Finite Group Databasebeta

← #14926347

Subgroups — #14926347

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×#10623335C212yesmaximal, complemented
2C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
3#13076942C212yesmaximal, complemented
4#13076895C212yesmaximal, complemented
5#13074360C212yesmaximal, complemented
6#13074352C212yesmaximal, complemented
7#13072163C218yesmaximal, complemented
8#13072148C218yesmaximal, complemented
9#13071230C211yesmaximal, characteristic, complemented
10C2×#10622833C212yesmaximal, complemented
11C2×C11×#534C211yesmaximal, characteristic, complemented
12C23×D4×C11C2212yes—
13C23×C22⋊D11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic, complemented
16C11×#534—28no—
17C2×C11×#123C2214yescomplemented
18C2×C11×#121C2212yes—
19C2×C11×#121C2212yes—
20C2×C11×#120C2214yescomplemented
21C22×C11×C22⋊C4C2211yescharacteristic
22C2×#67006C2214yescomplemented
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2214yescomplemented
25#10623335—216no—
26C2×#66992C2218yes—
27C2×#66991C2214yescomplemented
28C2×#66990C2214yescomplemented
29C2×#66988C2214yescomplemented
30C2×#66982C2214yescomplemented
31C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
32C22×Dic11⋊C4C2211yescharacteristic, complemented
33C22×C4×Dic11C2211yescharacteristic, complemented
34C2×(C22⋊D11)⋊C4—28no—
35C2×(C22⋊D11)⋊C4C2218yescomplemented
36#10622836C2214yescomplemented
37#10622835C2214yescomplemented
38#10622834C2214yescomplemented
39#10622833C2218yescomplemented
40#10622833C2214yescomplemented
41#10622833C2214yescomplemented
42#10622825C2212yescomplemented
43#10622825C2212yescomplemented
44C2×C11⋊#95C2214yescomplemented
45#10622606C2214yescomplemented
46#10622600C2214yescomplemented
47#10622593C2214yescomplemented
48#10622586C2214yescomplemented
49#10622574C2218yescomplemented
50#10622569C2218yescomplemented
51#10622563C2218yescomplemented
52#10622561C2218yescomplemented
53#10622557C2218yescomplemented
54C25×C11C2312yes—
55C25×C11C2311yescharacteristic
56C24×D11C2311yescharacteristic
57C22×D4×C11—28no—
58C22×D4×C11—28no—
59C22×D4×C11—28no—
60C22×D4×C11C2314yes—
61C22×D4×C11C2314yes—
62C22×D4×C11C2312yes—
63C22×D4×C11C2312yes—
64C23×C4×C11C2312yes—
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—24no—
68C22×C22⋊D11—24no—
69C22×C22⋊D11D418yescomplemented
70C22×C22⋊D11C2314yes—
71C22×C22⋊D11C2318yes—
72C23×Dic11—24no—
73C23×Dic11—44no—
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2314yes—
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2314yes—
79C22×C4×D11—24no—
80C22×C4×D11—44no—
81C22×C4×D11C2314yes—
82C11×#123—216no—
83C11×#121—28no—
84C11×#121—28no—
85C11×#120—216no—
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C22⋊C4D418yescomplemented
89C2×C11×C22⋊C4C2314yes—
90C2×C11×C22⋊C4C2314yes—
91C2×C11×C22⋊C4C2314yes—
92#67006—216no—
93C2×C22⋊Dic11—28no—
94C2×C22⋊Dic11—48no—
95C2×C22⋊Dic11C2314yes—
96C2×C22⋊Dic11C2318yes—
97C2×C22⋊Dic11C2318yes—
98C2×C22⋊Dic11C2314yes—
99C2×C22⋊Dic11C2318yes—
100#66992—232no—
101#66991—48no—
102#66990—216no—
103#66988—216no—
104#66982—216no—
105C2×(C2×D11)⋊C4—24no—
106C2×(C2×D11)⋊C4C2314yes—
107C2×(C2×D11)⋊C4C2318yes—
