Finite Group Databasebeta

← #14770960

Subgroups — #14770960

Order 2816.

1190 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66896C211yesmaximal, characteristic
2#13071495C211yesmaximal, characteristic, complemented
3D4×C22⋊Dic11C211yesmaximal, characteristic
4#13069296C212yesmaximal, complemented
5#13069246C212yesmaximal, complemented
6#13068875C212yesmaximal, complemented
7#13068707C211yesmaximal, characteristic, complemented
8#13068639C211yesmaximal, characteristic, complemented
9#102×Dic11C212yesmaximal, complemented
10#13068390C211yesmaximal, characteristic, complemented
11C11×#1786C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C22×C22⋊Dic11—21no—
14C2×D4×Dic11C2212yes—
15C22×C4⋊Dic11C2211yescharacteristic
16C23×C11⋊C8C2211yescharacteristic
17C2×C11×#102C2212yes—
18C2×C11×#102C2212yes—
19C2×C11×C22⋊C8C2211yescharacteristic
20C11×#380C2211yescharacteristic
21#10622860—21no—
22#10622834C2212yes—
23#10622833—22no—
24C2×#66896C418yescomplemented
25C2×#66896C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29#10622825C2211yescharacteristic
30C4×C22⋊Dic11C2211yescharacteristic
31C2×C8×Dic11C2212yescomplemented
32C4⋊C4×Dic11C2212yescomplemented
33#10622586C2212yescomplemented
34C2×#66872C2212yescomplemented
35#10622555—21no—
36C22⋊C4×Dic11—21no—
37#10622266—22no—
38#10622189C2212yescomplemented
39#10622189C2212yescomplemented
40#10622188C2212yescomplemented
41#10622167C2212yescomplemented
42C25×C11—21no—
43C22×D4×C11—24no—
44C22×D4×C11—21no—
45C22×D4×C11—22no—
46C22×D4×C11—42no—
47C22×D4×C11C2×C414yes—
48C22×D4×C11C2311yescharacteristic
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×Dic11—21no—
52C23×Dic11—22no—
53C22×C8×C11C2312yes—
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C22⋊C4—21no—
56C2×C22⋊Dic11—21no—
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11—22no—
59C2×C22⋊Dic11—22no—
60C2×C22⋊Dic11—44no—
61C2×C22⋊Dic11D411yescharacteristic
62C2×C22⋊Dic11D411yescharacteristic
63D4×Dic11—24no—
64D4×Dic11—42no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11C2×C414yescomplemented
68C2×C4⋊Dic11C2312yes—
69C2×C4⋊Dic11C2311yescharacteristic
70C2×C4⋊Dic11C2311yescharacteristic
71C2×Dic11⋊C4—22no—
72C2×C4×Dic11—22no—
73C2×C4×Dic11C2312yes—
74C22×C11⋊C8—42no—
75C22×C11⋊C8C2×C414yescomplemented
76C22×C11⋊C8C2311yescharacteristic
77C22×C11⋊C8C2311yescharacteristic
78C11×#102—24no—
79C11×#102—42no—
80C11×C22⋊C8—22no—
81C11×#95—21no—
82#66896C2×C414yes—
83#66896C2×C414yes—
84#66896C2×C414yescomplemented
85#66896C2×C414yescomplemented
86C11⋊#95—21no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89C11⋊#95D412yes—
90C8×Dic11—42no—
91#66872—42no—
92#22574—111nomaximal, Sylow
93C24×C11—21no—
94C24×C11—21no—
95C24×C11—24no—
96C24×C11—44no—
97C24×C11—42no—
98C24×C11—42no—
99C24×C11—82no—
100C24×C11C2×D411yescharacteristic
101C2×D4×C11—28no—
102C2×D4×C11—24no—
103C2×D4×C11—21no—
104C2×D4×C11—22no—
105C2×D4×C11—21no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—44no—
109C2×D4×C11—48no—
110C2×D4×C11—44no—
111C2×D4×C11C22×C412yes—
112C2×D4×C11C22×C412yes—
113C2×D4×C11#4114yes—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11C22×C412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11#4112yes—
120C22×C4×C11C2411yescharacteristic
121C22×Dic11—24no—
122C22×Dic11—21no—
123C22×Dic11—21no—
124C22×Dic11—22no—
125C22×Dic11—44no—
126C22×Dic11—44no—
127C22×Dic11—82no—
128C22×Dic11—82no—
129C22×Dic11C2×D412yes—
130C22×Dic11C2×D412yes—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C22⋊C4—42no—
137C22⋊Dic11—22no—
138C22⋊Dic11—44no—
139C22⋊Dic11—44no—
140C22⋊Dic11—42no—
141C22⋊Dic11—82no—
142C22⋊Dic11SD1614yes—
143C4⋊Dic11—24no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—22no—
147C4⋊Dic11—22no—
148C4⋊Dic11C22×C412yes—
149C4⋊Dic11C22×C412yes—
