Finite Group Databasebeta

← #14810400

Subgroups — #14810400

Order 2816.

1218 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic, complemented
2C2×#10622683C211yesmaximal, characteristic, complemented
3#13076958C211yesmaximal, characteristic
4#13069760C214yesmaximal, complemented
5#13069578C211yesmaximal, characteristic, complemented
6#13069577C211yesmaximal, characteristic, complemented
7#13068935C214yesmaximal, complemented
8C4×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
9C2×C11×#486C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×#127C2211yescharacteristic
12C2×#66999—21no—
13C2×Q8×Dic11—21no—
14C2×#66991—21no—
15C2×#66991—21no—
16C2×#66991C2212yes—
17#10623259—24no—
18#10623259—24no—
19C2×#66950—21no—
20C2×#66945C2212yes—
21C2×#66943C2212yes—
22C2×#66940—21no—
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—
44C22×C4×D11D411yescharacteristic
45C22×C4×D11D411yescharacteristic
46C22×C4×D11C2311yescharacteristic
47C22×Dic22—21no—
48C22×C8×C11C2312yes—
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8D414yescomplemented
51C11×#127—22no—
52C11×#127—22no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4C2312yes—
55C2×C42×C11C2311yescharacteristic
56C2×C22⋊Dic11—22no—
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11—22no—
59#66999—28no—
60Q8×Dic11—28no—
61#66991—28no—
62#66991—44no—
63#66991—44no—
64C2×(C2×D11)⋊C4—22no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11C2312yes—
70C2×C4⋊Dic11C2312yes—
71C2×Dic11⋊C4—22no—
72C2×C4×Dic11—22no—
73C2×C4×Dic11D411yescharacteristic
74C2×C4×Dic11D411yescharacteristic
75C2×C4×Dic11C2311yescharacteristic
76C22×C11⋊C8C2312yes—
77#66950—28no—
78#66945—24no—
79#66945—24no—
80#66943—24no—
81#66943—24no—
82#66940—28no—
83C42×D11—22no—
84C42×D11—22no—
85#66922—22no—
86#66922D414yescomplemented
87C11×#102—28no—
88C4×C8×C11—22no—
89#66896—28no—
90(C2×D11)⋊C8—24no—
91C4×C11⋊C8—22no—
92#25905—111nomaximal, Sylow
93C24×C11—22no—
94C23×D11C2×D411yescharacteristic
95C2×Q8×C11—24no—
96C2×Q8×C11—42no—
97C2×Q8×C11—42no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—24no—
101C2×D4×C11—24no—
102C2×D4×C11—42no—
103C2×D4×C11—42no—
104C2×D4×C11—42no—
105C2×D4×C11—42no—
106C2×D4×C11—42no—
107C2×D4×C11—42no—
108C22×C4×C11—22no—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2411yescharacteristic
112C2×C22⋊D11—44no—
113C2×C22⋊D11—44no—
114C2×C22⋊D11—44no—
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11C2×D411yescharacteristic
118C22×Dic11C2×D411yescharacteristic
119C22×Dic11C2×D411yescharacteristic
120C2×C4×D11—22no—
121C2×C4×D11—22no—
122C2×C4×D11—22no—
123C2×C4×D11—22no—
124C2×C4×D11—22no—
125C2×C4×D11—22no—
126C2×C4×D11—21no—
127C2×C4×D11—21no—
128C2×C4×D11—22no—
129C2×C4×D11#4114yes—
130C2×Dic22—24no—
131C2×Dic22—42no—
132C2×Dic22—42no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4C2×D414yes—
139C42×C11C2×D412yes—
140C42×C11C2×D412yes—
141C22⋊Dic11—44no—
142C22⋊Dic11—44no—
143C22⋊Dic11—44no—
144(C2×D11)⋊C4—28no—
145C4⋊Dic11—28no—
146C4⋊Dic11—24no—
147C4⋊Dic11—22no—
148C4⋊Dic11—24no—
149C4⋊Dic11—42no—
150C4⋊Dic11—42no—
151C4⋊Dic11C2×D414yes—
152Dic11⋊C4—28no—
153C4×Dic11—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—
161C2×#533—111no—
162C2×#486—111no—
163C2×#486D1111yescharacteristic, complemented
164#2856—111no—
165#2025—114no—
166#1990—111no—
167#1990—111no—
168#1875—114no—
169C4×C22⋊C8—111no—
170C23×C11—42no—
171C23×C11—42no—
172C23×C11—42no—
173C23×C11—42no—
174C23×C11—42no—
175C23×C11—42no—
176C23×C11—42no—
177C23×C11C22×D411yescharacteristic
178C22×D11—21no—
