Finite Group Databasebeta

← #14786406

Subgroups — #14786406

Order 2816.

1844 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66983C211yesmaximal, characteristic
2C2×#10622580C212yesmaximal, complemented
3#13069798C214yesmaximal, complemented
4#13068933C212yesmaximal, complemented
5#13068803C212yesmaximal, complemented
6#13068546C212yesmaximal, complemented
7#13068526C211yesmaximal, characteristic, complemented
8C2×C11×#380C211yesmaximal, characteristic, complemented
9C24×C4×C11C2211yescharacteristic
10C23×C22⋊D11—21no—
11C23×D44C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic, complemented
13C22×C11×C4⋊C4C2211yescharacteristic, complemented
14C22×C11×C22⋊C4—21no—
15C2×#66983—21no—
16C2×#66983—21no—
17C2×#66983—28no—
18C2×#66983C2212yes—
19C2×#66983C2212yes—
20C22×(C2×D11)⋊C4—21no—
21C22×C4⋊Dic11C2211yescharacteristic
22C11×#380—21no—
23C11×#380—21no—
24C11×#380C2212yes—
25C11×#380C2212yescomplemented
26C2×C11×#95—21no—
27C2×C22⋊(C11⋊C8)C2212yes—
28C2×C22⋊(C11⋊C8)C2212yescomplemented
29C2×C22⋊(C11⋊C8)C2212yescomplemented
30#10622580—28no—
31C2×#66873C2214yescomplemented
32C2×#66873C2214yescomplemented
33C2×#66871C2214yescomplemented
34#10622167C2214yescomplemented
35C25×C11D411yescharacteristic
36C24×D11—21no—
37C23×C4×C11—24no—
38C23×C4×C11—24no—
39C23×C4×C11—21no—
40C23×C4×C11—21no—
41C23×C4×C11—42no—
42C23×C4×C11D411yescharacteristic
43C23×C4×C11D411yescharacteristic
44C23×C4×C11D411yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C22×C22⋊D11—28no—
49C22×C22⋊D11—22no—
50C22×C22⋊D11—22no—
51C22×C22⋊D11—44no—
52C22×C22⋊D11—44no—
53C23×Dic11—21no—
54C22×D44—21no—
55C22×D44—24no—
56C22×D44—24no—
57C22×D44—42no—
58C22×D44C2312yes—
59C2×C11×C4⋊C4—24no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—42no—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—44no—
68#66983—28no—
69#66983—28no—
70#66983—24no—
71#66983—24no—
72#66983—24no—
73#66983D418yes—
74C2×(C2×D11)⋊C4—28no—
75C2×(C2×D11)⋊C4—22no—
76C2×(C2×D11)⋊C4—22no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—24no—
79C2×C4⋊Dic11C2312yes—
80C22×C11⋊C8C2314yes—
81C11×#95—22no—
82C11×#95—22no—
83C22⋊(C11⋊C8)—24no—
84C22⋊(C11⋊C8)—24no—
85C22⋊(C11⋊C8)—42no—
86#66873—28no—
87#66873—44no—
88#66871—28no—
89#24002—111nomaximal, Sylow
90C24×C11—22no—
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—41no—
95C24×C11—41no—
96C24×C11D814yes—
97C24×C11C2×D411yescharacteristic
98C24×C11C2×D411yescharacteristic
99C24×C11C2×D411yescharacteristic
100C23×D11—24no—
101C23×D11—22no—
102C23×D11—42no—
103C23×D11—42no—
104C23×D11—42no—
105C23×D11—42no—
106C23×D11—42no—
107C23×D11—42no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—41no—
124C22×C4×C11—41no—
125C22×C4×C11—41no—
126C22×C4×C11—416no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D414yes—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11#4114yes—
138C22×C4×C11C2411yescharacteristic
139C2×C22⋊D11—28no—
140C2×C22⋊D11—28no—
141C2×C22⋊D11—432no—
142C2×C22⋊D11—44no—
