Finite Group Databasebeta

← #14720238

Subgroups — #14720238

Order 2816.

1248 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4341C211yesmaximal, characteristic
2#13077247C211yesmaximal, characteristic, complemented
3D11×#432C211yesmaximal, characteristic, complemented
4#13067064C211yesmaximal, characteristic, complemented
5#13067062C211yesmaximal, characteristic, complemented
6#13067059C211yesmaximal, characteristic, complemented
7#13067047C214yesmaximal, complemented
8#13067000C214yesmaximal, complemented
9C11×#1490C211yesmaximal, characteristic, complemented
10C22×#4341C411yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C2×D4×Dic11C411yescharacteristic
13C2×C4×C22⋊D11—21no—
14C22×C4×Dic11—21no—
15C4×#4341—21no—
16C4×#4341—21no—
17C4×#4341—21no—
18C4×#4341—21no—
19C4×#4341C412yes—
20C4×#4341C412yes—
21C4×#4341C2212yes—
22C4×#4341C2212yes—
23C2×#66945C411yescharacteristic
24C2×#66940C411yescharacteristic
25C2×(C22⋊D11)⋊C4—21no—
26C2×#66930—21no—
27C2×C42×D11C2211yescharacteristic
28C2×C4×Dic22C2211yescharacteristic
29C11×#432C2211yescharacteristic
30C4×C11×M16C2211yescharacteristic
31#10622739—21no—
32#10622731—21no—
33#10622539C2211yescharacteristic
34C4×#4318C2211yescharacteristic
35#10622448C2212yescomplemented
36D11×C4⋊C8C2212yescomplemented
37D11×C22⋊C8—21no—
38#10622332—21no—
39#10622318—21no—
40#10622318—21no—
41#10622318—21no—
42D11×#97—21no—
43#10622298C2212yescomplemented
44#10622298C2212yescomplemented
45C11×D4⋊C8C2214yescomplemented
46D4⋊(C11⋊C8)C2214yescomplemented
47#10622122C2214yescomplemented
48#10622094C2214yescomplemented
49C22×D4×C11C2×C411yescharacteristic
50C23×C4×C11—21no—
51C22×C22⋊D11—21no—
52C23×Dic11—21no—
53C23×Dic11—21no—
54C2×#4341—28no—
55C2×#4341—21no—
56C2×#4341—21no—
57C2×#4341C2×C412yes—
58C2×#4341C2×C412yes—
59C22×C4×D11C2×C411yescharacteristic
60C22×C4×D11D411yescharacteristic
61C22×C4×D11D411yescharacteristic
62C22×Dic22C2×C411yescharacteristic
63C2×C11×M16—21no—
64C4×D4×C11—21no—
65C4×D4×C11—21no—
66C4×D4×C11C2×C412yes—
67C4×D4×C11C2312yes—
68C2×C11×C4⋊C4C2×C411yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C42×C11C2311yescharacteristic
71C2×C22⋊Dic11—21no—
72D4×Dic11—21no—
73D4×Dic11—21no—
74D4×Dic11C2×C412yes—
75D4×Dic11C2×C412yes—
76C4×C22⋊D11—22no—
77C4×C22⋊D11—22no—
78C4×C22⋊D11—22no—
79C4×C22⋊D11—22no—
80C2×(C2×D11)⋊C4—21no—
81C2×C4⋊Dic11C2×C411yescharacteristic
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×C4×Dic11—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—22no—
88C2×C4×Dic11—22no—
89C2×C4×Dic11—22no—
90C2×C4×Dic11—22no—
91C2×C4×Dic11C2×C411yescharacteristic
92C2×C4×Dic11D411yescharacteristic
93C2×C4×Dic11D411yescharacteristic
94C2×#4318—21no—
95C2×C8×D11—22no—
96#66945—21no—
97#66945—21no—
98#66945C2×C412yes—
99#66945C2×C412yes—
100#66940—21no—
101#66940—21no—
102#66940C2×C412yes—
103#66940C2×C412yes—
104(C22⋊D11)⋊C4—22no—
105(C22⋊D11)⋊C4—22no—
106(C22⋊D11)⋊C4—22no—
107(C22⋊D11)⋊C4—22no—
108#66930—22no—
109#66930—22no—