179C22×D11—21no—
180C22×D11—21no—
181C22×D11—21no—
182C22×D11—21no—
183C22×D11—21no—
184C22×D11#12412yes—
185Q8×C11—48no—
186D4×C11—44no—
187D4×C11—44no—
188D4×C11—84no—
189D4×C11—84no—
190C2×C4×C11—24no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11#12012yes—
194C2×C4×C11#12012yes—
195C2×C4×C11#13512yes—
196C2×C4×C11#13512yes—
197C2×C4×C11AGL(1,ℤ/8)12yes—
198C2×C4×C11AGL(1,ℤ/8)12yes—
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C2×#4112yes—
202C2×C4×C112−1+412yes—
203C22⋊D11—88no—
204C2×Dic11—21no—
205C2×Dic11—21no—
206C2×Dic11—21no—
207C2×Dic11—21no—
208C2×Dic11—24no—
209C2×Dic11—21no—
210C2×Dic11—21no—
211C2×Dic11—21no—
212C2×Dic11—21no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11#12412yes—
219C4×D11—24no—
220C4×D11—24no—
221C4×D11—44no—
222C4×D11—44no—
223Dic22—48no—
224C8×C11—42no—
225C11⋊C8—42no—
226#533—224no—
227#533—224no—
228C2×C4⋊Q8—111no—
229C2×C4⋊Q8C2×D1111yescharacteristic
230C2×#127C2×D1111yescharacteristic
231C2×#125—112no—
232C2×C22⋊Q8—221no—
233C2×C22⋊Q8—221no—
234C2×#121—112no—
235C2×#121—221no—
236C2×#121—221no—
237C2×C4×Q8—221no—
238C2×C4×Q8—221no—
239C2×#117—112no—
240C22×C42—111no—
241#486—24no—
242#486—224no—
243C2×#102—114no—
244C2×#102C2×D1114yes—
245C2×C22⋊C8—112no—
246C2×C4×C8—111no—
247C2×C4×C8C2×D1111yescharacteristic
248#390—112no—
249#390—221no—
250#390—221no—
251#384—111no—
252#340—114no—
253#340—114no—
254#336—112no—
255C22×C11—82no—
256C22×C11—82no—
257C22×C11—82no—
258C22×C11—82no—
259C22×C11—82no—
260C22×C11—82no—
261C22×C11—82no—
262C22×C11C2×#12011yescharacteristic
263C22×C11C2×#12411yescharacteristic
264C22×C11#53611yescharacteristic
265C22×C11C2×#13511yescharacteristic
266C22×C11C2×#13511yescharacteristic
267C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
268C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
269C2×D11—22no—
270C2×D11—22no—
271C2×D11—22no—
272C2×D11—41no—
273C2×D11—41no—
274C2×D11—41no—
275C2×D11—41no—
276C4×C11—44no—
277C4×C11#44914yes—
278C4×C11#44914yes—
279C4×C11#54812yes—
280C4×C11#54812yes—
281Dic11—22no—
282Dic11—44no—
283Dic11—41no—
284Dic11—41no—
285Dic11—82no—
286C22×Q8—21no—
287C22×Q8—221no—
288C22×D4—21no—
289C22×D4—21no—
290C22×D4—222no—
291C22×D4C22×D1112yes—
292C23×C4—111no—
293C23×C4—111no—
294C23×C4—111no—
295C22×C8—112no—
296C22×C8C22×D1112yes—
297C4⋊Q8—22no—
298C4⋊Q8—114no—
299C4⋊Q8—222no—
300C4⋊Q8C22⋊D1114yescomplemented
301#127—22no—
302#127—22no—
303#125—224no—
304#125—224no—
305C22⋊Q8—228no—
306C22⋊Q8—228no—
307#121—228no—
308#121—444no—
309#121—444no—
310C4×Q8—228no—
311C4×Q8—228no—
312#117—224no—
313#117—224no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—112no—
316C2×C4⋊C4—112no—
317C2×C4⋊C4—222no—
318C2×C4⋊C4—222no—
319C2×C4⋊C4—221no—
320C2×C4⋊C4—221no—
321C2×C4⋊C4—221no—
322C2×C4⋊C4C22×D1112yes—
323C2×C22⋊C4—222no—
324C2×C22⋊C4—222no—
325C2×C22⋊C4—222no—
326C2×C22⋊C4—222no—
327C2×C42—111no—
328C2×C42—111no—
329C2×C42—111no—
330C2×C42—222no—
331C2×C42—222no—
332C2×C42—222no—
333C2×C42C22×D1111yescharacteristic
334#102—28no—
335#102—228no—
336C22⋊C8—224no—
337C4×C8—22no—
338C4×C8—222no—
339C2×C11—162no—
340C2×C11#243611yescharacteristic
341C2×C11C2×#44911yescharacteristic
342C2×C11C2×#44911yescharacteristic
343C2×C11#313111yescharacteristic
344C2×C11#313811yescharacteristic
345C2×C11#322811yescharacteristic
346C2×C11#322811yescharacteristic
347D11—42no—
348C24—22no—
349C24—111no—
350C2×Q8—24no—
351C2×Q8—42no—
352C2×Q8—42no—
353C2×Q8—224no—
354C2×Q8—442no—
355C2×Q8—442no—
356C2×D4—22no—
357C2×D4—24no—
358C2×D4—24no—
359C2×D4—22no—
360C2×D4—42no—
