Finite Group Databasebeta

← #14810387

Subgroups — #14810387

Order 2816.

1446 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66941C211yesmaximal, characteristic, complemented
2C2×#10622373C212yesmaximal, complemented
3#13076959C211yesmaximal, characteristic
4#13069751C212yesmaximal, complemented
5#13069750C212yesmaximal, complemented
6#13069575C212yesmaximal, complemented
7#13068934C211yesmaximal, characteristic, complemented
8#13068933C211yesmaximal, characteristic, complemented
9#13068931C211yesmaximal, characteristic, complemented
10C22⋊C8×Dic11C211yesmaximal, characteristic, complemented
11C11×#1874C211yesmaximal, characteristic, complemented
12C23×Dic22—21no—
13C2×C11×#121C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×#66993C2211yescharacteristic
16C2×#66992—21no—
17C2×#66992—21no—
18C2×#66983C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×Dic11⋊C4—21no—
21C22×C4×Dic11C2211yescharacteristic
22C2×#66941—21no—
23C2×#66941—21no—
24C2×#66941—28no—
25C2×#66941C2212yes—
26C2×#66941C2212yes—
27C2×C11×#102C2212yes—
28C2×C11×C22⋊C8C2211yescharacteristic
29#10622834C2211yescharacteristic
30C2×#66896C2212yes—
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×#66885C2212yes—
33C2×C8×Dic11C2212yes—
34#10622601C2211yescharacteristic
35#10622589C2211yescharacteristic
36C2×#66873C2212yes—
37#10622570—21no—
38#10622570—21no—
39#10622373—28no—
40C11×#340C2212yes—
41#10622189C2212yes—
42#10622188C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×D4×C11—21no—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11C2311yescharacteristic
49C22×C22⋊D11—21no—
50C22×C22⋊D11—21no—
51C22×C22⋊D11—21no—
52C23×Dic11—21no—
53C23×Dic11D411yescharacteristic
54C23×Dic11D411yescharacteristic
55C22×D44C2311yescharacteristic
56C22×Dic22—28no—
57C22×Dic22—22no—
58C22×Dic22—22no—
59C22×Dic22—44no—
60C22×Dic22—44no—
61C22×C8×C11C2312yes—
62C11×#121—22no—
63C11×#121—22no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—24no—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C22⋊C4—21no—
69C2×C22⋊Dic11—21no—
70C2×C22⋊Dic11—21no—
71#66993—24no—
72#66992—44no—
73#66992—44no—
74#66983—22no—
75#66983—22no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—24no—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2312yes—
83C2×Dic11⋊C4—28no—
84C2×Dic11⋊C4—22no—
85C2×Dic11⋊C4—22no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×C4×Dic11—24no—
89C2×C4×Dic11D411yescharacteristic
90C2×C4×Dic11D411yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C2×C4×Dic11C2311yescharacteristic
93C22×C11⋊C8C2312yes—
94#66941—28no—
95#66941—28no—
96#66941—24no—
97#66941—24no—
98#66941—24no—
99#66941D418yescomplemented
100C11×#102—24no—
101C11×C22⋊C8—22no—
102#66896—24no—
103C22⋊(C11⋊C8)—22no—
104#66885—24no—
105C8×Dic11—24no—
106#66873—24no—
107#25903—111nomaximal, Sylow
108C24×C11—21no—
109C24×C11C2×D411yescharacteristic
110C23×D11—21no—
111C2×D4×C11—22no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—22no—
115C2×D4×C11—42no—
116C2×D4×C11—42no—
117C2×D4×C11—42no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—24no—
121C22×C4×C11—22no—
122C22×C4×C11—21no—
123C22×C4×C11—42no—
124C22×C4×C11—42no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11#4112yes—
