Finite Group Databasebeta

← #14755021

Subgroups — #14755021

Order 2816.

2278 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66948C211yesmaximal, characteristic
2C2×D11×#117C211yesmaximal, characteristic, complemented
3C2×#10622744C211yesmaximal, characteristic, complemented
4C2×#10622614C211yesmaximal, characteristic, complemented
5C2×#10622739C211yesmaximal, characteristic, complemented
6#13068937C214yesmaximal, complemented
7#13068932C214yesmaximal, complemented
8#13068335C211yesmaximal, characteristic, complemented
9C11×#1736C211yesmaximal, characteristic, complemented
10C23×D44—21no—
11C23×D44C2211yescharacteristic
12C23×C4×D11C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×(C2×D11)⋊C4—21no—
17C2×#66979C2211yescharacteristic
18C22×#4318C2211yescharacteristic
19D11×#117—24no—
20D11×#117—24no—
21C2×#66948—21no—
22C2×#66948—21no—
23C2×#66948—24no—
24C2×#66948C418yescomplemented
25C2×#66948C2212yes—
26C2×#66948C2212yes—
27C2×#66945C2212yescomplemented
28C2×C4⋊C4×D11C2212yescomplemented
29C2×C22⋊C4×D11—21no—
30C2×#66930—21no—
31C2×#66925—21no—
32C2×C42×D11—21no—
33#10622744—24no—
34#10622739—24no—
35C2×#66885C2214yescomplemented
36C2×(C2×D11)⋊C8C2212yescomplemented
37C2×(C2×D11)⋊C8C2212yescomplemented
38#10622614—24no—
39C2×#66873C2214yescomplemented
40C11×#340C2214yescomplemented
41#10622167C2214yescomplemented
42C24×D11—21no—
43C24×D11D411yescharacteristic
44C23×C4×C11—21no—
45C23×C4×C11C2311yescharacteristic
46C23×Dic11D411yescharacteristic
47C22×D44—22no—
48C22×D44—22no—
49C22×D44—22no—
50C22×D44—22no—
51C22×D44—28no—
52C22×D44—22no—
53C22×D44—22no—
54C22×D44—21no—
55C22×D44—22no—
56C22×D44—48no—
57C22×D44C2×C414yescomplemented
58C22×D44C2312yes—
59C22×C4×D11—22no—
60C22×C4×D11—22no—
61C22×C4×D11—22no—
62C22×C4×D11—22no—
63C22×C4×D11—22no—
64C22×C4×D11C2×C414yes—
65C22×C4×D11D411yescharacteristic
66C22×C4×D11D411yescharacteristic
67C22×C4×D11D414yes—
68C22×C4×D11C2311yescharacteristic
69C22×C4×D11C2311yescharacteristic
70C2×C11×M16—22no—
71C2×C11×M16—22no—
72C2×C11×M16—22no—
73C22×C8×C11C2312yes—
74C11×#117—22no—
75C11×#117D414yescomplemented
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4C2×C414yescomplemented
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C22⋊C4—21no—
82C2×C42×C11—21no—
83C2×C22⋊Dic11—21no—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—28no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—22no—
88#66979—22no—
89#66979D414yescomplemented
90C2×C4⋊Dic11C2312yes—
91C2×Dic11⋊C4—22no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—22no—
94C2×#4318—22no—
95C2×#4318—22no—
96C2×#4318—22no—
97C22×C11⋊C8C2312yes—
98#66948—28no—
99#66948—28no—
100#66948—24no—
101#66948—24no—
102#66948C2×C418yes—
103#66948C2×C418yescomplemented
104#66945—24no—
105#66945—24no—
106C4⋊C4×D11—24no—
107C4⋊C4×D11—24no—
108C22⋊C4×D11—28no—
109#66930—28no—
110#66925—28no—
111C42×D11—28no—
112#66885—28no—
113(C2×D11)⋊C8—24no—
114(C2×D11)⋊C8—24no—
115#66873—28no—
