Finite Group Databasebeta

← #14722376

Subgroups — #14722376

Order 2816.

1232 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623247C211yesmaximal, characteristic
2#13077246C211yesmaximal, characteristic, complemented
3D11×#432C211yesmaximal, characteristic, complemented
4#13067334C211yesmaximal, characteristic, complemented
5#13067332C211yesmaximal, characteristic, complemented
6#13067330C211yesmaximal, characteristic, complemented
7#13067318C214yesmaximal, complemented
8#13067290C214yesmaximal, complemented
9C11×#1555C211yesmaximal, 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×#432C2211yescharacteristic
28C11×#432C2211yescharacteristic
29#10622539C2211yescharacteristic
30#10622539C2211yescharacteristic
31#10622450C2212yescomplemented
32#10622448C2212yescomplemented
33#10622446C2212yescomplemented
34D11×C4⋊C8C2212yescomplemented
35#10622339—21no—
36D11×C22⋊C8—21no—
37#10622332—21no—
38#10622331—21no—
39#10622320—21no—
40#10622318—21no—
41#10622318—21no—
42D11×#97—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—
61C11×#127—21no—
62C11×#127—21no—
63C11×#127C2×C412yes—
64C11×#127C2312yes—
65C2×C42×C11C2311yescharacteristic
66C2×C22⋊Dic11—22no—
67C2×C22⋊Dic11—22no—
68#66991—22no—
69#66991—22no—
70#66991—22no—
71#66991—22no—
72#66991—22no—
73#66991—22no—
74#66991C2×C414yes—
75#66991C2×C414yes—
76#66989—22no—
77#66989—22no—
78#66989—22no—
79#66989—22no—
80D4×Dic11—22no—
81D4×Dic11—22no—
82D4×Dic11—22no—
83D4×Dic11—22no—
84D4×Dic11—22no—
85D4×Dic11—22no—
86D4×Dic11C2×C414yes—
87D4×Dic11C2×C414yes—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11C2×C412yes—
90C2×C4×Dic11C2×C411yescharacteristic
91C2×C4×Dic11D411yescharacteristic
92C2×C4×Dic11D411yescharacteristic
93C2×#4313—22no—
94C2×C8×D11—22no—
95C42×D11C2×C411yescharacteristic
96C42×D11C2×C411yescharacteristic
97C42×D11D411yescharacteristic
98C42×D11D411yescharacteristic
99C42×D11D411yescharacteristic
100C42×D11D411yescharacteristic
101C42×D11C2311yescharacteristic
102C42×D11C2311yescharacteristic
103#66922—21no—
104#66922—21no—
105#66922C2×C412yes—
106#66922C2312yes—
107C11×C4⋊C8C2312yes—
108C11×C4⋊C8C2312yes—
109C11×C22⋊C8—21no—
110C11×C22⋊C8—21no—
111C11×#97—21no—
112C11×#97—21no—
113C22⋊(C11⋊C8)—21no—
114C22⋊(C11⋊C8)—21no—
115(C2×D11)⋊C8—22no—
116(C2×D11)⋊C8—22no—
117#66879—22no—
118Dic11⋊C8—22no—
119Dic11⋊C8—22no—
120C8×Dic11—22no—
121C4⋊(C11⋊C8)C2312yes—
122C4⋊(C11⋊C8)C2312yes—
123#66867—21no—
124#66867—21no—
125#17744—111nomaximal, Sylow
126C24×C11—22no—
127C23×D11C22⋊C411yescharacteristic
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—44no—
134C2×D4×C11—44no—
135C2×D4×C11—44no—
136C2×D4×C11C22×C414yes—
137C22×C4×C11C22×C411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C2×C22⋊D11—24no—
141C2×C22⋊D11—24no—
142C2×C22⋊D11—48no—
143C22×Dic11—24no—
144C22×Dic11—24no—
145C22×Dic11—22no—
146C22×Dic11—48no—
147C22×Dic11C22⋊C411yescharacteristic
148C22×Dic11C22⋊C411yescharacteristic
149C22×Dic11C22⋊C411yescharacteristic
150#4341—48no—
151#4341—48no—
