Finite Group Databasebeta

← #14916742

Subgroups — #14916742

Order 2816.

3082 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66983C211yesmaximal, characteristic
2#13071770C214yesmaximal, complemented
3#13071632C214yesmaximal, complemented
4#13071495C212yesmaximal, complemented
5#13071436C212yesmaximal, complemented
6C22⋊C4×C22⋊D11C214yesmaximal, complemented
7#13071319C214yesmaximal, complemented
8#13071305C214yesmaximal, complemented
9#13071229C212yesmaximal, complemented
10#13071213C212yesmaximal, complemented
11#13070999C211yesmaximal, characteristic, complemented
12C2×C11×#380C211yesmaximal, characteristic, complemented
13C24×C4×C11C2211yescharacteristic
14C23×C22⋊D11C2212yes—
15C23×D44C2211yescharacteristic
16C22×C11×C4⋊C4C2212yescomplemented
17C22×C11×C22⋊C4C2212yes—
18C2×#66983C4116yescomplemented
19C2×#66983C2212yes—
20C2×#66983C2212yes—
21C2×#66983C2212yes—
22C2×#66983C2212yes—
23C2×C4×C22⋊D11C2218yescomplemented
24C22×(C2×D11)⋊C4C2212yes—
25C2×#66979C2212yescomplemented
26C22×C4⋊Dic11C2211yescharacteristic
27C2×#66946C2214yescomplemented
28C2×C22⋊C4×D11C2214yes—
29C11×#380C2212yes—
30C11×#380C2212yes—
31C11×#380C2212yescomplemented
32C11×#380C2212yescomplemented
33C2×C11×#95C2212yescomplemented
34#10622860C2212yes—
35#10622826C2218yescomplemented
36#10622825C2211yescharacteristic
37#10622825C2211yescharacteristic
38#10622825C2212yescomplemented
39#10622824C2212yescomplemented
40C4×C22⋊Dic11C2212yes—
41C4×C22⋊Dic11C2212yescomplemented
42#10622603C2218yescomplemented
43#10622602C2218yescomplemented
44#10622601C2214yescomplemented
45C4⋊C4×Dic11C2214yescomplemented
46#10622586C2214yescomplemented
47#10622570C2218yescomplemented
48#10622569C2218yescomplemented
49#10622568C2214yes—
50#10622555C2214yes—
51C22⋊C4×Dic11C2214yes—
52#10622283C2218yescomplemented
53#10622281C2218yescomplemented
54#10622278C2218yescomplemented
55#10622266C2218yescomplemented
56C25×C11C2311yescharacteristic
57C24×D11C2312yes—
58C23×C4×C11—44no—
59C23×C4×C11C2×C418yescomplemented
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2314yes—
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—48no—
68C22×C22⋊D11C2×C4116yescomplemented
69C22×C22⋊D11C2314yes—
70C22×C22⋊D11C2314yes—
71C23×Dic11C2312yes—
72C22×D44—44no—
73C22×D44C2×C418yescomplemented
74C22×D44C2312yes—
75C22×D44C2312yes—
76C22×C4×D11C2318yes—
77C2×C11×C4⋊C4—44no—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C22⋊C4—44no—
81C2×C11×C22⋊C4C2314yes—
82C2×C11×C22⋊C4C2314yes—
83C2×C22⋊Dic11C2312yes—
84C2×C22⋊Dic11C2314yes—
85C2×C22⋊Dic11C2312yes—
86C2×C22⋊Dic11C2314yes—
87#66983C2×C4116yescomplemented
88#66983C2×C4116yescomplemented
89#66983C2×C4116yescomplemented
90#66983C2×C4116yescomplemented
91C4×C22⋊D11—416no—
92C2×(C2×D11)⋊C4C2×C4116yescomplemented
93C2×(C2×D11)⋊C4C2318yes—
94C2×(C2×D11)⋊C4C2318yes—
95C2×(C2×D11)⋊C4C2318yes—
