Finite Group Databasebeta

← #14755204

Subgroups — #14755204

Order 2816.

1906 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4324C211yesmaximal, characteristic
2C2×#10622617C211yesmaximal, characteristic, complemented
3C2×#10622828C211yesmaximal, characteristic
4#13071200C211yesmaximal, characteristic, complemented
5#13068950C218yesmaximal, complemented
6#13068332C211yesmaximal, characteristic, complemented
7#13068313C211yesmaximal, characteristic, complemented
8C2×C11×#518C211yesmaximal, characteristic
9C23×D4×C11C2211yescharacteristic
10C23×Dic22C2211yescharacteristic
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—
18C22×#4324—24no—
19C22×#4324—24no—
20C22×#4324C418yescomplemented
21C22×#4324C2214yes—
22C2×#66979C2211yescharacteristic
23C22×#4318C2211yescharacteristic
24C23×C11⋊C8C2211yescharacteristic
25#10622828—24no—
26C2×#66896C2214yes—
27#10622617—24no—
28#10622587—22no—
29C2×#66874C2214yescomplemented
30#10622556—22no—
31#10622542C2214yescomplemented
32#10622167C2214yescomplemented
33#10622162C2214yescomplemented
34C25×C11—21no—
35C22×D4×C11—21no—
36C22×D4×C11—22no—
37C22×D4×C11—22no—
38C22×D4×C11—22no—
39C22×D4×C11C2×C414yes—
40C22×D4×C11D414yes—
41C22×D4×C11D414yes—
42C22×D4×C11C2312yes—
43C23×C4×C11—24no—
44C23×C4×C11C2311yescharacteristic
45C23×Dic11—21no—
46C22×Dic22—22no—
47C22×Dic22—22no—
48C22×Dic22—22no—
49C22×Dic22—22no—
50C22×Dic22—21no—
51C22×Dic22—22no—
52C22×Dic22C2×C414yescomplemented
53C22×Dic22C2312yes—
54C4×D4×C11—216no—
55C4×D4×C11—28no—
56C4×D4×C11—28no—
57C11×#117—22no—
58C11×#117—22no—
59C11×#117—22no—
60C11×#117D414yes—
61C2×C11×C4⋊C4D412yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C22⋊C4—216no—
64C2×C11×C22⋊C4—21no—
65C2×C11×C22⋊C4—24no—
66C2×C11×C22⋊C4D412yes—
67C2×C42×C11—21no—
68C2×C42×C11C2312yes—
69C2×C22⋊Dic11—21no—
70C2×#4324—232no—
71C2×#4324—28no—
72C2×#4324—28no—
73C2×#4324C2×C4116yescomplemented
74#66979—22no—
75#66979—22no—
76C2×C4⋊Dic11C2312yes—
77C2×C4×Dic11—21no—
78C2×#4318—22no—
79C2×#4318—22no—
80C2×#4318—22no—
81C22×C11⋊C8—22no—
82C22×C11⋊C8—22no—
83C22×C11⋊C8C2×C414yescomplemented
84C22×C11⋊C8C2312yes—
85C22×C11⋊C8C2312yes—
86#66896—28no—
87C11⋊#95—28no—
88#66874—28no—
89#20933—111nomaximal, Sylow
90C24×C11—22no—
91C24×C11—24no—
92C24×C11—24no—
93C24×C11—24no—
94C24×C11—84no—
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×C11C22⋊C4116yes—
106C2×D4×C11C22×C414yes—
107C2×D4×C11C2×D414yes—
108C2×D4×C11C2×D414yes—
109C22×C4×C11—22no—
110C22×C4×C11—216no—
111C22×C4×C11—88no—
112C22×C4×C11C22×C412yes—
113C22×C4×C11C2×D414yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D412yes—
118C22×C4×C11#4112yes—
119C22×C4×C11#4112yes—
120C22×C4×C11C2411yescharacteristic
121C22×Dic11—24no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—42no—
125C22×Dic11—42no—
126C2×Dic22—28no—
127C2×Dic22—28no—
128C2×Dic22—24no—
129C2×Dic22—22no—
130C2×Dic22—22no—
131C2×Dic22—22no—
132C2×Dic22—22no—
133C2×Dic22—22no—
134C2×Dic22—42no—
135C2×Dic22—44no—
136C2×Dic22—42no—
137C2×Dic22—44no—
138C2×Dic22C22×C414yes—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4C2×D414yes—
142C11×C22⋊C4—216no—
143C11×C22⋊C4—24no—
144C11×C22⋊C4—24no—
145C42×C11—24no—
146C42×C11—22no—
147C42×C11—22no—
148C22⋊Dic11—42no—
149#4324—232no—
150C4⋊Dic11—22no—
151C4⋊Dic11—22no—
152C4×Dic11—42no—
153#4318—44no—
154C2×C11⋊C8—28no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8C22×C414yes—