152#4341—48no—
153#4341—48no—
154C2×C4×D11—24no—
155C2×C4×D11—42no—
156C2×C4×D11—42no—
157C2×C4×D11C22⋊C411yescharacteristic
158C2×C4×D11C22⋊C411yescharacteristic
159C2×C4×D11C22⋊C411yescharacteristic
160C2×C4×D11C22⋊C411yescharacteristic
161C2×C4×D11C22⋊C411yescharacteristic
162C2×C4×D11C22⋊C411yescharacteristic
163C2×C4×D11C22×C411yescharacteristic
164C2×C4×D11C22×C411yescharacteristic
165C2×C4×D11C2×D411yescharacteristic
166C2×C4×D11C2×D411yescharacteristic
167C2×C4×D11C2×D411yescharacteristic
168C2×C4×D11C2×D411yescharacteristic
169C2×Dic22—22no—
170C2×Dic22—22no—
171C2×Dic22—44no—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C42×C11C22×C411yescharacteristic
175C42×C11C2×D411yescharacteristic
176C42×C11C2×D411yescharacteristic
177C42×C11C2411yescharacteristic
178C22⋊Dic11—24no—
179C22⋊Dic11—24no—
180C22⋊Dic11—24no—
181C22⋊Dic11—24no—
182C4⋊Dic11—22no—
183C4⋊Dic11—22no—
184C4⋊Dic11—22no—
185C4⋊Dic11C22×C414yes—
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
198C2×C11⋊C8—22no—
199C2×C11⋊C8—22no—
200#4313—44no—
201C8×D11—44no—
202C2×#532—111no—
203#2920—111no—
204C2×#432—111no—
205#1556—111no—
206#1556—111no—
207#1555—111no—
208#1555D1111yescharacteristic, complemented
209#1553—114no—
210#1547—114no—
211C23×C11—24no—
212C23×C11—44no—
213C23×C11—44no—
214C23×C11—44no—
215C23×C11C2×C22⋊C411yescharacteristic
216C22×D11—22no—
217C22×D11—22no—
218C22×D11—41no—
219C22×D11C2×C22⋊C411yescharacteristic
220C22×D11C2×C22⋊C411yescharacteristic
221D4×C11—44no—
222D4×C11—44no—
223D4×C11—44no—
224D4×C11—44no—
225D4×C11—44no—
226D4×C11—44no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11C2×C22⋊C411yescharacteristic
231C2×C4×C11C2×C22⋊C411yescharacteristic
232C2×C4×C11C2×C22⋊C411yescharacteristic
233C2×C4×C11C23×C411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C22⋊D11—48no—
237C22⋊D11—48no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—24no—
241C2×Dic11—41no—
242C2×Dic11—48no—
243C2×Dic11—44no—
244C2×Dic11—48no—
245C2×Dic11C2×C22⋊C411yescharacteristic
246C2×Dic11C2×C22⋊C411yescharacteristic
247C2×Dic11C2×C22⋊C411yescharacteristic
248C2×Dic11C2×C22⋊C411yescharacteristic
249C2×Dic11C2×C22⋊C411yescharacteristic
250C2×Dic11C2×C22⋊C411yescharacteristic
251C4×D11—22no—
252C4×D11—22no—
253C4×D11—22no—
254C4×D11—22no—
255C4×D11—22no—
256C4×D11—41no—
257C4×D11—41no—
258C4×D11—41no—
259C4×D11—41no—
260C4×D11—41no—
261C4×D11—41no—
262C4×D11AGL(1,ℤ/8)14yes—
263Dic22—44no—
264Dic22—44no—
265C8×C11—42no—
266C8×C11—42no—
267C11⋊C8—42no—
268C11⋊C8—42no—
269C22×#41—221no—
270#532—112no—
271#532—112no—
272#532—112no—
273#532—112no—
274#532—221no—
275#532—221no—
276#532—221no—
277#532—221no—
278C2×C4⋊Q8—111no—
279C2×#127C2×D1111yescharacteristic
280C2×#124—221no—
281C2×#121—112no—
282C2×#121—221no—
283C2×C4×D4—112no—
284C2×C4×D4—221no—
285C22×C42—111no—
286#432—111no—
287#432—111no—
288#432—112no—
289#432—221no—
290#432—221no—
291#432—221no—
292#432C2×D1111yescharacteristic
293#432C2×D1111yescharacteristic
294#431—112no—
295#431—221no—
296#423—112no—
