Finite Group Databasebeta

← #14763463

Subgroups — #14763463

Order 2816.

1166 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623211C211yesmaximal, characteristic
2C2×#10622298C211yesmaximal, characteristic, complemented
3D11×#382C211yesmaximal, characteristic, complemented
4#13069581C211yesmaximal, characteristic, complemented
5#13069580C211yesmaximal, characteristic, complemented
6#13069428C211yesmaximal, characteristic, complemented
7#13068930C212yesmaximal
8#13068920C212yesmaximal, complemented
9#13068629C212yesmaximal, complemented
10#13068624C212yesmaximal, complemented
11C11×#1958C211yesmaximal, characteristic, complemented
12C2×C11×#124C2211yescharacteristic
13C2×#66999C2211yescharacteristic
14C2×Q8×Dic11C2211yescharacteristic
15C2×#66991C2211yescharacteristic
16C2×D4×Dic11C2211yescharacteristic
17#10623211—24no—
18#10623211C418yescomplemented
19C2×C4⋊C4×D11C2212yes—
20C2×#66936—21no—
21C2×(C22⋊D11)⋊C4—21no—
22C2×#66932—21no—
23C2×#66930—21no—
24C2×C42×D11C2211yescharacteristic
25C2×#66923C2211yescharacteristic
26C2×C11×#103C2212yes—
27C2×C11×#102C2212yes—
28C2×C4×C8×C11C2211yescharacteristic
29C11×#382C2211yescharacteristic
30C2×#66899C2212yes—
31C2×#66896C2212yes—
32C2×(C2×D11)⋊C8C2212yes—
33C2×Dic11⋊C8C2212yes—
34#10622590C2212yes—
35#10622549C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622298—24no—
38D11×#95—21no—
39D11×#95—21no—
40#10622263—21no—
41#10622263—21no—
42#10622189C2212yes—
43#10622189C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11C2311yescharacteristic
48C22×C22⋊D11—21no—
49C23×Dic11—21no—
50C22×C4×D11—22no—
51C22×C4×D11D411yescharacteristic
52C22×C4×D11D411yescharacteristic
53C22×C4×D11C2311yescharacteristic
54C22×C8×C11C2312yes—
55C11×#124—22no—
56C11×#124C2×C414yescomplemented
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C22⋊C4—21no—
59C2×C11×C22⋊C4—21no—
60C2×C42×C11C2311yescharacteristic
61C2×C22⋊Dic11—21no—
62C2×C22⋊Dic11—21no—
63#66999—22no—
64#66999C2×C414yes—
65Q8×Dic11—22no—
66Q8×Dic11C2×C414yescomplemented
67#66991—22no—
68#66991C2×C414yes—
69D4×Dic11—22no—
70D4×Dic11C2×C414yescomplemented
71C2×(C2×D11)⋊C4—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11C2312yes—
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76C2×Dic11⋊C4—21no—
77C2×Dic11⋊C4—21no—
78C2×Dic11⋊C4—21no—
79C2×Dic11⋊C4—22no—
80C2×C4×Dic11—21no—
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11C2311yescharacteristic
84C22×C11⋊C8C2312yes—
85C4⋊C4×D11—42no—
86C4⋊C4×D11—42no—
87#66936—28no—
88(C22⋊D11)⋊C4—28no—
89#66932—28no—
90#66930—28no—
91C42×D11C2×C414yes—
92C42×D11D414yes—
93#66923—22no—
94#66923C2×C414yescomplemented
95C11×#103—42no—
96C11×#102—42no—
97C4×C8×C11—22no—
98C11×#95—21no—
99C11×#95—21no—
100#66899—42no—
101#66896—42no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—22no—
105C11⋊#95—22no—
106(C2×D11)⋊C8—24no—
