Finite Group Databasebeta

← #14926355

Subgroups — #14926355

Order 2816.

3690 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623024C211yesmaximal, characteristic, complemented
2C2×#10623024C212yesmaximal, complemented
3C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
4#13076948C212yesmaximal, complemented
5#13076899C212yesmaximal, complemented
6#13074361C212yesmaximal, complemented
7#13074353C212yesmaximal, complemented
8#13072165C218yesmaximal, complemented
9#13072150C218yesmaximal, complemented
10C2×#10622571C212yesmaximal, complemented
11C11×#2315C211yesmaximal, characteristic, complemented
12C23×C22⋊D11C2212yes—
13C23×C22⋊D11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic, complemented
16C22×C11×C22⋊C4C2212yes—
17C22×C11×C22⋊C4C2211yescharacteristic
18C2×#66983C2218yes—
19C2×#66983C2212yes—
20C2×#66983C2212yes—
21C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
22C22×(C2×D11)⋊C4C2214yescomplemented
23C22×Dic11⋊C4C2211yescharacteristic, complemented
24C22×C4×Dic11C2211yescharacteristic, complemented
25C2×#66948C2214yescomplemented
26#10623024—216no—
27#10623024—28no—
28C2×#66939C2214yescomplemented
29C2×#66939C2214yescomplemented
30C2×#66939C2214yescomplemented
31C2×#66935C2214yescomplemented
32C2×#66935C2214yescomplemented
33C2×#66935C2214yescomplemented
34C2×(C22⋊D11)⋊C4—28no—
35C2×(C22⋊D11)⋊C4C2218yescomplemented
36C11×#385C2218yescomplemented
37C11×#380C2212yescomplemented
38C11×#380C2212yescomplemented
39C2×C11⋊#95C2214yescomplemented
40#10622607C2218yescomplemented
41#10622604C2218yescomplemented
42#10622601C2214yescomplemented
43#10622600C2214yescomplemented
44#10622598C2214yescomplemented
45#10622571C2218yescomplemented
46#10622571C2214yescomplemented
47#10622571C2214yescomplemented
48#10622287C2214yescomplemented
49#10622285C2214yescomplemented
50#10622284C2214yescomplemented
51#10622283C2218yescomplemented
52#10622278C2218yescomplemented
53#10622274C2214yescomplemented
54C25×C11C2311yescharacteristic
55C24×D11C2312yes—
56C24×D11C2311yescharacteristic
57C23×C4×C11C2314yes—
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—24no—
61C22×C22⋊D11—24no—
62C22×C22⋊D11—28no—
63C22×C22⋊D11—28no—
64C22×C22⋊D11—28no—
65C22×C22⋊D11D418yescomplemented
66C22×C22⋊D11C2314yes—
67C22×C22⋊D11C2314yes—
68C22×C22⋊D11C2314yes—
69C23×Dic11—24no—
70C23×Dic11—44no—
71C23×Dic11C2312yes—
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2314yes—
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C22×D44C2312yes—
77C22×D44C2318yes—
78C22×D44C2312yes—
79C22×C4×D11—24no—
80C22×C4×D11—44no—
81C22×C4×D11C2314yes—
82C2×C11×C4⋊C4C2314yes—
83C2×C11×C4⋊C4C2314yes—
84C2×C11×C22⋊C4—28no—
85C2×C11×C22⋊C4D418yescomplemented
86C2×C11×C22⋊C4C2314yes—
87C2×C11×C22⋊C4C2314yes—
88C2×C11×C22⋊C4C2314yes—
89#66983—28no—
90#66983—28no—
91#66983—232no—
92C2×(C2×D11)⋊C4—24no—
93C2×(C2×D11)⋊C4—48no—
94C2×(C2×D11)⋊C4C2314yes—
95C2×(C2×D11)⋊C4C2314yes—
96C2×(C2×D11)⋊C4C2318yes—
97C2×(C2×D11)⋊C4C2314yes—
98C2×(C2×D11)⋊C4C2318yes—
99C2×(C2×D11)⋊C4C2318yes—
100C2×(C2×D11)⋊C4C2318yes—
101C2×C4⋊Dic11C2312yes—
102C2×C4⋊Dic11C2318yes—
103C2×C4⋊Dic11C2312yes—
104C2×Dic11⋊C4—24no—
105C2×Dic11⋊C4C2314yes—
106C2×C4×Dic11—24no—
107C2×C4×Dic11C2314yes—
108#66948—48no—
109#66939—216no—
110#66939—216no—
111#66939—216no—
