Finite Group Databasebeta

← #14764824

Subgroups — #14764824

Order 2816.

1176 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622724C211yesmaximal, characteristic, complemented
2C22×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
3C4×#66935C211yesmaximal, characteristic
4#13069414C212yesmaximal, complemented
5#13069230C212yesmaximal, complemented
6#13069229C212yesmaximal, complemented
7#13068912C212yesmaximal, complemented
8#13068906C211yesmaximal, characteristic, complemented
9#13068796C211yesmaximal, characteristic, complemented
10#13068525C211yesmaximal, characteristic, complemented
11C11×#1752C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C4×C22⋊D11C2211yescharacteristic
15C23×C11⋊C8C2211yescharacteristic
16C22×#4313C2211yescharacteristic, complemented
17C2×#66935C411yescharacteristic
18C2×C4×D44C2212yes—
19C2×C11×C22⋊C8C2211yescharacteristic
20C2×C11×#97C2212yescomplemented
21C4×C11×C22⋊C4C2211yescharacteristic
22C2×C22⋊(C11⋊C8)C2211yescharacteristic
23#10622724—24no—
24C2×(C2×D11)⋊C8—24no—
25C2×(C2×D11)⋊C8C2212yes—
26C2×(C2×D11)⋊C8C2212yes—
27C2×(C2×D11)⋊C8C2212yes—
28C2×(C2×D11)⋊C8C2212yes—
29C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
30C2×(C2×D11)⋊C8C2212yescomplemented
31C2×#66879C2211yescharacteristic, complemented
32C2×Dic11⋊C8C2211yescharacteristic, complemented
33#10622571C411yescharacteristic
34#10622568C411yescharacteristic
35#10622563C411yescharacteristic
36C4×(C2×D11)⋊C4C2212yes—
37C2×C4⋊(C11⋊C8)C2212yescomplemented
38#10622281C412yes—
39#10622278C412yes—
40C11×#336C2212yescomplemented
41#10622188C2212yescomplemented
42#10622162C2212yescomplemented
43C24×D11C2×C411yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C22×C22⋊D11C2×C411yescharacteristic
46C23×Dic11C2×C411yescharacteristic
47C22×D44C2×C412yes—
48C22×C4×D11—22no—
49C22×C4×D11—22no—
50C22×C4×D11—42no—
51C22×C4×D11—42no—
52C22×C4×D11C2×C412yes—
53C22×C4×D11C2312yes—
54C22×C4×D11C2311yescharacteristic
55C22×C8×C11—42no—
56C22×C8×C11D414yescomplemented
57C22×C8×C11C2312yes—
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C2×C11×C22⋊C4C2×C411yescharacteristic
61C2×C11×C22⋊C4C2×C411yescharacteristic
62C2×C42×C11C2312yes—
63C2×C22⋊Dic11C2×C411yescharacteristic
64C4×C22⋊D11—22no—
65C4×C22⋊D11—22no—
66C2×(C2×D11)⋊C4C2×C412yes—
67C2×(C2×D11)⋊C4C2×C411yescharacteristic
68C2×(C2×D11)⋊C4C2×C412yes—
69C2×(C2×D11)⋊C4C2×C412yes—
70C2×(C2×D11)⋊C4C2×C412yes—
71C2×C4⋊Dic11C2×C412yes—
72C2×Dic11⋊C4C2×C411yescharacteristic
73C2×C4×Dic11C2311yescharacteristic
74C22×C11⋊C8—22no—
75C22×C11⋊C8—42no—
76C22×C11⋊C8C2311yescharacteristic
77C22×C11⋊C8C2312yes—
78C22×C11⋊C8C2311yescharacteristic
79C2×#4313—22no—
80C2×#4313—42no—
81#66935—24no—
82C4×D44—42no—
83C4×D44—42no—
84C11×C22⋊C8—22no—
85C11×#97—42no—
86C11×#95C2×C412yes—
87C11⋊#95C2×C412yes—
88C11⋊#95C2×C412yes—
89C22⋊(C11⋊C8)—22no—
90(C2×D11)⋊C8—24no—
91(C2×D11)⋊C8—24no—
92(C2×D11)⋊C8—22no—
93(C2×D11)⋊C8—42no—
94(C2×D11)⋊C8—42no—
95(C2×D11)⋊C8—42no—
96#66879—22no—
97Dic11⋊C8—22no—
98C4⋊(C11⋊C8)—42no—
99#22034—111nomaximal, Sylow
100C24×C11C22×C411yescharacteristic
101C23×D11—22no—
102C23×D11—22no—
103C23×D11—42no—
104C23×D11—42no—
105C23×D11M1614yescomplemented
106C23×D11C22×C411yescharacteristic
107C23×D11C22×C412yes—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11C22×C412yes—
111C22×C4×C11C22×C412yes—
112C22×C4×C11C22×C411yescharacteristic
113C22×C4×C11C2×D412yes—
114C22×C4×C11#4112yes—
115C22×C4×C11C2411yescharacteristic
116C2×C22⋊D11—22no—
117C2×C22⋊D11—22no—
118C2×C22⋊D11—22no—
119C22×Dic11—22no—
120C22×Dic11—42no—
121C22×Dic11C22×C411yescharacteristic
122C22×Dic11C22×C411yescharacteristic
123C22×Dic11C22×C412yes—
124C22×Dic11C22×C411yescharacteristic
125C2×D44—24no—
126C2×D44—42no—
127C2×D44—42no—
128C2×C4×D11—24no—
129C2×C4×D11—22no—
130C2×C4×D11—21no—
131C2×C4×D11—21no—
132C2×C4×D11—22no—
133C2×C4×D11—22no—
134C2×C4×D11—22no—