116#20912—111nomaximal, Sylow
117C24×C11C2×D411yescharacteristic
118C23×D11—22no—
119C23×D11—22no—
120C23×D11—24no—
121C23×D11—24no—
122C23×D11—22no—
123C23×D11—42no—
124C23×D11—44no—
125C23×D11—44no—
126C23×D11—42no—
127C23×D11—42no—
128C23×D11C22⋊C414yes—
129C23×D11C2×D411yescharacteristic
130C23×D11C2×D411yescharacteristic
131C22×C4×C11—24no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—44no—
135C22×C4×C11C22×C412yes—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11#4112yes—
141C22×C4×C11#4112yes—
142C22×C4×C11C2411yescharacteristic
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11C22⋊C414yes—
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C2×D44—28no—
150C2×D44—28no—
151C2×D44—24no—
152C2×D44—28no—
153C2×D44—28no—
154C2×D44—22no—
155C2×D44—22no—
156C2×D44—22no—
157C2×D44—22no—
158C2×D44—22no—
159C2×D44—432no—
160C2×D44—48no—
161C2×D44—48no—
162C2×D44—42no—
163C2×D44—44no—
164C2×D44—44no—
165C2×D44—42no—
166C2×D44C22×C414yes—
167C2×C4×D11—28no—
168C2×C4×D11—28no—
169C2×C4×D11—28no—
170C2×C4×D11—22no—
171C2×C4×D11—22no—
172C2×C4×D11—28no—
173C2×C4×D11—28no—
174C2×C4×D11—22no—
175C2×C4×D11—22no—
176C2×C4×D11—21no—
177C2×C4×D11—21no—
178C2×C4×D11—21no—
179C2×C4×D11—21no—
180C2×C4×D11—21no—
181C2×C4×D11—21no—
182C2×C4×D11—21no—
183C2×C4×D11—21no—
184C2×C4×D11—44no—
185C2×C4×D11—44no—
186C2×C4×D11C22⋊C414yes—
187C2×C4×D11C22⋊C414yes—
188C2×C4×D11C22×C412yes—
189C2×C4×D11C22×C412yes—
190C2×C4×D11C2×D412yes—
191C2×C4×D11C2×D412yes—
192C11×M16—44no—
193C2×C8×C11—22no—
194C2×C8×C11—22no—
195C2×C8×C11—22no—
196C11×C4⋊C4—24no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—22no—
199C11×C4⋊C4C22×C414yes—
200C11×C4⋊C4C2×D414yescomplemented
201C11×C22⋊C4—24no—
202C42×C11—24no—
203C22⋊Dic11—24no—
204(C2×D11)⋊C4—28no—
205(C2×D11)⋊C4—28no—
206(C2×D11)⋊C4—28no—
207C4⋊Dic11—22no—
208C4⋊Dic11C2×D414yescomplemented
209Dic11⋊C4—28no—
210C4×Dic11—28no—
211C4×Dic11—24no—
212#4318—44no—
213C2×C11⋊C8—22no—
214C2×C11⋊C8—22no—
215C2×C11⋊C8—22no—
216C22×#121—111no—
217C22×#117—111no—
218C2×#418—111no—
219C2×#418—111no—
220C2×#407—111no—
221#1875—114no—
222#1874—114no—
223#1736—111no—
224#1736D1111yescharacteristic, complemented
225C23×C11—22no—
226C23×C11—22no—
227C23×C11C2×C22⋊C412yes—
228C23×C11#12012yes—
229C23×C11#12312yes—
230C23×C11C22×D411yescharacteristic
231C22×D11—21no—
232C22×D11—21no—
233C22×D11—22no—
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—22no—
237C22×D11—22no—
238C22×D11—28no—
239C22×D11—28no—
240C22×D11—24no—
241C22×D11—44no—
242C22×D11—48no—
243C22×D11—48no—
244C22×D11—48no—
245C22×D11—48no—
246C22×D11—42no—
247C22×D11—42no—
248C22×D11—44no—
249C22×D11—44no—
250C22×D11—48no—
251C22×D11—88no—
252C22×D11—88no—
253C22×D11C2×C22⋊C412yes—
254C22×D11C2×C22⋊C412yes—
255C22×D11AGL(1,ℤ/8)14yes—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11—48no—
259C2×C4×C11—42no—
260C2×C4×C11—44no—
261C2×C4×C11—42no—
262C2×C4×C11C2×C22⋊C412yes—
263C2×C4×C11C4×D414yes—
