Finite Group Databasebeta

← #14760448

Subgroups — #14760448

Order 2816.

1066 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622772C211yesmaximal, characteristic
2C2×#10622302C211yesmaximal, characteristic, complemented
3#13071303C212yesmaximal, complemented
4#13069493C211yesmaximal, characteristic, complemented
5#13069357C211yesmaximal, characteristic, complemented
6#13069296C212yesmaximal, complemented
7#13069041C212yesmaximal, complemented
8#13068650C211yesmaximal, characteristic, complemented
9C4×#66881C211yesmaximal, characteristic, complemented
10#13068441C212yesmaximal, complemented
11C2×C4×C11×D8C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C2×C4×D4×C11C2212yes—
14C2×#66991C2212yes—
15C22×#4313C2211yescharacteristic
16C22×C8×D11C2211yescharacteristic
17C2×#66925C2211yescharacteristic
18C4×C11×D8—24no—
19C2×C11×#107C2211yescharacteristic
20C2×C11×#102C2212yes—
21C2×C4×C8×C11C2211yescharacteristic
22#10622834C2212yes—
23C2×#66896C2212yes—
24C2×#66896C2212yes—
25#10622826—22no—
26#10622823—22no—
27#10622772C418yescomplemented
28C2×#66881C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30C2×#66879C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32#10622600C2212yes—
33#10622586C2212yes—
34#10622570—22no—
35#10622558—22no—
36C4×C4⋊Dic11C2212yes—
37C2×#66867C2211yescharacteristic
38#10622302—24no—
39#10622189C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C22×D4×C11C2312yes—
43C23×C4×C11—22no—
44C22×C22⋊D11—22no—
45C22×C4×D11C2311yescharacteristic
46C2×C11×D8—22no—
47C2×C11×D8—22no—
48C2×C11×D8C2×C414yes—
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C4×D4×C11—24no—
52C4×D4×C11—24no—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C22⋊C4—22no—
55C2×C42×C11C2311yescharacteristic
56C2×C22⋊Dic11—22no—
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11—22no—
59#66991—24no—
60#66991C2×C418yescomplemented
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4D411yescharacteristic
63C2×(C2×D11)⋊C4D411yescharacteristic
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2312yes—
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4D411yescharacteristic
68C2×Dic11⋊C4D411yescharacteristic
69C2×C4×Dic11—22no—
70C2×C4×Dic11C2311yescharacteristic
71C22×C11⋊C8C2311yescharacteristic
72C22×C11⋊C8C2311yescharacteristic
73C2×#4313—22no—
74C2×#4313—22no—
75C2×#4313C2×C414yescomplemented
76C2×C8×D11—22no—
77C2×C8×D11—22no—
78C2×C8×D11—22no—
79#66925—22no—
80#66925—22no—
81C11×#107—22no—
82C11×#102—24no—
83C4×C8×C11D414yescomplemented
84#66896—24no—
85#66896C2×C418yescomplemented
86C11⋊#95—22no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89#66881—22no—
90#66881C2×C414yescomplemented
91#66879—22no—
92C8×Dic11—22no—
93#66867—22no—
94#21536—111nomaximal, Sylow
95C24×C11—22no—
96C23×D11C2×D411yescharacteristic
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11C22×C414yes—
103C22×C4×C11—22no—
104C22×C4×C11—44no—
105C22×C4×C11—82no—
106C22×C4×C11—82no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2411yescharacteristic
110C2×C22⋊D11—28no—
111C2×C22⋊D11—82no—
112C2×C22⋊D11—82no—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11C2×D411yescharacteristic
116C22×Dic11C2×D411yescharacteristic
117C22×Dic11C2×D411yescharacteristic
118C2×C4×D11—21no—
119C2×C4×D11—21no—
120C2×C4×D11—21no—
121C2×C4×D11—21no—
122C2×C4×D11C22×C412yes—
123C2×C4×D11#4112yes—
124C11×D8—28no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11C22×C412yes—
128C2×C8×C11C2×D412yes—
129C2×C8×C11C2×D412yes—
130C2×C8×C11#4112yes—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C22⋊C4—44no—
134C42×C11C2×D412yes—
135C42×C11#4112yes—
136C22⋊Dic11—28no—
137C22⋊Dic11—82no—
138C22⋊Dic11—82no—
139(C2×D11)⋊C4—22no—
140(C2×D11)⋊C4—22no—