161C23×SD16—111no—
162C2×#518D1111yescharacteristic
163C2×#419—111no—
164C2×#418—111no—
165#2310—111no—
166#1877—118no—
167#1735—111no—
168#1729—111no—
169C23×C11—24no—
170C23×C11—24no—
171C23×C11—24no—
172C23×C11—24no—
173C23×C11—216no—
174C23×C11—48no—
175C23×C11—88no—
176C23×C11—88no—
177C23×C11—88no—
178C23×C11C4×D412yes—
179C23×C11#12012yes—
180C23×C11#12112yes—
181C23×C11C22×D411yescharacteristic
182D4×C11—24no—
183D4×C11—24no—
184D4×C11—24no—
185D4×C11—216no—
186D4×C11C2×C22⋊C418yes—
187C2×C4×C11—24no—
188C2×C4×C11—24no—
189C2×C4×C11—28no—
190C2×C4×C11—44no—
191C2×C4×C11—816no—
192C2×C4×C11C2×C22⋊C414yes—
193C2×C4×C11C4×D414yes—
194C2×C4×C11C4×D412yes—
195C2×C4×C11#12012yes—
196C2×C4×C11#12114yes—
197C2×C4×C11#12112yes—
198C2×C4×C11#12314yes—
199C2×C4×C11C23×C411yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×Dic11—24no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—48no—
209C2×Dic11—42no—
210C2×Dic11—44no—
211Dic22—24no—
212Dic22—24no—
213Dic22—42no—
214Dic22—42no—
215Dic22—48no—
216C11⋊C8—24no—
217C11⋊C8—42no—
218C23×Q8—111no—
219C23×D4C2×D1111yescharacteristic
220C22×SD16—114no—
221C22×SD16—118no—
222C22×SD16—224no—
223C22×SD16—224no—
224C22×M16—111no—
225C23×C8—111no—
226#518—24no—
227#518—24no—
228C2×C4×D4—22no—
229C2×C4×D4C2×D1114yes—
230C2×#117—111no—
231C2×#117C2×D1111yescharacteristic
232C2×#117C2×D1111yescharacteristic
233C22×C22⋊C4—22no—
234#419—224no—
235#418—224no—
236C2×#103—114no—
237C2×#102—114no—
238#391—114no—
239#391—222no—
240#381—222no—
241#340—114no—
242#336—114no—
243C22×C11—24no—
244C22×C11—24no—
245C22×C11—24no—
246C22×C11—28no—
247C22×C11—48no—
248C22×C11—48no—
249C22×C11—48no—
250C22×C11—816no—
251C22×C11#38614yes—
252C22×C11C2×C4×D411yescharacteristic
253C22×C11C2×#12011yescharacteristic
254C22×C11C2×#12111yescharacteristic
255C22×C11#57714yes—
256C4×C11—44no—
257C4×C11—44no—
258C4×C11#38614yes—
259C4×C11C22×C22⋊C411yescharacteristic
260C4×C11C2×C4×D411yescharacteristic
261C4×C11C2×#12111yescharacteristic
262C4×C11C2×#12311yescharacteristic
263Dic11—44no—
264Dic11—82no—
265C25—21no—
266C22×Q8—114no—
267C22×Q8—112no—
268C22×Q8—222no—
269C22×Q8—221no—
270C22×Q8—222no—
271C22×Q8—222no—
272C22×Q8—222no—
273C22×Q8—222no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—21no—
277C22×D4—22no—
278C22×D4C4×D1114yes—
279C22×D4D4414yes—
280C22×D4C22⋊D1114yes—
281C22×D4C22×D1112yes—
282C23×C4—24no—
283C23×C4—221no—
284C23×C4C22×D1111yescharacteristic
285C2×SD16—1116no—
286C2×SD16—2232no—
287C2×SD16—228no—
288C2×SD16—228no—
289C2×M16—222no—
290C2×M16—222no—
291C2×M16—222no—
292C22×C8—114no—
293C22×C8—112no—
294C22×C8—112no—
295C22×C8—222no—
296C22×C8—222no—
297C4×D4—216no—
298C4×D4—28no—
299C4×D4—28no—
300#117—22no—
301#117—22no—
302#117—22no—
303#117—222no—
304#117—222no—
305#117C22⋊D1114yes—
306C2×C4⋊C4—112no—
307C2×C4⋊C4C22⋊D1112yes—
308C2×C4⋊C4C22×D1112yes—
309C2×C22⋊C4—216no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—221no—
313C2×C22⋊C4C22⋊D1112yes—
314C2×C42—21no—
315C2×C42—221no—
316C2×C42C22×D1112yes—
317#103—228no—
318#102—228no—
319#95—228no—
320C2×C11—24no—
321C2×C11—48no—
322C2×C11C2×#38611yescharacteristic
323C2×C11#294912yes—
324C2×C11#300912yes—
325C2×C11#304212yes—
326C24—22no—
327C24—24no—
328C24—24no—
329C24—24no—
330C24—84no—
331C24C2×C22⋊D1111yescharacteristic
332C2×Q8—114no—
333C2×Q8—224no—
334C2×Q8—222no—
335C2×Q8—228no—
336C2×Q8—228no—
