Finite Group Databasebeta

← #14763111

Subgroups — #14763111

Order 2816.

1474 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67000C211yesmaximal, characteristic
2C2×#10622332C211yesmaximal, characteristic, complemented
3#13071018C211yesmaximal, characteristic, complemented
4#13069545C214yesmaximal, complemented
5#13069429C214yesmaximal, complemented
6#13068551C211yesmaximal, characteristic, complemented
7#13068548C211yesmaximal, characteristic
8#13068546C211yesmaximal, characteristic
9C11×#1787C211yesmaximal, characteristic, complemented
10C23×Q8×C11C2211yescharacteristic
11C23×D44C2211yescharacteristic
12C2×#67000—21no—
13C2×#67000—21no—
14C2×#67000—24no—
15C2×#67000C418yescomplemented
16C2×#67000C2212yes—
17C2×#67000C2212yes—
18C22×(C2×D11)⋊C4—21no—
19C22×(C2×D11)⋊C4—21no—
20C22×C4×Dic11C2211yescharacteristic
21C2×#66930—21no—
22C2×C11×#103C2214yescomplemented
23C2×C11×C22⋊C8C2211yescharacteristic
24C11×#380C2211yescharacteristic
25C2×#66899C2214yescomplemented
26#10622825C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×#66885C2214yes—
29C2×#66879C2212yescomplemented
30C2×Dic11⋊C8C2212yescomplemented
31#10622589C2212yescomplemented
32C4⋊C4×Dic11C2212yescomplemented
33C2×#66873C2214yes—
34#10622555—21no—
35#10622332—24no—
36#10622263—21no—
37#10622262—21no—
38C24×D11—21no—
39C22×Q8×C11—22no—
40C22×Q8×C11—21no—
41C22×Q8×C11—44no—
42C22×Q8×C11C2×C414yes—
43C22×Q8×C11C2312yes—
44C23×C4×C11—21no—
45C23×C4×C11C2311yescharacteristic
46C23×Dic11D411yescharacteristic
47C23×Dic11D411yescharacteristic
48C22×D44—21no—
49C22×D44—22no—
50C22×D44—44no—
51C22×D44C2×C414yes—
52C22×D44C2312yes—
53C22×C8×C11C2312yes—
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C22⋊C4—21no—
56C2×C22⋊Dic11—21no—
57#67000—28no—
58#67000—28no—
59#67000—24no—
60#67000—24no—
61#67000C2×C418yes—
62#67000C2×C418yes—
63C2×(C2×D11)⋊C4—28no—
64C2×(C2×D11)⋊C4—28no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×C4⋊Dic11C2312yes—
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—22no—
72C2×C4×Dic11—22no—
73C2×C4×Dic11C2×C414yes—
74C2×C4×Dic11D411yescharacteristic
75C2×C4×Dic11D411yescharacteristic
76C2×C4×Dic11D414yes—
77C2×C4×Dic11C2311yescharacteristic
78C2×C4×Dic11C2311yescharacteristic
79C22×C11⋊C8C2312yes—
80#66930—44no—
81C11×#103—44no—
82C11×C22⋊C8—22no—
83C11×#95—21no—
84#66899—44no—
85C11⋊#95—21no—
86C11⋊#95—22no—
87C22⋊(C11⋊C8)—22no—
88#66885—44no—
89#66879—24no—
90Dic11⋊C8—24no—
91#66873—44no—
92#21808—111nomaximal, Sylow
93C24×C11C2×D411yescharacteristic
94C23×D11—24no—
95C23×D11—22no—
96C23×D11—44no—
97C23×D11—44no—
98C23×D11—42no—
99C23×D11—42no—
100C2×Q8×C11—24no—
101C2×Q8×C11—22no—
102C2×Q8×C11—24no—
103C2×Q8×C11—24no—
104C2×Q8×C11—48no—
