Finite Group Databasebeta

← #14763449

Subgroups — #14763449

Order 2816.

1502 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623256C211yesmaximal, characteristic
2C2×#10622298C211yesmaximal, characteristic, complemented
3D11×#384C211yesmaximal, characteristic, complemented
4#13069578C211yesmaximal, characteristic, complemented
5#13069422C211yesmaximal, characteristic, complemented
6#13069421C211yesmaximal, characteristic, complemented
7#13068932C214yesmaximal, complemented
8#13068615C214yesmaximal, complemented
9C11×#1990C211yesmaximal, characteristic, complemented
10C22×#4343—21no—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#67000—21no—
13#10623256—24no—
14#10623256C418yescomplemented
15C2×#66948—21no—
16C2×#66948C2212yes—
17C2×#66946—21no—
18C2×#66946C2212yes—
19C2×C4⋊C4×D11—21no—
20C2×C4⋊C4×D11—21no—
21C2×C4⋊C4×D11C2212yes—
22C2×#66927C2211yescharacteristic
23C2×C42×D11C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C11×#384C2211yescharacteristic
26C2×#66885C2214yes—
27C2×(C2×D11)⋊C8C2212yes—
28C2×Dic11⋊C8C2212yes—
29#10622589—21no—
30#10622589—21no—
31#10622589C2212yes—
32C2×#66873C2214yes—
33#10622548C2211yescharacteristic
34C2×C4×C11⋊C8C2211yescharacteristic
35#10622298—24no—
36C11×#340C2214yes—
37#10622167C2214yes—
38C22×Q8×C11—21no—
39C2×#4343—28no—
40C2×#4343—44no—
41C2×#4343—44no—
42C22×D44—22no—
43C22×D44—21no—
44C22×D44—21no—
45C22×D44C2312yes—
46C22×C4×D11—22no—
47C22×C4×D11—22no—
48C22×C4×D11D411yescharacteristic
49C22×C4×D11D411yescharacteristic
50C22×C4×D11C2311yescharacteristic
51C22×C8×C11C2312yes—
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8C2×C414yescomplemented
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C4⋊C4C2312yes—
59C2×C42×C11C2311yescharacteristic
60#67000—28no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—22no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11C2312yes—
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—22no—
69C2×C4×Dic11D411yescharacteristic
70C2×C4×Dic11D411yescharacteristic
71C2×C4×Dic11C2311yescharacteristic
72C22×C11⋊C8C2312yes—
73#66948—28no—
74#66948—24no—
75#66948C2×C418yes—
76#66946—28no—
77#66946—24no—
78#66946C2×C418yescomplemented
79C4⋊C4×D11—44no—
80C4⋊C4×D11—44no—
81C4⋊C4×D11—44no—
82#66927—22no—
83#66927C2×C414yescomplemented
84C42×D11C2×C414yes—
85C42×D11D414yes—
86C4×C8×C11—22no—
87#66885—44no—
88(C2×D11)⋊C8—24no—
89Dic11⋊C8—24no—
90#66873—44no—
91C4×C11⋊C8—22no—
92#21859—111nomaximal, Sylow
93C23×D11—22no—
94C23×D11C2×D411yescharacteristic
95C2×Q8×C11—24no—
96C2×Q8×C11—42no—
97C2×Q8×C11—42no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2411yescharacteristic
103C22×Dic11—22no—
104C22×Dic11C2×D411yescharacteristic
105C22×Dic11C2×D411yescharacteristic
106C22×Dic11C2×D411yescharacteristic
107#4343—432no—
108C2×D44—28no—
109C2×D44—24no—
110C2×D44—24no—
111C2×D44—22no—
112C2×D44—24no—
