Finite Group Databasebeta

← #14809949

Subgroups — #14809949

Order 2816.

1338 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic
2C2×#10622294C211yesmaximal, characteristic, complemented
3C2×#10622694C211yesmaximal, characteristic, complemented
4#13076969C211yesmaximal, characteristic
5#13069861C214yesmaximal, complemented
6#13069417C211yesmaximal, characteristic, complemented
7#13068549C214yesmaximal
8C4×(C2×D11)⋊C8C211yesmaximal, characteristic
9C11×#1956C211yesmaximal, characteristic, complemented
10C22×Q8×D11C2212yes—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#66997C2212yes—
13D11×C4⋊Q8—24no—
14D11×C4⋊Q8—24no—
15C2×#66950—21no—
16C2×C4⋊C4×D11—21no—
17C2×C4⋊C4×D11—21no—
18C2×#66941—21no—
19C2×#66941—21no—
20C2×C42×D11C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C2×C11×#103C2214yes—
24C2×C4×C8×C11C2211yescharacteristic
25C11×#384C2211yescharacteristic
26C2×#66899C2214yes—
27C2×(C2×D11)⋊C8C2212yes—
28C2×#66880C2214yes—
29#10622694—24no—
30#10622600—21no—
31#10622600C2212yes—
32#10622598—21no—
33#10622598C2212yes—
34#10622587—21no—
35C2×#66874C2214yes—
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622294—24no—
38#10622188C2212yes—
39C22×Q8×C11C2312yes—
40C2×Q8×D11—24no—
41C2×Q8×D11—24no—
42C2×Q8×D11—28no—
43C2×Q8×D11—44no—
44C22×C4×D11—22no—
45C22×C4×D11D411yescharacteristic
46C22×C4×D11D411yescharacteristic
47C22×C4×D11C2311yescharacteristic
48C22×Dic22—22no—
49C22×Dic22—21no—
50C22×Dic22C2312yes—
51C22×C8×C11C2312yes—
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8D414yes—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4C2312yes—
59C2×C42×C11C2311yescharacteristic
60#66997—24no—
61#66997—24no—
62C2×(C2×D11)⋊C4—22no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11C2312yes—
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4—22no—
70C2×C4×Dic11D411yescharacteristic
71C2×C4×Dic11D411yescharacteristic
72C2×C4×Dic11C2311yescharacteristic
73C22×C11⋊C8C2312yes—
74#66950—44no—
75C4⋊C4×D11—28no—
76C4⋊C4×D11—28no—
77#66941—28no—
78#66941—28no—
79C42×D11—22no—
80C42×D11—22no—
81#66922—22no—
82#66922—22no—
83#66922—22no—
84#66922D414yes—
85C11×#103—44no—
86C4×C8×C11—22no—
87#66899—28no—
88C11⋊#95—22no—
89C11⋊#95—22no—
90(C2×D11)⋊C8—24no—
91#66880—28no—
92#66874—44no—
93C4×C11⋊C8—22no—
94#25856—111nomaximal, Sylow
95C23×D11C2×D411yescharacteristic
96C2×Q8×C11—22no—
97C2×Q8×C11—24no—
98C2×Q8×C11—24no—
99C2×Q8×C11C2×D414yes—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2411yescharacteristic
105C22×Dic11—22no—
106C22×Dic11—22no—
107C22×Dic11C2×D411yescharacteristic
108C22×Dic11C2×D411yescharacteristic
109C22×Dic11C2×D411yescharacteristic
110Q8×D11—416no—
111Q8×D11—416no—
112C2×C4×D11—28no—
113C2×C4×D11—22no—
114C2×C4×D11—22no—
115C2×C4×D11—22no—
116C2×C4×D11—22no—
117C2×C4×D11—21no—
118C2×C4×D11—21no—
119C2×C4×D11—22no—
120C2×C4×D11—44no—
121C2×C4×D11—44no—
122C2×C4×D11SD1614yes—
123C2×C4×D11Q1614yes—
124C2×C4×D11#4114yes—
125C2×Dic22—28no—
126C2×Dic22—22no—
127C2×Dic22—24no—
128C2×Dic22—24no—
129C2×Dic22—44no—
130C2×Dic22—44no—
131C2×Dic22—42no—
132C2×Dic22—42no—
133C2×Dic22—42no—
134C2×Dic22C2×D414yes—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—42no—
142C11×C4⋊C4—42no—
143C42×C11C2×D412yes—
144C42×C11C2×D412yes—
145(C2×D11)⋊C4—44no—
146C4⋊Dic11—24no—
147C4⋊Dic11—24no—
148C4⋊Dic11—22no—
149C4⋊Dic11—22no—
150C4⋊Dic11—44no—
151C4⋊Dic11—42no—
152Dic11⋊C4—28no—
153Dic11⋊C4—28no—
154C4×Dic11—22no—
155C4×Dic11—22no—
156C4×Dic11—21no—
