Finite Group Databasebeta

← #14760469

Subgroups — #14760469

Order 2816.

1170 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
1C2×#10622748C211yesmaximal, characteristic
2C2×#10622482C211yesmaximal, characteristic, complemented
3C2×M16×Dic11C211yesmaximal, characteristic, complemented
4#13071122C212yesmaximal, complemented
5#13069480C211yesmaximal, characteristic, complemented
6#13069342C211yesmaximal, characteristic, complemented
7#13069297C212yesmaximal, complemented
8#13069052C212yesmaximal, complemented
9#13068515C211yesmaximal, characteristic, complemented
10#13068440C212yesmaximal, complemented
11C11×#1809C211yesmaximal, characteristic, complemented
12C22×C11×M16C2211yescharacteristic
13C2×#66983C2212yes—
14C22×C4×Dic11C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C22×D88C2211yescharacteristic
17C2×#66946C2212yes—
18C2×(C22⋊D11)⋊C4—22no—
19C2×C11×#107C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C11×#380C2212yes—
22#10622748C418yescomplemented
23M16×Dic11—24no—
24C2×#66885C2212yes—
25C2×#66881C2211yescharacteristic
26C2×#66879C2211yescharacteristic
27C2×#66879C2211yescharacteristic
28C2×C8×Dic11C2211yescharacteristic
29C2×C8×Dic11C2211yescharacteristic
30#10622601C2212yes—
31C4⋊C4×Dic11C2212yes—
32#10622586C2212yes—
33C2×#66873C2212yes—
34C2×#66873C2212yes—
35#10622571—22no—
36#10622482—24no—
37#10622282—22no—
38#10622279—22no—
39C11×#340C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C23×C4×C11C2311yescharacteristic
43C22×C22⋊D11—22no—
44C23×Dic11D412yes—
45C22×D44C2312yes—
46C22×C4×D11—22no—
47C2×C11×M16—22no—
48C2×C11×M16—22no—
49C2×C11×M16C2×C414yescomplemented
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C22⋊C4—22no—
55#66983—24no—
56#66983C2×C418yescomplemented
57C2×(C2×D11)⋊C4—22no—
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×C4⋊Dic11C2312yes—
62C2×Dic11⋊C4—22no—
63C2×C4×Dic11—22no—
64C2×C4×Dic11—22no—
65C2×C4×Dic11—22no—
66C2×C4×Dic11D412yes—
67C2×C4×Dic11C2311yescharacteristic
68C2×C4×Dic11C2311yescharacteristic
69C2×#4318—22no—
70C2×#4318—22no—
71C2×#4318—22no—
72C22×C11⋊C8C2311yescharacteristic
73C22×C11⋊C8C2311yescharacteristic
74C2×D88—22no—
75C2×D88—22no—
76C2×D88C2×C414yescomplemented
77#66946—24no—
78#66946—24no—
79(C22⋊D11)⋊C4—48no—
80C11×#107—22no—
81C11×#106—22no—
82C11×#95—22no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85#66885C2×C418yescomplemented
86#66881C2×C414yescomplemented
87#66879—22no—
88#66879D414yescomplemented
89C8×Dic11—22no—
90C8×Dic11—22no—
91#66873—24no—
92#66873—24no—
93#21538—111nomaximal, Sylow
94C24×C11C2×D411yescharacteristic
95C23×D11—22no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11C22×C412yes—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11#4112yes—
105C22×C4×C11C2411yescharacteristic
106C2×C22⋊D11—28no—
107C2×C22⋊D11—44no—
108C2×C22⋊D11—44no—
109C22×Dic11—24no—
110C22×Dic11—24no—
111C22×Dic11—22no—
112C22×Dic11—42no—
113C22×Dic11C2×D412yes—
114C22×Dic11C2×D412yes—
115C2×D44—22no—
116C2×D44—22no—
117C2×D44—22no—
118C2×D44—22no—
119C2×D44—22no—
120C2×D44C22×C414yes—
121C2×C4×D11—44no—
122C2×C4×D11—44no—
123C2×C4×D11—44no—
124C11×M16—28no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11C22×C412yes—
128C2×C8×C11C22×C412yes—
129C2×C8×C11C2×D412yes—
130C2×C8×C11#4112yes—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C22⋊C4—44no—
136(C2×D11)⋊C4—28no—
137(C2×D11)⋊C4—44no—
138(C2×D11)⋊C4—44no—
139(C2×D11)⋊C4—44no—
140C4⋊Dic11—22no—
141C4⋊Dic11C22×C414yes—
142Dic11⋊C4—44no—
143C4×Dic11—24no—
144C4×Dic11—21no—
145C4×Dic11—21no—
146C4×Dic11—44no—