113C2×D44—24no—
114C2×D44—44no—
115C2×D44—44no—
116C2×D44—42no—
117C2×D44—42no—
118C2×D44—42no—
119C2×D44—42no—
120C2×D44C22×C414yes—
121C2×C4×D11—28no—
122C2×C4×D11—22no—
123C2×C4×D11—22no—
124C2×C4×D11—22no—
125C2×C4×D11—22no—
126C2×C4×D11—44no—
127C2×C4×D11—44no—
128C2×C4×D11—44no—
129C2×C4×D11—44no—
130C2×C4×D11—44no—
131C2×C4×D11C22⋊C414yes—
132C2×C4×D11C22⋊C414yes—
133C2×C4×D11D814yes—
134C2×C4×D11SD1614yes—
135C2×C4×D11C22×C412yes—
136C2×C4×D11C2×D412yes—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—42no—
144C11×C4⋊C4—42no—
145C11×C4⋊C4C22×C414yes—
146C42×C11C22×C412yes—
147C42×C11C2×D412yes—
148(C2×D11)⋊C4—28no—
149(C2×D11)⋊C4—28no—
150C4⋊Dic11—24no—
151C4⋊Dic11—42no—
152C4⋊Dic11—42no—
153Dic11⋊C4—44no—
154Dic11⋊C4—44no—
155Dic11⋊C4—44no—
156C4×Dic11C22⋊C414yes—
157C4×Dic11C22⋊C414yes—
158C4×Dic11C22×C412yes—
159C4×Dic11C2×D412yes—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—22no—
163C2×#532—111no—
164C2×#431—111no—
165C2×#384—111no—
166#1990—111no—
167#1990D1111yescharacteristic, complemented
168#1957—111no—
169#1957—111no—
170#1874—114no—
171#1802—114no—
172C23×C11C22×D411yescharacteristic
173C22×D11—21no—
174C22×D11—21no—
175C22×D11—21no—
176C22×D11—21no—
177C22×D11—24no—
178C22×D11—42no—
179C22×D11—42no—
180C22×D11—42no—
181C22×D11—42no—
182C22×D11—42no—
183C22×D11—42no—
184C22×D11C2×C22⋊C412yes—
185C22×D11C2×D812yes—
186C22×D11C2×SD1612yes—
187Q8×C11—48no—
188C2×C4×C11—24no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11C2×C22⋊C412yes—
195C2×C4×C11C2×C22⋊C412yes—
196C2×C4×C11C2×D812yes—
197C2×C4×C11C2×SD1612yes—
198C2×C4×C11AGL(1,ℤ/8)12yes—
199C2×C4×C11#13712yes—
200C2×C4×C11C23×C411yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11H(5,𝔽2)12yes—
203C2×C4×C112−1+412yes—
204C2×Dic11—21no—
205C2×Dic11—21no—
206C2×Dic11—21no—
207C2×Dic11—21no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11C2×C22⋊C412yes—
212C2×Dic11C2×C22⋊C412yes—
213C2×Dic11C2×C22⋊C412yes—
214C2×Dic11C2×D812yes—
215C2×Dic11C2×SD1612yes—
216D44—28no—
217D44—416no—
218D44—44no—
219D44—48no—
220D44—48no—
221C4×D11—24no—
222C4×D11—24no—
223C4×D11—28no—
224C4×D11—416no—
225C4×D11—88no—
226C4×D11#102116yescomplemented
227C8×C11—42no—
228C11⋊C8—42no—
229C22×#41—221no—
230#532—118no—
231#532—224no—
232C2×C4⋊Q8C2×D1111yescharacteristic
233C2×#127—111no—
234C2×#124—221no—
235C2×#121—112no—
236C2×#121—221no—
237C2×C4×D4—112no—
238C2×C4×D4—221no—
239C22×C4⋊C4—112no—
240C22×C4⋊C4—221no—
241C22×C4⋊C4—221no—
242C22×C42—111no—
243#431—224no—
244C2×C4⋊C8—112no—
245C2×#102—114no—
246C2×#102—114no—
247C2×C22⋊C8—112no—
248C2×C4×C8—111no—
249C2×C4×C8C2×D1111yescharacteristic
250#384—112no—
251#384—111no—
252#384—221no—
253#384—221no—
254#384C2×D1111yescharacteristic
255#340—114no—
256#340C2×D1114yes—
257C22×C11C22×C22⋊C411yescharacteristic
258C22×C11#53511yescharacteristic
259C22×C11#53611yescharacteristic
