Finite Group Databasebeta

← #14762837

Subgroups — #14762837

Order 2816.

1486 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
1C2×#10623137C211yesmaximal, characteristic
2C2×#10622339C211yesmaximal, characteristic, complemented
3#13070995C211yesmaximal, characteristic, complemented
4#13069051C212yesmaximal, complemented
5#13069048C212yesmaximal, complemented
6#13068939C211yesmaximal, characteristic, complemented
7#13068928C211yesmaximal, characteristic, complemented
8#13068926C211yesmaximal, characteristic, complemented
9#13068709C212yesmaximal, complemented
10#13068553C212yesmaximal, complemented
11C11×#1875C211yesmaximal, characteristic, complemented
12C22×#4341C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C2×C11×#121C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C2×#66991C2211yescharacteristic
17C2×#66990—21no—
18C2×D4×Dic11—21no—
19C2×#66979C2211yescharacteristic
20C2×#66977C2211yescharacteristic
21C22×#4313C2212yes—
22#10623137—24no—
23#10623137C418yescomplemented
24C2×#66950C2211yescharacteristic
25C2×#66945C2211yescharacteristic
26C2×#66936—21no—
27C2×(C22⋊D11)⋊C4—21no—
28C2×C11×#102C2212yescomplemented
29C2×C11×C22⋊C8C2211yescharacteristic
30C2×#66896C2212yescomplemented
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×(C2×D11)⋊C8C2212yes—
33C2×#66880C2212yescomplemented
34#10622600C2212yes—
35#10622600C2212yes—
36C2×#66874C2212yescomplemented
37#10622568—21no—
38#10622556—21no—
39C4×(C2×D11)⋊C4—21no—
40C4×(C2×D11)⋊C4—21no—
41#10622339—24no—
42C11×#340C2212yescomplemented
43#10622189C2212yescomplemented
44#10622167C2212yescomplemented
45#10622167C2212yescomplemented
46C24×D11D411yescharacteristic
47C22×D4×C11—21no—
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C22×C22⋊D11—21no—
51C22×C22⋊D11—21no—
52C23×Dic11—21no—
53C23×Dic11D411yescharacteristic
54C2×#4341—22no—
55C2×#4341—42no—
56C2×#4341—42no—
57C2×#4341C2×C414yes—
58C22×C4×D11—42no—
59C22×C4×D11—42no—
60C22×C4×D11C2×C414yes—
61C22×C4×D11D411yescharacteristic
62C22×C4×D11D411yescharacteristic
63C22×C4×D11D414yes—
64C22×C4×D11C2311yescharacteristic
65C22×C4×D11C2311yescharacteristic
66C22×Dic22C2311yescharacteristic
67C22×C8×C11C2312yes—
68C11×#121—22no—
69C11×#121C2×C414yes—
70C11×#117—42no—
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C42×C11—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79#66991—22no—
80#66991C2×C414yes—
81#66990—28no—
82D4×Dic11—28no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4—22no—
87#66979—42no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11C2312yes—
90C2×C4⋊Dic11C2311yescharacteristic
91#66977—22no—
92#66977C2×C414yes—
93C2×Dic11⋊C4—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C22×C11⋊C8C2312yes—
97C2×#4313—24no—
98C2×#4313—42no—
99C2×#4313—42no—
100#66950—22no—
101#66950C2×C414yes—
102#66945—22no—
103#66945C2×C414yes—
104#66936—28no—
105(C22⋊D11)⋊C4—28no—
106C11×#102—42no—
107C11×C22⋊C8—22no—
108#66896—42no—
109C11⋊#95—22no—
110C11⋊#95—22no—
111C22⋊(C11⋊C8)—22no—
112(C2×D11)⋊C8—24no—
113#66880—42no—
114#66874—42no—
115#21766—111nomaximal, Sylow
116C24×C11—21no—
117C24×C11C2×D411yescharacteristic
118C23×D11—41no—
119C23×D11—41no—
120C23×D11—42no—
121C23×D11—42no—
122C23×D11C22⋊C414yes—
123C23×D11C2×D411yescharacteristic
124C23×D11C2×D411yescharacteristic
125C2×D4×C11—24no—