96C2×(C2×D11)⋊C4C2314yes—
97C2×(C2×D11)⋊C4C2314yes—
98#66979—44no—
99C2×C4⋊Dic11C2×C418yescomplemented
100C2×C4⋊Dic11C2312yes—
101C2×C4⋊Dic11C2312yes—
102C2×C4⋊Dic11C2312yes—
103C2×C4⋊Dic11C2312yes—
104C2×Dic11⋊C4C2318yes—
105C2×C4×Dic11C2314yes—
106C2×C4×Dic11C2318yes—
107#66946—48no—
108C22⋊C4×D11—48no—
109C11×#95C2314yes—
110C11×#95C2314yes—
111C11⋊#95C2314yes—
112C11⋊#95C2318yes—
113C11⋊#95C2318yes—
114C11⋊#95C2312yes—
115C11⋊#95C2312yes—
116#34379—111nomaximal, Sylow
117C24×C11—22no—
118C24×C11—24no—
119C24×C11—22no—
120C24×C11—42no—
121C24×C11C22×C414yes—
122C24×C11C2411yescharacteristic
123C24×C11C2411yescharacteristic
124C24×C11C2411yescharacteristic
125C23×D11—24no—
126C23×D11—24no—
127C23×D11—44no—
128C23×D11—44no—
129C23×D11C22×C418yes—
130C23×D11C2414yes—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—24no—
134C22×C4×C11—28no—
135C22×C4×C11—416no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11—44no—
140C22×C4×C11—44no—
141C22×C4×C11C22×C414yes—
142C22×C4×C11C22×C414yes—
143C22×C4×C11C22×C414yes—
144C22×C4×C11C22×C414yes—
145C22×C4×C11C22×C414yes—
146C22×C4×C11C22×C414yes—
147C22×C4×C11C2418yes—
148C22×C4×C11C2411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C2×C22⋊D11—216no—
153C2×C22⋊D11—48no—
154C2×C22⋊D11—432no—
155C2×C22⋊D11C22×C4116yes—
156C2×C22⋊D11C22×C4116yes—
157C22×Dic11—44no—
158C22×Dic11C22×C418yes—
159C22×Dic11C2414yes—
160C22×Dic11C2414yes—
161C22×Dic11C2414yes—
162C2×D44—28no—
163C2×D44—44no—
164C2×D44—416no—
165C2×D44C22×C418yes—
166C2×D44C22×C418yes—
167C2×C4×D11—48no—
168C2×C4×D11—48no—
169C2×C4×D11—48no—
170C11×C4⋊C4—28no—
171C11×C4⋊C4—44no—
172C11×C22⋊C4—28no—
173C11×C22⋊C4—44no—
174C22⋊Dic11—24no—
175C22⋊Dic11—28no—
176C22⋊Dic11—24no—
177C22⋊Dic11—44no—
178(C2×D11)⋊C4—48no—
179(C2×D11)⋊C4—48no—
180(C2×D11)⋊C4—48no—
181(C2×D11)⋊C4C22×C4116yes—
182(C2×D11)⋊C4C22×C4116yes—
183C4⋊Dic11—42no—
184C4⋊Dic11—42no—
185C4⋊Dic11C22×C418yes—
186C4⋊Dic11C22×C418yes—
187Dic11⋊C4—48no—
188C4×Dic11—28no—
189C4×Dic11—48no—
190C22×#121—111no—
191#2377—114no—
192#2361—114no—
193#2345—112no—
194D4×C22⋊C4—112no—
195D4×C22⋊C4—114no—
196#2325—114no—
197#2324—114no—
198#2315—112no—
199#2312—112no—
200#2280—111no—
201C2×#380D1111yescharacteristic, complemented
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—21no—
206C23×C11—21no—
207C23×C11—28no—
208C23×C11—28no—
209C23×C11—22no—
210C23×C11—21no—
211C23×C11—22no—
212C23×C11—21no—
213C23×C11—44no—
214C23×C11—48no—
215C23×C11—48no—
216C23×C11C23×C412yes—
217C23×C11C23×C412yes—
218C23×C11C23×C412yes—
219C23×C11H(5,𝔽2)12yes—
220C23×C11H(5,𝔽2)14yes—
221C23×C112−1+412yes—
222C23×C11C2511yescharacteristic
223C22×D11—24no—
224C22×D11—28no—
225C22×D11—28no—
226C22×D11—24no—
227C22×D11—216no—
228C22×D11—48no—
229C22×D11—48no—
230C22×D11—88no—
231C22×D11—88no—
232C22×D11C23×C418yes—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—28no—