105C2×Q8×C11—44no—
106C2×Q8×C11—48no—
107C2×Q8×C11C22×C414yes—
108C22×C4×C11—24no—
109C22×C4×C11—24no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—44no—
113C22×C4×C11C22×C412yes—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2411yescharacteristic
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—42no—
121C22×Dic11C22⋊C414yes—
122C22×Dic11C22⋊C414yes—
123C22×Dic11C2×D411yescharacteristic
124C22×Dic11C2×D411yescharacteristic
125C22×Dic11C2×D411yescharacteristic
126C22×Dic11C2×D411yescharacteristic
127C2×D44—24no—
128C2×D44—22no—
129C2×D44—24no—
130C2×D44—24no—
131C2×D44—48no—
132C2×D44—44no—
133C2×D44—48no—
134C2×D44C22×C414yes—
135C2×C8×C11—22no—
136C2×C8×C11—24no—
137C11×C4⋊C4—24no—
138C11×C22⋊C4—42no—
139C22⋊Dic11—42no—
140(C2×D11)⋊C4—28no—
141(C2×D11)⋊C4—28no—
142(C2×D11)⋊C4—28no—
143(C2×D11)⋊C4—28no—
144C4⋊Dic11—24no—
145Dic11⋊C4—44no—
146Dic11⋊C4—44no—
147C4×Dic11—44no—
148C4×Dic11C22⋊C414yes—
149C4×Dic11C22⋊C414yes—
150C4×Dic11C22×C412yes—
151C4×Dic11C22×C412yes—
152C4×Dic11C2×D412yes—
153C4×Dic11C2×D412yes—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—24no—
156C22×#124—111no—
157C2×#432—111no—
158#2285—111no—
159#1983—114no—
160#1959—114no—
161#1787—111no—
162#1787D1111yescharacteristic, complemented
163#1786—111no—
164#1786—111no—
165C23×C11—22no—
166C23×C11—22no—
167C23×C11C2×C22⋊C412yes—
168C23×C11AGL(1,ℤ/8)12yes—
169C23×C11#13712yes—
170C23×C11C22×D411yescharacteristic
171C22×D11—24no—
172C22×D11—48no—
173C22×D11—48no—
174C22×D11—44no—
175C22×D11—42no—
176C22×D11—42no—
177C22×D11—44no—
178C22×D11—48no—
179C22×D11—88no—
180C22×D11—88no—
181Q8×C11—24no—
182Q8×C11—24no—
183Q8×C11—48no—
184Q8×C11—44no—
185C2×C4×C11—22no—
186C2×C4×C11—24no—
187C2×C4×C11—24no—
188C2×C4×C11—24no—
189C2×C4×C11—48no—
190C2×C4×C11—44no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11C2×C22⋊C412yes—
195C2×C4×C11C23×C411yescharacteristic
196C2×C4×C11C22×D411yescharacteristic
197C2×C4×C11H(5,𝔽2)14yes—
198C2×Dic11—21no—
199C2×Dic11—21no—
200C2×Dic11—21no—
201C2×Dic11—21no—
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—28no—
205C2×Dic11—44no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11C2×C22⋊C412yes—
210C2×Dic11C2×C22⋊C412yes—
211C2×Dic11C2×C22⋊C412yes—
212C2×Dic11C2×C22⋊C412yes—
213D44—24no—
214D44—24no—
215D44—48no—
216D44—44no—
217C8×C11—42no—
218C11⋊C8—42no—
219C23×Q8C2×D1111yescharacteristic
220C23×D4—111no—
221C2×#124—112no—
222C2×#124—112no—
223C2×#124—118no—
224C2×#124—221no—
225C2×#124—221no—
226C2×#124—224no—
227C2×#117—221no—
228C22×C22⋊C4—221no—
229C22×C22⋊C4—221no—
230C22×C42—111no—
231#432—224no—
232C2×C4⋊C8—112no—
233C2×#103—114no—
234C2×#103C2×D1114yescomplemented
235C2×#102—114no—
