Finite Group Databasebeta

← #14720184

Subgroups — #14720184

Order 2816.

1268 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4343C211yesmaximal, characteristic
2#13077248C211yesmaximal, characteristic, complemented
3D11×#431C211yesmaximal, characteristic, complemented
4#13067049C214yesmaximal, complemented
5#13067045C211yesmaximal, characteristic, complemented
6#13067042C211yesmaximal, characteristic, complemented
7#13067040C211yesmaximal, characteristic, complemented
8#13066997C214yesmaximal, complemented
9C11×#1487C211yesmaximal, 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×#431C2211yescharacteristic
30C11×#423C2211yescharacteristic
31#10622739—21no—
32M16×Dic11—21no—
33#10622538C2211yescharacteristic
34#10622537C2211yescharacteristic
35#10622448—21no—
36#10622448C2212yescomplemented
37#10622446—21no—
38#10622446—21no—
39#10622446C2212yescomplemented
40D11×C4⋊C8—21no—
41D11×C22⋊C8—21no—
42#10622331—21no—
43#10622298C2212yescomplemented
44C4×C8×D11C2212yescomplemented
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⋊C8—21no—
125C11×C4⋊C8—21no—
126C11×C4⋊C8C2312yes—
127C11×C22⋊C8—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—
135C8×Dic11—22no—
136C8×Dic11—22no—
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2312yes—
140C4×C11⋊C8C2312yes—
141#17443—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—22no—
177C2×C4×D11—22no—
178C2×C4×D11—42no—
179C2×C4×D11—44no—
180C2×C4×D11—42no—
181C2×C4×D11—42no—
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×D11C22×C411yescharacteristic
189C2×C4×D11C22×C411yescharacteristic
190C2×C4×D11C2×D411yescharacteristic
191C2×C4×D11C2×D411yescharacteristic
192C2×C4×D11C2×D411yescharacteristic
193C2×C4×D11C2×D411yescharacteristic
194C11×M16—42no—
195C2×C8×C11—22no—
196C2×C8×C11—22no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—22no—
200C11×C4⋊C4C22×C412yes—
201C42×C11—22no—
202C42×C11—22no—
203C42×C11C22×C411yescharacteristic
204C42×C11C2×D411yescharacteristic
205C42×C11C2×D411yescharacteristic
206C42×C11C2411yescharacteristic
207(C2×D11)⋊C4—22no—
208(C2×D11)⋊C4—22no—
209(C2×D11)⋊C4—22no—
210(C2×D11)⋊C4—22no—
211(C2×D11)⋊C4—22no—
212(C2×D11)⋊C4—22no—
213C4⋊Dic11—22no—
214C4⋊Dic11—22no—
215C4⋊Dic11—21no—
216C4⋊Dic11C22×C412yes—
217C4×Dic11—22no—
218C4×Dic11—22no—
219C4×Dic11—22no—
220C4×Dic11—22no—
221C4×Dic11C22⋊C411yescharacteristic
222C4×Dic11C22⋊C411yescharacteristic
223C4×Dic11C22⋊C411yescharacteristic
224C4×Dic11C22⋊C411yescharacteristic
225C4×Dic11C22⋊C411yescharacteristic
226C4×Dic11C22⋊C411yescharacteristic
227C4×Dic11C22×C411yescharacteristic
228C4×Dic11C22×C411yescharacteristic
229C4×Dic11C2×D411yescharacteristic
230C4×Dic11C2×D411yescharacteristic
231C4×Dic11C2×D411yescharacteristic
232C4×Dic11C2×D411yescharacteristic
233#4318—42no—
234C2×C11⋊C8—22no—
235C2×C11⋊C8—22no—
236C8×D11—44no—
237C2×C4×#41—111no—
238#2920—111no—
239C2×#431—111no—
240#1488—114no—
241#1487—111no—
242#1487D1111yescharacteristic, complemented