237C2×C4×C11—28no—
238C2×C4×C11—28no—
239C2×C4×C11—28no—
240C2×C4×C11—28no—
241C2×C4×C11—28no—
242C2×C4×C11—44no—
243C2×C4×C11—44no—
244C2×C4×C11—44no—
245C2×C4×C11—88no—
246C2×C4×C11C23×C412yes—
247C2×C4×C11C23×C412yes—
248C2×C4×C11C23×C412yes—
249C2×C4×C11C23×C412yes—
250C2×C4×C11H(5,𝔽2)14yes—
251C22⋊D11—232no—
252C22⋊D11—416no—
253C2×Dic11—28no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—48no—
261C2×Dic11C23×C418yes—
262D44—216no—
263D44—48no—
264C4×D11—816no—
265C23×D4—112no—
266C23×D4—111no—
267C24×C4C2×D1111yescharacteristic
268C2×#121—112no—
269C2×#121—112no—
270C2×#121—112no—
271C2×#121—112no—
272C2×#121—1116no—
273C2×C4×D4—118no—
274C2×C4×D4—114no—
275C2×#117—112no—
276C22×C4⋊C4—111no—
277C22×C4⋊C4C2×D1112yescomplemented
278C22×C22⋊C4—112no—
279C22×C22⋊C4—114no—
280C22×C22⋊C4C2×D1112yes—
281#390—114no—
282#390—118no—
283#389—114no—
284#388—118no—
285#388—118no—
286#387—118no—
287#386—118no—
288#386—118no—
289#386—118no—
290#385—118no—
291#385—118no—
292#381—112no—
293#380—111no—
294#380—111no—
295#380—112no—
296#380—114no—
297#380C2×D1112yes—
298#380C2×D1112yes—
299#380C2×D1112yescomplemented
300#380C2×D1112yescomplemented
301#379—112no—
302#379—114no—
303C4×C4⋊C4—114no—
304C4×C22⋊C4—112no—
305C4×C22⋊C4—112no—
306C4×C22⋊C4—114no—
307C2×#95C2×D1112yescomplemented
308C22×C11—22no—
309C22×C11—22no—
310C22×C11—22no—
311C22×C11—22no—
312C22×C11—24no—
313C22×C11—24no—
314C22×C11—24no—
315C22×C11—24no—
316C22×C11—22no—
317C22×C11—22no—
318C22×C11—22no—
319C22×C11—416no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11#51814yes—
323C22×C11#52014yes—
324C22×C11C24×C411yescharacteristic
325C22×C11C2×H(5,𝔽2)12yes—
326C22×C11C2×H(5,𝔽2)11yescharacteristic
327C22×C11C2×H(5,𝔽2)12yes—
328C22×C11C2×2−1+411yescharacteristic
329C2×D11—28no—
330C2×D11—28no—
331C2×D11—28no—
332C2×D11—48no—
333C2×D11—48no—
334C2×D11—816no—
335C4×C11—22no—
336C4×C11—22no—
337C4×C11—22no—
338C4×C11—48no—
339C4×C11#51814yes—
340Dic11—28no—
341Dic11—44no—
342Dic11—44no—
343C25—112no—
344C25C22×D1111yescharacteristic
345C22×D4—114no—
346C22×D4—1116no—
347C22×D4—114no—
348C22×D4—118no—
349C22×D4—112no—
350C22×D4—112no—
351C22×D4—444no—
352C22×D4—448no—
353C23×C4—44no—
354C23×C4—112no—
355C23×C4—118no—
356C23×C4C4×D1118yescomplemented
357C23×C4C22×D1111yescharacteristic
358C23×C4C22×D1111yescharacteristic
359C23×C4C22×D1111yescharacteristic
360C23×C4C22×D1114yes—
361C23×C4C22×D1111yescharacteristic
362C23×C4C22×D1111yescharacteristic
363C23×C4C22×D1111yescharacteristic
364#121—1116no—
365#121—1116no—
366#121—1116no—
367#121—1116no—
368C4×D4—448no—
369C4×D4—4416no—
370#117—444no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—118no—
373C2×C4⋊C4—112no—
374C2×C4⋊C4—112no—
375C2×C4⋊C4—112no—
376C2×C4⋊C4—112no—
377C2×C4⋊C4—118no—
378C2×C4⋊C4C22×D1114yes—