297C2×C4⋊C8—112no—
298#407—221no—
299C2×C22⋊C8—221no—
300C4×M16—221no—
301C2×#97—221no—
302#332—114no—
303#332—114no—
304#331—114no—
305#331C2×D1114yescomplemented
306C22×C11—21no—
307C22×C11—21no—
308C22×C11—44no—
309C22×C11—44no—
310C22×C11—44no—
311C22×C11—88no—
312C22×C11#41312yes—
313C22×C11C22×C22⋊C411yescharacteristic
314C2×D11—21no—
315C2×D11—21no—
316C2×D11—21no—
317C2×D11—21no—
318C2×D11—21no—
319C2×D11—44no—
320C2×D11#41812yes—
321C4×C11—21no—
322C4×C11—21no—
323C4×C11—21no—
324C4×C11—21no—
325C4×C11C2×AGL(1,ℤ/8)12yes—
326C4×C11#57512yes—
327Dic11—21no—
328Dic11—21no—
329Dic11—21no—
330Dic11—21no—
331Dic11—21no—
332Dic11—44no—
333Dic11#41812yes—
334C2×#41—222no—
335C2×#41—222no—
336C2×#41—222no—
337C2×#41—222no—
338C2×#41—448no—
339C22×Q8—221no—
340C22×D4—21no—
341C22×D4—21no—
342C22×D4—222no—
343C22×D4C4×D1112yes—
344C23×C4—111no—
345C23×C4—111no—
346C23×C4—111no—
347C23×C4—222no—
348C2×M16—222no—
349C22×C8—222no—
350C4⋊Q8—112no—
351C4⋊Q8—112no—
352C4⋊Q8—221no—
353C4⋊Q8—221no—
354#127—21no—
355#127—21no—
356#127C4×D1112yes—
357#127C22×D1112yes—
358#124—222no—
359#124—222no—
360#124—222no—
361#124—222no—
362#121—114no—
363#121—114no—
364#121—222no—
365#121—222no—
366#121—222no—
367#121—222no—
368#121—222no—
369#121—222no—
370C4×D4—114no—
371C4×D4—114no—
372C4×D4—222no—
373C4×D4—222no—
374C4×D4—222no—
375C4×D4—222no—
376C4×D4—222no—
377C4×D4—222no—
378C2×C4⋊C4—112no—
379C2×C4⋊C4—221no—
380C2×C22⋊C4—222no—
381C2×C22⋊C4—222no—
382C2×C42—111no—
383C2×C42—111no—
384C2×C42—111no—
385C2×C42—111no—
386C2×C42—111no—
387C2×C42—111no—
388C2×C42—111no—
389C2×C42—111no—
390C2×C42—111no—
391C2×C42—111no—
392C2×C42—111no—
393C2×C42C22×D1111yescharacteristic
394C4⋊C8—112no—
395C4⋊C8—112no—
396C4⋊C8—222no—
397C4⋊C8—222no—
398C4⋊C8C22×D1112yes—
399C4⋊C8C22×D1112yes—
400C22⋊C8—21no—
401C22⋊C8—21no—
402C22⋊C8—222no—
403C22⋊C8—222no—
404C22⋊C8—221no—
405C22⋊C8—221no—
406#97—21no—
407#97—21no—
408#97—222no—
409#97—221no—
410#97—221no—
411C4×C8—222no—
412C2×C11—22no—
413C2×C11—84no—
414C2×C11C2×#41311yescharacteristic
415C2×C11C2×#41811yescharacteristic
416C2×C11#289611yescharacteristic
417D11—22no—
418D11—41no—
419C24—22no—
420C24—111no—
421#41—448no—
422#41—448no—
423#41—448no—
424#41—448no—
425C2×Q8—222no—
426C2×Q8—222no—
427C2×Q8—444no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—44no—
436C2×D4—224no—
437C2×D4—224no—
438C2×D4—448no—
439C2×D4C2×C4×D1114yes—
440C22×C4—111no—
441C22×C4—111no—
442C22×C4—111no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—111no—
447C22×C4—111no—
448C22×C4—111no—
449C22×C4—111no—
450C22×C4—111no—
451C22×C4—111no—
452C22×C4—111no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—224no—
456C22×C4—224no—
457C22×C4—224no—
458C22×C4—222no—
459C22×C4—442no—
460C22×C4—442no—
461C22×C4—448no—
462C22×C4C2×C4×D1111yescharacteristic
463C22×C4D4×D1111yescharacteristic
464C22×C4D4×D1111yescharacteristic
465M16—444no—
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—222no—
469C2×C8—222no—
470C2×C8—444no—
