Finite Group Databasebeta

← #14758989

Subgroups — #14758989

Order 2816.

1230 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623155C211yesmaximal, characteristic
2C22×#66879C211yesmaximal, characteristic, complemented
3#13071018C211yesmaximal, characteristic, complemented
4#13069583C212yesmaximal, complemented
5#13069429C212yesmaximal, complemented
6#13069044C211yesmaximal, characteristic
7#13069042C211yesmaximal, characteristic
8#13069040C211yesmaximal, characteristic, complemented
9#13068448C212yesmaximal, complemented
10#13068440C212yesmaximal, complemented
11C11×#1892C211yesmaximal, characteristic, complemented
12C23×C8×C11C2211yescharacteristic
13C2×C11×C22⋊Q8C2211yescharacteristic
14C2×#67000C2211yescharacteristic
15C2×Q8×Dic11C2211yescharacteristic
16C2×#66983C2211yescharacteristic
17C22×C4×Dic11C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19#10623155—24no—
20#10623155C418yescomplemented
21C2×#66951—21no—
22C2×#66946C2211yescharacteristic
23C2×#66945—21no—
24C2×#66943C2211yescharacteristic
25C2×#66939—21no—
26C2×(C22⋊D11)⋊C4—21no—
27C2×#66930—21no—
28C2×C11×#103C2212yes—
29C11×#380C2211yescharacteristic
30C2×#66899C2212yes—
31#10622825C2211yescharacteristic
32C2×#66885C2212yes—
33C2×#66879—24no—
34C2×#66879C2212yes—
35C2×#66879C2212yes—
36#10622589C2212yes—
37C4⋊C4×Dic11C2212yes—
38C2×#66873C2212yes—
39#10622555—21no—
40#10622263—21no—
41#10622262—21no—
42C11×#340C2212yes—
43#10622189C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C22×Q8×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C22×C22⋊D11—21no—
49C23×Dic11D411yescharacteristic
50C23×Dic11D411yescharacteristic
51C22×D44C2311yescharacteristic
52C22×C4×D11—21no—
53C22×C8×C11—22no—
54C22×C8×C11—24no—
55C22×C8×C11C2312yes—
56C11×C22⋊Q8—22no—
57C11×C22⋊Q8C2×C414yes—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C22⋊C4—21no—
62C2×C11×C22⋊C4—21no—
63C2×C22⋊Dic11—21no—
64#67000—22no—
65#67000C2×C414yes—
66Q8×Dic11—22no—
67Q8×Dic11C2×C414yes—
68#66983—22no—
69#66983C2×C414yes—
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11C2312yes—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×Dic11⋊C4—21no—
79C2×Dic11⋊C4—22no—
80C2×Dic11⋊C4—22no—
81C2×C4×Dic11—21no—
82C2×C4×Dic11—22no—
83C2×C4×Dic11C2×C414yes—
84C2×C4×Dic11D411yescharacteristic
85C2×C4×Dic11D411yescharacteristic
86C2×C4×Dic11D414yes—
87C2×C4×Dic11C2311yescharacteristic
88C2×C4×Dic11C2311yescharacteristic
89C22×C11⋊C8—22no—
90C22×C11⋊C8—24no—
91C22×C11⋊C8C2312yes—
92#66951—28no—
93#66946—22no—
94#66946C2×C414yes—
95#66945—28no—
96#66943—22no—
97#66943C2×C414yes—
98#66939—28no—
99(C22⋊D11)⋊C4—28no—
100#66930—44no—
101C11×#103—24no—
102C11×#95—21no—
103#66899—24no—
104C11⋊#95—21no—
105C11⋊#95—22no—
106#66885—24no—
107#66879—24no—
108#66879—24no—
109#66873—24no—
110#21406—111nomaximal, Sylow
111C24×C11C2×D411yescharacteristic