379C2×C4⋊C4C22×D1114yes—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—1116no—
382C2×C22⋊C4—114no—
383C2×C22⋊C4—114no—
384C2×C22⋊C4—112no—
385C2×C22⋊C4—114no—
386C2×C22⋊C4—112no—
387C2×C22⋊C4—114no—
388C2×C22⋊C4—118no—
389C2×C22⋊C4—118no—
390C2×C22⋊C4—118no—
391C2×C22⋊C4—448no—
392C2×C22⋊C4C22×D1114yes—
393C2×C22⋊C4C22×D1114yes—
394C2×C42—114no—
395C2×C42—118no—
396#95—112no—
397#95—114no—
398#95—112no—
399#95—118no—
400#95—118no—
401#95C22×D1114yes—
402#95C22×D1114yes—
403C2×C11—24no—
404C2×C11—24no—
405C2×C11—42no—
406C2×C11C2×#51811yescharacteristic
407C2×C11C2×#51811yescharacteristic
408C2×C11C2×#52011yescharacteristic
409C2×C11#353612yes—
410C2×C11#353712yes—
411D11—48no—
412C24—22no—
413C24—22no—
414C24—24no—
415C24—42no—
416C24—114no—
417C24—118no—
418C24—224no—
419C24—224no—
420C24—444no—
421C24—444no—
422C24C2×C4×D1114yes—
423C24C23×D1111yescharacteristic
424C24C23×D1111yescharacteristic
425C24C23×D1111yescharacteristic
426C2×D4—1116no—
427C2×D4—1116no—
428C2×D4—118no—
429C2×D4—118no—
430C2×D4—2216no—
431C2×D4—228no—
432C2×D4—4416no—
433C2×D4—444no—
434C2×D4—448no—
435C2×D4—4432no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—28no—
440C22×C4—416no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—44no—
445C22×C4—44no—
446C22×C4—114no—
447C22×C4—118no—
448C22×C4—114no—
449C22×C4—114no—
450C22×C4—448no—
451C22×C4—448no—
452C22×C4—448no—
453C22×C4—444no—
454C22×C4C2×C4×D1114yes—
455C22×C4C2×C4×D1114yes—
456C22×C4C2×C4×D1114yes—
457C22×C4C2×C4×D1114yes—
458C22×C4C2×C4×D1114yes—
459C22×C4C2×C4×D1114yes—
460C22×C4C23×D1118yes—
461C22×C4C23×D1111yescharacteristic
462C22×C4C23×D1111yescharacteristic
463C22×C4C23×D1111yescharacteristic
464C22×C4C23×D1111yescharacteristic
465C4⋊C4—28no—
466C4⋊C4—44no—
467C4⋊C4—118no—
468C4⋊C4—118no—
469C4⋊C4—442no—
470C4⋊C4—442no—
471C4⋊C4—448no—
472C22⋊C4—28no—
473C22⋊C4—44no—
474C22⋊C4—1116no—
475C22⋊C4—1116no—
476C22⋊C4—224no—
477C22⋊C4—224no—
478C22⋊C4—228no—
479C22⋊C4—448no—
480C22⋊C4—448no—
481C22⋊C4—448no—
482C22⋊C4—444no—
483C42—228no—
484C42—448no—
485C11#3437911yescharacteristic, complemented, Sylow
486C23—22no—
487C23—22no—
488C23—21no—
489C23—21no—
490C23—22no—
491C23—28no—
492C23—28no—
493C23—21no—
494C23—22no—
495C23—21no—
496C23—22no—
497C23—44no—
498C23—48no—
499C23—48no—
500C23—118no—
501C23—224no—
502C23—228no—
503C23—224no—
504C23—228no—
505C23—2216no—
506C23—448no—
507C23—448no—
508C23—888no—
509C23—888no—
510C23C22×C4×D1112yes—
511C23C22×C4×D1112yes—
512C23C22×C4×D1112yes—
513C23#6703712yes—
514C23#6704012yes—
515C23#6704214yes—
516C23C24×D1111yescharacteristic
517D4—2232no—
518D4—2216no—
519D4—448no—
520D4—4416no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—28no—
525C2×C4—28no—
526C2×C4—28no—
527C2×C4—28no—
528C2×C4—28no—
529C2×C4—28no—
530C2×C4—44no—
531C2×C4—44no—
532C2×C4—44no—
533C2×C4—88no—
534C2×C4—118no—
535C2×C4—228no—
