Finite Group Databasebeta

← #14764827

Subgroups — #14764827

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×#10622624C211yesmaximal, characteristic, complemented
2C22×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
3C4×#66990C211yesmaximal, characteristic
4#13069412C212yesmaximal, complemented
5#13069230C212yesmaximal, complemented
6#13069227C212yesmaximal, complemented
7#13068911C212yesmaximal, complemented
8#13068794C211yesmaximal, characteristic, complemented
9#13068525C211yesmaximal, characteristic, complemented
10#13068395C211yesmaximal, characteristic, complemented
11C11×#1869C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66990C411yescharacteristic
16C2×C4×C22⋊D11C2212yes—
17C22×#4318C2211yescharacteristic, complemented
18C23×C11⋊C8C2211yescharacteristic
19C2×C11×C22⋊C8C2211yescharacteristic
20C2×C11×C22⋊C8C2212yescomplemented
21#10622833C411yescharacteristic
22C4×C22⋊Dic11C2211yescharacteristic
23C2×C22⋊(C11⋊C8)C2211yescharacteristic
24C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
25C2×(C2×D11)⋊C8—24no—
26C2×(C2×D11)⋊C8C2212yes—
27C2×(C2×D11)⋊C8C2212yes—
28C2×(C2×D11)⋊C8C2212yes—
29C2×(C2×D11)⋊C8C2212yes—
30C2×#66879C2212yescomplemented
31C2×Dic11⋊C8C2212yescomplemented
32#10622624—24no—
33#10622602C412yes—
34#10622569C412yes—
35#10622568C411yescharacteristic
36#10622559C411yescharacteristic
37C4×(C2×D11)⋊C4C2212yes—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
39C2×#66867C2211yescharacteristic, complemented
40C11×#336C2212yescomplemented
41#10622188C2212yescomplemented
42#10622188C2212yescomplemented
43C24×D11C2×C411yescharacteristic
44C22×D4×C11C2×C411yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C22×C22⋊D11C2×C412yes—
48C23×Dic11C2×C411yescharacteristic
49C22×C4×D11—22no—
50C22×C4×D11—22no—
51C22×C4×D11—42no—
52C22×C4×D11—42no—
53C22×C4×D11C2×C412yes—
54C22×C4×D11C2312yes—
55C22×C8×C11—22no—
56C22×C8×C11—42no—
57C22×C8×C11C2312yes—
58C22×C8×C11C2312yes—
59C4×D4×C11—22no—
60C4×D4×C11—22no—
61C2×C11×C4⋊C4C2×C411yescharacteristic
62C2×C11×C22⋊C4C2×C411yescharacteristic
63C2×C11×C22⋊C4C2×C411yescharacteristic
64C2×C42×C11C2311yescharacteristic
65C2×C22⋊Dic11C2×C411yescharacteristic
66C2×C22⋊Dic11C2×C411yescharacteristic
67C2×C22⋊Dic11C2×C412yes—
68#66990—24no—
69C4×C22⋊D11—42no—
70C4×C22⋊D11—42no—
71C2×(C2×D11)⋊C4C2×C412yes—
72C2×(C2×D11)⋊C4C2×C412yes—
73C2×(C2×D11)⋊C4C2×C412yes—
74C2×Dic11⋊C4C2×C412yes—
75C2×C4×Dic11C2312yes—
76C2×#4318—22no—
77C2×#4318—42no—
78C22×C11⋊C8—42no—
79C22×C11⋊C8D414yescomplemented
80C22×C11⋊C8C2311yescharacteristic
81C22×C11⋊C8C2311yescharacteristic
82C22×C11⋊C8C2311yescharacteristic
83C22×C11⋊C8C2311yescharacteristic
84C11×C22⋊C8—22no—
85C11×C22⋊C8—42no—
86C11⋊#95C2×C412yes—
87C11⋊#95C2×C412yes—
88C11⋊#95C2×C412yes—
89C22⋊(C11⋊C8)—22no—
90C22⋊(C11⋊C8)—22no—
91(C2×D11)⋊C8—24no—
92(C2×D11)⋊C8—24no—
93(C2×D11)⋊C8—42no—
94(C2×D11)⋊C8—42no—
95#66879—42no—
96Dic11⋊C8—42no—
97C4⋊(C11⋊C8)—22no—
98#66867—22no—
99#22034—111nomaximal, Sylow