108C2×C4⋊Dic11C2314yes—
109C2×C4⋊Dic11C2314yes—
110C2×Dic11⋊C4—24no—
111C2×Dic11⋊C4C2314yes—
112C2×Dic11⋊C4C2318yes—
113C2×C4×Dic11—24no—
114C2×C4×Dic11C2314yes—
115(C22⋊D11)⋊C4—232no—
116C11⋊#95C2314yes—
117C11⋊#95C2318yes—
118C11⋊#95C2318yes—
119C11⋊#95C2314yes—
120#34984—111nomaximal, Sylow
121C24×C11—24no—
122C24×C11—24no—
123C24×C11—24no—
124C24×C11—42no—
125C24×C11—42no—
126C24×C11—44no—
127C24×C11—44no—
128C24×C11C2×D414yes—
129C24×C11C2×D414yes—
130C24×C11#4114yes—
131C24×C11C2414yes—
132C24×C11C2411yescharacteristic
133C24×C11C2412yes—
134C23×D11—22no—
135C23×D11—22no—
136C23×D11—42no—
137C23×D11—42no—
138C23×D11C2×D414yes—
139C23×D11C2412yes—
140C2×D4×C11—28no—
141C2×D4×C11—28no—
142C2×D4×C11—28no—
143C2×D4×C11—28no—
144C2×D4×C11—28no—
145C2×D4×C11—28no—
146C2×D4×C11—24no—
147C2×D4×C11—24no—
148C2×D4×C11—44no—
149C2×D4×C11—44no—
150C2×D4×C11—432no—
151C22×C4×C11—24no—
152C22×C4×C11—24no—
153C22×C4×C11—24no—
154C22×C4×C11—42no—
155C22×C4×C11—42no—
156C22×C4×C11C2×D414yes—
157C22×C4×C11C2×D414yes—
158C22×C4×C11C2414yes—
159C22×C4×C11C2412yes—
160C22×C4×C11C2412yes—
161C2×C22⋊D11—232no—
162C2×C22⋊D11—28no—
163C2×C22⋊D11—28no—
164C2×C22⋊D11—216no—
165C2×C22⋊D11—48no—
166C2×C22⋊D11—48no—
167C2×C22⋊D11C2×D4116yes—
168C22×Dic11—24no—
169C22×Dic11—28no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—28no—
173C22×Dic11—22no—
174C22×Dic11—28no—
175C22×Dic11—22no—
176C22×Dic11—44no—
177C22×Dic11—42no—
178C22×Dic11—44no—
179C22×Dic11—44no—
180C22×Dic11—416no—
181C22×Dic11C2×D414yes—
182C22×Dic11C2412yes—
183C22×Dic11C2418yes—
184C22×Dic11C2412yes—
185C22×Dic11C2412yes—
186C2×C4×D11—28no—
187C2×C4×D11—28no—
188C2×C4×D11—44no—
189C2×C4×D11—416no—
190C11×C4⋊C4—24no—
191C11×C4⋊C4—24no—
192C11×C22⋊C4—28no—
193C11×C22⋊C4—28no—
194C11×C22⋊C4C2×D4116yes—
195C22⋊Dic11—216no—
196C22⋊Dic11—216no—
197C22⋊Dic11—28no—
198C22⋊Dic11—28no—
199C22⋊Dic11—48no—
200(C2×D11)⋊C4—216no—
201(C2×D11)⋊C4—28no—
202C4⋊Dic11—44no—
203C4⋊Dic11—44no—
204Dic11⋊C4—216no—
205Dic11⋊C4—28no—
206C4×Dic11—28no—
207C2×#534—112no—
208C2×#534D1111yescharacteristic, complemented
209C22×C4×D4—111no—
210#2854—112no—
211#2847—112no—
212#2618—112no—
213#2617—112no—
214#2425—118no—
215#2424—118no—
216#2315—111no—
217C2×#386—112no—
218C23×C11—24no—
219C23×C11—22no—
220C23×C11—24no—
221C23×C11—22no—
222C23×C11—24no—
223C23×C11—24no—
224C23×C11—24no—
225C23×C11—28no—
226C23×C11—28no—
227C23×C11—44no—
228C23×C11—48no—
229C23×C11—44no—
230C23×C11—48no—
231C23×C11—416no—
232C23×C11—48no—
233C23×C11—84no—
234C23×C11—84no—
235C23×C11—88no—
236C23×C11#121116yescomplemented
237C23×C11C22×D412yes—
238C23×C11C22×D414yes—
239C23×C11C22×D414yes—
240C23×C11C22×D412yes—
241C23×C11C2×#4112yes—
242C23×C11C2×#4114yes—
243C23×C11C2511yescharacteristic
244C22×D11—28no—
245C22×D11—22no—
246C22×D11—22no—
247C22×D11—24no—
248C22×D11—24no—
249C22×D11—48no—
250C22×D11—44no—
251C22×D11—48no—
252C22×D11—44no—
253C22×D11C22×D414yes—
254D4×C11—416no—
255D4×C11—416no—
256D4×C11—84no—
257D4×C11—84no—
258C2×C4×C11—24no—
259C2×C4×C11—24no—
260C2×C4×C11—24no—
261C2×C4×C11—24no—
262C2×C4×C11—24no—
263C2×C4×C11—44no—
264C2×C4×C11—44no—
265C2×C4×C11—48no—