112C23×D11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11C22×C412yes—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11C22×C412yes—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2411yescharacteristic
126C2×C22⋊D11—24no—
127C2×C22⋊D11—42no—
128C2×C22⋊D11—42no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—21no—
132C22×Dic11—22no—
133C22×Dic11—42no—
134C22×Dic11C22⋊C414yes—
135C22×Dic11C22⋊C414yes—
136C22×Dic11C2×D411yescharacteristic
137C22×Dic11C2×D411yescharacteristic
138C22×Dic11C2×D411yescharacteristic
139C22×Dic11C2×D411yescharacteristic
140C2×D44—21no—
141C2×D44—22no—
142C2×D44—22no—
143C2×D44C22×C412yes—
144C2×C4×D11—24no—
145C2×C4×D11—44no—
146C2×C8×C11—28no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11#4114yes—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4C22×C412yes—
155C11×C22⋊C4—24no—
156C11×C22⋊C4—42no—
157C22⋊Dic11—42no—
158(C2×D11)⋊C4—24no—
159(C2×D11)⋊C4—24no—
160(C2×D11)⋊C4—24no—
161(C2×D11)⋊C4—24no—
162C4⋊Dic11—24no—
163C4⋊Dic11—24no—
164C4⋊Dic11—21no—
165C4⋊Dic11—22no—
166C4⋊Dic11—22no—
167C4⋊Dic11C22×C412yes—
168Dic11⋊C4—24no—
169Dic11⋊C4—44no—
170Dic11⋊C4—44no—
171C4×Dic11—24no—
172C4×Dic11—44no—
173C4×Dic11C22⋊C414yes—
174C4×Dic11C22⋊C414yes—
175C4×Dic11C22×C412yes—
176C4×Dic11C22×C412yes—
177C4×Dic11C2×D412yes—
178C4×Dic11C2×D412yes—
179C2×C11⋊C8—28no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8#4114yes—
183C2×#529—111no—
184C22×#97—111no—
185#2285—111no—
186#1992—112no—
187#1959—112no—
188#1893—111no—
189#1893—111no—
190#1892—111no—
191#1892D1111yescharacteristic, complemented
192#1763—112no—
193#1762—112no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11C2×C22⋊C412yes—
197C23×C11AGL(1,ℤ/8)12yes—
198C23×C11#13712yes—
199C23×C11C22×D411yescharacteristic
200C22×D11—22no—
201C22×D11—42no—
202C22×D11—41no—
203C22×D11—41no—
204C22×D11—42no—
205Q8×C11—24no—
206Q8×C11—41no—
207Q8×C11—41no—
208C2×C4×C11—22no—
209C2×C4×C11—24no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11C2×C22⋊C412yes—
220C2×C4×C11C23×C411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C2×#4112yes—
223C2×C4×C11C2×#4112yes—
224C22⋊D11—48no—
225C2×Dic11—21no—
226C2×Dic11—21no—
227C2×Dic11—21no—
228C2×Dic11—21no—
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—28no—
232C2×Dic11—22no—
233C2×Dic11—44no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11C2×C22⋊C412yes—
240C2×Dic11C2×C22⋊C412yes—
241C2×Dic11C2×C22⋊C412yes—
242C2×Dic11C2×C22⋊C412yes—
243D44—24no—
244D44—41no—
245D44—41no—
246C4×D11—48no—
247C8×C11—24no—
248C11⋊C8—24no—
249C23×C8—111no—
250C23×C8C2×D1111yescharacteristic
251#529—118no—
252#529—224no—
253C2×#126—221no—
254C2×#125—111no—
255C2×#124—111no—
256C2×#123—221no—
257C2×C22⋊Q8C2×D1111yescharacteristic
258C2×#121—111no—
259C2×C4×Q8—111no—
260C2×C4×D4—111no—
261C2×C4×D4—221no—
262C2×#117—221no—
263C2×#117—221no—
264C22×C42—111no—
265C2×#103—112no—
266C2×#103C2×D1112yes—
267C2×#102—112no—
268C2×#102—112no—
