Finite Group Databasebeta

← #14763523

Subgroups — #14763523

Order 2816.

1366 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623127C211yesmaximal, characteristic
2C2×#10622332C211yesmaximal, characteristic, complemented
3#13071019C211yesmaximal, characteristic, complemented
4#13069587C212yesmaximal, complemented
5#13069438C212yesmaximal, complemented
6#13068939C211yesmaximal, characteristic, complemented
7#13068938C211yesmaximal, characteristic, complemented
8#13068936C211yesmaximal, characteristic, complemented
9#13068615C212yesmaximal, complemented
10#13068614C212yesmaximal, complemented
11C11×#1875C211yesmaximal, characteristic, complemented
12C22×#4341—21no—
13C2×C11×#121C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C2×#66993C2211yescharacteristic
16C2×#66992—21no—
17C2×D4×Dic11C2211yescharacteristic
18C2×#66983C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21#10623127—24no—
22#10623127C418yescomplemented
23C2×#66946C2211yescharacteristic
24C2×#66941C2211yescharacteristic
25C2×#66938—21no—
26C2×(C22⋊D11)⋊C4—21no—
27C2×C11×#102C2212yes—
28C2×C11×C22⋊C8C2211yescharacteristic
29C2×#66896C2212yes—
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×#66885C2212yes—
32C2×#66879C2212yes—
33C2×Dic11⋊C8C2212yes—
34#10622590C2212yes—
35#10622589C2212yes—
36C2×#66873C2212yes—
37#10622555—21no—
38#10622555—21no—
39C4×Dic11⋊C4—21no—
40C4×Dic11⋊C4—21no—
41#10622332—24no—
42C11×#340C2212yes—
43#10622189C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C22×D4×C11—21no—
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C22×C22⋊D11—21no—
50C22×C22⋊D11—21no—
51C22×C22⋊D11—21no—
52C23×Dic11—21no—
53C23×Dic11D411yescharacteristic
54C23×Dic11D411yescharacteristic
55C2×#4341—28no—
56C2×#4341—48no—
57C22×D44C2311yescharacteristic
58C22×C4×D11—21no—
59C22×Dic22—21no—
60C22×C8×C11C2312yes—
61C11×#121—22no—
62C11×#121C2×C414yes—
63C11×#117—42no—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—21no—
68C2×C42×C11—21no—
69C2×C22⋊Dic11—21no—
70C2×C22⋊Dic11—21no—
71#66993—22no—
72#66993C2×C414yes—
73#66992—28no—
74D4×Dic11—22no—
75D4×Dic11C2×C414yes—
76#66983—22no—
77#66983C2×C414yes—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80#66979—42no—
81C2×C4⋊Dic11C2312yes—
82C2×C4⋊Dic11C2311yescharacteristic
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—22no—
85C2×Dic11⋊C4—22no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11C2×C414yes—
88C2×C4×Dic11D411yescharacteristic
89C2×C4×Dic11D411yescharacteristic
90C2×C4×Dic11D414yes—
91C2×C4×Dic11C2311yescharacteristic
92C2×C4×Dic11C2311yescharacteristic
93C22×C11⋊C8C2312yes—
94#66946—22no—
95#66946C2×C414yes—
96#66941—22no—
97#66941C2×C414yes—
98#66938—28no—
99(C22⋊D11)⋊C4—28no—
100C11×#102—42no—
101C11×C22⋊C8—22no—
102#66896—42no—
103C11⋊#95—22no—
104C11⋊#95—22no—
105C22⋊(C11⋊C8)—22no—
106#66885—42no—
107#66879—24no—
108Dic11⋊C8—24no—
109#66873—42no—
110#21869—111nomaximal, Sylow
111C24×C11—21no—
112C24×C11C2×D411yescharacteristic