112#66935—216no—
113#66935—216no—
114#66935—216no—
115(C22⋊D11)⋊C4—232no—
116C11×#95C2314yes—
117C11×#95C2314yes—
118C11⋊#95C2318yes—
119C11⋊#95C2318yes—
120#34984—111nomaximal, Sylow
121C24×C11—42no—
122C24×C11—42no—
123C24×C11C2×D414yes—
124C24×C11C2×D414yes—
125C24×C11#4114yes—
126C24×C11C2412yes—
127C24×C11C2411yescharacteristic
128C23×D11—22no—
129C23×D11—22no—
130C23×D11—24no—
131C23×D11—24no—
132C23×D11—24no—
133C23×D11—42no—
134C23×D11—42no—
135C23×D11—44no—
136C23×D11—44no—
137C23×D11C2×D414yes—
138C23×D11C2414yes—
139C23×D11C2412yes—
140C22×C4×C11—28no—
141C22×C4×C11—42no—
142C22×C4×C11—42no—
143C22×C4×C11—44no—
144C22×C4×C11—44no—
145C22×C4×C11C2×D414yes—
146C22×C4×C11C2×D414yes—
147C22×C4×C11C2418yes—
148C22×C4×C11C2412yes—
149C22×C4×C11C2412yes—
150C2×C22⋊D11—232no—
151C2×C22⋊D11—28no—
152C2×C22⋊D11—28no—
153C2×C22⋊D11—28no—
154C2×C22⋊D11—28no—
155C2×C22⋊D11—28no—
156C2×C22⋊D11—28no—
157C2×C22⋊D11—28no—
158C2×C22⋊D11—28no—
159C2×C22⋊D11—432no—
160C2×C22⋊D11C2×D4116yes—
161C22×Dic11—24no—
162C22×Dic11—28no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—28no—
166C22×Dic11—24no—
167C22×Dic11—24no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—24no—
171C22×Dic11—44no—
172C22×Dic11—42no—
173C22×Dic11—416no—
174C22×Dic11C2×D414yes—
175C22×Dic11C2412yes—
176C22×Dic11C2414yes—
177C22×Dic11C2412yes—
178C22×Dic11C2412yes—
179C2×D44—216no—
180C2×D44—24no—
181C2×D44—24no—
182C2×D44—44no—
183C2×D44—48no—
184C2×D44—44no—
185C2×D44—48no—
186C2×C4×D11—28no—
187C2×C4×D11—28no—
188C2×C4×D11—44no—
189C2×C4×D11—416no—
190C11×C4⋊C4—44no—
191C11×C4⋊C4—44no—
192C11×C22⋊C4—28no—
193C11×C22⋊C4—28no—
194C11×C22⋊C4C2×D4116yes—
195(C2×D11)⋊C4—216no—
196(C2×D11)⋊C4—216no—
197(C2×D11)⋊C4—216no—
198(C2×D11)⋊C4—28no—
199(C2×D11)⋊C4—28no—
200(C2×D11)⋊C4—28no—
201(C2×D11)⋊C4—48no—
202C4⋊Dic11—216no—
203C4⋊Dic11—24no—
204C4⋊Dic11—24no—
205Dic11⋊C4—28no—
206C4×Dic11—28no—
207C2×#534—112no—
208C2×#534—111no—
209C22×C4×D4—111no—
210#2854—112no—
211#2847—112no—
212#2618—112no—
213#2617—112no—
214#2425—118no—
215#2424—118no—
216#2315D1111yescharacteristic, complemented
217C2×#386—112no—
218C23×C11—22no—
219C23×C11—24no—
220C23×C11—22no—
221C23×C11—24no—
222C23×C11—44no—
223C23×C11—44no—
224C23×C11—48no—
225C23×C11—48no—
226C23×C11#121116yescomplemented
227C23×C11C22×D414yes—
228C23×C11C22×D412yes—
229C23×C11C22×D412yes—
230C23×C11C22×D414yes—
231C23×C11C2×#4112yes—
232C23×C11C2×#4114yes—
233C23×C11C2511yescharacteristic
234C22×D11—28no—
235C22×D11—22no—
236C22×D11—22no—
237C22×D11—24no—
238C22×D11—24no—
239C22×D11—24no—
240C22×D11—24no—
241C22×D11—24no—
242C22×D11—28no—
243C22×D11—28no—
244C22×D11—48no—
245C22×D11—44no—
246C22×D11—48no—
247C22×D11—44no—
248C22×D11—416no—
249C22×D11—48no—
250C22×D11—84no—
251C22×D11—84no—
252C22×D11—88no—
253C22×D11C22×D414yes—
254C2×C4×C11—24no—
255C2×C4×C11—24no—
256C2×C4×C11—28no—
257C2×C4×C11—28no—
258C2×C4×C11—28no—
259C2×C4×C11—44no—
260C2×C4×C11—44no—
261C2×C4×C11—88no—
262C2×C4×C11C22×D414yes—
263C2×C4×C11C22×D414yes—
264C22⋊D11—232no—
265C22⋊D11—416no—
266C22⋊D11—416no—
267C2×Dic11—28no—
268C2×Dic11—28no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—24no—
275C2×Dic11—24no—
276C2×Dic11—24no—
277C2×Dic11—24no—
278C2×Dic11—416no—
279C2×Dic11—44no—
280C2×Dic11—48no—
