Finite Group Databasebeta

← #14753579

Subgroups — #14753579

Order 2816.

1542 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66945C211yesmaximal, characteristic
2C2×#10622339C211yesmaximal, characteristic
3D11×#380C211yesmaximal, characteristic
4#13068710C214yesmaximal, complemented
5#13068707C211yesmaximal, characteristic, complemented
6#13068704C211yesmaximal, characteristic, complemented
7#13068702C211yesmaximal, characteristic, complemented
8#13068334C214yesmaximal, complemented
9C11×#1823C211yesmaximal, characteristic, complemented
10C23×C4×D11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×(C2×D11)⋊C4—21no—
13C22×C4⋊Dic11C2211yescharacteristic
14C22×C4×Dic11—21no—
15C22×#4313C2212yes—
16C2×#66945—21no—
17C2×#66945—21no—
18C2×#66945—24no—
19C2×#66945C418yescomplemented
20C2×#66945C2212yes—
21C2×#66945C2212yes—
22C2×C4⋊C4×D11C2212yes—
23C2×C22⋊C4×D11—21no—
24C2×C11×C22⋊C8C2211yescharacteristic
25C11×#380C2211yescharacteristic
26#10622825C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×(C2×D11)⋊C8C2212yes—
29#10622600C2212yes—
30#10622555—21no—
31#10622339—24no—
32#10622280—21no—
33D11×#95—21no—
34C11×#340C2214yescomplemented
35#10622189C2214yescomplemented
36#10622167C2214yescomplemented
37#10622167C2214yescomplemented
38C24×D11D411yescharacteristic
39C23×C4×C11—21no—
40C23×C4×C11C2311yescharacteristic
41C23×Dic11—21no—
42C23×Dic11D411yescharacteristic
43C22×C4×D11—28no—
44C22×C4×D11—22no—
45C22×C4×D11C2×C414yes—
46C22×C4×D11D411yescharacteristic
47C22×C4×D11D411yescharacteristic
48C22×C4×D11D414yes—
49C22×C4×D11C2311yescharacteristic
50C22×C4×D11C2311yescharacteristic
51C22×C8×C11C2312yes—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4C2×C414yescomplemented
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C22⋊C4—21no—
58C2×C22⋊Dic11—21no—
59C2×(C2×D11)⋊C4—28no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—22no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11C2×C414yescomplemented
66C2×C4⋊Dic11C2312yes—
67C2×C4⋊Dic11C2312yes—
68C2×Dic11⋊C4—22no—
69C2×C4×Dic11—28no—
70C2×C4×Dic11—22no—
71C2×C4×Dic11—22no—
72C22×C11⋊C8C2312yes—
73C2×#4313—24no—
74C2×#4313—28no—
75#66945—28no—
76#66945—28no—
77#66945—24no—
78#66945—24no—
79#66945C2×C418yes—
80#66945C2×C418yescomplemented
81C4⋊C4×D11—28no—
82C22⋊C4×D11—44no—
83C11×C22⋊C8—22no—
84C11×#95—21no—
85C11⋊#95—21no—
86C11⋊#95—22no—
87C22⋊(C11⋊C8)—22no—
88(C2×D11)⋊C8—24no—
89#20702—111nomaximal, Sylow
90C24×C11C2×D411yescharacteristic
91C23×D11—22no—
92C23×D11—22no—
93C23×D11—24no—
94C23×D11—42no—
95C23×D11C22⋊C414yes—
96C23×D11C2×D411yescharacteristic
97C23×D11C2×D411yescharacteristic
98C22×C4×C11—24no—
99C22×C4×C11—24no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—42no—
103C22×C4×C11—42no—
