Finite Group Databasebeta

← #14685148

Subgroups — #14685148

Order 2816.

7490 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×D44C211yesmaximal, characteristic, complemented
2C22×#66990C212yesmaximal, complemented
3C2×#10622573C214yesmaximal, complemented
4C2×#10622568C212yesmaximal, complemented
5#13066856C214yesmaximal, complemented
6#13066839C211yesmaximal, characteristic, complemented
7C2×C11×#386C211yesmaximal, characteristic, complemented
8C25×D11C2212yes—
9C23×D4×C11C2211yescharacteristic
10C24×C4×C11C2211yescharacteristic
11C23×C22⋊D11C2214yescomplemented
12C23×D44—28no—
13C23×D44—24no—
14C23×D44—216no—
15C23×D44C2214yes—
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2212yescomplemented
18C22×C22⋊Dic11C2212yes—
19C2×#66990—28no—
20C2×#66990—28no—
21C2×#66990—28no—
22C22×(C2×D11)⋊C4C2214yescomplemented
23C22×(C2×D11)⋊C4C2218yescomplemented
24C11×#386—24no—
25C2×C11×#95C2212yescomplemented
26C2×C11⋊#95C2214yescomplemented
27#10622573—216no—
28#10622568—28no—
29C25×C11C2311yescharacteristic
30C25×C11C2311yescharacteristic
31C24×D11—24no—
32C24×D11—24no—
33C24×D11—216no—
34C24×D11—24no—
35C24×D11—24no—
36C24×D11—24no—
37C24×D11—24no—
38C24×D11—48no—
39C24×D11D418yescomplemented
40C24×D11C2314yes—
41C22×D4×C11—24no—
42C22×D4×C11—24no—
43C22×D4×C11—22no—
44C22×D4×C11—22no—
45C22×D4×C11D414yescomplemented
46C23×C4×C11—24no—
47C23×C4×C11—28no—
48C23×C4×C11D414yescomplemented
49C23×C4×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2312yes—
52C22×C22⋊D11—28no—
53C22×C22⋊D11—28no—
54C22×C22⋊D11—216no—
55C22×C22⋊D11—28no—
56C22×C22⋊D11—48no—
57C23×Dic11C2314yes—
58C22×D44—232no—
59C22×D44—2128no—
60C22×D44—264no—
61C22×D44—216no—
62C22×D44—216no—
63C22×D44—28no—
64C22×D44—28no—
65C22×D44D4116yescomplemented
66C2×C11×C22⋊C4—24no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—28no—
69C2×C11×C22⋊C4—24no—
70C2×C22⋊Dic11—24no—
71C2×C22⋊Dic11—24no—
72C2×C22⋊Dic11D418yescomplemented
73#66990—264no—
74C2×(C2×D11)⋊C4—28no—
75C2×(C2×D11)⋊C4—28no—
76C2×(C2×D11)⋊C4—28no—
77C2×(C2×D11)⋊C4—216no—
78C2×(C2×D11)⋊C4—216no—
79C2×(C2×D11)⋊C4—48no—
80C11×#95—24no—
81C11⋊#95—28no—
82#14715—111nomaximal, Sylow
83C24×C11—24no—
84C24×C11—24no—
85C24×C11—21no—
86C24×C11—24no—
87C24×C11—22no—
88C24×C11—22no—
89C24×C11—21no—
90C24×C11—24no—
91C24×C11C2×D412yes—
92C24×C11C2×D414yes—
93C24×C11C2×D414yes—
94C24×C11C2×D412yes—
95C24×C11C2×D412yescomplemented
96C24×C11#4112yes—
97C24×C11C2411yescharacteristic
98C23×D11—232no—
99C23×D11—232no—
100C23×D11—216no—
101C23×D11—24no—
102C23×D11—24no—
103C23×D11—24no—
104C23×D11—24no—
105C23×D11—24no—
106C23×D11—28no—
107C23×D11—24no—
108C23×D11—28no—
109C23×D11—28no—
110C23×D11—232no—
111C23×D11—216no—
112C23×D11—216no—
113C23×D11—416no—
114C23×D11—432no—
115C23×D11—432no—
116C23×D11—432no—
117C23×D11—432no—
118C23×D11—416no—
119C23×D11—416no—
120C23×D11—48no—
121C23×D11—48no—
122C23×D11—48no—
123C23×D11—48no—
124C23×D11C2×D418yes—
125C23×D11C2×D4116yes—
126C2×D4×C11—216no—
127C2×D4×C11—28no—
128C2×D4×C11—44no—
129C2×D4×C11—48no—
130C2×D4×C11—44no—
131C22×C4×C11—232no—
132C22×C4×C11—28no—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—216no—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—21no—
140C22×C4×C11—22no—
