Finite Group Databasebeta

← #14720240

Subgroups — #14720240

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×#4343C211yesmaximal, characteristic
2#13077247C211yesmaximal, characteristic, complemented
3D11×#432C211yesmaximal, characteristic, complemented
4#13067063C211yesmaximal, characteristic, complemented
5#13067060C211yesmaximal, characteristic, complemented
6#13067058C211yesmaximal, characteristic, complemented
7#13067049C214yesmaximal, complemented
8#13067002C214yesmaximal, complemented
9C11×#1491C211yesmaximal, characteristic, complemented
10C22×#4343C411yescharacteristic
11C2×C4×Q8×C11C2211yescharacteristic
12C2×Q8×Dic11C411yescharacteristic
13C4×#4343—21no—
14C4×#4343—21no—
15C4×#4343—21no—
16C4×#4343—21no—
17C4×#4343C412yes—
18C4×#4343C412yes—
19C4×#4343C2212yes—
20C4×#4343C2212yes—
21C2×#66946—21no—
22C2×#66946C411yescharacteristic
23C2×#66945—21no—
24C2×#66945C411yescharacteristic
25C2×C4×D44—21no—
26C2×C4×D44C2211yescharacteristic
27C2×C42×D11—21no—
28C2×C42×D11C2211yescharacteristic
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×Q8⋊C8C2214yescomplemented
46Q8⋊(C11⋊C8)C2214yescomplemented
47#10622121C2214yescomplemented
48#10622097C2214yescomplemented
49C22×Q8×C11C2×C411yescharacteristic
50C2×#4343—28no—
51C2×#4343—21no—
52C2×#4343—21no—
53C2×#4343C2×C412yes—
54C2×#4343C2×C412yes—
55C22×D44—21no—
56C22×D44C2×C411yescharacteristic
57C22×C4×D11—21no—
58C22×C4×D11—21no—
59C22×C4×D11—21no—
60C22×C4×D11C2×C411yescharacteristic
61C22×C4×D11D411yescharacteristic
62C22×C4×D11D411yescharacteristic
63C2×C11×M16—21no—
64C4×Q8×C11—21no—
65C4×Q8×C11—21no—
66C4×Q8×C11C2×C412yes—
67C4×Q8×C11C2312yes—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2×C411yescharacteristic
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72Q8×Dic11—21no—
73Q8×Dic11—21no—
74Q8×Dic11C2×C412yes—
75Q8×Dic11C2×C412yes—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11C2×C411yescharacteristic
81C2×C4×Dic11—21no—
82C2×C4×Dic11—21no—
83C2×C4×Dic11C2×C411yescharacteristic
84C2×C4×Dic11D411yescharacteristic
85C2×C4×Dic11D411yescharacteristic
86C2×#4318—21no—
87C2×C8×D11—22no—
88#66946—22no—
89#66946—22no—
90#66946—22no—
91#66946—22no—
92#66946—21no—
93#66946—21no—
94#66946C2×C412yes—
95#66946C2×C412yes—
96#66945—21no—
97#66945—21no—
98#66945—22no—
99#66945—22no—
100#66945—22no—
101#66945—22no—
102#66945C2×C412yes—
103#66945C2×C412yes—
104C4×D44—22no—
105C4×D44—22no—
106C4×D44—22no—
107C4×D44—22no—
108C4×D44—21no—
109C4×D44—21no—
110C4×D44C2×C412yes—
111C4×D44C2312yes—
112C42×D11—22no—
113C42×D11—22no—
114C42×D11—22no—
115C42×D11—22no—
116C42×D11C2×C411yescharacteristic
117C42×D11C2×C411yescharacteristic
118C42×D11D411yescharacteristic
119C42×D11D411yescharacteristic
120C42×D11D411yescharacteristic
121C42×D11D411yescharacteristic
122C42×D11C2311yescharacteristic
123C42×D11C2311yescharacteristic
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
142C23×D11—21no—
143C23×D11C22⋊C411yescharacteristic
144C2×Q8×C11—24no—
145C2×Q8×C11—21no—
146C2×Q8×C11C22×C412yes—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×Dic11—21no—
153C22×Dic11C22⋊C411yescharacteristic
154C22×Dic11C22⋊C411yescharacteristic
155C22×Dic11C22⋊C411yescharacteristic
156#4343—28no—
157#4343—28no—
158#4343—24no—
159#4343—24no—
160#4343—24no—
161#4343M1618yescomplemented
162C2×D44—28no—
163C2×D44—24no—
164C2×D44—22no—
165C2×D44—22no—
166C2×D44—21no—
167C2×D44C22×C412yes—
168C2×C4×D11—28no—
169C2×C4×D11—22no—
170C2×C4×D11—22no—
171C2×C4×D11—24no—
172C2×C4×D11—22no—
173C2×C4×D11—22no—
174C2×C4×D11—22no—
175C2×C4×D11—22no—
176C2×C4×D11—42no—
177C2×C4×D11—42no—
178C2×C4×D11—44no—
179C2×C4×D11—44no—
180C2×C4×D11C22⋊C411yescharacteristic
181C2×C4×D11C22⋊C411yescharacteristic
182C2×C4×D11C22⋊C411yescharacteristic
