Finite Group Databasebeta

← #14755358

Subgroups — #14755358

Order 2816.

1974 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623056C211yesmaximal, characteristic
2C2×#10623052C211yesmaximal, characteristic, complemented
3#13077136C211yesmaximal, characteristic, complemented
4#13077133C211yesmaximal, characteristic, complemented
5C22×#66887C211yesmaximal, characteristic, complemented
6#13069013C214yesmaximal, complemented
7#13069003C214yesmaximal, complemented
8#13068326C211yesmaximal, characteristic, complemented
9C11×#1733C211yesmaximal, characteristic, complemented
10C22×#4339C2211yescharacteristic
11C23×D44C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17#10623056—24no—
18#10623056C418yescomplemented
19#10623052—22no—
20#10623052—22no—
21#10623052—22no—
22#10623052C2214yes—
23C2×#66948—22no—
24C2×#66946—22no—
25C2×#66935—22no—
26C2×C22⋊C4×D11—22no—
27C2×#66928C2212yes—
28C2×#66927C2212yes—
29C2×C4×D44—22no—
30#10622746—22no—
31#10622744C2212yescomplemented
32C2×#66887—24no—
33C2×#66887C2214yes—
34#10622733C2212yescomplemented
35#10622726—22no—
36#10622617C2212yescomplemented
37#10622615—22no—
38#10622614C2212yescomplemented
39#10622579—22no—
40C11×#339C2214yescomplemented
41#10622161C2214yescomplemented
42C24×D11D412yes—
43C23×C4×C11C2311yescharacteristic
44C22×C22⋊D11—21no—
45C2×#4339—22no—
46C2×#4339—21no—
47C2×#4339—21no—
48C2×#4339—21no—
49C2×#4339—21no—
50C2×#4339—22no—
51C2×#4339—22no—
52C2×#4339C2×C414yescomplemented
53C22×D44—21no—
54C22×D44—21no—
55C22×D44—21no—
56C22×D44—21no—
57C22×D44—22no—
58C22×D44—22no—
59C22×D44—24no—
60C22×D44C2×C414yes—
61C22×D44D412yes—
62C22×D44D414yes—
63C22×D44C2311yescharacteristic
64C22×D44C2312yes—
65C22×C4×D11—21no—
66C22×C4×D11—24no—
67C22×Dic22C2311yescharacteristic
68C2×C11×M16—21no—
69C2×C11×M16—22no—
70C2×C11×M16—22no—
71C2×C11×M16C2312yes—
72C22×C8×C11—21no—
73C11×#117—21no—
74C11×#117—21no—
75C11×#117—22no—
76C11×#117C2×C414yescomplemented
77C11×#117D412yescomplemented
78C11×#117C2312yes—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4D412yescomplemented
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C42×C11—21no—
84C2×C42×C11C2312yes—
85C2×C22⋊Dic11—21no—
86C2×(C2×D11)⋊C4—24no—
87C2×(C2×D11)⋊C4—24no—
88#66979—21no—
89#66979—21no—
90#66979D412yescomplemented
91#66979C2312yes—
92C2×C4⋊Dic11D412yescomplemented
93C2×C4×Dic11—21no—
94C2×#4318—21no—
95C2×#4318—22no—
96C2×#4318—22no—
97C2×#4318C2312yes—
98C22×C11⋊C8—21no—
99#66948—216no—
100#66946—28no—
101#66946—28no—
102#66935—216no—
103C22⋊C4×D11—28no—
104C22⋊C4×D11—28no—
105#66928—24no—
106#66928C2×C418yescomplemented
107#66927—24no—
108#66927C2×C418yescomplemented
109C4×D44—28no—
110C4×D44—28no—
111#66887—28no—
112#66885—24no—
113#66880—24no—
114#66874—24no—
115#66873—24no—
116#20953—111nomaximal, Sylow
117C24×C11C2×D411yescharacteristic
118C23×D11—22no—
119C23×D11—22no—
120C23×D11—24no—
121C23×D11—21no—
122C23×D11—84no—
123C23×D11C22⋊C418yes—
124C23×D11C2×D414yes—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11C22×C412yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11#4112yes—
135C22×C4×C11#4112yes—
136C22×C4×C11C2411yescharacteristic
137C2×C22⋊D11—24no—
138C2×C22⋊D11—41no—