264C2×C4×C11C4×D414yes—
265C2×C4×C11#12012yes—
266C2×C4×C11#12114yes—
267C2×C4×C11#12114yes—
268C2×C4×C11#12312yes—
269C2×C4×C11C23×C411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—28no—
280C2×Dic11—24no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11C2×C22⋊C412yes—
284C2×Dic11C2×C22⋊C412yes—
285D44—24no—
286D44—24no—
287D44—416no—
288D44—416no—
289D44—42no—
290D44—42no—
291D44—48no—
292C4×D11—22no—
293C4×D11—22no—
294C4×D11—22no—
295C4×D11—22no—
296C4×D11—22no—
297C4×D11—22no—
298C4×D11—22no—
299C4×D11—22no—
300C4×D11—28no—
301C4×D11—28no—
302C4×D11—416no—
303C8×C11—42no—
304C11⋊C8—42no—
305C23×D4—111no—
306C23×D4—221no—
307C24×C4—111no—
308C22×M16—111no—
309C22×M16C2×D1111yescharacteristic
310C2×#121—112no—
311C2×#121—112no—
312C2×#121—118no—
313C2×#121—221no—
314C2×#121—224no—
315C2×#121—221no—
316C2×#117—111no—
317C2×#117—112no—
318C2×#117—221no—
319C2×#117—221no—
320C2×#117—224no—
321C2×#117—224no—
322C2×#117C2×D1111yescharacteristic
323C22×C4⋊C4—112no—
324C22×C4⋊C4C2×D1111yescharacteristic
325C22×C22⋊C4—221no—
326C22×C22⋊C4—221no—
327C22×C42—221no—
328#418—224no—
329#418—224no—
330C2×#102—114no—
331C2×#102—114no—
332#407—224no—
333C2×C22⋊C8—112no—
334C2×C22⋊C8—112no—
335#340—114no—
336#340C2×D1114yescomplemented
337C22×C11—24no—
338C22×C11—22no—
339C22×C11—22no—
340C22×C11—24no—
341C22×C11#38614yes—
342C22×C11C22×C22⋊C411yescharacteristic
343C22×C11C2×#12011yescharacteristic
344C22×C11C2×#12311yescharacteristic
345C22×C11C2×AGL(1,ℤ/8)12yes—
346C22×C11#57512yes—
347C2×D11—24no—
348C2×D11—22no—
349C2×D11—24no—
350C2×D11—22no—
351C2×D11—22no—
352C2×D11—22no—
353C2×D11—22no—
354C2×D11—416no—
355C2×D11—42no—
356C2×D11—42no—
357C2×D11—44no—
358C2×D11—44no—
359C2×D11—44no—
360C2×D11—816no—
361C2×D11—84no—
362C2×D11—84no—
363C2×D11#41814yescomplemented
364C4×C11—44no—
365C4×C11—44no—
366C4×C11#38614yes—
367C4×C11C2×C4×D411yescharacteristic
368C4×C11C2×C4×D411yescharacteristic
369C4×C11C2×#12111yescharacteristic
370C4×C11C2×#12111yescharacteristic
371Dic11—22no—
372Dic11—22no—
373Dic11—44no—
374C25—111no—
375C25—221no—
376C22×D4—114no—
377C22×D4—112no—
378C22×D4—228no—
379C22×D4—222no—
380C22×D4—222no—
381C22×D4—222no—
382C22×D4—222no—
383C22×D4—222no—
384C22×D4—221no—
385C22×D4—222no—
386C22×D4—222no—
387C22×D4—448no—
388C23×C4—21no—
389C23×C4—111no—
390C23×C4—114no—
391C23×C4—111no—
392C23×C4—114no—
393C23×C4—111no—
394C23×C4—111no—
395C23×C4—111no—
396C23×C4—222no—
397C23×C4—222no—
398C23×C4—222no—
399C23×C4—222no—
400C23×C4—222no—
401C23×C4C22×D1111yescharacteristic
402C2×M16—22no—
403C2×M16—22no—
404C2×M16—22no—
405C2×M16—222no—
406C2×M16—222no—
407C2×M16—222no—
408C22×C8—112no—
409C22×C8C22×D1112yes—
410#121—118no—
411#121—118no—
412#121—228no—
413#121—228no—
414#121—224no—
415#121—224no—
416#117—22no—
417#117—114no—
418#117—228no—
419#117—228no—
420#117—224no—
421#117—222no—
422#117—224no—
423#117D4414yescomplemented
424C2×C4⋊C4—21no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—112no—