110#66930—22no—
111#66930—22no—
112C42×D11C2×C411yescharacteristic
113C42×D11C2×C411yescharacteristic
114C42×D11D411yescharacteristic
115C42×D11D411yescharacteristic
116C42×D11D411yescharacteristic
117C42×D11D411yescharacteristic
118C42×D11C2311yescharacteristic
119C42×D11C2311yescharacteristic
120C4×Dic22—21no—
121C4×Dic22—21no—
122C4×Dic22C2×C412yes—
123C4×Dic22C2312yes—
124C11×C4⋊C8C2312yes—
125C11×C22⋊C8—21no—
126C11×#97—21no—
127C11×#97—21no—
128C4×C8×C11C2312yes—
129C22⋊(C11⋊C8)—21no—
130(C2×D11)⋊C8—22no—
131(C2×D11)⋊C8—22no—
132(C2×D11)⋊C8—22no—
133#66879—22no—
134Dic11⋊C8—22no—
135Dic11⋊C8—22no—
136Dic11⋊C8—22no—
137C4⋊(C11⋊C8)C2312yes—
138#66867—21no—
139#66867—21no—
140C4×C11⋊C8C2312yes—
141#17452—111nomaximal, Sylow
142C24×C11—21no—
143C23×D11C22⋊C411yescharacteristic
144C2×D4×C11—24no—
145C2×D4×C11—21no—
146C2×D4×C11C22×C412yes—
147C22×C4×C11—21no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—44no—
151C22×C4×C11C22×C411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C2×C22⋊D11—28no—
155C2×C22⋊D11—22no—
156C2×C22⋊D11—22no—
157C22×Dic11—28no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—44no—
165C22×Dic11C22⋊C411yescharacteristic
166C22×Dic11C22⋊C411yescharacteristic
167C22×Dic11C22⋊C411yescharacteristic
168#4341—28no—
169#4341—28no—
170#4341—24no—
171#4341—24no—
172#4341—24no—
173#4341M1618yescomplemented
174C2×C4×D11—24no—
175C2×C4×D11—42no—
176C2×C4×D11—42no—
177C2×C4×D11C22⋊C411yescharacteristic
178C2×C4×D11C22⋊C411yescharacteristic
179C2×C4×D11C22⋊C411yescharacteristic
180C2×C4×D11C22⋊C411yescharacteristic
181C2×C4×D11C22⋊C411yescharacteristic
182C2×C4×D11C22⋊C411yescharacteristic
183C2×C4×D11C22×C411yescharacteristic
184C2×C4×D11C22×C411yescharacteristic
185C2×C4×D11C2×D411yescharacteristic
186C2×C4×D11C2×D411yescharacteristic
187C2×C4×D11C2×D411yescharacteristic
188C2×C4×D11C2×D411yescharacteristic
189C2×Dic22—24no—
190C2×Dic22—21no—
191C2×Dic22C22×C412yes—
192C11×M16—42no—
193C2×C8×C11—22no—
194C2×C8×C11—22no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4C22×C412yes—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—22no—
199C42×C11C22×C411yescharacteristic
200C42×C11C2×D411yescharacteristic
201C42×C11C2×D411yescharacteristic
202C42×C11C2411yescharacteristic
203C22⋊Dic11—22no—
204C22⋊Dic11—22no—
205(C2×D11)⋊C4—22no—
206(C2×D11)⋊C4—22no—
207C4⋊Dic11—21no—
208C4⋊Dic11C22×C412yes—
209Dic11⋊C4—22no—
210Dic11⋊C4—22no—
211Dic11⋊C4—22no—
212Dic11⋊C4—22no—
213C4×Dic11—22no—
214C4×Dic11—22no—
215C4×Dic11—22no—
216C4×Dic11—22no—
217C4×Dic11—22no—
218C4×Dic11—22no—
219C4×Dic11C22⋊C411yescharacteristic
220C4×Dic11C22⋊C411yescharacteristic
221C4×Dic11C22⋊C411yescharacteristic
222C4×Dic11C22⋊C411yescharacteristic
223C4×Dic11C22⋊C411yescharacteristic
224C4×Dic11C22⋊C411yescharacteristic
225C4×Dic11C22×C411yescharacteristic
226C4×Dic11C22×C411yescharacteristic
227C4×Dic11C2×D411yescharacteristic
228C4×Dic11C2×D411yescharacteristic
229C4×Dic11C2×D411yescharacteristic