139C2×C22⋊D11—41no—
140C2×C22⋊D11—42no—
141C22×Dic11—22no—
142C22×Dic11—21no—
143#4339—24no—
144#4339—24no—
145#4339—24no—
146#4339—24no—
147#4339—42no—
148#4339—42no—
149#4339—42no—
150#4339—42no—
151C2×D44—216no—
152C2×D44—24no—
153C2×D44—24no—
154C2×D44—24no—
155C2×D44—24no—
156C2×D44—22no—
157C2×D44—22no—
158C2×D44—24no—
159C2×D44—24no—
160C2×D44—24no—
161C2×D44—24no—
162C2×D44—24no—
163C2×D44—22no—
164C2×D44—22no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—22no—
169C2×D44—22no—
170C2×D44—21no—
171C2×D44—21no—
172C2×D44—88no—
173C2×D44C22⋊C418yes—
174C2×D44C22×C414yes—
175C2×D44C22×C412yescomplemented
176C2×D44C2×D414yes—
177C2×C4×D11—216no—
178C2×C4×D11—24no—
179C2×C4×D11—41no—
180C2×C4×D11—41no—
181C2×C4×D11—42no—
182C2×C4×D11—88no—
183C2×Dic22—21no—
184C2×Dic22—21no—
185C2×Dic22—21no—
186C2×Dic22—21no—
187C2×Dic22—21no—
188C2×Dic22C22×C412yescomplemented
189C11×M16—22no—
190C11×M16—22no—
191C11×M16—42no—
192C2×C8×C11—22no—
193C2×C8×C11—42no—
194C11×C4⋊C4—24no—
195C11×C4⋊C4—22no—
196C11×C4⋊C4C2×D414yes—
197C11×C22⋊C4—24no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—22no—
200C42×C11—22no—
201C42×C11—22no—
202C42×C11—22no—
203C42×C11C22×C414yescomplemented
204C22⋊Dic11—22no—
205C22⋊Dic11—22no—
206(C2×D11)⋊C4—216no—
207(C2×D11)⋊C4—216no—
208C4⋊Dic11—22no—
209C4⋊Dic11C2×D414yes—
210C4×Dic11—22no—
211C4×Dic11—22no—
212#4318—22no—
213#4318—22no—
214#4318—42no—
215C2×C11⋊C8—22no—
216C2×C11⋊C8—42no—
217C2×#535—111no—
218C2×#518—111no—
219#2896—111no—
220#2896—111no—
221C22×#100—111no—
222#1887—114no—
223#1885—114no—
224#1733—111no—
225#1733D1111yescharacteristic, complemented
226C23×C11—42no—
227C23×C11C2×C22⋊C412yes—
228C23×C11#12011yescharacteristic
229C23×C11#12011yescharacteristic
230C23×C11#12312yes—
231C23×C11C22×D411yescharacteristic
232C22×D11—24no—
233C22×D11—28no—
234C22×D11—24no—
235C22×D11—28no—
236C22×D11—22no—
237C22×D11—48no—
238C22×D11—48no—
239C22×D11—44no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—88no—
243C22×D11—84no—
244C22×D11—88no—
245C22×D11C2×C22⋊C418yes—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—44no—
249C2×C4×C11—44no—
250C2×C4×C11C2×C22⋊C412yes—
251C2×C4×C11C4×D412yes—
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#12112yes—
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—44no—
269C22⋊D11—44no—
270C2×Dic11—22no—
271C2×Dic11—24no—
272C2×Dic11—44no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275D44—24no—
276D44—24no—
277D44—22no—
278D44—22no—
279D44—24no—
280D44—24no—
281D44—28no—
282D44—28no—
283D44—41no—
284D44—41no—
285D44—816no—
286C4×D11—44no—
287C4×D11—44no—
288C4×D11—816no—
289Dic22—22no—
290Dic22—22no—
291Dic22—41no—
292Dic22—41no—
293C8×C11—42no—
294C11⋊C8—42no—
295C22×#41—111no—
296C23×D4—111no—
297C22×M16—111no—
298C22×M16C2×D1111yescharacteristic
299#535—118no—
300#535—224no—
301C2×#127—112no—
302C2×#124—112no—
303C2×#121—222no—
304C2×#120—222no—
305#518—114no—
306#518—222no—
307#518—222no—
308#518—222no—
309C2×C4×D4—222no—
310C2×C4×D4—222no—
311C2×#117—111no—
312C2×#117C2×D1111yescharacteristic
313C2×#117C2×D1111yescharacteristic
314C22×C22⋊C4—222no—
315#419—112no—
316#419—112no—
317#418—112no—
318#418—112no—
319#417—222no—
