Finite Group Databasebeta

← #14722365

Subgroups — #14722365

Order 2816.

1178 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic
2#13077248C211yesmaximal, characteristic
3#13077244C211yesmaximal, characteristic
4#13067331C214yesmaximal, complemented
5#13067302C211yesmaximal, characteristic, complemented
6#13067301C211yesmaximal, characteristic, complemented
7#13067300C211yesmaximal, characteristic, complemented
8#13067286C214yesmaximal, complemented
9C11×#1549C211yesmaximal, characteristic, complemented
10C22×Q8×D11—21no—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#66997—21no—
13D11×C4⋊Q8—21no—
14D11×C4⋊Q8—21no—
15D11×C4⋊Q8—21no—
16D11×C4⋊Q8—21no—
17D11×C4⋊Q8C412yes—
18D11×C4⋊Q8C412yes—
19D11×C4⋊Q8C2212yes—
20D11×C4⋊Q8C2212yes—
21C2×C4⋊C4×D11—21no—
22C2×C4⋊C4×D11C412yes—
23C2×#66941—21no—
24C2×#66941C412yes—
25C2×C42×D11C2211yescharacteristic
26C2×#66922C2211yescharacteristic
27C11×#431C2211yescharacteristic
28C11×#423C2211yescharacteristic
29#10622739—21no—
30M16×Dic11—21no—
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33#10622450C2212yes—
34#10622448—21no—
35#10622448C2212yes—
36#10622448C2212yes—
37#10622446—21no—
38#10622446C2212yes—
39#10622339—21no—
40#10622332—21no—
41C4×#4313—21no—
42#10622298—21no—
43C11×#332C2214yescomplemented
44#10622185C2214yescomplemented
45#10622124C2214yescomplemented
46#10622120C2214yescomplemented
47C22×Q8×C11—21no—
48C2×Q8×D11—22no—
49C2×Q8×D11—22no—
50C2×Q8×D11—22no—
51C2×Q8×D11—22no—
52C2×Q8×D11—48no—
53C22×C4×D11—22no—
54C22×C4×D11C2×C411yescharacteristic
55C22×C4×D11D411yescharacteristic
56C22×C4×D11D411yescharacteristic
57C22×Dic22—21no—
58C22×Dic22—22no—
59C2×C11×M16—21no—
60C11×C4⋊Q8—21no—
61C11×C4⋊Q8—21no—
62C11×C4⋊Q8C2×C412yes—
63C11×C4⋊Q8C2312yes—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4C2×C412yes—
66C2×C42×C11C2311yescharacteristic
67#66997—22no—
68#66997—22no—
69#66997—22no—
70#66997—22no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11C2×C412yes—
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4—22no—
75C2×C4×Dic11C2×C411yescharacteristic
76C2×C4×Dic11D411yescharacteristic
77C2×C4×Dic11D411yescharacteristic
78C2×#4318—21no—
79C2×#4313—22no—
80C4⋊C4×D11—22no—
81C4⋊C4×D11—22no—
82C4⋊C4×D11—22no—
83C4⋊C4×D11—22no—
84C4⋊C4×D11—22no—
85C4⋊C4×D11—22no—
86C4⋊C4×D11C2×C414yes—
87C4⋊C4×D11C2×C414yes—
88#66941—22no—
89#66941—22no—
90#66941—22no—
91#66941—22no—
92#66941—22no—
93#66941—22no—
94#66941C2×C414yes—
95#66941C2×C414yes—
96C42×D11C2×C411yescharacteristic
97C42×D11C2×C411yescharacteristic
98C42×D11D411yescharacteristic
99C42×D11D411yescharacteristic
100C42×D11D411yescharacteristic
101C42×D11D411yescharacteristic
102C42×D11C2311yescharacteristic
103C42×D11C2311yescharacteristic
104#66922—21no—
105#66922—21no—
106#66922C2×C412yes—
107#66922C2312yes—
108C11×C4⋊C8—21no—
109C11×C4⋊C8C2312yes—
110C11×C4⋊C8C2312yes—
111C11×C22⋊C8—21no—
112C4×C8×C11—21no—
113C22⋊(C11⋊C8)—21no—
114(C2×D11)⋊C8—22no—
115(C2×D11)⋊C8—22no—
116(C2×D11)⋊C8—22no—
117#66879—22no—
118#66879—22no—
119Dic11⋊C8—22no—
120C8×Dic11—22no—
121C4⋊(C11⋊C8)—21no—
122C4⋊(C11⋊C8)C2312yes—
123C4⋊(C11⋊C8)C2312yes—
124C4×C11⋊C8—21no—
125#17742—111nomaximal, Sylow
126C23×D11C22⋊C411yescharacteristic
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11—44no—