183C2×C4×D11C22⋊C411yescharacteristic
184C2×C4×D11C22⋊C411yescharacteristic
185C2×C4×D11C22⋊C411yescharacteristic
186C2×C4×D11C22×C411yescharacteristic
187C2×C4×D11C22×C411yescharacteristic
188C2×C4×D11C2×D411yescharacteristic
189C2×C4×D11C2×D411yescharacteristic
190C2×C4×D11C2×D411yescharacteristic
191C2×C4×D11C2×D411yescharacteristic
192C11×M16—42no—
193C2×C8×C11—22no—
194C2×C8×C11—22no—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4C22×C412yes—
199C42×C11—22no—
200C42×C11—22no—
201C42×C11C22×C411yescharacteristic
202C42×C11C2×D411yescharacteristic
203C42×C11C2×D411yescharacteristic
204C42×C11C2411yescharacteristic
205(C2×D11)⋊C4—22no—
206(C2×D11)⋊C4—22no—
207(C2×D11)⋊C4—22no—
208(C2×D11)⋊C4—22no—
209(C2×D11)⋊C4—22no—
210(C2×D11)⋊C4—22no—
211C4⋊Dic11—22no—
212C4⋊Dic11—22no—
213C4⋊Dic11—21no—
214C4⋊Dic11C22×C412yes—
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#1491D1111yescharacteristic, complemented
240#1490—111no—
241#1490—111no—
242#1488—114no—
243#1477—114no—
244C23×C11C2×C22⋊C411yescharacteristic
245C22×D11—24no—
246C22×D11—22no—
247C22×D11—22no—
248C22×D11—22no—
249C22×D11—41no—
250C22×D11—42no—
251C22×D11—42no—
252C22×D11C2×C22⋊C411yescharacteristic
253C22×D11C2×C22⋊C411yescharacteristic
254Q8×C11—24no—
255Q8×C11—22no—
256Q8×C11C2×M1614yes—
257C2×C4×C11—24no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—42no—
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
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—41no—
274C2×Dic11—42no—
275C2×Dic11C2×C22⋊C411yescharacteristic
276C2×Dic11C2×C22⋊C411yescharacteristic
277C2×Dic11C2×C22⋊C411yescharacteristic
278C2×Dic11C2×C22⋊C411yescharacteristic
279C2×Dic11C2×C22⋊C411yescharacteristic
280C2×Dic11C2×C22⋊C411yescharacteristic
281D44—28no—
282D44—24no—
283D44—28no—
284D44—22no—
285D44C2×M1614yes—
286C4×D11—28no—
287C4×D11—22no—
288C4×D11—22no—
289C4×D11—22no—
290C4×D11—22no—
291C4×D11—28no—
292C4×D11—22no—
293C4×D11—41no—
294C4×D11—41no—
295C4×D11—41no—
296C4×D11—41no—
297C4×D11—41no—
298C4×D11—41no—
299C4×D11—44no—
300C4×D11—44no—
301C4×D11—44no—
302C4×D11—44no—
303C4×D11C2×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×Q8C2×D1111yescharacteristic
319C2×C4×D4—111no—
320C2×C4×D4—111no—
321C2×C4×D4—221no—
322C2×C4×D4—221no—
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⋊C8C2×D1114yescomplemented
345D4⋊C8—114no—
346D4⋊C8—114no—
347C22×C11—21no—
348C22×C11—21no—
349C22×C11#42112yes—
350C22×C11C22×C22⋊C411yescharacteristic
351C2×D11—21no—
352C2×D11—21no—
353C2×D11—24no—
354C2×D11—21no—
355C2×D11—21no—
356C2×D11—21no—
357C2×D11—44no—
358C2×D11—48no—
359C2×D11—42no—
360C2×D11—42no—
361C2×D11#40712yes—
362C4×C11—24no—
363C4×C11—21no—
364C4×C11—21no—
365C4×C11—21no—
366C4×C11—21no—
367C4×C11—42no—
368C4×C11C22×M1612yes—
369C4×C11#57512yes—
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×Q8C4×D1111yescharacteristic
383C22×D4—111no—
384C22×D4—221no—
385C23×C4—111no—
386C23×C4—111no—
387C23×C4—111no—
388C23×C4—221no—
389C23×C4—221no—
390C23×C4—221no—
391C2×M16—21no—
392C2×M16—221no—
393C22×C8—222no—
394C4×Q8—21no—
395C4×Q8—21no—
396C4×Q8—112no—
397C4×Q8—112no—
398C4×Q8—221no—
399C4×Q8—221no—
400C4×Q8C4×D1112yes—
401C4×Q8C22×D1112yes—
402C4×D4—112no—
403C4×D4—112no—
404C4×D4—112no—
405C4×D4—112no—
406C4×D4—222no—
407C4×D4—222no—
408C4×D4—222no—
409C4×D4—222no—
410C4×D4—221no—
411C4×D4—221no—
412C4×D4—222no—
413C4×D4—222no—
414C4×D4—222no—
415C4×D4—222no—
416C4×D4—221no—
417C4×D4—221no—
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—21no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4C4×D1111yescharacteristic
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C42—21no—
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—111no—
