Finite Group Databasebeta

← #14722385

Subgroups — #14722385

Order 2816.

1276 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623247C211yesmaximal, characteristic
2#13077244C211yesmaximal, characteristic, complemented
3D11×#423C211yesmaximal, characteristic, complemented
4#13067335C214yesmaximal, complemented
5#13067302C211yesmaximal, characteristic, complemented
6#13067300C211yesmaximal, characteristic, complemented
7#13067290C214yesmaximal, complemented
8#13067284C211yesmaximal, characteristic, complemented
9C11×#1545C211yesmaximal, characteristic, complemented
10C22×#4341—21no—
11C2×C11×#127C2211yescharacteristic
12C2×#66991—21no—
13C2×#66991C412yes—
14C2×#66989—21no—
15C2×D4×Dic11—21no—
16C2×D4×Dic11C412yes—
17C2×M16×D11—21no—
18#10623247—21no—
19#10623247—21no—
20#10623247—21no—
21#10623247—21no—
22#10623247C412yes—
23#10623247C412yes—
24#10623247C2212yes—
25#10623247C2212yes—
26C2×C42×D11C2211yescharacteristic
27C2×#66922C2211yescharacteristic
28C11×#431C2211yescharacteristic
29C11×#423C2211yescharacteristic
30#10622731—21no—
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33#10622450—21no—
34#10622450C2212yescomplemented
35#10622450C2212yescomplemented
36#10622448C2212yescomplemented
37D11×C4⋊C8—21no—
38D11×C4⋊C8C2212yescomplemented
39#10622339—21no—
40#10622332—21no—
41C4×#4313—21no—
42#10622298—21no—
43C11×#331C2214yescomplemented
44#10622182C2214yescomplemented
45#10622124C2214yescomplemented
46#10622120C2214yescomplemented
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11C2×C412yes—
50C22×C22⋊D11—22no—
51C23×Dic11—22no—
52C2×#4341—22no—
53C2×#4341—22no—
54C2×#4341—22no—
55C2×#4341—22no—
56C2×#4341—48no—
57C22×C4×D11C2×C411yescharacteristic
58C22×C4×D11D411yescharacteristic
59C22×C4×D11D411yescharacteristic
60C22×Dic22—21no—
61C2×C11×M16—21no—
62C11×#127—21no—
63C11×#127—21no—
64C11×#127C2×C412yes—
65C11×#127C2312yes—
66C2×C42×C11C2311yescharacteristic
67C2×C22⋊Dic11—22no—
68C2×C22⋊Dic11—22no—
69#66991—22no—
70#66991—22no—
71#66991—22no—
72#66991—22no—
73#66991—22no—
74#66991—22no—
75#66991C2×C414yes—
76#66991C2×C414yes—
77#66989—22no—
78#66989—22no—
79#66989—22no—
80#66989—22no—
81D4×Dic11—22no—
82D4×Dic11—22no—
83D4×Dic11—22no—
84D4×Dic11—22no—
85D4×Dic11—22no—
86D4×Dic11—22no—
87D4×Dic11C2×C414yes—
88D4×Dic11C2×C414yes—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11C2×C412yes—
91C2×C4×Dic11C2×C411yescharacteristic
92C2×C4×Dic11D411yescharacteristic
93C2×C4×Dic11D411yescharacteristic
94C2×#4318—21no—
95M16×D11—44no—
96C2×#4313—22no—
97C2×#4313—22no—
98C2×C8×D11—22no—
99C42×D11C2×C411yescharacteristic
100C42×D11C2×C411yescharacteristic
101C42×D11D411yescharacteristic
102C42×D11D411yescharacteristic
103C42×D11D411yescharacteristic
104C42×D11D411yescharacteristic
105C42×D11C2311yescharacteristic
106C42×D11C2311yescharacteristic
107#66922—21no—
108#66922—21no—
109#66922C2×C412yes—
110#66922C2312yes—
111C11×C4⋊C8—21no—
112C11×C4⋊C8C2312yes—
113C11×C4⋊C8C2312yes—
114C11×C22⋊C8—21no—
115C4×C8×C11—21no—
116C22⋊(C11⋊C8)—21no—
117(C2×D11)⋊C8—22no—
118#66879—22no—
119Dic11⋊C8—22no—
120Dic11⋊C8—22no—
121Dic11⋊C8—22no—
122C4⋊(C11⋊C8)—21no—
123C4⋊(C11⋊C8)C2312yes—
124C4⋊(C11⋊C8)C2312yes—
125C4×C11⋊C8—21no—
126#17745—111nomaximal, Sylow
127C24×C11—22no—
128C23×D11C22⋊C411yescharacteristic