230C4×Dic11C2×D411yescharacteristic
231#4318—42no—
232C2×C11⋊C8—22no—
233C2×C11⋊C8—22no—
234C8×D11—44no—
235C2×C4×#41—111no—
236#2920—111no—
237C2×#432—111no—
238#1491—111no—
239#1491—111no—
240#1490—111no—
241#1490D1111yescharacteristic, complemented
242#1488—114no—
243#1477—114no—
244C23×C11—24no—
245C23×C11—22no—
246C23×C11—42no—
247C23×C11—42no—
248C23×C11C2×C22⋊C411yescharacteristic
249C22×D11—22no—
250C22×D11—22no—
251C22×D11—41no—
252C22×D11C2×C22⋊C411yescharacteristic
253C22×D11C2×C22⋊C411yescharacteristic
254D4×C11—24no—
255D4×C11—22no—
256D4×C11C2×M1614yes—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—44no—
262C2×C4×C11—42no—
263C2×C4×C11—44no—
264C2×C4×C11C2×C22⋊C411yescharacteristic
265C2×C4×C11C2×C22⋊C411yescharacteristic
266C2×C4×C11C2×C22⋊C411yescharacteristic
267C2×C4×C11C23×C411yescharacteristic
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270C22⋊D11—28no—
271C22⋊D11—28no—
272C2×Dic11—24no—
273C2×Dic11—28no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—28no—
278C2×Dic11—22no—
279C2×Dic11—41no—
280C2×Dic11—44no—
281C2×Dic11—44no—
282C2×Dic11—42no—
283C2×Dic11C2×C22⋊C411yescharacteristic
284C2×Dic11C2×C22⋊C411yescharacteristic
285C2×Dic11C2×C22⋊C411yescharacteristic
286C2×Dic11C2×C22⋊C411yescharacteristic
287C2×Dic11C2×C22⋊C411yescharacteristic
288C2×Dic11C2×C22⋊C411yescharacteristic
289C4×D11—22no—
290C4×D11—22no—
291C4×D11—22no—
292C4×D11—22no—
293C4×D11—22no—
294C4×D11—41no—
295C4×D11—41no—
296C4×D11—41no—
297C4×D11—41no—
298C4×D11—41no—
299C4×D11—41no—
300C4×D11C2×M1614yes—
301Dic22—24no—
302Dic22—22no—
303Dic22C2×M1614yes—
304C8×C11—42no—
305C8×C11—42no—
306C11⋊C8—42no—
307C11⋊C8—42no—
308C22×#41—111no—
309C4×#41—112no—
310C4×#41—112no—
311C4×#41—112no—
312C4×#41—112no—
313C4×#41—221no—
314C4×#41—221no—
315C4×#41—221no—
316C4×#41—221no—
317C2×C4×Q8—111no—
318C2×C4×Q8—111no—
319C2×C4×D4—111no—
320C2×C4×D4—221no—
321C2×C4×D4—221no—
322C2×C4×D4C2×D1111yescharacteristic
323C2×#117—111no—
324C2×#117—221no—
325C22×C42—111no—
326C22×C42—221no—
327#432—111no—
328#432—112no—
329#432—221no—
330#432—221no—
331#432—221no—
332#432—221no—
333#432C2×D1111yescharacteristic
334#431—112no—
335#431—112no—
336#423—221no—
337C2×C4⋊C8—112no—
338#407—221no—
339C2×C22⋊C8—221no—
340C4×M16—111no—
341C4×M16C2×D1111yescharacteristic
342C2×#97—221no—
343Q8⋊C8—114no—
344Q8⋊C8—114no—
345D4⋊C8—114no—
346D4⋊C8C2×D1114yescomplemented
347C22×C11—21no—
348C22×C11—21no—
349C22×C11—24no—
350C22×C11—48no—
351C22×C11—42no—
352C22×C11—42no—
353C22×C11#42112yes—
354C22×C11C22×C22⋊C411yescharacteristic
355C2×D11—21no—
356C2×D11—21no—
357C2×D11—21no—
358C2×D11—21no—
359C2×D11—21no—
360C2×D11—44no—
361C2×D11#40712yes—
362C4×C11—21no—
363C4×C11—21no—
364C4×C11—21no—
365C4×C11—21no—
366C4×C11—42no—
367C4×C11C22×M1612yes—
368C4×C11#57512yes—
369Dic11—24no—
370Dic11—21no—
371Dic11—21no—
372Dic11—21no—
373Dic11—21no—
374Dic11—21no—
375Dic11—42no—
376Dic11#40712yes—
377C2×#41—112no—
378C2×#41—112no—
379C2×#41—221no—
