Finite Group Databasebeta

← #14810386

Subgroups — #14810386

Order 2816.

1446 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×#10622683C211yesmaximal, characteristic, complemented
3#13076958C211yesmaximal, characteristic
4#13069750C214yesmaximal, complemented
5#13069578C211yesmaximal, characteristic, complemented
6#13069577C211yesmaximal, characteristic, complemented
7#13068930C214yesmaximal, complemented
8C4×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
9C2×C11×#486C211yesmaximal, characteristic, complemented
10C22×Q8×D11—21no—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C11×#127C2211yescharacteristic
13C2×#66997—21no—
14C2×#66991—21no—
15C2×#66991—21no—
16C2×#66991C2212yes—
17D11×C4⋊Q8—24no—
18D11×C4⋊Q8—24no—
19C2×C4⋊C4×D11—21no—
20C2×C4⋊C4×D11C2212yes—
21C2×#66941—21no—
22C2×#66941C2212yes—
23C2×C42×D11C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25C11×#486—24no—
26C2×C11×#102C2214yes—
27C2×C4×C8×C11C2211yescharacteristic
28#10622834—21no—
29#10622834—21no—
30#10622834C2212yes—
31C2×#66896C2214yes—
32C2×(C2×D11)⋊C8C2212yes—
33#10622683—24no—
34#10622548C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622189C2214yes—
37#10622188C2212yes—
38#10622167C2214yes—
39C22×Q8×C11—21no—
40C22×D4×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11C2312yes—
43C22×C22⋊D11—22no—
44C2×Q8×D11—28no—
45C2×Q8×D11—44no—
46C2×Q8×D11—44no—
47C22×C4×D11—22no—
48C22×C4×D11D411yescharacteristic
49C22×C4×D11D411yescharacteristic
50C22×C4×D11C2311yescharacteristic
51C22×Dic22—21no—
52C22×Dic22—22no—
53C22×C8×C11C2312yes—
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8D414yescomplemented
56C11×#127—22no—
57C11×#127—22no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4C2312yes—
60C2×C42×C11C2311yescharacteristic
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11—22no—
63C2×C22⋊Dic11—22no—
64#66997—28no—
65#66991—28no—
66#66991—44no—
67#66991—44no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11C2312yes—
72C2×C4⋊Dic11C2312yes—
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4—22no—
75C2×C4×Dic11D411yescharacteristic
76C2×C4×Dic11D411yescharacteristic
77C2×C4×Dic11C2311yescharacteristic
78C22×C11⋊C8C2312yes—
79C4⋊C4×D11—28no—
80C4⋊C4×D11—24no—
81C4⋊C4×D11—24no—
82#66941—28no—
83#66941—24no—
84#66941—24no—
85C42×D11—22no—
86C42×D11—22no—
87#66922—22no—
88#66922D414yescomplemented
89C11×#102—28no—
90C4×C8×C11—22no—
91#66896—28no—
92(C2×D11)⋊C8—24no—
93C4×C11⋊C8—22no—
94#25903—111nomaximal, Sylow
95C24×C11—22no—
96C23×D11C2×D411yescharacteristic
97C2×Q8×C11—24no—
98C2×Q8×C11—42no—
99C2×Q8×C11—42no—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—24no—
103C2×D4×C11—24no—
104C2×D4×C11—42no—
105C2×D4×C11—42no—
106C2×D4×C11—42no—
107C2×D4×C11—42no—
108C2×D4×C11—42no—
109C2×D4×C11—42no—
110C22×C4×C11—22no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2411yescharacteristic