260C22×C11C22×D811yescharacteristic
261C22×C11C22×SD1611yescharacteristic
262C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
263C22×C11C2×#13711yescharacteristic
264C2×D11—22no—
265C2×D11—22no—
266C2×D11—22no—
267C2×D11—22no—
268C2×D11—22no—
269C2×D11—22no—
270C2×D11—44no—
271C2×D11—44no—
272C2×D11—44no—
273C2×D11—82no—
274C2×D11—82no—
275C2×D11—82no—
276C2×D11—82no—
277C2×D11C2×#10214yes—
278C4×C11—44no—
279C4×C11—82no—
280C4×C11C2×#10214yes—
281C4×C11#41714yes—
282C4×C11#52012yes—
283C4×C11#53712yes—
284Dic11—22no—
285Dic11—22no—
286Dic11—82no—
287Dic11C2×#10214yes—
288C2×#41—228no—
289C2×#41—444no—
290C2×#41—444no—
291C22×Q8—21no—
292C22×D4—112no—
293C22×D4—222no—
294C22×D4—221no—
295C22×D4—221no—
296C23×C4—111no—
297C23×C4—111no—
298C23×C4—111no—
299C23×C4—222no—
300C23×C4—222no—
301C22×C8—112no—
302C22×C8C22×D1112yes—
303C4⋊Q8—22no—
304C4⋊Q8C4×D1114yescomplemented
305#127—114no—
306#127—222no—
307#124—228no—
308#121—118no—
309#121—224no—
310#121—228no—
311C4×D4—118no—
312C4×D4—224no—
313C4×D4—228no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—112no—
318C2×C4⋊C4—222no—
319C2×C4⋊C4—222no—
320C2×C4⋊C4—222no—
321C2×C4⋊C4—221no—
322C2×C4⋊C4—221no—
323C2×C4⋊C4—444no—
324C2×C4⋊C4—444no—
325C2×C4⋊C4—444no—
326C2×C4⋊C4C22×D1112yes—
327C2×C4⋊C4C22×D1112yes—
328C2×C22⋊C4—222no—
329C2×C22⋊C4—222no—
330C2×C42—111no—
331C2×C42—111no—
332C2×C42—111no—
333C2×C42—114no—
334C2×C42—114no—
335C2×C42C22×D1111yescharacteristic
336C4⋊C8—224no—
337#102—444no—
338#102—444no—
339C22⋊C8—224no—
340C4×C8—22no—
341C4×C8—222no—
342C2×C11#231111yescharacteristic
343C2×C11C22×#10211yescharacteristic
344C2×C11C2×#41711yescharacteristic
345C2×C11#320511yescharacteristic
346C2×C11#320611yescharacteristic
347C2×C11#322611yescharacteristic
348C2×C11#322711yescharacteristic
349D11—24no—
350D11—84no—
351C24—111no—
352C24—222no—
353#41—4432no—
354C2×Q8—24no—
355C2×Q8—42no—
356C2×Q8—42no—
357C2×D4—114no—
358C2×D4—228no—
359C2×D4—224no—
360C2×D4—224no—
361C2×D4—222no—
362C2×D4—224no—
363C2×D4—224no—
364C2×D4—444no—
365C2×D4—444no—
366C2×D4—442no—
367C2×D4—442no—
368C2×D4—442no—
369C2×D4—442no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—111no—
373C22×C4—114no—
374C22×C4—114no—
375C22×C4—114no—
376C22×C4—111no—
377C22×C4—111no—
378C22×C4—114no—
379C22×C4—112no—
380C22×C4—112no—
381C22×C4—228no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—222no—
385C22×C4—222no—
386C22×C4—222no—
387C22×C4—444no—
388C22×C4—444no—
389C22×C4—444no—
390C22×C4—444no—
391C22×C4—444no—
392C22×C4D4×D1111yescharacteristic
393C22×C4D4×D1111yescharacteristic
394C22×C4C23×D1111yescharacteristic
395C2×C8—22no—
396C2×C8—22no—
397C2×C8—22no—
398C2×C8—222no—
399C2×C8—222no—
400C2×C8—222no—
401C4⋊C4—24no—
402C4⋊C4—22no—
403C4⋊C4—24no—
404C4⋊C4—42no—
405C4⋊C4—42no—
406C4⋊C4—224no—
407C4⋊C4—444no—
408C4⋊C4—444no—
409C4⋊C4—444no—
410C4⋊C4—442no—
