Finite Group Databasebeta

← #14756809

Subgroups — #14756809

Order 2816.

1042 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622398C211yesmaximal, characteristic
2#13071074C211yesmaximal, characteristic, complemented
3C4×D4×Dic11C211yesmaximal, characteristic, complemented
4#13069242C211yesmaximal, characteristic, complemented
5#13069237C211yesmaximal, characteristic, complemented
6#13069198C211yesmaximal, characteristic, complemented
7#13069197C211yesmaximal, characteristic, complemented
8#13068964C211yesmaximal, characteristic
9#13068962C211yesmaximal, characteristic
10#13068865C211yesmaximal, characteristic, complemented
11#13068516C211yesmaximal, characteristic, complemented
12#13068443C211yesmaximal, characteristic, complemented
13#13068440C211yesmaximal, characteristic, complemented
14#13068363C211yesmaximal, characteristic, complemented
15C11×#1864C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C22×#4323C2211yescharacteristic
20C22×C4×Dic11—21no—
21C2×#66946C2211yescharacteristic
22C2×#66945—21no—
23C2×C11×#106C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C4×C22⋊Dic11—21no—
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66879C2211yescharacteristic
33C2×#66879C2211yescharacteristic
34#10622603—21no—
35#10622601C2211yescharacteristic
36#10622598C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39C4⋊C4×Dic11C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C22⋊C4×Dic11—21no—
43C22⋊C4×Dic11—21no—
44#10622552C2211yescharacteristic
45C4×C4⋊Dic11C2211yescharacteristic
46C42×Dic11C2211yescharacteristic
47#10622398C418yescomplemented
48#10622283—21no—
49#10622279—21no—
50C11×#340C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×Dic11—21no—
63C23×Dic11—21no—
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C42×C11C2311yescharacteristic
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78D4×Dic11—22no—
79D4×Dic11—22no—
80D4×Dic11—22no—
81D4×Dic11C2×C414yes—
82C2×#4323—22no—
83C2×#4323—22no—
84C2×#4323C2×C414yes—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—44no—
99C2×C4×Dic11D411yescharacteristic
100C2×C4×Dic11D411yescharacteristic
101C2×C4×Dic11D411yescharacteristic
102C2×C4×Dic11D411yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107#66946—22no—
108#66946C2×C414yescomplemented
109#66945—44no—
110C11×#106—22no—
111C11×#102—22no—
112C11×#102C2×C414yes—
113C11×#95—21no—
114#66896—22no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120#66885—22no—
121#66885C2×C414yescomplemented
122#66882—22no—
123#66879—22no—
124#66879C2×C414yescomplemented
125#66873—22no—
126#66872C2×C414yescomplemented
127#21122—111nomaximal, Sylow
128C24×C11—21no—
129C23×D11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11C22×C412yes—
134C2×D4×C11#4112yes—
135C2×D4×C11#4112yes—
136C22×C4×C11—24no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—42no—
141C22×C4×C11—42no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—24no—
146C22×Dic11—24no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—42no—
151C22×Dic11—42no—
152C22×Dic11—42no—
153C22×Dic11—42no—
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44C22×C412yes—
164C2×C4×D11—24no—
165C2×C4×D11—42no—
166C2×C4×D11—42no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11C22×C412yes—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4C22×C412yes—
179C11×C4⋊C4#4112yes—
180C11×C22⋊C4—24no—
181C42×C11—21no—
182C42×C11—21no—
183C22⋊Dic11—24no—
184C22⋊Dic11—24no—
185#4323—28no—
186(C2×D11)⋊C4—24no—
187(C2×D11)⋊C4—42no—
188(C2×D11)⋊C4—42no—
189(C2×D11)⋊C4—42no—
190(C2×D11)⋊C4—42no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—42no—
196C4⋊Dic11C22×C412yes—
197C4⋊Dic11#4112yes—
198C4×Dic11—22no—
199C4×Dic11—22no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—41no—
203C4×Dic11—41no—
204C4×Dic11—42no—
205C4×Dic11—42no—
206C4×Dic11—42no—
207C4×Dic11—42no—
208C4×Dic11C22×C412yes—
209C4×Dic11#4112yes—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8C22×C412yes—
216C2×#442—111no—
217#2293—111no—
218C42×D4—111no—
219#1926—111no—
220#1925—111no—
221#1920—111no—
222#1919—111no—
223#1879—111no—
224#1879—111no—
225#1864D1111yescharacteristic, complemented
226#1862—111no—
227#1776—111no—
228#1762—111no—
