Finite Group Databasebeta

← #14792678

Subgroups — #14792678

Order 2816.

1002 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078556C211yesmaximal, characteristic, complemented
2C2×#10622830C211yesmaximal, characteristic
3#13077274C211yesmaximal, characteristic, complemented
4#13069976C212yesmaximal, complemented
5#13069871C212yesmaximal, complemented
6#13069525C212yesmaximal, complemented
7#13069281C212yesmaximal, complemented
8#13069079C211yesmaximal, characteristic, complemented
9#13068821C211yesmaximal, characteristic, complemented
10#13068537C211yesmaximal, characteristic, complemented
11C2×C11×#418C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C22×#4323C2212yes—
16C2×#66983C2211yescharacteristic
17C11×#418—21no—
18C11×#418—21no—
19C11×#418C2212yes—
20C11×#418C2212yes—
21C2×C11×#102—21no—
22C2×C11×#102—21no—
23#10622830—21no—
24#10622830—21no—
25#10622830—22no—
26C2×#66897C2212yes—
27C2×#66897C2212yes—
28C2×#66896C2212yes—
29#10622820C2211yescharacteristic
30#10622820C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×#66887C2212yescomplemented
33C2×#66886C2212yescomplemented
34#10622616—21no—
35#10622616—21no—
36#10622614C2211yescharacteristic, complemented
37#10622614C2211yescharacteristic, complemented
38#10622613—22no—
39#10622612C2212yescomplemented
40#10622610C2212yescomplemented
41#10622608C2211yescharacteristic, complemented
42#10622608C2211yescharacteristic, complemented
43#10622581—21no—
44#10622580—21no—
45#10622539—21no—
46#10622538—21no—
47#10622196C2212yescomplemented
48#10622192C2212yescomplemented
49C25×C11—21no—
50C22×D4×C11—24no—
51C22×D4×C11—21no—
52C22×D4×C11—21no—
53C22×D4×C11—21no—
54C22×D4×C11—21no—
55C22×D4×C11—21no—
56C22×D4×C11—42no—
57C22×D4×C11C2312yes—
58C23×C4×C11C2311yescharacteristic
59C22×C22⋊D11—21no—
60C22×D44C2311yescharacteristic
61C2×C11×M16—21no—
62C2×C11×M16—42no—
63C2×C11×M16C2312yes—
64C22×C8×C11—21no—
65C11×#117—21no—
66C11×#117—21no—
67C11×#117D411yescharacteristic
68C11×#117D411yescharacteristic
69C11×#117C2311yescharacteristic
70C11×#117C2311yescharacteristic
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C42×C11—21no—
75C2×#4323—24no—
76C2×#4323—22no—
77C2×#4323—22no—
78C2×#4323—42no—
79#66983—21no—
80#66983—21no—
81#66983—21no—
82#66983—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×#4318C2311yescharacteristic
86C2×#4318C2312yes—
87C2×#4318C2311yescharacteristic
88C22×C11⋊C8C2312yes—
89C11×#102—22no—
90C11×#102—22no—
91C11×#102—22no—
92C11×#102—22no—
93#66897—24no—
94#66897—42no—
95#66896—22no—
96#66896—22no—
97C22⋊(C11⋊C8)—21no—
98C22⋊(C11⋊C8)—21no—
99C22⋊(C11⋊C8)—21no—
100C22⋊(C11⋊C8)—21no—
101C22⋊(C11⋊C8)D411yescharacteristic
102C22⋊(C11⋊C8)D411yescharacteristic
103C22⋊(C11⋊C8)D412yes—
104#66887—42no—
105#66886—42no—
106#66873—21no—
107#66873—21no—
108#66873—21no—
109#66873—21no—
110#66872—21no—
111#66872—21no—
112#66871—21no—
113#66871—21no—
114C4⋊(C11⋊C8)—22no—
115C4⋊(C11⋊C8)—22no—
116#66867—22no—
117C4×C11⋊C8—22no—
118#24520—111nomaximal, Sylow
119C24×C11—22no—