114C2×C22⋊D11—44no—
115C2×C22⋊D11—44no—
116C2×C22⋊D11—44no—
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11C2×D411yescharacteristic
120C22×Dic11C2×D411yescharacteristic
121C22×Dic11C2×D411yescharacteristic
122Q8×D11—432no—
123C2×C4×D11—28no—
124C2×C4×D11—22no—
125C2×C4×D11—22no—
126C2×C4×D11—22no—
127C2×C4×D11—22no—
128C2×C4×D11—21no—
129C2×C4×D11—21no—
130C2×C4×D11—22no—
131C2×C4×D11—44no—
132C2×C4×D11—44no—
133C2×C4×D11D814yes—
134C2×C4×D11SD1614yes—
135C2×C4×D11#4114yes—
136C2×Dic22—28no—
137C2×Dic22—24no—
138C2×Dic22—44no—
139C2×Dic22—44no—
140C2×Dic22—42no—
141C2×Dic22—42no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4C2×D414yes—
148C42×C11C2×D412yes—
149C42×C11C2×D412yes—
150C22⋊Dic11—44no—
151C22⋊Dic11—44no—
152C22⋊Dic11—44no—
153C4⋊Dic11—24no—
154C4⋊Dic11—22no—
155C4⋊Dic11—24no—
156C4⋊Dic11—42no—
157C4⋊Dic11—42no—
158C4⋊Dic11C2×D414yes—
159Dic11⋊C4—28no—
160Dic11⋊C4—28no—
161C4×Dic11—22no—
162C4×Dic11—22no—
163C4×Dic11—21no—
164C4×Dic11—21no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C22×C4⋊Q8—111no—
169C2×#486—111no—
170C2×#486D1111yescharacteristic, complemented
171#2856—111no—
172#2023—114no—
173#1990—111no—
174#1990—111no—
175#1874—114no—
176C4×C22⋊C8—111no—
177C23×C11—42no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11C22×D411yescharacteristic
185C22×D11—21no—
186C22×D11—21no—
187C22×D11—21no—
188C22×D11—21no—
189C22×D11#12412yes—
190C22×D11C2×D812yes—
191C22×D11C2×SD1612yes—
192Q8×C11—48no—
193D4×C11—44no—
194D4×C11—44no—
195D4×C11—84no—
196D4×C11—84no—
197C2×C4×C11—24no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11#12012yes—
201C2×C4×C11#12012yes—
202C2×C4×C11C2×D812yes—
203C2×C4×C11C2×SD1612yes—
204C2×C4×C11AGL(1,ℤ/8)12yes—
205C2×C4×C11#13712yes—
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11C2×#4112yes—
209C2×C4×C112−1+412yes—
210C22⋊D11—88no—
211C2×Dic11—21no—
212C2×Dic11—21no—
213C2×Dic11—21no—
214C2×Dic11—21no—
215C2×Dic11—21no—
216C2×Dic11—21no—
217C2×Dic11—24no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11#12412yes—
224C2×Dic11C2×D812yes—
225C2×Dic11C2×SD1612yes—
226C4×D11—24no—
227C4×D11—24no—
228C4×D11—28no—
229C4×D11—28no—
230C4×D11—416no—
231Dic22—416no—
232Dic22—48no—
233C8×C11—42no—
234C11⋊C8—42no—
235C23×Q8—221no—
236C2×C4⋊Q8—112no—
237C2×C4⋊Q8—111no—
238C2×C4⋊Q8—221no—
239C2×C4⋊Q8—221no—
240C2×C4⋊Q8—224no—
241C2×C4⋊Q8—224no—
242C2×C4⋊Q8C2×D1111yescharacteristic
243C2×#127C2×D1111yescharacteristic
244C2×#121—112no—
245C2×#121—221no—
246C2×#121—221no—
247C22×C4⋊C4—112no—
248C22×C4⋊C4—221no—
249C22×C42—111no—
250#486—24no—
251#486—224no—
252C2×#102—114no—
253C2×#102C2×D1114yes—
254C2×C22⋊C8—112no—
255C2×C4×C8—111no—
256C2×C4×C8C2×D1111yescharacteristic
257#390—112no—
258#390—221no—
259#390—221no—
260#384—111no—
261#340—114no—
262#340—114no—
263#336—112no—
264C22×C11—82no—
265C22×C11—82no—
266C22×C11—82no—
267C22×C11—82no—
268C22×C11—82no—