127C22×C4×C11#4112yes—
128C22×C4×C11C2411yescharacteristic
129C2×C22⋊D11—42no—
130C2×C22⋊D11—42no—
131C2×C22⋊D11—42no—
132C2×C22⋊D11—42no—
133C2×C22⋊D11—42no—
134C2×C22⋊D11—42no—
135C2×C22⋊D11—42no—
136C2×C22⋊D11—42no—
137C2×C22⋊D11—42no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—24no—
143C22×Dic11—22no—
144C22×Dic11—21no—
145C22×Dic11—42no—
146C22×Dic11—42no—
147C22×Dic11D814yes—
148C22×Dic11SD1614yes—
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C2×D44—22no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—22no—
157C2×Dic22—28no—
158C2×Dic22—28no—
159C2×Dic22—432no—
160C2×Dic22—44no—
161C2×Dic22—44no—
162C2×Dic22—44no—
163C2×Dic22—44no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4C2×D414yes—
172C11×C22⋊C4—42no—
173C22⋊Dic11—42no—
174C22⋊Dic11—42no—
175(C2×D11)⋊C4—42no—
176(C2×D11)⋊C4—42no—
177(C2×D11)⋊C4—42no—
178C4⋊Dic11—24no—
179C4⋊Dic11—22no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11C2×D414yes—
183Dic11⋊C4—28no—
184Dic11⋊C4—28no—
185Dic11⋊C4—42no—
186Dic11⋊C4—42no—
187C4×Dic11—22no—
188C4×Dic11—22no—
189C4×Dic11—22no—
190C4×Dic11C2×D414yes—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C22×C4⋊Q8—111no—
195C2×#486—112no—
196#2856—111no—
197#2023—112no—
198#2023—112no—
199#1990—112no—
200#1874—111no—
201#1874—111no—
202#1874—111no—
203#1874D1111yescharacteristic, complemented
204C4×C22⋊C8—111no—
205C23×C11—21no—
206C23×C11—21no—
207C23×C11—21no—
208C23×C11—21no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11#12412yes—
217C23×C11C2×D812yes—
218C23×C11C2×SD1612yes—
219C23×C11C22×D411yescharacteristic
220C22×D11—41no—
221C22×D11—41no—
222C22×D11—41no—
223C22×D11—41no—
224C22×D11—41no—
225C22×D11—41no—
226C22×D11—41no—
227D4×C11—42no—
228D4×C11—42no—
229D4×C11—84no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—48no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11#12412yes—
242C2×C4×C11C22×D412yes—
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C112−1+412yes—
246C22⋊D11—84no—
247C22⋊D11—84no—
248C22⋊D11—84no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—28no—
254C2×Dic11—28no—
255C2×Dic11—24no—
256C2×Dic11—48no—
257C2×Dic11—42no—
258C2×Dic11—42no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11#12012yes—
263C2×Dic11#12012yes—
264C2×Dic11C2×D812yes—
265C2×Dic11C2×D812yes—
266C2×Dic11C2×SD1612yes—
267C2×Dic11C2×SD1612yes—
268C2×Dic11AGL(1,ℤ/8)12yes—
269C2×Dic11#13712yes—
270D44—42no—
271D44—42no—
272Dic22—416no—
273Dic22—416no—
274C8×C11—42no—
275C11⋊C8—42no—
276C23×Q8—221no—
277C2×C4⋊Q8—112no—
278C2×C4⋊Q8—112no—
279C2×C4⋊Q8—221no—
280C2×C4⋊Q8—221no—
281C2×C4⋊Q8—228no—
282C2×#127—111no—
283C2×#121—111no—
284C2×#121—221no—
285C2×#121—221no—
286C2×#121C2×D1111yescharacteristic
287C22×C4⋊C4—111no—
288C22×C4⋊C4—221no—
289C22×C4⋊C4C2×D1111yescharacteristic
290C22×C42—111no—
291#486—228no—
292C2×#102—112no—
293C2×#102—112no—
294C2×#102—112no—
295C2×#102C2×D1112yes—
296C2×C22⋊C8—111no—
297C2×C22⋊C8C2×D1111yescharacteristic
298C2×C4×C8—112no—
299#390—111no—
300#390—111no—
301#390—221no—
302#390—221no—
303#384—111no—
304#340—112no—
305#340—112no—
306#340—112no—
307#340C2×D1112yes—
308#336—112no—
309C22×C11—22no—
310C22×C11—22no—
311C22×C11—22no—
312C22×C11—22no—
313C22×C11—22no—