120C24×C11—44no—
121C24×C11—41no—
122C24×C11—41no—
123C24×C11—82no—
124C24×C11—82no—
125C24×C11#4111yescharacteristic
126C23×D11—21no—
127C2×D4×C11—24no—
128C2×D4×C11—24no—
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—44no—
137C2×D4×C11—42no—
138C2×D4×C11—42no—
139C2×D4×C11—41no—
140C2×D4×C11—41no—
141C2×D4×C11#4114yes—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11#4111yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C2×C22⋊D11—41no—
153C2×C22⋊D11—41no—
154C2×C22⋊D11—82no—
155C22×Dic11—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—22no—
159C2×D44—22no—
160C11×M16—22no—
161C11×M16—22no—
162C11×M16—42no—
163C2×C8×C11—22no—
164C2×C8×C11—42no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4C2×D411yescharacteristic
168C11×C4⋊C4C2×D411yescharacteristic
169C11×C4⋊C4C2×D411yescharacteristic
170C11×C4⋊C4C2×D411yescharacteristic
171C11×C22⋊C4—21no—
172C11×C22⋊C4—21no—
173C11×C22⋊C4—21no—
174C11×C22⋊C4—21no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179#4323—44no—
180#4323—44no—
181(C2×D11)⋊C4—41no—
182(C2×D11)⋊C4—41no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185#4318—22no—
186#4318—22no—
187#4318—22no—
188#4318—22no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8C2×D412yes—
195C2×C11⋊C8C2×D412yes—
196#3094—111no—
197C2×#447—111no—
198#2924—111no—
199C2×#418D1111yescharacteristic, complemented
200#2063—112no—
201#2045—112no—
202#1978—112no—
203#1931—112no—
204#1900—111no—
205#1855—111no—
206#1783—111no—
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—24no—
210C23×C11—41no—
211C23×C11—44no—
212C23×C11—44no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—82no—
216C23×C11—82no—
217C23×C11—82no—
218C23×C11—82no—
219C23×C11—82no—
220C23×C11—816no—
221C23×C11—82no—
222C23×C11#12111yescharacteristic
223C23×C11#12111yescharacteristic
224C23×C11C2×#4111yescharacteristic
225C22×D11—41no—
226C22×D11—42no—
227C22×D11—81no—
228C22×D11—81no—
229D4×C11—24no—
230D4×C11—24no—
231D4×C11—44no—
232D4×C11—44no—
233D4×C11—42no—
234D4×C11—42no—
235C2×C4×C11—22no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—42no—
247C2×C4×C11—81no—
248C2×C4×C11#12111yescharacteristic
249C2×C4×C11#12111yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C2×#4112yes—
253C2×C4×C11H(5,𝔽2)12yes—
254C22⋊D11—82no—
255C22⋊D11—82no—
256C2×Dic11—41no—
257C2×Dic11—81no—
258D44—41no—
259D44—41no—
260D44—42no—
261C8×C11—42no—
262C11⋊C8—22no—
263C11⋊C8—22no—
264C11⋊C8—41no—
265C11⋊C8—41no—
266C11⋊C8—42no—
267C23×D4C2×D1111yescharacteristic
268C22×D8—112no—
269C22×M16C2×D1111yescharacteristic
270C2×#121—111no—
271C2×#117C2×D1111yescharacteristic
272#482—221no—
273#482—221no—
274#481—221no—
275#480—221no—
276#447—221no—
277#447—221no—
278#447—222no—
279#433—222no—
280#432—221no—
281#431—221no—
282C2×#108—112no—
283#428—111no—
284#428—111no—
285#424—112no—
286#418—21no—
287#418—21no—
288#418—111no—
289#418—111no—
290#418C2×D1112yes—
291#418C2×D1112yes—
292C2×#102—21no—
293C2×#102—21no—
294C2×#102—112no—
295C2×#100—112no—