445C2×C42—222no—
446C2×C42—222no—
447C2×C42—222no—
448C2×C42—222no—
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×C11C2×#40711yescharacteristic
471C2×C11#289611yescharacteristic
472C2×C11C2×#42111yescharacteristic
473D11—22no—
474D11—41no—
475D11—44no—
476C24—111no—
477C24—221no—
478#41—118no—
479#41—224no—
480#41—224no—
481#41—228no—
482#41—228no—
483#41—224no—
484C2×Q8—24no—
485C2×Q8—21no—
486C2×Q8C2×C4×D1112yes—
487C2×D4—112no—
488C2×D4—224no—
489C2×D4—222no—
490C2×D4—222no—
491C2×D4—228no—
492C2×D4—221no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—111no—
496C22×C4—111no—
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—222no—
511C22×C4—222no—
512C22×C4—224no—
513C22×C4—222no—
514C22×C4—222no—
515C22×C4—228no—
516C22×C4—221no—
517C22×C4—222no—
518C22×C4—222no—
519C22×C4—442no—
520C22×C4—442no—
521C22×C4—444no—
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—22no—
534C4⋊C4—21no—
535C4⋊C4—22no—
536C4⋊C4—112no—
537C4⋊C4—222no—
538C4⋊C4—222no—
539C4⋊C4—221no—
540C4⋊C4C2×C4×D1112yes—
541C22⋊C4—222no—
542C22⋊C4—222no—
543C22⋊C4—222no—
544C22⋊C4—222no—
545C22⋊C4—222no—
546C22⋊C4—222no—
547C42—22no—
548C42—22no—
549C42—111no—
550C42—111no—
551C42—111no—
552C42—111no—
553C42—111no—
554C42—111no—
555C42—111no—
556C42—111no—
557C42—111no—
558C42—111no—
559C42—111no—
560C42—111no—
561C42—222no—
562C42—222no—
563C42—222no—
564C42—222no—
565C42C2×C4×D1111yescharacteristic
566C42D4×D1111yescharacteristic
567C42D4×D1111yescharacteristic
568C42C23×D1111yescharacteristic
569C11#1745211yescharacteristic, complemented, Sylow
570C23—111no—
571C23—111no—
572C23—222no—
573C23—224no—
574C23—222no—
575C23—222no—
576C23—441no—
577C23—442no—
578C23—442no—
579C23C22⋊C4×D1111yescharacteristic
580Q8—24no—
581Q8—22no—
582Q8M16×D1114yes—
583D4—114no—
584D4—228no—
585D4—228no—
586D4—224no—
587D4—222no—
588C2×C4—24no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—42no—
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—228no—
604C2×C4—222no—
605C2×C4—228no—
606C2×C4—222no—
607C2×C4—222no—
608C2×C4—222no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—444no—
619C2×C4—444no—
620C2×C4—444no—
621C2×C4—441no—
622C2×C4—442no—
623C2×C4—444no—
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—112no—
637C22—221no—
638C22—221no—
639C22—224no—
640C22—221no—
641C22—221no—
642C22—221no—
643C22—444no—
644C22—448no—
645C22—442no—
646C22—442no—
647C22#1062243412yes—
648C22C2×C22⋊C4×D1111yescharacteristic
649C4—24no—
650C4—21no—
651C4—21no—
652C4—21no—
653C4—21no—
654C4—42no—
655C4—112no—
656C4—221no—
657C4—221no—
658C4—221no—
659C4—221no—
660C4—221no—
661C4—442no—
662C4C2×M16×D1112yes—
663C4#1062330812yes—
664C2—22no—
665C2—222no—
666C2—441no—
667C2—444no—
668C2D11×#40711yescharacteristic
669C2#1307713411yescharacteristic
670C2C2×#1062243411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1491C2
socleC22×C11C22×C22⋊C4
prime radicalC22×#4343C4
cosocleC42×C11C24
hypercenter#1491D11
hypocenterC11#17452
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1491

Complements

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

NH ≅ G/Ntype
2. #13077247C2semidirect
3. D11×#432C2semidirect
4. #13067063C2semidirect
5. #13067060C2semidirect
6. #13067058C2semidirect
7. #13067049C2semidirect
8. #13067002C2semidirect
9. C11×#1491C2semidirect
35. #10622448C22semidirect
36. D11×C4⋊C8C22semidirect
43. #10622298C22semidirect
44. #10622298C22semidirect
45. C11×Q8⋊C8C22semidirect
46. Q8⋊(C11⋊C8)C22semidirect
47. #10622121C22semidirect
48. #10622097C22semidirect
161. #4343M16semidirect
239. #1491D11semidirect
344. Q8⋊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×#43432
#130772472
D11×#4322
#130670632
#130670602
#130670582
#130670492
#130670022
C11×#14912
#1745211