Finite Group Databasebeta

← #14780925

Subgroups — #14780925

Order 2816.

2706 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×#67002C211yesmaximal, characteristic, complemented
2C22×#66993C211yesmaximal, characteristic, complemented
3C2×#10622744C211yesmaximal, characteristic, complemented
4C2×#10622828C211yesmaximal, characteristic, complemented
5#13071107C211yesmaximal, characteristic, complemented
6#13069702C214yesmaximal, complemented
7#13069685C214yesmaximal, complemented
8#13068309C211yesmaximal, characteristic, complemented
9C22×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C23×D4×C11C2211yescharacteristic
12C23×C22⋊D11—22no—
13C23×D44C2211yescharacteristic
14C2×C11×AGL(1,ℤ/8)—24no—
15C2×C11×AGL(1,ℤ/8)—24no—
16C2×C11×AGL(1,ℤ/8)—24no—
17C22×C11×SD16C2212yescomplemented
18C22×C11×D8C2212yescomplemented
19C22×C11×M16C2211yescharacteristic
20C2×#67002—24no—
21C2×#67002—24no—
22C2×#67002—24no—
23C22×#4325C2212yescomplemented
24C2×#66993—24no—
25C2×#66993—24no—
26C2×#66993—22no—
27C2×#66993C2214yes—
28C22×#4323C2212yescomplemented
29C2×#66979C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C22×#4318C2211yescharacteristic
32#10622843C2212yescomplemented
33#10622834C2212yescomplemented
34#10622833—22no—
35#10622828—24no—
36C2×#66896C2214yescomplemented
37C4×C22⋊Dic11—22no—
38#10622744—24no—
39C2×#66885C2214yescomplemented
40#10622188C2214yescomplemented
41C25×C11—21no—
42C24×D11—21no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41D414yescomplemented
49C22×Q8×C11C2311yescharacteristic
50C22×D4×C11—21no—
51C22×D4×C11—22no—
52C22×D4×C11—22no—
53C22×D4×C11—22no—
54C22×D4×C11—22no—
55C22×D4×C11—21no—
56C22×D4×C11—22no—
57C22×D4×C11D414yes—
58C22×D4×C11C2312yes—
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—216no—
63C22×C22⋊D11—28no—
64C22×C22⋊D11—416no—
65C23×Dic11D412yes—
66C22×D44—22no—
67C22×D44—22no—
68C22×D44—22no—
69C22×D44—22no—
70C22×D44—21no—
71C22×D44—22no—
72C22×D44D414yes—
73C22×D44C2312yes—
74C11×AGL(1,ℤ/8)—232no—
75C2×C11×SD16—24no—
76C2×C11×SD16—24no—
77C2×C11×SD16—24no—
78C2×C11×D8—24no—
79C2×C11×D8—24no—
80C2×C11×D8—24no—
81C2×C11×M16—22no—
82C2×C11×M16—22no—
83C2×C11×M16D414yescomplemented
84C22×C8×C11C2312yes—
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—24no—
87#67002—232no—
88C2×#4325—24no—
89C2×#4325—24no—
90C2×#4325—24no—
91#66993—216no—
92#66993—28no—
93#66993—28no—
94C2×#4323—24no—
95C2×#4323—24no—
96C2×#4323—24no—
97#66979—22no—
98#66979—22no—
99C2×C4⋊Dic11C2312yes—
100C2×C4×Dic11—22no—
101C2×C4×Dic11—22no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11D412yes—
104C2×C4×Dic11C2312yes—
105C2×#4318—22no—
106C2×#4318—22no—
107C2×#4318D414yescomplemented
108C22×C11⋊C8C2312yes—
109#66896—28no—