269C22×C11—82no—
270C22×C11—82no—
271C22×C11C2×#12011yescharacteristic
272C22×C11C2×#12411yescharacteristic
273C22×C11#53611yescharacteristic
274C22×C11C22×D811yescharacteristic
275C22×C11C22×SD1611yescharacteristic
276C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
277C22×C11C2×#13711yescharacteristic
278C2×D11—22no—
279C2×D11—22no—
280C2×D11—22no—
281C2×D11—22no—
282C2×D11—22no—
283C2×D11—22no—
284C2×D11#48614yescomplemented
285C4×C11—44no—
286C4×C11#44714yes—
287C4×C11#44814yes—
288C4×C11#54812yes—
289C4×C11#54812yes—
290Dic11—22no—
291Dic11—22no—
292Dic11—22no—
293Dic11—44no—
294Dic11—82no—
295C22×Q8—21no—
296C22×Q8—222no—
297C22×Q8—228no—
298C22×Q8—221no—
299C22×Q8—444no—
300C22×Q8—444no—
301C22×D4—21no—
302C22×D4—21no—
303C22×D4—222no—
304C22×D4C22×D1112yes—
305C23×C4—111no—
306C23×C4—111no—
307C23×C4—111no—
308C23×C4—222no—
309C22×C8—112no—
310C22×C8C22×D1112yes—
311C4⋊Q8—22no—
312C4⋊Q8—114no—
313C4⋊Q8—224no—
314C4⋊Q8—228no—
315C4⋊Q8—228no—
316C4⋊Q8—224no—
317C4⋊Q8—222no—
318C4⋊Q8C22⋊D1114yescomplemented
319#127—22no—
320#127—22no—
321#121—228no—
322#121—444no—
323#121—444no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—112no—
326C2×C4⋊C4—112no—
327C2×C4⋊C4—224no—
328C2×C4⋊C4—228no—
329C2×C4⋊C4—222no—
330C2×C4⋊C4—222no—
331C2×C4⋊C4—221no—
332C2×C4⋊C4—224no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4—221no—
335C2×C4⋊C4C22×D1112yes—
336C2×C22⋊C4—222no—
337C2×C22⋊C4—222no—
338C2×C22⋊C4—222no—
339C2×C42—111no—
340C2×C42—111no—
341C2×C42—111no—
342C2×C42—222no—
343C2×C42—222no—
344C2×C42C22×D1111yescharacteristic
345#102—28no—
346#102—228no—
347C22⋊C8—224no—
348C4×C8—22no—
349C4×C8—222no—
350C2×C11—162no—
351C2×C11#243611yescharacteristic
352C2×C11C2×#44711yescharacteristic
353C2×C11C2×#44811yescharacteristic
354C2×C11C2×#48611yescharacteristic
355C2×C11#314111yescharacteristic
356C2×C11#322611yescharacteristic
357C2×C11#322711yescharacteristic
358D11—24no—
359C24—22no—
360C24—111no—
361C2×Q8—24no—
362C2×Q8—42no—
363C2×Q8—42no—
364C2×Q8—228no—
365C2×Q8—224no—
366C2×Q8—444no—
367C2×Q8—444no—
368C2×Q8—4432no—
369C2×Q8—442no—
370C2×Q8—442no—
371C2×D4—22no—
372C2×D4—24no—
373C2×D4—24no—
374C2×D4—22no—
375C2×D4—42no—
376C2×D4—42no—
377C2×D4—42no—
378C2×D4—42no—
379C2×D4—42no—
380C2×D4—42no—
381C2×D4—444no—
382C2×D4—444no—
383C2×D4—444no—
384C22×C4—22no—
385C22×C4—111no—
386C22×C4—111no—
387C22×C4—111no—
388C22×C4—114no—
389C22×C4—114no—
390C22×C4—114no—
391C22×C4—228no—
392C22×C4—222no—
393C22×C4—222no—
394C22×C4—222no—
395C22×C4—222no—
396C22×C4—221no—
397C22×C4—222no—
398C22×C4—221no—
399C22×C4—222no—
400C22×C4—222no—
401C22×C4—444no—
402C22×C4—444no—
403C22×C4D4×D1111yescharacteristic
404C22×C4D4×D1111yescharacteristic
405C22×C4C23×D1111yescharacteristic
406C2×C8—22no—
407C2×C8—22no—
408C2×C8—22no—
409C2×C8—222no—
410C2×C8—222no—
411C2×C8—222no—
412C4⋊C4—24no—
413C4⋊C4—22no—
414C4⋊C4—114no—