380C2×#41—221no—
381C2×#41—228no—
382C22×Q8—111no—
383C22×D4—221no—
384C22×D4C4×D1111yescharacteristic
385C23×C4—21no—
386C23×C4—111no—
387C23×C4—111no—
388C23×C4—111no—
389C23×C4—221no—
390C23×C4—221no—
391C2×M16—21no—
392C2×M16—221no—
393C22×C8—222no—
394C4×Q8—112no—
395C4×Q8—112no—
396C4×Q8—112no—
397C4×Q8—112no—
398C4×Q8—221no—
399C4×Q8—221no—
400C4×Q8—221no—
401C4×Q8—221no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—112no—
405C4×D4—112no—
406C4×D4—221no—
407C4×D4—221no—
408C4×D4—222no—
409C4×D4—222no—
410C4×D4—222no—
411C4×D4—222no—
412C4×D4—222no—
413C4×D4—222no—
414C4×D4—222no—
415C4×D4—222no—
416C4×D4C4×D1112yes—
417C4×D4C22×D1112yes—
418#117—112no—
419#117—112no—
420#117—222no—
421#117—222no—
422#117—222no—
423#117—222no—
424#117—221no—
425#117—221no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4C4×D1111yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C42—111no—
434C2×C42—111no—
435C2×C42—111no—
436C2×C42—111no—
437C2×C42—111no—
438C2×C42—111no—
439C2×C42—111no—
440C2×C42—111no—
441C2×C42—111no—
442C2×C42—111no—
443C2×C42—111no—
444C2×C42—222no—
445C2×C42—222no—
446C2×C42—222no—
447C2×C42—222no—
448C2×C42—221no—
449C2×C42—221no—
450C2×C42—221no—
451C2×C42C22×D1111yescharacteristic
452C4⋊C8—112no—
453C4⋊C8—222no—
454C4⋊C8—222no—
455C4⋊C8—222no—
456C4⋊C8C22×D1112yes—
457C22⋊C8—21no—
458C22⋊C8—222no—
459C22⋊C8—222no—
460C22⋊C8—222no—
461C22⋊C8—221no—
462#97—21no—
463#97—21no—
464#97—222no—
465#97—221no—
466#97—221no—
467C4×C8—112no—
468C4×C8C22×D1112yes—
469C2×C11—22no—
470C2×C11—44no—
471C2×C11C2×#40711yescharacteristic
472C2×C11#289611yescharacteristic
473C2×C11C2×#42111yescharacteristic
474D11—22no—
475D11—41no—
476C24—21no—
477C24—111no—
478#41—118no—
479#41—224no—
480#41—224no—
481#41—228no—
482#41—228no—
483#41—224no—
484C2×Q8—112no—
485C2×Q8—224no—
486C2×Q8—221no—
487C2×D4—24no—
488C2×D4—21no—
489C2×D4—222no—
490C2×D4—222no—
491C2×D4—228no—
492C2×D4C2×C4×D1112yes—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—44no—
497C22×C4—111no—
498C22×C4—111no—
499C22×C4—111no—
500C22×C4—111no—
501C22×C4—111no—
502C22×C4—111no—
503C22×C4—111no—
504C22×C4—111no—
505C22×C4—111no—
506C22×C4—111no—
507C22×C4—111no—
508C22×C4—111no—
509C22×C4—111no—
510C22×C4—111no—
511C22×C4—111no—
512C22×C4—224no—
513C22×C4—222no—
514C22×C4—222no—
515C22×C4—222no—
516C22×C4—222no—
517C22×C4—228no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—442no—
521C22×C4—442no—
522C22×C4—444no—
523C22×C4C2×C4×D1111yescharacteristic
524C22×C4D4×D1111yescharacteristic
525C22×C4D4×D1111yescharacteristic
526M16—42no—
527M16—442no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—222no—
531C2×C8—222no—
532C2×C8—444no—
533C4⋊C4—21no—
534C4⋊C4—112no—
535C4⋊C4—222no—
536C4⋊C4—222no—
537C4⋊C4—221no—
538C4⋊C4—222no—
539C4⋊C4—222no—
540C4⋊C4C2×C4×D1112yes—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—222no—
544C22⋊C4—222no—
545C22⋊C4—222no—
546C22⋊C4—222no—
547C42—111no—
548C42—111no—
549C42—111no—