337C2×Q8—222no—
338C2×Q8—222no—
339C2×Q8—222no—
340C2×Q8—222no—
341C2×Q8—444no—
342C2×Q8—442no—
343C2×Q8—444no—
344C2×Q8—442no—
345C2×D4—28no—
346C2×D4—24no—
347C2×D4—28no—
348C2×D4—28no—
349C2×D4—24no—
350C2×D4—24no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—22no—
354C2×D4(C2×D11)⋊C4116yes—
355C2×D4C2×C4×D1114yes—
356C2×D4C2×D4414yes—
357C2×D4C2×C22⋊D1114yes—
358C22×C4—22no—
359C22×C4—216no—
360C22×C4—88no—
361C22×C4—224no—
362C22×C4—222no—
363C22×C4—222no—
364C22×C4—442no—
365C22×C4—442no—
366C22×C4C2×C4×D1112yes—
367C22×C4C2×D4412yes—
368C22×C4#433912yes—
369C22×C4#433912yes—
370C22×C4C2×C22⋊D1114yes—
371C22×C4C2×C22⋊D1112yes—
372C22×C4C2×C22⋊D1111yescharacteristic
373C22×C4C2×C22⋊D1112yes—
374C22×C4C23×D1111yescharacteristic
375SD16—2232no—
376M16—444no—
377C2×C8—114no—
378C2×C8—228no—
379C2×C8—222no—
380C2×C8—222no—
381C2×C8—222no—
382C2×C8—222no—
383C2×C8—222no—
384C4⋊C4—24no—
385C4⋊C4—22no—
386C4⋊C4—222no—
387C4⋊C4—222no—
388C4⋊C4C2×C22⋊D1114yes—
389C22⋊C4—216no—
390C22⋊C4—24no—
391C22⋊C4—24no—
392C22⋊C4—442no—
393C42—24no—
394C42—22no—
395C42—22no—
396C42—442no—
397C11#2093311yescharacteristic, complemented, Sylow
398C23—24no—
399C23—24no—
400C23—24no—
401C23—24no—
402C23—216no—
403C23—48no—
404C23—88no—
405C23—88no—
406C23—88no—
407C23C4×C22⋊D1112yes—
408C23#6698312yes—
409C23#6700612yes—
410C23C22×C22⋊D1111yescharacteristic
411Q8—224no—
412Q8—224no—
413Q8—442no—
414Q8—442no—
415Q8—448no—
416D4—24no—
417D4—24no—
418D4—24no—
419D4—216no—
420D4C2×(C2×D11)⋊C418yes—
421C2×C4—28no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—44no—
425C2×C4—816no—
426C2×C4—224no—
427C2×C4—442no—
428C2×C4—448no—
429C2×C4—442no—
430C2×C4—442no—
431C2×C4—444no—
432C2×C4C2×(C2×D11)⋊C414yes—
433C2×C4C4×C22⋊D1114yes—
434C2×C4C4×C22⋊D1112yes—
435C2×C4#6698214yes—
436C2×C4#6698314yes—
437C2×C4#6698312yes—
438C2×C4#6700612yes—
439C2×C4C22×C4×D1111yescharacteristic
440C2×C4C22×D4411yescharacteristic
441C2×C4C2×#433911yescharacteristic
442C2×C4C2×#433911yescharacteristic
443C2×C4C22×C22⋊D1111yescharacteristic
444C2×C4C22×C22⋊D1111yescharacteristic
445C8—224no—
446C8—442no—
447C22—24no—
448C22—24no—
449C22—24no—
450C22—28no—
451C22—48no—
452C22—48no—
453C22—48no—
454C22—816no—
455C22#1062282614yes—
456C22C2×C4×C22⋊D1111yescharacteristic
457C22C2×#6698311yescharacteristic
458C22#1062336714yes—
459C22C2×#6700611yescharacteristic
460C4—44no—
461C4—44no—
462C4—444no—
463C4—882no—
464C4#1062282614yes—
465C4C22×(C2×D11)⋊C411yescharacteristic
466C4C2×C4×C22⋊D1111yescharacteristic
467C4C2×#6698211yescharacteristic
468C4C2×#6698311yescharacteristic
469C2—24no—
470C2—48no—
471C2C2×#1062282611yescharacteristic
472C2#1307747312yes—
473C2#1307789312yes—
474C2#1307812812yes—
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#20933
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
2. C2×#10622617C2semidirect
4. #13071200C2semidirect
5. #13068950C2semidirect
6. #13068332C2semidirect
7. #13068313C2semidirect
20. C22×#4324C4semidirect
29. C2×#66874C22semidirect
31. #10622542C22semidirect
32. #10622167C22semidirect
33. #10622162C22semidirect
52. C22×Dic22C2×C4semidirect
73. C2×#4324C2×C4semidirect
83. C22×C11⋊C8C2×C4semidirect
397. C11#20933semidirect

Maximal subgroups

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

subgroupindex
C23×#43242
C2×#106226172
C2×#106228282
#130712002
#130689502
#130683322
#130683132
C2×C11×#5182
#2093311