141C22×C4×C11—24no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11C2×D418yes—
145C22×C4×C11C2×D414yes—
146C22×C4×C11C2×D412yescomplemented
147C2×C22⋊D11—232no—
148C2×C22⋊D11—432no—
149C2×C22⋊D11—432no—
150C2×C22⋊D11—416no—
151C2×C22⋊D11—416no—
152C22×Dic11—28no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—28no—
156C22×Dic11C2×D418yescomplemented
157C2×D44—2256no—
158C2×D44—232no—
159C2×D44—232no—
160C2×D44—264no—
161C2×D44—264no—
162C2×D44—232no—
163C11×C22⋊C4—44no—
164C11×C22⋊C4—48no—
165C22⋊Dic11—216no—
166(C2×D11)⋊C4—232no—
167(C2×D11)⋊C4—432no—
168C24×D4—111no—
169C22×#120—112no—
170C2×#392—114no—
171C2×#386D1111yescharacteristic, complemented
172C2×#379—112no—
173#1438—114no—
174C22⋊#95—111no—
175C23×C11—24no—
176C23×C11—28no—
177C23×C11—28no—
178C23×C11—24no—
179C23×C11—28no—
180C23×C11—216no—
181C23×C11—28no—
182C23×C11—24no—
183C23×C11—22no—
184C23×C11—28no—
185C23×C11—42no—
186C23×C11—44no—
187C23×C11—41no—
188C23×C11—42no—
189C23×C11—41no—
190C23×C11—44no—
191C23×C11—42no—
192C23×C11—48no—
193C23×C11—44no—
194C23×C11#12018yes—
195C23×C11#12014yes—
196C23×C11#12118yes—
197C23×C11#12114yes—
198C23×C11#12714yes—
199C23×C11C22×D411yescharacteristic
200C23×C11C22×D412yes—
201C23×C11C22×D414yes—
202C23×C11C22×D412yes—
203C23×C11C22×D411yescharacteristic
204C23×C11C2×#4111yescharacteristic
205C23×C11H(5,𝔽2)14yes—
206C22×D11—264no—
207C22×D11—28no—
208C22×D11—28no—
209C22×D11—216no—
210C22×D11—28no—
211C22×D11—216no—
212C22×D11—28no—
213C22×D11—28no—
214C22×D11—28no—
215C22×D11—216no—
216C22×D11—216no—
217C22×D11—216no—
218C22×D11—216no—
219C22×D11—464no—
220C22×D11—464no—
221C22×D11—432no—
222C22×D11—464no—
223C22×D11—464no—
224C22×D11—464no—
225C22×D11—464no—
226C22×D11—44no—
227C22×D11—44no—
228C22×D11—44no—
229C22×D11—44no—
230C22×D11—48no—
231C22×D11—48no—
232C22×D11—48no—
233C22×D11—48no—
234C22×D11—48no—
235C22×D11—48no—
236C22×D11—432no—
237C22×D11#120116yescomplemented
238D4×C11—416no—
239C2×C4×C11—232no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—216no—
243C2×C4×C11—24no—
244C2×C4×C11—22no—
245C2×C4×C11—41no—
246C2×C4×C11—42no—
247C2×C4×C11—41no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—48no—
252C2×C4×C11#12018yescomplemented
253C22⋊D11—464no—
254C2×Dic11—28no—
255C2×Dic11—216no—
256C2×Dic11—44no—
257C2×Dic11—44no—
258C2×Dic11—48no—
259D44—2128no—
260C26—112no—
261C23×D4—114no—
262C23×D4—114no—
263C23×D4—2216no—
264C23×D4—228no—
265C23×D4—224no—
266C23×D4C2×D1111yescharacteristic
267C24×C4C2×D1111yescharacteristic
268C2×#120—228no—
269C2×#120—228no—
270C2×#120—228no—
271C22×C22⋊C4—112no—
272C22×C22⋊C4—114no—
273C22×C22⋊C4—118no—
274C22×C22⋊C4C2×D1111yescharacteristic
275C22×C22⋊C4C2×D1112yescomplemented
276#392—2216no—
277#386—24no—
278#379—228no—
279C2×#95—114no—
280C2×#95C2×D1112yescomplemented
281C22×C11—24no—
282C22×C11—24no—
283C22×C11—216no—
284C22×C11—28no—
285C22×C11—216no—
286C22×C11—28no—
287C22×C11—42no—
288C22×C11—48no—
289C22×C11—44no—
290C22×C11—81no—
291C22×C11—81no—
292C22×C11—84no—
293C22×C11—82no—
294C22×C11#39218yescomplemented
295C22×C11C2×#12012yes—
296C22×C11C2×#12011yescharacteristic
297C22×C11C2×#12012yes—
298C22×C11C2×#12014yes—
299C22×C11C2×#12112yes—
300C22×C11C2×#12111yescharacteristic
301C22×C11C2×#12711yescharacteristic