104C22×C4×C11C22×C412yes—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2411yescharacteristic
108C22×Dic11—24no—
109C22×Dic11—24no—
110C22×Dic11—22no—
111C22×Dic11—22no—
112C22×Dic11—44no—
113C22×Dic11C22⋊C414yes—
114C22×Dic11C2×D411yescharacteristic
115C22×Dic11C2×D411yescharacteristic
116C2×C4×D11—24no—
117C2×C4×D11—216no—
118C2×C4×D11—216no—
119C2×C4×D11—24no—
120C2×C4×D11—24no—
121C2×C4×D11—44no—
122C2×C4×D11—44no—
123C2×C4×D11—44no—
124C2×C4×D11C22⋊C414yes—
125C2×C4×D11C22⋊C414yes—
126C2×C4×D11C22×C412yes—
127C2×C4×D11C22×C412yes—
128C2×C4×D11C2×D412yes—
129C2×C4×D11C2×D412yes—
130C2×C4×D11#4118yes—
131C2×C8×C11—22no—
132C2×C8×C11—24no—
133C11×C4⋊C4—24no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4C22×C414yes—
137C11×C22⋊C4—42no—
138C22⋊Dic11—42no—
139(C2×D11)⋊C4—28no—
140(C2×D11)⋊C4—28no—
141(C2×D11)⋊C4—44no—
142C4⋊Dic11—24no—
143C4⋊Dic11—22no—
144C4⋊Dic11—24no—
145C4⋊Dic11C22×C414yes—
146Dic11⋊C4—44no—
147C4×Dic11—28no—
148C4×Dic11—28no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—24no—
151#4313—48no—
152C22×#117—111no—
153C2×#407—111no—
154C2×#380—111no—
155#1825—114no—
156#1824—111no—
157#1824—111no—
158#1823—111no—
159#1823D1111yescharacteristic, complemented
160#1736—114no—
161C23×C11—22no—
162C23×C11—22no—
163C23×C11C2×C22⋊C412yes—
164C23×C11AGL(1,ℤ/8)12yes—
165C23×C11#13712yes—
166C23×C11C22×D411yescharacteristic
167C22×D11—21no—
168C22×D11—21no—
169C22×D11—22no—
170C22×D11—22no—
171C22×D11—21no—
172C22×D11—21no—
173C22×D11—22no—
174C22×D11—28no—
175C22×D11—28no—
176C22×D11—44no—
177C22×D11—48no—
178C22×D11—48no—
179C22×D11C2×C22⋊C412yes—
180C22×D11C2×C22⋊C412yes—
181C22×D11#12314yes—
182C2×C4×C11—22no—
183C2×C4×C11—24no—
184C2×C4×C11—24no—
185C2×C4×C11—24no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—48no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11C2×C22⋊C412yes—
193C2×C4×C11C23×C411yescharacteristic
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C2×#4114yes—
196C2×Dic11—22no—
197C2×Dic11—28no—
198C2×Dic11—24no—
199C2×Dic11—48no—
200C2×Dic11—44no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11C2×C22⋊C412yes—
205C2×Dic11C2×C22⋊C412yes—
206C2×Dic11#12314yes—
207C4×D11—28no—
208C4×D11—24no—
209C4×D11—24no—
210C4×D11—28no—
211C4×D11—88no—
212C4×D11#11718yes—
213C4×D11#12318yes—
214C8×C11—42no—
215C11⋊C8—42no—
216C24×C4—111no—
217C22×M16—112no—
218C2×#117—112no—
219C2×#117—112no—
220C2×#117—118no—
221C2×#117—221no—
222C2×#117—221no—
223C2×#117—224no—
224C22×C4⋊C4—111no—
225C22×C4⋊C4—112no—
226C22×C4⋊C4C2×D1111yescharacteristic
227C22×C22⋊C4—221no—
228C22×C22⋊C4—221no—
229C22×C42—221no—
230#407—224no—
231C2×C22⋊C8—111no—
232C2×C22⋊C8—112no—
233C2×C22⋊C8C2×D1111yescharacteristic
234#380—111no—
235#380—112no—
236#380—221no—
237#380—221no—
