Finite Group Databasebeta

← #14722373

Subgroups — #14722373

Order 2816.

1230 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623256C211yesmaximal, characteristic
2#13077248C211yesmaximal, characteristic, complemented
3#13077244C211yesmaximal, characteristic, complemented
4#13067337C214yesmaximal, complemented
5#13067320C214yesmaximal, complemented
6#13067288C211yesmaximal, characteristic, complemented
7#13067285C211yesmaximal, characteristic, complemented
8#13067283C211yesmaximal, characteristic, complemented
9C11×#1546C211yesmaximal, characteristic, complemented
10C22×#4343—21no—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#67000—21no—
13#10623256—21no—
14#10623256—21no—
15#10623256—21no—
16#10623256—21no—
17#10623256C412yes—
18#10623256C412yes—
19#10623256C2212yes—
20#10623256C2212yes—
21C2×#66948—21no—
22C2×#66948C412yes—
23C2×#66946—21no—
24C2×#66946C412yes—
25C2×#66927C2211yescharacteristic
26C2×C42×D11C2211yescharacteristic
27C11×#431C2211yescharacteristic
28C11×#423C2211yescharacteristic
29#10622739—21no—
30M16×Dic11—21no—
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33#10622450C2212yescomplemented
34#10622448—21no—
35#10622448C2212yescomplemented
36#10622448C2212yescomplemented
37#10622446—21no—
38#10622446C2212yescomplemented
39#10622339—21no—
40#10622332—21no—
41C4×#4313—21no—
42#10622298—21no—
43C11×#332C2214yescomplemented
44#10622185C2214yescomplemented
45#10622123C2214yescomplemented
46#10622123C2214yescomplemented
47C22×Q8×C11—21no—
48C2×#4343—22no—
49C2×#4343—22no—
50C2×#4343—22no—
51C2×#4343—22no—
52C2×#4343—44no—
53C2×#4343—44no—
54C22×D44—22no—
55C22×D44—21no—
56C22×D44—21no—
57C22×D44C2×C412yes—
58C22×C4×D11—22no—
59C22×C4×D11C2×C411yescharacteristic
60C22×C4×D11D411yescharacteristic
61C22×C4×D11D411yescharacteristic
62C2×C11×M16—21no—
63C11×C4⋊Q8—21no—
64C11×C4⋊Q8—21no—
65C11×C4⋊Q8C2×C412yes—
66C11×C4⋊Q8C2312yes—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4C2×C412yes—
69C2×C42×C11C2311yescharacteristic
70#67000—22no—
71#67000—22no—
72#67000—22no—
73#67000—22no—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4—22no—
76C2×C4×Dic11C2×C411yescharacteristic
77C2×C4×Dic11D411yescharacteristic
78C2×C4×Dic11D411yescharacteristic
79C2×#4318—21no—
80C2×#4313—22no—
81#66948—22no—
82#66948—22no—
83#66948—22no—
84#66948—22no—
85#66948—22no—
86#66948—22no—
87#66948C2×C414yes—
88#66948C2×C414yes—
89#66946—22no—
90#66946—22no—
91#66946—22no—
92#66946—22no—
93#66946—22no—
94#66946—22no—
95#66946C2×C414yes—
96#66946C2×C414yes—
97#66927—21no—
98#66927—21no—
99#66927C2×C412yes—
100#66927C2312yes—
101C42×D11C2×C411yescharacteristic
102C42×D11C2×C411yescharacteristic
103C42×D11D411yescharacteristic
104C42×D11D411yescharacteristic
105C42×D11D411yescharacteristic
106C42×D11D411yescharacteristic
107C42×D11C2311yescharacteristic
108C42×D11C2311yescharacteristic
109C11×C4⋊C8—21no—
110C11×C4⋊C8C2312yes—
111C11×C4⋊C8C2312yes—
112C11×C22⋊C8—21no—
113C4×C8×C11—21no—
114C22⋊(C11⋊C8)—21no—
115(C2×D11)⋊C8—22no—
116(C2×D11)⋊C8—22no—
117(C2×D11)⋊C8—22no—
118#66879—22no—
119#66879—22no—
120Dic11⋊C8—22no—
121C8×Dic11—22no—
122C4⋊(C11⋊C8)—21no—
123C4⋊(C11⋊C8)C2312yes—
124C4⋊(C11⋊C8)C2312yes—
125C4×C11⋊C8—21no—
126#17743—111nomaximal, Sylow
127C23×D11—22no—
128C23×D11C22⋊C411yescharacteristic
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—42no—
132C2×Q8×C11—42no—
133C22×C4×C11—22no—