427C2×C4⋊C4—224no—
428C2×C4⋊C4—222no—
429C2×C4⋊C4—224no—
430C2×C4⋊C4C4×D1114yescomplemented
431C2×C4⋊C4C22×D1112yes—
432C2×C4⋊C4C22×D1112yes—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—228no—
435C2×C22⋊C4—228no—
436C2×C22⋊C4—222no—
437C2×C22⋊C4—222no—
438C2×C22⋊C4—222no—
439C2×C22⋊C4—221no—
440C2×C42—21no—
441C2×C42—228no—
442C2×C42—222no—
443C2×C42—221no—
444#102—228no—
445#102—228no—
446C22⋊C8—224no—
447C22⋊C8—224no—
448C2×C11—24no—
449C2×C11C2×#38611yescharacteristic
450C2×C11C2×#41811yescharacteristic
451C2×C11#289611yescharacteristic
452C2×C11#300612yes—
453C2×C11#309412yes—
454D11—24no—
455D11—42no—
456D11—84no—
457C24—111no—
458C24—111no—
459C24—114no—
460C24—224no—
461C24—222no—
462C24—222no—
463C24—224no—
464C24—222no—
465C24—442no—
466C24—444no—
467C24—444no—
468C24—442no—
469C24—442no—
470C24D4×D1111yescharacteristic
471C2×D4—114no—
472C2×D4—228no—
473C2×D4—228no—
474C2×D4—228no—
475C2×D4—224no—
476C2×D4—228no—
477C2×D4—222no—
478C2×D4—222no—
479C2×D4—222no—
480C2×D4—222no—
481C2×D4—222no—
482C2×D4—448no—
483C2×D4—4432no—
484C2×D4—448no—
485C2×D4—442no—
486C2×D4—444no—
487C2×D4—442no—
488C2×D4—444no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—44no—
493C22×C4—114no—
494C22×C4—111no—
495C22×C4—111no—
496C22×C4—114no—
497C22×C4—114no—
498C22×C4—112no—
499C22×C4—112no—
500C22×C4—112no—
501C22×C4—112no—
502C22×C4—228no—
503C22×C4—222no—
504C22×C4—222no—
505C22×C4—228no—
506C22×C4—222no—
507C22×C4—222no—
508C22×C4—228no—
509C22×C4—228no—
510C22×C4—222no—
511C22×C4—222no—
512C22×C4—228no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—221no—
521C22×C4—222no—
522C22×C4—444no—
523C22×C4—444no—
524C22×C4C2×C4×D1112yes—
525C22×C4C2×D4412yes—
526C22×C4#433912yes—
527C22×C4D4×D1111yescharacteristic
528C22×C4D4×D1112yes—
529C22×C4D4×D1112yes—
530C22×C4#434312yes—
531C22×C4C23×D1111yescharacteristic
532M16—44no—
533M16—444no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—222no—
538C2×C8—222no—
539C2×C8—222no—
540C4⋊C4—24no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—114no—
544C4⋊C4—228no—
545C4⋊C4—222no—
546C4⋊C4C2×C4×D1114yes—
547C4⋊C4C2×D4414yescomplemented
548C22⋊C4—24no—
549C22⋊C4—228no—
550C22⋊C4—228no—
551C22⋊C4—228no—
552C22⋊C4—224no—
553C42—24no—
554C42—228no—
555C42—224no—
556C11#2091211yescharacteristic, complemented, Sylow
557C23—22no—
558C23—22no—
559C23—112no—
560C23—114no—
561C23—112no—
562C23—228no—
563C23—221no—
564C23—221no—
565C23—222no—
566C23—221no—
567C23—221no—
568C23—228no—
569C23—222no—
570C23—222no—
571C23—224no—
572C23—444no—
573C23—448no—
574C23—448no—
575C23—448no—
576C23—448no—
577C23—442no—
578C23—442no—
579C23—448no—
580C23—444no—
581C23—444no—
582C23—888no—
583C23—888no—
584C23C22⋊C4×D1112yes—
585C23#6693512yes—
586C23#6694712yes—
587C23C2×D4×D1111yescharacteristic
588D4—224no—
589D4—224no—
590D4—4416no—
591D4—4416no—
592D4—442no—
593D4—442no—
594D4—448no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—48no—
