Finite Group Databasebeta

← #14755302

Subgroups — #14755302

Order 2816.

1862 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66985C211yesmaximal, characteristic
2#13081817C211yesmaximal, characteristic, complemented
3C2×#10622752C211yesmaximal, characteristic, complemented
4#13071198C211yesmaximal, characteristic, complemented
5#13068989C218yesmaximal, complemented
6#13068354C211yesmaximal, characteristic, complemented
7#13068325C211yesmaximal, characteristic, complemented
8C2×C11×#418C211yesmaximal, characteristic, complemented
9C23×D4×C11C2211yescharacteristic
10C22×#4339C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C22×#4324—21no—
14C2×#66985—24no—
15C2×#66985—22no—
16C2×#66985C418yescomplemented
17C2×#66985C2214yes—
18C22×#4323—21no—
19C2×#66979C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22#10623054C2214yescomplemented
23#10623053—22no—
24#10623052—21no—
25D11×#117—22no—
26#10623047—21no—
27#10623035—22no—
28#10623017—22no—
29C4×#4339—22no—
30C11×#418—22no—
31C11×#418C2214yescomplemented
32C2×C11×#102—22no—
33#10622860—22no—
34#10622834—22no—
35#10622834C2214yescomplemented
36#10622752—24no—
37C2×#66889C2214yescomplemented
38#10622192C2214yescomplemented
39#10622170C2214yescomplemented
40C25×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11—21no—
43C22×D4×C11—22no—
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11—22no—
48C22×D4×C11—22no—
49C22×D4×C11C2×C414yescomplemented
50C22×D4×C11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C22×C22⋊D11—21no—
53C2×#4339—21no—
54C2×#4339—21no—
55C2×#4339—22no—
56C2×#4339—22no—
57C2×#4339C2×C414yes—
58C2×#4339D414yes—
59C2×#4339D412yes—
60C2×#4339C2312yes—
61C22×D44D411yescharacteristic
62C22×C4×D11—21no—
63C22×Dic22D411yescharacteristic
64C2×C11×M16—21no—
65C2×C11×M16—22no—
66C2×C11×M16—22no—
67C2×C11×M16C2312yes—
68C22×C8×C11—21no—
69C11×#117—21no—
70C11×#117—21no—
71C11×#117D412yes—
72C11×#117C2312yes—
73C2×C11×C4⋊C4D412yes—
74C2×C11×C22⋊C4—21no—
75C2×C42×C11—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—28no—
78C2×C22⋊Dic11D412yes—
79C2×#4324—28no—
80C2×#4324—24no—
81#66985—216no—
82#66985—28no—
83#66985C2×C4116yescomplemented
84C2×#4323—28no—
85C2×#4323—24no—
86C4×C22⋊D11—28no—
87#66979—21no—
88#66979—21no—
89#66979—21no—
90#66979—21no—
91#66979—22no—
92#66979—22no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11C2312yes—
95C2×C4×Dic11D412yes—
96C2×C4×Dic11C2312yes—
97C2×#4318—22no—
98C2×#4318—21no—
99C2×#4318C2×C414yescomplemented
100C2×#4318C2312yes—
101C22×C11⋊C8—21no—
102#66946—24no—
103#66945—24no—
104C4⋊C4×D11—24no—
105#66940—24no—
106(C22⋊D11)⋊C4—28no—
107C22⋊C4×D11—24no—
108#66930—24no—
109C4×D44—24no—
110#66925—24no—
111C42×D11—24no—
112C4×Dic22—24no—