236C2×#102—114no—
237C2×C22⋊C8—111no—
238C2×C22⋊C8C2×D1111yescharacteristic
239C2×#97—112no—
240#384—112no—
241#382—221no—
242#380—111no—
243#380—221no—
244#380C2×D1111yescharacteristic
245C4×C4⋊C4—112no—
246C4×C4⋊C4—221no—
247C22×C11—22no—
248C22×C11—22no—
249C22×C11—24no—
250C22×C11—24no—
251C22×C11#41714yes—
252C22×C11C22×C22⋊C411yescharacteristic
253C22×C11#53512yes—
254C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
255C22×C11C2×#13711yescharacteristic
256C22×C11#57512yes—
257C2×D11—44no—
258C2×D11—44no—
259C2×D11—44no—
260C2×D11—816no—
261C2×D11—84no—
262C2×D11—84no—
263C4×C11—22no—
264C4×C11—44no—
265C4×C11—82no—
266C4×C11#51812yes—
267C4×C11#53512yes—
268Dic11—22no—
269Dic11—22no—
270Dic11—22no—
271Dic11—22no—
272Dic11—82no—
273C25—221no—
274C22×Q8—22no—
275C22×Q8—21no—
276C22×Q8—44no—
277C22×Q8C4×D1114yes—
278C22×Q8C22×D1112yes—
279C22×D4—114no—
280C22×D4—112no—
281C22×D4—221no—
282C22×D4—222no—
283C22×D4—444no—
284C23×C4—21no—
285C23×C4—111no—
286C23×C4—111no—
287C23×C4C22×D1111yescharacteristic
288C22×C8—112no—
289C22×C8C22×D1112yes—
290#124—118no—
291#124—118no—
292#124—228no—
293#124—228no—
294#124—224no—
295#124—224no—
296#117—444no—
297C2×C4⋊C4—112no—
298C2×C4⋊C4—222no—
299C2×C4⋊C4—222no—
300C2×C4⋊C4C22×D1112yes—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—228no—
303C2×C22⋊C4—228no—
304C2×C22⋊C4—222no—
305C2×C22⋊C4—222no—
306C2×C22⋊C4—222no—
307C2×C22⋊C4—222no—
308C2×C22⋊C4—221no—
309C2×C42—114no—
310C2×C42—111no—
311C2×C42—111no—
312C2×C42—114no—
313C2×C42—111no—
314C2×C42—111no—
315C2×C42—222no—
316C4⋊C8—224no—
317#103—44no—
318#103—444no—
319#102—444no—
320#102—444no—
321C22⋊C8—22no—
322C22⋊C8—222no—
323#97—224no—
324#95—21no—
325#95—222no—
326#95—221no—
327C2×C11—24no—
328C2×C11#230911yescharacteristic
329C2×C11C2×#41711yescharacteristic
330C2×C11#289611yescharacteristic
331C2×C11#321312yes—
332C2×C11#321512yes—
333D11—84no—
334C24—224no—
335C24—222no—
336C24—444no—
337C24—444no—
338C24—442no—
339C24—442no—
340C24D4×D1111yescharacteristic
341C2×Q8—24no—
342C2×Q8—22no—
343C2×Q8—24no—
344C2×Q8—24no—
345C2×Q8—48no—
346C2×Q8—44no—
347C2×Q8—48no—
348C2×Q8C2×C4×D1114yes—
349C2×D4—114no—
350C2×D4—224no—
351C2×D4—222no—
352C2×D4—224no—
353C2×D4—224no—
354C2×D4—448no—
355C2×D4—444no—
356C2×D4—448no—
357C22×C4—24no—
358C22×C4—24no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—44no—
362C22×C4—114no—
363C22×C4—111no—
364C22×C4—111no—
365C22×C4—111no—
366C22×C4—111no—
367C22×C4—114no—
368C22×C4—222no—
369C22×C4—222no—
370C22×C4—222no—
371C22×C4—442no—
372C22×C4C2×C4×D1112yes—
373C22×C4D4×D1111yescharacteristic
374C22×C4D4×D1112yes—
375C22×C4C23×D1111yescharacteristic
376C2×C8—22no—
377C2×C8—24no—
