Finite Group Databasebeta

← #14754788

Subgroups — #14754788

Order 2816.

1598 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622611C211yesmaximal, characteristic, complemented
2C2×#10622828C211yesmaximal, characteristic
3C22×#66896C211yesmaximal, characteristic
4#13071232C211yesmaximal, characteristic, complemented
5#13068877C214yesmaximal, complemented
6#13068863C214yesmaximal, complemented
7#13068337C211yesmaximal, characteristic, complemented
8#13068313C211yesmaximal, characteristic, complemented
9C2×C11×#518C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C11×#518—24no—
12C11×#518—24no—
13C2×C4×D4×C11—22no—
14C2×C4×D4×C11C2214yes—
15C2×C11×#117C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C22×C11×C22⋊C4—22no—
18C2×#66979C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22#10622828—24no—
23C2×#66896C418yescomplemented
24C2×#66896C2214yes—
25C2×#66896C2212yes—
26C2×#66896C2212yes—
27#10622611—24no—
28#10622586—22no—
29C2×#66872C2212yescomplemented
30C2×#66871C2212yescomplemented
31#10622555—22no—
32#10622541C2214yescomplemented
33#10622167C2214yescomplemented
34#10622162C2212yescomplemented
35#10622162C2212yescomplemented
36C25×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11—22no—
39C22×D4×C11—22no—
40C22×D4×C11—22no—
41C22×D4×C11C2×C414yes—
42C22×D4×C11D414yes—
43C22×D4×C11Q814yes—
44C22×D4×C11C2312yes—
45C23×C4×C11—24no—
46C23×C4×C11C2311yescharacteristic
47C23×Dic11—21no—
48C4×D4×C11—216no—
49C4×D4×C11—28no—
50C4×D4×C11—28no—
51C11×#117—22no—
52C11×#117—22no—
53C11×#117—22no—
54C11×#117D414yes—
55C2×C11×C4⋊C4D412yes—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C22⋊C4—216no—
58C2×C11×C22⋊C4—21no—
59C2×C11×C22⋊C4—24no—
60C2×C11×C22⋊C4D412yes—
61C2×C42×C11—21no—
62C2×C42×C11C2312yes—
63C2×C22⋊Dic11—21no—
64#66979—22no—
65#66979—22no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11C2×C414yescomplemented
69C2×C4⋊Dic11C2312yes—
70C2×C4⋊Dic11C2312yes—
71C2×Dic11⋊C4—24no—
72C2×C4×Dic11—21no—
73C2×#4318—22no—
74C2×#4318—22no—
75C2×#4318—22no—
76C22×C11⋊C8—22no—
77C22×C11⋊C8—22no—
78C22×C11⋊C8C2×C414yescomplemented
79C22×C11⋊C8C2312yes—
80C22×C11⋊C8C2311yescharacteristic
81C22×C11⋊C8C2311yescharacteristic
82#66896—28no—
83#66896C2×C418yescomplemented
84#66896C2×C418yescomplemented
85C11⋊#95—24no—
86#66872—24no—
87#66871—24no—
88#20879—111nomaximal, Sylow
89C24×C11—22no—
90C24×C11—24no—
91C24×C11—24no—
92C24×C11—24no—
93C24×C11—82no—
94C24×C11—82no—
95C24×C11C2×D411yescharacteristic
96C2×D4×C11—28no—
97C2×D4×C11—24no—
98C2×D4×C11—24no—
99C2×D4×C11—28no—
100C2×D4×C11—24no—
101C2×D4×C11—28no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11C4⋊C4116yescomplemented
106C2×D4×C11C22×C414yes—
107C2×D4×C11C2×D414yes—