113C11×#102—28no—
114#66889—28no—
115#20945—111nomaximal, Sylow
116C24×C11—22no—
117C24×C11—24no—
118C24×C11—41no—
119C24×C11—41no—
120C24×C11—42no—
121C24×C11—84no—
122C24×C11C2×D411yescharacteristic
123C23×D11—21no—
124C2×D4×C11—24no—
125C2×D4×C11—24no—
126C2×D4×C11—24no—
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—41no—
135C2×D4×C11—41no—
136C2×D4×C11—42no—
137C2×D4×C11—42no—
138C2×D4×C11—42no—
139C2×D4×C11—42no—
140C2×D4×C11—42no—
141C2×D4×C11C22×C414yes—
142C22×C4×C11—22no—
143C22×C4×C11C22×C412yes—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11#4112yes—
151C22×C4×C11#4112yes—
152C22×C4×C11C2411yescharacteristic
153C2×C22⋊D11—24no—
154C2×C22⋊D11—22no—
155C2×C22⋊D11—24no—
156C2×C22⋊D11—22no—
157C22×Dic11—21no—
158C22×Dic11—22no—
159C22×Dic11C2×D414yes—
160#4339—24no—
161#4339—24no—
162#4339—24no—
163#4339—24no—
164#4339—24no—
165#4339—22no—
166#4339—22no—
167#4339C22⋊C418yescomplemented
168#4339C22×C414yes—
169#4339C2×D414yes—
170C2×D44—21no—
171C2×D44—22no—
172C2×D44C22⋊C414yescomplemented
173C2×D44C2×D412yes—
174C2×C4×D11—28no—
175C2×C4×D11—24no—
176C2×C4×D11—22no—
177C2×C4×D11—24no—
178C2×C4×D11—22no—
179C2×Dic22—21no—
180C2×Dic22—22no—
181C2×Dic22C22⋊C414yescomplemented
182C2×Dic22C2×D412yes—
183C11×M16—22no—
184C11×M16—22no—
185C11×M16—42no—
186C2×C8×C11—22no—
187C2×C8×C11—42no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4C2×D414yes—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—22no—
192C42×C11—22no—
193C42×C11—22no—
194C22⋊Dic11—22no—
195C22⋊Dic11—22no—
196C22⋊Dic11—42no—
197C22⋊Dic11—88no—
198#4324—216no—
199#4323—216no—
200(C2×D11)⋊C4—28no—
201C4⋊Dic11—22no—
202C4⋊Dic11—22no—
203C4⋊Dic11—42no—
204Dic11⋊C4—28no—
205C4×Dic11—28no—
206C4×Dic11—22no—
207C4×Dic11—22no—
208C4×Dic11—22no—
209C4×Dic11—22no—
210#4318—24no—
211#4318—22no—
212#4318C22×C414yes—
213C2×C11⋊C8—24no—
214C2×C11⋊C8—22no—
215C22×AGL(1,ℤ/8)—111no—
216#3428—111no—
217C2×#421—111no—
218C2×#418D1111yescharacteristic, complemented
219#2309—111no—
220#1883—118no—
221#1742—111no—
222#1733—111no—
223C23×C11—24no—
224C23×C11—42no—
225C23×C11—48no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11—44no—
229C23×C11—44no—
230C23×C11—84no—
231C23×C11—84no—
232C23×C11—88no—
233C23×C11—88no—
234C23×C11C4×D412yes—
235C23×C11#12011yescharacteristic
236C23×C11#12011yescharacteristic
237C23×C11#12112yes—
238C23×C11C22×D411yescharacteristic
239C22×D11—22no—
240C22×D11—24no—
241C22×D11—82no—
242D4×C11—24no—
243D4×C11—24no—
244D4×C11—42no—
245D4×C11—42no—
246D4×C11—44no—
247D4×C11—44no—
248C2×C4×C11—24no—
249C2×C4×C11—82no—
250C2×C4×C11C2×C22⋊C412yes—
251C2×C4×C11C2×C22⋊C412yes—
252C2×C4×C11C4×D412yes—
253C2×C4×C11C4×D412yes—
254C2×C4×C11C4×D412yes—