361C2×D4—42no—
362C2×D4—42no—
363C2×D4—42no—
364C2×D4—42no—
365C2×D4—42no—
366C2×D4—444no—
367C2×D4—444no—
368C2×D4—444no—
369C22×C4—22no—
370C22×C4—111no—
371C22×C4—114no—
372C22×C4—111no—
373C22×C4—111no—
374C22×C4—221no—
375C22×C4—222no—
376C22×C4—221no—
377C22×C4—222no—
378C22×C4—222no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—222no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—222no—
385C22×C4D4×D1111yescharacteristic
386C22×C4D4×D1111yescharacteristic
387C22×C4C23×D1111yescharacteristic
388C2×C8—22no—
389C2×C8—22no—
390C2×C8—22no—
391C2×C8—222no—
392C2×C8—222no—
393C2×C8—222no—
394C4⋊C4—24no—
395C4⋊C4—22no—
396C4⋊C4—114no—
397C4⋊C4—228no—
398C4⋊C4—228no—
399C4⋊C4—224no—
400C4⋊C4—222no—
401C4⋊C4—224no—
402C4⋊C4—442no—
403C4⋊C4—442no—
404C4⋊C4C2×C22⋊D1114yes—
405C22⋊C4—228no—
406C22⋊C4—444no—
407C22⋊C4—444no—
408C22⋊C4—444no—
409C42—228no—
410C42—222no—
411C42—222no—
412C42—221no—
413C42—221no—
414C42D4×D1112yes—
415C42C2×C22⋊D1112yes—
416C11#2590511yescharacteristic, complemented, Sylow
417C23—42no—
418C23—42no—
419C23—42no—
420C23—42no—
421C23—42no—
422C23—42no—
423C23—42no—
424C23—112no—
425C23—221no—
426C23—221no—
427C23—221no—
428C23—221no—
429C23—221no—
430C23—221no—
431C23C2×D4×D1111yescharacteristic
432Q8—48no—
433Q8—448no—
434D4—44no—
435D4—44no—
436D4—84no—
437D4—84no—
438D4—888no—
439C2×C4—24no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—112no—
443C2×C4—221no—
444C2×C4—221no—
445C2×C4—224no—
446C2×C4—224no—
447C2×C4—221no—
448C2×C4—221no—
449C2×C4—221no—
450C2×C4—221no—
451C2×C4—221no—
452C2×C4—221no—
453C2×C4—224no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4—444no—
457C2×C4—444no—
458C2×C4—442no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4#6696412yes—
462C2×C4#6696512yes—
463C2×C4#6696712yes—
464C2×C4#6696912yes—
465C2×C4#6699012yes—
466C2×C4#6699012yes—
467C2×C4C2×D4×D1111yescharacteristic
468C2×C4#41×D1112yes—
469C2×C4#6704312yes—
470C2×C4C22×C22⋊D1111yescharacteristic
471C8—42no—
472C8—442no—
473C22—82no—
474C22—82no—
475C22—82no—
476C22—82no—
477C22—82no—
478C22—82no—
479C22—82no—
480C22—222no—
481C22—222no—
482C22—222no—
483C22—441no—
484C22—441no—
485C22—441no—
486C22—441no—
487C22D11×#12411yescharacteristic
488C22#1062320611yescharacteristic
489C22C2×#6696411yescharacteristic
490C22C2×#6696511yescharacteristic
491C22C2×#6696711yescharacteristic
492C22C2×#6696911yescharacteristic
493C22C2×#6699011yescharacteristic
494C4—44no—
495C4—222no—
496C4—441no—
497C4—441no—
498C4—444no—
499C4—882no—
500C4#1062277114yes—
501C4#1062278514yes—
502C4#1062320812yes—
503C4#1062336212yes—
504C2—162no—
505C2—442no—
506C2#1307227111yescharacteristic
507C2C2×#1062277111yescharacteristic
508C2C2×#1062278511yescharacteristic
509C2#1307893511yescharacteristic
510C2#1307898711yescharacteristic
511C2#1307974711yescharacteristic
512C2#1307974911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#486C2
socleC23×C11C22×D4
prime radical#13076958C2
hypercenterC2×#486D11
hypocenterC11#25905
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×#10623259C2semidirect
2. C2×#10622683C2semidirect
4. #13069760C2semidirect
5. #13069578C2semidirect
6. #13069577C2semidirect
7. #13068935C2semidirect
8. C4×(C2×D11)⋊C8C2semidirect
9. C2×C11×#486C2semidirect
50. C11×C4⋊Q8D4semidirect
86. #66922D4semidirect
163. C2×#486D11semidirect
300. C4⋊Q8C22⋊D11semidirect
416. C11#25905semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×#106226832
#130769582
#130697602
#130695782
#130695772
#130689352
C4×(C2×D11)⋊C82
C2×C11×#4862
#2590511