130C22×C4×C11—22no—
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×Dic11—22no—
135C22×Dic11C22⋊C411yescharacteristic
136C22×Dic11C22⋊C411yescharacteristic
137C22×Dic11C22⋊C411yescharacteristic
138Q8×D11—48no—
139Q8×D11—48no—
140Q8×D11—48no—
141Q8×D11—48no—
142C2×C4×D11—24no—
143C2×C4×D11—24no—
144C2×C4×D11—24no—
145C2×C4×D11—24no—
146C2×C4×D11—22no—
147C2×C4×D11—22no—
148C2×C4×D11—48no—
149C2×C4×D11C22⋊C411yescharacteristic
150C2×C4×D11C22⋊C411yescharacteristic
151C2×C4×D11C22⋊C411yescharacteristic
152C2×C4×D11C22⋊C411yescharacteristic
153C2×C4×D11C22⋊C411yescharacteristic
154C2×C4×D11C22⋊C411yescharacteristic
155C2×C4×D11C22×C411yescharacteristic
156C2×C4×D11C22×C411yescharacteristic
157C2×C4×D11C2×D411yescharacteristic
158C2×C4×D11C2×D411yescharacteristic
159C2×C4×D11C2×D411yescharacteristic
160C2×C4×D11C2×D411yescharacteristic
161C2×Dic22—24no—
162C2×Dic22—24no—
163C2×Dic22—22no—
164C2×Dic22—22no—
165C2×Dic22—44no—
166C2×Dic22—48no—
167C11×M16—42no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4C22×C414yes—
174C42×C11C22×C411yescharacteristic
175C42×C11C2×D411yescharacteristic
176C42×C11C2×D411yescharacteristic
177C42×C11C2411yescharacteristic
178C4⋊Dic11—22no—
179C4⋊Dic11—22no—
180C4⋊Dic11—22no—
181C4⋊Dic11C22×C414yes—
182Dic11⋊C4—24no—
183Dic11⋊C4—24no—
184Dic11⋊C4—24no—
185Dic11⋊C4—24no—
186C4×Dic11C22⋊C411yescharacteristic
187C4×Dic11C22⋊C411yescharacteristic
188C4×Dic11C22⋊C411yescharacteristic
189C4×Dic11C22⋊C411yescharacteristic
190C4×Dic11C22⋊C411yescharacteristic
191C4×Dic11C22⋊C411yescharacteristic
192C4×Dic11C22×C411yescharacteristic
193C4×Dic11C22×C411yescharacteristic
194C4×Dic11C2×D411yescharacteristic
195C4×Dic11C2×D411yescharacteristic
196C4×Dic11C2×D411yescharacteristic
197C4×Dic11C2×D411yescharacteristic
198#4318—42no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—22no—
201#4313—44no—
202C22×C4⋊Q8—111no—
203#2920—111no—
204#2920—111no—
205#1556—114no—
206#1549—111no—
207#1549—111no—
208#1549—111no—
209#1549D1111yescharacteristic, complemented
210#1546—114no—
211C23×C11C2×C22⋊C411yescharacteristic
212C22×D11—22no—
213C22×D11—22no—
214C22×D11—22no—
215C22×D11C2×C22⋊C411yescharacteristic
216C22×D11C2×C22⋊C411yescharacteristic
217Q8×C11—44no—
218Q8×C11—44no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—24no—
222C2×C4×C11—44no—
223C2×C4×C11C2×C22⋊C411yescharacteristic
224C2×C4×C11C2×C22⋊C411yescharacteristic
225C2×C4×C11C2×C22⋊C411yescharacteristic
226C2×C4×C11#13712yes—
227C2×C4×C11#13712yes—
228C2×C4×C11C23×C411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—24no—
235C2×Dic11—44no—
236C2×Dic11C2×C22⋊C411yescharacteristic
237C2×Dic11C2×C22⋊C411yescharacteristic
238C2×Dic11C2×C22⋊C411yescharacteristic
239C2×Dic11C2×C22⋊C411yescharacteristic
240C2×Dic11C2×C22⋊C411yescharacteristic
241C2×Dic11C2×C22⋊C411yescharacteristic
242C4×D11—22no—
243C4×D11—22no—
244C4×D11—22no—
245C4×D11—21no—
246C4×D11—21no—
247C4×D11—21no—
248C4×D11—21no—
249C4×D11—22no—
250C4×D11—22no—
251C4×D11—22no—
252C4×D11—22no—
253C4×D11—22no—
254C4×D11—48no—
255C4×D11—48no—
256C4×D11#10114yes—
257C4×D11AGL(1,ℤ/8)14yes—
258Dic22—48no—
259Dic22—44no—
260Dic22—44no—
261Dic22—48no—
262C8×C11—42no—
263C8×C11—42no—
264C11⋊C8—42no—