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×Dic11C22⋊C411yescharacteristic
138C22×Dic11C22⋊C411yescharacteristic
139C22×Dic11C22⋊C411yescharacteristic
140#4343—44no—
141#4343—44no—
142#4343—44no—
143#4343—44no—
144#4343—48no—
145#4343—48no—
146C2×D44—24no—
147C2×D44—24no—
148C2×D44—22no—
149C2×D44—22no—
150C2×D44—22no—
151C2×D44—22no—
152C2×D44—22no—
153C2×D44—44no—
154C2×D44—44no—
155C2×D44—48no—
156C2×D44—42no—
157C2×D44—42no—
158C2×D44C22×C414yes—
159C2×C4×D11—24no—
160C2×C4×D11—24no—
161C2×C4×D11—22no—
162C2×C4×D11—22no—
163C2×C4×D11—42no—
164C2×C4×D11—42no—
165C2×C4×D11—48no—
166C2×C4×D11C22⋊C411yescharacteristic
167C2×C4×D11C22⋊C411yescharacteristic
168C2×C4×D11C22⋊C411yescharacteristic
169C2×C4×D11C22⋊C411yescharacteristic
170C2×C4×D11C22⋊C411yescharacteristic
171C2×C4×D11C22⋊C411yescharacteristic
172C2×C4×D11C22×C411yescharacteristic
173C2×C4×D11C22×C411yescharacteristic
174C2×C4×D11C2×D411yescharacteristic
175C2×C4×D11C2×D411yescharacteristic
176C2×C4×D11C2×D411yescharacteristic
177C2×C4×D11C2×D411yescharacteristic
178C11×M16—42no—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4C22×C414yes—
185C42×C11C22×C411yescharacteristic
186C42×C11C2×D411yescharacteristic
187C42×C11C2×D411yescharacteristic
188C42×C11C2411yescharacteristic
189(C2×D11)⋊C4—24no—
190(C2×D11)⋊C4—24no—
191(C2×D11)⋊C4—24no—
192(C2×D11)⋊C4—24no—
193C4×Dic11C22⋊C411yescharacteristic
194C4×Dic11C22⋊C411yescharacteristic
195C4×Dic11C22⋊C411yescharacteristic
196C4×Dic11C22⋊C411yescharacteristic
197C4×Dic11C22⋊C411yescharacteristic
198C4×Dic11C22⋊C411yescharacteristic
199C4×Dic11C22×C411yescharacteristic
200C4×Dic11C22×C411yescharacteristic
201C4×Dic11C2×D411yescharacteristic
202C4×Dic11C2×D411yescharacteristic
203C4×Dic11C2×D411yescharacteristic
204C4×Dic11C2×D411yescharacteristic
205#4318—42no—
206C2×C11⋊C8—22no—
207C2×C11⋊C8—22no—
208#4313—44no—
209C2×#532—111no—
210#2920—111no—
211#2920—111no—
212#1557—114no—
213#1553—114no—
214#1546—111no—
215#1546D1111yescharacteristic, complemented
216#1545—111no—
217#1545—111no—
218C23×C11C2×C22⋊C411yescharacteristic
219C22×D11—22no—
220C22×D11—24no—
221C22×D11—41no—
222C22×D11—41no—
223C22×D11—44no—
224C22×D11—44no—
225C22×D11—44no—
226C22×D11C2×C22⋊C411yescharacteristic
227C22×D11C2×C22⋊C411yescharacteristic
228Q8×C11—42no—
229Q8×C11—42no—
230Q8×C11—44no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—44no—
235C2×C4×C11C2×C22⋊C411yescharacteristic
236C2×C4×C11C2×C22⋊C411yescharacteristic
237C2×C4×C11C2×C22⋊C411yescharacteristic
238C2×C4×C11AGL(1,ℤ/8)12yes—
239C2×C4×C11AGL(1,ℤ/8)12yes—
240C2×C4×C11C23×C411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×Dic11—22no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11C2×C22⋊C411yescharacteristic
247C2×Dic11C2×C22⋊C411yescharacteristic
248C2×Dic11C2×C22⋊C411yescharacteristic
249C2×Dic11C2×C22⋊C411yescharacteristic
250C2×Dic11C2×C22⋊C411yescharacteristic
251C2×Dic11C2×C22⋊C411yescharacteristic
252D44—44no—
253D44—44no—
254D44—48no—
255D44—48no—
256D44—42no—
257D44—42no—
258D44—44no—
259D44—44no—
260D44—44no—
261C4×D11—21no—
262C4×D11—21no—
263C4×D11—21no—
264C4×D11—21no—
265C4×D11—22no—
266C4×D11—22no—
267C4×D11—22no—
268C4×D11—22no—
269C4×D11—22no—
270C4×D11—22no—
271C4×D11—41no—
272C4×D11—41no—
273C4×D11—41no—
274C4×D11—41no—
275C4×D11—48no—
276C4×D11—48no—
277C8×C11—42no—
278C8×C11—42no—
279C11⋊C8—42no—
280C11⋊C8—42no—
281C22×#41—221no—
282#532—112no—
283#532—112no—