415C4⋊C4—228no—
416C4⋊C4—228no—
417C4⋊C4—224no—
418C4⋊C4—222no—
419C4⋊C4—224no—
420C4⋊C4—442no—
421C4⋊C4—442no—
422C4⋊C4C2×C22⋊D1114yes—
423C22⋊C4—444no—
424C22⋊C4—444no—
425C22⋊C4—444no—
426C42—222no—
427C42—222no—
428C42—221no—
429C42—221no—
430C42D4×D1112yes—
431C42C2×C22⋊D1112yes—
432C11#2590311yescharacteristic, complemented, Sylow
433C23—42no—
434C23—42no—
435C23—42no—
436C23—42no—
437C23—42no—
438C23—42no—
439C23—42no—
440C23—112no—
441C23—112no—
442C23—112no—
443C23—221no—
444C23—221no—
445C23—221no—
446C23—221no—
447C23C2×D4×D1111yescharacteristic
448Q8—48no—
449Q8—4416no—
450Q8—448no—
451D4—44no—
452D4—44no—
453D4—84no—
454D4—84no—
455D4—888no—
456C2×C4—24no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—112no—
460C2×C4—112no—
461C2×C4—112no—
462C2×C4—221no—
463C2×C4—221no—
464C2×C4—221no—
465C2×C4—221no—
466C2×C4—221no—
467C2×C4—221no—
468C2×C4—228no—
469C2×C4—228no—
470C2×C4—224no—
471C2×C4—224no—
472C2×C4—224no—
473C2×C4—4416no—
474C2×C4—442no—
475C2×C4—442no—
476C2×C4—442no—
477C2×C4—442no—
478C2×C4—442no—
479C2×C4D8×D1112yes—
480C2×C4#6696412yes—
481C2×C4SD16×D1112yes—
482C2×C4#6696812yes—
483C2×C4#6699012yes—
484C2×C4#6699012yes—
485C2×C4C2×D4×D1111yescharacteristic
486C2×C4#41×D1112yes—
487C2×C4#6704312yes—
488C2×C4C22×C22⋊D1111yescharacteristic
489C8—42no—
490C8—442no—
491C22—82no—
492C22—82no—
493C22—82no—
494C22—82no—
495C22—82no—
496C22—82no—
497C22—82no—
498C22—114no—
499C22—222no—
500C22—222no—
501C22—222no—
502C22—222no—
503C22—222no—
504C22—222no—
505C22D11×#12411yescharacteristic
506C22#1062320611yescharacteristic
507C22C2×D8×D1111yescharacteristic
508C22C2×#6696411yescharacteristic
509C22C2×SD16×D1111yescharacteristic
510C22C2×#6696811yescharacteristic
511C22C2×#6699011yescharacteristic
512C4—44no—
513C4—222no—
514C4—222no—
515C4—222no—
516C4—444no—
517C4—882no—
518C4#1062276914yes—
519C4#1062278314yes—
520C4#1062320812yes—
521C4#1062336212yes—
522C2—162no—
523C2—224no—
524C2#1307227111yescharacteristic
525C2C2×#1062276911yescharacteristic
526C2C2×#1062278311yescharacteristic
527C2D11×#48611yescharacteristic
528C2#1307900611yescharacteristic
529C2#1307973311yescharacteristic
530C2#1307974011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#486C2
socleC23×C11C22×D4
prime radical#13076958C2
hypercenterC2×#486D11
hypocenterC11#25903
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
1. C2×D11×C4⋊Q8C2semidirect
2. C2×#10622683C2semidirect
4. #13069750C2semidirect
5. #13069578C2semidirect
6. #13069577C2semidirect
7. #13068930C2semidirect
8. C4×(C2×D11)⋊C8C2semidirect
9. C2×C11×#486C2semidirect
55. C11×C4⋊Q8D4semidirect
88. #66922D4semidirect
170. C2×#486D11semidirect
284. C2×D11#486semidirect
318. C4⋊Q8C22⋊D11semidirect
432. C11#25903semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
C2×#106226832
#130769582
#130697502
#130695782
#130695772
#130689302
C4×(C2×D11)⋊C82
C2×C11×#4862
#2590311