314C22×C11—22no—
315C22×C11—81no—
316C22×C11—81no—
317C22×C11—81no—
318C22×C11—81no—
319C22×C11—81no—
320C22×C11—81no—
321C22×C11—81no—
322C22×C11#48614yescomplemented
323C22×C11C2×#12011yescharacteristic
324C22×C11C2×#12411yescharacteristic
325C22×C11#53611yescharacteristic
326C22×C11C22×D811yescharacteristic
327C22×C11C22×SD1611yescharacteristic
328C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
329C22×C11C2×#13711yescharacteristic
330C2×D11—81no—
331C2×D11—81no—
332C2×D11—81no—
333C2×D11—81no—
334C2×D11—81no—
335C2×D11—81no—
336C2×D11—81no—
337C4×C11—22no—
338C4×C11—44no—
339C4×C11—81no—
340C4×C11#54812yes—
341C4×C11#54812yes—
342Dic11—22no—
343Dic11—22no—
344Dic11—44no—
345Dic11—81no—
346Dic11#44714yes—
347Dic11#44814yes—
348C22×Q8—222no—
349C22×Q8—222no—
350C22×Q8—228no—
351C22×Q8—444no—
352C22×Q8—444no—
353C22×D4—21no—
354C22×D4—111no—
355C22×D4—221no—
356C22×D4—221no—
357C22×D4—221no—
358C22×D4C22×D1111yescharacteristic
359C23×C4—21no—
360C23×C4—111no—
361C23×C4—111no—
362C23×C4—221no—
363C23×C4C22×D1111yescharacteristic
364C22×C8—112no—
365C22×C8C22×D1112yes—
366C4⋊Q8—118no—
367C4⋊Q8—224no—
368C4⋊Q8—224no—
369C4⋊Q8—228no—
370C4⋊Q8—228no—
371C4⋊Q8—224no—
372#127—224no—
373#121—22no—
374#121—22no—
375#121—222no—
376#121—222no—
377#121—444no—
378#121—444no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—24no—
381C2×C4⋊C4—112no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—224no—
384C2×C4⋊C4—222no—
385C2×C4⋊C4—222no—
386C2×C4⋊C4—228no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4C22×D1111yescharacteristic
391C2×C4⋊C4C22×D1112yes—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—221no—
394C2×C22⋊C4—221no—
395C2×C22⋊C4—221no—
396C2×C22⋊C4—221no—
397C2×C22⋊C4—221no—
398C2×C42—111no—
399C2×C42—111no—
400C2×C42—111no—
401C2×C42—111no—
402C2×C42—224no—
403#102—24no—
404#102—224no—
405#102—224no—
406#102—224no—
407C22⋊C8—22no—
408C22⋊C8—222no—
409C4×C8—224no—
410C2×C11—24no—
411C2×C11—161no—
412C2×C11#243611yescharacteristic
413C2×C11C2×#44711yescharacteristic
414C2×C11C2×#44811yescharacteristic
415C2×C11C2×#48611yescharacteristic
416C2×C11#314111yescharacteristic
417C2×C11#322611yescharacteristic
418C2×C11#322711yescharacteristic
419D11—161no—
420C24—21no—
421C24—221no—
422C24D4×D1111yescharacteristic
423C2×Q8—228no—
424C2×Q8—228no—
425C2×Q8—444no—
426C2×Q8—444no—
427C2×Q8—444no—
428C2×Q8—4432no—
429C2×Q8—444no—
430C2×D4—21no—
431C2×D4—22no—
432C2×D4—21no—
433C2×D4—22no—
434C2×D4—42no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4—221no—
438C2×D4—222no—
439C2×D4—221no—
440C2×D4—222no—
441C2×D4—442no—
442C2×D4—442no—
443C2×D4—442no—
444C2×D4—442no—
445C2×D4—442no—
446C2×D4—442no—
447C2×D4—442no—
448C2×D4—442no—
449C2×D4—442no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—24no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—111no—
458C22×C4—111no—
459C22×C4—114no—
460C22×C4—114no—
461C22×C4—111no—
462C22×C4—111no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—222no—
466C22×C4—222no—
467C22×C4—224no—
468C22×C4—222no—
469C22×C4—221no—
470C22×C4—442no—
471C22×C4—442no—
472C22×C4#433912yes—
473C22×C4D4×D1111yescharacteristic
474C22×C4#434112yes—
475C22×C4C23×D1111yescharacteristic