284#532—112no—
285#532—112no—
286#532—221no—
287#532—221no—
288#532—221no—
289#532—221no—
290C2×C4⋊Q8C2×D1111yescharacteristic
291C2×#127—111no—
292C2×#124—221no—
293C2×#121—112no—
294C2×#121—221no—
295C2×C4×D4—112no—
296C2×C4×D4—221no—
297C22×C42—111no—
298#432—112no—
299#432—112no—
300#432—221no—
301#432—221no—
302#431—111no—
303#431—112no—
304#431—221no—
305#431—221no—
306#431C2×D1111yescharacteristic
307#423—111no—
308#423—112no—
309#423C2×D1111yescharacteristic
310#407—221no—
311#407—221no—
312C4×M16—221no—
313C4×M16—221no—
314#332—114no—
315#332C2×D1114yescomplemented
316#331—114no—
317#331—114no—
318C22×C11—21no—
319C22×C11—21no—
320C22×C11#41812yes—
321C22×C11C22×C22⋊C411yescharacteristic
322C2×D11—21no—
323C2×D11—21no—
324C2×D11—21no—
325C2×D11—21no—
326C2×D11—21no—
327C2×D11—21no—
328C2×D11—44no—
329C2×D11—44no—
330C2×D11—44no—
331C2×D11—44no—
332C2×D11—88no—
333C4×C11—21no—
334C4×C11—21no—
335C4×C11—44no—
336C4×C11#41312yes—
337C4×C11#41812yes—
338C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
339C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
340C4×C11#57512yes—
341Dic11—21no—
342Dic11—21no—
343Dic11—21no—
344Dic11—21no—
345Dic11—21no—
346Dic11—21no—
347C2×#41—222no—
348C2×#41—222no—
349C2×#41—222no—
350C2×#41—222no—
351C2×#41—444no—
352C2×#41—444no—
353C22×Q8—21no—
354C22×D4—112no—
355C22×D4—222no—
356C22×D4—221no—
357C22×D4—221no—
358C23×C4—111no—
359C23×C4—111no—
360C23×C4—111no—
361C23×C4—222no—
362C2×M16—21no—
363C2×M16—222no—
364C2×M16—221no—
365C4⋊Q8—21no—
366C4⋊Q8—21no—
367C4⋊Q8C4×D1112yes—
368C4⋊Q8C22×D1112yes—
369#127—112no—
370#127—112no—
371#127—221no—
372#127—221no—
373#124—222no—
374#124—222no—
375#124—222no—
376#124—222no—
377#121—114no—
378#121—114no—
379#121—222no—
380#121—222no—
381#121—222no—
382#121—222no—
383#121—222no—
384#121—222no—
385C4×D4—114no—
386C4×D4—114no—
387C4×D4—222no—
388C4×D4—222no—
389C4×D4—222no—
390C4×D4—222no—
391C4×D4—222no—
392C4×D4—222no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4C4×D1112yes—
395C2×C22⋊C4—222no—
396C2×C22⋊C4—222no—
397C2×C42—111no—
398C2×C42—111no—
399C2×C42—111no—
400C2×C42—111no—
401C2×C42—111no—
402C2×C42—111no—
403C2×C42—111no—
404C2×C42—111no—
405C2×C42—111no—
406C2×C42—111no—
407C2×C42—111no—
408C2×C42C22×D1111yescharacteristic
409C4⋊C8—21no—
410C4⋊C8—112no—
411C4⋊C8—112no—
412C4⋊C8—222no—
413C4⋊C8—221no—
414C4⋊C8C22×D1112yes—
415C4⋊C8C22×D1112yes—
416C22⋊C8—21no—
417C22⋊C8—222no—
418C22⋊C8—222no—
419C22⋊C8—222no—
420C22⋊C8—221no—
421#97—222no—
422#97—222no—
423C4×C8—21no—
424C4×C8—222no—
425C4×C8—221no—
426C2×C11—22no—
427C2×C11C2×#41311yescharacteristic
428C2×C11C2×#41811yescharacteristic
429C2×C11#289611yescharacteristic
430D11—41no—
431D11—41no—
432D11—84no—
433C24—111no—
434C24—222no—
435#41—444no—
436#41—444no—
437#41—444no—
438#41—444no—
439#41—448no—
440#41—448no—
441C2×Q8—22no—
442C2×Q8—22no—
443C2×Q8—42no—
444C2×Q8—42no—
445C2×D4—114no—
446C2×D4—224no—
447C2×D4—224no—
448C2×D4—222no—
449C2×D4—222no—
450C2×D4—222no—
451C2×D4—222no—
452C2×D4—222no—
453C2×D4—444no—
454C2×D4—444no—
455C2×D4—448no—
456C2×D4—442no—
457C2×D4—442no—
458C22×C4—22no—
459C22×C4—111no—
460C22×C4—111no—
461C22×C4—111no—
462C22×C4—111no—
463C22×C4—111no—
464C22×C4—111no—
465C22×C4—111no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—111no—
471C22×C4—111no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—224no—