100C24×C11C22×C411yescharacteristic
101C24×C11C22×C411yescharacteristic
102C23×D11—22no—
103C23×D11—22no—
104C23×D11—42no—
105C23×D11—42no—
106C23×D11M1614yescomplemented
107C23×D11C22×C412yes—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11C22×C411yescharacteristic
118C22×C4×C11C22×C411yescharacteristic
119C22×C4×C11C22×C411yescharacteristic
120C22×C4×C11C22×C411yescharacteristic
121C22×C4×C11C2×D412yes—
122C22×C4×C11#4112yes—
123C22×C4×C11C2411yescharacteristic
124C2×C22⋊D11—24no—
125C2×C22⋊D11—42no—
126C2×C22⋊D11—42no—
127C22×Dic11—22no—
128C22×Dic11—42no—
129C22×Dic11C22×C412yes—
130C22×Dic11C22×C412yes—
131C22×Dic11C22×C412yes—
132C2×C4×D11—24no—
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—22no—
150C2×C8×C11—44no—
151C11×C4⋊C4—22no—
152C11×C22⋊C4—22no—
153C11×C22⋊C4—22no—
154C42×C11—21no—
155C42×C11—21no—
156C22⋊Dic11—22no—
157C22⋊Dic11—22no—
158C22⋊Dic11—42no—
159(C2×D11)⋊C4—24no—
160(C2×D11)⋊C4—42no—
161(C2×D11)⋊C4—42no—
162Dic11⋊C4—42no—
163C4×Dic11—22no—
164C4×Dic11—22no—
165#4318—44no—
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—44no—
173C2×C11⋊C8C2×D412yes—
174C2×C11⋊C8C2×D412yes—
175C2×#435—111no—
176C22×C22⋊C8—111no—
177C4×#120—111no—
178#1955—112no—
179#1924—112no—
180#1924—112no—
181#1870—112no—
182#1869D1111yescharacteristic, complemented
183#1850—111no—
184#1779—111no—
185#1752—111no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—21no—
189C23×C11—22no—
190C23×C11—21no—
191C23×C11—21no—
192C23×C11—22no—
193C23×C11C4×D412yes—
194C23×C11C2×M1612yes—
195C23×C11#13112yes—
196C23×C11C23×C411yescharacteristic
197C22×D11—22no—
198C22×D11—22no—
199C22×D11—22no—
200C22×D11—22no—
201C22×D11—22no—
202C22×D11—22no—
203C22×D11—28no—
204C22×D11—48no—
205C22×D11—44no—
206C22×D11—44no—
207C22×D11—48no—
208C22×D11C2×M1614yes—
209D4×C11—44no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—24no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—22no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—22no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—42no—
224C2×C4×C11C4×D412yes—
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C2×#4111yescharacteristic
227C2×C4×C11H(5,𝔽2)12yes—
228C2×C4×C11H(5,𝔽2)12yes—
229C22⋊D11—48no—
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—44no—
240C4×D11—48no—
241C4×D11—42no—
242C4×D11—42no—
243C4×D11—42no—
244C4×D11—42no—
245C8×C11—42no—
246C8×C11—42no—
247C11⋊C8—22no—
248C11⋊C8—22no—
249C11⋊C8—41no—
250C11⋊C8—41no—
251C24×C4—111no—
252C22×M16—111no—
253C23×C8—111no—
254C23×C8C2×D1111yescharacteristic
255C2×#120—111no—
256C2×C4×D4—112no—
257C2×C4×D4C2×D1111yescharacteristic
258#435—224no—
259C2×C4⋊C8—111no—
260C2×C4⋊C8—112no—
261C2×C22⋊C8—111no—
262C2×C22⋊C8—111no—
263C2×C22⋊C8—112no—
264C2×C22⋊C8—112no—
265C2×C22⋊C8—112no—
266C2×C22⋊C8—112no—
267C2×C22⋊C8—224no—
268C2×C22⋊C8C2×D1111yescharacteristic
269C2×C22⋊C8C2×D1112yescomplemented
270C2×#97—111no—
271C2×#97—112no—
272#386—111no—
273#386—112no—
274#385—112no—
275#385—111no—
276#379—111no—
