Finite Group Databasebeta

← #14727636

Subgroups — #14727636

Order 2816.

1034 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079369C211yesmaximal, characteristic, complemented
2#13079364C211yesmaximal, characteristic
3#13074358C211yesmaximal, characteristic, complemented
4#13067613C214yesmaximal, complemented
5#13067545C214yesmaximal, complemented
6#13067188C211yesmaximal, characteristic, complemented
7#13067184C211yesmaximal, characteristic, complemented
8C2×#10622166C211yesmaximal, characteristic, complemented
9C2×C11×#539C211yesmaximal, characteristic, complemented
10C11×#539—22no—
11C11×#539—22no—
12C11×#539—22no—
13C11×#539C2214yes—
14C2×C11×#126—21no—
15C2×C11×#125—21no—
16C2×C11×#123—21no—
17C2×C11×#123—21no—
18C2×C11×C22⋊Q8—21no—
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×C4×D4×C11—21no—
22C22×C11×C4⋊C4C2211yescharacteristic
23C2×#66983C2211yescharacteristic
24C2×#66982—21no—
25#10622840—21no—
26#10622830—21no—
27#10622826—21no—
28#10622825C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31#10622661—22no—
32#10622659C2212yescomplemented
33#10622656C2212yescomplemented
34#10622651—22no—
35#10622649C2212yes—
36#10622646C2212yes—
37#10622607—22no—
38#10622604C2212yescomplemented
39#10622596C2212yescomplemented
40#10622581—21no—
41#10622580—21no—
42#10622176C2214yescomplemented
43#10622175C2214yes—
44#10622166C2214yescomplemented
45C22×Q8×C11D411yescharacteristic
46C22×D4×C11—21no—
47C22×D4×C11D411yescharacteristic
48C23×C4×C11—21no—
49C23×C4×C11D411yescharacteristic
50C23×C4×C11D411yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C22×C22⋊D11—21no—
53C22×D44C2311yescharacteristic
54C11×#126—24no—
55C11×#126—24no—
56C11×#125—24no—
57C11×#125—24no—
58C11×#123—24no—
59C11×#123—24no—
60C11×#123—24no—
61C11×#123—24no—
62C11×C22⋊Q8—24no—
63C11×C22⋊Q8—24no—
64C11×C22⋊Q8—21no—
65C11×C22⋊Q8—21no—
66C11×C22⋊Q8D412yes—
67C11×C22⋊Q8C2312yes—
68C11×#121—21no—
69C11×#121—21no—
70C11×#121D412yes—
71C11×#121C2312yes—
72C4×D4×C11—24no—
73C4×D4×C11—24no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4D412yes—
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C4⋊C4D411yescharacteristic
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C42×C11—21no—
92C2×C22⋊Dic11—21no—
93C2×#4325—22no—
94C2×#4323—22no—
95#66983—21no—
96#66983—21no—
97#66983—21no—
98#66983—21no—
99#66982—44no—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4—22no—
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11C2311yescharacteristic
105C2×Dic11⋊C4—22no—
106C22×C11⋊C8—21no—
107C22×C11⋊C8—21no—
108#66899—22no—
109#66896—22no—
110C11⋊#95—22no—
111C11⋊#95C2312yes—
112C22⋊(C11⋊C8)—21no—
113C22⋊(C11⋊C8)—21no—
114C22⋊(C11⋊C8)C2312yes—
115C22⋊(C11⋊C8)C2312yes—
116#66873—22no—
117#66873—22no—
118#66872—22no—
119#66871—22no—
120#18288—111nomaximal, Sylow
121C24×C11—21no—
122C24×C11C2×D411yescharacteristic
123C23×D11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—81no—
126C2×Q8×C11C2×D412yes—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—21no—
130C2×D4×C11—42no—
131C2×D4×C11—42no—
132C2×D4×C11—81no—
133C2×D4×C11C2×D412yes—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—24no—
143C22×C4×C11—21no—
144C22×C4×C11—81no—
145C22×C4×C11—81no—
146C22×C4×C11—82no—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C2×C22⋊D11—41no—
156C2×C22⋊D11—41no—
157C2×C22⋊D11—42no—
158C2×C22⋊D11—42no—
159C22×Dic11—21no—
160C22×Dic11—22no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—81no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—24no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4C2×D412yes—
176C11×C4⋊C4C2×D412yes—
177C11×C22⋊C4—24no—
178C11×C22⋊C4—24no—
179C11×C22⋊C4—24no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—22no—
184C42×C11—24no—