243#1486—111no—
244#1486—111no—
245#1476—114no—
246C23×C11C2×C22⋊C411yescharacteristic
247C22×D11—24no—
248C22×D11—22no—
249C22×D11—22no—
250C22×D11—22no—
251C22×D11—41no—
252C22×D11—42no—
253C22×D11—42no—
254C22×D11C2×C22⋊C411yescharacteristic
255C22×D11C2×C22⋊C411yescharacteristic
256Q8×C11—24no—
257Q8×C11—22no—
258Q8×C11C2×M1614yes—
259C2×C4×C11—24no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—41no—
264C2×C4×C11—42no—
265C2×C4×C11C2×C22⋊C411yescharacteristic
266C2×C4×C11C2×C22⋊C411yescharacteristic
267C2×C4×C11C2×C22⋊C411yescharacteristic
268C2×C4×C11#13512yes—
269C2×C4×C11#13512yes—
270C2×C4×C11C23×C411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—42no—
278C2×Dic11C2×C22⋊C411yescharacteristic
279C2×Dic11C2×C22⋊C411yescharacteristic
280C2×Dic11C2×C22⋊C411yescharacteristic
281C2×Dic11C2×C22⋊C411yescharacteristic
282C2×Dic11C2×C22⋊C411yescharacteristic
283C2×Dic11C2×C22⋊C411yescharacteristic
284D44—28no—
285D44—24no—
286D44—28no—
287D44—22no—
288D44C2×M1614yes—
289C4×D11—28no—
290C4×D11—22no—
291C4×D11—22no—
292C4×D11—21no—
293C4×D11—21no—
294C4×D11—21no—
295C4×D11—21no—
296C4×D11—22no—
297C4×D11—22no—
298C4×D11—28no—
299C4×D11—22no—
300C4×D11—22no—
301C4×D11—22no—
302C4×D11—41no—
303C4×D11—41no—
304C4×D11—44no—
305C4×D11—42no—
306C4×D11—42no—
307C4×D11—44no—
308C4×D11—44no—
309C4×D11C2×M1614yes—
310C8×C11—42no—
311C8×C11—42no—
312C11⋊C8—42no—
313C11⋊C8—42no—
314C22×#41—111no—
315C4×#41—112no—
316C4×#41—112no—
317C4×#41—112no—
318C4×#41—112no—
319C4×#41—221no—
320C4×#41—221no—
321C4×#41—221no—
322C4×#41—221no—
323C2×C4×Q8—111no—
324C2×C4×Q8C2×D1111yescharacteristic
325C2×C4×D4—111no—
326C2×C4×D4—111no—
327C2×C4×D4—221no—
328C2×C4×D4—221no—
329C2×#117—111no—
330C2×#117—221no—
331C22×C42—111no—
332C22×C42—221no—
333#432—112no—
334#432—221no—
335#431—111no—
336#431—112no—
337#431—112no—
338#431—221no—
339#431—221no—
340#431—221no—
341#431C2×D1111yescharacteristic
342#423—111no—
343#423C2×D1111yescharacteristic
344C2×C4⋊C8—221no—
345#407—221no—
346C2×C22⋊C8—221no—
347C4×M16—221no—
348C2×C4×C8—112no—
349Q8⋊C8—114no—
350Q8⋊C8C2×D1114yescomplemented
351D4⋊C8—114no—
352D4⋊C8—114no—
353C22×C11—21no—
354C22×C11—21no—
355C22×C11#41612yes—
356C22×C11C22×C22⋊C411yescharacteristic
357C2×D11—21no—
358C2×D11—21no—
359C2×D11—24no—
360C2×D11—21no—
361C2×D11—21no—
362C2×D11—21no—
363C2×D11—44no—
364C2×D11—48no—
365C2×D11—42no—
366C2×D11—42no—
367C2×D11#40712yes—
368C4×C11—24no—
369C4×C11—21no—
370C4×C11—21no—
371C4×C11—21no—
372C4×C11—42no—
373C4×C11#41612yes—
374C4×C11C22×M1612yes—
375C4×C11C2×#13511yescharacteristic
376C4×C11C2×#13511yescharacteristic
377Dic11—21no—
378Dic11—21no—
379Dic11—21no—
380Dic11—21no—
381Dic11—42no—
382Dic11#40712yes—
383Dic11#42112yes—
384C2×#41—112no—
385C2×#41—112no—
386C2×#41—221no—
387C2×#41—221no—
388C2×#41—228no—
389C22×Q8C4×D1111yescharacteristic
390C22×D4—111no—
391C22×D4—221no—
392C23×C4—111no—
393C23×C4—111no—
394C23×C4—111no—
