#106227332
C2×#106227392
#130696252
#130696202
#130683352
C2×C11×#4172
#2339211