266C2×C4×C11C22×D414yes—
267C2×C4×C11C22×D414yes—
268C22⋊D11—232no—
269C22⋊D11—816no—
270C2×Dic11—28no—
271C2×Dic11—28no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—28no—
278C2×Dic11—28no—
279C2×Dic11—24no—
280C2×Dic11—28no—
281C2×Dic11—416no—
282C2×Dic11—44no—
283C2×Dic11—88no—
284C2×Dic11C22×D414yes—
285C2×Dic11H(5,𝔽2)14yes—
286C4×D11—416no—
287C23×D4—111no—
288C23×D4C2×D1112yes—
289C24×C4—111no—
290C24×C4—111no—
291#534—28no—
292#534—2216no—
293C2×#123—114no—
294C2×#123—114no—
295C2×#123C2×D1114yescomplemented
296C2×#121—118no—
297C2×#121—114no—
298C2×#121C2×D1112yes—
299C2×#121C2×D1112yes—
300C2×#120—114no—
301C2×#120—114no—
302C2×#120C2×D1114yescomplemented
303C2×C4×D4—118no—
304C2×C4×D4—228no—
305C22×C4⋊C4—111no—
306C22×C22⋊C4—112no—
307C22×C22⋊C4—111no—
308C22×C22⋊C4—114no—
309C22×C22⋊C4C2×D1111yescharacteristic
310C22×C42—111no—
311#398—114no—
312#397—114no—
313#396—118no—
314#394—114no—
315#394—118no—
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#385—118no—
325#380—112no—
326#380—112no—
327#380—114no—
328C2×#95—114no—
329C22×C11—24no—
330C22×C11—28no—
331C22×C11—22no—
332C22×C11—24no—
333C22×C11—22no—
334C22×C11—24no—
335C22×C11—24no—
336C22×C11—28no—
337C22×C11—416no—
338C22×C11—44no—
339C22×C11—48no—
340C22×C11—44no—
341C22×C11—44no—
342C22×C11—48no—
343C22×C11—816no—
344C22×C11C2×#12118yes—
345C22×C11C2×#12114yes—
346C22×C11C23×D411yescharacteristic
347C22×C11C23×D411yescharacteristic
348C22×C11C22×#4111yescharacteristic
349C22×C11C2×H(5,𝔽2)12yes—
350C22×C11#58512yes—
351C2×D11—24no—
352C2×D11—28no—
353C2×D11—416no—
354C2×D11—44no—
355C2×D11—42no—
356C2×D11—42no—
357C4×C11—24no—
358C4×C11—24no—
359C4×C11—44no—
360Dic11—24no—
361Dic11—24no—
362Dic11—42no—
363Dic11—48no—
364C25—111no—
365C25C22×D1112yes—
366C25C22×D1111yescharacteristic
367C22×D4—28no—
368C22×D4—28no—
369C22×D4—28no—
370C22×D4—118no—
371C22×D4—114no—
372C22×D4—118no—
373C22×D4—224no—
374C22×D4—224no—
375C22×D4C22×D1114yes—
376C22×D4C22×D1114yes—
377C22×D4C22×D1112yes—
378C22×D4C22×D1112yes—
379C23×C4—111no—
380C23×C4—111no—
381C23×C4—114no—
382C23×C4—114no—
383C23×C4—111no—
384C23×C4—114no—
385C23×C4—224no—
386C23×C4—224no—
387C23×C4—444no—
388C23×C4—444no—
389C23×C4C22×D1112yes—
390C23×C4C22×D1111yescharacteristic
391C23×C4C22×D1111yescharacteristic
392#123—216no—
393#123—2216no—
394#123—2216no—
395#121—28no—
396#121—28no—
397#121—2232no—
398#121—448no—
399#120—216no—
400#120—2216no—
401#120—2216no—
402C4×D4—2232no—
403C2×C4⋊C4—114no—
404C2×C4⋊C4—118no—
405C2×C4⋊C4—114no—
406C2×C4⋊C4—114no—
407C2×C4⋊C4—224no—
408C2×C4⋊C4C22×D1112yes—
409C2×C4⋊C4C22×D1112yes—
410C2×C22⋊C4—114no—
411C2×C22⋊C4—114no—
412C2×C22⋊C4—118no—
413C2×C22⋊C4—118no—
414C2×C22⋊C4—114no—
415C2×C22⋊C4—118no—
416C2×C22⋊C4—118no—
417C2×C22⋊C4—228no—
418C2×C22⋊C4—224no—
419C2×C22⋊C4—448no—
420C2×C22⋊C4C22⋊D1118yescomplemented
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#95—114no—
429#95—114no—
430C2×C11—24no—
431C2×C11—28no—
432C2×C11—84no—
433C2×C11C22×#12111yescharacteristic
434C2×C11#345912yes—
435C2×C11#348411yescharacteristic
436C2×C11#348511yescharacteristic
437C2×C11#349612yes—
438D11—44no—
439C24—24no—
440C24—24no—
