Finite Group Databasebeta

← #14722370

Subgroups — #14722370

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×#10623247C211yesmaximal, characteristic
2#13077248C211yesmaximal, characteristic, complemented
3#13077244C211yesmaximal, characteristic, complemented
4#13067335C214yesmaximal, complemented
5#13067318C214yesmaximal, complemented
6#13067289C211yesmaximal, characteristic, complemented
7#13067287C211yesmaximal, characteristic, 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—
17#10623247—21no—
18#10623247—21no—
19#10623247—21no—
20#10623247—21no—
21#10623247C412yes—
22#10623247C412yes—
23#10623247C2212yes—
24#10623247C2212yes—
25C2×C42×D11C2211yescharacteristic
26C2×#66922C2211yescharacteristic
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×#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—44no—
57C2×#4341—44no—
58C22×C4×D11C2×C411yescharacteristic
59C22×C4×D11D411yescharacteristic
60C22×C4×D11D411yescharacteristic
61C22×Dic22—21no—
62C2×C11×M16—21no—
63C11×#127—21no—
64C11×#127—21no—
65C11×#127C2×C412yes—
66C11×#127C2312yes—
67C2×C42×C11C2311yescharacteristic
68C2×C22⋊Dic11—22no—
69C2×C22⋊Dic11—22no—
70#66991—22no—
71#66991—22no—
72#66991—22no—
73#66991—22no—
74#66991—22no—
75#66991—22no—
76#66991C2×C414yes—
77#66991C2×C414yes—
78#66989—22no—
79#66989—22no—
80#66989—22no—
81#66989—22no—
82D4×Dic11—22no—
83D4×Dic11—22no—
84D4×Dic11—22no—
85D4×Dic11—22no—
86D4×Dic11—22no—
87D4×Dic11—22no—
88D4×Dic11C2×C414yes—
89D4×Dic11C2×C414yes—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11C2×C412yes—
92C2×C4×Dic11C2×C411yescharacteristic
93C2×C4×Dic11D411yescharacteristic
94C2×C4×Dic11D411yescharacteristic
95C2×#4318—21no—
96C2×#4313—22no—
97C42×D11C2×C411yescharacteristic
98C42×D11C2×C411yescharacteristic
99C42×D11D411yescharacteristic
100C42×D11D411yescharacteristic
101C42×D11D411yescharacteristic
102C42×D11D411yescharacteristic
103C42×D11C2311yescharacteristic
104C42×D11C2311yescharacteristic
105#66922—21no—
106#66922—21no—
107#66922C2×C412yes—
108#66922C2312yes—
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
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—44no—
153#4341—44no—
154#4341—44no—
155#4341—44no—
156#4341—48no—
157#4341—48no—
158C2×C4×D11—22no—
159C2×C4×D11—22no—
160C2×C4×D11—42no—
161C2×C4×D11—42no—
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×D11C22×C411yescharacteristic
169C2×C4×D11C22×C411yescharacteristic
170C2×C4×D11C2×D411yescharacteristic
171C2×C4×D11C2×D411yescharacteristic
172C2×C4×D11C2×D411yescharacteristic
173C2×C4×D11C2×D411yescharacteristic
174C2×Dic22—22no—
175C2×Dic22—22no—
176C2×Dic22—42no—
177C2×Dic22—42no—
178C11×M16—42no—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C42×C11C22×C411yescharacteristic
182C42×C11C2×D411yescharacteristic
183C42×C11C2×D411yescharacteristic
184C42×C11C2411yescharacteristic
185C22⋊Dic11—24no—
186C22⋊Dic11—24no—
187C22⋊Dic11—24no—
188C22⋊Dic11—24no—
189C4⋊Dic11—22no—
190C4⋊Dic11—22no—
191C4⋊Dic11—22no—
192C4⋊Dic11C22×C414yes—
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#1546—111no—
216#1545—111no—
217#1545D1111yescharacteristic, complemented
218C23×C11—24no—
219C23×C11—44no—
220C23×C11—44no—
221C23×C11—44no—
222C23×C11C2×C22⋊C411yescharacteristic
223C22×D11—22no—
224C22×D11—41no—
225C22×D11—41no—
226C22×D11C2×C22⋊C411yescharacteristic
227C22×D11C2×C22⋊C411yescharacteristic
228D4×C11—44no—
229D4×C11—44no—
230D4×C11—42no—
231D4×C11—42no—
232D4×C11—44no—
233D4×C11—44no—
234D4×C11—44no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11C2×C22⋊C411yescharacteristic
238C2×C4×C11C2×C22⋊C411yescharacteristic
239C2×C4×C11C2×C22⋊C411yescharacteristic
240C2×C4×C11AGL(1,ℤ/8)12yes—
241C2×C4×C11AGL(1,ℤ/8)12yes—
242C2×C4×C11C23×C411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C22⋊D11—48no—
246C22⋊D11—48no—
247C2×Dic11—22no—
248C2×Dic11—24no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—48no—
252C2×Dic11—48no—
253C2×Dic11—44no—
254C2×Dic11C2×C22⋊C411yescharacteristic
255C2×Dic11C2×C22⋊C411yescharacteristic
256C2×Dic11C2×C22⋊C411yescharacteristic
257C2×Dic11C2×C22⋊C411yescharacteristic
258C2×Dic11C2×C22⋊C411yescharacteristic
259C2×Dic11C2×C22⋊C411yescharacteristic
260C4×D11—21no—
261C4×D11—21no—
262C4×D11—21no—