320#417—222no—
321#416—222no—
322#416—222no—
323C2×#100—114no—
324C2×#100—224no—
325#339—114no—
326#339C2×D1114yescomplemented
327C22×C11—22no—
328C22×C11—22no—
329C22×C11—22no—
330C22×C11—42no—
331C22×C11—42no—
332C22×C11#38612yes—
333C22×C11#38612yes—
334C22×C11C22×C22⋊C411yescharacteristic
335C22×C11C2×#12011yescharacteristic
336C22×C11C2×#12311yescharacteristic
337C2×D11—28no—
338C2×D11—416no—
339C2×D11—48no—
340C2×D11—48no—
341C2×D11—44no—
342C2×D11—42no—
343C2×D11—84no—
344C2×D11—88no—
345C2×D11—82no—
346C2×D11—82no—
347C4×C11—44no—
348C4×C11—44no—
349C4×C11#38612yes—
350C4×C11#38612yes—
351C4×C11C2×C4×D411yescharacteristic
352C4×C11C2×C4×D411yescharacteristic
353C4×C11C2×#12111yescharacteristic
354C4×C11C2×#12111yescharacteristic
355Dic11—44no—
356Dic11—42no—
357C25—112no—
358C2×#41—114no—
359C2×#41—222no—
360C2×#41—221no—
361C2×#41—221no—
362C2×#41—222no—
363C2×#41—221no—
364C2×#41—221no—
365C2×#41—222no—
366C22×Q8—111no—
367C22×D4—114no—
368C22×D4—112no—
369C22×D4—114no—
370C22×D4—112no—
371C22×D4—111no—
372C22×D4—224no—
373C22×D4—221no—
374C22×D4—221no—
375C22×D4—221no—
376C22×D4—222no—
377C22×D4—221no—
378C22×D4—221no—
379C22×D4—222no—
380C23×C4—224no—
381C23×C4—221no—
382C23×C4C22×D1111yescharacteristic
383C2×M16—21no—
384C2×M16—22no—
385C2×M16—22no—
386C2×M16—112no—
387C2×M16—221no—
388C2×M16—222no—
389C2×M16—222no—
390C2×M16C22×D1112yes—
391C22×C8—21no—
392C22×C8—221no—
393#127—118no—
394#127—224no—
395#124—118no—
396#124—224no—
397#121—2216no—
398#120—2216no—
399C4×D4—228no—
400C4×D4—228no—
401C4×D4—228no—
402C4×D4—228no—
403#117—21no—
404#117—21no—
405#117—22no—
406#117—112no—
407#117—112no—
408#117—221no—
409#117—221no—
410#117C4×D1114yescomplemented
411#117D4412yescomplemented
412#117C22×D1112yes—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—112no—
415C2×C4⋊C4D4412yescomplemented
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—228no—
419C2×C22⋊C4—228no—
420C2×C22⋊C4—224no—
421C2×C22⋊C4—224no—
422C2×C22⋊C4—221no—
423C2×C42—21no—
424C2×C42—221no—
425C2×C42C22×D1112yes—
426#103—224no—
427#103—224no—
428#102—224no—
429#102—224no—
430#100—228no—
431C2×C11—21no—
432C2×C11—22no—
433C2×C11—21no—
434C2×C11—22no—
435C2×C11C2×#38611yescharacteristic
436C2×C11#301912yes—
437D11—48no—
438D11—82no—
439C24—114no—
440C24—118no—
441C24—222no—
442C24—222no—
443C24—224no—
444C24—221no—
445C24—884no—
446C24D4×D1111yescharacteristic
447#41—224no—
448#41—224no—
449#41—224no—
450#41—224no—
451#41—442no—
452#41—442no—
453#41—442no—
454#41—442no—
455C2×Q8—112no—
456C2×Q8—221no—
457C2×Q8—221no—
458C2×Q8—221no—
459C2×Q8—221no—
460C2×Q8—221no—
461C2×D4—118no—
462C2×D4—114no—
463C2×D4—112no—
464C2×D4—114no—
465C2×D4—2216no—
466C2×D4—224no—
467C2×D4—224no—
468C2×D4—224no—
469C2×D4—222no—
470C2×D4—222no—
471C2×D4—224no—
472C2×D4—224no—
473C2×D4—224no—
474C2×D4—224no—
475C2×D4—224no—
476C2×D4—224no—
477C2×D4—224no—
478C2×D4—222no—
479C2×D4—221no—
480C2×D4—222no—
481C2×D4—221no—
482C2×D4—222no—
483C2×D4—221no—
484C2×D4—221no—
485C2×D4—222no—
486C2×D4—221no—
487C2×D4—441no—
488C2×D4—441no—
489C2×D4—442no—
490C2×D4—888no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—2216no—
494C22×C4—222no—
495C22×C4—221no—
496C22×C4—224no—