185C22⋊Dic11—42no—
186#4325—82no—
187#4323—82no—
188(C2×D11)⋊C4—44no—
189(C2×D11)⋊C4—41no—
190(C2×D11)⋊C4—41no—
191(C2×D11)⋊C4—82no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—81no—
195Dic11⋊C4—44no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8—81no—
199C2×C11⋊C8—81no—
200C2×#539D1111yescharacteristic, complemented
201#3187—111no—
202#3186—111no—
203#2618—111no—
204#1609—114no—
205#1597—114no—
206#1520—111no—
207#1519—111no—
208C2×#324—111no—
209C23×C11—22no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11#12011yescharacteristic
216C23×C11#12011yescharacteristic
217C23×C11#13512yes—
218C23×C11AGL(1,ℤ/8)12yes—
219C23×C11C22×D411yescharacteristic
220C22×D11—42no—
221C22×D11—42no—
222C22×D11—41no—
223C22×D11—41no—
224C22×D11—41no—
225Q8×C11—42no—
226Q8×C11—81no—
227D4×C11—42no—
228D4×C11—42no—
229D4×C11—42no—
230D4×C11—44no—
231D4×C11—81no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—81no—
253C2×C4×C11—84no—
254C2×C4×C11#12011yescharacteristic
255C2×C4×C11#12011yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C22⋊D11—82no—
259C22⋊D11—82no—
260C2×Dic11—42no—
261C2×Dic11—42no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—42no—
266D44—42no—
267D44—42no—
268C11⋊C8—42no—
269C11⋊C8—42no—
270#539—22no—
271#539—22no—
272#539—22no—
273#539C2×D1114yes—
274C2×#126—21no—
275C2×#125—21no—
276C2×#123—21no—
277C2×#123—21no—
278C2×#123—221no—
279C2×C22⋊Q8—21no—
280C2×C22⋊Q8C2×D1111yescharacteristic
281C2×#121—111no—
282C2×#121C2×D1111yescharacteristic
283C2×C4×D4—21no—
284C22×C4⋊C4C2×D1111yescharacteristic
285#483—112no—
286#481—221no—
287#480—112no—
288#480—221no—
289#466—222no—
290#465—222no—
291#450—112no—
292#448—221no—
293#447—112no—
294#447—221no—
295C2×C22⋊C8—111no—
296C2×C22⋊C8—111no—
297#398—112no—
298#396—222no—
299#394—112no—
300#386—221no—
301#380—111no—
302#328—114no—
303#327—114no—
304#324—114no—
305C22×C11—21no—
306C22×C11—21no—
307C22×C11—21no—
308C22×C11—21no—
309C22×C11—21no—
310C22×C11—21no—
311C22×C11—42no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—84no—
317C22×C11#44912yes—
318C22×C11#44912yes—
319C22×C11C2×#12011yescharacteristic
320C22×C11C2×#13511yescharacteristic
321C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
322C2×D11—82no—
323C2×D11—82no—
324C2×D11—81no—
325C2×D11—81no—
326C2×D11—81no—
327C4×C11—21no—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—42no—
332C4×C11—42no—
333C4×C11—42no—
334C4×C11—42no—
335C4×C11—42no—
336Dic11—82no—
337Dic11—81no—
338C22×Q8C22⋊D1111yescharacteristic
339C22×D4—21no—
340C22×D4—111no—
341C22×D4—221no—
342C22×D4C22⋊D1111yescharacteristic
343C23×C4—21no—
344C23×C4C22⋊D1111yescharacteristic
345C23×C4C22⋊D1111yescharacteristic
346C23×C4C22×D1111yescharacteristic
347C2×SD16—222no—
348C2×D8—222no—
349C22×C8—221no—
350C22×C8—221no—
351#126—24no—
352#126—24no—
353#125—24no—
354#125—24no—
355#123—24no—
356#123—24no—
357#123—24no—
358#123—24no—
359#123—444no—
360C22⋊Q8—24no—
361C22⋊Q8—24no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8C22⋊D1112yes—
365C22⋊Q8C22×D1112yes—
366#121—21no—
367#121—21no—
368#121—221no—
369#121—221no—
370#121—221no—
371#121—221no—
372#121C22⋊D1112yes—
373#121C22×D1112yes—
374C4×D4—24no—
375C4×D4—24no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—222no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4C22⋊D1112yes—
388C2×C4⋊C4C22⋊D1111yescharacteristic
389C2×C4⋊C4C22⋊D1111yescharacteristic
390C2×C4⋊C4C22×D1112yes—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—221no—
397C2×C22⋊C4—221no—
398C2×C22⋊C4—222no—
399C2×C22⋊C4—222no—
400C2×C42—21no—
401#107—222no—
402#106—222no—
403#103—222no—
404#102—222no—
405#102—222no—
406#102—222no—
407C22⋊C8—112no—
408C22⋊C8—112no—
409C22⋊C8—221no—
410C22⋊C8—221no—
411#95—112no—
412#95—222no—