110C11⋊#95—24no—
111#66885—28no—
112#23430—111nomaximal, Sylow
113C24×C11—24no—
114C24×C11—21no—
115C24×C11—22no—
116C24×C11—48no—
117C24×C11—42no—
118C24×C11—42no—
119C24×C11C2×D411yescharacteristic
120C23×D11—24no—
121C23×D11—22no—
122C23×D11—48no—
123C23×D11—42no—
124C23×D11—42no—
125C11×#41—28no—
126C11×#41—28no—
127C11×#41—44no—
128C11×#41—44no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11C2×D412yescomplemented
135C2×D4×C11—24no—
136C2×D4×C11—28no—
137C2×D4×C11—24no—
138C2×D4×C11—28no—
139C2×D4×C11—22no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—22no—
147C2×D4×C11—22no—
148C2×D4×C11—21no—
149C2×D4×C11—42no—
150C2×D4×C11—42no—
151C2×D4×C11—44no—
152C2×D4×C11—44no—
153C2×D4×C11—42no—
154C2×D4×C11—42no—
155C2×D4×C11C2×D414yes—
156C2×D4×C11C2×D412yescomplemented
157C22×C4×C11—21no—
158C22×C4×C11—24no—
159C22×C4×C11—42no—
160C22×C4×C11—42no—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D412yes—
167C22×C4×C11#4112yes—
168C22×C4×C11C2411yescharacteristic
169C2×C22⋊D11—232no—
170C2×C22⋊D11—464no—
171C2×C22⋊D11—416no—
172C2×C22⋊D11—416no—
173C22×Dic11—28no—
174C22×Dic11—24no—
175C22×Dic11—22no—
176C22×Dic11C2×D414yes—
177C2×D44—24no—
178C2×D44—28no—
179C2×D44—28no—
180C2×D44—22no—
181C2×D44—22no—
182C2×D44—22no—
183C2×D44—22no—
184C2×D44—22no—
185C2×D44—44no—
186C2×D44—44no—
187C2×D44—42no—
188C2×D44—42no—
189C2×D44C2×D414yes—
190C11×SD16—216no—
191C11×D8—216no—
192C11×M16—28no—
193C2×C8×C11—22no—
194C2×C8×C11—22no—
195C2×C8×C11C2×D414yescomplemented
196C22⋊Dic11—48no—
197C22⋊Dic11—42no—
198#4325—216no—
199#4323—216no—
200C4⋊Dic11—22no—
201C4⋊Dic11—22no—
202C4×Dic11—24no—
203C4×Dic11—22no—
204C4×Dic11—22no—
205C4×Dic11—42no—
206#4318—28no—
207C2×C11⋊C8—22no—
208C2×C11⋊C8—22no—
209C2×C11⋊C8C2×D414yescomplemented
210C22×AGL(1,ℤ/8)—111no—
211C22×AGL(1,ℤ/8)D1111yescharacteristic, complemented
212C22×#127—111no—
213C2×#418—111no—
214C2×#418—111no—
215#2297—111no—
216#2014—114no—
217#2011—114no—
218#1728—111no—
219C23×C11—24no—
220C23×C11—24no—
221C23×C11—22no—
222C23×C11—416no—
223C23×C11—41no—
224C23×C11—42no—
225C23×C11—41no—
226C23×C11—42no—
227C23×C11—44no—
228C23×C11—48no—
229C23×C11—48no—
230C23×C11—88no—
231C23×C11—88no—
232C23×C11#12012yes—
233C23×C11#12112yes—
234C23×C11#12712yes—
235C23×C11C22×D411yescharacteristic
236C22×D11—24no—
237C22×D11—416no—
238C22×D11—42no—
239C22×D11—42no—
240C22×D11—48no—
241C22×D11—48no—
242C22×D11—88no—
243C22×D11—88no—
244Q8×C11—22no—
245Q8×C11—22no—
246Q8×C11—41no—
247Q8×C11—41no—
248D4×C11—22no—
249D4×C11—22no—
250D4×C11—24no—
251D4×C11—24no—
252D4×C11—48no—
253D4×C11—42no—
254D4×C11—42no—
255D4×C11—41no—
256D4×C11—41no—
257D4×C11—48no—
258C2×C4×C11—22no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—48no—