135C2×C4×D11—22no—
136C2×C4×D11—22no—
137C2×C4×D11—22no—
138C2×C4×D11—22no—
139C2×C4×D11—42no—
140C2×C4×D11—42no—
141C2×C4×D11—44no—
142C2×C4×D11—44no—
143C2×C4×D11—48no—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—44no—
150C2×C8×C11C2×D412yes—
151C2×C8×C11C2×D412yes—
152C11×C22⋊C4—22no—
153C11×C22⋊C4—22no—
154C42×C11—22no—
155C42×C11—22no—
156C22⋊Dic11—22no—
157(C2×D11)⋊C4—24no—
158(C2×D11)⋊C4—22no—
159(C2×D11)⋊C4—42no—
160(C2×D11)⋊C4—42no—
161(C2×D11)⋊C4—42no—
162C4⋊Dic11—42no—
163Dic11⋊C4—22no—
164C4×Dic11—21no—
165C4×Dic11—21no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—44no—
174#4313—44no—
175C2×#435—111no—
176C22×C22⋊C8—111no—
177C4×#120—111no—
178#1955—112no—
179#1924—112no—
180#1924—112no—
181#1870—112no—
182#1869—111no—
183#1850—111no—
184#1779—111no—
185#1752D1111yescharacteristic, complemented
186C23×C11—22no—
187C23×C11—22no—
188C23×C11C4×D412yes—
189C23×C11C2×M1612yes—
190C23×C11#13112yes—
191C23×C11C23×C411yescharacteristic
192C22×D11—22no—
193C22×D11—22no—
194C22×D11—22no—
195C22×D11—22no—
196C22×D11—22no—
197C22×D11—22no—
198C22×D11—28no—
199C22×D11—21no—
200C22×D11—22no—
201C22×D11—21no—
202C22×D11—21no—
203C22×D11—22no—
204C22×D11—48no—
205C22×D11—44no—
206C22×D11—44no—
207C22×D11—48no—
208C22×D11C2×M1614yes—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—24no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11C4×D412yes—
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C11H(5,𝔽2)12yes—
223C2×C4×C11H(5,𝔽2)12yes—
224C22⋊D11—44no—
225C2×Dic11—21no—
226C2×Dic11—21no—
227C2×Dic11—21no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—21no—
233C2×Dic11—21no—
234C2×Dic11—22no—
235C2×Dic11—44no—
236D44—48no—
237C4×D11—48no—
238C4×D11—41no—
239C4×D11—42no—
240C4×D11—41no—
241C4×D11—42no—
242C4×D11—42no—
243C4×D11—42no—
244C4×D11—42no—
245C8×C11—22no—
246C8×C11—22no—
247C8×C11—42no—
248C11⋊C8—41no—
249C11⋊C8—41no—
250C11⋊C8—42no—
251C24×C4—111no—
252C22×M16—111no—
253C23×C8—111no—
254C23×C8C2×D1111yescharacteristic
255C2×#120—111no—
256C2×C4×D4—111no—
257C2×C4×D4—112no—
258#435—224no—
259C2×C4⋊C8—111no—
260C2×C4⋊C8—112no—
261C2×C22⋊C8—111no—
262C2×C22⋊C8—112no—
263C2×C22⋊C8—112no—
264C2×C22⋊C8—111no—
265C2×C22⋊C8—112no—
266C2×C22⋊C8—112no—
267C2×C22⋊C8—112no—
268C2×C22⋊C8—224no—
269C2×C22⋊C8C2×D1111yescharacteristic
270C2×#97—111no—
271C2×#97C2×D1112yescomplemented
272#386—111no—
273#386—112no—
274#385—111no—
275#385—112no—
276#379—111no—
277C4×C22⋊C4—112no—
278C4×C22⋊C4C2×D1111yescharacteristic
279#336—112no—
280#336—112no—
281#336C2×D1112yescomplemented
282C22×C11—22no—
283C22×C11—22no—
284C22×C11—24no—
285C22×C11—24no—
286C22×C11#43514yes—
287C22×C11C2×C4×D411yescharacteristic
288C22×C11#51812yes—
289C22×C11C22×M1611yescharacteristic
290C22×C11C2×#13111yescharacteristic
291C22×C11#56812yes—
292C2×D11—24no—
293C2×D11—24no—
294C2×D11—24no—
295C2×D11—416no—
296C2×D11—42no—
297C2×D11—42no—
298C2×D11—42no—
299C2×D11—42no—
300C2×D11—41no—
301C2×D11—41no—
302C2×D11—41no—
303C2×D11—42no—
304C2×D11—42no—
305C4×C11—22no—
306C4×C11—42no—
307C4×C11—42no—
308C4×C11#53411yescharacteristic
309C4×C11#53511yescharacteristic
310C4×C11#53812yes—
311Dic11—42no—
312Dic11—41no—
313Dic11—41no—
314Dic11—41no—
315C25—111no—
316C22×D4—111no—
317C22×D4—112no—
318C23×C4—111no—
319C23×C4—111no—
320C23×C4—112no—
321C23×C4—112no—
322C23×C4—222no—
323C23×C4—222no—
324C23×C4—442no—
325C23×C4—442no—
326C23×C4C22×D1111yescharacteristic
327C2×M16—222no—
328C2×M16—442no—
329C22×C8—42no—
330C22×C8—112no—
331C22×C8—111no—
332C22×C8—111no—
333C22×C8—222no—
334C22×C8—442no—
335C22×C8D4414yescomplemented
336C22×C8C22×D1112yes—
337C22×C8C22×D1111yescharacteristic
338C22×C8C22×D1111yescharacteristic
339#120—224no—
340C4×D4—222no—
341C4×D4—222no—
342C4×D4—442no—
343C4×D4—442no—
344C2×C4⋊C4—111no—
345C2×C4⋊C4—112no—
346C2×C22⋊C4—111no—
347C2×C22⋊C4—111no—
348C2×C22⋊C4—112no—
349C2×C22⋊C4—112no—