108C2×D4×C11C2×Q814yes—
109C22×C4×C11—22no—
110C22×C4×C11—216no—
111C22×C4×C11—84no—
112C22×C4×C11—84no—
113C22×C4×C11C22×C412yes—
114C22×C4×C11C2×D414yes—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×Q812yes—
119C22×C4×C11#4112yes—
120C22×C4×C11#4112yes—
121C22×C4×C11C2411yescharacteristic
122C22×Dic11—24no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—82no—
126C11×C4⋊C4—24no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4C2×D414yes—
129C11×C22⋊C4—216no—
130C11×C22⋊C4—24no—
131C11×C22⋊C4—24no—
132C42×C11—24no—
133C42×C11—22no—
134C42×C11—22no—
135C22⋊Dic11—42no—
136C4⋊Dic11—24no—
137C4⋊Dic11—22no—
138C4⋊Dic11—22no—
139C4⋊Dic11—22no—
140C4⋊Dic11C22×C414yes—
141Dic11⋊C4—84no—
142C4×Dic11—42no—
143#4318—44no—
144C2×C11⋊C8—28no—
145C2×C11⋊C8—21no—
146C2×C11⋊C8—21no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8C22×C412yes—
153C2×C11⋊C8C22×C412yes—
154C2×#518D1111yescharacteristic
155C2×#427—111no—
156C2×#418—111no—
157C22×#102—111no—
158#2316—111no—
159#1864—114no—
160#1862—114no—
161#1736—111no—
162#1729—111no—
163C23×C11—22no—
164C23×C11—22no—
165C23×C11—24no—
166C23×C11—24no—
167C23×C11—24no—
168C23×C11—216no—
169C23×C11—44no—
170C23×C11—44no—
171C23×C11—88no—
172C23×C11—84no—
173C23×C11—84no—
174C23×C11—88no—
175C23×C11C4×D412yes—
176C23×C11#12012yes—
177C23×C11C22⋊Q812yes—
178C23×C11C22×D411yescharacteristic
179D4×C11—24no—
180D4×C11—24no—
181D4×C11—24no—
182D4×C11—216no—
183D4×C11C2×C4⋊C418yes—
184C2×C4×C11—24no—
185C2×C4×C11—24no—
186C2×C4×C11—24no—
187C2×C4×C11—24no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—816no—
191C2×C4×C11C2×C4⋊C414yes—
192C2×C4×C11C4×D414yes—
193C2×C4×C11C4×D412yes—
194C2×C4×C11#12012yes—
195C2×C4×C11C22⋊Q814yes—
196C2×C4×C11C22⋊Q812yes—
197C2×C4×C11#12314yes—
198C2×C4×C11C23×C411yescharacteristic
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C22×Q811yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×Dic11—24no—
205C2×Dic11—44no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—84no—
210C11⋊C8—22no—
211C11⋊C8—22no—
212C11⋊C8—42no—
213C23×D4C2×D1111yescharacteristic
214C22×M16—111no—
215C23×C8—111no—
216#518—24no—
217#518—24no—
218C2×C4×D4—22no—
219C2×C4×D4C2×D1114yes—
220C2×#117—111no—
221C2×#117C2×D1111yescharacteristic
222C2×#117C2×D1111yescharacteristic
223C22×C4⋊C4—111no—
224C22×C22⋊C4—22no—
225#427—224no—
226C2×#107—112no—
227C2×#106—112no—
228#418—224no—
229C2×#102—112no—
230C2×#102—112no—
231C2×#102—118no—
232C2×#102—114no—
233#389—114no—
234#389—222no—
235#380—222no—
236#340—114no—
237#336—112no—
238#336—112no—
239C22×C11—24no—
240C22×C11—22no—
241C22×C11—22no—
242C22×C11—24no—
243C22×C11—28no—
244C22×C11—48no—
245C22×C11—44no—
246C22×C11—44no—
247C22×C11—48no—
248C22×C11—816no—