265C11⋊C8—42no—
266C23×Q8—221no—
267C2×C4⋊Q8—112no—
268C2×C4⋊Q8—112no—
269C2×C4⋊Q8—112no—
270C2×C4⋊Q8—112no—
271C2×C4⋊Q8—112no—
272C2×C4⋊Q8—111no—
273C2×C4⋊Q8—221no—
274C2×C4⋊Q8—221no—
275C2×C4⋊Q8—221no—
276C2×C4⋊Q8—221no—
277C2×C4⋊Q8—221no—
278C2×C4⋊Q8—221no—
279C2×C4⋊Q8C2×D1111yescharacteristic
280C22×C4⋊C4—112no—
281C22×C4⋊C4—221no—
282C22×C42—111no—
283#432—112no—
284#432—112no—
285#432—221no—
286#432—221no—
287#431—111no—
288#431—112no—
289#431—221no—
290#431—221no—
291#431C2×D1111yescharacteristic
292#423—111no—
293#423—112no—
294#423C2×D1111yescharacteristic
295#407—221no—
296#407—221no—
297C4×M16—221no—
298C4×M16—221no—
299#332—114no—
300#332—114no—
301#332—114no—
302#332C2×D1114yescomplemented
303C22×C11—21no—
304C22×C11—21no—
305C22×C11#41912yes—
306C22×C11C22×C22⋊C411yescharacteristic
307C2×D11—28no—
308C2×D11—21no—
309C2×D11—21no—
310C2×D11—21no—
311C2×D11—21no—
312C2×D11C2×#10112yes—
313C2×D11#41812yes—
314C4×C11—21no—
315C4×C11—21no—
316C4×C11—44no—
317C4×C11C2×#10112yes—
318C4×C11#41912yes—
319C4×C11C2×AGL(1,ℤ/8)12yes—
320C4×C11C2×#13711yescharacteristic
321C4×C11C2×#13711yescharacteristic
322Dic11—21no—
323Dic11—21no—
324Dic11—21no—
325Dic11—21no—
326Dic11—44no—
327Dic11C2×#10112yes—
328Dic11#41812yes—
329C22×Q8—21no—
330C22×Q8—222no—
331C22×Q8—222no—
332C22×Q8—222no—
333C22×Q8—222no—
334C22×Q8—222no—
335C22×Q8—221no—
336C22×Q8—448no—
337C23×C4—111no—
338C23×C4—111no—
339C23×C4—111no—
340C23×C4—222no—
341C2×M16—21no—
342C2×M16—222no—
343C2×M16—221no—
344C4⋊Q8—21no—
345C4⋊Q8—21no—
346C4⋊Q8—114no—
347C4⋊Q8—114no—
348C4⋊Q8—112no—
349C4⋊Q8—112no—
350C4⋊Q8—222no—
351C4⋊Q8—222no—
352C4⋊Q8—222no—
353C4⋊Q8—222no—
354C4⋊Q8—222no—
355C4⋊Q8—222no—
356C4⋊Q8—222no—
357C4⋊Q8—222no—
358C4⋊Q8—222no—
359C4⋊Q8—222no—
360C4⋊Q8—221no—
361C4⋊Q8—221no—
362C4⋊Q8C4×D1112yes—
363C4⋊Q8C22×D1112yes—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—112no—
366C2×C4⋊C4—114no—
367C2×C4⋊C4—114no—
368C2×C4⋊C4—222no—
369C2×C4⋊C4—222no—
370C2×C4⋊C4—222no—
371C2×C4⋊C4—222no—
372C2×C4⋊C4—222no—
373C2×C4⋊C4—222no—
374C2×C4⋊C4—222no—
375C2×C4⋊C4—222no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4C4×D1112yes—
378C2×C42—111no—
379C2×C42—111no—
380C2×C42—111no—
381C2×C42—111no—
382C2×C42—111no—
383C2×C42—111no—
384C2×C42—111no—
385C2×C42—111no—
386C2×C42—111no—
387C2×C42—111no—
388C2×C42—111no—
389C2×C42C22×D1111yescharacteristic
390C4⋊C8—21no—
391C4⋊C8—112no—
392C4⋊C8—112no—
393C4⋊C8—222no—
394C4⋊C8—221no—
395C4⋊C8C22×D1112yes—
396C4⋊C8C22×D1112yes—
397C22⋊C8—21no—
398C22⋊C8—222no—
399C22⋊C8—222no—
400C22⋊C8—222no—
401C22⋊C8—221no—
402#97—222no—
403#97—222no—
404C4×C8—21no—
405C4×C8—222no—
406C4×C8—221no—
407C2×C11—22no—
408C2×C11C22×#10111yescharacteristic
409C2×C11C2×#41811yescharacteristic
410C2×C11C2×#41911yescharacteristic
411D11—22no—
412D11—22no—
413C24—111no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—44no—
417C2×Q8—224no—
418C2×Q8—224no—
419C2×Q8—222no—
420C2×Q8—222no—
421C2×Q8—444no—
422C2×Q8—448no—
423C2×Q8—448no—
424C2×Q8—448no—
425C2×Q8—448no—
426C2×Q8—448no—
427C22×C4—22no—
428C22×C4—111no—
429C22×C4—111no—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—111no—
433C22×C4—111no—
434C22×C4—111no—
435C22×C4—111no—
436C22×C4—111no—
437C22×C4—111no—
438C22×C4—111no—