395C23×C4—221no—
396C23×C4—221no—
397C23×C4—221no—
398C2×M16—21no—
399C2×M16—221no—
400C22×C8—222no—
401C4×Q8—21no—
402C4×Q8—21no—
403C4×Q8—112no—
404C4×Q8—112no—
405C4×Q8—221no—
406C4×Q8—221no—
407C4×Q8C4×D1112yes—
408C4×Q8C22×D1112yes—
409C4×D4—112no—
410C4×D4—112no—
411C4×D4—112no—
412C4×D4—112no—
413C4×D4—222no—
414C4×D4—222no—
415C4×D4—222no—
416C4×D4—222no—
417C4×D4—221no—
418C4×D4—221no—
419C4×D4—222no—
420C4×D4—222no—
421C4×D4—222no—
422C4×D4—222no—
423C4×D4—221no—
424C4×D4—221no—
425#117—112no—
426#117—112no—
427#117—222no—
428#117—222no—
429#117—222no—
430#117—222no—
431#117—221no—
432#117—221no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—111no—
435C2×C4⋊C4—221no—
436C2×C4⋊C4C4×D1111yescharacteristic
437C2×C22⋊C4—221no—
438C2×C22⋊C4—221no—
439C2×C22⋊C4—221no—
440C2×C42—21no—
441C2×C42—111no—
442C2×C42—111no—
443C2×C42—111no—
444C2×C42—111no—
445C2×C42—111no—
446C2×C42—111no—
447C2×C42—111no—
448C2×C42—111no—
449C2×C42—111no—
450C2×C42—111no—
451C2×C42—111no—
452C2×C42—222no—
453C2×C42—222no—
454C2×C42—222no—
455C2×C42—222no—
456C2×C42—221no—
457C2×C42—221no—
458C2×C42C22×D1111yescharacteristic
459C4⋊C8—21no—
460C4⋊C8—21no—
461C4⋊C8—112no—
462C4⋊C8—222no—
463C4⋊C8—221no—
464C4⋊C8—221no—
465C4⋊C8C22×D1112yes—
466C22⋊C8—21no—
467C22⋊C8—222no—
468C22⋊C8—222no—
469C22⋊C8—222no—
470C22⋊C8—221no—
471#97—222no—
472C4×C8—112no—
473C4×C8—222no—
474C4×C8—222no—
475C4×C8C22×D1112yes—
476C2×C11—22no—
477C2×C11C2×#40711yescharacteristic
478C2×C11C2×#41611yescharacteristic
479C2×C11C2×#42111yescharacteristic
480D11—22no—
481D11—41no—
482D11—44no—
483C24—111no—
484C24—221no—
485#41—118no—
486#41—224no—
487#41—224no—
488#41—228no—
489#41—228no—
490#41—224no—
491C2×Q8—24no—
492C2×Q8—21no—
493C2×Q8C2×C4×D1112yes—
494C2×D4—112no—
495C2×D4—224no—
496C2×D4—222no—
497C2×D4—222no—
498C2×D4—228no—
499C2×D4—221no—
500C22×C4—21no—
501C22×C4—21no—
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—111no—
513C22×C4—111no—
514C22×C4—111no—
515C22×C4—111no—
516C22×C4—111no—
517C22×C4—222no—
518C22×C4—222no—
519C22×C4—224no—
520C22×C4—222no—
521C22×C4—222no—
522C22×C4—228no—
523C22×C4—222no—
524C22×C4—222no—
525C22×C4—221no—
526C22×C4—222no—
527C22×C4—222no—
528C22×C4—442no—
529C22×C4—444no—
530C22×C4—442no—
531C22×C4—442no—
532C22×C4C2×C4×D1111yescharacteristic
533C22×C4D4×D1111yescharacteristic
534C22×C4D4×D1111yescharacteristic
535M16—42no—
536M16—442no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—222no—
540C2×C8—222no—
541C2×C8—444no—
542C4⋊C4—22no—
543C4⋊C4—21no—
544C4⋊C4—22no—
545C4⋊C4—112no—
546C4⋊C4—222no—
547C4⋊C4—222no—
548C4⋊C4—221no—
549C4⋊C4C2×C4×D1112yes—
550C22⋊C4—222no—
551C22⋊C4—222no—
552C22⋊C4—222no—
553C22⋊C4—222no—
554C22⋊C4—222no—
555C22⋊C4—222no—
556C42—22no—
557C42—22no—
558C42—111no—
559C42—111no—
560C42—111no—
561C42—111no—
562C42—111no—
563C42—111no—
564C42—111no—
565C42—111no—
566C42—111no—
567C42—111no—
568C42—111no—
569C42—111no—
570C42—222no—
571C42—222no—