536C2×C4—224no—
537C2×C4—224no—
538C2×C4—224no—
539C2×C4—224no—
540C2×C4—224no—
541C2×C4—224no—
542C2×C4—448no—
543C2×C4—8816no—
544C2×C4C22×C4×D1112yes—
545C2×C4C22×C4×D1112yes—
546C2×C4C22×C4×D1112yes—
547C2×C4C22×C4×D1112yes—
548C2×C4#6703714yes—
549C22—22no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—24no—
554C22—24no—
555C22—24no—
556C22—24no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—416no—
561C22—42no—
562C22—42no—
563C22—228no—
564C22—228no—
565C22—228no—
566C22—448no—
567C22—448no—
568C22—8816no—
569C22#1062303514yes—
570C22#1062305214yes—
571C22C23×C4×D1111yescharacteristic
572C22C2×#6703712yes—
573C22C2×#6703711yescharacteristic
574C22C2×#6704011yescharacteristic
575C22C2×#6704212yes—
576C4—22no—
577C4—22no—
578C4—22no—
579C4—48no—
580C4—228no—
581C4—444no—
582C4—444no—
583C4#1062301714yes—
584C2—24no—
585C2—24no—
586C2—42no—
587C2—448no—
588C2C2×#1062301711yescharacteristic
589C2C2×#1062305211yescharacteristic
590C2C2×#1062303511yescharacteristic
591C2#1308284512yes—
592C2#1308285112yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC2×C11×#380C2
socle, cosocleC23×C11C25
prime radicalC22×#66983C2
hypercenterC2×#380D11
hypocenterC11#34379
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. #13071770C2semidirect
3. #13071632C2semidirect
4. #13071495C2semidirect
5. #13071436C2semidirect
6. C22⋊C4×C22⋊D11C2semidirect
7. #13071319C2semidirect
8. #13071305C2semidirect
9. #13071229C2semidirect
10. #13071213C2semidirect
11. #13070999C2semidirect
12. C2×C11×#380C2semidirect
16. C22×C11×C4⋊C4C22semidirect
18. C2×#66983C4semidirect
23. C2×C4×C22⋊D11C22semidirect
25. C2×#66979C22semidirect
27. C2×#66946C22semidirect
31. C11×#380C22semidirect
32. C11×#380C22semidirect
33. C2×C11×#95C22semidirect
35. #10622826C22semidirect
38. #10622825C22semidirect
39. #10622824C22semidirect
41. C4×C22⋊Dic11C22semidirect
42. #10622603C22semidirect
43. #10622602C22semidirect
44. #10622601C22semidirect
45. C4⋊C4×Dic11C22semidirect
46. #10622586C22semidirect
47. #10622570C22semidirect
48. #10622569C22semidirect
52. #10622283C22semidirect
53. #10622281C22semidirect
54. #10622278C22semidirect
55. #10622266C22semidirect
59. C23×C4×C11C2×C4semidirect
68. C22×C22⋊D11C2×C4semidirect
73. C22×D44C2×C4semidirect
87. #66983C2×C4semidirect
88. #66983C2×C4semidirect
89. #66983C2×C4semidirect
90. #66983C2×C4semidirect
92. C2×(C2×D11)⋊C4C2×C4semidirect
99. C2×C4⋊Dic11C2×C4semidirect
201. C2×#380D11semidirect
277. C22×C4⋊C4C2×D11semidirect
299. #380C2×D11semidirect
300. #380C2×D11semidirect
307. C2×#95C2×D11semidirect
356. C23×C4C4×D11semidirect
485. C11#34379semidirect

Maximal subgroups

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

subgroupindex
C22×#669832
#130717702
#130716322
#130714952
#130714362
C22⋊C4×C22⋊D112
#130713192
#130713052
#130712292
#130712132
#130709992
C2×C11×#3802
#3437911