141(C2×D11)⋊C4—82no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145C4⋊Dic11C22×C414yes—
146Dic11⋊C4—22no—
147Dic11⋊C4—22no—
148Dic11⋊C4—82no—
149C4×Dic11—21no—
150C4×Dic11—21no—
151C4×Dic11—82no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8C22×C412yes—
157C2×C11⋊C8#4112yes—
158#4313—28no—
159C8×D11—28no—
160C2×#469—111no—
161C2×C4×D8D1111yescharacteristic, complemented
162C2×#405—111no—
163#2324—112no—
164#1972—111no—
165#1944—111no—
166#1934—112no—
167#1893—112no—
168#1809—111no—
169C4×#106—111no—
170#1762—112no—
171C23×C11—24no—
172C23×C11—42no—
173C23×C11—42no—
174C23×C11—42no—
175C23×C11—42no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11C22×D411yescharacteristic
179C22×D11—21no—
180C22×D11—21no—
181C22×D11—22no—
182C22×D11—22no—
183C22×D11C4×D412yes—
184D4×C11—24no—
185D4×C11—24no—
186D4×C11—42no—
187D4×C11—42no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—88no—
194C2×C4×C11#12112yes—
195C2×C4×C11#12112yes—
196C2×C4×C11C23×C411yescharacteristic
197C2×C4×C11C22×D411yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C22⋊D11—88no—
203C2×Dic11—21no—
204C2×Dic11—21no—
205C2×Dic11—24no—
206C2×Dic11—21no—
207C2×Dic11—21no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11C4×D412yes—
216C4×D11—22no—
217C4×D11—22no—
218C4×D11—22no—
219C4×D11—22no—
220C8×C11—22no—
221C8×C11C4×D414yes—
222C11⋊C8—22no—
223C11⋊C8—22no—
224C22×D8C2×D1111yescharacteristic
225C22×M16—111no—
226C23×C8—111no—
227C2×#121—112no—
228C2×C4×D4C2×D1112yes—
229C2×#117—111no—
230#469—118no—
231C4×D8—24no—
232C2×#107C2×D1111yescharacteristic
233C2×#106—111no—
234C2×#106—111no—
235C2×#102—112no—
236C2×#102—112no—
237C2×#102C2×D1112yes—
238#405—224no—
239C2×#97—111no—
240C2×#97—111no—
241C2×C4×C8—111no—
242C2×C4×C8C2×D1111yescharacteristic
243#390—112no—
244#390—222no—
245#389—112no—
246#388—222no—
247#386—222no—
248#385—222no—
249#380—112no—
250C4×C4⋊C4—112no—
251#340—112no—
252#340—112no—
253#340—112no—
254C22×C11—44no—
255C22×C11—44no—
256C22×C11—44no—
257C22×C11—82no—
258C22×C11—82no—
259C22×C11—82no—
260C22×C11—82no—
261C22×C11C2×C4×D411yescharacteristic
262C22×C11C2×#12111yescharacteristic
263C22×C11#53211yescharacteristic
264C22×C11#57612yes—
265C22×C11#57712yes—
266C2×D11—24no—
267C2×D11—22no—
268C2×D11—42no—
269C2×D11—41no—
270C2×D11—41no—
271C4×C11—22no—
272C4×C11—22no—
273C4×C11—82no—
274C4×C11C2×C4×D411yescharacteristic
275C4×C11C4×#4111yescharacteristic
276C4×C11#52511yescharacteristic
277C4×C11#52911yescharacteristic
278Dic11—22no—
279Dic11—44no—
280Dic11—41no—
281Dic11—41no—
282Dic11—82no—
283C22×D4—222no—
284C22×D4C22×D1112yes—
285C23×C4—22no—
286C23×C4—111no—
287C2×D8—22no—
288C2×D8—22no—
289C2×D8C4×D1114yes—
290C2×M16—114no—
291C2×M16—222no—
292C2×M16—222no—
293C22×C8—111no—
294C22×C8—111no—
295C22×C8—222no—
296C22×C8—222no—
297C22×C8—222no—
298C22×C8C22×D1111yescharacteristic
299C22×C8C22×D1111yescharacteristic
300#121—118no—
301#121—224no—
302C4×D4—24no—
303C4×D4—24no—
304#117—222no—
305#117—222no—
306C2×C4⋊C4—112no—
307C2×C4⋊C4—111no—
308C2×C4⋊C4—111no—
309C2×C4⋊C4—112no—
310C2×C4⋊C4—222no—
311C2×C4⋊C4C22×D1112yes—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—111no—
314C2×C22⋊C4—111no—
315C2×C22⋊C4—222no—
316C2×C22⋊C4—222no—
317C2×C22⋊C4—222no—
318C2×C22⋊C4—222no—
319C2×C42—111no—
320C2×C42—222no—
321C2×C42C22×D1111yescharacteristic
322#107—22no—
323#106—114no—
324#106—222no—
325#102—24no—
326#102—118no—
327#102—224no—
328#97—222no—
329#97—222no—
330C4×C8—222no—
331C4×C8C22⋊D1114yescomplemented
332#95—222no—
333#95—222no—
334#95—222no—
335C2×C11—84no—
336C2×C11C4×#12111yescharacteristic
337C2×C11#294612yes—
338C2×C11#305811yescharacteristic
339C2×C11#306011yescharacteristic
340C2×C11#317912yes—
341D11—42no—
342C24—22no—
343C24—111no—