281C2×Dic11C22×D414yes—
282C2×Dic11H(5,𝔽2)14yes—
283D44—84no—
284D44—84no—
285D44—816no—
286C4×D11—416no—
287C23×D4—111no—
288C23×D4—112no—
289C24×C4—111no—
290C24×C4—111no—
291#534—2216no—
292#534—228no—
293C2×#123—114no—
294C2×#123—114no—
295C2×#123—114no—
296C2×#121—112no—
297C2×#121—112no—
298C2×#121—118no—
299C2×#121—114no—
300C2×#120—114no—
301C2×#120—114no—
302C2×#120—114no—
303C2×C4×D4—118no—
304C2×C4×D4—228no—
305C22×C4⋊C4—111no—
306C22×C22⋊C4—111no—
307C22×C22⋊C4—114no—
308C22×C22⋊C4C2×D1112yes—
309C22×C22⋊C4C2×D1111yescharacteristic
310C22×C42—111no—
311#398—114no—
312#397—114no—
313#396—118no—
314#394—118no—
315#394—114no—
316#392—114no—
317#390—114no—
318#389—114no—
319#388—118no—
320#386—114no—
321#386—114no—
322#386—118no—
323#386—118no—
324#385C2×D1118yescomplemented
325#380—114no—
326#380C2×D1112yescomplemented
327#380C2×D1112yescomplemented
328C2×#95—114no—
329C22×C11—24no—
330C22×C11—28no—
331C22×C11—22no—
332C22×C11—24no—
333C22×C11—22no—
334C22×C11—24no—
335C22×C11—28no—
336C22×C11—24no—
337C22×C11—416no—
338C22×C11C2×#12114yes—
339C22×C11C2×#12118yes—
340C22×C11C23×D411yescharacteristic
341C22×C11C23×D411yescharacteristic
342C22×C11C22×#4111yescharacteristic
343C22×C11C2×H(5,𝔽2)12yes—
344C22×C11#58512yes—
345C2×D11—24no—
346C2×D11—28no—
347C2×D11—416no—
348C2×D11—44no—
349C2×D11—42no—
350C2×D11—42no—
351C2×D11—44no—
352C2×D11—48no—
353C2×D11—44no—
354C2×D11—44no—
355C2×D11—48no—
356C2×D11—816no—
357C4×C11—24no—
358C4×C11—24no—
359C4×C11—48no—
360Dic11—24no—
361Dic11—24no—
362Dic11—44no—
363Dic11—42no—
364C25—111no—
365C25—112no—
366C25C22×D1111yescharacteristic
367C22×D4—118no—
368C22×D4—114no—
369C22×D4—114no—
370C22×D4—114no—
371C22×D4—112no—
372C22×D4—118no—
373C22×D4—112no—
374C22×D4—224no—
375C22×D4—224no—
376C22×D4—228no—
377C22×D4—228no—
378C22×D4—228no—
379C23×C4—111no—
380C23×C4—112no—
381C23×C4—111no—
382C23×C4—114no—
383C23×C4—111no—
384C23×C4—114no—
385C23×C4—224no—
386C23×C4—224no—
387C23×C4—444no—
388C23×C4—444no—
389C23×C4C22×D1114yes—
390C23×C4C22×D1111yescharacteristic
391C23×C4C22×D1111yescharacteristic
392#123—2216no—
393#123—2216no—
394#123—2216no—
395#121—2232no—
396#121—228no—
397#121—228no—
398#121—448no—
399#120—2216no—
400#120—2216no—
401#120—2216no—
402C4×D4—2232no—
403C2×C4⋊C4—114no—
404C2×C4⋊C4—112no—
405C2×C4⋊C4—118no—
406C2×C4⋊C4—112no—
407C2×C4⋊C4—224no—
408C2×C4⋊C4C22×D1114yes—
409C2×C4⋊C4C22×D1114yes—
410C2×C22⋊C4—28no—
411C2×C22⋊C4—114no—
412C2×C22⋊C4—118no—
413C2×C22⋊C4—118no—
414C2×C22⋊C4—114no—
415C2×C22⋊C4—114no—
416C2×C22⋊C4—118no—
417C2×C22⋊C4—118no—
418C2×C22⋊C4—224no—
419C2×C22⋊C4—448no—
420C2×C22⋊C4D4418yescomplemented
421C2×C22⋊C4C22×D1114yes—
422C2×C22⋊C4C22×D1114yes—
423C2×C22⋊C4C22×D1114yes—
424C2×C42—114no—
425C2×C42—224no—
426#95—118no—
427#95—118no—
428#95C22×D1114yes—
429#95C22×D1114yes—
430C2×C11—24no—
431C2×C11—28no—
432C2×C11C22×#12111yescharacteristic
433C2×C11#345912yes—
434C2×C11#348411yescharacteristic
435C2×C11#348511yescharacteristic
436C2×C11#349612yes—
437D11—44no—
438D11—84no—
439C24—42no—
440C24—42no—
441C24—112no—
442C24—114no—
443C24—114no—
444C24—222no—
445C24—222no—
446C24—224no—
447C24—224no—
448C24—224no—
449C24—442no—
450C24—442no—
451C24—444no—
452C24—444no—
453C24C2×D4414yes—
454C24D4×D1114yes—
455C24#434314yes—