262C2×C4×C11#12014yes—
263C2×C4×C11#12012yes—
264C2×C4×C11#12014yes—
265C2×C4×C11#12114yes—
266C2×C4×C11#12114yes—
267C2×C4×C11#12112yes—
268C2×C4×C11#12712yes—
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C22⋊D11—464no—
276C2×Dic11—216no—
277C2×Dic11—24no—
278C2×Dic11—24no—
279C2×Dic11—42no—
280C2×Dic11—44no—
281C2×Dic11AGL(1,ℤ/8)18yescomplemented
282D44—24no—
283D44—24no—
284D44—42no—
285D44—42no—
286D44—48no—
287C8×C11—24no—
288C11⋊C8—24no—
289C22×#41C2×D1111yescharacteristic
290C23×D4—111no—
291C23×D4—222no—
292C23×D4C2×D1111yescharacteristic
293C2×AGL(1,ℤ/8)—24no—
294C2×AGL(1,ℤ/8)—24no—
295C2×AGL(1,ℤ/8)—24no—
296C2×AGL(1,ℤ/8)—224no—
297C2×AGL(1,ℤ/8)—224no—
298C2×AGL(1,ℤ/8)—224no—
299C22×SD16—112no—
300C22×SD16C2×D1112yescomplemented
301C22×D8—112no—
302C22×D8C2×D1112yescomplemented
303C22×M16—111no—
304C22×M16C2×D1111yescharacteristic
305C2×#127—114no—
306C2×#127—222no—
307C2×#127—224no—
308C2×#127—224no—
309C2×#117—111no—
310C22×C42—111no—
311#418—224no—
312#418—224no—
313C2×#102—114no—
314C2×#102—114no—
315#391—112no—
316#390—112no—
317#386—222no—
318C4×C22⋊C4—222no—
319#336—114no—
320C22×C11—24no—
321C22×C11—24no—
322C22×C11—24no—
323C22×C11—42no—
324C22×C11—44no—
325C22×C11—48no—
326C22×C11—44no—
327C22×C11—816no—
328C22×C11—82no—
329C22×C11—84no—
330C22×C11—82no—
331C22×C11—84no—
332C22×C11#39214yes—
333C22×C11C2×#12011yescharacteristic
334C22×C11C2×#12111yescharacteristic
335C22×C11C2×#12711yescharacteristic
336C22×C11C2×AGL(1,ℤ/8)14yes—
337C2×D11—44no—
338C2×D11—48no—
339C2×D11—816no—
340C2×D11—84no—
341C2×D11—84no—
342C4×C11—42no—
343C4×C11#39214yes—
344C4×C11C2×#12011yescharacteristic
345C4×C11C2×#12011yescharacteristic
346C4×C11C2×#12111yescharacteristic
347C4×C11C2×#12111yescharacteristic
348Dic11—28no—
349Dic11—82no—
350C25—21no—
351C25—221no—
352C2×#41—22no—
353C2×#41—22no—
354C2×#41—22no—
355C2×#41—22no—
356C2×#41—22no—
357C2×#41C22⋊D1114yescomplemented
358C22×Q8C22×D1111yescharacteristic
359C22×D4—21no—
360C22×D4—22no—
361C22×D4—22no—
362C22×D4—21no—
363C22×D4—22no—
364C22×D4—22no—
365C22×D4—22no—
366C22×D4—114no—
367C22×D4—112no—
368C22×D4—228no—
369C22×D4—2216no—
370C22×D4—222no—
371C22×D4—221no—
372C22×D4—222no—
373C22×D4—222no—
374C22×D4—222no—
375C22×D4—222no—
376C22×D4—4416no—
377C22×D4C22⋊D1114yes—
378C22×D4C22×D1112yes—
379C22×D4C22×D1111yescharacteristic
380C23×C4—21no—
381C23×C4—112no—
382C23×C4C22×D1111yescharacteristic
383AGL(1,ℤ/8)—232no—
384AGL(1,ℤ/8)—2232no—
385C2×SD16—24no—
386C2×SD16—24no—
387C2×SD16—24no—
388C2×SD16—224no—
389C2×SD16—224no—
390C2×SD16—224no—
391C2×D8—24no—
392C2×D8—24no—
393C2×D8—24no—
394C2×D8—224no—
395C2×D8—224no—
396C2×D8—224no—
397C2×M16—22no—
398C2×M16—22no—
399C2×M16—114no—