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—222no—
480C2×C8—222no—
481C2×C8—222no—
482C4⋊C4—24no—
483C4⋊C4—22no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—114no—
487C4⋊C4—228no—
488C4⋊C4—228no—
489C4⋊C4—224no—
490C4⋊C4—222no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—442no—
494C4⋊C4—442no—
495C4⋊C4D4×D1114yes—
496C22⋊C4—42no—
497C22⋊C4—442no—
498C22⋊C4—442no—
499C22⋊C4—442no—
500C22⋊C4—442no—
501C22⋊C4—442no—
502C42—114no—
503C42—222no—
504C42—222no—
505C42—222no—
506C11#2590311yescharacteristic, complemented, Sylow
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—441no—
519C23—441no—
520C23—441no—
521C23—441no—
522C23—441no—
523C23—441no—
524C23—441no—
525C23#6693812yes—
526C23D8×D1112yes—
527C23SD16×D1112yes—
528C23C2×D4×D1111yescharacteristic
529Q8—4416no—
530Q8—4416no—
531D4—42no—
532D4—42no—
533D4—84no—
534D4—442no—
535D4—442no—
536D4—884no—
537D4—884no—
538D4—884no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—48no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—112no—
551C2×C4—112no—
552C2×C4—112no—
553C2×C4—112no—
554C2×C4—112no—
555C2×C4—112no—
556C2×C4—112no—
557C2×C4—112no—
558C2×C4—228no—
559C2×C4—228no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—224no—
565C2×C4—448no—
566C2×C4—442no—
567C2×C4—442no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4#6693812yes—
572C2×C4C2×#433911yescharacteristic
573C2×C4C2×D4×D1112yes—
574C2×C4C2×#434111yescharacteristic
575C2×C4#6704312yes—
576C8—42no—
577C8—442no—
578C22—22no—
579C22—22no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—22no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—881no—
592C22—881no—
593C22—881no—
594C22—881no—
595C22—881no—
596C22—881no—
597C22—881no—
598C22#1062237314yescomplemented
599C22C2×#6693811yescharacteristic
600C22D11×#12011yescharacteristic
601C22#1062317911yescharacteristic
602C22C2×D8×D1111yescharacteristic
603C22C2×SD16×D1111yescharacteristic
604C22D11×AGL(1,ℤ/8)11yescharacteristic
605C22D11×#13711yescharacteristic
606C4—22no—
607C4—44no—
608C4—81no—
609C4—114no—
610C4—114no—
611C4—222no—
612C4—222no—
613C4—444no—
614C4—881no—
615C4#1062308312yes—
616C4#1062312912yes—
617C2—24no—
618C2—161no—
619C2—1761no—
620C2#1307227211yescharacteristic
621C2D11×#44711yescharacteristic
622C2D11×#44811yescharacteristic
623C2C2×#1062237311yescharacteristic
624C2#1307900711yescharacteristic
625C2#1307973511yescharacteristic
626C2#1307974211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1874C2
socleC23×C11C22×D4
prime radical#13076959C2
hypercenter#1874D11
hypocenterC11#25903
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
1. C22×#66941C2semidirect
2. C2×#10622373C2semidirect
4. #13069751C2semidirect
5. #13069750C2semidirect
6. #13069575C2semidirect
7. #13068934C2semidirect
8. #13068933C2semidirect
9. #13068931C2semidirect
10. C22⋊C8×Dic11C2semidirect
11. C11×#1874C2semidirect
99. #66941D4semidirect
203. #1874D11semidirect
322. C22×C11#486semidirect
506. C11#25903semidirect
598. C22#10622373semidirect

Maximal subgroups

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

subgroupindex
C22×#669412
C2×#106223732
#130769592
#130697512
#130697502
#130695752
#130689342
#130689332
#130689312
C22⋊C8×Dic112
C11×#18742
#2590311