143C2×C22⋊D11—44no—
144C2×C22⋊D11—44no—
145C2×C22⋊D11—44no—
146C22×Dic11—24no—
147C22×Dic11—22no—
148C22×Dic11—42no—
149C22×Dic11—42no—
150C2×D44—24no—
151C2×D44—22no—
152C2×D44—24no—
153C2×D44—24no—
154C2×D44—416no—
155C2×D44—42no—
156C2×D44—42no—
157C2×D44C2×D414yes—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4—42no—
162C11×C22⋊C4—44no—
163C11×C22⋊C4—44no—
164(C2×D11)⋊C4—28no—
165(C2×D11)⋊C4—28no—
166C4⋊Dic11—24no—
167C4⋊Dic11—22no—
168C4⋊Dic11C2×D414yes—
169C2×C11⋊C8—24no—
170C2×C11⋊C8—24no—
171C2×C11⋊C8—24no—
172C22×#121—111no—
173C2×#480—112no—
174C2×#380D1111yescharacteristic, complemented
175#2033—114no—
176#1874—112no—
177#1852—112no—
178#1786—112no—
179#1779—111no—
180C23×C11—21no—
181C23×C11—21no—
182C23×C11—21no—
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—21no—
191C23×C11—21no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—28no—
195C23×C11—28no—
196C23×C11—44no—
197C23×C11—44no—
198C23×C11—44no—
199C23×C11—44no—
200C23×C11—44no—
201C23×C11#12012yes—
202C23×C11#12312yes—
203C23×C11C2×D812yes—
204C23×C11C2×D812yes—
205C23×C11C2×D812yes—
206C23×C11AGL(1,ℤ/8)12yes—
207C23×C11#13712yes—
208C23×C11C22×D411yescharacteristic
209C22×D11—24no—
210C22×D11—48no—
211C22×D11—48no—
212C22×D11—48no—
213C22×D11—42no—
214C22×D11—42no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11—42no—
218C22×D11—42no—
219C22×D11—84no—
220C22×D11—84no—
221C22×D11—84no—
222C22×D11—84no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—28no—
228C2×C4×C11—28no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—44no—
233C2×C4×C11—44no—
234C2×C4×C11—44no—
235C2×C4×C11—44no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—84no—
243C2×C4×C11—84no—
244C2×C4×C11#12012yes—
245C2×C4×C11#12312yes—
246C2×C4×C11C22×D412yes—
247C2×C4×C11C2×#4112yes—
248C2×C4×C11H(5,𝔽2)12yes—
249C22⋊D11—416no—
250C22⋊D11—416no—
251C2×Dic11—24no—
252C2×Dic11—48no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255D44—28no—
256D44—48no—
257D44—44no—
258C11⋊C8—44no—
259C23×D4—111no—
260C23×D4—221no—
261C24×C4C2×D1111yescharacteristic
262C2×#121—112no—
263C2×#121—112no—
264C2×#121—228no—
265C2×#121—221no—
266C2×#121—221no—
267C22×C4⋊C4—111no—
268C22×C4⋊C4C2×D1111yescharacteristic, complemented
269C22×C4⋊C4C2×D1111yescharacteristic, complemented
270C22×C22⋊C4—21no—
271C22×C22⋊C4—221no—
272#480—228no—
273C2×#107—114no—
274C2×#102—114no—
275C2×#102—114no—
276C2×C22⋊C8—112no—
277C2×C22⋊C8—112no—
278C2×C22⋊C8—112no—
279#380—21no—
280#380—21no—
281#380C2×D1112yes—
282#380C2×D1112yescomplemented
283C2×#95—21no—
284#340—114no—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—22no—
297C22×C11—22no—
298C22×C11—22no—
299C22×C11—22no—
300C22×C11—416no—
301C22×C11—41no—
302C22×C11—41no—
303C22×C11—41no—
304C22×C11—41no—
305C22×C11#44714yes—
306C22×C11#48014yescomplemented
307C22×C11C2×#12011yescharacteristic
308C22×C11C2×#12311yescharacteristic
309C22×C11#53411yescharacteristic
310C22×C11C22×D811yescharacteristic
