Finite Group Databasebeta

← #14759271

Subgroups — #14759271

Order 2816.

1786 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C8×D11C211yesmaximal, characteristic, complemented
2C2×D4×C11⋊C8C211yesmaximal, characteristic, complemented
3C2×(C22⋊D11)⋊C8C212yesmaximal, complemented
4C4×#66990C211yesmaximal, characteristic
5#13068905C212yesmaximal, complemented
6#13068795C212yesmaximal, complemented
7#13068794C211yesmaximal, characteristic, complemented
8#13068525C211yesmaximal, characteristic, complemented
9#13068390C211yesmaximal, characteristic, complemented
10#13068386C212yesmaximal, complemented
11C11×#1869C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66990C411yescharacteristic
16C2×C4×C22⋊D11C2212yes—
17C23×C11⋊C8C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic, complemented
19C22×C8×D11—24no—
20C22×C8×D11—28no—
21C22×C8×D11C2212yes—
22C22×C8×D11C2212yes—
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2212yescomplemented
25#10622833C411yescharacteristic
26C4×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
29C2×(C2×D11)⋊C8C2212yes—
30C2×(C2×D11)⋊C8C2212yes—
31C2×Dic11⋊C8C2212yescomplemented
32C2×C8×Dic11C2212yescomplemented
33D4×C11⋊C8—24no—
34#10622602C412yes—
35#10622569C412yes—
36#10622568C411yescharacteristic
37#10622559C411yescharacteristic
38C4×(C2×D11)⋊C4C2212yes—
39C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
40C2×C4×C11⋊C8C2211yescharacteristic, complemented
41(C22⋊D11)⋊C8—28no—
42C11×#336C2212yescomplemented
43#10622188C2212yescomplemented
44#10622188C2212yescomplemented
45C24×D11C2×C411yescharacteristic
46C22×D4×C11C2×C411yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C22×C22⋊D11C2×C412yes—
50C23×Dic11C2×C411yescharacteristic
51C22×C4×D11—22no—
52C22×C4×D11—22no—
53C22×C4×D11—24no—
54C22×C4×D11—24no—
55C22×C4×D11C2×C412yes—
56C22×C4×D11C2312yes—
57C22×C8×C11—22no—
58C22×C8×C11—24no—
59C22×C8×C11C2312yes—
60C22×C8×C11C2312yes—
61C4×D4×C11—22no—
62C4×D4×C11—22no—
63C2×C11×C4⋊C4C2×C411yescharacteristic
64C2×C11×C22⋊C4C2×C411yescharacteristic
65C2×C11×C22⋊C4C2×C411yescharacteristic
66C2×C42×C11C2311yescharacteristic
67C2×C22⋊Dic11C2×C412yes—
68C2×C22⋊Dic11C2×C411yescharacteristic
69C2×C22⋊Dic11C2×C411yescharacteristic
70#66990C818yescomplemented
71C4×C22⋊D11—24no—
72C4×C22⋊D11—24no—
73C2×(C2×D11)⋊C4C2×C412yes—
74C2×(C2×D11)⋊C4C2×C412yes—
75C2×(C2×D11)⋊C4C2×C412yes—
76C2×Dic11⋊C4C2×C412yes—
77C2×C4×Dic11C2312yes—
78C22×C11⋊C8—24no—
79C22×C11⋊C8—24no—
80C22×C11⋊C8—22no—
81C22×C11⋊C8D414yescomplemented
82C22×C11⋊C8C2311yescharacteristic
83C22×C11⋊C8C2311yescharacteristic
84C22×C11⋊C8C2311yescharacteristic
85C22×C11⋊C8C2311yescharacteristic
86C2×C8×D11—232no—
87C2×C8×D11—24no—
88C2×C8×D11—24no—
89C2×C8×D11—24no—
90C2×C8×D11—24no—