475C22×C4—224no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—442no—
479C22×C4—442no—
480C22×C4—448no—
481C22×C4C2×C4×D1111yescharacteristic
482C22×C4D4×D1111yescharacteristic
483C22×C4D4×D1111yescharacteristic
484M16—42no—
485M16—444no—
486M16—442no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—222no—
490C2×C8—222no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4C2×C4×D1114yes—
495C22⋊C4—224no—
496C22⋊C4—224no—
497C22⋊C4—224no—
498C22⋊C4—224no—
499C42—111no—
500C42—111no—
501C42—111no—
502C42—111no—
503C42—111no—
504C42—111no—
505C42—111no—
506C42—111no—
507C42—111no—
508C42—111no—
509C42—111no—
510C42—111no—
511C42C2×C4×D1111yescharacteristic
512C42D4×D1111yescharacteristic
513C42D4×D1111yescharacteristic
514C42C23×D1111yescharacteristic
515C11#1774311yescharacteristic, complemented, Sylow
516C23—111no—
517C23—111no—
518C23—222no—
519C23—224no—
520C23—441no—
521C23—441no—
522C23—444no—
523C23—444no—
524C23—444no—
525C23C22⋊C4×D1111yescharacteristic
526Q8—42no—
527Q8—42no—
528Q8—44no—
529D4—444no—
530D4—444no—
531D4—448no—
532D4—448no—
533D4—442no—
534D4—442no—
535D4—444no—
536D4—444no—
537D4—444no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—44no—
542C2×C4—111no—
543C2×C4—111no—
544C2×C4—111no—
545C2×C4—111no—
546C2×C4—111no—
547C2×C4—111no—
548C2×C4—222no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—222no—
554C2×C4—222no—
555C2×C4—222no—
556C2×C4—222no—
557C2×C4—222no—
558C2×C4—222no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—448no—
564C2×C4—448no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4C22⋊C4×D1111yescharacteristic
568C2×C4C22⋊C4×D1111yescharacteristic
569C2×C4C22⋊C4×D1111yescharacteristic
570C2×C4#6696412yes—
571C2×C4#6696712yes—
572C2×C4C22×C4×D1111yescharacteristic
573C2×C4C2×D4×D1111yescharacteristic
574C2×C4C2×D4×D1111yescharacteristic
575C8—42no—
576C8—42no—
577C8—442no—
578C8—442no—
579C22—21no—
580C22—21no—
581C22—221no—
582C22—221no—
583C22—221no—
584C22—221no—
585C22—221no—
586C22—221no—
587C22—444no—
588C22—444no—
589C22—444no—
590C22—444no—
591C22—888no—
592C22#1062238312yes—
593C22C2×C22⋊C4×D1111yescharacteristic
594C4—21no—
595C4—21no—
596C4—44no—
597C4—221no—
598C4—221no—
599C4—221no—
600C4—221no—
601C4—221no—
602C4—221no—
603C4#1062236412yes—
604C4#1062238312yes—
605C4C2×#6696411yescharacteristic
606C4C2×#6696711yescharacteristic
607C4#1062330812yes—
608C2—22no—
609C2—441no—
610C2—441no—
611C2—884no—
612C2C2×#1062236411yescharacteristic
613C2C2×#1062238311yescharacteristic
614C2#1307713411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1546C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623256C2
cosocleC42×C11C24
hypercenter#1546D11
hypocenterC11#17743
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
2. #13077248C2semidirect
3. #13077244C2semidirect
4. #13067337C2semidirect
5. #13067320C2semidirect
6. #13067288C2semidirect
7. #13067285C2semidirect
8. #13067283C2semidirect
9. C11×#1546C2semidirect
33. #10622450C22semidirect
35. #10622448C22semidirect
36. #10622448C22semidirect
38. #10622446C22semidirect
43. C11×#332C22semidirect
44. #10622185C22semidirect
45. #10622123C22semidirect
46. #10622123C22semidirect
215. #1546D11semidirect
315. #332C2×D11semidirect
515. C11#17743semidirect

Maximal subgroups

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

subgroupindex
C2×#106232562
#130772482
#130772442
#130673372
#130673202
#130672882
#130672852
#130672832
C11×#15462
#1774311