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—44no—
135C2×D4×C11—44no—
136C2×D4×C11—42no—
137C2×D4×C11—42no—
138C2×D4×C11C22×C414yes—
139C22×C4×C11C22×C411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C2×C22⋊D11—24no—
143C2×C22⋊D11—24no—
144C2×C22⋊D11—48no—
145C22×Dic11—24no—
146C22×Dic11—24no—
147C22×Dic11—22no—
148C22×Dic11—48no—
149C22×Dic11C22⋊C411yescharacteristic
150C22×Dic11C22⋊C411yescharacteristic
151C22×Dic11C22⋊C411yescharacteristic
152#4341—48no—
153#4341—48no—
154#4341—48no—
155#4341—48no—
156C2×C4×D11—24no—
157C2×C4×D11—22no—
158C2×C4×D11—22no—
159C2×C4×D11—42no—
160C2×C4×D11C22⋊C411yescharacteristic
161C2×C4×D11C22⋊C411yescharacteristic
162C2×C4×D11C22⋊C411yescharacteristic
163C2×C4×D11C22⋊C411yescharacteristic
164C2×C4×D11C22⋊C411yescharacteristic
165C2×C4×D11C22⋊C411yescharacteristic
166C2×C4×D11C22×C411yescharacteristic
167C2×C4×D11C22×C411yescharacteristic
168C2×C4×D11C2×D411yescharacteristic
169C2×C4×D11C2×D411yescharacteristic
170C2×C4×D11C2×D411yescharacteristic
171C2×C4×D11C2×D411yescharacteristic
172C2×Dic22—22no—
173C2×Dic22—22no—
174C2×Dic22—44no—
175C11×M16—42no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C42×C11C22×C411yescharacteristic
179C42×C11C2×D411yescharacteristic
180C42×C11C2×D411yescharacteristic
181C42×C11C2411yescharacteristic
182C22⋊Dic11—24no—
183C22⋊Dic11—24no—
184C22⋊Dic11—24no—
185C22⋊Dic11—24no—
186C4⋊Dic11—22no—
187C4⋊Dic11—22no—
188C4⋊Dic11—22no—
189C4⋊Dic11C22×C414yes—
190C4×Dic11C22⋊C411yescharacteristic
191C4×Dic11C22⋊C411yescharacteristic
192C4×Dic11C22⋊C411yescharacteristic
193C4×Dic11C22⋊C411yescharacteristic
194C4×Dic11C22⋊C411yescharacteristic
195C4×Dic11C22⋊C411yescharacteristic
196C4×Dic11C22×C411yescharacteristic
197C4×Dic11C22×C411yescharacteristic
198C4×Dic11C2×D411yescharacteristic
199C4×Dic11C2×D411yescharacteristic
200C4×Dic11C2×D411yescharacteristic
201C4×Dic11C2×D411yescharacteristic
202#4318—42no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—22no—
205#4313—44no—
206#4313—44no—
207C8×D11—44no—
208C2×#532—111no—
209#2920—111no—
210C2×#423—111no—
211#1557—114no—
212#1549—111no—
213#1549—111no—
214#1547—114no—
215#1545—111no—
216#1545D1111yescharacteristic, complemented
217C23×C11—24no—
218C23×C11—44no—
219C23×C11—44no—
220C23×C11—44no—
221C23×C11C2×C22⋊C411yescharacteristic
222C22×D11—22no—
223C22×D11—22no—
224C22×D11—41no—
225C22×D11C2×C22⋊C411yescharacteristic
226C22×D11C2×C22⋊C411yescharacteristic
227D4×C11—44no—
228D4×C11—44no—
229D4×C11—44no—
230D4×C11—42no—
231D4×C11—42no—
232D4×C11—44no—
233D4×C11—44no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11C2×C22⋊C411yescharacteristic
237C2×C4×C11C2×C22⋊C411yescharacteristic
238C2×C4×C11C2×C22⋊C411yescharacteristic
239C2×C4×C11AGL(1,ℤ/8)12yes—
240C2×C4×C11#13712yes—
241C2×C4×C11C23×C411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C22⋊D11—48no—
245C22⋊D11—48no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—24no—
249C2×Dic11—41no—
250C2×Dic11—48no—
251C2×Dic11—44no—
252C2×Dic11—48no—
253C2×Dic11C2×C22⋊C411yescharacteristic
254C2×Dic11C2×C22⋊C411yescharacteristic
255C2×Dic11C2×C22⋊C411yescharacteristic
256C2×Dic11C2×C22⋊C411yescharacteristic
257C2×Dic11C2×C22⋊C411yescharacteristic
258C2×Dic11C2×C22⋊C411yescharacteristic
259C4×D11—22no—
260C4×D11—21no—
261C4×D11—21no—