91C2×C8×D11—24no—
92C2×C8×D11D418yescomplemented
93C11×C22⋊C8—22no—
94C11×C22⋊C8—24no—
95C11⋊#95C2×C412yes—
96C11⋊#95C2×C412yes—
97C11⋊#95C2×C412yes—
98C22⋊(C11⋊C8)—22no—
99C22⋊(C11⋊C8)—22no—
100(C2×D11)⋊C8—24no—
101(C2×D11)⋊C8—24no—
102Dic11⋊C8—24no—
103C8×Dic11—24no—
104C4⋊(C11⋊C8)—22no—
105C4×C11⋊C8—22no—
106C8×#120—111nomaximal, Sylow
107C24×C11C22×C411yescharacteristic
108C24×C11C22×C411yescharacteristic
109C23×D11—22no—
110C23×D11—22no—
111C23×D11—24no—
112C23×D11—24no—
113C23×D11C2×C814yescomplemented
114C23×D11C22×C412yes—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11C2×C814yescomplemented
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—21no—
124C22×C4×C11C22×C411yescharacteristic
125C22×C4×C11C22×C411yescharacteristic
126C22×C4×C11C22×C411yescharacteristic
127C22×C4×C11C22×C411yescharacteristic
128C22×C4×C11C2×D412yes—
129C22×C4×C11#4112yes—
130C22×C4×C11C2411yescharacteristic
131C2×C22⋊D11—24no—
132C2×C22⋊D11—24no—
133C2×C22⋊D11C2×C818yescomplemented
134C22×Dic11—24no—
135C22×Dic11—22no—
136C22×Dic11C22×C412yes—
137C22×Dic11C22×C412yes—
138C22×Dic11C22×C412yes—
139C2×C4×D11—28no—
140C2×C4×D11—28no—
141C2×C4×D11—216no—
142C2×C4×D11—24no—
143C2×C4×D11—24no—
144C2×C4×D11—24no—
145C2×C4×D11—22no—
146C2×C4×D11—22no—
147C2×C4×D11—22no—
148C2×C4×D11—22no—
149C2×C4×D11C2×D414yes—
150C2×C4×D11#4114yes—
151C2×C8×C11—28no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C2×C8×C11—22no—
157C2×C8×C11C2×D414yes—
158C11×C4⋊C4—22no—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—22no—
161C42×C11—21no—
162C42×C11—21no—
163C22⋊Dic11—24no—
164C22⋊Dic11—22no—
165C22⋊Dic11C2×C814yescomplemented
166(C2×D11)⋊C4—24no—
167(C2×D11)⋊C4—24no—
168(C2×D11)⋊C4C2×C818yescomplemented
169Dic11⋊C4—24no—
170C4×Dic11—22no—
171C4×Dic11—22no—
172C2×C11⋊C8—28no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—44no—
179C2×C11⋊C8C2×D412yes—
180C2×C11⋊C8C2×D412yes—
181C2×C11⋊C8C2×D414yes—
182C8×D11—216no—
183C8×D11—216no—
184C24×C8—111no—
185C2×C8×D4—112no—
186C2×C8×D4—111no—
187C4×#120—111no—
188#1869—112no—
189#1869D1111yescharacteristic, complemented
190#1850—112no—
191#1850—111no—
192#1779—111no—
193C8×C22⋊C4—111no—
194C8×C22⋊C4—112no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—21no—
199C23×C11—22no—
200C23×C11—21no—
201C23×C11C4×D412yes—
202C23×C11C22×C812yes—
203C23×C11C22×C812yescomplemented
204C23×C11#13112yes—
205C23×C11C23×C411yescharacteristic
206C22×D11—28no—
207C22×D11—216no—
208C22×D11—28no—
209C22×D11—22no—
210C22×D11—22no—
211C22×D11—22no—
212C22×D11—22no—
213C22×D11—28no—
214C22×D11—216no—
215C22×D11C4×D414yes—
216C22×D11C22×C814yes—
217C22×D11#13114yes—
218D4×C11—28no—
219C2×C4×C11—21no—
220C2×C4×C11—22no—