439C22×C4—111no—
440C22×C4—111no—
441C22×C4—111no—
442C22×C4—111no—
443C22×C4—224no—
444C22×C4—224no—
445C22×C4—224no—
446C22×C4—224no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—448no—
451C22×C4C2×C4×D1111yescharacteristic
452C22×C4D4×D1111yescharacteristic
453C22×C4D4×D1111yescharacteristic
454M16—42no—
455M16—444no—
456M16—442no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—222no—
460C2×C8—222no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—114no—
465C4⋊C4—224no—
466C4⋊C4—224no—
467C4⋊C4—224no—
468C4⋊C4—224no—
469C4⋊C4—222no—
470C4⋊C4—222no—
471C4⋊C4—222no—
472C4⋊C4C2×C4×D1114yes—
473C42—111no—
474C42—111no—
475C42—111no—
476C42—111no—
477C42—111no—
478C42—111no—
479C42—111no—
480C42—111no—
481C42—111no—
482C42—111no—
483C42—111no—
484C42—111no—
485C42C2×C4×D1111yescharacteristic
486C42D4×D1111yescharacteristic
487C42D4×D1111yescharacteristic
488C42C23×D1111yescharacteristic
489C11#1774211yescharacteristic, complemented, Sylow
490C23—111no—
491C23—111no—
492C23—222no—
493C23—222no—
494C23—222no—
495C23C22⋊C4×D1111yescharacteristic
496Q8—44no—
497Q8—44no—
498Q8—444no—
499Q8—448no—
500Q8—448no—
501Q8—444no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—24no—
505C2×C4—44no—
506C2×C4—111no—
507C2×C4—111no—
508C2×C4—114no—
509C2×C4—114no—
510C2×C4—111no—
511C2×C4—111no—
512C2×C4—111no—
513C2×C4—111no—
514C2×C4—222no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—222no—
518C2×C4—222no—
519C2×C4—222no—
520C2×C4—222no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—222no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—222no—
529C2×C4—224no—
530C2×C4—448no—
531C2×C4—448no—
532C2×C4—444no—
533C2×C4C22⋊C4×D1111yescharacteristic
534C2×C4C22⋊C4×D1111yescharacteristic
535C2×C4C22⋊C4×D1111yescharacteristic
536C2×C4#6696812yes—
537C2×C4#6697112yes—
538C2×C4C22×C4×D1111yescharacteristic
539C2×C4C2×D4×D1111yescharacteristic
540C2×C4C2×D4×D1111yescharacteristic
541C8—42no—
542C8—42no—
543C8—442no—
544C8—442no—
545C22—21no—
546C22—21no—
547C22—112no—
548C22—112no—
549C22—228no—
550C22—221no—
551C22—221no—
552C22—221no—
553C22—221no—
554C22#1062241512yes—
555C22C2×C22⋊C4×D1111yescharacteristic
556C4—21no—
557C4—21no—
558C4—44no—
559C4—112no—
560C4—112no—
561C4—221no—
562C4—221no—
563C4—221no—
564C4—221no—
565C4—444no—
566C4D11×#10112yes—
567C4#1062241512yes—
568C4C2×#6696811yescharacteristic
569C4C2×#6697111yescharacteristic
570C4D11×AGL(1,ℤ/8)12yes—
571C2—22no—
572C2—222no—
573C2—222no—
574C2C2×D11×#10111yescharacteristic
575C2D11×#41811yescharacteristic
576C2C2×#1062241511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1549C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC42×C11C24
hypercenter#1549D11
hypocenterC11#17742
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
4. #13067331C2semidirect
5. #13067302C2semidirect
6. #13067301C2semidirect
7. #13067300C2semidirect
8. #13067286C2semidirect
9. C11×#1549C2semidirect
43. C11×#332C22semidirect
44. #10622185C22semidirect
45. #10622124C22semidirect
46. #10622120C22semidirect
209. #1549D11semidirect
302. #332C2×D11semidirect
489. C11#17742semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
#130772482
#130772442
#130673312
#130673022
#130673012
#130673002
#130672862
C11×#15492
#1774211