126C2×D4×C11—21no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—44no—
130C2×D4×C11C22×C412yes—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11C22×C412yes—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2411yescharacteristic
139C2×C22⋊D11—24no—
140C2×C22⋊D11—24no—
141C2×C22⋊D11—42no—
142C2×C22⋊D11—42no—
143C2×C22⋊D11—44no—
144C22×Dic11—24no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—22no—
148C22×Dic11—41no—
149C22×Dic11—41no—
150C22×Dic11—42no—
151C22×Dic11—42no—
152C22×Dic11C22⋊C414yes—
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155#4341—48no—
156#4341—48no—
157C2×C4×D11—22no—
158C2×C4×D11—22no—
159C2×C4×D11—22no—
160C2×C4×D11—22no—
161C2×C4×D11—41no—
162C2×C4×D11—41no—
163C2×C4×D11—41no—
164C2×C4×D11—41no—
165C2×C4×D11—48no—
166C2×C4×D11—48no—
167C2×C4×D11C22⋊C414yes—
168C2×C4×D11C22⋊C414yes—
169C2×C4×D11C22×C412yes—
170C2×C4×D11C22×C412yes—
171C2×C4×D11C2×D412yes—
172C2×C4×D11C2×D412yes—
173C2×Dic22—21no—
174C2×Dic22—22no—
175C2×Dic22—22no—
176C2×Dic22C22×C412yes—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4C22×C412yes—
184C11×C22⋊C4—24no—
185C11×C22⋊C4—42no—
186C42×C11—42no—
187C22⋊Dic11—24no—
188C22⋊Dic11—24no—
189C22⋊Dic11—42no—
190(C2×D11)⋊C4—24no—
191(C2×D11)⋊C4—24no—
192(C2×D11)⋊C4—44no—
193(C2×D11)⋊C4—44no—
194C4⋊Dic11—24no—
195C4⋊Dic11—21no—
196C4⋊Dic11—22no—
197C4⋊Dic11—22no—
198C4⋊Dic11C22×C412yes—
199Dic11⋊C4—24no—
200C4×Dic11—24no—
201C4×Dic11—42no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—22no—
205#4313—48no—
206C2×#525—111no—
207C2×#407—111no—
208#2280—111no—
209#1895—112no—
210#1894—112no—
211#1875—111no—
212#1875D1111yescharacteristic, complemented
213#1873—111no—
214#1873—111no—
215#1825—112no—
216#1788—112no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—42no—
225C23×C11—42no—
226C23×C11C2×C22⋊C412yes—
227C23×C11C22×D411yescharacteristic
228C22×D11—21no—
229C22×D11—21no—
230C22×D11—21no—
231C22×D11—21no—
232C22×D11—22no—
233C22×D11—22no—
234C22×D11—22no—
235C22×D11—22no—
236C22×D11—44no—
237C22×D11—44no—
238C22×D11—44no—
239C22×D11—48no—
240C22×D11—48no—
241C22×D11C2×C22⋊C412yes—
242C22×D11C2×C22⋊C412yes—
243D4×C11—24no—
244D4×C11—48no—
245D4×C11—42no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—22no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11C2×C22⋊C412yes—
256C2×C4×C11C23×C411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11H(5,𝔽2)12yes—
259C2×C4×C11H(5,𝔽2)12yes—
260C22⋊D11—48no—
261C22⋊D11—48no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—44no—
269C2×Dic11—48no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11C2×C22⋊C412yes—
277C2×Dic11C2×C22⋊C412yes—
278C4×D11—24no—
279C4×D11—24no—
280C4×D11—24no—
281C4×D11—24no—
282C4×D11—44no—
283C4×D11—44no—
284Dic22—24no—
285Dic22—42no—
286C8×C11—42no—
287C11⋊C8—42no—
288C22×#41—111no—
289C24×C4—111no—
290C22×M16—112no—
291#525—118no—
292#525—224no—
293C2×#123—221no—
294C2×C22⋊Q8—111no—
295C2×C22⋊Q8—111no—
296C2×#121—111no—
297C2×#121C2×D1111yescharacteristic
298C2×#120—221no—
299C2×C4×D4—221no—
300C2×C4×D4—221no—
301C2×#117—111no—
302C2×#117—111no—
303C2×#117C2×D1111yescharacteristic
304C2×#103—112no—
305C2×#103—112no—
306C2×#102—112no—
307C2×#102C2×D1112yescomplemented
308#407—224no—
309C2×C22⋊C8—111no—
310C2×C22⋊C8—112no—
311C2×C22⋊C8C2×D1111yescharacteristic
312#381—221no—