221C2×C4×C11—21no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—22no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—22no—
229C2×C4×C11—41no—
230C2×C4×C11—42no—
231C2×C4×C11—41no—
232C2×C4×C11C4×D412yes—
233C2×C4×C11C22×C812yescomplemented
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D412yes—
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4112yes—
238C22⋊D11—216no—
239C2×Dic11—28no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11C4×D414yes—
248C2×Dic11C22×C814yescomplemented
249C4×D11—216no—
250C4×D11—24no—
251C4×D11—24no—
252C4×D11—24no—
253C4×D11—24no—
254C8×C11—24no—
255C8×C11—42no—
256C11⋊C8—22no—
257C11⋊C8—41no—
258C11⋊C8—41no—
259C11⋊C8#12014yescomplemented
260C24×C4—111no—
261C23×C8—111no—
262C23×C8—112no—
263C23×C8—111no—
264C23×C8—112no—
265C23×C8—224no—
266C23×C8—228no—
267C23×C8C2×D1111yescharacteristic
268C2×#120—111no—
269C2×C4×D4—112no—
270C2×C4×D4C2×D1111yescharacteristic
271C8×D4—228no—
272C8×D4—224no—
273C2×C4⋊C8—112no—
274C2×C4⋊C8—111no—
275C2×C22⋊C8—111no—
276C2×C22⋊C8—111no—
277C2×C22⋊C8—112no—
278C2×C22⋊C8—112no—
279C2×C22⋊C8C2×D1111yescharacteristic
280C2×C22⋊C8C2×D1112yescomplemented
281C2×C4×C8—112no—
282C2×C4×C8—111no—
283#386—111no—
284#386—112no—
285#385—112no—
286#385—111no—
287#379—111no—
288C4×C22⋊C4—111no—
289C4×C22⋊C4—112no—
290#336—112no—
291#336—112no—
292#336C2×D1112yescomplemented
293C22×C11—24no—
294C22×C11—22no—
295C22×C11—24no—
296C22×C11—22no—
297C22×C11—22no—
298C22×C11—24no—
299C22×C11—42no—
300C22×C11—41no—
301C22×C11—41no—
302C22×C11C8×D414yescomplemented
303C22×C11C2×C4×D411yescharacteristic
304C22×C11C2×C4×D412yes—
305C22×C11C23×C811yescharacteristic
306C22×C11C2×#13111yescharacteristic
307C22×C11C2×#13112yes—
308C2×D11—232no—
309C2×D11—24no—
310C2×D11—24no—
311C2×D11—24no—
312C2×D11—24no—
313C2×D11—24no—
314C2×D11—24no—
315C2×D11C8×D418yescomplemented
316C4×C11—22no—
317C4×C11—22no—
318C4×C11—41no—
319C4×C11—41no—
320C4×C11C2×#12011yescharacteristic
321C4×C11#52512yes—
322C4×C11#52511yescharacteristic
323Dic11—24no—
324Dic11—24no—
325Dic11—42no—
326C25—111no—
327C22×D4—112no—
328C22×D4C4×D1111yescharacteristic
329C23×C4—112no—
330C23×C4—111no—
331C23×C4—112no—
332C23×C4—224no—
333C23×C4—224no—
334C23×C4—222no—
335C23×C4—222no—
336C23×C4C22×D1111yescharacteristic
337C23×C4C22×D1111yescharacteristic
338C22×C8—22no—
339C22×C8—24no—
340C22×C8—111no—
341C22×C8—114no—
342C22×C8—111no—
343C22×C8—118no—
344C22×C8—111no—
345C22×C8—111no—
346C22×C8—224no—
347C22×C8—224no—
348C22×C8—224no—
349C22×C8—224no—
350C22×C8—2232no—
351C22×C8—224no—
352C22×C8—224no—
353C22×C8—222no—
354C22×C8—224no—
355C22×C8C22×D1112yes—
356C22×C8C22×D1112yes—
357#120—118no—
358C4×D4—22no—
359C4×D4—22no—
360C4×D4—224no—
361C4×D4—224no—
362C2×C4⋊C4—112no—
363C2×C4⋊C4C4×D1111yescharacteristic