456C24C23×D1112yes—
457C24C23×D1111yescharacteristic
458C2×D4—1116no—
459C2×D4—2216no—
460C2×D4—2232no—
461C2×D4—228no—
462C2×D4—228no—
463C2×D4—228no—
464C2×D4—228no—
465C2×D4—228no—
466C2×D4—228no—
467C2×D4—228no—
468C2×D4—228no—
469C2×D4—224no—
470C2×D4—224no—
471C2×D4—444no—
472C2×D4—448no—
473C2×D4—444no—
474C2×D4—448no—
475C2×D4—4432no—
476C22×C4—28no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—44no—
480C22×C4—44no—
481C22×C4—114no—
482C22×C4—112no—
483C22×C4—112no—
484C22×C4—112no—
485C22×C4—114no—
486C22×C4—228no—
487C22×C4—224no—
488C22×C4—228no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4—228no—
494C22×C4—224no—
495C22×C4—224no—
496C22×C4—224no—
497C22×C4—228no—
498C22×C4—444no—
499C22×C4—4416no—
500C22×C4—444no—
501C22×C4—442no—
502C22×C4—4416no—
503C22×C4C2×D4414yes—
504C22×C4C2×D4414yes—
505C22×C4C23×D1118yes—
506C22×C4C23×D1112yes—
507C22×C4C23×D1112yes—
508C4⋊C4—44no—
509C4⋊C4—44no—
510C4⋊C4—2216no—
511C4⋊C4—228no—
512C4⋊C4—224no—
513C4⋊C4—224no—
514C22⋊C4—28no—
515C22⋊C4—28no—
516C22⋊C4—2216no—
517C22⋊C4—2216no—
518C22⋊C4—2216no—
519C22⋊C4—228no—
520C22⋊C4—228no—
521C22⋊C4—228no—
522C22⋊C4—448no—
523C22⋊C4C2×D44116yes—
524C42—228no—
525C11#3498411yescharacteristic, complemented, Sylow
526C23—24no—
527C23—22no—
528C23—24no—
529C23—22no—
530C23—44no—
531C23—44no—
532C23—48no—
533C23—48no—
534C23—114no—
535C23—228no—
536C23—222no—
537C23—222no—
538C23—224no—
539C23—224no—
540C23—224no—
541C23—224no—
542C23—224no—
543C23—228no—
544C23—228no—
545C23—448no—
546C23—444no—
547C23—444no—
548C23—448no—
549C23—4416no—
550C23—448no—
551C23—888no—
552C23—884no—
553C23—884no—
554C23#66948116yescomplemented
555C23C22×D4414yes—
556C23C22×D4412yes—
557C23C2×D4×D1112yes—
558C23C2×D4×D1114yes—
559C23C2×#434312yes—
560C23C2×#434314yes—
561C23C24×D1111yescharacteristic
562D4—2232no—
563D4—4416no—
564D4—4416no—
565D4—884no—
566D4—884no—
567D4—8816no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—28no—
571C2×C4—28no—
572C2×C4—28no—
573C2×C4—44no—
574C2×C4—44no—
575C2×C4—88no—
576C2×C4—114no—
577C2×C4—114no—
578C2×C4—228no—
579C2×C4—228no—
580C2×C4—222no—
581C2×C4—222no—
582C2×C4—222no—
583C2×C4—222no—
584C2×C4—222no—
585C2×C4—224no—
586C2×C4—224no—
587C2×C4—224no—
588C2×C4—224no—
589C2×C4—4416no—
590C2×C4—4416no—
591C2×C4—444no—
592C2×C4—448no—
593C2×C4C22×D4414yes—
594C2×C4C22×D4414yes—
595C22—28no—
596C22—24no—
597C22—22no—
598C22—24no—
599C22—22no—
600C22—24no—
601C22—24no—
602C22—28no—
603C22—416no—
604C22—228no—
605C22—224no—
606C22—4416no—
607C22—442no—
608C22—442no—
609C22—444no—
610C22—448no—
611C22—444no—
612C22—444no—
613C22—448no—
614C22—444no—
615C22—8816no—
616C22C2×#6694814yes—
617C22C2×#6694818yes—
618C22C23×D4411yescharacteristic
619C22C22×D4×D1111yescharacteristic
620C22C22×#434311yescharacteristic
621C22D11×H(5,𝔽2)12yes—
622C22#1062345512yes—
623C4—24no—
624C4—24no—
625C4—48no—
626C4—224no—
627C4—224no—
628C4—442no—
629C4—444no—
630C2—24no—
631C2—28no—
632C2—444no—
633C2—884no—
634C2C22×#6694811yescharacteristic
635C2#1308202812yes—
636C2#1308225211yescharacteristic
637C2#1308226111yescharacteristic
638C2#1308237712yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2315C2
hypercenter#2315D11
hypocenterC11#34984
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2315