277C4×C22⋊C4—111no—
278C4×C22⋊C4—112no—
279#336—112no—
280#336—112no—
281#336C2×D1112yescomplemented
282C22×C11—22no—
283C22×C11—22no—
284C22×C11—24no—
285C22×C11—24no—
286C22×C11—41no—
287C22×C11—41no—
288C22×C11—41no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11#43514yes—
292C22×C11C2×C4×D411yescharacteristic
293C22×C11#51812yes—
294C22×C11C22×M1611yescharacteristic
295C22×C11C2×#13111yescharacteristic
296C22×C11#56812yes—
297C2×D11—24no—
298C2×D11—24no—
299C2×D11—24no—
300C2×D11—416no—
301C2×D11—42no—
302C2×D11—42no—
303C2×D11—42no—
304C2×D11—42no—
305C4×C11—22no—
306C4×C11—41no—
307C4×C11—41no—
308C4×C11—41no—
309C4×C11#53411yescharacteristic
310C4×C11#53511yescharacteristic
311C4×C11#53812yes—
312Dic11—42no—
313Dic11—42no—
314Dic11—42no—
315C25—111no—
316C22×D4—112no—
317C22×D4C4×D1111yescharacteristic
318C23×C4—111no—
319C23×C4—112no—
320C23×C4—112no—
321C23×C4—222no—
322C23×C4—222no—
323C23×C4—442no—
324C23×C4—442no—
325C23×C4C22×D1111yescharacteristic
326C23×C4C22×D1111yescharacteristic
327C2×M16—222no—
328C2×M16—442no—
329C22×C8—22no—
330C22×C8—42no—
331C22×C8—111no—
332C22×C8—111no—
333C22×C8—114no—
334C22×C8—111no—
335C22×C8—111no—
336C22×C8—442no—
337C22×C8C22×D1112yes—
338C22×C8C22×D1112yes—
339#120—224no—
340C4×D4—22no—
341C4×D4—22no—
342C4×D4—442no—
343C4×D4—442no—
344C2×C4⋊C4—112no—
345C2×C4⋊C4C4×D1111yescharacteristic
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—112no—
355C2×C42C22×D1111yescharacteristic
356C4⋊C8—222no—
357C4⋊C8—442no—
358C22⋊C8—22no—
359C22⋊C8—42no—
360C22⋊C8—224no—
361C22⋊C8—224no—
362C22⋊C8—222no—
363C22⋊C8—222no—
364C22⋊C8—442no—
365C22⋊C8—442no—
366#97—222no—
367#97—442no—
368#95—112no—
369#95—112no—
370#95—112no—
371C2×C11—24no—
372C2×C11—81no—
373C2×C11#232111yescharacteristic
374C2×C11C2×#43511yescharacteristic
375C2×C11#293011yescharacteristic
376C2×C11#297312yes—
377C2×C11#297612yes—
378D11—44no—
379C24—112no—
380C24—114no—
381C24—222no—
382C24—222no—
383C24—442no—
384C24—442no—
385C24C2×C4×D1111yescharacteristic
386C24C2×C4×D1111yescharacteristic
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—224no—
391C2×D4—442no—
392C2×D4—442no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—112no—
400C22×C4—112no—
401C22×C4—112no—
402C22×C4—222no—
403C22×C4—224no—
404C22×C4—222no—
405C22×C4—222no—
406C22×C4—222no—
407C22×C4—222no—
408C22×C4—222no—
409C22×C4—222no—
410C22×C4—442no—
411C22×C4—442no—
412C22×C4—444no—
413C22×C4—448no—
414C22×C4—444no—
415C22×C4—442no—
416C22×C4C2×C4×D1111yescharacteristic
417C22×C4C2×C4×D1111yescharacteristic
418C22×C4C2×C4×D1111yescharacteristic
419C22×C4C2×C4×D1111yescharacteristic
420C22×C4D4×D1112yes—
421C22×C4#434112yes—
422C22×C4C23×D1111yescharacteristic
423M16—444no—
424C2×C8—22no—
425C2×C8—22no—
426C2×C8—22no—
427C2×C8—22no—
428C2×C8—22no—
429C2×C8—22no—
430C2×C8—44no—
431C2×C8—112no—
432C2×C8—112no—
433C2×C8—222no—
434C2×C8—222no—
435C2×C8—221no—
436C2×C8—221no—
437C2×C8—222no—
438C2×C8—222no—
439C2×C8—444no—