364C2×C22⋊C4—111no—
365C2×C22⋊C4—112no—
366C2×C22⋊C4—112no—
367C2×C22⋊C4—111no—
368C2×C22⋊C4—112no—
369C2×C22⋊C4—112no—
370C2×C22⋊C4C4×D1111yescharacteristic
371C2×C22⋊C4C4×D1111yescharacteristic
372C2×C42—112no—
373C2×C42C22×D1111yescharacteristic
374C4⋊C8—222no—
375C4⋊C8—224no—
376C22⋊C8—22no—
377C22⋊C8—24no—
378C22⋊C8—224no—
379C22⋊C8—224no—
380C22⋊C8—222no—
381C22⋊C8—222no—
382C4×C8—222no—
383C4×C8—224no—
384#95—112no—
385#95—112no—
386#95—112no—
387C2×C11—24no—
388C2×C11—42no—
389C2×C11C4×#12011yescharacteristic
390C2×C11C2×C8×D412yes—
391C2×C11C2×C8×D411yescharacteristic
392C2×C11#292912yes—
393C2×C11#292911yescharacteristic
394D11—28no—
395C24—112no—
396C24—114no—
397C24—224no—
398C24—224no—
399C24—222no—
400C24—222no—
401C24C2×C4×D1111yescharacteristic
402C24C2×C4×D1111yescharacteristic
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—118no—
406C2×D4—224no—
407C2×D4—224no—
408C2×D4C8×D1114yescomplemented
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—112no—
416C22×C4—112no—
417C22×C4—114no—
418C22×C4—114no—
419C22×C4—112no—
420C22×C4—224no—
421C22×C4—224no—
422C22×C4—228no—
423C22×C4—2216no—
424C22×C4—228no—
425C22×C4—224no—
426C22×C4—222no—
427C22×C4—224no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4C2×C4×D1111yescharacteristic
433C22×C4C2×C4×D1111yescharacteristic
434C22×C4C2×C4×D1111yescharacteristic
435C22×C4C2×C4×D1111yescharacteristic
436C22×C4D4×D1112yes—
437C22×C4#434112yes—
438C22×C4C23×D1111yescharacteristic
439C2×C8—28no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—114no—
446C2×C8—112no—
447C2×C8—112no—
448C2×C8—2216no—
449C2×C8—2216no—
450C2×C8—228no—
451C2×C8—222no—
452C2×C8—221no—
453C2×C8—222no—
454C2×C8—221no—
455C2×C8—222no—
456C2×C8—444no—
457C2×C8D4×D1114yes—
458C4⋊C4—22no—
459C4⋊C4—224no—
460C22⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4—114no—
463C22⋊C4—118no—
464C22⋊C4—224no—
465C22⋊C4—224no—
466C22⋊C4—224no—
467C22⋊C4—222no—
468C42—21no—
469C42—21no—
470C42—222no—
471C42—222no—
472C11C8×#12011yescharacteristic, complemented, Sylow
473C23—22no—
474C23—22no—
475C23—21no—
476C23—21no—
477C23—22no—
478C23—22no—
479C23—114no—
480C23—114no—
481C23—114no—
482C23—2216no—
483C23—228no—
484C23—2216no—
485C23—228no—
486C23—222no—
487C23—222no—
488C23—222no—
489C23—222no—
490C23—228no—
491C23(C22⋊D11)⋊C412yes—
492C23C2×C8×D1112yes—
493C23C2×C8×D1112yescomplemented
494C23#6696012yes—
495C23C22×C4×D1111yescharacteristic
496D4—28no—
497D4—2216no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—24no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—41no—
511C2×C4—114no—
512C2×C4—114no—
513C2×C4—2216no—
514C2×C4—228no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—222no—
518C2×C4—222no—
519C2×C4—224no—
520C2×C4—224no—
521C2×C4—224no—