302C22×C11#53414yes—
303C22×C11#53512yes—
304C22×C11D4214yes—
305C22×C11D4218yes—
306C22×C11#54614yes—
307C2×D11—216no—
308C2×D11—216no—
309C2×D11—216no—
310C2×D11—4128no—
311C2×D11—48no—
312C2×D11—48no—
313C2×D11—48no—
314C2×D11—416no—
315C2×D11—416no—
316C2×D11—48no—
317C2×D11—416no—
318C2×D11—416no—
319C4×C11—28no—
320C4×C11—42no—
321C4×C11—82no—
322Dic11—48no—
323C25—114no—
324C25—118no—
325C25—2216no—
326C25—224no—
327C25—224no—
328C25—224no—
329C25—224no—
330C25—224no—
331C25—224no—
332C25—448no—
333C25C22×D1111yescharacteristic
334C25C22×D1111yescharacteristic
335C22×D4—22no—
336C22×D4—24no—
337C22×D4—24no—
338C22×D4—22no—
339C22×D4—1116no—
340C22×D4—2216no—
341C22×D4—2216no—
342C22×D4—22128no—
343C22×D4—2232no—
344C22×D4—2264no—
345C22×D4—228no—
346C22×D4—228no—
347C22×D4—228no—
348C22×D4—2216no—
349C22×D4—228no—
350C22×D4—228no—
351C22×D4—448no—
352C22×D4D4414yescomplemented
353C23×C4—24no—
354C23×C4—28no—
355C23×C4—114no—
356C23×C4C22⋊D1114yescomplemented
357C23×C4C22×D1112yes—
358C23×C4C22×D1111yescharacteristic
359C23×C4C22×D1112yes—
360#120—2264no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—118no—
366C2×C22⋊C4—228no—
367C2×C22⋊C4—228no—
368C2×C22⋊C4—224no—
369C2×C22⋊C4—224no—
370C2×C22⋊C4—228no—
371C2×C22⋊C4—2216no—
372C2×C22⋊C4—2216no—
373C2×C22⋊C4—448no—
374#95—24no—
375#95—228no—
376C2×C11—28no—
377C2×C11—82no—
378C2×C11C2×#39211yescharacteristic
379C2×C11#240314yes—
380C2×C11#240812yes—
381C2×C11#241014yes—
382C2×C11#243312yes—
383C2×C11#261311yescharacteristic
384C2×C11#284611yescharacteristic
385D11—416no—
386C24—24no—
387C24—24no—
388C24—21no—
389C24—24no—
390C24—22no—
391C24—22no—
392C24—24no—
393C24—21no—
394C24—1116no—
395C24—118no—
396C24—2232no—
397C24—2232no—
398C24—2232no—
399C24—2216no—
400C24—224no—
401C24—224no—
402C24—224no—
403C24—224no—
404C24—224no—
405C24—228no—
406C24—228no—
407C24—228no—
408C24—224no—
409C24—2216no—
410C24—2216no—
411C24—4416no—
412C24—4432no—
413C24—4432no—
414C24—4432no—
415C24—4432no—
416C24—4416no—
417C24—4416no—
418C24—448no—
419C24—448no—
420C24—448no—
421C24—448no—
422C24C2×D4412yes—
423C24C2×D4412yescomplemented
424C24#433912yes—
425C24D4×D1114yes—
426C24D4×D1114yes—
427C24C2×C22⋊D1112yes—
428C24C23×D1111yescharacteristic
429C2×D4—216no—
430C2×D4—28no—
431C2×D4—48no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—2264no—
435C2×D4—22256no—
436C2×D4—2232no—
437C2×D4—2232no—
438C2×D4—2264no—
439C2×D4—2232no—
440C2×D4—2232no—
441C2×D4—4432no—
442C2×D4—4432no—
443C2×D4—4416no—
444C2×D4—4416no—
445C22×C4—232no—
446C22×C4—28no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—216no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—22no—
458C22×C4—118no—
459C22×C4—224no—
460C22×C4—228no—
461C22×C4—224no—
462C22×C4—228no—
463C22×C4C2×D4412yescomplemented
464C22×C4D4×D1118yes—
465C22×C4C2×C22⋊D1114yes—
466C22⋊C4—44no—
467C22⋊C4—48no—
468C22⋊C4—2232no—
469C22⋊C4—2216no—
470C22⋊C4—4432no—
471C11#1471511yescharacteristic, complemented, Sylow
472C23—24no—
473C23—28no—
474C23—28no—
475C23—24no—
476C23—28no—
477C23—216no—
478C23—28no—
479C23—24no—
480C23—22no—
481C23—28no—
482C23—42no—
483C23—42no—
484C23—41no—
485C23—41no—
486C23—44no—
487C23—42no—
488C23—44no—
489C23—48no—
490C23—44no—
491C23—1116no—