269C2×#97—112no—
270C2×#97—112no—
271C2×#97—224no—
272#384—112no—
273#382—221no—
274#380—111no—
275#380—221no—
276#380C2×D1111yescharacteristic
277C4×C4⋊C4—112no—
278C4×C4⋊C4—221no—
279#340—112no—
280#340—112no—
281#340—112no—
282#340C2×D1112yes—
283C22×C11—22no—
284C22×C11—24no—
285C22×C11—24no—
286C22×C11—22no—
287C22×C11#41714yes—
288C22×C11C22×C22⋊C411yescharacteristic
289C22×C11#53212yes—
290C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
291C22×C11C2×#13711yescharacteristic
292C22×C11#57512yes—
293C2×D11—42no—
294C2×D11—42no—
295C2×D11—42no—
296C2×D11—82no—
297C2×D11—82no—
298C4×C11—22no—
299C4×C11—42no—
300C4×C11—42no—
301C4×C11—82no—
302C4×C11C4×#4112yes—
303C4×C11#52511yescharacteristic
304C4×C11#52511yescharacteristic
305Dic11—22no—
306Dic11—22no—
307Dic11—22no—
308Dic11—22no—
309Dic11—42no—
310Dic11—82no—
311C22×Q8C22×D1111yescharacteristic
312C22×D4—111no—
313C22×D4—221no—
314C23×C4—111no—
315C23×C4—111no—
316C23×C4—221no—
317C23×C4C22×D1111yescharacteristic
318C22×C8—22no—
319C22×C8—24no—
320C22×C8—112no—
321C22×C8—224no—
322C22×C8—222no—
323C22×C8C22×D1112yes—
324#126—228no—
325#125—114no—
326#125—222no—
327#124—114no—
328#124—222no—
329#123—228no—
330C22⋊Q8—22no—
331C22⋊Q8C4×D1114yes—
332#121—114no—
333#121—222no—
334C4×Q8—114no—
335C4×Q8—222no—
336C4×D4—114no—
337C4×D4—222no—
338C4×D4—228no—
339#117—228no—
340#117—444no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—111no—
343C2×C4⋊C4—112no—
344C2×C4⋊C4—221no—
345C2×C4⋊C4—221no—
346C2×C4⋊C4—221no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4C22×D1112yes—
350C2×C4⋊C4C22×D1111yescharacteristic
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—221no—
354C2×C22⋊C4—221no—
355C2×C22⋊C4—221no—
356C2×C22⋊C4—221no—
357C2×C22⋊C4—221no—
358C2×C42—114no—
359C2×C42—111no—
360C2×C42—111no—
361C2×C42—114no—
362C2×C42—111no—
363C2×C42—111no—
364C2×C42—221no—
365C2×C42—222no—
366#103—24no—
367#103—224no—
368#102—224no—
369#102—224no—
370#97—224no—
371#97—224no—
372#95—21no—
373#95—222no—
374#95—221no—
375C2×C11—24no—
376C2×C11#229711yescharacteristic
377C2×C11C2×#41711yescharacteristic
378C2×C11#289611yescharacteristic
379C2×C11#318012yes—
380C2×C11#318112yes—
381D11—82no—
382C24—221no—
383C24D4×D1111yescharacteristic
384C2×Q8—21no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8C2×C4×D1112yes—
388C2×D4—112no—
389C2×D4—224no—
390C2×D4—221no—
391C2×D4—222no—
392C2×D4—222no—
393C2×D4—442no—
394C2×D4—442no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—114no—
401C22×C4—111no—
402C22×C4—111no—
403C22×C4—111no—
404C22×C4—111no—
405C22×C4—114no—
406C22×C4—224no—
407C22×C4—222no—
408C22×C4—222no—
409C22×C4—221no—
410C22×C4—222no—
411C22×C4—444no—
412C22×C4—442no—
413C22×C4C2×C4×D1112yes—
414C22×C4D4×D1111yescharacteristic
415C22×C4D4×D1112yes—
416C22×C4C23×D1111yescharacteristic
417C2×C8—28no—
418C2×C8—22no—
419C2×C8—22no—
420C2×C8—114no—