400C2×M16—222no—
401C2×M16—222no—
402C2×M16C22⋊D1114yescomplemented
403C22×C8—112no—
404C22×C8C22×D1112yes—
405#127—228no—
406#127—2216no—
407#127—228no—
408#117—222no—
409#117—222no—
410C2×C4⋊C4—112no—
411C2×C22⋊C4—224no—
412C2×C22⋊C4—221no—
413C2×C42—112no—
414C2×C42—112no—
415C2×C42—222no—
416C2×C42—222no—
417C2×C42—221no—
418#102—228no—
419#102—228no—
420#95—224no—
421C2×C11—24no—
422C2×C11—82no—
423C2×C11—84no—
424C2×C11C2×#39211yescharacteristic
425C2×C11#300312yes—
426C2×C11#303812yes—
427C2×C11#315112yes—
428D11—84no—
429C24—24no—
430C24—21no—
431C24—22no—
432C24—48no—
433C24—42no—
434C24—42no—
435C24—224no—
436C24—222no—
437C24—448no—
438C24—442no—
439C24—442no—
440C24D4×D1111yescharacteristic
441#41—28no—
442#41—28no—
443#41—44no—
444#41—44no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8C2×C22⋊D1112yescomplemented
451C2×D4—24no—
452C2×D4—24no—
453C2×D4—28no—
454C2×D4—28no—
455C2×D4—22no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4—44no—
468C2×D4—44no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—114no—
472C2×D4—2232no—
473C2×D4—228no—
474C2×D4—224no—
475C2×D4—228no—
476C2×D4—222no—
477C2×D4—222no—
478C2×D4—222no—
479C2×D4—222no—
480C2×D4—222no—
481C2×D4—4416no—
482C2×D4—4464no—
483C2×D4—4416no—
484C2×D4—444no—
485C2×D4—442no—
486C2×D4—442no—
487C2×D4—444no—
488C2×D4C2×C22⋊D1114yes—
489C2×D4C2×C22⋊D1112yescomplemented
490C22×C4—21no—
491C22×C4—24no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—114no—
495C22×C4—228no—
496C22×C4—224no—
497C22×C4—222no—
498C22×C4D4×D1112yes—
499C22×C4D4×D1111yescharacteristic
500C22×C4D4×D1112yes—
501C22×C4#434112yes—
502C22×C4C2×C22⋊D1112yes—
503C22×C4C2×C22⋊D1112yes—
504C22×C4C2×C22⋊D1112yes—
505C22×C4C23×D1111yescharacteristic
506SD16—216no—
507SD16—2216no—
508D8—216no—
509D8—2216no—
510M16—28no—
511M16—228no—
512C2×C8—22no—
513C2×C8—22no—
514C2×C8—114no—
515C2×C8—222no—
516C2×C8—222no—
517C2×C8C2×C22⋊D1114yescomplemented
518C4⋊C4—222no—
519C4⋊C4—222no—
520C22⋊C4—448no—
521C22⋊C4—442no—
522C42—224no—
523C42—222no—
524C42—222no—
525C42—442no—
526C11#2343011yescharacteristic, complemented, Sylow
527C23—24no—
528C23—24no—
529C23—22no—
530C23—416no—
531C23—44no—
532C23—48no—
533C23—41no—
534C23—42no—
535C23—41no—
536C23—42no—
537C23—48no—
538C23—88no—
539C23—88no—
540C23—224no—
541C23—4416no—
542C23—448no—
543C23—442no—
544C23—442no—
545C23—448no—
546C23—888no—
547C23—888no—
548C23#6699012yes—
549C23#6699212yes—
550C23#6699312yes—
551C23C2×D4×D1111yescharacteristic
552Q8—22no—
553Q8—22no—
554Q8—41no—
555Q8—41no—
556D4—22no—
557D4—24no—
558D4—22no—
559D4—24no—
560D4—48no—
561D4—42no—
562D4—42no—
563D4—41no—
564D4—41no—
565D4—48no—
566D4—224no—
567D4—224no—
568D4—4464no—
569D4—442no—