311C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
312C22×C11C2×#13711yescharacteristic
313C22×C11#57511yescharacteristic
314C2×D11—44no—
315C2×D11—44no—
316C2×D11—44no—
317C2×D11—816no—
318C2×D11—82no—
319C2×D11—82no—
320C2×D11—82no—
321C2×D11—82no—
322C4×C11—22no—
323C4×C11—22no—
324C4×C11—41no—
325C4×C11—82no—
326C4×C11—82no—
327C4×C11#54614yes—
328Dic11—44no—
329C25—221no—
330C25C22⋊D1111yescharacteristic
331C22×D4—112no—
332C22×D4—224no—
333C22×D4—228no—
334C22×D4—222no—
335C22×D4—222no—
336C22×D4—224no—
337C22×D4—221no—
338C22×D4—442no—
339C22×D4—444no—
340C22×D4—444no—
341C23×C4—24no—
342C23×C4—24no—
343C23×C4—21no—
344C23×C4—21no—
345C23×C4—42no—
346C23×C4—221no—
347C23×C4C22⋊D1111yescharacteristic
348C23×C4C22⋊D1111yescharacteristic
349C23×C4C22⋊D1111yescharacteristic
350C23×C4C22×D1111yescharacteristic
351C23×C4C22×D1111yescharacteristic
352C23×C4C22×D1111yescharacteristic
353C22×C8—114no—
354#121—118no—
355#121—224no—
356#121—224no—
357#121—228no—
358#121—228no—
359#121—224no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4—112no—
365C2×C4⋊C4—224no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4C22×D1112yes—
368C2×C4⋊C4C22×D1112yes—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—228no—
373C2×C22⋊C4—222no—
374C2×C22⋊C4—222no—
375#107—228no—
376#102—228no—
377#102—444no—
378C22⋊C8—224no—
379C22⋊C8—224no—
380C22⋊C8—442no—
381#95—22no—
382#95—22no—
383C2×C11—24no—
384C2×C11—24no—
385C2×C11—42no—
386C2×C11#240511yescharacteristic
387C2×C11C2×#44711yescharacteristic
388C2×C11#300711yescharacteristic
389C2×C11C2×#48011yescharacteristic
390C2×C11#309411yescharacteristic
391C2×C11#318611yescharacteristic
392C2×C11#319311yescharacteristic
393D11—84no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—41no—
399C24—41no—
400C24—224no—
401C24—222no—
402C24—442no—
403C24—442no—
404C24—442no—
405C24—442no—
406C24—442no—
407C24—442no—
408C24#432314yes—
409C24C2×C22⋊D1111yescharacteristic
410C24C2×C22⋊D1111yescharacteristic
411C24C2×C22⋊D1111yescharacteristic
412C2×D4—114no—
413C2×D4—224no—
414C2×D4—228no—
415C2×D4—228no—
416C2×D4—224no—
417C2×D4—222no—
418C2×D4—224no—
419C2×D4—4416no—
420C2×D4—442no—
421C2×D4—4432no—
422C2×D4—444no—
423C2×D4—444no—
424C2×D4—444no—
425C2×D4—444no—
426C2×D4—442no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—416no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—224no—
453C22×C4—222no—
454C22×C4—442no—
455C22×C4—442no—
456C22×C4#433914yes—
457C22×C4D4×D1114yes—
458C22×C4C2×C22⋊D1111yescharacteristic
459C22×C4C2×C22⋊D1111yescharacteristic
460C22×C4C2×C22⋊D1111yescharacteristic
461C22×C4C23×D1111yescharacteristic
462C2×C8—224no—
463C2×C8—224no—
464C2×C8—224no—
465C4⋊C4—24no—
466C4⋊C4—24no—
467C4⋊C4—42no—
468C4⋊C4—42no—
469C4⋊C4—114no—
470C4⋊C4—224no—
471C4⋊C4—222no—
472C22⋊C4—44no—
473C22⋊C4—44no—
474C22⋊C4—228no—
475C22⋊C4—228no—
476C11#2400211yescharacteristic, complemented, Sylow
477C23—21no—
478C23—21no—
479C23—21no—
480C23—21no—