497C22×C4—441no—
498C22×C4—441no—
499C22×C4—442no—
500C22×C4—888no—
501C22×C4C2×C4×D1112yes—
502C22×C4C2×D4411yescharacteristic
503C22×C4C2×D4411yescharacteristic
504C22×C4#433912yes—
505C22×C4D4×D1111yescharacteristic
506C22×C4D4×D1112yes—
507C22×C4D4×D1111yescharacteristic
508C22×C4D4×D1111yescharacteristic
509C22×C4#434312yes—
510C22×C4C23×D1111yescharacteristic
511M16—22no—
512M16—22no—
513M16—42no—
514M16—222no—
515M16—222no—
516M16—442no—
517C2×C8—22no—
518C2×C8—42no—
519C2×C8—222no—
520C2×C8—442no—
521C4⋊C4—24no—
522C4⋊C4—22no—
523C4⋊C4—114no—
524C4⋊C4—222no—
525C4⋊C4C2×D4414yes—
526C22⋊C4—24no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—2216no—
530C22⋊C4—2216no—
531C22⋊C4—222no—
532C22⋊C4—222no—
533C42—22no—
534C42—22no—
535C42—22no—
536C42—222no—
537C42—222no—
538C42C2×C4×D1114yescomplemented
539C11#2095311yescharacteristic, complemented, Sylow
540C23—42no—
541C23—118no—
542C23—224no—
543C23—228no—
544C23—224no—
545C23—228no—
546C23—222no—
547C23—448no—
548C23—448no—
549C23—444no—
550C23—441no—
551C23—441no—
552C23—884no—
553C23—888no—
554C23—888no—
555C23C22⋊C4×D1112yes—
556C23#6693511yescharacteristic
557C23#6693511yescharacteristic
558C23#6694712yes—
559C23C2×D4×D1111yescharacteristic
560Q8—222no—
561Q8—222no—
562Q8—441no—
563Q8—441no—
564D4—224no—
565D4—222no—
566D4—224no—
567D4—224no—
568D4—222no—
569D4—224no—
570D4—228no—
571D4—228no—
572D4—444no—
573D4—444no—
574D4—441no—
575D4—441no—
576D4—8816no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—44no—
580C2×C4—44no—
581C2×C4—222no—
582C2×C4—224no—
583C2×C4—444no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—444no—
587C2×C4—444no—
588C2×C4—8816no—
589C2×C4C4×D4412yes—
590C2×C4C4×D4412yes—
591C2×C4C22⋊C4×D1112yes—
592C2×C4#6693511yescharacteristic
593C2×C4#6693511yescharacteristic
594C2×C4#6693712yes—
595C2×C4#6693712yes—
596C2×C4#6694612yes—
597C2×C4#6694612yes—
598C2×C4#6694712yes—
599C2×C4#6694812yes—
600C2×C4#6694812yes—
601C2×C4C22×C4×D1111yescharacteristic
602C2×C4C22×D4411yescharacteristic
603C2×C4C2×#433911yescharacteristic
604C2×C4C2×D4×D1111yescharacteristic
605C2×C4C2×D4×D1111yescharacteristic
606C2×C4C2×#434311yescharacteristic
607C8—42no—
608C8—442no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—42no—
613C22—42no—
614C22—228no—
615C22—448no—
616C22—4416no—
617C22—444no—
618C22—448no—
619C22—442no—
620C22—884no—
621C22—888no—
622C22—882no—
623C22—882no—
624C22#1062227812yes—
625C22#1062227812yes—
626C22C2×C22⋊C4×D1111yescharacteristic
627C22C2×#6693511yescharacteristic
628C22C2×#6694711yescharacteristic
629C4—44no—
630C4—44no—
631C4—442no—
632C4—444no—
633C4#1062227812yes—
634C4#1062227812yes—
635C4C2×C4×D4411yescharacteristic
636C4C2×#6693711yescharacteristic
637C4C2×#6694611yescharacteristic
638C4C2×#6694811yescharacteristic
639C2—21no—
640C2—22no—
641C2—21no—
642C2—22no—
643C2—448no—
644C2—882no—
645C2C2×#1062227811yescharacteristic
646C2#1307797512yes—
subgroupG/H
centerC22C2×#66935
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1733C2
socleC22×C11C2×#120
prime radicalC2×#10623056C2
cosocleC22×C4×C11C24
hypercenter#1733D11
hypocenterC11#20953
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1733

