Finite Group Databasebeta

← #14760476

Subgroups — #14760476

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×#10622324C211yesmaximal, characteristic, complemented
3C4×#66983C212yesmaximal, complemented
4#13069482C211yesmaximal, characteristic, complemented
5#13069344C211yesmaximal, characteristic, complemented
6#13069299C212yesmaximal, complemented
7#13069054C212yesmaximal, complemented
8#13068649C211yesmaximal, characteristic, complemented
9#13068513C211yesmaximal, characteristic, complemented
10#13068442C212yesmaximal, complemented
11C2×C4×C11×M16C211yesmaximal, characteristic, complemented
12C22×C11×M16C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C2×#66983C2212yes—
16C2×C4×C22⋊D11—22no—
17C22×D88C2211yescharacteristic
18C2×C4×D44C2212yes—
19C4×C11×M16—24no—
20C2×C11×#97C2211yescharacteristic
21C2×C11×#97C2211yescharacteristic
22C2×C4×C8×C11C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24#10622826—22no—
25#10622825C2212yes—
26#10622748C418yescomplemented
27C2×#66885C2212yes—
28C2×#66885C2212yes—
29C2×#66885C2212yes—
30C2×#66882C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33#10622553—22no—
34#10622552C2212yes—
35C4×(C2×D11)⋊C4—22no—
36C4×C4⋊Dic11C2212yes—
37#10622541C2212yes—
38#10622324—24no—
39#10622189C2212yes—
40#10622189C2212yes—
41#10622189C2212yes—
42C23×C4×C11D412yes—
43C23×C4×C11C2311yescharacteristic
44C22×C22⋊D11—22no—
45C22×D44C2312yes—
46C22×C4×D11—22no—
47C2×C11×M16—22no—
48C2×C11×M16—22no—
49C2×C11×M16—22no—
50C2×C11×M16—22no—
51C2×C11×M16—22no—
52C2×C11×M16C2×C414yescomplemented
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C2×C42×C11—22no—
58C2×C42×C11—22no—
59C2×C42×C11D412yes—
60C2×C42×C11C2311yescharacteristic
61C2×C42×C11C2311yescharacteristic
62C2×C22⋊Dic11—22no—
63#66983—24no—
64#66983C2×C418yescomplemented
65C4×C22⋊D11—48no—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×C4⋊Dic11C2312yes—
71C2×C4⋊Dic11C2312yes—
72C2×C4⋊Dic11C2312yes—
73C2×Dic11⋊C4—22no—
74C2×C4×Dic11—22no—
75C2×D88—22no—
76C2×D88—22no—
77C2×D88C2×C414yescomplemented
78C4×D44—24no—
79C4×D44—24no—
80C11×#97—22no—
81C11×#97D414yescomplemented
82C4×C8×C11—22no—
83C4×C8×C11—22no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87#66885—24no—
88#66885—24no—
89#66885C2×C418yescomplemented
90#66882—22no—
91#66881—22no—
92#66881C2×C414yescomplemented
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—24no—
101C22×C4×C11—24no—
102C22×C4×C11—42no—
103C22×C4×C11C22×C412yes—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D412yes—
107C22×C4×C11#4112yes—
108C22×C4×C11C2411yescharacteristic
109C2×C22⋊D11—28no—
110C2×C22⋊D11—44no—
111C2×C22⋊D11—44no—
112C22×Dic11—22no—
113C22×Dic11—22no—
114C22×Dic11—22no—
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—
125C11×M16—28no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11C22×C412yes—
133C2×C8×C11C22×C412yes—
134C2×C8×C11C2×D412yes—
135C2×C8×C11C2×D412yes—
136C2×C8×C11#4112yes—
137C2×C8×C11#4112yes—
138C42×C11—24no—
139C42×C11—21no—
140C42×C11—21no—
141C42×C11C2×D412yes—
142C42×C11#4112yes—
143C22⋊Dic11—44no—
144(C2×D11)⋊C4—28no—
145(C2×D11)⋊C4—44no—
146(C2×D11)⋊C4—44no—
147(C2×D11)⋊C4—44no—