249C22×C11#38514yes—
250C22×C11C2×C4×D411yescharacteristic
251C22×C11C2×#12011yescharacteristic
252C22×C11C2×C22⋊Q811yescharacteristic
253C22×C11#57612yes—
254C22×C11#57712yes—
255C4×C11—44no—
256C4×C11—44no—
257C4×C11#38514yes—
258C4×C11C22×C4⋊C411yescharacteristic
259C4×C11C2×C4×D411yescharacteristic
260C4×C11C2×C22⋊Q811yescharacteristic
261C4×C11C2×#12311yescharacteristic
262Dic11—44no—
263Dic11—82no—
264C25—21no—
265C22×D4—22no—
266C22×D4—22no—
267C22×D4—21no—
268C22×D4—22no—
269C22×D4Dic2214yes—
270C22×D4C4×D1114yes—
271C22×D4C22⋊D1114yes—
272C22×D4C22×D1112yes—
273C23×C4—24no—
274C23×C4—221no—
275C23×C4C22×D1111yescharacteristic
276C2×M16—222no—
277C2×M16—222no—
278C2×M16—222no—
279C22×C8—114no—
280C22×C8—111no—
281C22×C8—111no—
282C22×C8—112no—
283C22×C8—222no—
284C22×C8—222no—
285C4×D4—216no—
286C4×D4—28no—
287C4×D4—28no—
288#117—22no—
289#117—22no—
290#117—22no—
291#117—222no—
292#117—222no—
293#117C22⋊D1114yes—
294C2×C4⋊C4—114no—
295C2×C4⋊C4—112no—
296C2×C4⋊C4—112no—
297C2×C4⋊C4—222no—
298C2×C4⋊C4—221no—
299C2×C4⋊C4—224no—
300C2×C4⋊C4C22⋊D1112yes—
301C2×C4⋊C4C22×D1112yes—
302C2×C22⋊C4—216no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—221no—
306C2×C22⋊C4C22⋊D1112yes—
307C2×C42—21no—
308C2×C42—221no—
309C2×C42C22×D1112yes—
310#107—224no—
311#106—224no—
312#102—118no—
313#102—118no—
314#102—228no—
315#95—224no—
316C2×C11—24no—
317C2×C11—48no—
318C2×C11C2×#38511yescharacteristic
319C2×C11#294811yescharacteristic
320C2×C11#294911yescharacteristic
321C2×C11#301212yes—
322C2×C11#308112yes—
323C24—22no—
324C24—24no—
325C24—24no—
326C24—24no—
327C24—82no—
328C24—82no—
329C24C2×C22⋊D1111yescharacteristic
330C2×D4—28no—
331C2×D4—24no—
332C2×D4—28no—
333C2×D4—24no—
334C2×D4—28no—
335C2×D4—24no—
336C2×D4—22no—
337C2×D4—22no—
338C2×D4—22no—
339C2×D4Dic11⋊C4116yescomplemented
340C2×D4C2×Dic2214yes—
341C2×D4C2×C4×D1114yes—
342C2×D4C2×C22⋊D1114yes—
343C22×C4—22no—
344C22×C4—216no—
345C22×C4—84no—
346C22×C4—84no—
347C22×C4—222no—
348C22×C4—224no—
349C22×C4—222no—
350C22×C4—882no—
351C22×C4C2×Dic2212yes—
352C22×C4C2×C4×D1112yes—
353C22×C4#433912yes—
354C22×C4#433912yes—
355C22×C4C2×C22⋊D1114yes—
356C22×C4C2×C22⋊D1112yes—
357C22×C4C2×C22⋊D1111yescharacteristic
358C22×C4C2×C22⋊D1112yes—
359C22×C4C23×D1111yescharacteristic
360M16—444no—
361C2×C8—112no—
362C2×C8—112no—
363C2×C8—228no—
364C2×C8—221no—
365C2×C8—221no—
366C2×C8—221no—
367C2×C8—221no—
368C2×C8—222no—
369C2×C8—222no—
370C2×C8—222no—
371C4⋊C4—24no—
372C4⋊C4—22no—
373C4⋊C4—114no—
374C4⋊C4—224no—
375C4⋊C4—222no—
376C4⋊C4—222no—
377C4⋊C4—222no—
378C4⋊C4—884no—
379C4⋊C4C2×C22⋊D1114yes—
380C22⋊C4—216no—
381C22⋊C4—24no—
382C22⋊C4—24no—
383C22⋊C4—442no—
384C42—24no—
385C42—22no—
386C42—22no—
387C42—442no—