481C23—21no—
482C23—21no—
483C23—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—28no—
490C23—21no—
491C23—21no—
492C23—28no—
493C23—44no—
494C23—44no—
495C23—44no—
496C23—44no—
497C23—44no—
498C23—224no—
499C23—448no—
500C23—448no—
501C23—448no—
502C23—442no—
503C23—442no—
504C23—442no—
505C23—442no—
506C23—442no—
507C23—442no—
508C23—884no—
509C23—884no—
510C23—884no—
511C23—884no—
512C23#6698212yes—
513C23C2×#432312yes—
514C23C2×#432312yes—
515C23C2×#432312yes—
516C23#6699012yes—
517C23#6699512yes—
518C23#6700212yes—
519C23C22×C22⋊D1111yescharacteristic
520D4—228no—
521D4—448no—
522D4—4416no—
523D4—4416no—
524D4—444no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—28no—
530C2×C4—28no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—44no—
535C2×C4—44no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—84no—
545C2×C4—84no—
546C2×C4—224no—
547C2×C4—448no—
548C2×C4—442no—
549C2×C4—442no—
550C2×C4#6698212yes—
551C2×C4#6699012yes—
552C2×C4C2×#433912yes—
553C2×C4C2×D4×D1112yes—
554C2×C4#6703712yes—
555C8—444no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—416no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—444no—
577C22—444no—
578C22—444no—
579C22—8816no—
580C22—882no—
581C22—882no—
582C22—882no—
583C22—882no—
584C22#1062258014yescomplemented
585C22#1062264914yes—
586C22C2×#6698211yescharacteristic
587C22C22×#432311yescharacteristic
588C22C2×#6699011yescharacteristic
589C22#1062333511yescharacteristic
590C22C2×#6699511yescharacteristic
591C22C2×#6700211yescharacteristic
592C22#1062335311yescharacteristic
593C4—22no—
594C4—22no—
595C4—41no—
596C4—82no—
597C4—82no—
598C4—444no—
599C4#1062302114yes—
600C2—24no—
601C2—24no—
602C2—42no—
603C2—884no—
604C2#1307194311yescharacteristic
605C2C2×#1062264911yescharacteristic
606C2#1307787411yescharacteristic
607C2C2×#1062258011yescharacteristic
608C2#1307855611yescharacteristic
609C2#1307936411yescharacteristic
610C2#1307941811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#380C2
socleC23×C11C22×D4
prime radicalC22×#66983C2
hypercenterC2×#380D11
hypocenterC11#24002
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#10622580C2semidirect
3. #13069798C2semidirect
4. #13068933C2semidirect
5. #13068803C2semidirect
6. #13068546C2semidirect
7. #13068526C2semidirect
8. C2×C11×#380C2semidirect
12. C22×C11×C4⋊C4C22semidirect
13. C22×C11×C4⋊C4C22semidirect
25. C11×#380C22semidirect
28. C2×C22⋊(C11⋊C8)C22semidirect
29. C2×C22⋊(C11⋊C8)C22semidirect
31. C2×#66873C22semidirect
32. C2×#66873C22semidirect
33. C2×#66871C22semidirect
34. #10622167C22semidirect
174. C2×#380D11semidirect
268. C22×C4⋊C4C2×D11semidirect
269. C22×C4⋊C4C2×D11semidirect
282. #380C2×D11semidirect
306. C22×C11#480semidirect
476. C11#24002semidirect
584. C22#10622580semidirect

Maximal subgroups

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

subgroupindex
C22×#669832
C2×#106225802
#130697982
#130689332
#130688032
#130685462
#130685262
C2×C11×#3802
#2400211