255C2×C4×C11#12011yescharacteristic
256C2×C4×C11#12011yescharacteristic
257C2×C4×C11#12112yes—
258C2×C4×C11#12112yes—
259C2×C4×C11#12112yes—
260C2×C4×C11#12312yes—
261C2×C4×C11#12312yes—
262C2×C4×C11C23×C411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C22⋊D11—24no—
269C22⋊D11—24no—
270C22⋊D11—28no—
271C2×Dic11—22no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—44no—
275C2×Dic11—44no—
276C2×Dic11—42no—
277D44—22no—
278D44—24no—
279D44C2×C22⋊C414yes—
280C4×D11—24no—
281C4×D11—24no—
282C4×D11—28no—
283C4×D11—88no—
284Dic22—22no—
285Dic22—24no—
286Dic22C2×C22⋊C414yes—
287C8×C11—42no—
288C11⋊C8—24no—
289C22×#41—111no—
290C23×D4C2×D1111yescharacteristic
291C2×AGL(1,ℤ/8)—114no—
292C2×AGL(1,ℤ/8)—118no—
293C2×AGL(1,ℤ/8)—222no—
294C2×AGL(1,ℤ/8)—224no—
295C22×SD16—221no—
296C22×D8—221no—
297C22×M16—111no—
298C22×M16C2×D1111yescharacteristic
299#520—114no—
300#520—222no—
301#519—221no—
302#518—222no—
303#518—221no—
304C4×#41—222no—
305C4×#41—222no—
306C2×#117—111no—
307C2×#117—111no—
308C2×#117—222no—
309C2×#117C2×D1111yescharacteristic
310#421—224no—
311C2×#104—114no—
312#418—22no—
313#418C2×D1114yescomplemented
314C2×#102—22no—
315#390—114no—
316#390—222no—
317#379—222no—
318#343—114no—
319#339—114no—
320C22×C11—22no—
321C22×C11—22no—
322C22×C11—22no—
323C22×C11—42no—
324C22×C11—42no—
325C22×C11—48no—
326C22×C11—44no—
327C22×C11—84no—
328C22×C11—88no—
329C22×C11—88no—
330C22×C11—84no—
331C22×C11#38612yes—
332C22×C11#38612yes—
333C22×C11C2×C4×D411yescharacteristic
334C22×C11C2×#12011yescharacteristic
335C22×C11C2×#12111yescharacteristic
336C2×D11—24no—
337C2×D11—44no—
338C2×D11—84no—
339C4×C11—44no—
340C4×C11#38612yes—
341C4×C11#38612yes—
342C4×C11C22×C22⋊C411yescharacteristic
343C4×C11C2×C4×D411yescharacteristic
344C4×C11C2×#12111yescharacteristic
345C4×C11C2×#12311yescharacteristic
346Dic11—24no—
347Dic11—44no—
348Dic11—82no—
349C25—21no—
350C2×#41—114no—
351C2×#41—112no—
352C2×#41—114no—
353C2×#41—112no—
354C2×#41—222no—
355C2×#41—221no—
356C2×#41—222no—
357C2×#41—221no—
358C22×Q8—111no—
359C22×D4—22no—
360C22×D4—21no—
361C22×D4—21no—
362C22×D4—22no—
363C22×D4—21no—
364C22×D4—22no—
365C22×D4—21no—
366C22×D4—21no—
367C22×D4—111no—
368C22×D4—221no—
369C22×D4C4×D1114yescomplemented
370C22×D4C22×D1112yes—
371C23×C4—221no—
372C23×C4C22×D1111yescharacteristic
373AGL(1,ℤ/8)—1116no—
374AGL(1,ℤ/8)—2216no—
375AGL(1,ℤ/8)—228no—
376C2×SD16—228no—
377C2×SD16—224no—
378C2×D8—228no—
379C2×D8—224no—
380C2×M16—21no—
381C2×M16—22no—
382C2×M16—22no—
383C2×M16—114no—
384C2×M16—112no—
385C2×M16—222no—
386C2×M16—221no—
387C2×M16C22×D1112yes—
388C22×C8—21no—
389C22×C8—221no—
390C4×Q8—224no—
391C4×Q8—224no—
392C4×D4—224no—
393C4×D4—228no—
394C4×D4—224no—
395C4×D4—228no—
396#117—21no—