413C2×C11—21no—
414C2×C11—21no—
415C2×C11—22no—
416C2×C11—22no—
417C2×C11—82no—
418C2×C11C2×#44911yescharacteristic
419C2×C11#302011yescharacteristic
420C2×C11#302611yescharacteristic
421D11—161no—
422C24—21no—
423C24—221no—
424C24C2×C22⋊D1111yescharacteristic
425C2×Q8—21no—
426C2×Q8—81no—
427C2×Q8C2×C22⋊D1112yes—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—21no—
431C2×D4—42no—
432C2×D4—42no—
433C2×D4—81no—
434C2×D4—221no—
435C2×D4—221no—
436C2×D4—442no—
437C2×D4—442no—
438C2×D4—441no—
439C2×D4—441no—
440C2×D4—881no—
441C2×D4C2×C22⋊D1112yes—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—24no—
451C22×C4—21no—
452C22×C4—81no—
453C22×C4—81no—
454C22×C4—82no—
455C22×C4—222no—
456C22×C4—221no—
457C22×C4C2×C22⋊D1112yes—
458C22×C4C2×C22⋊D1112yes—
459C22×C4C2×C22⋊D1111yescharacteristic
460C22×C4C2×C22⋊D1111yescharacteristic
461C22×C4C2×C22⋊D1111yescharacteristic
462C22×C4C2×C22⋊D1111yescharacteristic
463C22×C4C2×C22⋊D1111yescharacteristic
464C22×C4C23×D1111yescharacteristic
465SD16—882no—
466D8—882no—
467C2×C8—222no—
468C2×C8—222no—
469C2×C8—881no—
470C2×C8—881no—
471C4⋊C4—24no—
472C4⋊C4—24no—
473C4⋊C4—24no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—444no—
485C4⋊C4—881no—
486C4⋊C4C2×C22⋊D1112yes—
487C4⋊C4C2×C22⋊D1112yes—
488C22⋊C4—24no—
489C22⋊C4—24no—
490C22⋊C4—24no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—444no—
496C22⋊C4—442no—
497C22⋊C4—441no—
498C22⋊C4—441no—
499C22⋊C4—882no—
500C42—24no—
501C11#1828811yescharacteristic, complemented, Sylow
502C23—22no—
503C23—41no—
504C23—41no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—442no—
509C23—442no—
510C23—441no—
511C23—441no—
512C23—441no—
513C23#6700212yes—
514C23#6700312yes—
515C23#6700611yescharacteristic
516C23#6700611yescharacteristic
517C23C22×C22⋊D1111yescharacteristic
518Q8—42no—
519Q8—81no—
520D4—42no—
521D4—42no—
522D4—42no—
523D4—44no—
524D4—81no—
525D4—442no—
526D4—442no—
527D4—882no—
528D4—882no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—81no—
550C2×C4—84no—
551C2×C4—442no—
552C2×C4—442no—
553C2×C4—442no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4#6700611yescharacteristic
558C2×C4#6700611yescharacteristic
559C2×C4C22×C22⋊D1111yescharacteristic
560C2×C4C22×C22⋊D1111yescharacteristic
561C8—442no—
562C8—442no—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—42no—
574C22—84no—
575C22—882no—
576C22—882no—
577C22—881no—
578C22—881no—
579C22—881no—
580C22#1062285112yes—
581C22#1062285112yes—
582C22C2×#6700211yescharacteristic
583C22C2×#6700311yescharacteristic
584C22C2×#6700611yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—42no—
590C4—42no—
591C4—42no—
592C4—42no—
593C4—42no—
594C4—882no—
595C4—881no—
596C2—21no—
597C2—22no—
598C2—21no—
599C2—22no—
600C2—82no—
601C2—1761no—
602C2C2×#1062285111yescharacteristic
603C2#1307798011yescharacteristic
604C2#1307801311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#539C2
socleC22×C11C2×#120
prime radical#13079364C2
hypercenterC2×#539D11
hypocenterC11#18288
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#539

Complements

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

NH ≅ G/Ntype
1. #13079369C2semidirect
3. #13074358C2semidirect
4. #13067613C2semidirect
5. #13067545C2semidirect
6. #13067188C2semidirect
7. #13067184C2semidirect
8. C2×#10622166C2semidirect
9. C2×C11×#539C2semidirect
32. #10622659C22semidirect
33. #10622656C22semidirect
38. #10622604C22semidirect
39. #10622596C22semidirect
42. #10622176C22semidirect
44. #10622166C22semidirect
200. C2×#539D11semidirect
501. C11#18288semidirect

Maximal subgroups

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

subgroupindex
#130793692
#130793642
#130743582
#130676132
#130675452
#130671882
#130671842
C2×#106221662
C2×C11×#5392
#1828811