313#380—112no—
314#380—112no—
315#379—221no—
316C4×C22⋊C4—221no—
317C4×C22⋊C4—221no—
318#340—112no—
319#340—112no—
320#340—112no—
321#340C2×D1112yescomplemented
322C22×C11—22no—
323C22×C11—22no—
324C22×C11—22no—
325C22×C11—42no—
326C22×C11—42no—
327C22×C11—42no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11—82no—
331C22×C11—82no—
332C22×C11C22×C22⋊C411yescharacteristic
333C22×C11#53411yescharacteristic
334C22×C11#53411yescharacteristic
335C22×C11#57512yes—
336C22×C11#57512yes—
337C2×D11—22no—
338C2×D11—22no—
339C2×D11—22no—
340C2×D11—22no—
341C2×D11—22no—
342C2×D11—22no—
343C2×D11—416no—
344C2×D11—42no—
345C2×D11—42no—
346C2×D11—42no—
347C2×D11—42no—
348C4×C11—22no—
349C4×C11—42no—
350C4×C11—82no—
351C4×C11#51812yes—
352C4×C11#53412yes—
353Dic11—22no—
354Dic11—22no—
355Dic11—42no—
356Dic11—42no—
357Dic11—82no—
358C25—111no—
359C2×#41—114no—
360C2×#41—222no—
361C2×#41—442no—
362C2×#41—442no—
363C22×Q8—111no—
364C22×D4—21no—
365C22×D4—221no—
366C22×D4—221no—
367C22×D4C22×D1111yescharacteristic
368C23×C4—111no—
369C23×C4—111no—
370C23×C4—111no—
371C23×C4—114no—
372C23×C4—111no—
373C23×C4—111no—
374C23×C4—114no—
375C23×C4—221no—
376C23×C4—442no—
377C23×C4—442no—
378C23×C4C22×D1111yescharacteristic
379C2×M16—224no—
380C2×M16—442no—
381C2×M16—442no—
382C22×C8—112no—
383C22×C8C22×D1112yes—
384#123—228no—
385C22⋊Q8—114no—
386C22⋊Q8—114no—
387C22⋊Q8—222no—
388C22⋊Q8—222no—
389#121—22no—
390#121—114no—
391#121—222no—
392#121C4×D1114yes—
393#120—228no—
394C4×D4—228no—
395C4×D4—228no—
396#117—42no—
397#117—114no—
398#117—222no—
399#117—442no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—112no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4C22×D1112yes—
405C2×C4⋊C4C22×D1111yescharacteristic
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—222no—
413C2×C22⋊C4—222no—
414C2×C22⋊C4—221no—
415C2×C42—21no—
416C2×C42—221no—
417C2×C42—221no—
418#103—442no—
419#103—442no—
420#102—42no—
421#102—442no—
422C22⋊C8—22no—
423C22⋊C8—224no—
424C22⋊C8—222no—
425#95—222no—
426#95—222no—
427C2×C11—42no—
428C2×C11—82no—
429C2×C11#230811yescharacteristic
430C2×C11#289611yescharacteristic
431C2×C11#289611yescharacteristic
432C2×C11#319712yes—
433C2×C11#319712yes—
434D11—42no—
435D11—42no—
436C24—21no—
437C24—111no—
438C24—111no—
439C24—114no—
440C24—441no—
441C24—441no—
442C24—442no—
443C24—442no—
444C24D4×D1111yescharacteristic
445#41—448no—
446#41—448no—
447C2×Q8—112no—
448C2×Q8—221no—
449C2×Q8—222no—
450C2×Q8—222no—
451C2×D4—24no—
452C2×D4—21no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—44no—
456C2×D4—224no—
457C2×D4—224no—
458C2×D4—442no—
459C2×D4—442no—
460C2×D4—444no—
461C2×D4C2×C4×D1112yes—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—114no—
469C22×C4—112no—
470C22×C4—112no—
471C22×C4—112no—
472C22×C4—112no—
473C22×C4—114no—
474C22×C4—114no—
475C22×C4—224no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—222no—
483C22×C4—448no—
484C22×C4—448no—
485C22×C4—441no—
486C22×C4—441no—
487C22×C4—441no—
488C22×C4—441no—
489C22×C4—441no—
490C22×C4—441no—
491C22×C4—442no—
492C22×C4—442no—
493C22×C4C2×C4×D1112yes—
494C22×C4D4×D1111yescharacteristic
495C22×C4D4×D1112yes—
496C22×C4C23×D1111yescharacteristic
497M16—448no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—222no—
502C2×C8—222no—
503C2×C8—222no—