440C4⋊C4—22no—
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—21no—
451C42—21no—
452C42—222no—
453C42—222no—
454C11#2203411yescharacteristic, complemented, Sylow
455C23—22no—
456C23—22no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—22no—
461C23—22no—
462C23—114no—
463C23—222no—
464C23—222no—
465C23—222no—
466C23—222no—
467C23—222no—
468C23—222no—
469C23—228no—
470C23—448no—
471C23—444no—
472C23—444no—
473C23—448no—
474C23(C22⋊D11)⋊C412yes—
475C23#6695412yes—
476C23M16×D1112yes—
477C23C22×C4×D1111yescharacteristic
478D4—44no—
479D4—448no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—222no—
495C2×C4—222no—
496C2×C4—222no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—222no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—448no—
504C2×C4—444no—
505C2×C4—442no—
506C2×C4—442no—
507C2×C4—442no—
508C2×C4—442no—
509C2×C4(C22⋊D11)⋊C412yes—
510C2×C4C2×D4×D1111yescharacteristic
511C2×C4C2×#434111yescharacteristic
512C2×C4#6703712yes—
513C2×C4#6704212yes—
514C8—42no—
515C8—42no—
516C8—222no—
517C8—222no—
518C8—441no—
519C8—441no—
520C22—22no—
521C22—24no—
522C22—24no—
523C22—22no—
524C22—41no—
525C22—41no—
526C22—42no—
527C22—42no—
528C22—41no—
529C22—224no—
530C22—224no—
531C22—224no—
532C22—4416no—
533C22—442no—
534C22—442no—
535C22—442no—
536C22—442no—
537C22#1062234114yes—
538C22C2×(C22⋊D11)⋊C411yescharacteristic
539C22#1062307612yes—
540C22C2×#6695411yescharacteristic
541C22C2×M16×D1111yescharacteristic
542C22#1062328112yes—
543C4—22no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—442no—
548C4—442no—
549C4—442no—
550C4#1062312311yescharacteristic
551C4#1062314812yes—
552C4#1062318411yescharacteristic
553C2—24no—
554C2—81no—
555C2—444no—
556C2#1307127911yescharacteristic
557C2C2×#1062234111yescharacteristic
558C2#1307732211yescharacteristic
559C2#1307764112yes—
560C2#1307765812yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1869C2
prime radicalC2×#66990C4
cosocleC22×C4×C11C24
hypercenter#1869D11
hypocenterC11#22034
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
1. C2×#10622624C2semidirect
2. C22×(C2×D11)⋊C8C2semidirect
4. #13069412C2semidirect
5. #13069230C2semidirect
6. #13069227C2semidirect
7. #13068911C2semidirect
8. #13068794C2semidirect
9. #13068525C2semidirect
10. #13068395C2semidirect
11. C11×#1869C2semidirect
17. C22×#4318C22semidirect
20. C2×C11×C22⋊C8C22semidirect
24. C2×C22⋊(C11⋊C8)C22semidirect
30. C2×#66879C22semidirect
31. C2×Dic11⋊C8C22semidirect
38. C2×C4⋊(C11⋊C8)C22semidirect
39. C2×#66867C22semidirect
40. C11×#336C22semidirect
41. #10622188C22semidirect
42. #10622188C22semidirect
79. C22×C11⋊C8D4semidirect
106. C23×D11M16semidirect
182. #1869D11semidirect
269. C2×C22⋊C8C2×D11semidirect
281. #336C2×D11semidirect
454. C11#22034semidirect

Maximal subgroups

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

subgroupindex
C2×#106226242
C22×(C2×D11)⋊C82
C4×#669902
#130694122
#130692302
#130692272
#130689112
#130687942
#130685252
#130683952
C11×#18692
#2203411