107Dic11⋊C8—24no—
108C4×C11⋊C8—22no—
109#21861—111nomaximal, Sylow
110C24×C11—21no—
111C23×D11C2×D411yescharacteristic
112C2×Q8×C11—21no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11C22×C412yes—
116C2×D4×C11—21no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11C22×C412yes—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C2×C22⋊D11—24no—
126C2×C22⋊D11—44no—
127C22×Dic11—24no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—22no—
131C22×Dic11—44no—
132C22×Dic11C2×D411yescharacteristic
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C2×C4×D11—24no—
136C2×C4×D11—22no—
137C2×C4×D11—22no—
138C2×C4×D11—42no—
139C2×C4×D11—44no—
140C2×C4×D11—44no—
141C2×C4×D11—44no—
142C2×C4×D11C22⋊C414yes—
143C2×C4×D11C22⋊C414yes—
144C2×C4×D11C22×C412yes—
145C2×C4×D11C2×D412yes—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C22⋊C4—24no—
152C11×C22⋊C4—24no—
153C42×C11C22×C412yes—
154C42×C11C2×D412yes—
155C22⋊Dic11—24no—
156C22⋊Dic11—24no—
157(C2×D11)⋊C4—24no—
158C4⋊Dic11—24no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161C4⋊Dic11—22no—
162C4⋊Dic11—22no—
163C4⋊Dic11C22×C412yes—
164C4⋊Dic11C22×C412yes—
165Dic11⋊C4—24no—
166Dic11⋊C4—24no—
167Dic11⋊C4—24no—
168Dic11⋊C4—44no—
169C4×Dic11—24no—
170C4×Dic11C22⋊C414yes—
171C4×Dic11C22⋊C414yes—
172C4×Dic11C22×C412yes—
173C4×Dic11C2×D412yes—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×#529—111no—
178C2×#431—111no—
179C2×#382—111no—
180#1991—111no—
181#1991—111no—
182#1958—111no—
183#1958D1111yescharacteristic, complemented
184#1874—112no—
185#1872—112no—
186#1805—112no—
187#1804—112no—
188C23×C11—22no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11C22×D411yescharacteristic
194C22×D11—21no—
195C22×D11—21no—
196C22×D11—22no—
197C22×D11C2×C22⋊C412yes—
198C22×D11#13514yes—
199Q8×C11—24no—
200Q8×C11—42no—
201D4×C11—24no—
202D4×C11—42no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11C2×C22⋊C412yes—
212C2×C4×C11C2×C22⋊C412yes—
213C2×C4×C11C23×C411yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11H(5,𝔽2)12yes—
216C2×C4×C112−1+412yes—
217C22⋊D11—48no—
218C2×Dic11—21no—
219C2×Dic11—21no—
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—48no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230C2×Dic11C2×C22⋊C412yes—
231C2×Dic11C2×C22⋊C412yes—
232C2×Dic11C2×C22⋊C412yes—
233C4×D11—28no—
234C4×D11—24no—
235C4×D11—24no—
236C4×D11—44no—
237C4×D11—88no—
238C8×C11—42no—
239C11⋊C8—42no—
240#529—118no—
241#529—224no—
242C2×#126—221no—
243C2×#125—111no—
244C2×#124C2×D1111yescharacteristic
245C2×#123—221no—
246C2×C22⋊Q8—111no—
247C2×#121—111no—
248C2×C4×Q8—111no—
249C2×C4×D4—111no—
250C2×C4×D4—221no—
251C2×#117—221no—
252C22×C4⋊C4—112no—
253C22×C42—111no—
254#431—224no—
255C2×C4⋊C8—112no—
256C2×#103—112no—
257C2×#103C2×D1112yes—
258C2×#102—112no—
259C2×#102C2×D1112yes—
260C2×C22⋊C8—112no—
261C2×C4×C8—111no—