388C11#2087911yescharacteristic, complemented, Sylow
389C23—22no—
390C23—22no—
391C23—24no—
392C23—24no—
393C23—24no—
394C23—216no—
395C23—44no—
396C23—44no—
397C23—88no—
398C23—88no—
399C23—84no—
400C23—84no—
401C23#6697712yes—
402C23C4×C22⋊D1112yes—
403C23#6700612yes—
404C23C22×C22⋊D1111yescharacteristic
405D4—24no—
406D4—24no—
407D4—24no—
408D4—216no—
409D4C2×Dic11⋊C418yes—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—816no—
417C2×C4—224no—
418C2×C4—444no—
419C2×C4—442no—
420C2×C4—442no—
421C2×C4—442no—
422C2×C4—884no—
423C2×C4C2×Dic11⋊C414yes—
424C2×C4#6697714yes—
425C2×C4#6697712yes—
426C2×C4C4×C22⋊D1114yes—
427C2×C4C4×C22⋊D1112yes—
428C2×C4#6698214yes—
429C2×C4#6700612yes—
430C2×C4C22×Dic2211yescharacteristic
431C2×C4C22×C4×D1111yescharacteristic
432C2×C4C2×#433911yescharacteristic
433C2×C4C2×#433911yescharacteristic
434C2×C4C22×C22⋊D1111yescharacteristic
435C2×C4C22×C22⋊D1111yescharacteristic
436C8—222no—
437C8—222no—
438C8—442no—
439C22—24no—
440C22—24no—
441C22—22no—
442C22—22no—
443C22—28no—
444C22—48no—
445C22—48no—
446C22—44no—
447C22—44no—
448C22—816no—
449C22#1062282314yes—
450C22C2×#6697711yescharacteristic
451C22C2×C4×C22⋊D1111yescharacteristic
452C22#1062336612yes—
453C22#1062336712yes—
454C22C2×#6700611yescharacteristic
455C4—44no—
456C4—44no—
457C4—444no—
458C4—882no—
459C4#1062282314yes—
460C4C22×Dic11⋊C411yescharacteristic
461C4C2×#6697711yescharacteristic
462C4C2×C4×C22⋊D1111yescharacteristic
463C4C2×#6698211yescharacteristic
464C2—24no—
465C2—48no—
466C2C2×#1062282311yescharacteristic
467C2#1307746611yescharacteristic
468C2#1307747311yescharacteristic
469C2#1307792012yes—
470C2#1307844712yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#518C2
socleC23×C11C22×D4
prime radicalC23×D4×C11C22
cosocleC22×C4×C11C24
hypercenterC2×#518D11
hypocenterC11#20879
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#518

Complements

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

NH ≅ G/Ntype
1. C2×#10622611C2semidirect
4. #13071232C2semidirect
5. #13068877C2semidirect
6. #13068863C2semidirect
7. #13068337C2semidirect
8. #13068313C2semidirect
23. C2×#66896C4semidirect
29. C2×#66872C22semidirect
30. C2×#66871C22semidirect
32. #10622541C22semidirect
33. #10622167C22semidirect
34. #10622162C22semidirect
35. #10622162C22semidirect
68. C2×C4⋊Dic11C2×C4semidirect
78. C22×C11⋊C8C2×C4semidirect
83. #66896C2×C4semidirect
84. #66896C2×C4semidirect
105. C2×D4×C11C4⋊C4semidirect
339. C2×D4Dic11⋊C4semidirect
388. C11#20879semidirect

Maximal subgroups

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

subgroupindex
C2×#106226112
C2×#106228282
C22×#668962
#130712322
#130688772
#130688632
#130683372
#130683132
C2×C11×#5182
#2087911