550C42—111no—
551C42—111no—
552C42—111no—
553C42—111no—
554C42—111no—
555C42—111no—
556C42—111no—
557C42—111no—
558C42—111no—
559C42—222no—
560C42—222no—
561C42—222no—
562C42—222no—
563C42—222no—
564C42—222no—
565C42C2×C4×D1111yescharacteristic
566C42D4×D1111yescharacteristic
567C42D4×D1111yescharacteristic
568C42C23×D1111yescharacteristic
569C11#1745211yescharacteristic, complemented, Sylow
570C23—24no—
571C23—22no—
572C23—42no—
573C23—42no—
574C23—111no—
575C23—111no—
576C23—222no—
577C23—222no—
578C23—441no—
579C23C22⋊C4×D1111yescharacteristic
580Q8—114no—
581Q8—224no—
582Q8—222no—
583D4—24no—
584D4—22no—
585D4—228no—
586D4—228no—
587D4M16×D1114yes—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—44no—
593C2×C4—42no—
594C2×C4—44no—
595C2×C4—111no—
596C2×C4—114no—
597C2×C4—111no—
598C2×C4—111no—
599C2×C4—111no—
600C2×C4—111no—
601C2×C4—111no—
602C2×C4—222no—
603C2×C4—222no—
604C2×C4—222no—
605C2×C4—228no—
606C2×C4—224no—
607C2×C4—228no—
608C2×C4—222no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—222no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—444no—
622C2×C4—444no—
623C2×C4—442no—
624C2×C4C22⋊C4×D1111yescharacteristic
625C2×C4C22⋊C4×D1111yescharacteristic
626C2×C4C22⋊C4×D1111yescharacteristic
627C2×C4C22×C4×D1111yescharacteristic
628C2×C4C2×D4×D1111yescharacteristic
629C2×C4C2×D4×D1111yescharacteristic
630C8—42no—
631C8—42no—
632C8—442no—
633C8—442no—
634C22—21no—
635C22—21no—
636C22—24no—
637C22—48no—
638C22—42no—
639C22—42no—
640C22—112no—
641C22—221no—
642C22—221no—
643C22—221no—
644C22—221no—
645C22—221no—
646C22—444no—
647C22#1062243412yes—
648C22C2×C22⋊C4×D1111yescharacteristic
649C4—21no—
650C4—21no—
651C4—21no—
652C4—21no—
653C4—42no—
654C4—112no—
655C4—221no—
656C4—224no—
657C4—221no—
658C4—221no—
659C4—221no—
660C4—221no—
661C4—442no—
662C4C2×M16×D1112yes—
663C4#1062330412yes—
664C2—22no—
665C2—44no—
666C2—222no—
667C2—441no—
668C2D11×#40711yescharacteristic
669C2#1307713011yescharacteristic
670C2C2×#1062243411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1490C2
socleC22×C11C22×C22⋊C4
prime radicalC22×#4341C4
cosocleC42×C11C24
hypercenter#1490D11
hypocenterC11#17452
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1490

Complements

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

NH ≅ G/Ntype
2. #13077247C2semidirect
3. D11×#432C2semidirect
4. #13067064C2semidirect
5. #13067062C2semidirect
6. #13067059C2semidirect
7. #13067047C2semidirect
8. #13067000C2semidirect
9. C11×#1490C2semidirect
35. #10622448C22semidirect
36. D11×C4⋊C8C22semidirect
43. #10622298C22semidirect
44. #10622298C22semidirect
45. C11×D4⋊C8C22semidirect
46. D4⋊(C11⋊C8)C22semidirect
47. #10622122C22semidirect
48. #10622094C22semidirect
173. #4341M16semidirect
241. #1490D11semidirect
346. D4⋊C8C2×D11semidirect
569. C11#17452semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43412
#130772472
D11×#4322
#130670642
#130670622
#130670592
#130670472
#130670002
C11×#14902
#1745211