263C4×D11—21no—
264C4×D11—22no—
265C4×D11—22no—
266C4×D11—22no—
267C4×D11—22no—
268C4×D11—22no—
269C4×D11—22no—
270C4×D11—41no—
271C4×D11—41no—
272C4×D11—41no—
273C4×D11—41no—
274Dic22—42no—
275Dic22—42no—
276Dic22—44no—
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⋊Q8—111no—
291C2×#127C2×D1111yescharacteristic
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#332—114no—
316#331—114no—
317#331C2×D1114yescomplemented
318C22×C11—21no—
319C22×C11—21no—
320C22×C11—44no—
321C22×C11—44no—
322C22×C11—44no—
323C22×C11—88no—
324C22×C11#41812yes—
325C22×C11C22×C22⋊C411yescharacteristic
326C2×D11—21no—
327C2×D11—21no—
328C2×D11—21no—
329C2×D11—21no—
330C2×D11—21no—
331C2×D11—21no—
332C2×D11—44no—
333C4×C11—21no—
334C4×C11—21no—
335C4×C11#41312yes—
336C4×C11#41812yes—
337C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
338C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
339C4×C11#57512yes—
340Dic11—21no—
341Dic11—21no—
342Dic11—21no—
343Dic11—21no—
344Dic11—21no—
345Dic11—21no—
346Dic11—44no—
347C2×#41—222no—
348C2×#41—222no—
349C2×#41—222no—
350C2×#41—222no—
351C2×#41—444no—
352C2×#41—444no—
353C22×Q8—221no—
354C22×D4—21no—
355C22×D4—21no—
356C22×D4—222no—
357C22×D4C4×D1112yes—
358C23×C4—111no—
359C23×C4—111no—
360C23×C4—111no—
361C23×C4—222no—
362C2×M16—21no—
363C2×M16—222no—
364C2×M16—221no—
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—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×C11—84no—
428C2×C11C2×#41311yescharacteristic
429C2×C11C2×#41811yescharacteristic
430C2×C11#289611yescharacteristic
431D11—41no—
432D11—41no—
433C24—22no—
434C24—111no—
435#41—444no—
436#41—444no—
437#41—444no—
438#41—444no—
439#41—448no—
440#41—448no—
441C2×Q8—222no—
442C2×Q8—222no—
443C2×Q8—442no—
444C2×Q8—442no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4—224no—
455C2×D4—224no—
456C2×D4—448no—
457C2×D4C2×C4×D1114yes—
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—111no—
469C22×C4—111no—
470C22×C4—111no—
471C22×C4—111no—
472C22×C4—111no—
473C22×C4—224no—
474C22×C4—224no—
475C22×C4—222no—
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—114no—
492C4⋊C4—222no—
493C4⋊C4—222no—
494C4⋊C4—222no—
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—24no—
517C23—44no—
518C23—44no—
519C23—44no—
520C23—111no—
521C23—111no—
522C23—222no—
523C23—441no—
524C23—441no—
525C23C22⋊C4×D1111yescharacteristic
526Q8—442no—
527Q8—442no—
528Q8—444no—
529D4—44no—
530D4—44no—
531D4—42no—
532D4—42no—
533D4—44no—
534D4—44no—
535D4—44no—
536D4—448no—
537D4—448no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—111no—
541C2×C4—111no—
542C2×C4—111no—
543C2×C4—111no—
544C2×C4—111no—
545C2×C4—111no—
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—222no—
557C2×C4—224no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—448no—
565C2×C4—448no—
566C2×C4—444no—
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—44no—
582C22—44no—
583C22—44no—
584C22—88no—
585C22—221no—
586C22—221no—
587C22—221no—
588C22—221no—
589C22—221no—
590C22—221no—
591C22—444no—
592C22#1062238312yes—
593C22C2×C22⋊C4×D1111yescharacteristic
594C4—21no—
595C4—21no—
596C4—221no—
597C4—221no—
598C4—221no—
599C4—221no—
600C4—221no—
601C4—221no—
602C4—444no—
603C4#1062235812yes—
604C4#1062238312yes—
605C4C2×#6696411yescharacteristic
606C4C2×#6696711yescharacteristic
607C4#1062330412yes—
608C2—22no—
609C2—84no—
610C2—441no—
611C2—441no—
612C2C2×#1062235811yescharacteristic
613C2C2×#1062238311yescharacteristic
614C2#1307713011yescharacteristic
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#17743
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. #13077248C2semidirect
3. #13077244C2semidirect
4. #13067335C2semidirect
5. #13067318C2semidirect
6. #13067289C2semidirect
7. #13067287C2semidirect
8. #13067284C2semidirect
9. C11×#1545C2semidirect
33. #10622450C22semidirect
35. #10622448C22semidirect
36. #10622448C22semidirect
38. #10622446C22semidirect
43. C11×#331C22semidirect
44. #10622182C22semidirect
45. #10622124C22semidirect
46. #10622120C22semidirect
217. #1545D11semidirect
317. #331C2×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×#106232472
#130772482
#130772442
#130673352
#130673182
#130672892
#130672872
#130672842
C11×#15452
#1774311