471C4⋊C4—114no—
472C4⋊C4—222no—
473C4⋊C4—222no—
474C4⋊C4—222no—
475C22⋊C4—224no—
476C22⋊C4—224no—
477C22⋊C4—224no—
478C22⋊C4—224no—
479C42—111no—
480C42—111no—
481C42—111no—
482C42—111no—
483C42—111no—
484C42—111no—
485C42—111no—
486C42—111no—
487C42—111no—
488C42—111no—
489C42—111no—
490C42—111no—
491C42C2×C4×D1111yescharacteristic
492C42D4×D1111yescharacteristic
493C42D4×D1111yescharacteristic
494C42C23×D1111yescharacteristic
495C11#1774411yescharacteristic, complemented, Sylow
496C23—24no—
497C23—44no—
498C23—44no—
499C23—44no—
500C23—111no—
501C23—111no—
502C23—222no—
503C23—222no—
504C23—441no—
505C23C22⋊C4×D1111yescharacteristic
506Q8—444no—
507Q8—444no—
508D4—44no—
509D4—44no—
510D4—44no—
511D4—44no—
512D4—44no—
513D4—44no—
514D4—448no—
515D4—448no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—111no—
520C2×C4—114no—
521C2×C4—111no—
522C2×C4—111no—
523C2×C4—111no—
524C2×C4—111no—
525C2×C4—111no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—222no—
529C2×C4—222no—
530C2×C4—222no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4—224no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—448no—
541C2×C4—441no—
542C2×C4—448no—
543C2×C4—444no—
544C2×C4C22⋊C4×D1111yescharacteristic
545C2×C4C22⋊C4×D1111yescharacteristic
546C2×C4C22⋊C4×D1111yescharacteristic
547C2×C4C22×C4×D1111yescharacteristic
548C2×C4C2×D4×D1111yescharacteristic
549C2×C4C2×D4×D1111yescharacteristic
550C8—42no—
551C8—42no—
552C8—442no—
553C8—442no—
554C22—21no—
555C22—21no—
556C22—44no—
557C22—44no—
558C22—44no—
559C22—88no—
560C22—112no—
561C22—221no—
562C22—221no—
563C22—221no—
564C22—221no—
565C22—221no—
566C22—444no—
567C22#1062235812yes—
568C22C2×C22⋊C4×D1111yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—112no—
574C4—221no—
575C4—221no—
576C4—221no—
577C4—221no—
578C4—221no—
579C4—444no—
580C4D11×AGL(1,ℤ/8)12yes—
581C4#1062330412yes—
582C2—22no—
583C2—84no—
584C2—222no—
585C2—441no—
586C2C2×#1062235811yescharacteristic
587C2D11×#41811yescharacteristic
588C2#1307713011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1555C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623247C2
cosocleC42×C11C24
hypercenter#1555D11
hypocenterC11#17744
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1555

Complements

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

NH ≅ G/Ntype
2. #13077246C2semidirect
3. D11×#432C2semidirect
4. #13067334C2semidirect
5. #13067332C2semidirect
6. #13067330C2semidirect
7. #13067318C2semidirect
8. #13067290C2semidirect
9. C11×#1555C2semidirect
31. #10622450C22semidirect
32. #10622448C22semidirect
33. #10622446C22semidirect
34. D11×C4⋊C8C22semidirect
43. C11×#331C22semidirect
44. #10622182C22semidirect
45. #10622124C22semidirect
46. #10622120C22semidirect
208. #1555D11semidirect
305. #331C2×D11semidirect
495. C11#17744semidirect

Maximal subgroups

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

subgroupindex
C2×#106232472
#130772462
D11×#4322
#130673342
#130673322
#130673302
#130673182
#130672902
C11×#15552
#1774411