147C4×Dic11C2×D412yes—
148C4×Dic11#4112yes—
149#4318—28no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—21no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8C2×D412yes—
155C2×C11⋊C8#4112yes—
156D88—28no—
157C2×#469—111no—
158C2×#442—111no—
159C2×C4×M16—111no—
160C4×#121—112no—
161#1970—111no—
162#1941—111no—
163#1934—112no—
164#1895—112no—
165#1809D1111yescharacteristic, complemented
166#1776—111no—
167#1762—112no—
168C23×C11—21no—
169C23×C11—21no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11C4×D412yes—
173C23×C11C22×D411yescharacteristic
174C22×D11—24no—
175C22×D11—42no—
176C22×D11—42no—
177C22×D11—42no—
178C22×D11—42no—
179C22×D11—42no—
180C22×D11—42no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11C4×D412yes—
194C2×C4×C11C23×C411yescharacteristic
195C2×C4×C11C22×D411yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C22⋊D11—416no—
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—22no—
205C2×Dic11—24no—
206C2×Dic11—48no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11#12114yes—
210C2×Dic11AGL(1,ℤ/8)14yes—
211D44—24no—
212D44—24no—
213D44—42no—
214D44—42no—
215C4×D11—88no—
216C8×C11—22no—
217C8×C11C4×D414yescomplemented
218C11⋊C8—22no—
219C11⋊C8—22no—
220C22×D8—111no—
221C22×M16—111no—
222C22×M16C2×D1111yescharacteristic
223C2×#121—112no—
224C2×C4×D4—112no—
225C2×C4×D4—222no—
226C22×C42—111no—
227#469—118no—
228#442—224no—
229C2×#107C2×D1111yescharacteristic
230C2×#106—111no—
231C2×#106C2×D1111yescharacteristic
232C2×#102—112no—
233C2×#102—112no—
234C2×#102—112no—
235C4×M16—224no—
236C2×#97—111no—
237C2×#97—111no—
238C2×C4×C8—111no—
239C2×C4×C8—111no—
240#390—112no—
241#389—112no—
242#388—222no—
243#386—222no—
244#380C2×D1112yes—
245C4×C4⋊C4—112no—
246C4×C22⋊C4—222no—
247#340—112no—
248#340—112no—
249#340C2×D1112yes—
250C22×C11—24no—
251C22×C11—22no—
252C22×C11—41no—
253C22×C11—41no—
254C22×C11—42no—
255C22×C11C2×C4×D411yescharacteristic
256C22×C11C2×#12111yescharacteristic
257C22×C11#53211yescharacteristic
258C22×C11C2×AGL(1,ℤ/8)12yes—
259C22×C11#57512yes—
260C2×D11—44no—
261C2×D11—44no—
262C2×D11—44no—
263C2×D11—82no—
264C2×D11—82no—
265C2×D11—82no—
266C2×D11—82no—
267C4×C11—22no—
268C4×C11—82no—
269C4×C11—82no—
270C4×C11C2×C4×D411yescharacteristic
271C4×C11C4×#4111yescharacteristic
272C4×C11#52511yescharacteristic
273C4×C11#52911yescharacteristic
274Dic11—24no—
275Dic11—24no—
276Dic11—44no—
277C22×D4—112no—
278C22×D4—222no—
279C23×C4—112no—
280C23×C4—222no—
281C23×C4C22×D1111yescharacteristic
282C2×D8—114no—
283C2×D8—222no—
284C2×D8—222no—
285C2×M16—22no—
286C2×M16—22no—
287C2×M16—222no—
288C2×M16—222no—
289C2×M16—222no—
290C2×M16C4×D1114yescomplemented
291C22×C8—111no—
292C22×C8—111no—
293C22×C8C22×D1111yescharacteristic
294C22×C8C22×D1111yescharacteristic
295#121—118no—
296#121—224no—
297C4×D4—224no—
298C4×D4—224no—
299C4×D4—448no—
300C2×C4⋊C4—112no—
301C2×C4⋊C4—222no—
302C2×C4⋊C4C22×D1112yes—
303C2×C4⋊C4C22×D1112yes—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—222no—
306C2×C22⋊C4—222no—
307C2×C22⋊C4—222no—
308C2×C22⋊C4—222no—
309C2×C42—111no—
310C2×C42—112no—
311C2×C42—111no—
312C2×C42—222no—
313C2×C42—222no—
314C2×C42—222no—
315#107—22no—
316#106—22no—
317#106—114no—
318#102—118no—
319#102—224no—
320#102—224no—
321#97—114no—
322#97—222no—
323C4×C8—222no—
324C4×C8—222no—
325#95—22no—
326#95—222no—
327#95—222no—
328C2×C11—42no—
329C2×C11C4×#12111yescharacteristic
330C2×C11C4×AGL(1,ℤ/8)12yes—
331C2×C11#305512yes—
332C2×C11#318311yescharacteristic
333C2×C11#318411yescharacteristic
334D11—84no—
335C24—222no—