150Dic11⋊C4—82no—
151C4×Dic11—22no—
152C4×Dic11—22no—
153C4×Dic11—82no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—44no—
157C2×C11⋊C8C22×C412yes—
158C2×C11⋊C8C22×C412yes—
159C22×#102—111no—
160#2345—111no—
161D4×C22⋊C4—111no—
162#1934—112no—
163#1926—112no—
164#1864—112no—
165#1824—111no—
166#1807—111no—
167#1786D1111yescharacteristic
168C4×#102—112no—
169C8×C22⋊C4—111no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11—22no—
173C23×C11—24no—
174C23×C11—22no—
175C23×C11—48no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—42no—
183C23×C11—48no—
184C23×C11—84no—
185C23×C11—88no—
186C23×C11—88no—
187C23×C11C4×D412yes—
188C23×C11C2×SD1612yes—
189C23×C11#13512yes—
190C23×C11C22×D411yescharacteristic
191D4×C11—22no—
192D4×C11—22no—
193D4×C11—22no—
194D4×C11—24no—
195D4×C11—48no—
196D4×C11—42no—
197D4×C11#11714yes—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—24no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11C4×D412yes—
206C2×C4×C11C23×C411yescharacteristic
207C2×C4×C11C2×#4112yes—
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11H(5,𝔽2)12yes—
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—88no—
223C2×Dic11—84no—
224C2×Dic11C2×SD1614yes—
225C8×C11—42no—
226C11⋊C8—22no—
227C11⋊C8—22no—
228C23×D4C2×D1111yescharacteristic
229C23×C8—111no—
230C2×C4×D4—112no—
231C22×C4⋊C4—111no—
232C22×C22⋊C4—221no—
233C2×#106—112no—
234C2×#102—111no—
235C2×#102—111no—
236C2×#102—111no—
237C2×#102—111no—
238C2×#102—118no—
239C2×#102C2×D1112yes—
240C2×#102C2×D1112yes—
241C2×C22⋊C8C2×D1111yescharacteristic
242C2×C4×C8—112no—
243#390—112no—
244#389—112no—
245#387—222no—
246#386—222no—
247#380—111no—
248#380—221no—
249#380C2×D1111yescharacteristic
250#379—221no—
251C4×C4⋊C4—112no—
252C4×C22⋊C4—111no—
253C4×C22⋊C4—221no—
254#340—112no—
255#340—112no—
256#340—112no—
257#336—112no—
258C22×C11—22no—
259C22×C11—22no—
260C22×C11—24no—
261C22×C11—24no—
262C22×C11—24no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—44no—
266C22×C11—44no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—816no—
271C22×C11—82no—
272C22×C11—82no—
273C22×C11C4×SD1614yes—
274C22×C11C2×C4×D411yescharacteristic
275C22×C11#54612yes—
276C22×C11C22×SD1611yescharacteristic
277C22×C11C2×#13511yescharacteristic
278C22×C11#57612yes—
279C4×C11—22no—
280C4×C11—82no—
281C4×C11C2×#11711yescharacteristic
282C4×C11#51811yescharacteristic
283C4×C11#55112yes—
284Dic11—24no—
285Dic11—42no—
286Dic11—42no—
287Dic11—42no—
288Dic11—82no—
289C25—21no—
290C22×D4—24no—
291C22×D4—21no—
292C22×D4—22no—
293C22×D4—42no—
294C22×D4C4×D1114yes—
295C22×D4C22×D1111yescharacteristic
296C22×D4C22×D1111yescharacteristic
297C23×C4—222no—
298C23×C4—221no—
299C23×C4C22×D1111yescharacteristic
300C22×C8—111no—
301C22×C8—111no—
302C22×C8—114no—
303C22×C8—442no—
304C22×C8C22×D1112yes—
305C4×D4—224no—
306C4×D4—442no—
307C2×C4⋊C4—114no—
308C2×C4⋊C4—111no—
309C2×C4⋊C4—111no—
310C2×C4⋊C4—112no—
311C2×C4⋊C4—221no—
312C2×C4⋊C4—222no—
313C2×C4⋊C4—222no—
314C2×C4⋊C4C22×D1112yes—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—111no—
317C2×C22⋊C4—111no—
318C2×C22⋊C4—222no—
319C2×C22⋊C4—222no—
320C2×C22⋊C4—221no—
321C2×C22⋊C4—222no—
322C2×C22⋊C4—444no—
323C2×C42—112no—
324C2×C42—222no—
325#106—442no—
326#102—24no—
327#102—42no—
328#102—114no—
329#102—114no—
330#102—114no—
331#102—114no—
332C22⋊C8—22no—
333C4×C8—442no—
334#95—21no—
335#95—112no—
336#95—222no—
337#95—222no—
338#95—221no—
339C2×C11—24no—
340C2×C11—44no—
341C2×C11—82no—
342C2×C11#234211yescharacteristic
343C2×C11C2×C4×SD1611yescharacteristic
344C2×C11#294811yescharacteristic
345C2×C11#329512yes—
346C2×C11#329712yes—
347C24—21no—
348C24—21no—
349C24—24no—
350C24—44no—
351C24—42no—
352C24—42no—
353C24—82no—
354C24D4×D1111yescharacteristic
355C2×D4—28no—
356C2×D4—24no—