262C2×C4×C8C2×D1111yescharacteristic
263#382—112no—
264#382—111no—
265#382—221no—
266#382—221no—
267#382C2×D1111yescharacteristic
268C2×#95—221no—
269C2×#95—221no—
270#340—112no—
271#340—112no—
272#340—112no—
273#340—112no—
274C22×C11—42no—
275C22×C11—42no—
276C22×C11—42no—
277C22×C11—82no—
278C22×C11—82no—
279C22×C11C22×C22⋊C411yescharacteristic
280C22×C11#53511yescharacteristic
281C22×C11#53611yescharacteristic
282C22×C11C2×#13512yes—
283C22×C11#57512yes—
284C2×D11—22no—
285C2×D11—22no—
286C2×D11—24no—
287C2×D11—24no—
288C2×D11#41614yes—
289C4×C11—22no—
290C4×C11—22no—
291C4×C11—42no—
292C4×C11—82no—
293C4×C11#52012yes—
294C4×C11#53712yes—
295Dic11—22no—
296Dic11—22no—
297Dic11—22no—
298Dic11—42no—
299Dic11—42no—
300Dic11—82no—
301C22×Q8C22×D1111yescharacteristic
302C22×D4—221no—
303C22×D4C22×D1111yescharacteristic
304C23×C4—111no—
305C23×C4—111no—
306C23×C4—111no—
307C23×C4—222no—
308C23×C4—221no—
309C22×C8—112no—
310C22×C8C22×D1112yes—
311#126—228no—
312#125—114no—
313#125—222no—
314#124—22no—
315#124C4×D1114yescomplemented
316#123—228no—
317C22⋊Q8—114no—
318C22⋊Q8—222no—
319#121—114no—
320#121—222no—
321C4×Q8—114no—
322C4×Q8—222no—
323C4×D4—114no—
324C4×D4—222no—
325C4×D4—228no—
326#117—228no—
327C2×C4⋊C4—111no—
328C2×C4⋊C4—111no—
329C2×C4⋊C4—112no—
330C2×C4⋊C4—221no—
331C2×C4⋊C4—221no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4—222no—
335C2×C4⋊C4—442no—
336C2×C4⋊C4—442no—
337C2×C4⋊C4C22×D1112yes—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—221no—
341C2×C22⋊C4—221no—
342C2×C22⋊C4—221no—
343C2×C42—111no—
344C2×C42—111no—
345C2×C42—111no—
346C2×C42—114no—
347C2×C42—114no—
348C2×C42—221no—
349C2×C42C22×D1111yescharacteristic
350C4⋊C8—224no—
351#103—42no—
352#103—442no—
353#102—42no—
354#102—442no—
355C22⋊C8—224no—
356C4×C8—22no—
357C4×C8—222no—
358#95—21no—
359#95—21no—
360#95—222no—
361#95—222no—
362#95—221no—
363#95—221no—
364C2×C11—82no—
365C2×C11#231111yescharacteristic
366C2×C11C2×#41611yescharacteristic
367C2×C11#289611yescharacteristic
368C2×C11#321112yes—
369C2×C11#323212yes—
370D11—24no—
371C24—21no—
372C24—111no—
373C2×Q8—21no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8C2×C4×D1112yes—
377C2×D4—21no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—224no—
381C2×D4—444no—
382C2×D4C2×C4×D1112yes—
383C22×C4—21no—
384C22×C4—22no—
385C22×C4—111no—
386C22×C4—111no—
387C22×C4—111no—
388C22×C4—114no—
389C22×C4—112no—
390C22×C4—112no—
391C22×C4—114no—
392C22×C4—224no—
393C22×C4—224no—
394C22×C4—222no—
395C22×C4—222no—
396C22×C4—221no—
397C22×C4—221no—
398C22×C4—222no—
399C22×C4—442no—
400C22×C4—444no—
401C22×C4—444no—
402C22×C4—444no—
403C22×C4—444no—
404C22×C4D4×D1111yescharacteristic
405C22×C4D4×D1111yescharacteristic
406C22×C4C23×D1111yescharacteristic
407C2×C8—22no—
408C2×C8—22no—
409C2×C8—22no—
410C2×C8—222no—
411C2×C8—222no—