148C4⋊Dic11—22no—
149C4⋊Dic11—22no—
150C4⋊Dic11—22no—
151C4⋊Dic11—22no—
152C4⋊Dic11—22no—
153C4⋊Dic11C22×C414yes—
154Dic11⋊C4—44no—
155C4×Dic11—44no—
156D88—28no—
157C2×#469—111no—
158C2×#442—111no—
159C2×C4×M16D1111yescharacteristic, complemented
160C4×#121—112no—
161#1970—111no—
162#1941—111no—
163#1934—112no—
164#1895—112no—
165#1809—111no—
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—22no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—48no—
192C2×C4×C11C4×D412yes—
193C2×C4×C11#12114yes—
194C2×C4×C11AGL(1,ℤ/8)14yes—
195C2×C4×C11C23×C411yescharacteristic
196C2×C4×C11C22×D411yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C22⋊D11—416no—
202C2×Dic11—24no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211D44—24no—
212D44—24no—
213D44—42no—
214D44—42no—
215C4×D11—88no—
216C8×C11—22no—
217C8×C11—22no—
218C8×C11—22no—
219C8×C11C4×D414yescomplemented
220C22×D8—111no—
221C22×M16C2×D1111yescharacteristic
222C22×M16C2×D1111yescharacteristic
223C2×#121—112no—
224C2×C4×D4—112no—
225C2×C4×D4—222no—
226C22×C42C2×D1111yescharacteristic
227#469—118no—
228#442—224no—
229C2×#107—111no—
230C2×#106—111no—
231C2×#106—111no—
232C2×#102—112no—
233C2×#102—112no—
234C2×#102—112no—
235C4×M16—24no—
236C2×#97C2×D1111yescharacteristic
237C2×#97C2×D1111yescharacteristic
238C2×C4×C8C2×D1111yescharacteristic
239C2×C4×C8C2×D1111yescharacteristic
240#390—112no—
241#389—112no—
242#388—222no—
243#386—222no—
244#380—112no—
245C4×C4⋊C4—112no—
246C4×C22⋊C4—222no—
247#340—112no—
248#340—112no—
249#340—112no—
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—24no—
268C4×C11—24no—
269C4×C11—22no—
270C4×C11C2×C4×D411yescharacteristic
271C4×C11C4×#4111yescharacteristic
272C4×C11#52511yescharacteristic
273C4×C11#52911yescharacteristic
274Dic11—44no—
275Dic11—82no—
276Dic11—82no—
277C22×D4—112no—
278C22×D4—222no—
279C23×C4—222no—
280C23×C4D4412yes—
281C23×C4C22×D1111yescharacteristic
282C2×D8—114no—
283C2×D8—222no—
284C2×D8—222no—
285C2×M16—22no—
286C2×M16—22no—
287C2×M16—22no—
288C2×M16—22no—
289C2×M16—22no—
290C2×M16C4×D1114yescomplemented
291C22×C8C22×D1111yescharacteristic
292C22×C8C22×D1111yescharacteristic
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—112no—
302C2×C4⋊C4—112no—
303C2×C4⋊C4—222no—
304C2×C22⋊C4—222no—
305C2×C22⋊C4—222no—
306C2×C22⋊C4—222no—
307C2×C22⋊C4—222no—
308C2×C22⋊C4—222no—
309C2×C42—22no—
310C2×C42—22no—
311C2×C42—222no—
312C2×C42D4412yes—
313C2×C42C22×D1111yescharacteristic
314C2×C42C22×D1111yescharacteristic
315#107—222no—
316#106—114no—
317#106—222no—
318#102—118no—
319#102—224no—
320#102—224no—
321#97—22no—
322#97C22⋊D1114yescomplemented
323C4×C8—22no—
324C4×C8—22no—
325#95—222no—
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—
336C24C2×D4411yescharacteristic
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—24no—
351C22×C4—24no—
352C22×C4—42no—
353C22×C4—222no—
354C22×C4—222no—
355C22×C4—222no—
356C22×C4—444no—
357C22×C4—444no—
358C22×C4—444no—
359C22×C4C2×C4×D1112yes—
360C22×C4C2×D4411yescharacteristic
361C22×C4C2×D4412yes—
362C22×C4C2×D4412yes—
363C22×C4#433912yes—
364C22×C4C23×D1111yescharacteristic
365D8—228no—
366M16—28no—
