Finite Group Databasebeta

← #14675402

Subgroups — #14675402

Order 2816.

1630 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622557C212yesmaximal
2C2×#10622559C211yesmaximal, characteristic
3#13066853C211yesmaximal, characteristic
4#13066851C212yesmaximal, complemented
5#13066849C212yesmaximal, complemented
6Dic11⋊#95C212yesmaximal, complemented
7#13066842C212yesmaximal, complemented
8#13066838C212yesmaximal
9C11×#1437C211yesmaximal, characteristic
10C24×Dic11C2211yescharacteristic
11C22×C11×C22⋊C4C2212yes—
12C22×C11×C22⋊C4C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×C22⋊Dic11C2212yes—
15C22×C22⋊Dic11C2211yescharacteristic
16C22×Dic11⋊C4C2212yes—
17C22×Dic11⋊C4C2212yes—
18C22×C4×Dic11C2211yescharacteristic
19C22×C4×Dic11C2212yes—
20C2×C11×#95C2211yescharacteristic
21C2×C11×#95C2212yes—
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31#10622559C418yescomplemented
32#10622557C4116yescomplemented
33C25×C11C2311yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2312yes—
36C23×C4×C11C2312yes—
37C23×C4×C11C2311yescharacteristic
38C23×Dic11—41no—
39C23×Dic11—41no—
40C23×Dic11—42no—
41C23×Dic11—42no—
42C23×Dic11C2×C414yes—
43C23×Dic11C2312yes—
44C23×Dic11C2312yes—
45C23×Dic11C2312yes—
46C23×Dic11C2312yes—
47C2×C11×C22⋊C4—41no—
48C2×C11×C22⋊C4—42no—
49C2×C11×C22⋊C4—41no—
50C2×C11×C22⋊C4—42no—
51C2×C11×C22⋊C4C2×C418yes—
52C2×C11×C22⋊C4C2×C414yes—
53C2×C42×C11—41no—
54C2×C42×C11—42no—
55C2×C22⋊Dic11—42no—
56C2×C22⋊Dic11—42no—
57C2×C22⋊Dic11C2×C418yes—
58C2×C22⋊Dic11C2×C418yes—
59C2×C22⋊Dic11C2×C414yes—
60C2×Dic11⋊C4—42no—
61C2×Dic11⋊C4—42no—
62C2×Dic11⋊C4—42no—
63C2×Dic11⋊C4—42no—
64C2×Dic11⋊C4C2×C418yes—
65C2×Dic11⋊C4C2×C418yescomplemented
66C2×C4×Dic11—42no—
67C2×C4×Dic11—42no—
68C2×C4×Dic11—41no—
69C2×C4×Dic11—42no—
70C2×C4×Dic11C2×C418yescomplemented
71C11×#95—41no—
72C11×#95—42no—
73C11⋊#95—41no—
74C11⋊#95—42no—
75C11⋊#95—42no—
76C11⋊#95—42no—
77C11⋊#95—42no—
78C11⋊#95—42no—
79C11⋊#95C2×C418yes—
80C11⋊#95C2×C418yescomplemented
81C11⋊#95C2×C418yescomplemented
82#13831—111nomaximal, Sylow
83C24×C11—22no—
84C24×C11—22no—
85C24×C11—21no—
86C24×C11—21no—
87C24×C11—22no—
88C24×C11—22no—
89C24×C11—22no—
90C24×C11C22×C414yes—
91C24×C11C22×C412yes—
92C24×C11C2411yescharacteristic
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—21no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11C22×C412yes—
114C22×C4×C11C22×C414yes—
115C22×C4×C11C22×C414yes—
116C22×C4×C11C22×C412yes—
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—44no—
140C22×Dic11—48no—
141C22×Dic11—44no—
142C22×Dic11—48no—
143C22×Dic11—44no—
144C22×Dic11C22×C414yes—
145C22×Dic11C22×C414yes—
146C22×Dic11C22×C414yes—
147C22×Dic11C22×C414yes—
148C22×Dic11C22×C414yes—
149C22×Dic11C22×C414yes—
150C11×C22⋊C4—48no—
151C11×C22⋊C4—44no—
152C42×C11—44no—
153C22⋊Dic11—48no—
154C22⋊Dic11C42116yescomplemented
155Dic11⋊C4—48no—
156Dic11⋊C4—48no—
157C4×Dic11—48no—
158C4×Dic11—44no—
159C2×#388—112no—
160C2×#385—111no—
161#1437—111no—
162#1437D1111yescharacteristic
163#1436—112no—
164#1436—112no—
165C4⋊#95—112no—
166#1434—112no—
167C22⋊#95—112no—
168C23×C11—24no—
169C23×C11—22no—
170C23×C11—24no—
171C23×C11—24no—
172C23×C11—22no—
173C23×C11—24no—
174C23×C11—24no—
175C23×C11—24no—
176C23×C11—24no—
177C23×C11—24no—
178C23×C11—41no—
179C23×C11—42no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11—41no—
187C23×C11—42no—
188C23×C11C2×C4214yes—
189C23×C11C23×C411yescharacteristic
190C23×C11C23×C412yes—
191C23×C11H(5,𝔽2)12yes—