441C24—24no—
442C24—42no—
443C24—42no—
444C24—44no—
445C24—44no—
446C24—112no—
447C24—114no—
448C24—222no—
449C24—222no—
450C24—442no—
451C24—442no—
452C24D4×D1114yes—
453C24#434114yes—
454C24C2×C22⋊D1114yes—
455C24C23×D1114yes—
456C24C23×D1111yescharacteristic
457C24C23×D1112yes—
458C2×D4—28no—
459C2×D4—28no—
460C2×D4—28no—
461C2×D4—28no—
462C2×D4—28no—
463C2×D4—28no—
464C2×D4—24no—
465C2×D4—24no—
466C2×D4—44no—
467C2×D4—44no—
468C2×D4—432no—
469C2×D4—1116no—
470C2×D4—2232no—
471C2×D4—228no—
472C2×D4—228no—
473C2×D4—2216no—
474C2×D4—448no—
475C2×D4—448no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—114no—
482C22×C4—112no—
483C22×C4—112no—
484C22×C4—118no—
485C22×C4—112no—
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—228no—
495C22×C4—228no—
496C22×C4—444no—
497C22×C4—4416no—
498C22×C4—444no—
499C22×C4—442no—
500C22×C4—444no—
501C22×C4—444no—
502C22×C4—4416no—
503C22×C4C2×C22⋊D1114yes—
504C22×C4C2×C22⋊D1114yes—
505C22×C4C23×D1114yes—
506C22×C4C23×D1112yes—
507C22×C4C23×D1112yes—
508C4⋊C4—24no—
509C4⋊C4—24no—
510C4⋊C4—2216no—
511C4⋊C4—228no—
512C4⋊C4—444no—
513C4⋊C4—444no—
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×C22⋊D11116yes—
524C42—228no—
525C11#3498411yescharacteristic, complemented, Sylow
526C23—22no—
527C23—24no—
528C23—22no—
529C23—24no—
530C23—24no—
531C23—24no—
532C23—28no—
533C23—28no—
534C23—24no—
535C23—44no—
536C23—48no—
537C23—48no—
538C23—44no—
539C23—416no—
540C23—48no—
541C23—88no—
542C23—84no—
543C23—84no—
544C23—114no—
545C23—228no—
546C23—222no—
547C23—224no—
548C23—224no—
549C23—222no—
550C23—448no—
551C23—444no—
552C23—444no—
553C23—448no—
554C23#66991116yescomplemented
555C23C2×D4×D1112yes—
556C23C2×D4×D1114yes—
557C23C2×#434114yes—
558C23C2×#434112yes—
559C23C22×C22⋊D1114yes—
560C23C22×C22⋊D1112yes—
561C23C24×D1111yescharacteristic
562D4—416no—
563D4—416no—
564D4—84no—
565D4—84no—
566D4—2232no—
567D4—8816no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—44no—
574C2×C4—44no—
575C2×C4—48no—
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—228no—
585C2×C4—228no—
586C2×C4—224no—
587C2×C4—228no—
588C2×C4—222no—
589C2×C4—4416no—
590C2×C4—4416no—
591C2×C4—444no—
592C2×C4—888no—
593C2×C4C22×C22⋊D1114yes—
594C2×C4C22×C22⋊D1114yes—
595C22—28no—
596C22—24no—
597C22—22no—
598C22—24no—
599C22—22no—
600C22—24no—
601C22—28no—
602C22—24no—
603C22—416no—
604C22—48no—
605C22—44no—
606C22—44no—
607C22—48no—
608C22—44no—
609C22—816no—
610C22—228no—
611C22—224no—
612C22—4416no—
613C22—442no—
614C22—442no—
615C22—444no—
616C22C2×#6699118yes—
617C22C2×#6699114yes—
618C22C22×D4×D1111yescharacteristic
619C22C22×#434111yescharacteristic
620C22D11×H(5,𝔽2)12yes—
621C22#1062345512yes—
622C22C23×C22⋊D1111yescharacteristic
623C4—24no—
624C4—24no—
625C4—44no—
626C4—224no—
627C4—224no—
628C4—448no—
629C4—442no—
630C2—28no—
631C2—24no—
632C2—84no—
633C2—444no—
634C2C22×#6699111yescharacteristic
635C2#1308202212yes—
636C2#1308224711yescharacteristic
637C2#1308225611yescharacteristic
638C2#1308237712yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C11×#534C2
hypercenterC2×#534D11
hypocenterC11#34984
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#534