296C2×#100—112no—
297C2×#100—112no—
298#407—111no—
299#407—111no—
300C2×C22⋊C8—111no—
301#405—112no—
302#343—112no—
303#341—112no—
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—21no—
307C22×C11—21no—
308C22×C11—21no—
309C22×C11—21no—
310C22×C11—21no—
311C22×C11—44no—
312C22×C11—44no—
313C22×C11—84no—
314C22×C11—84no—
315C22×C11—88no—
316C22×C11—88no—
317C22×C11—82no—
318C22×C11—82no—
319C22×C11#47212yes—
320C22×C11C2×#12111yescharacteristic
321C22×C11#55112yes—
322C2×D11—81no—
323C2×D11—81no—
324C2×D11—81no—
325C2×D11—162no—
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—41no—
329C4×C11—41no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11#52511yescharacteristic
333C4×C11#53511yescharacteristic
334C4×C11#54612yes—
335Dic11—81no—
336C25—21no—
337C22×D4—24no—
338C22×D4—21no—
339C22×D4—21no—
340C22×D4—21no—
341C22×D4—21no—
342C22×D4—21no—
343C22×D4—42no—
344C22×D4—111no—
345C22×D4—221no—
346C22×D4C22×D1112yes—
347C23×C4C22×D1111yescharacteristic
348C2×D8—222no—
349C2×D8—222no—
350C2×D8—224no—
351C2×D8—442no—
352C2×M16—21no—
353C2×M16—42no—
354C2×M16—111no—
355C2×M16—112no—
356C2×M16—111no—
357C2×M16C22×D1112yes—
358C22×C8—21no—
359C22×C8—112no—
360#121—221no—
361#121—221no—
362#121—221no—
363#121—221no—
364#117—21no—
365#117—21no—
366#117C22⋊D1111yescharacteristic
367#117C22⋊D1111yescharacteristic
368#117C22×D1111yescharacteristic
369#117C22×D1111yescharacteristic
370C2×C4⋊C4—111no—
371C2×C4⋊C4C22⋊D1111yescharacteristic
372C2×C4⋊C4C22⋊D1111yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—221no—
375C2×C42—21no—
376#108—442no—
377#107—221no—
378#107—221no—
379#106—221no—
380#106—221no—
381C4⋊C8—222no—
382C4⋊C8—222no—
383#102—22no—
384#102—22no—
385#102—22no—
386#102—22no—
387#102—222no—
388#102—222no—
389#102—221no—
390#102—221no—
391#102—221no—
392#102—221no—
393#100—224no—
394#100—442no—
395#100—442no—
396C22⋊C8—111no—
397C22⋊C8—111no—
398C22⋊C8—112no—
399C22⋊C8—221no—
400C22⋊C8—221no—
401C22⋊C8—221no—
402C22⋊C8—221no—
403#97—222no—
404C4×C8—222no—
405C2×C11—22no—
406C2×C11—22no—
407C2×C11—41no—
408C2×C11—84no—
409C2×C11#241111yescharacteristic
410C2×C11C2×#47211yescharacteristic
411C2×C11#306811yescharacteristic
412D11—161no—
413C24—22no—
414C24—44no—
415C24—41no—
416C24—41no—
417C24—82no—
418C24—82no—
419C24—221no—
420C24#434111yescharacteristic
421C2×D4—24no—
422C2×D4—24no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—44no—
429C2×D4—44no—
430C2×D4—44no—
431C2×D4—42no—
432C2×D4—42no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—222no—
436C2×D4—221no—
437C2×D4—222no—
438C2×D4—221no—
439C2×D4—441no—
440C2×D4—441no—
441C2×D4—882no—
442C2×D4#433914yes—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—221no—
448C22×C4D4×D1111yescharacteristic
449C22×C4D4×D1111yescharacteristic
450C22×C4#434111yescharacteristic
451C22×C4C2×C22⋊D1111yescharacteristic
452C22×C4C2×C22⋊D1111yescharacteristic
453C22×C4C23×D1111yescharacteristic
454D8—444no—
455D8—444no—
456M16—22no—
457M16—22no—
458M16—42no—
459M16—222no—
460M16—222no—