522C2×C4—224no—
523C2×C4—222no—
524C2×C4—222no—
525C2×C4—222no—
526C2×C4(C22⋊D11)⋊C412yes—
527C2×C4C2×C8×D1112yescomplemented
528C2×C4C2×D4×D1112yes—
529C2×C4C2×D4×D1111yescharacteristic
530C2×C4C2×#434111yescharacteristic
531C2×C4#41×D1112yes—
532C8—24no—
533C8—42no—
534C8—114no—
535C8—222no—
536C8—441no—
537C8—441no—
538C22—22no—
539C22—24no—
540C22—24no—
541C22—22no—
542C22—24no—
543C22—22no—
544C22—41no—
545C22—42no—
546C22—41no—
547C22—118no—
548C22—2232no—
549C22—224no—
550C22—224no—
551C22—224no—
552C22—224no—
553C22—224no—
554C22—224no—
555C22(C22⋊D11)⋊C814yescomplemented
556C22C2×(C22⋊D11)⋊C411yescharacteristic
557C22C4×D4×D1112yes—
558C22C22×C8×D1111yescharacteristic
559C22C2×#6696011yescharacteristic
560C22D11×#13112yes—
561C4—22no—
562C4—22no—
563C4—41no—
564C4—41no—
565C4—224no—
566C4—224no—
567C4—442no—
568C4D11×#12011yescharacteristic
569C4#1062313712yes—
570C4#1062318711yescharacteristic
571C2—24no—
572C2—42no—
573C2—228no—
574C2#1307112111yescharacteristic
575C2C8×D4×D1112yes—
576C2C2×(C22⋊D11)⋊C811yescharacteristic
577C2#1307730712yes—
578C2#1307731311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C23×C8
FittingC11×#1869C2
socleC23×C11C23×C4
prime radicalC2×#66990C4
cosocleC22×C4×C11C24
hypercenter#1869D11
hypocenterC11C8×#120
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
1. C23×C8×D11C2semidirect
2. C2×D4×C11⋊C8C2semidirect
3. C2×(C22⋊D11)⋊C8C2semidirect
5. #13068905C2semidirect
6. #13068795C2semidirect
7. #13068794C2semidirect
8. #13068525C2semidirect
9. #13068390C2semidirect
10. #13068386C2semidirect
11. C11×#1869C2semidirect
18. C23×C11⋊C8C22semidirect
24. C2×C11×C22⋊C8C22semidirect
28. C2×C22⋊(C11⋊C8)C22semidirect
31. C2×Dic11⋊C8C22semidirect
32. C2×C8×Dic11C22semidirect
39. C2×C4⋊(C11⋊C8)C22semidirect
40. C2×C4×C11⋊C8C22semidirect
42. C11×#336C22semidirect
43. #10622188C22semidirect
44. #10622188C22semidirect
70. #66990C8semidirect
81. C22×C11⋊C8D4semidirect
92. C2×C8×D11D4semidirect
113. C23×D11C2×C8semidirect
117. C2×D4×C11C2×C8semidirect
133. C2×C22⋊D11C2×C8semidirect
165. C22⋊Dic11C2×C8semidirect
168. (C2×D11)⋊C4C2×C8semidirect
189. #1869D11semidirect
203. C23×C11C22×C8semidirect
233. C2×C4×C11C22×C8semidirect
248. C2×Dic11C22×C8semidirect
259. C11⋊C8#120semidirect
280. C2×C22⋊C8C2×D11semidirect
292. #336C2×D11semidirect
302. C22×C11C8×D4semidirect
315. C2×D11C8×D4semidirect
408. C2×D4C8×D11semidirect
472. C11C8×#120semidirect
493. C23C2×C8×D11semidirect
527. C2×C4C2×C8×D11semidirect
555. C22(C22⋊D11)⋊C8semidirect

Maximal subgroups

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

subgroupindex
C23×C8×D112
C2×D4×C11⋊C82
C2×(C22⋊D11)⋊C82
C4×#669902
#130689052
#130687952
#130687942
#130685252
#130683902
#130683862
C11×#18692
C8×#12011