229#1762—111no—
230#1745—111no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11C22×D411yescharacteristic
239C22×D11—22no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246D4×C11—22no—
247D4×C11—22no—
248D4×C11—22no—
249D4×C11#11714yescomplemented
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—22no—
253C2×C4×C11—21no—
254C2×C4×C11—22no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—48no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11AGL(1,ℤ/8)12yes—
266C2×C4×C11C23×C411yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—22no—
279C2×Dic11—21no—
280C2×Dic11—22no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—48no—
284C2×Dic11—48no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11C4×D412yes—
293C2×Dic11C4×D412yes—
294C2×Dic11AGL(1,ℤ/8)12yes—
295D44—22no—
296D44—22no—
297D44—41no—
298D44—41no—
299C4×D11—48no—
300C8×C11—22no—
301C8×C11—41no—
302C11⋊C8—22no—
303C11⋊C8—41no—
304C22×D8—111no—
305C2×C4×D4—111no—
306C2×C4×D4—111no—
307C2×C4×D4—111no—
308C2×C4×D4C2×D1111yescharacteristic
309C2×#117—221no—
310C22×C42—221no—
311#442—118no—
312C2×#107—111no—
313C2×#106—111no—
314C2×#106C2×D1111yescharacteristic
315C2×#102—111no—
316C2×#102—111no—
317C2×#102—111no—
318C2×#102—111no—
319C2×#102C2×D1111yescharacteristic
320C2×#102C2×D1111yescharacteristic
321C2×#97—111no—
322C2×#97—111no—
323#390—111no—
324#390—111no—
325#389—111no—
326#389C2×D1111yescharacteristic
327#388—221no—
328#388—221no—
329C4×C4⋊C4—111no—
330C4×C4⋊C4—111no—
331C4×C4⋊C4—111no—
332C4×C4⋊C4—111no—
333C4×C22⋊C4—221no—
334C4×C22⋊C4—221no—
335C4×C22⋊C4—221no—
336C4×C22⋊C4—221no—
337C43—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343#340C2×D1111yescharacteristic
344#336—111no—
345#336—111no—
346#336—111no—
347#336C2×D1111yescharacteristic
348C22×C11—24no—
349C22×C11—42no—
350C22×C11—42no—
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11C2×C4×D411yescharacteristic
356C22×C11#52511yescharacteristic
357C22×C11#52511yescharacteristic
358C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
359C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
360C22×C11#57511yescharacteristic
361C22×C11#57511yescharacteristic
362C2×D11—42no—
363C2×D11—42no—
364C2×D11—42no—
365C2×D11—81no—
366C2×D11—81no—
367C2×D11—81no—
368C2×D11—81no—
369C4×C11—22no—
370C4×C11—42no—
371C4×C11—41no—
372C4×C11—42no—
373C4×C11—81no—
374C4×C11C2×#11711yescharacteristic
375C4×C11C4×#4111yescharacteristic
376C4×C11#52911yescharacteristic
377C4×C11#52911yescharacteristic
378Dic11—22no—
379Dic11—22no—
380Dic11—22no—
381Dic11—42no—
382Dic11—41no—
383Dic11—42no—
384Dic11—81no—
385C22×D4—111no—
386C22×D4C22×D1111yescharacteristic
387C23×C4—21no—
388C23×C4—221no—
389C23×C4—221no—
390C23×C4—221no—
391C2×D8—114no—
392C2×D8—222no—
393C2×D8—222no—
394C22×C8—111no—
395C22×C8—111no—
396C22×C8C22×D1111yescharacteristic
397C22×C8C22×D1111yescharacteristic
398C4×D4—22no—
399C4×D4—22no—
400C4×D4—114no—
401C4×D4—114no—
402C4×D4—222no—
403C4×D4—222no—
404C4×D4—222no—
405C4×D4—222no—
406#117—444no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4C22×D1111yescharacteristic
413C2×C4⋊C4C22×D1111yescharacteristic
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C22⋊C4—21no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C22⋊C4—221no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C42—111no—
424C2×C42—111no—
425C2×C42—111no—
426C2×C42—111no—
427C2×C42—111no—
428C2×C42—111no—
429C2×C42—221no—
430C2×C42—221no—
431C2×C42—221no—
432C2×C42—221no—
433C2×C42—444no—
434C2×C42C22×D1111yescharacteristic
435#107—222no—
436#106—22no—
437#106—114no—
438#102—22no—
439#102—114no—
440#102—222no—
441#102—222no—
442#102—222no—
443#102C4×D1114yes—
444#97—114no—
445#97—222no—
446#95—21no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451#95—221no—
452C2×C11—44no—
453C2×C11#229011yescharacteristic
454C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
455C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
456C2×C11#310911yescharacteristic
457C2×C11#311111yescharacteristic
458C2×C11#311411yescharacteristic
459C2×C11#311511yescharacteristic
460D11—82no—
461C24—21no—
462C24—221no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—112no—
467C2×D4—221no—