461M16—222no—
462M16—222no—
463C2×C8—22no—
464C2×C8—42no—
465C2×C8—112no—
466C2×C8—112no—
467C2×C8—222no—
468C2×C8—222no—
469C2×C8—222no—
470C2×C8—221no—
471C2×C8—221no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4C2×C22⋊D1111yescharacteristic
477C4⋊C4C2×C22⋊D1111yescharacteristic
478C4⋊C4C2×C22⋊D1111yescharacteristic
479C4⋊C4C2×C22⋊D1111yescharacteristic
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—441no—
485C22⋊C4—441no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C11#2452011yescharacteristic, complemented, Sylow
491C23—22no—
492C23—22no—
493C23—24no—
494C23—41no—
495C23—44no—
496C23—44no—
497C23—42no—
498C23—42no—
499C23—82no—
500C23—82no—
501C23—82no—
502C23—82no—
503C23—82no—
504C23—816no—
505C23—82no—
506C23—441no—
507C23—442no—
508C23—881no—
509C23—881no—
510C23#6699211yescharacteristic
511C23#6699211yescharacteristic
512C23C2×#434111yescharacteristic
513D4—24no—
514D4—24no—
515D4—44no—
516D4—44no—
517D4—42no—
518D4—42no—
519D4—442no—
520D4—441no—
521D4—441no—
522D4—882no—
523D4—882no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—42no—
536C2×C4—81no—
537C2×C4—441no—
538C2×C4—881no—
539C2×C4#6699211yescharacteristic
540C2×C4#6699211yescharacteristic
541C2×C4C2×#433912yes—
542C2×C4C2×D4×D1111yescharacteristic
543C2×C4#6703712yes—
544C2×C4C22×C22⋊D1111yescharacteristic
545C8—42no—
546C8—222no—
547C8—222no—
548C8—442no—
549C8—441no—
550C8—441no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—44no—
559C22—44no—
560C22—84no—
561C22—84no—
562C22—88no—
563C22—88no—
564C22—82no—
565C22—82no—
566C22—881no—
567C22—881no—
568C22—881no—
569C22—1762no—
570C22#1062281212yes—
571C22#1062302612yes—
572C22C2×#6699211yescharacteristic
573C4—21no—
574C4—21no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—881no—
580C4#1062302112yes—
581C4#1062332211yescharacteristic
582C4#1062333611yescharacteristic
583C2—22no—
584C2—22no—
585C2—41no—
586C2—84no—
587C2—1761no—
588C2#1307200111yescharacteristic
589C2C2×#1062281211yescharacteristic
590C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#418C2
socleC22×C11C2×#121
prime radicalC2×#10622830C2
hypercenterC2×#418D11
hypocenterC11#24520
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
1. #13078556C2semidirect
3. #13077274C2semidirect
4. #13069976C2semidirect
5. #13069871C2semidirect
6. #13069525C2semidirect
7. #13069281C2semidirect
8. #13069079C2semidirect
9. #13068821C2semidirect
10. #13068537C2semidirect
11. C2×C11×#418C2semidirect
32. C2×#66887C22semidirect
33. C2×#66886C22semidirect
36. #10622614C22semidirect
37. #10622614C22semidirect
39. #10622612C22semidirect
40. #10622610C22semidirect
41. #10622608C22semidirect
42. #10622608C22semidirect
47. #10622196C22semidirect
48. #10622192C22semidirect
199. C2×#418D11semidirect
490. C11#24520semidirect

Maximal subgroups

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

subgroupindex
#130785562
C2×#106228302
#130772742
#130699762
#130698712
#130695252
#130692812
#130690792
#130688212
#130685372
C2×C11×#4182
#2452011