113C23×D11—21no—
114C2×D4×C11—24no—
115C2×D4×C11—21no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—44no—
119C2×D4×C11C22×C412yes—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11C22×C412yes—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2411yescharacteristic
128C2×C22⋊D11—24no—
129C2×C22⋊D11—24no—
130C2×C22⋊D11—24no—
131C2×C22⋊D11—44no—
132C2×C22⋊D11—44no—
133C2×C22⋊D11—44no—
134C22×Dic11—24no—
135C22×Dic11—24no—
136C22×Dic11—21no—
137C22×Dic11—22no—
138C22×Dic11—42no—
139C22×Dic11—44no—
140C22×Dic11C22⋊C414yes—
141C22×Dic11C22⋊C414yes—
142C22×Dic11C2×D411yescharacteristic
143C22×Dic11C2×D411yescharacteristic
144C22×Dic11C2×D411yescharacteristic
145C22×Dic11C2×D411yescharacteristic
146#4341—432no—
147C2×D44—21no—
148C2×D44—22no—
149C2×D44—22no—
150C2×D44C22×C412yes—
151C2×C4×D11—24no—
152C2×C4×D11—44no—
153C2×Dic22—24no—
154C2×Dic22—44no—
155C2×C8×C11—22no—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4C22×C412yes—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—42no—
164C42×C11—42no—
165C22⋊Dic11—24no—
166C22⋊Dic11—42no—
167(C2×D11)⋊C4—24no—
168(C2×D11)⋊C4—24no—
169C4⋊Dic11—21no—
170C4⋊Dic11—22no—
171C4⋊Dic11—22no—
172C4⋊Dic11C22×C412yes—
173Dic11⋊C4—24no—
174Dic11⋊C4—44no—
175Dic11⋊C4—44no—
176C4×Dic11—42no—
177C4×Dic11C22⋊C414yes—
178C4×Dic11C22⋊C414yes—
179C4×Dic11C22×C412yes—
180C4×Dic11C22×C412yes—
181C4×Dic11C2×D412yes—
182C4×Dic11C2×D412yes—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×#532—111no—
187C2×#432—111no—
188#2285—111no—
189#1993—112no—
190#1961—112no—
191#1875—111no—
192#1875—111no—
193#1875—111no—
194#1875D1111yescharacteristic, complemented
195#1802—112no—
196#1802—112no—
197C23×C11—21no—
198C23×C11—21no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11C2×C22⋊C412yes—
207C23×C11C22×D411yescharacteristic
208C22×D11—22no—
209C22×D11—41no—
210C22×D11—41no—
211C22×D11—42no—
212C22×D11—42no—
213D4×C11—24no—
214D4×C11—48no—
215D4×C11—42no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—22no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11C2×C22⋊C412yes—
226C2×C4×C11C23×C411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11H(5,𝔽2)12yes—
229C2×C4×C112−1+412yes—
230C22⋊D11—48no—
231C22⋊D11—48no—
232C22⋊D11—48no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—28no—
237C2×Dic11—22no—
238C2×Dic11—44no—
239C2×Dic11—42no—
240C2×Dic11—48no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11C2×C22⋊C412yes—
245C2×Dic11C2×C22⋊C412yes—
246C2×Dic11C2×C22⋊C412yes—
247C2×Dic11C2×C22⋊C412yes—
248C2×Dic11AGL(1,ℤ/8)14yes—
249D44—24no—
250D44—42no—
251C4×D11—48no—
252Dic22—48no—
253C8×C11—42no—
254C11⋊C8—42no—
255C22×#41—221no—
256#532—118no—
257#532—224no—
258C2×C4⋊Q8—111no—
259C2×#127—111no—
260C2×#124—221no—
261C2×#121—111no—
262C2×#121—221no—
263C2×#121C2×D1111yescharacteristic
264C2×C4×D4—111no—
265C2×C4×D4—111no—
266C2×C4×D4—221no—
267C2×#117—111no—
268C2×#117C2×D1111yescharacteristic
269C22×C42—111no—