572C42—222no—
573C42—222no—
574C42C2×C4×D1111yescharacteristic
575C42D4×D1111yescharacteristic
576C42D4×D1111yescharacteristic
577C42C23×D1111yescharacteristic
578C11#1744311yescharacteristic, complemented, Sylow
579C23—111no—
580C23—111no—
581C23—222no—
582C23—224no—
583C23—222no—
584C23—222no—
585C23—441no—
586C23—442no—
587C23—442no—
588C23C22⋊C4×D1111yescharacteristic
589Q8—24no—
590Q8—22no—
591Q8M16×D1114yes—
592D4—114no—
593D4—228no—
594D4—228no—
595D4—224no—
596D4—222no—
597C2×C4—24no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—41no—
602C2×C4—42no—
603C2×C4—111no—
604C2×C4—111no—
605C2×C4—114no—
606C2×C4—111no—
607C2×C4—111no—
608C2×C4—111no—
609C2×C4—111no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—228no—
614C2×C4—222no—
615C2×C4—228no—
616C2×C4—222no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—222no—
620C2×C4—221no—
621C2×C4—221no—
622C2×C4—221no—
623C2×C4—221no—
624C2×C4—222no—
625C2×C4—222no—
626C2×C4—222no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—444no—
630C2×C4—444no—
631C2×C4—442no—
632C2×C4—442no—
633C2×C4—442no—
634C2×C4—444no—
635C2×C4C22⋊C4×D1111yescharacteristic
636C2×C4C22⋊C4×D1111yescharacteristic
637C2×C4C22⋊C4×D1111yescharacteristic
638C2×C4#6696912yes—
639C2×C4#6697212yes—
640C2×C4C22×C4×D1111yescharacteristic
641C2×C4C2×D4×D1111yescharacteristic
642C2×C4C2×D4×D1111yescharacteristic
643C8—42no—
644C8—42no—
645C8—442no—
646C8—442no—
647C22—21no—
648C22—21no—
649C22—112no—
650C22—221no—
651C22—221no—
652C22—224no—
653C22—221no—
654C22—221no—
655C22—221no—
656C22—444no—
657C22—448no—
658C22—442no—
659C22—442no—
660C22#1062241712yes—
661C22C2×C22⋊C4×D1111yescharacteristic
662C4—24no—
663C4—21no—
664C4—21no—
665C4—21no—
666C4—42no—
667C4—112no—
668C4—112no—
669C4—221no—
670C4—221no—
671C4—221no—
672C4—221no—
673C4—442no—
674C4#1062241712yes—
675C4C2×M16×D1112yes—
676C4C2×#6696911yescharacteristic
677C4C2×#6697211yescharacteristic
678C2—22no—
679C2—222no—
680C2—441no—
681C2—444no—
682C2D11×#40711yescharacteristic
683C2C2×#1062241711yescharacteristic
684C2D11×#42111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1487C2
socleC22×C11C22×C22⋊C4
prime radicalC22×#4343C4
cosocleC42×C11C24
hypercenter#1487D11
hypocenterC11#17443
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
2. #13077248C2semidirect
3. D11×#431C2semidirect
4. #13067049C2semidirect
5. #13067045C2semidirect
6. #13067042C2semidirect
7. #13067040C2semidirect
8. #13066997C2semidirect
9. C11×#1487C2semidirect
36. #10622448C22semidirect
39. #10622446C22semidirect
43. #10622298C22semidirect
44. C4×C8×D11C22semidirect
45. C11×Q8⋊C8C22semidirect
46. Q8⋊(C11⋊C8)C22semidirect
47. #10622121C22semidirect
48. #10622097C22semidirect
161. #4343M16semidirect
242. #1487D11semidirect
350. Q8⋊C8C2×D11semidirect
578. C11#17443semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43432
#130772482
D11×#4312
#130670492
#130670452
#130670422
#130670402
#130669972
C11×#14872
#1744311