238#380C2×D1111yescharacteristic
239C2×#95—221no—
240#340—114no—
241#340—114no—
242#340—114no—
243#340C2×D1114yescomplemented
244C22×C11—24no—
245C22×C11—24no—
246C22×C11—22no—
247C22×C11—22no—
248C22×C11#41714yes—
249C22×C11C22×C22⋊C411yescharacteristic
250C22×C11C2×#12312yes—
251C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
252C22×C11C2×#13711yescharacteristic
253C22×C11#57512yes—
254C2×D11—24no—
255C2×D11—24no—
256C2×D11—22no—
257C2×D11—22no—
258C2×D11—22no—
259C2×D11—22no—
260C2×D11—22no—
261C2×D11—416no—
262C2×D11—42no—
263C2×D11—42no—
264C2×D11#38114yes—
265C4×C11—22no—
266C4×C11—44no—
267C4×C11—82no—
268C4×C11C2×#11712yes—
269C4×C11C2×#12312yes—
270Dic11—22no—
271Dic11—44no—
272Dic11—82no—
273Dic11#38114yes—
274C25—111no—
275C23×C4—21no—
276C23×C4—111no—
277C23×C4—111no—
278C23×C4—114no—
279C23×C4—111no—
280C23×C4—111no—
281C23×C4—114no—
282C23×C4—111no—
283C23×C4—228no—
284C23×C4—222no—
285C23×C4—221no—
286C23×C4C22×D1111yescharacteristic
287C2×M16—228no—
288C2×M16—224no—
289C22×C8—112no—
290C22×C8C22×D1112yes—
291#117—118no—
292#117—118no—
293#117—228no—
294#117—228no—
295#117—224no—
296#117—224no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—114no—
300C2×C4⋊C4—112no—
301C2×C4⋊C4—112no—
302C2×C4⋊C4—228no—
303C2×C4⋊C4—221no—
304C2×C4⋊C4—222no—
305C2×C4⋊C4—222no—
306C2×C4⋊C4C4×D1114yescomplemented
307C2×C4⋊C4C22×D1112yes—
308C2×C4⋊C4C22×D1112yes—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—228no—
311C2×C22⋊C4—222no—
312C2×C22⋊C4—222no—
313C2×C22⋊C4—222no—
314C2×C22⋊C4—221no—
315C2×C22⋊C4—444no—
316C2×C42—228no—
317C2×C42—222no—
318C2×C42—222no—
319C22⋊C8—22no—
320C22⋊C8—224no—
321C22⋊C8—222no—
322#95—21no—
323#95—222no—
324#95—221no—
325C2×C11—24no—
326C2×C11C2×#38111yescharacteristic
327C2×C11C2×#41711yescharacteristic
328C2×C11#289611yescharacteristic
329C2×C11#309412yes—
330C2×C11#309512yes—
331D11—24no—
332D11—42no—
333C24—111no—
334C24—111no—
335C24—114no—
336C24—224no—
337C24—222no—
338C24—222no—
339C24—442no—
340C24D4×D1111yescharacteristic
341C22×C4—24no—
342C22×C4—24no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—111no—
348C22×C4—112no—
349C22×C4—112no—
350C22×C4—118no—
351C22×C4—114no—
352C22×C4—111no—
353C22×C4—114no—
354C22×C4—114no—
355C22×C4—112no—
356C22×C4—112no—
357C22×C4—224no—
358C22×C4—2216no—
359C22×C4—2216no—
360C22×C4—224no—
361C22×C4—224no—
362C22×C4—224no—
363C22×C4—224no—
364C22×C4—222no—
365C22×C4—222no—
366C22×C4—444no—
367C22×C4—444no—
368C22×C4—444no—
369C22×C4—444no—
370C22×C4C2×C4×D1112yes—
371C22×C4D4×D1111yescharacteristic
372C22×C4D4×D1112yes—
373C22×C4C23×D1111yescharacteristic
374M16—448no—
375C2×C8—22no—
376C2×C8—24no—
377C2×C8—222no—
378C2×C8—224no—
379C4⋊C4—24no—
380C4⋊C4—22no—
381C4⋊C4—24no—
382C4⋊C4—114no—
383C4⋊C4—224no—
384C4⋊C4—222no—