357C2×D4—21no—
358C2×D4—22no—
359C2×D4—21no—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—44no—
363C2×D4—48no—
364C2×D4—44no—
365C2×D4C2×C4×D1112yes—
366C2×D4C2×C4×D1112yes—
367C2×D4#434114yes—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—112no—
372C22×C4—112no—
373C22×C4—221no—
374C22×C4—221no—
375C22×C4—224no—
376C22×C4—222no—
377C22×C4—444no—
378C22×C4—444no—
379C22×C4—882no—
380C22×C4—882no—
381C22×C4C2×C4×D1112yes—
382C22×C4D4×D1111yescharacteristic
383C22×C4#434112yes—
384C22×C4C23×D1111yescharacteristic
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—22no—
388C2×C8—112no—
389C2×C8—112no—
390C2×C8—222no—
391C2×C8—222no—
392C2×C8—444no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—112no—
396C4⋊C4—112no—
397C4⋊C4—224no—
398C4⋊C4—221no—
399C4⋊C4—221no—
400C4⋊C4—222no—
401C4⋊C4—222no—
402C4⋊C4—882no—
403C22⋊C4—42no—
404C22⋊C4—114no—
405C22⋊C4—222no—
406C22⋊C4—444no—
407C22⋊C4—444no—
408C22⋊C4—442no—
409C22⋊C4—882no—
410C42—222no—
411C42—222no—
412C42—882no—
413C11#2257411yescharacteristic, complemented, Sylow
414C23—22no—
415C23—22no—
416C23—22no—
417C23—24no—
418C23—22no—
419C23—48no—
420C23—41no—
421C23—41no—
422C23—42no—
423C23—41no—
424C23—41no—
425C23—42no—
426C23—42no—
427C23—48no—
428C23—84no—
429C23—88no—
430C23—88no—
431C23(C22⋊D11)⋊C412yes—
432C23#6696512yes—
433C23SD16×D1112yes—
434C23C2×D4×D1111yescharacteristic
435D4—22no—
436D4—22no—
437D4—22no—
438D4—24no—
439D4—48no—
440D4—42no—
441D4#6693014yes—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—24no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—114no—
450C2×C4—222no—
451C2×C4—222no—
452C2×C4—222no—
453C2×C4—222no—
454C2×C4—222no—
455C2×C4—222no—
456C2×C4—222no—
457C2×C4—442no—
458C2×C4—442no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4—888no—
463C2×C4—884no—
464C2×C4(C22⋊D11)⋊C412yes—
465C2×C4C22×C4×D1111yescharacteristic
466C2×C4C2×#434112yes—
467C2×C4C2×#434111yescharacteristic
468C2×C4#6703712yes—
469C8—42no—
470C8—222no—
471C8—222no—
472C22—22no—
473C22—24no—
474C22—24no—
475C22—22no—
476C22—24no—
477C22—44no—
478C22—42no—
479C22—44no—
480C22—42no—
481C22—42no—
482C22—42no—
483C22—42no—
484C22—816no—
485C22—82no—
486C22—82no—
487C22#1062237114yes—
488C22C2×(C22⋊D11)⋊C411yescharacteristic
489C22#1062312212yes—
490C22C2×#6696511yescharacteristic
491C22C2×SD16×D1111yescharacteristic
492C22#1062330512yes—
493C4—22no—
494C4—82no—
495C4—224no—
496C4—442no—
497C4—442no—
498C4—442no—
499C4—882no—
500C4C2×#6693011yescharacteristic
501C4#1062301711yescharacteristic
502C4#1062311812yes—
503C2—24no—
504C2—44no—
505C2—82no—
506C2#1307146711yescharacteristic
507C2C2×#1062237111yescharacteristic
508C2#1307746411yescharacteristic
509C2#1308043312yes—
510C2#1308047012yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1786C2
socleC23×C11C22×D4
prime radicalC23×D4×C11C22
cosocleC22×C4×C11C24
hypercenter#1786D11
hypocenterC11#22574
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
2. #13071495C2semidirect
4. #13069296C2semidirect
5. #13069246C2semidirect
6. #13068875C2semidirect
7. #13068707C2semidirect
8. #13068639C2semidirect
9. #102×Dic11C2semidirect
10. #13068390C2semidirect
24. C2×#66896C4semidirect
31. C2×C8×Dic11C22semidirect
32. C4⋊C4×Dic11C22semidirect
33. #10622586C22semidirect
34. C2×#66872C22semidirect
38. #10622189C22semidirect
39. #10622189C22semidirect
40. #10622188C22semidirect
41. #10622167C22semidirect
67. C2×C4⋊Dic11C2×C4semidirect
75. C22×C11⋊C8C2×C4semidirect
84. #66896C2×C4semidirect
85. #66896C2×C4semidirect
413. C11#22574semidirect

Maximal subgroups

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

subgroupindex
C22×#668962
#130714952
D4×C22⋊Dic112
#130692962
#130692462
#130688752
#130687072
#130686392
#102×Dic112
#130683902
C11×#17862
#2257411