262C4×D11—22no—
263C4×D11—21no—
264C4×D11—21no—
265C4×D11—22no—
266C4×D11—22no—
267C4×D11—22no—
268C4×D11—22no—
269C4×D11—22no—
270C4×D11—41no—
271C4×D11—41no—
272C4×D11AGL(1,ℤ/8)14yes—
273Dic22—44no—
274Dic22—44no—
275C8×C11—42no—
276C8×C11—42no—
277C11⋊C8—42no—
278C11⋊C8—42no—
279C22×#41—221no—
280C22×M16—221no—
281#532—112no—
282#532—112no—
283#532—112no—
284#532—112no—
285#532—221no—
286#532—221no—
287#532—221no—
288#532—221no—
289C2×C4⋊Q8—111no—
290C2×#127C2×D1111yescharacteristic
291C2×#124—221no—
292C2×#121—112no—
293C2×#121—221no—
294C2×C4×D4—112no—
295C2×C4×D4—221no—
296C22×C42—111no—
297#432—112no—
298#432—221no—
299#431—111no—
300#431—221no—
301#431C2×D1111yescharacteristic
302#423—111no—
303#423—112no—
304#423—112no—
305#423—221no—
306#423—221no—
307#423C2×D1111yescharacteristic
308C2×C4⋊C8—112no—
309C2×C4⋊C8—221no—
310#407—221no—
311C4×M16—221no—
312#332—114no—
313#332—114no—
314#331—114no—
315#331C2×D1114yescomplemented
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—44no—
319C22×C11—44no—
320C22×C11—44no—
321C22×C11—88no—
322C22×C11#41712yes—
323C22×C11C22×C22⋊C411yescharacteristic
324C2×D11—21no—
325C2×D11—21no—
326C2×D11—21no—
327C2×D11—21no—
328C2×D11—21no—
329C2×D11—44no—
330C2×D11#41812yes—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11#41312yes—
334C4×C11#41712yes—
335C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
336C4×C11C2×AGL(1,ℤ/8)12yes—
337C4×C11C2×#13711yescharacteristic
338Dic11—21no—
339Dic11—21no—
340Dic11—21no—
341Dic11—21no—
342Dic11—21no—
343Dic11—44no—
344Dic11#41812yes—
345C2×#41—222no—
346C2×#41—222no—
347C2×#41—222no—
348C2×#41—222no—
349C2×#41—448no—
350C22×Q8—221no—
351C22×D4—21no—
352C22×D4—21no—
353C22×D4—222no—
354C22×D4C4×D1112yes—
355C23×C4—111no—
356C23×C4—111no—
357C23×C4—111no—
358C23×C4—222no—
359C2×M16—21no—
360C2×M16—222no—
361C2×M16—222no—
362C2×M16—221no—
363C2×M16—444no—
364C22×C8—222no—
365C4⋊Q8—112no—
366C4⋊Q8—112no—
367C4⋊Q8—221no—
368C4⋊Q8—221no—
369#127—21no—
370#127—21no—
371#127C4×D1112yes—
372#127C22×D1112yes—
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—112no—
394C2×C4⋊C4—221no—
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—222no—
414C4⋊C8—222no—
415C4⋊C8—221no—
416C4⋊C8C22×D1112yes—
417C4⋊C8C22×D1112yes—
418C22⋊C8—21no—
419C22⋊C8—222no—
420C22⋊C8—221no—
421#97—222no—
422C4×C8—21no—
423C4×C8—221no—
424C2×C11—22no—
425C2×C11—84no—
426C2×C11C2×#41311yescharacteristic
427C2×C11C2×#41811yescharacteristic
428C2×C11C2×#41711yescharacteristic
429D11—22no—
430D11—41no—
431C24—22no—
432C24—111no—
433#41—448no—
434#41—448no—
435#41—448no—
436#41—448no—
437C2×Q8—222no—
438C2×Q8—222no—
439C2×Q8—444no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—44no—
446C2×D4—44no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—224no—
450C2×D4—224no—
451C2×D4—448no—
452C2×D4C2×C4×D1114yes—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—111no—
457C22×C4—111no—
458C22×C4—111no—
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—224no—
469C22×C4—224no—
470C22×C4—224no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—222no—
474C22×C4—442no—
475C22×C4—448no—
476C22×C4C2×C4×D1111yescharacteristic
477C22×C4D4×D1111yescharacteristic
478C22×C4D4×D1111yescharacteristic
479M16—42no—
480M16—444no—
481M16—444no—