Complements

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

NH ≅ G/Ntype
2. C2×#10623052C2semidirect
3. #13077136C2semidirect
4. #13077133C2semidirect
5. C22×#66887C2semidirect
6. #13069013C2semidirect
7. #13069003C2semidirect
8. #13068326C2semidirect
9. C11×#1733C2semidirect
18. #10623056C4semidirect
31. #10622744C22semidirect
34. #10622733C22semidirect
36. #10622617C22semidirect
38. #10622614C22semidirect
40. C11×#339C22semidirect
41. #10622161C22semidirect
52. C2×#4339C2×C4semidirect
76. C11×#117C2×C4semidirect
77. C11×#117D4semidirect
80. C2×C11×C4⋊C4D4semidirect
90. #66979D4semidirect
92. C2×C4⋊Dic11D4semidirect
106. #66928C2×C4semidirect
108. #66927C2×C4semidirect
175. C2×D44C22×C4semidirect
188. C2×Dic22C22×C4semidirect
203. C42×C11C22×C4semidirect
225. #1733D11semidirect
326. #339C2×D11semidirect
410. #117C4×D11semidirect
411. #117D44semidirect
415. C2×C4⋊C4D44semidirect
538. C42C2×C4×D11semidirect
539. C11#20953semidirect

Maximal subgroups

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

subgroupindex
C2×#106230562
C2×#106230522
#130771362
#130771332
C22×#668872
#130690132
#130690032
#130683262
C11×#17332
#2095311