411C4⋊C4—442no—
412C4⋊C4C2×C4×D1114yes—
413C22⋊C4—228no—
414C22⋊C4—228no—
415C42—114no—
416C42—114no—
417C42—112no—
418C42—112no—
419C42C2×C4×D1112yes—
420C42D4×D1112yes—
421C11#2185911yescharacteristic, complemented, Sylow
422C23—112no—
423C23—112no—
424C23—112no—
425C23—221no—
426C23—221no—
427C23—221no—
428C23—221no—
429C23—224no—
430C23—442no—
431C23—442no—
432C23—442no—
433C23—442no—
434C23—442no—
435C23—442no—
436C23C2×D4×D1111yescharacteristic
437Q8—48no—
438D4—228no—
439D4—4416no—
440D4—448no—
441D4—444no—
442D4—448no—
443C2×C4—24no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—112no—
450C2×C4—112no—
451C2×C4—112no—
452C2×C4—1116no—
453C2×C4—112no—
454C2×C4—112no—
455C2×C4—221no—
456C2×C4—221no—
457C2×C4—221no—
458C2×C4—221no—
459C2×C4—224no—
460C2×C4—224no—
461C2×C4—228no—
462C2×C4—4416no—
463C2×C4—442no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4—888no—
467C2×C4C22⋊C4×D1112yes—
468C2×C4C22⋊C4×D1112yes—
469C2×C4D8×D1112yes—
470C2×C4SD16×D1112yes—
471C2×C4#6696712yes—
472C2×C4#6697112yes—
473C2×C4C22×C4×D1111yescharacteristic
474C2×C4C2×D4×D1111yescharacteristic
475C2×C4#6704012yes—
476C2×C4#6704212yes—
477C8—42no—
478C8—442no—
479C22—114no—
480C22—222no—
481C22—222no—
482C22—222no—
483C22—222no—
484C22—222no—
485C22—222no—
486C22—444no—
487C22—444no—
488C22—444no—
489C22—882no—
490C22—882no—
491C22—882no—
492C22—882no—
493C22C2×C22⋊C4×D1111yescharacteristic
494C22#1062320511yescharacteristic
495C22#1062325511yescharacteristic
496C22C2×D8×D1111yescharacteristic
497C22C2×SD16×D1111yescharacteristic
498C22C2×#6696711yescharacteristic
499C22C2×#6697111yescharacteristic
500C4—44no—
501C4—82no—
502C4—114no—
503C4—222no—
504C4—222no—
505C4—882no—
506C4D11×#10214yes—
507C4#1062241614yes—
508C4#1062310512yes—
509C4#1062316012yes—
510C2—224no—
511C2—884no—
512C2#1307120711yescharacteristic
513C2C2×D11×#10211yescharacteristic
514C2C2×#1062241611yescharacteristic
515C2#1307953511yescharacteristic
516C2#1307954211yescharacteristic
517C2#1307973811yescharacteristic
518C2#1307974511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1990C2
socleC23×C11C22×D4
prime radicalC2×#10623256C2
cosocleC22×C4×C11C24
hypercenter#1990D11
hypocenterC11#21859
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
2. C2×#10622298C2semidirect
3. D11×#384C2semidirect
4. #13069578C2semidirect
5. #13069422C2semidirect
6. #13069421C2semidirect
7. #13068932C2semidirect
8. #13068615C2semidirect
9. C11×#1990C2semidirect
14. #10623256C4semidirect
53. C11×C4⋊Q8C2×C4semidirect
78. #66946C2×C4semidirect
83. #66927C2×C4semidirect
167. #1990D11semidirect
226. C4×D11#102semidirect
304. C4⋊Q8C4×D11semidirect
421. C11#21859semidirect

Maximal subgroups

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

subgroupindex
C2×#106232562
C2×#106222982
D11×#3842
#130695782
#130694222
#130694212
#130689322
#130686152
C11×#19902
#2185911