468C2×D4—221no—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—221no—
472C2×D4C2×C4×D1112yes—
473C2×D4#434112yes—
474C2×D4#434312yes—
475C22×C4—24no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—111no—
484C22×C4—111no—
485C22×C4—224no—
486C22×C4—224no—
487C22×C4—224no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—442no—
492C22×C4—442no—
493C22×C4—442no—
494C22×C4—442no—
495C22×C4—442no—
496C22×C4—442no—
497C22×C4D4×D1111yescharacteristic
498C22×C4D4×D1111yescharacteristic
499C22×C4C23×D1111yescharacteristic
500D8—228no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—112no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8C2×C4×D1112yes—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—42no—
518C4⋊C4—112no—
519C4⋊C4—112no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—442no—
525C4⋊C4C2×C4×D1112yes—
526C4⋊C4#434112yes—
527C22⋊C4—24no—
528C22⋊C4—224no—
529C22⋊C4—224no—
530C22⋊C4—224no—
531C22⋊C4—442no—
532C22⋊C4—442no—
533C22⋊C4—442no—
534C22⋊C4—442no—
535C42—21no—
536C42—21no—
537C42—112no—
538C42—112no—
539C42—222no—
540C42—222no—
541C42—221no—
542C42—221no—
543C42—441no—
544C42—441no—
545C42—442no—
546C42—442no—
547C42—442no—
548C42—442no—
549C11#2112211yescharacteristic, complemented, Sylow
550C23—22no—
551C23—22no—
552C23—22no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—222no—
558C23—441no—
559C23—441no—
560C23—441no—
561C23—441no—
562C23—441no—
563C23—441no—
564C23C2×D4×D1111yescharacteristic
565D4—22no—
566D4—22no—
567D4—22no—
568D4—222no—
569D4—222no—
570D4—441no—
571D4—441no—
572D4#6694514yescomplemented
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—48no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—112no—
589C2×C4—112no—
590C2×C4—112no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—222no—
600C2×C4—221no—
601C2×C4—222no—
602C2×C4—448no—
603C2×C4—448no—
604C2×C4—448no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4#6696712yes—
613C2×C4C22×C4×D1111yescharacteristic
614C2×C4C2×#434111yescharacteristic
615C2×C4C2×#434111yescharacteristic
616C2×C4C2×#434311yescharacteristic
617C2×C4#41×D1111yescharacteristic
618C2×C4#41×D1111yescharacteristic
619C8—22no—
620C8—41no—
621C8—222no—
622C8—441no—
623C22—24no—
624C22—42no—
625C22—42no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—442no—
631C22—442no—
632C22—442no—
633C22—881no—
634C22—881no—
635C22—881no—
636C22—881no—
637C22C4×D4×D1111yescharacteristic
638C22#1062311711yescharacteristic
639C22#1062315811yescharacteristic
640C22C2×#6696711yescharacteristic
641C22#1062329911yescharacteristic
642C22D11×AGL(1,ℤ/8)11yescharacteristic
643C22#1062330411yescharacteristic
644C4—22no—
645C4—42no—
646C4—42no—
647C4—41no—
648C4—81no—
649C4—222no—
650C4—222no—
651C4—222no—
652C4—442no—
653C4—442no—
654C4—441no—
655C4—881no—
656C4C2×#6694511yescharacteristic
657C4C4×#434111yescharacteristic
658C4#1062315511yescharacteristic
659C4#1062318011yescharacteristic
660C2—44no—
661C2—882no—
662C2#1307105211yescharacteristic
663C2C4×#6696711yescharacteristic
664C2#1307742711yescharacteristic
665C2#1307870911yescharacteristic
666C2#1307873011yescharacteristic
667C2#1307875511yescharacteristic
668C2#1307876011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1864C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
cosocleC22×C4×C11C24
hypercenter#1864D11
hypocenterC11#21122
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
2. #13071074C2semidirect
3. C4×D4×Dic11C2semidirect
4. #13069242C2semidirect
5. #13069237C2semidirect
6. #13069198C2semidirect
7. #13069197C2semidirect
10. #13068865C2semidirect
11. #13068516C2semidirect
12. #13068443C2semidirect
13. #13068440C2semidirect
14. #13068363C2semidirect
15. C11×#1864C2semidirect
47. #10622398C4semidirect
108. #66946C2×C4semidirect
121. #66885C2×C4semidirect
124. #66879C2×C4semidirect
126. #66872C2×C4semidirect
225. #1864D11semidirect
249. D4×C11#117semidirect
549. C11#21122semidirect
572. D4#66945semidirect

Maximal subgroups

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

subgroupindex
C2×#106223982
#130710742
C4×D4×Dic112
#130692422
#130692372
#130691982
#130691972
#130689642
#130689622
#130688652
#130685162
#130684432
#130684402
#130683632
C11×#18642
#2112211