397#117—21no—
398#117—224no—
399#117—224no—
400#117—221no—
401#117—221no—
402#117—221no—
403#117—221no—
404#117—224no—
405#117—222no—
406#117—222no—
407#117C22⋊D1112yes—
408#117C22×D1112yes—
409C2×C4⋊C4—112no—
410C2×C4⋊C4—224no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4C22⋊D1112yes—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—112no—
415C2×C22⋊C4—224no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—228no—
418C2×C42—21no—
419C2×C42—112no—
420C2×C42—112no—
421C2×C42—224no—
422#104—228no—
423#102—28no—
424C2×C11—21no—
425C2×C11—22no—
426C2×C11—21no—
427C2×C11—22no—
428C2×C11—84no—
429C2×C11C2×#38611yescharacteristic
430C2×C11#302112yes—
431D11—44no—
432C24—22no—
433C24—24no—
434C24—42no—
435C24—41no—
436C24—41no—
437C24—84no—
438C24—221no—
439C24D4×D1111yescharacteristic
440#41—118no—
441#41—114no—
442#41—114no—
443#41—224no—
444#41—224no—
445#41—224no—
446#41—224no—
447#41—224no—
448#41—222no—
449#41—222no—
450C2×Q8—114no—
451C2×Q8—112no—
452C2×Q8—222no—
453C2×Q8—221no—
454C2×D4—24no—
455C2×D4—24no—
456C2×D4—24no—
457C2×D4—24no—
458C2×D4—24no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—42no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—114no—
472C2×D4—112no—
473C2×D4—224no—
474C2×D4—224no—
475C2×D4—222no—
476C2×D4—222no—
477C2×D4—222no—
478C2×D4—221no—
479C2×D4C2×C4×D1114yes—
480C22×C4—22no—
481C22×C4—114no—
482C22×C4—228no—
483C22×C4—221no—
484C22×C4—224no—
485C22×C4—222no—
486C22×C4—224no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4C2×C4×D1112yes—
490C22×C4#433912yes—
491C22×C4D4×D1111yescharacteristic
492C22×C4D4×D1111yescharacteristic
493C22×C4D4×D1112yes—
494C22×C4D4×D1111yescharacteristic
495C22×C4#434112yes—
496C22×C4C2×C22⋊D1111yescharacteristic
497C22×C4C2×C22⋊D1111yescharacteristic
498C22×C4C23×D1111yescharacteristic
499SD16—2216no—
500D8—2216no—
501M16—22no—
502M16—22no—
503M16—42no—
504M16—114no—
505M16—224no—
506M16—222no—
507C2×C8—22no—
508C2×C8—42no—
509C2×C8—224no—
510C2×C8—222no—
511C4⋊C4—22no—
512C4⋊C4—228no—
513C4⋊C4—222no—
514C4⋊C4—222no—
515C4⋊C4—442no—
516C4⋊C4C2×C22⋊D1114yes—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—228no—
520C22⋊C4—222no—
521C22⋊C4—222no—
522C22⋊C4—442no—
523C22⋊C4—888no—
524C42—22no—
525C42—22no—
526C42—228no—
527C42—222no—
528C42—222no—
529C42—222no—
530C42—222no—
531C11#2094511yescharacteristic, complemented, Sylow
532C23—24no—
533C23—42no—
534C23—48no—
535C23—42no—
536C23—42no—
537C23—44no—
538C23—44no—
539C23—84no—
540C23—84no—
541C23—88no—
542C23—88no—
543C23—222no—
544C23—224no—
545C23—882no—
546C23(C22⋊D11)⋊C412yes—
547C23#6693712yes—
548C23#6699011yescharacteristic
549C23#6699011yescharacteristic
550C23C2×D4×D1111yescharacteristic
551Q8—114no—
552Q8—222no—