Complements

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

NH ≅ G/Ntype
1. C2×#10623024C2semidirect
2. C2×#10623024C2semidirect
3. C22×(C22⋊D11)⋊C4C2semidirect
4. #13076948C2semidirect
5. #13076899C2semidirect
6. #13074361C2semidirect
7. #13074353C2semidirect
8. #13072165C2semidirect
9. #13072150C2semidirect
10. C2×#10622571C2semidirect
11. C11×#2315C2semidirect
15. C23×C4×D11C22semidirect
21. C22×(C2×D11)⋊C4C22semidirect
22. C22×(C2×D11)⋊C4C22semidirect
23. C22×Dic11⋊C4C22semidirect
24. C22×C4×Dic11C22semidirect
25. C2×#66948C22semidirect
28. C2×#66939C22semidirect
29. C2×#66939C22semidirect
30. C2×#66939C22semidirect
31. C2×#66935C22semidirect
32. C2×#66935C22semidirect
33. C2×#66935C22semidirect
35. C2×(C22⋊D11)⋊C4C22semidirect
36. C11×#385C22semidirect
37. C11×#380C22semidirect
38. C11×#380C22semidirect
39. C2×C11⋊#95C22semidirect
40. #10622607C22semidirect
41. #10622604C22semidirect
42. #10622601C22semidirect
43. #10622600C22semidirect
44. #10622598C22semidirect
45. #10622571C22semidirect
46. #10622571C22semidirect
47. #10622571C22semidirect
48. #10622287C22semidirect
49. #10622285C22semidirect
50. #10622284C22semidirect
51. #10622283C22semidirect
52. #10622278C22semidirect
53. #10622274C22semidirect
65. C22×C22⋊D11D4semidirect
85. C2×C11×C22⋊C4D4semidirect
216. #2315D11semidirect
226. C23×C11#121semidirect
324. #385C2×D11semidirect
326. #380C2×D11semidirect
327. #380C2×D11semidirect
420. C2×C22⋊C4D44semidirect
525. C11#34984semidirect
554. C23#66948semidirect

Maximal subgroups

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

subgroupindex
C2×#106230242
C22×(C22⋊D11)⋊C42
#130769482
#130768992
#130743612
#130743532
#130721652
#130721502
C2×#106225712
C11×#23152
#3498411