336C24D4×D1111yescharacteristic
337C2×D4—114no—
338C2×D4—228no—
339C2×D4—222no—
340C2×D4—222no—
341C2×D4—222no—
342C2×D4—222no—
343C2×D4—222no—
344C2×D4—444no—
345C2×D4—444no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—112no—
353C22×C4—112no—
354C22×C4—224no—
355C22×C4—224no—
356C22×C4—222no—
357C22×C4—444no—
358C22×C4—444no—
359C22×C4—444no—
360C22×C4—442no—
361C22×C4C2×C4×D1112yes—
362C22×C4D4×D1111yescharacteristic
363C22×C4#434312yes—
364C22×C4C23×D1111yescharacteristic
365D8—228no—
366M16—28no—
367M16—228no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—112no—
371C2×C8—112no—
372C2×C8—221no—
373C2×C8—221no—
374C2×C8—221no—
375C2×C8—221no—
376C2×C8C2×C4×D1112yes—
377C2×C8C2×C4×D1112yes—
378C2×C8D4×D1112yes—
379C2×C8#434112yes—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—114no—
385C4⋊C4—222no—
386C4⋊C4—444no—
387C22⋊C4—44no—
388C22⋊C4—228no—
389C22⋊C4—444no—
390C22⋊C4—444no—
391C22⋊C4—444no—
392C42—112no—
393C42—112no—
394C42—224no—
395C42—221no—
396C42—221no—
397C42—444no—
398C11#2153811yescharacteristic, complemented, Sylow
399C23—22no—
400C23—22no—
401C23—21no—
402C23—21no—
403C23—224no—
404C23—442no—
405C23—442no—
406C23—442no—
407C23—442no—
408C23—442no—
409C23—442no—
410C23#6694612yes—
411C23C2×D4×D1111yescharacteristic
412D4—224no—
413D4—224no—
414D4—4416no—
415D4—442no—
416D4—442no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—114no—
430C2×C4—114no—
431C2×C4—222no—
432C2×C4—222no—
433C2×C4—222no—
434C2×C4—222no—
435C2×C4—224no—
436C2×C4—448no—
437C2×C4—442no—
438C2×C4—442no—
439C2×C4—888no—
440C2×C4#6694612yes—
441C2×C4C22×C4×D1111yescharacteristic
442C2×C4C2×D4×D1111yescharacteristic
443C2×C4C2×#434111yescharacteristic
444C2×C4C2×#434311yescharacteristic
445C2×C4#41×D1111yescharacteristic
446C2×C4#41×D1111yescharacteristic
447C8—22no—
448C8—222no—
449C8—222no—
450C8(C22⋊D11)⋊C414yescomplemented
451C22—22no—
452C22—24no—
453C22—41no—
454C22—41no—
455C22—42no—
456C22—444no—
457C22—444no—
458C22—444no—
459C22—882no—
460C22—882no—
461C22—882no—
462C22—882no—
463C22C2×#6694611yescharacteristic
464C22#1062312711yescharacteristic
465C22D11×#12111yescharacteristic
466C22D11×AGL(1,ℤ/8)12yes—
467C22#1062330812yes—
468C4—22no—
469C4—82no—
470C4—82no—
471C4—224no—
472C4—224no—
473C4—444no—
474C4C2×(C22⋊D11)⋊C411yescharacteristic
475C4#1062305311yescharacteristic
476C4#1062315511yescharacteristic
477C4#1062315811yescharacteristic
478C2—42no—
479C2—884no—
480C2#1307112211yescharacteristic
481C2#1307742312yes—
482C2#1307823012yes—
483C2#1307934611yescharacteristic
484C2#1307934911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1809C2
socleC23×C11C22×D4
prime radicalC2×#10622748C2
cosocleC22×C4×C11C24
hypercenter#1809D11
hypocenterC11#21538
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
2. C2×#10622482C2semidirect
3. C2×M16×Dic11C2semidirect
4. #13071122C2semidirect
5. #13069480C2semidirect
6. #13069342C2semidirect
7. #13069297C2semidirect
8. #13069052C2semidirect
9. #13068515C2semidirect
10. #13068440C2semidirect
11. C11×#1809C2semidirect
22. #10622748C4semidirect
49. C2×C11×M16C2×C4semidirect
56. #66983C2×C4semidirect
76. C2×D88C2×C4semidirect
85. #66885C2×C4semidirect
86. #66881C2×C4semidirect
88. #66879D4semidirect
165. #1809D11semidirect
217. C8×C11C4×D4semidirect
290. C2×M16C4×D11semidirect
398. C11#21538semidirect
450. C8(C22⋊D11)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#106227482
C2×#106224822
C2×M16×Dic112
#130711222
#130694802
#130693422
#130692972
#130690522
#130685152
#130684402
C11×#18092
#2153811