157C4×Dic11—21no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C22×C4⋊Q8—111no—
162C2×#487—111no—
163C2×#487—111no—
164#2857—111no—
165#2043—114no—
166#1956—111no—
167#1956D1111yescharacteristic, complemented
168#1787—114no—
169C4×C22⋊C8—111no—
170C23×C11C22×D411yescharacteristic
171C22×D11—21no—
172C22×D11—21no—
173C22×D11—21no—
174C22×D11—21no—
175C22×D11#12412yes—
176C22×D11C2×SD1612yes—
177C22×D11C2×Q1612yes—
178Q8×C11—28no—
179Q8×C11—44no—
180C2×C4×C11—24no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11#12012yes—
187C2×C4×C11#12012yes—
188C2×C4×C11C2×SD1612yes—
189C2×C4×C11C2×Q1612yes—
190C2×C4×C11#13712yes—
191C2×C4×C11#13712yes—
192C2×C4×C11C22×D411yescharacteristic
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C2×#4112yes—
195C2×C4×C11H(5,𝔽2)12yes—
196C2×Dic11—21no—
197C2×Dic11—21no—
198C2×Dic11—21no—
199C2×Dic11—21no—
200C2×Dic11—21no—
201C2×Dic11—21no—
202C2×Dic11—24no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11#12412yes—
209C2×Dic11C2×SD1612yes—
210C2×Dic11C2×Q1612yes—
211C4×D11—24no—
212C4×D11—24no—
213C4×D11—28no—
214C4×D11—28no—
215C4×D11—416no—
216Dic22—28no—
217Dic22—416no—
218Dic22—44no—
219Dic22—84no—
220C8×C11—42no—
221C11⋊C8—42no—
222C23×Q8—112no—
223C2×C4⋊Q8—112no—
224C2×C4⋊Q8—111no—
225C2×C4⋊Q8—111no—
226C2×C4⋊Q8—221no—
227C2×C4⋊Q8—221no—
228C2×C4⋊Q8—224no—
229C2×C4⋊Q8—224no—
230C2×C4⋊Q8C2×D1111yescharacteristic
231C2×C22⋊Q8—221no—
232C22×C4⋊C4—221no—
233C22×C4⋊C4—221no—
234C22×C42—111no—
235#487—224no—
236#487—224no—
237C2×#103—114no—
238C2×#103—114no—
239C2×#103—114no—
240C2×#103C2×D1114yes—
241C2×C22⋊C8—112no—
242C2×C4×C8—111no—
243C2×C4×C8C2×D1111yescharacteristic
244#391—221no—
245#389—112no—
246#389—221no—
247#384C2×D1111yescharacteristic
248#380—112no—
249#380—221no—
250#336—112no—
251C22×C11C2×#12011yescharacteristic
252C22×C11C2×#12411yescharacteristic
253C22×C11#53511yescharacteristic
254C22×C11C22×SD1611yescharacteristic
255C22×C11C22×Q1611yescharacteristic
256C22×C11C2×#13711yescharacteristic
257C22×C11C2×#13711yescharacteristic
258C2×D11—22no—
259C2×D11—22no—
260C2×D11—22no—
261C2×D11—22no—
262C2×D11—22no—
263C2×D11—22no—
264C2×D11#48714yescomplemented
265C4×C11—44no—
266C4×C11—82no—
267C4×C11#44814yes—
268C4×C11#45114yes—
269C4×C11#54612yes—
270C4×C11#54612yes—
271Dic11—22no—
272Dic11—22no—
273Dic11—22no—
274Dic11—44no—
275Dic11—82no—
276C22×Q8—112no—
277C22×Q8—222no—
278C22×Q8—228no—
279C22×Q8—224no—
280C22×Q8—224no—
281C22×Q8—221no—
282C22×Q8—444no—
283C22×Q8C22×D1112yes—
284C23×C4—111no—
285C23×C4—111no—
286C23×C4—111no—
287C23×C4—222no—
288C22×C8—112no—
289C22×C8C22×D1112yes—
290C4⋊Q8—22no—
291C4⋊Q8—114no—
292C4⋊Q8—228no—
293C4⋊Q8—228no—
294C4⋊Q8—224no—
295C4⋊Q8—224no—
296C4⋊Q8—222no—
297C4⋊Q8—222no—
298C4⋊Q8—222no—
299C4⋊Q8D4414yes—
300C22⋊Q8—444no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—112no—
306C2×C4⋊C4—228no—
307C2×C4⋊C4—228no—
308C2×C4⋊C4—222no—
309C2×C4⋊C4—222no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4—221no—
312C2×C4⋊C4—222no—
313C2×C4⋊C4—221no—
314C2×C4⋊C4C22×D1112yes—
315C2×C22⋊C4—222no—
316C2×C42—111no—
317C2×C42—111no—
318C2×C42—111no—
319C2×C42—222no—
320C2×C42—222no—
321C2×C42C22×D1111yescharacteristic
322#103—44no—
323#103—228no—
324#103—228no—
325#103—444no—
326C22⋊C8—224no—
327C4×C8—22no—
328C4×C8—222no—
329#95—222no—
330#95—222no—
331C2×C11#243511yescharacteristic
332C2×C11C2×#44811yescharacteristic
333C2×C11C2×#45111yescharacteristic
334C2×C11C2×#48711yescharacteristic
335C2×C11#313911yescharacteristic