412C2×C8—222no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—112no—
416C4⋊C4—112no—
417C4⋊C4—224no—
418C4⋊C4—224no—
419C4⋊C4—224no—
420C4⋊C4—224no—
421C4⋊C4—221no—
422C4⋊C4—221no—
423C4⋊C4—222no—
424C4⋊C4—222no—
425C4⋊C4—444no—
426C22⋊C4—24no—
427C22⋊C4—24no—
428C22⋊C4—224no—
429C22⋊C4—224no—
430C22⋊C4—224no—
431C42—114no—
432C42—114no—
433C42—112no—
434C42—112no—
435C42—224no—
436C42C2×C4×D1112yes—
437C42D4×D1112yes—
438C11#2186111yescharacteristic, complemented, Sylow
439C23—22no—
440C23—41no—
441C23—42no—
442C23—42no—
443C23—41no—
444C23—112no—
445C23—114no—
446C23—221no—
447C23—222no—
448C23—221no—
449C23C2×D4×D1111yescharacteristic
450Q8—24no—
451Q8—42no—
452D4—24no—
453D4—42no—
454D4—448no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—112no—
464C2×C4—112no—
465C2×C4—112no—
466C2×C4—228no—
467C2×C4—221no—
468C2×C4—222no—
469C2×C4—222no—
470C2×C4—221no—
471C2×C4—224no—
472C2×C4—224no—
473C2×C4—222no—
474C2×C4—222no—
475C2×C4—444no—
476C2×C4—448no—
477C2×C4—442no—
478C2×C4—442no—
479C2×C4—442no—
480C2×C4—442no—
481C2×C4—442no—
482C2×C4—888no—
483C2×C4C22⋊C4×D1112yes—
484C2×C4C22⋊C4×D1112yes—
485C2×C4C22×C4×D1111yescharacteristic
486C2×C4C2×D4×D1111yescharacteristic
487C2×C4#6703712yes—
488C2×C4#6704312yes—
489C8—42no—
490C8—442no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—82no—
495C22—82no—
496C22—114no—
497C22—224no—
498C22—222no—
499C22—222no—
500C22—224no—
501C22C2×C22⋊C4×D1111yescharacteristic
502C22#1062320611yescharacteristic
503C22#1062324611yescharacteristic
504C22D11×#13512yes—
505C22#1062329912yes—
506C4—22no—
507C4—22no—
508C4—42no—
509C4—82no—
510C4—222no—
511C4—222no—
512C4—222no—
513C4—442no—
514C4—442no—
515C4—882no—
516C4#1062307712yes—
517C4#1062313912yes—
518C2—82no—
519C2—224no—
520C2#1307120611yescharacteristic
521C2D11×#41611yescharacteristic
522C2#1307713111yescharacteristic
523C2#1307957612yes—
524C2#1307977912yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1958C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
cosocleC22×C4×C11C24
hypercenter#1958D11
hypocenterC11#21861
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1958

Complements

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

NH ≅ G/Ntype
2. C2×#10622298C2semidirect
3. D11×#382C2semidirect
4. #13069581C2semidirect
5. #13069580C2semidirect
6. #13069428C2semidirect
8. #13068920C2semidirect
9. #13068629C2semidirect
10. #13068624C2semidirect
11. C11×#1958C2semidirect
18. #10623211C4semidirect
56. C11×#124C2×C4semidirect
66. Q8×Dic11C2×C4semidirect
70. D4×Dic11C2×C4semidirect
94. #66923C2×C4semidirect
183. #1958D11semidirect
315. #124C4×D11semidirect
438. C11#21861semidirect

Maximal subgroups

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

subgroupindex
C2×#106232112
C2×#106222982
D11×#3822
#130695812
#130695802
#130694282
#130689302
#130689202
#130686292
#130686242
C11×#19582
#2186111