570D4—448no—
571D4—442no—
572C2×C4—22no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—48no—
576C2×C4—118no—
577C2×C4—2216no—
578C2×C4—224no—
579C2×C4—224no—
580C2×C4—444no—
581C2×C4—442no—
582C2×C4#6699014yes—
583C2×C4#6699012yes—
584C2×C4#6699114yes—
585C2×C4#6699214yes—
586C2×C4#6699212yes—
587C2×C4#6699312yes—
588C2×C4#6700614yes—
589C2×C4C2×D4×D1111yescharacteristic
590C2×C4C2×D4×D1111yescharacteristic
591C2×C4C2×#434111yescharacteristic
592C2×C4C22×C22⋊D1111yescharacteristic
593C2×C4C22×C22⋊D1111yescharacteristic
594C2×C4C22×C22⋊D1111yescharacteristic
595C8—24no—
596C8—224no—
597C22—24no—
598C22—24no—
599C22—24no—
600C22—44no—
601C22—48no—
602C22—42no—
603C22—44no—
604C22—816no—
605C22—84no—
606C22—82no—
607C22—84no—
608C22—82no—
609C22—448no—
610C22—444no—
611C22—8816no—
612C22—884no—
613C22—884no—
614C22#1062283614yes—
615C22D11×AGL(1,ℤ/8)14yes—
616C22C2×#6699011yescharacteristic
617C22C2×#6699211yescharacteristic
618C22C2×#6699311yescharacteristic
619C4—42no—
620C4—228no—
621C4—882no—
622C4#1062283614yes—
623C4C2×#6699011yescharacteristic
624C4C2×#6699111yescharacteristic
625C4C2×#6699211yescharacteristic
626C4C2×#6700611yescharacteristic
627C2—24no—
628C2—84no—
629C2—82no—
630C2—884no—
631C2C2×#1062283611yescharacteristic
632C2#1307784112yes—
633C2#1307809412yes—
634C2#1307906412yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×AGL(1,ℤ/8)C2
socleC23×C11C22×D4
hypercenterC22×AGL(1,ℤ/8)D11
hypocenterC11#23430
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C22×#67002C2semidirect
2. C22×#66993C2semidirect
3. C2×#10622744C2semidirect
4. C2×#10622828C2semidirect
5. #13071107C2semidirect
6. #13069702C2semidirect
7. #13069685C2semidirect
8. #13068309C2semidirect
9. C22×C11×AGL(1,ℤ/8)C2semidirect
17. C22×C11×SD16C22semidirect
18. C22×C11×D8C22semidirect
23. C22×#4325C22semidirect
28. C22×#4323C22semidirect
32. #10622843C22semidirect
33. #10622834C22semidirect
36. C2×#66896C22semidirect
39. C2×#66885C22semidirect
40. #10622188C22semidirect
48. C2×C11×#41D4semidirect
83. C2×C11×M16D4semidirect
107. C2×#4318D4semidirect
134. C2×Q8×C11C2×D4semidirect
156. C2×D4×C11C2×D4semidirect
195. C2×C8×C11C2×D4semidirect
209. C2×C11⋊C8C2×D4semidirect
211. C22×AGL(1,ℤ/8)D11semidirect
281. C2×Dic11AGL(1,ℤ/8)semidirect
300. C22×SD16C2×D11semidirect
302. C22×D8C2×D11semidirect
357. C2×#41C22⋊D11semidirect
402. C2×M16C22⋊D11semidirect
450. C2×Q8C2×C22⋊D11semidirect
489. C2×D4C2×C22⋊D11semidirect
517. C2×C8C2×C22⋊D11semidirect
526. C11#23430semidirect

Maximal subgroups

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

subgroupindex
C22×#670022
C22×#669932
C2×#106227442
C2×#106228282
#130711072
#130697022
#130696852
#130683092
C22×C11×AGL(1,ℤ/8)2
#2343011