504C4⋊C4—21no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—112no—
508C4⋊C4—224no—
509C4⋊C4—224no—
510C4⋊C4—221no—
511C4⋊C4—222no—
512C4⋊C4—222no—
513C4⋊C4C2×C4×D1112yes—
514C22⋊C4—24no—
515C22⋊C4—42no—
516C22⋊C4—224no—
517C22⋊C4—224no—
518C22⋊C4—224no—
519C22⋊C4—224no—
520C22⋊C4—444no—
521C22⋊C4—444no—
522C22⋊C4—442no—
523C42—42no—
524C42—224no—
525C42—442no—
526C11#2176611yescharacteristic, complemented, Sylow
527C23—22no—
528C23—22no—
529C23—21no—
530C23—21no—
531C23—22no—
532C23—42no—
533C23—42no—
534C23—41no—
535C23—41no—
536C23—112no—
537C23—112no—
538C23—222no—
539C23—222no—
540C23—222no—
541C23—222no—
542C23—221no—
543C23—221no—
544C23—221no—
545C23—221no—
546C23—444no—
547C23—444no—
548C23—444no—
549C23—448no—
550C23—448no—
551C23C22⋊C4×D1112yes—
552C23C2×D4×D1111yescharacteristic
553Q8—224no—
554Q8—442no—
555D4—24no—
556D4—48no—
557D4—42no—
558D4—448no—
559D4—448no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—112no—
570C2×C4—112no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—224no—
578C2×C4—224no—
579C2×C4—222no—
580C2×C4—222no—
581C2×C4—444no—
582C2×C4—444no—
583C2×C4—444no—
584C2×C4—448no—
585C2×C4—442no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—442no—
589C2×C4—442no—
590C2×C4—442no—
591C2×C4C22⋊C4×D1112yes—
592C2×C4C22×C4×D1111yescharacteristic
593C2×C4C2×D4×D1111yescharacteristic
594C2×C4#6703712yes—
595C2×C4#6704212yes—
596C8—42no—
597C8—442no—
598C22—22no—
599C22—22no—
600C22—22no—
601C22—42no—
602C22—42no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—82no—
607C22—82no—
608C22—222no—
609C22—222no—
610C22—222no—
611C22—222no—
612C22—222no—
613C22—222no—
614C22—4416no—
615C22—442no—
616C22—442no—
617C22—442no—
618C22—442no—
619C22C2×C22⋊C4×D1111yescharacteristic
620C22#1062312011yescharacteristic
621C22#1062318411yescharacteristic
622C22#1062329912yes—
623C22#1062330412yes—
624C4—22no—
625C4—42no—
626C4—82no—
627C4—222no—
628C4—222no—
629C4—442no—
630C4—442no—
631C4—882no—
632C4#1062307612yes—
633C4#1062313612yes—
634C2—42no—
635C2—82no—
636C2—442no—
637C2—442no—
638C2#1307119011yescharacteristic
639C2#1307713011yescharacteristic
640C2#1307713111yescharacteristic
641C2#1307945512yes—
642C2#1307945612yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1875C2
socleC23×C11C22×D4
prime radicalC2×#10623137C2
cosocleC22×C4×C11C24
hypercenter#1875D11
hypocenterC11#21766
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1875

Complements

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

NH ≅ G/Ntype
2. C2×#10622339C2semidirect
3. #13070995C2semidirect
4. #13069051C2semidirect
5. #13069048C2semidirect
6. #13068939C2semidirect
7. #13068928C2semidirect
8. #13068926C2semidirect
9. #13068709C2semidirect
10. #13068553C2semidirect
11. C11×#1875C2semidirect
23. #10623137C4semidirect
28. C2×C11×#102C22semidirect
30. C2×#66896C22semidirect
33. C2×#66880C22semidirect
36. C2×#66874C22semidirect
42. C11×#340C22semidirect
43. #10622189C22semidirect
44. #10622167C22semidirect
45. #10622167C22semidirect
212. #1875D11semidirect
307. C2×#102C2×D11semidirect
321. #340C2×D11semidirect
526. C11#21766semidirect

Maximal subgroups

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

subgroupindex
C2×#106231372
C2×#106223392
#130709952
#130690512
#130690482
#130689392
#130689282
#130689262
#130687092
#130685532
C11×#18752
#2176611