344C2×D4—22no—
345C2×D4—22no—
346C2×D4—22no—
347C2×D4—22no—
348C2×D4—22no—
349C2×D4—228no—
350C2×D4—882no—
351C2×D4—882no—
352C2×D4C2×C4×D1114yes—
353C22×C4—22no—
354C22×C4—44no—
355C22×C4—82no—
356C22×C4—82no—
357C22×C4—111no—
358C22×C4—112no—
359C22×C4—112no—
360C22×C4—111no—
361C22×C4—111no—
362C22×C4—221no—
363C22×C4—221no—
364C22×C4—221no—
365C22×C4—221no—
366C22×C4—222no—
367C22×C4—222no—
368C22×C4D4×D1111yescharacteristic
369C22×C4D4×D1111yescharacteristic
370C22×C4C23×D1111yescharacteristic
371D8—28no—
372M16—228no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8—112no—
376C2×C8—112no—
377C2×C8—228no—
378C2×C8—221no—
379C2×C8—221no—
380C2×C8—221no—
381C2×C8—221no—
382C2×C8C2×C4×D1112yes—
383C2×C8#433912yes—
384C2×C8C2×C22⋊D1112yes—
385C2×C8C2×C22⋊D1112yes—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—114no—
389C4⋊C4—222no—
390C4⋊C4—222no—
391C4⋊C4—222no—
392C4⋊C4—222no—
393C4⋊C4—222no—
394C4⋊C4—882no—
395C22⋊C4—44no—
396C22⋊C4—228no—
397C22⋊C4—222no—
398C22⋊C4—222no—
399C22⋊C4—882no—
400C22⋊C4—882no—
401C22⋊C4—882no—
402C42—221no—
403C42—221no—
404C42—882no—
405C42#434112yes—
406C42C2×C22⋊D1112yes—
407C11#2153611yescharacteristic, complemented, Sylow
408C23—24no—
409C23—42no—
410C23—42no—
411C23—42no—
412C23—42no—
413C23—42no—
414C23—42no—
415C23—112no—
416C23—222no—
417C23—222no—
418C23—221no—
419C23—221no—
420C23C2×D4×D1111yescharacteristic
421D4—24no—
422D4—24no—
423D4—42no—
424D4—42no—
425D4—888no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—88no—
432C2×C4—112no—
433C2×C4—221no—
434C2×C4—221no—
435C2×C4—222no—
436C2×C4—222no—
437C2×C4—222no—
438C2×C4—222no—
439C2×C4—222no—
440C2×C4—222no—
441C2×C4—224no—
442C2×C4—221no—
443C2×C4—221no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4#6699112yes—
450C2×C4#6699112yes—
451C2×C4C22×C4×D1111yescharacteristic
452C2×C4C2×#433911yescharacteristic
453C2×C4C2×#434111yescharacteristic
454C2×C4#41×D1111yescharacteristic
455C2×C4#41×D1111yescharacteristic
456C2×C4C22×C22⋊D1111yescharacteristic
457C8—22no—
458C8—222no—
459C8—222no—
460C8C4×C22⋊D1114yes—
461C22—44no—
462C22—44no—
463C22—44no—
464C22—82no—
465C22—82no—
466C22—82no—
467C22—82no—
468C22—222no—
469C22—224no—
470C22—441no—
471C22—442no—
472C22—441no—
473C22C4×D4×D1111yescharacteristic
474C22#1062307911yescharacteristic
475C22#1062328812yes—
476C22#1062330112yes—
477C22C2×#6699111yescharacteristic
478C4—22no—
479C4—22no—
480C4—82no—
481C4—222no—
482C4—441no—
483C4—444no—
484C4—441no—
485C4—882no—
486C4C4×#434111yescharacteristic
487C4#1062308811yescharacteristic
488C4C2×C4×C22⋊D1111yescharacteristic
489C4#1062335911yescharacteristic
490C2—84no—
491C2—442no—
492C2C4×#6699111yescharacteristic
493C2#1307744112yes—
494C2#1307826011yescharacteristic
495C2#1307827411yescharacteristic
496C2#1307930312yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C4×C11×D8C2
socleC23×C11C22×D4
prime radicalC2×#10622772C2
cosocleC22×C4×C11C24
hypercenterC2×C4×D8D11
hypocenterC11#21536
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
2. C2×#10622302C2semidirect
3. #13071303C2semidirect
4. #13069493C2semidirect
5. #13069357C2semidirect
6. #13069296C2semidirect
7. #13069041C2semidirect
8. #13068650C2semidirect
9. C4×#66881C2semidirect
10. #13068441C2semidirect
11. C2×C4×C11×D8C2semidirect
27. #10622772C4semidirect
60. #66991C2×C4semidirect
75. C2×#4313C2×C4semidirect
83. C4×C8×C11D4semidirect
85. #66896C2×C4semidirect
90. #66881C2×C4semidirect
161. C2×C4×D8D11semidirect
331. C4×C8C22⋊D11semidirect
407. C11#21536semidirect

Maximal subgroups

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

subgroupindex
C2×#106227722
C2×#106223022
#130713032
#130694932
#130693572
#130692962
#130690412
#130686502
C4×#668812
#130684412
C2×C4×C11×D82
#2153611