553Q8—224no—
554D4—24no—
555D4—24no—
556D4—42no—
557D4—42no—
558D4—44no—
559D4—44no—
560D4—114no—
561D4—224no—
562D4—224no—
563D4—228no—
564D4—222no—
565D4—224no—
566C2×C4—24no—
567C2×C4—82no—
568C2×C4—222no—
569C2×C4—224no—
570C2×C4—224no—
571C2×C4—224no—
572C2×C4—228no—
573C2×C4—224no—
574C2×C4—444no—
575C2×C4—444no—
576C2×C4—442no—
577C2×C4—888no—
578C2×C4C22⋊C4×D1112yes—
579C2×C4C22⋊C4×D1112yes—
580C2×C4(C22⋊D11)⋊C412yes—
581C2×C4#6693612yes—
582C2×C4#6693612yes—
583C2×C4#6693712yes—
584C2×C4C4×C22⋊D1112yes—
585C2×C4C4×C22⋊D1112yes—
586C2×C4#6699011yescharacteristic
587C2×C4#6699011yescharacteristic
588C2×C4#6699112yes—
589C2×C4#6699112yes—
590C2×C4C22×C4×D1111yescharacteristic
591C2×C4C2×#433911yescharacteristic
592C2×C4C2×D4×D1111yescharacteristic
593C2×C4C2×D4×D1111yescharacteristic
594C2×C4C2×#434111yescharacteristic
595C2×C4C22×C22⋊D1111yescharacteristic
596C8—42no—
597C8—224no—
598C22—22no—
599C22—22no—
600C22—22no—
601C22—42no—
602C22—42no—
603C22—48no—
604C22—44no—
605C22—84no—
606C22—88no—
607C22—88no—
608C22—84no—
609C22—224no—
610C22—444no—
611C22—884no—
612C22#1062256912yes—
613C22#1062256912yes—
614C22C2×(C22⋊D11)⋊C411yescharacteristic
615C22C2×#6693711yescharacteristic
616C22C2×#6699011yescharacteristic
617C4—44no—
618C4—224no—
619C4—444no—
620C4—882no—
621C4#1062256912yes—
622C4#1062256912yes—
623C4C2×C22⋊C4×D1111yescharacteristic
624C4C2×#6693611yescharacteristic
625C4C2×C4×C22⋊D1111yescharacteristic
626C4C2×#6699111yescharacteristic
627C2—21no—
628C2—21no—
629C2—22no—
630C2—22no—
631C2—84no—
632C2—444no—
633C2C2×#1062256911yescharacteristic
634C2#1307798512yes—
subgroupG/H
centerC22C2×#66990
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#418C2
socleC22×C11C2×#120
prime radicalC22×#66985C2
cosocleC22×C4×C11C24
hypercenterC2×#418D11
hypocenterC11#20945
LCSG ▷ C2×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
2. #13081817C2semidirect
3. C2×#10622752C2semidirect
4. #13071198C2semidirect
5. #13068989C2semidirect
6. #13068354C2semidirect
7. #13068325C2semidirect
8. C2×C11×#418C2semidirect
16. C2×#66985C4semidirect
22. #10623054C22semidirect
31. C11×#418C22semidirect
35. #10622834C22semidirect
37. C2×#66889C22semidirect
38. #10622192C22semidirect
39. #10622170C22semidirect
49. C22×D4×C11C2×C4semidirect
83. #66985C2×C4semidirect
99. C2×#4318C2×C4semidirect
167. #4339C22⋊C4semidirect
172. C2×D44C22⋊C4semidirect
181. C2×Dic22C22⋊C4semidirect
218. C2×#418D11semidirect
313. #418C2×D11semidirect
369. C22×D4C4×D11semidirect
531. C11#20945semidirect

Maximal subgroups

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

subgroupindex
C22×#669852
#130818172
C2×#106227522
#130711982
#130689892
#130683542
#130683252
C2×C11×#4182
#2094511