192C23×C11H(5,𝔽2)12yes—
193C23×C11H(5,𝔽2)11yescharacteristic
194C23×C11H(5,𝔽2)11yescharacteristic
195C23×C11H(5,𝔽2)12yes—
196C23×C112−1+412yes—
197C23×C112−1+412yes—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—41no—
209C2×C4×C11—42no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—41no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—41no—
221C2×C4×C11—42no—
222C2×Dic11—24no—
223C2×Dic11—24no—
224C2×Dic11—24no—
225C2×Dic11—24no—
226C2×Dic11—24no—
227C2×Dic11—24no—
228C2×Dic11—24no—
229C2×Dic11—24no—
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—24no—
233C2×Dic11—24no—
234C2×Dic11—24no—
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—416no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11C2×C4218yes—
251C24×C4—111no—
252C22×C4⋊C4—112no—
253C22×C4⋊C4—112no—
254C22×C22⋊C4—111no—
255C22×C22⋊C4—112no—
256C22×C22⋊C4C2×D1112yes—
257C22×C22⋊C4C2×D1111yescharacteristic
258C22×C42—112no—
259C22×C42—111no—
260C22×C42C2×D1111yescharacteristic
261#388—1116no—
262#385—118no—
263C2×#95—112no—
264C2×#95—112no—
265C2×#95—112no—
266C2×#95—112no—
267C2×#95—112no—
268C2×#95—112no—
269C2×#95—112no—
270C2×#95—112no—
271C2×#95—111no—
272C2×#95C2×D1111yescharacteristic
273C2×#95C2×D1112yes—
274C22×C11—24no—
275C22×C11—28no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11—44no—
279C22×C11—44no—
280C22×C11—44no—
281C22×C11—44no—
282C22×C11—44no—
283C22×C11C22×C4211yescharacteristic
284C22×C11#51811yescharacteristic
285C22×C11#51812yes—
286C22×C11#51812yes—
287C22×C11#51812yes—
288C22×C11#51911yescharacteristic
289C22×C11#52012yes—
290C22×C11#52012yes—
291C22×C11#52012yes—
292C22×C11#52012yes—
293C22×C11#52012yes—
294C22×C11#56011yescharacteristic
295C22×C11#56011yescharacteristic
296C22×C11#56012yes—
297C22×C11H(3,𝔽4)11yescharacteristic
298C22×C11#56212yes—
299C22×C11#56212yes—
300C22×C11#56212yes—
301C22×C11#56312yes—
302C22×C11#56311yescharacteristic
303C22×C11#56312yes—
304C4×C11—42no—
305C4×C11—42no—
306C4×C11—44no—
307C4×C11—44no—
308Dic11—28no—
309Dic11—44no—
310Dic11—44no—
311Dic11—44no—
312C25C22×D1111yescharacteristic
313C23×C4—112no—
314C23×C4—112no—
315C23×C4—112no—
316C23×C4—112no—
317C23×C4—114no—
318C23×C4—441no—
319C23×C4—441no—
320C23×C4—442no—
321C23×C4—442no—
322C23×C4C22×D1111yescharacteristic
323C23×C4C22×D1112yes—
324C23×C4C22×D1111yescharacteristic
325C23×C4C22×D1112yes—
326C2×C4⋊C4—118no—
327C2×C4⋊C4—118no—
328C2×C4⋊C4—442no—
329C2×C4⋊C4—442no—
330C2×C4⋊C4—442no—
331C2×C4⋊C4—442no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—41no—
334C2×C22⋊C4—41no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—114no—
337C2×C22⋊C4—118no—
338C2×C22⋊C4—118no—
339C2×C22⋊C4—442no—
340C2×C22⋊C4—442no—
341C2×C22⋊C4C4×D1114yes—
342C2×C22⋊C4C4×D1118yes—
343C2×C42—41no—
344C2×C42—42no—
345C2×C42—118no—
346C2×C42—442no—
347C2×C42—442no—
348C2×C42—441no—
349C2×C42—442no—
350#95—41no—
351#95—42no—
352#95—118no—
353#95—118no—
354#95—118no—
355#95—442no—
356#95—442no—
357#95—442no—
358#95—442no—
359#95—441no—
360#95—442no—
361C2×C11—44no—
362C2×C11#227411yescharacteristic
363C2×C11#227512yes—
364C2×C11#237511yescharacteristic
365C2×C11#237611yescharacteristic
366C2×C11#237612yes—
367C2×C11#237712yes—
368C2×C11#237812yes—
369C2×C11#237912yes—
370C2×C11#238312yes—
371C24—22no—
372C24—21no—
373C24—21no—
374C24—22no—
375C24—22no—
376C24—22no—
377C24—22no—
378C24C2×C4×D1114yes—
379C24C2×C4×D1112yes—
380C24C23×D1111yescharacteristic