598C2×C4—44no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—112no—
602C2×C4—112no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—221no—
607C2×C4—228no—
608C2×C4—222no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—222no—
614C2×C4—222no—
615C2×C4—222no—
616C2×C4—228no—
617C2×C4—228no—
618C2×C4—224no—
619C2×C4—4416no—
620C2×C4—442no—
621C2×C4—442no—
622C2×C4C4×D4414yes—
623C2×C4C22⋊C4×D1112yes—
624C2×C4#6693512yes—
625C2×C4#6693714yes—
626C2×C4#6694614yes—
627C2×C4#6694712yes—
628C2×C4#6694814yes—
629C2×C4C22×C4×D1111yescharacteristic
630C2×C4C22×D4411yescharacteristic
631C2×C4C2×#433911yescharacteristic
632C2×C4C2×D4×D1111yescharacteristic
633C2×C4C2×D4×D1111yescharacteristic
634C2×C4C2×#434311yescharacteristic
635C8—42no—
636C8—442no—
637C22—24no—
638C22—24no—
639C22—22no—
640C22—22no—
641C22—114no—
642C22—224no—
643C22—224no—
644C22—222no—
645C22—222no—
646C22—222no—
647C22—222no—
648C22—222no—
649C22—4416no—
650C22—442no—
651C22—442no—
652C22—444no—
653C22—444no—
654C22—444no—
655C22—8816no—
656C22—884no—
657C22—884no—
658C22#1062227814yes—
659C22C2×C22⋊C4×D1111yescharacteristic
660C22C2×#6693511yescharacteristic
661C22C2×#6694711yescharacteristic
662C22D11×AGL(1,ℤ/8)12yes—
663C22#1062330812yes—
664C4—44no—
665C4—44no—
666C4—222no—
667C4—222no—
668C4—444no—
669C4#1062227814yes—
670C4C2×C4×D4411yescharacteristic
671C4C2×#6693711yescharacteristic
672C4C2×#6694611yescharacteristic
673C4C2×#6694811yescharacteristic
674C2—24no—
675C2—224no—
676C2—442no—
677C2—884no—
678C2C2×#1062227811yescharacteristic
679C2D11×#41811yescharacteristic
680C2#1307713411yescharacteristic
681C2#1307786912yes—
682C2#1307855812yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1736C2
socleC23×C11C22×D4
prime radicalC22×#66948C2
cosocleC22×C4×C11C24
hypercenter#1736D11
hypocenterC11#20912
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
2. C2×D11×#117C2semidirect
3. C2×#10622744C2semidirect
4. C2×#10622614C2semidirect
5. C2×#10622739C2semidirect
6. #13068937C2semidirect
7. #13068932C2semidirect
8. #13068335C2semidirect
9. C11×#1736C2semidirect
24. C2×#66948C4semidirect
27. C2×#66945C22semidirect
28. C2×C4⋊C4×D11C22semidirect
35. C2×#66885C22semidirect
36. C2×(C2×D11)⋊C8C22semidirect
37. C2×(C2×D11)⋊C8C22semidirect
39. C2×#66873C22semidirect
40. C11×#340C22semidirect
41. #10622167C22semidirect
57. C22×D44C2×C4semidirect
75. C11×#117D4semidirect
78. C2×C11×C4⋊C4C2×C4semidirect
89. #66979D4semidirect
103. #66948C2×C4semidirect
200. C11×C4⋊C4C2×D4semidirect
208. C4⋊Dic11C2×D4semidirect
224. #1736D11semidirect
336. #340C2×D11semidirect
363. C2×D11#418semidirect
423. #117D44semidirect
430. C2×C4⋊C4C4×D11semidirect
547. C4⋊C4C2×D44semidirect
556. C11#20912semidirect

Maximal subgroups

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

subgroupindex
C22×#669482
C2×D11×#1172
C2×#106227442
C2×#106226142
C2×#106227392
#130689372
#130689322
#130683352
C11×#17362
#2091211