270#432—224no—
271C2×C4⋊C8—112no—
272C2×#102—112no—
273C2×#102—112no—
274C2×#102—112no—
275C2×#102C2×D1112yes—
276C2×C22⋊C8—111no—
277C2×C22⋊C8C2×D1111yescharacteristic
278C2×#97—112no—
279#384—112no—
280#382—112no—
281#380—221no—
282#380—221no—
283C4×C4⋊C4—221no—
284C4×C4⋊C4—221no—
285#340—112no—
286#340—112no—
287#340—112no—
288#340C2×D1112yes—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—82no—
298C22×C11—82no—
299C22×C11C22×C22⋊C411yescharacteristic
300C22×C11#53511yescharacteristic
301C22×C11#53611yescharacteristic
302C22×C11C2×AGL(1,ℤ/8)12yes—
303C22×C11#57512yes—
304C2×D11—42no—
305C2×D11—42no—
306C2×D11—42no—
307C2×D11—82no—
308C2×D11—82no—
309C4×C11—22no—
310C4×C11—42no—
311C4×C11—82no—
312C4×C11#52012yes—
313C4×C11#53712yes—
314Dic11—22no—
315Dic11—22no—
316Dic11—22no—
317Dic11—42no—
318Dic11—82no—
319Dic11#41814yes—
320C2×#41—228no—
321C2×#41—448no—
322C22×Q8—221no—
323C22×D4—21no—
324C22×D4—111no—
325C22×D4—221no—
326C22×D4—221no—
327C22×D4—221no—
328C22×D4C22×D1111yescharacteristic
329C23×C4—111no—
330C23×C4—111no—
331C23×C4—221no—
332C23×C4—221no—
333C23×C4C22×D1111yescharacteristic
334C22×C8—112no—
335C22×C8C22×D1112yes—
336C4⋊Q8—114no—
337C4⋊Q8—222no—
338#127—114no—
339#127—222no—
340#124—228no—
341#121—22no—
342#121—114no—
343#121—228no—
344#121—222no—
345#121C4×D1114yes—
346C4×D4—114no—
347C4×D4—114no—
348C4×D4—228no—
349C4×D4—222no—
350C4×D4—222no—
351#117—42no—
352#117—442no—
353C2×C4⋊C4—111no—
354C2×C4⋊C4—112no—
355C2×C4⋊C4—221no—
356C2×C4⋊C4—222no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4C22×D1112yes—
359C2×C4⋊C4C22×D1111yescharacteristic
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—221no—
363C2×C22⋊C4—221no—
364C2×C22⋊C4—221no—
365C2×C22⋊C4—221no—
366C2×C42—21no—
367C2×C42—114no—
368C2×C42—111no—
369C2×C42—111no—
370C2×C42—114no—
371C2×C42—111no—
372C2×C42—111no—
373C2×C42—221no—
374C4⋊C8—224no—
375#102—42no—
376#102—442no—
377#102—442no—
378#102—442no—
379C22⋊C8—22no—
380C22⋊C8—222no—
381#97—224no—
382#95—222no—
383#95—222no—
384C2×C11—42no—
385C2×C11—82no—
386C2×C11#231111yescharacteristic
387C2×C11C2×#41811yescharacteristic
388C2×C11#289611yescharacteristic
389C2×C11#321412yes—
390C2×C11#323512yes—
391D11—82no—
392C24—21no—
393C24—221no—
394C24D4×D1111yescharacteristic
395#41—4432no—
396C2×Q8—224no—
397C2×Q8—444no—
398C2×D4—24no—
399C2×D4—21no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—44no—
403C2×D4—112no—
404C2×D4—224no—
405C2×D4—224no—
406C2×D4—224no—
407C2×D4—221no—
408C2×D4—222no—
409C2×D4—222no—
410C2×D4—444no—
411C2×D4—444no—
412C2×D4—444no—
413C2×D4C2×C4×D1112yes—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—111no—
419C22×C4—114no—
420C22×C4—111no—
421C22×C4—111no—
422C22×C4—111no—
423C22×C4—114no—
424C22×C4—224no—
425C22×C4—224no—
426C22×C4—224no—
427C22×C4—221no—
428C22×C4—222no—
429C22×C4—444no—
430C22×C4—444no—
431C22×C4—442no—
432C22×C4C2×C4×D1112yes—
433C22×C4D4×D1111yescharacteristic