492C23—2264no—
493C23—228no—
494C23—228no—
495C23—2216no—
496C23—228no—
497C23—2216no—
498C23—2216no—
499C23—2216no—
500C23—228no—
501C23—2216no—
502C23—2216no—
503C23—228no—
504C23—228no—
505C23—4464no—
506C23—4464no—
507C23—4464no—
508C23—4464no—
509C23—4464no—
510C23—4464no—
511C23—4432no—
512C23—444no—
513C23—444no—
514C23—444no—
515C23—444no—
516C23—448no—
517C23—448no—
518C23—4432no—
519C23—448no—
520C23—448no—
521C23—448no—
522C23—448no—
523C23#6693518yes—
524C23#6693718yes—
525C23#6698314yes—
526C23#6699014yes—
527C23#6699314yes—
528C23C22×D4411yescharacteristic
529C23C2×#433911yescharacteristic
530C23C2×D4×D1112yes—
531C23C2×D4×D1112yes—
532C23C2×D4×D1114yes—
533C23#6704214yes—
534C23C22×C22⋊D1111yescharacteristic
535D4—416no—
536D4—22128no—
537D4—4464no—
538C2×C4—232no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—216no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—48no—
551C2×C4—228no—
552C2×C4—2216no—
553C2×C4—448no—
554C2×C4—444no—
555C2×C4—444no—
556C2×C4#6699018yescomplemented
557C22—216no—
558C22—28no—
559C22—216no—
560C22—28no—
561C22—24no—
562C22—24no—
563C22—48no—
564C22—44no—
565C22—42no—
566C22—84no—
567C22—82no—
568C22—81no—
569C22—81no—
570C22—2216no—
571C22—2216no—
572C22—2216no—
573C22—44128no—
574C22—448no—
575C22—4416no—
576C22—4416no—
577C22—448no—
578C22—4416no—
579C22—4416no—
580C22—448no—
581C22—448no—
582C22#1062257318yescomplemented
583C22C2×#6693512yes—
584C22C2×#6693712yes—
585C22D4×D4414yes—
586C22#1062308114yes—
587C22D11×#12014yes—
588C22#1062314018yes—
589C22#1062318414yes—
590C22C2×#6698311yescharacteristic
591C22C2×#6699012yes—
592C22C2×#6699011yescharacteristic
593C22C2×#6699311yescharacteristic
594C22#1062336112yes—
595C4—28no—
596C4—42no—
597C4—82no—
598C4—448no—
599C2—28no—
600C2—82no—
601C2—4416no—
602C2C2×#1062257311yescharacteristic
603C2#1307192814yes—
604C2#1307197212yes—
605C2#1307199314yes—
606C2#1307225412yes—
607C2#1307433211yescharacteristic
608C2#1307689211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC2×C11×#386C2
hypercenterC2×#386D11
hypocenterC11#14715
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C24×D44C2semidirect
2. C22×#66990C2semidirect
3. C2×#10622573C2semidirect
4. C2×#10622568C2semidirect
5. #13066856C2semidirect
6. #13066839C2semidirect
7. C2×C11×#386C2semidirect
11. C23×C22⋊D11C22semidirect
17. C22×C11×C22⋊C4C22semidirect
22. C22×(C2×D11)⋊C4C22semidirect
23. C22×(C2×D11)⋊C4C22semidirect
25. C2×C11×#95C22semidirect
26. C2×C11⋊#95C22semidirect
39. C24×D11D4semidirect
45. C22×D4×C11D4semidirect
48. C23×C4×C11D4semidirect
65. C22×D44D4semidirect
72. C2×C22⋊Dic11D4semidirect
95. C24×C11C2×D4semidirect
146. C22×C4×C11C2×D4semidirect
156. C22×Dic11C2×D4semidirect
171. C2×#386D11semidirect
237. C22×D11#120semidirect
252. C2×C4×C11#120semidirect
275. C22×C22⋊C4C2×D11semidirect
280. C2×#95C2×D11semidirect
294. C22×C11#392semidirect
352. C22×D4D44semidirect
356. C23×C4C22⋊D11semidirect
423. C24C2×D44semidirect
463. C22×C4C2×D44semidirect
471. C11#14715semidirect
556. C2×C4#66990semidirect
582. C22#10622573semidirect

Maximal subgroups

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

subgroupindex
C24×D442
C22×#669902
C2×#106225732
C2×#106225682
#130668562
#130668392
C2×C11×#3862
#1471511