421C2×C8—228no—
422C2×C8—222no—
423C2×C8—222no—
424C2×C8#434114yes—
425C4⋊C4—24no—
426C4⋊C4—21no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—112no—
430C4⋊C4—224no—
431C4⋊C4—224no—
432C4⋊C4—224no—
433C4⋊C4—221no—
434C4⋊C4—222no—
435C4⋊C4—222no—
436C4⋊C4—444no—
437C4⋊C4—444no—
438C4⋊C4C2×C4×D1112yes—
439C22⋊C4—24no—
440C22⋊C4—42no—
441C22⋊C4—224no—
442C22⋊C4—224no—
443C22⋊C4—224no—
444C22⋊C4—224no—
445C22⋊C4—442no—
446C42—114no—
447C42—114no—
448C42—112no—
449C42—112no—
450C42—112no—
451C42—112no—
452C42—224no—
453C42—444no—
454C11#2140611yescharacteristic, complemented, Sylow
455C23—22no—
456C23—22no—
457C23—222no—
458C23—441no—
459C23—441no—
460C23—442no—
461C23—442no—
462C23C22⋊C4×D1112yes—
463C23#6696712yes—
464C23#6697112yes—
465C23C2×D4×D1111yescharacteristic
466Q8—24no—
467Q8—41no—
468Q8—41no—
469D4—224no—
470D4—448no—
471D4—441no—
472D4—441no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—112no—
485C2×C4—112no—
486C2×C4—112no—
487C2×C4—112no—
488C2×C4—221no—
489C2×C4—221no—
490C2×C4—221no—
491C2×C4—221no—
492C2×C4—222no—
493C2×C4—222no—
494C2×C4—228no—
495C2×C4—222no—
496C2×C4—448no—
497C2×C4—444no—
498C2×C4—441no—
499C2×C4—441no—
500C2×C4—442no—
501C2×C4—442no—
502C2×C4—442no—
503C2×C4C22⋊C4×D1112yes—
504C2×C4C22×C4×D1111yescharacteristic
505C2×C4C2×D4×D1111yescharacteristic
506C2×C4C2×#434112yes—
507C2×C4#41×D1112yes—
508C8—24no—
509C8—224no—
510C22—24no—
511C22—24no—
512C22—22no—
513C22—22no—
514C22—442no—
515C22—442no—
516C22—442no—
517C22—882no—
518C22—882no—
519C22#1062241614yes—
520C22C2×C22⋊C4×D1111yescharacteristic
521C22#1062312712yes—
522C22C2×#6696711yescharacteristic
523C22C2×#6697111yescharacteristic
524C22#1062329912yes—
525C4—22no—
526C4—42no—
527C4—42no—
528C4—82no—
529C4—222no—
530C4—222no—
531C4—222no—
532C4—222no—
533C4—442no—
534C4—882no—
535C4C4×#434112yes—
536C4#1062311711yescharacteristic
537C4#1062318711yescharacteristic
538C2—24no—
539C2—882no—
540C2#1307110111yescharacteristic
541C2C2×#1062241611yescharacteristic
542C2#1307713111yescharacteristic
543C2#1307930712yes—
544C2#1307932012yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1892C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
cosocleC22×C4×C11C24
hypercenter#1892D11
hypocenterC11#21406
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1892

Complements

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

NH ≅ G/Ntype
2. C22×#66879C2semidirect
3. #13071018C2semidirect
4. #13069583C2semidirect
5. #13069429C2semidirect
8. #13069040C2semidirect
9. #13068448C2semidirect
10. #13068440C2semidirect
11. C11×#1892C2semidirect
20. #10623155C4semidirect
191. #1892D11semidirect
454. C11#21406semidirect

Maximal subgroups

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

subgroupindex
C2×#106231552
C22×#668792
#130710182
#130695832
#130694292
#130690442
#130690422
#130690402
#130684482
#130684402
C11×#18922
#2140611