482M16—442no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—222no—
486C2×C8—222no—
487C2×C8—444no—
488C4⋊C4—114no—
489C4⋊C4—222no—
490C4⋊C4—222no—
491C4⋊C4—222no—
492C22⋊C4—224no—
493C22⋊C4—224no—
494C22⋊C4—224no—
495C22⋊C4—224no—
496C42—111no—
497C42—111no—
498C42—111no—
499C42—111no—
500C42—111no—
501C42—111no—
502C42—111no—
503C42—111no—
504C42—111no—
505C42—111no—
506C42—111no—
507C42—111no—
508C42C2×C4×D1111yescharacteristic
509C42D4×D1111yescharacteristic
510C42D4×D1111yescharacteristic
511C42C23×D1111yescharacteristic
512C11#1774511yescharacteristic, complemented, Sylow
513C23—24no—
514C23—44no—
515C23—44no—
516C23—44no—
517C23—111no—
518C23—111no—
519C23—222no—
520C23—222no—
521C23—441no—
522C23C22⋊C4×D1111yescharacteristic
523Q8—444no—
524Q8—444no—
525D4—44no—
526D4—44no—
527D4—42no—
528D4—42no—
529D4—44no—
530D4—44no—
531D4—44no—
532D4—448no—
533D4—448no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—111no—
537C2×C4—114no—
538C2×C4—111no—
539C2×C4—111no—
540C2×C4—111no—
541C2×C4—111no—
542C2×C4—111no—
543C2×C4—222no—
544C2×C4—222no—
545C2×C4—222no—
546C2×C4—222no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—222no—
552C2×C4—222no—
553C2×C4—222no—
554C2×C4—222no—
555C2×C4—222no—
556C2×C4—224no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—448no—
560C2×C4—441no—
561C2×C4—448no—
562C2×C4—444no—
563C2×C4C22⋊C4×D1111yescharacteristic
564C2×C4C22⋊C4×D1111yescharacteristic
565C2×C4C22⋊C4×D1111yescharacteristic
566C2×C4#6696412yes—
567C2×C4#6696812yes—
568C2×C4C22×C4×D1111yescharacteristic
569C2×C4C2×D4×D1111yescharacteristic
570C2×C4C2×D4×D1111yescharacteristic
571C8—42no—
572C8—42no—
573C8—442no—
574C8—442no—
575C22—21no—
576C22—21no—
577C22—44no—
578C22—44no—
579C22—44no—
580C22—88no—
581C22—112no—
582C22—221no—
583C22—221no—
584C22—221no—
585C22—221no—
586C22—221no—
587C22—444no—
588C22#1062238412yes—
589C22C2×C22⋊C4×D1111yescharacteristic
590C4—21no—
591C4—21no—
592C4—112no—
593C4—221no—
594C4—221no—
595C4—221no—
596C4—221no—
597C4—221no—
598C4—444no—
599C4#1062235812yes—
600C4#1062238412yes—
601C4C2×#6696411yescharacteristic
602C4C2×#6696811yescharacteristic
603C4D11×AGL(1,ℤ/8)12yes—
604C2—22no—
605C2—84no—
606C2—222no—
607C2—441no—
608C2C2×#1062235811yescharacteristic
609C2D11×#41811yescharacteristic
610C2C2×#1062238411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1545C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623247C2
cosocleC42×C11C24
hypercenter#1545D11
hypocenterC11#17745
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1545

Complements

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

NH ≅ G/Ntype
2. #13077244C2semidirect
3. D11×#423C2semidirect
4. #13067335C2semidirect
5. #13067302C2semidirect
6. #13067300C2semidirect
7. #13067290C2semidirect
8. #13067284C2semidirect
9. C11×#1545C2semidirect
34. #10622450C22semidirect
35. #10622450C22semidirect
36. #10622448C22semidirect
38. D11×C4⋊C8C22semidirect
43. C11×#331C22semidirect
44. #10622182C22semidirect
45. #10622124C22semidirect
46. #10622120C22semidirect
216. #1545D11semidirect
315. #331C2×D11semidirect
512. C11#17745semidirect

Maximal subgroups

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

subgroupindex
C2×#106232472
#130772442
D11×#4232
#130673352
#130673022
#130673002
#130672902
#130672842
C11×#15452
#1774511