350C2×C22⋊C4—112no—
351C2×C22⋊C4—112no—
352C2×C22⋊C4C4×D1111yescharacteristic
353C2×C22⋊C4C4×D1111yescharacteristic
354C2×C42—111no—
355C2×C42C22×D1112yes—
356C4⋊C8—222no—
357C4⋊C8—442no—
358C22⋊C8—22no—
359C22⋊C8—222no—
360C22⋊C8—224no—
361C22⋊C8—224no—
362C22⋊C8—222no—
363C22⋊C8—442no—
364C22⋊C8—442no—
365C22⋊C8—442no—
366#97—42no—
367#97—222no—
368#95—112no—
369#95—112no—
370#95C4×D1112yes—
371C2×C11—24no—
372C2×C11#232111yescharacteristic
373C2×C11C2×#43511yescharacteristic
374C2×C11#293011yescharacteristic
375C2×C11#297312yes—
376C2×C11#297612yes—
377D11—44no—
378D11—81no—
379C24—112no—
380C24—114no—
381C24—111no—
382C24—222no—
383C24—222no—
384C24—442no—
385C24—442no—
386C24C2×C4×D1111yescharacteristic
387C2×D4—224no—
388C2×D4—222no—
389C2×D4—222no—
390C2×D4—222no—
391C2×D4—442no—
392C2×D4—442no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—111no—
396C22×C4—111no—
397C22×C4—112no—
398C22×C4—111no—
399C22×C4—222no—
400C22×C4—224no—
401C22×C4—222no—
402C22×C4—221no—
403C22×C4—221no—
404C22×C4—222no—
405C22×C4—222no—
406C22×C4—222no—
407C22×C4—222no—
408C22×C4—222no—
409C22×C4—222no—
410C22×C4—222no—
411C22×C4—442no—
412C22×C4—442no—
413C22×C4—444no—
414C22×C4—444no—
415C22×C4—448no—
416C22×C4—442no—
417C22×C4C2×C4×D1112yes—
418C22×C4C2×C4×D1112yes—
419C22×C4C2×C4×D1111yescharacteristic
420C22×C4C2×D4412yes—
421C22×C4#433912yes—
422C22×C4C23×D1111yescharacteristic
423M16—444no—
424C2×C8—22no—
425C2×C8—22no—
426C2×C8—22no—
427C2×C8—22no—
428C2×C8—22no—
429C2×C8—44no—
430C2×C8—221no—
431C2×C8—222no—
432C2×C8—221no—
433C2×C8—222no—
434C2×C8—222no—
435C2×C8—222no—
436C2×C8—222no—
437C2×C8—444no—
438C2×C8C2×D4412yes—
439C2×C8C2×D4412yes—
440C4⋊C4—222no—
441C4⋊C4—442no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—224no—
445C22⋊C4—222no—
446C22⋊C4—222no—
447C22⋊C4—442no—
448C22⋊C4—442no—
449C22⋊C4—442no—
450C42—22no—
451C42—22no—
452C42—221no—
453C42—221no—
454C11#2203411yescharacteristic, complemented, Sylow
455C23—22no—
456C23—22no—
457C23—114no—
458C23—222no—
459C23—222no—
460C23—222no—
461C23—222no—
462C23—222no—
463C23—222no—
464C23—228no—
465C23—221no—
466C23—221no—
467C23—221no—
468C23—222no—
469C23—222no—
470C23—448no—
471C23—444no—
472C23—444no—
473C23—448no—
474C23C4×D4412yes—
475C23M16×D1112yes—
476C23#6696012yes—
477C23C22×C4×D1111yescharacteristic
478D4—448no—
479D4—444no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—221no—
491C2×C4—221no—
492C2×C4—221no—
493C2×C4—222no—
494C2×C4—221no—
495C2×C4—221no—
496C2×C4—222no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—448no—
501C2×C4—444no—
502C2×C4—441no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—441no—
506C2×C4—442no—
507C2×C4—442no—
508C2×C4—442no—
509C2×C4C4×D4412yes—
510C2×C4C22×D4411yescharacteristic
511C2×C4C2×#433911yescharacteristic
512C2×C4#6703712yes—
513C2×C4#6704212yes—
514C8—22no—
515C8—22no—
516C8—42no—
517C8—441no—
518C8—442no—
519C8—441no—
520C22—22no—
521C22—24no—
522C22—24no—
523C22—22no—
524C22—224no—
525C22—224no—
526C22—224no—
527C22—4416no—
528C22—442no—
529C22—442no—
530C22—442no—
531C22—442no—
532C22—441no—
533C22—441no—
534C22—442no—
535C22—442no—
536C22—441no—
537C22#1062231914yes—
538C22C2×C4×D4411yescharacteristic
539C22#1062307612yes—
540C22C2×M16×D1111yescharacteristic
541C22C2×#6696011yescharacteristic
542C22#1062328112yes—
543C4—22no—
544C4—42no—
545C4—42no—
546C4—441no—
547C4—441no—
548C4—442no—
549C4—441no—
550C4#1062302411yescharacteristic
551C4#1062305611yescharacteristic
552C4#1062309112yes—
553C2—24no—
554C2—444no—
555C2—881no—
556C2#1307127611yescharacteristic
557C2C2×#1062231911yescharacteristic
558C2#1307732111yescharacteristic
559C2#1307764112yes—
560C2#1307766512yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1752C2
prime radicalC2×#66935C4
cosocleC22×C4×C11C24
hypercenter#1752D11
hypocenterC11#22034
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1752