Complements

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

NH ≅ G/Ntype
1. C2×#10623335C2semidirect
2. C22×(C22⋊D11)⋊C4C2semidirect
3. #13076942C2semidirect
4. #13076895C2semidirect
5. #13074360C2semidirect
6. #13074352C2semidirect
7. #13072163C2semidirect
8. #13072148C2semidirect
9. #13071230C2semidirect
10. C2×#10622833C2semidirect
11. C2×C11×#534C2semidirect
15. C23×C4×D11C22semidirect
17. C2×C11×#123C22semidirect
20. C2×C11×#120C22semidirect
22. C2×#67006C22semidirect
24. C22×C22⋊Dic11C22semidirect
27. C2×#66991C22semidirect
28. C2×#66990C22semidirect
29. C2×#66988C22semidirect
30. C2×#66982C22semidirect
31. C22×(C2×D11)⋊C4C22semidirect
32. C22×Dic11⋊C4C22semidirect
33. C22×C4×Dic11C22semidirect
35. C2×(C22⋊D11)⋊C4C22semidirect
36. #10622836C22semidirect
37. #10622835C22semidirect
38. #10622834C22semidirect
39. #10622833C22semidirect
40. #10622833C22semidirect
41. #10622833C22semidirect
42. #10622825C22semidirect
43. #10622825C22semidirect
44. C2×C11⋊#95C22semidirect
45. #10622606C22semidirect
46. #10622600C22semidirect
47. #10622593C22semidirect
48. #10622586C22semidirect
49. #10622574C22semidirect
50. #10622569C22semidirect
51. #10622563C22semidirect
52. #10622561C22semidirect
53. #10622557C22semidirect
69. C22×C22⋊D11D4semidirect
88. C2×C11×C22⋊C4D4semidirect
208. C2×#534D11semidirect
236. C23×C11#121semidirect
295. C2×#123C2×D11semidirect
302. C2×#120C2×D11semidirect
420. C2×C22⋊C4C22⋊D11semidirect
525. C11#34984semidirect
554. C23#66991semidirect

Maximal subgroups

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

subgroupindex
C2×#106233352
C22×(C22⋊D11)⋊C42
#130769422
#130768952
#130743602
#130743522
#130721632
#130721482
#130712302
C2×#106228332
C2×C11×#5342
#3498411