336C2×C11#320611yescharacteristic
337C2×C11#320911yescharacteristic
338D11—24no—
339C24—111no—
340C2×Q8—22no—
341C2×Q8—24no—
342C2×Q8—24no—
343C2×Q8—114no—
344C2×Q8—228no—
345C2×Q8—222no—
346C2×Q8—224no—
347C2×Q8—224no—
348C2×Q8—444no—
349C2×Q8—444no—
350C2×Q8—4416no—
351C2×Q8—4416no—
352C2×Q8—442no—
353C2×Q8—442no—
354C2×Q8—442no—
355C2×Q8C2×D4414yes—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—111no—
359C22×C4—111no—
360C22×C4—111no—
361C22×C4—114no—
362C22×C4—114no—
363C22×C4—114no—
364C22×C4—228no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4—222no—
368C22×C4—222no—
369C22×C4—221no—
370C22×C4—221no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4—222no—
374C22×C4—444no—
375C22×C4—444no—
376C22×C4D4×D1111yescharacteristic
377C22×C4D4×D1111yescharacteristic
378C22×C4C23×D1111yescharacteristic
379C2×C8—22no—
380C2×C8—22no—
381C2×C8—22no—
382C2×C8—222no—
383C2×C8—222no—
384C2×C8—222no—
385C4⋊C4—24no—
386C4⋊C4—24no—
387C4⋊C4—24no—
388C4⋊C4—42no—
389C4⋊C4—42no—
390C4⋊C4—228no—
391C4⋊C4—228no—
392C4⋊C4—224no—
393C4⋊C4—224no—
394C4⋊C4—222no—
395C4⋊C4—222no—
396C4⋊C4—444no—
397C4⋊C4—442no—
398C22⋊C4—444no—
399C42—222no—
400C42—222no—
401C42—221no—
402C42—221no—
403C42C2×D4412yes—
404C42D4×D1112yes—
405C11#2585611yescharacteristic, complemented, Sylow
406C23—112no—
407C23—112no—
408C23—112no—
409C23—221no—
410C23—221no—
411C23—221no—
412C23—221no—
413C23C2×D4×D1111yescharacteristic
414Q8—28no—
415Q8—44no—
416Q8—228no—
417Q8—4416no—
418Q8—444no—
419Q8—884no—
420C2×C4—24no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—112no—
427C2×C4—112no—
428C2×C4—112no—
429C2×C4—221no—
430C2×C4—221no—
431C2×C4—221no—
432C2×C4—221no—
433C2×C4—221no—
434C2×C4—221no—
435C2×C4—224no—
436C2×C4—224no—
437C2×C4—228no—
438C2×C4—228no—
439C2×C4—224no—
440C2×C4—4416no—
441C2×C4—442no—
442C2×C4—442no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4#6693512yes—
447C2×C4#6693512yes—
448C2×C4SD16×D1112yes—
449C2×C4#6696812yes—
450C2×C4Q16×D1112yes—
451C2×C4#6697112yes—
452C2×C4C22×D4411yescharacteristic
453C2×C4C2×D4×D1111yescharacteristic
454C2×C4#6703712yes—
455C2×C4#41×D1112yes—
456C8—42no—
457C8—442no—
458C22—114no—
459C22—222no—
460C22—222no—
461C22—222no—
462C22—222no—
463C22—222no—
464C22—222no—
465C22C2×#6693511yescharacteristic
466C22D11×#12411yescharacteristic
467C22#1062324611yescharacteristic
468C22C2×SD16×D1111yescharacteristic
469C22C2×#6696811yescharacteristic
470C22C2×Q16×D1111yescharacteristic
471C22C2×#6697111yescharacteristic
472C4—44no—
473C4—82no—
474C4—222no—
475C4—222no—
476C4—222no—
477C4—444no—
478C4—882no—
479C4#1062241914yes—
480C4#1062242114yes—
481C4#1062308512yes—
482C4#1062314312yes—
483C2—224no—
484C2#1307226611yescharacteristic
485C2C2×#1062241911yescharacteristic
486C2C2×#1062242111yescharacteristic
487C2D11×#48711yescharacteristic
488C2#1307899311yescharacteristic
489C2#1307953711yescharacteristic
490C2#1307956011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1956C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#1956D11
hypocenterC11#25856
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
2. C2×#10622294C2semidirect
3. C2×#10622694C2semidirect
5. #13069861C2semidirect
6. #13069417C2semidirect
9. C11×#1956C2semidirect
167. #1956D11semidirect
264. C2×D11#487semidirect
405. C11#25856semidirect

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×#106222942
C2×#106226942
#130769692
#130698612
#130694172
#130685492
C4×(C2×D11)⋊C82
C11×#19562
#2585611