385C4⋊C4—224no—
386C4⋊C4—444no—
387C4⋊C4C2×C4×D1114yes—
388C22⋊C4—42no—
389C22⋊C4—228no—
390C22⋊C4—228no—
391C22⋊C4—444no—
392C22⋊C4—442no—
393C42—228no—
394C42—228no—
395C11#2070211yescharacteristic, complemented, Sylow
396C23—22no—
397C23—22no—
398C23—112no—
399C23—114no—
400C23—112no—
401C23—228no—
402C23—221no—
403C23—221no—
404C23—222no—
405C23—221no—
406C23—221no—
407C23—222no—
408C23—228no—
409C23—222no—
410C23—444no—
411C23—448no—
412C23—448no—
413C23C22⋊C4×D1112yes—
414C23#6696412yes—
415C23#6696812yes—
416C23C2×D4×D1111yescharacteristic
417C2×C4—22no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—24no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—48no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—112no—
428C2×C4—114no—
429C2×C4—118no—
430C2×C4—118no—
431C2×C4—112no—
432C2×C4—228no—
433C2×C4—228no—
434C2×C4—228no—
435C2×C4—222no—
436C2×C4—224no—
437C2×C4—224no—
438C2×C4—224no—
439C2×C4—448no—
440C2×C4—444no—
441C2×C4—442no—
442C2×C4—442no—
443C2×C4—442no—
444C2×C4—888no—
445C2×C4C22⋊C4×D1112yes—
446C2×C4C22×C4×D1111yescharacteristic
447C2×C4C2×D4×D1111yescharacteristic
448C2×C4#41×D1114yes—
449C8—42no—
450C8—442no—
451C22—24no—
452C22—24no—
453C22—22no—
454C22—22no—
455C22—114no—
456C22—224no—
457C22—224no—
458C22—222no—
459C22—222no—
460C22—222no—
461C22—222no—
462C22—222no—
463C22—4416no—
464C22—442no—
465C22—442no—
466C22#1062238414yes—
467C22C2×C22⋊C4×D1111yescharacteristic
468C22D11×#12312yes—
469C22C2×#6696411yescharacteristic
470C22C2×#6696811yescharacteristic
471C22#1062330812yes—
472C4—22no—
473C4—44no—
474C4—82no—
475C4—114no—
476C4—222no—
477C4—444no—
478C4—882no—
479C4D11×#11712yes—
480C4D11×#12312yes—
481C2—24no—
482C2—224no—
483C2—442no—
484C2D11×#38111yescharacteristic
485C2C2×#1062238411yescharacteristic
486C2#1307713411yescharacteristic
487C2#1307855112yes—
488C2#1307855912yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1823C2
socleC23×C11C22×D4
prime radicalC24×D11D4
cosocleC22×C4×C11C24
hypercenter#1823D11
hypocenterC11#20702
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
4. #13068710C2semidirect
5. #13068707C2semidirect
6. #13068704C2semidirect
7. #13068702C2semidirect
8. #13068334C2semidirect
9. C11×#1823C2semidirect
19. C2×#66945C4semidirect
34. C11×#340C22semidirect
35. #10622189C22semidirect
36. #10622167C22semidirect
37. #10622167C22semidirect
54. C2×C11×C4⋊C4C2×C4semidirect
65. C2×C4⋊Dic11C2×C4semidirect
80. #66945C2×C4semidirect
159. #1823D11semidirect
243. #340C2×D11semidirect
306. C2×C4⋊C4C4×D11semidirect
395. C11#20702semidirect

Maximal subgroups

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

subgroupindex
C22×#669452
C2×#106223392
D11×#3802
#130687102
#130687072
#130687042
#130687022
#130683342
C11×#18232
#2070211