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—114no—
402C22×C4—114no—
403C22×C4—114no—
404C22×C4—114no—
405C22×C4—114no—
406C22×C4—114no—
407C22×C4—222no—
408C22×C4—222no—
409C22×C4—222no—
410C22×C4—222no—
411C22×C4—222no—
412C22×C4—222no—
413C22×C4—222no—
414C22×C4—222no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—444no—
430C22×C4—448no—
431C22×C4—444no—
432C22×C4—448no—
433C22×C4—444no—
434C22×C4C2×C4×D1112yes—
435C22×C4C2×C4×D1114yes—
436C22×C4C2×C4×D1114yes—
437C22×C4C2×C4×D1112yes—
438C4⋊C4—448no—
439C4⋊C4—448no—
440C22⋊C4—48no—
441C22⋊C4—44no—
442C22⋊C4—1116no—
443C22⋊C4—448no—
444C42—44no—
445C42—448no—
446C42—444no—
447C11#1383111yescharacteristic, complemented, Sylow
448C23—22no—
449C23—24no—
450C23—22no—
451C23—24no—
452C23—24no—
453C23—24no—
454C23—24no—
455C23—24no—
456C23—24no—
457C23—24no—
458C23—42no—
459C23—41no—
460C23—41no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23—41no—
465C23—42no—
466C23—42no—
467C23—41no—
468C23C42×D1114yes—
469C23C22×C4×D1111yescharacteristic
470C23C22×C4×D1112yes—
471C23#6703712yes—
472C23#6703711yescharacteristic
473C23#6703712yes—
474C23#6703711yescharacteristic
475C23#6704212yes—
476C23#6704312yes—
477C23#6704312yes—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—41no—
502C2×C4—118no—
503C2×C4—224no—
504C2×C4—224no—
505C2×C4—224no—
506C2×C4—224no—
507C2×C4—224no—
508C2×C4—224no—
509C2×C4—224no—
510C2×C4—224no—
511C2×C4—224no—
512C2×C4—224no—
513C2×C4—224no—
514C2×C4—224no—
515C2×C4—224no—
516C2×C4—224no—
517C2×C4—224no—
518C2×C4—4416no—
519C2×C4—442no—
520C2×C4—442no—
521C2×C4—442no—
522C2×C4—442no—
523C2×C4—442no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—442no—
527C2×C4—442no—
528C2×C4—442no—
529C2×C4—442no—
530C2×C4—442no—
531C22—24no—
532C22—28no—
533C22—42no—
534C22—42no—
535C22—44no—
536C22—44no—
537C22—44no—
538C22—44no—
539C22—44no—
540C22C2×C42×D1111yescharacteristic
541C22#1062301711yescharacteristic
542C22#1062301712yes—
543C22#1062304711yescharacteristic
544C22#1062305412yes—
545C22#1062307612yes—
546C22#1062307612yes—
547C22#1062307712yes—
548C22#1062307712yes—
549C22#1062307712yes—
550C22#1062307712yes—
551C22#1062312611yescharacteristic
552C22#1062315112yes—
553C22#1062315212yes—
554C22#1062315212yes—
555C22#1062318211yescharacteristic
556C22#1062319812yes—
557C22#1062320312yes—
558C22#1062321411yescharacteristic
559C22#1062324312yes—
560C22#1062325111yescharacteristic
561C4—42no—
562C4—42no—
563C4—44no—
564C4—44no—
565C4—228no—
566C4—444no—
567C4—444no—
568C4—444no—
569C2—44no—
570C2#1307097111yescharacteristic
571C2#1307097512yes—
572C2#1307175311yescharacteristic
573C2#1307175911yescharacteristic
574C2#1307176612yes—
575C2#1307176812yes—
576C2#1307177612yes—
577C2#1307178512yes—
578C2#1307180312yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC11×#1437C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenter#1437D11
hypocenterC11#13831
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
4. #13066851C2semidirect
5. #13066849C2semidirect
6. Dic11⋊#95C2semidirect
7. #13066842C2semidirect
31. #10622559C4semidirect
32. #10622557C4semidirect
65. C2×Dic11⋊C4C2×C4semidirect
70. C2×C4×Dic11C2×C4semidirect
80. C11⋊#95C2×C4semidirect
81. C11⋊#95C2×C4semidirect
154. C22⋊Dic11C42semidirect
447. C11#13831semidirect

Maximal subgroups

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

subgroupindex
C2×#106225572
C2×#106225592
#130668532
#130668512
#130668492
Dic11⋊#952
#130668422
#130668382
C11×#14372
#1383111