378C2×C8—222no—
379C2×C8—224no—
380C4⋊C4—24no—
381C4⋊C4—224no—
382C4⋊C4—444no—
383C4⋊C4—444no—
384C22⋊C4—42no—
385C22⋊C4—228no—
386C22⋊C4—228no—
387C22⋊C4—228no—
388C22⋊C4—228no—
389C22⋊C4—442no—
390C42—114no—
391C42—114no—
392C42—112no—
393C42—112no—
394C42—112no—
395C42—112no—
396C42—444no—
397C11#2180811yescharacteristic, complemented, Sylow
398C23—22no—
399C23—22no—
400C23—224no—
401C23—448no—
402C23—448no—
403C23—442no—
404C23—442no—
405C23—444no—
406C23—444no—
407C23—448no—
408C23—888no—
409C23—888no—
410C23C22⋊C4×D1112yes—
411C23#6696712yes—
412C23#6697112yes—
413C23C2×D4×D1111yescharacteristic
414Q8—24no—
415Q8—24no—
416Q8—48no—
417Q8—44no—
418D4—224no—
419D4—224no—
420D4—448no—
421D4—444no—
422C2×C4—22no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—48no—
427C2×C4—44no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—112no—
432C2×C4—112no—
433C2×C4—112no—
434C2×C4—112no—
435C2×C4—221no—
436C2×C4—221no—
437C2×C4—221no—
438C2×C4—221no—
439C2×C4—222no—
440C2×C4—222no—
441C2×C4—228no—
442C2×C4—444no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4C22⋊C4×D1112yes—
447C2×C4C22×C4×D1111yescharacteristic
448C2×C4C2×D4×D1111yescharacteristic
449C2×C4#6703714yes—
450C8—42no—
451C8—442no—
452C22—24no—
453C22—24no—
454C22—22no—
455C22—22no—
456C22—444no—
457C22—444no—
458C22—444no—
459C22—8816no—
460C22—884no—
461C22—884no—
462C22#1062241614yes—
463C22C2×C22⋊C4×D1111yescharacteristic
464C22#1062312312yes—
465C22C2×#6696711yescharacteristic
466C22C2×#6697111yescharacteristic
467C22#1062330812yes—
468C4—22no—
469C4—44no—
470C4—82no—
471C4—222no—
472C4—222no—
473C4—222no—
474C4—222no—
475C4—882no—
476C4#1062301712yes—
477C4#1062312312yes—
478C2—24no—
479C2—884no—
480C2#1307119711yescharacteristic
481C2C2×#1062241611yescharacteristic
482C2#1307713411yescharacteristic
483C2#1307960212yes—
484C2#1307961812yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1787C2
socleC23×C11C22×D4
prime radicalC23×D44C22
cosocleC22×C4×C11C24
hypercenter#1787D11
hypocenterC11#21808
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
2. C2×#10622332C2semidirect
3. #13071018C2semidirect
4. #13069545C2semidirect
5. #13069429C2semidirect
6. #13068551C2semidirect
9. C11×#1787C2semidirect
15. C2×#67000C4semidirect
22. C2×C11×#103C22semidirect
25. C2×#66899C22semidirect
29. C2×#66879C22semidirect
30. C2×Dic11⋊C8C22semidirect
31. #10622589C22semidirect
32. C4⋊C4×Dic11C22semidirect
162. #1787D11semidirect
234. C2×#103C2×D11semidirect
397. C11#21808semidirect

Maximal subgroups

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

subgroupindex
C22×#670002
C2×#106223322
#130710182
#130695452
#130694292
#130685512
#130685482
#130685462
C11×#17872
#2180811