Complements

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

NH ≅ G/Ntype
1. C2×#10622724C2semidirect
2. C22×(C2×D11)⋊C8C2semidirect
4. #13069414C2semidirect
5. #13069230C2semidirect
6. #13069229C2semidirect
7. #13068912C2semidirect
8. #13068906C2semidirect
9. #13068796C2semidirect
10. #13068525C2semidirect
11. C11×#1752C2semidirect
16. C22×#4313C22semidirect
20. C2×C11×#97C22semidirect
29. C2×(C2×D11)⋊C8C22semidirect
30. C2×(C2×D11)⋊C8C22semidirect
31. C2×#66879C22semidirect
32. C2×Dic11⋊C8C22semidirect
37. C2×C4⋊(C11⋊C8)C22semidirect
40. C11×#336C22semidirect
41. #10622188C22semidirect
42. #10622162C22semidirect
56. C22×C8×C11D4semidirect
105. C23×D11M16semidirect
185. #1752D11semidirect
271. C2×#97C2×D11semidirect
281. #336C2×D11semidirect
335. C22×C8D44semidirect
454. C11#22034semidirect

Maximal subgroups

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

subgroupindex
C2×#106227242
C22×(C2×D11)⋊C82
C4×#669352
#130694142
#130692302
#130692292
#130689122
#130689062
#130687962
#130685252
C11×#17522
#2203411