367M16—28no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—21no—
374C2×C8C2×C4×D1112yes—
375C2×C8C2×C4×D1112yes—
376C2×C8#433912yes—
377C2×C8#433912yes—
378C2×C8C2×C22⋊D1112yes—
379C2×C8C2×C22⋊D1112yes—
380C4⋊C4—114no—
381C4⋊C4—222no—
382C4⋊C4—222no—
383C4⋊C4—222no—
384C4⋊C4—222no—
385C4⋊C4—222no—
386C4⋊C4—444no—
387C22⋊C4—228no—
388C22⋊C4—444no—
389C22⋊C4—444no—
390C22⋊C4—444no—
391C22⋊C4—444no—
392C42—24no—
393C42—21no—
394C42—21no—
395C42—444no—
396C42#433912yes—
397C42C2×C22⋊D1112yes—
398C11#2153811yescharacteristic, complemented, Sylow
399C23—21no—
400C23—22no—
401C23—22no—
402C23—21no—
403C23—224no—
404C23—442no—
405C23—442no—
406C23—442no—
407C23—442no—
408C23—442no—
409C23—442no—
410C23C4×D4412yes—
411C23C22×D4411yescharacteristic
412D4—224no—
413D4—224no—
414D4—4416no—
415D4—442no—
416D4—442no—
417C2×C4—21no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—21no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—48no—
428C2×C4—224no—
429C2×C4—442no—
430C2×C4—442no—
431C2×C4—442no—
432C2×C4—442no—
433C2×C4—442no—
434C2×C4—442no—
435C2×C4—442no—
436C2×C4—442no—
437C2×C4—888no—
438C2×C4C4×D4412yes—
439C2×C4#6696114yes—
440C2×C4#6698314yes—
441C2×C4C22×C4×D1111yescharacteristic
442C2×C4C2×#433911yescharacteristic
443C2×C4C2×#433911yescharacteristic
444C2×C4C2×#433911yescharacteristic
445C2×C4C2×#433911yescharacteristic
446C2×C4C22×C22⋊D1111yescharacteristic
447C8—22no—
448C8—22no—
449C8—22no—
450C8C4×C22⋊D1114yescomplemented
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×C4×D4411yescharacteristic
464C22#1062300811yescharacteristic
465C22C2×#6696112yes—
466C22#1062327912yes—
467C22C2×#6698311yescharacteristic
468C4—22no—
469C4—24no—
470C4—24no—
471C4—444no—
472C4—882no—
473C4—882no—
474C4C4×#433911yescharacteristic
475C4#1062301011yescharacteristic
476C4C2×C4×C22⋊D1111yescharacteristic
477C4#1062332211yescharacteristic
478C2—42no—
479C2—884no—
480C2C4×#6698311yescharacteristic
481C2C4×#6696112yes—
482C2#1307823512yes—
483C2#1307934511yescharacteristic
484C2#1307935411yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C4×C11×M16C2
socleC23×C11C22×D4
prime radicalC2×#10622748C2
cosocleC22×C4×C11C24
hypercenterC2×C4×M16D11
hypocenterC11#21538
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×C4×M16

Complements

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

NH ≅ G/Ntype
2. C2×#10622324C2semidirect
3. C4×#66983C2semidirect
4. #13069482C2semidirect
5. #13069344C2semidirect
6. #13069299C2semidirect
7. #13069054C2semidirect
8. #13068649C2semidirect
9. #13068513C2semidirect
10. #13068442C2semidirect
11. C2×C4×C11×M16C2semidirect
26. #10622748C4semidirect
52. C2×C11×M16C2×C4semidirect
64. #66983C2×C4semidirect
77. C2×D88C2×C4semidirect
81. C11×#97D4semidirect
89. #66885C2×C4semidirect
92. #66881C2×C4semidirect
159. C2×C4×M16D11semidirect
219. C8×C11C4×D4semidirect
290. C2×M16C4×D11semidirect
322. #97C22⋊D11semidirect
398. C11#21538semidirect
450. C8C4×C22⋊D11semidirect

Maximal subgroups

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

subgroupindex
C2×#106227482
C2×#106223242
C4×#669832
#130694822
#130693442
#130692992
#130690542
#130686492
#130685132
#130684422
C2×C4×C11×M162
#2153811