434C22×C4D4×D1112yes—
435C22×C4C23×D1111yescharacteristic
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—222no—
440C2×C8—222no—
441C2×C8—222no—
442C4⋊C4—21no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—112no—
446C4⋊C4—224no—
447C4⋊C4—221no—
448C4⋊C4—222no—
449C4⋊C4—222no—
450C4⋊C4—444no—
451C4⋊C4—444no—
452C4⋊C4C2×C4×D1112yes—
453C22⋊C4—24no—
454C22⋊C4—42no—
455C22⋊C4—224no—
456C22⋊C4—224no—
457C22⋊C4—224no—
458C22⋊C4—442no—
459C42—42no—
460C42—114no—
461C42—114no—
462C42—112no—
463C42—112no—
464C42—112no—
465C42—112no—
466C42—442no—
467C11#2186911yescharacteristic, complemented, Sylow
468C23—22no—
469C23—22no—
470C23—21no—
471C23—21no—
472C23—22no—
473C23—42no—
474C23—42no—
475C23—41no—
476C23—41no—
477C23—222no—
478C23—442no—
479C23—442no—
480C23—441no—
481C23—441no—
482C23C22⋊C4×D1112yes—
483C23C2×D4×D1111yescharacteristic
484Q8—448no—
485D4—24no—
486D4—48no—
487D4—42no—
488D4—224no—
489D4—448no—
490D4—448no—
491D4—448no—
492D4—442no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—112no—
503C2×C4—114no—
504C2×C4—112no—
505C2×C4—112no—
506C2×C4—112no—
507C2×C4—228no—
508C2×C4—222no—
509C2×C4—222no—
510C2×C4—222no—
511C2×C4—222no—
512C2×C4—448no—
513C2×C4—448no—
514C2×C4—444no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4—442no—
519C2×C4C22⋊C4×D1112yes—
520C2×C4C22×C4×D1111yescharacteristic
521C2×C4C2×D4×D1111yescharacteristic
522C2×C4#6703712yes—
523C2×C4#6704312yes—
524C8—42no—
525C8—442no—
526C22—22no—
527C22—22no—
528C22—22no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—82no—
535C22—82no—
536C22—442no—
537C22—442no—
538C22—442no—
539C22—882no—
540C22—882no—
541C22C2×C22⋊C4×D1111yescharacteristic
542C22#1062312311yescharacteristic
543C22#1062317911yescharacteristic
544C22#1062329912yes—
545C22D11×AGL(1,ℤ/8)12yes—
546C4—22no—
547C4—42no—
548C4—82no—
549C4—114no—
550C4—222no—
551C4—222no—
552C4—222no—
553C4—442no—
554C4—882no—
555C4#1062307712yes—
556C4#1062312812yes—
557C2—42no—
558C2—82no—
559C2—882no—
560C2#1307120311yescharacteristic
561C2D11×#41811yescharacteristic
562C2#1307713111yescharacteristic
563C2#1307960812yes—
564C2#1307981112yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1875C2
socleC23×C11C22×D4
prime radicalC2×#10623127C2
cosocleC22×C4×C11C24
hypercenter#1875D11
hypocenterC11#21869
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1875

Complements

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

NH ≅ G/Ntype
2. C2×#10622332C2semidirect
3. #13071019C2semidirect
4. #13069587C2semidirect
5. #13069438C2semidirect
6. #13068939C2semidirect
7. #13068938C2semidirect
8. #13068936C2semidirect
9. #13068615C2semidirect
10. #13068614C2semidirect
11. C11×#1875C2semidirect
22. #10623127C4semidirect
194. #1875D11semidirect
467. C11#21869semidirect

Maximal subgroups

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

subgroupindex
C2×#106231272
C2×#106223322
#130710192
#130695872
#130694382
#130689392
#130689382
#130689362
#130686152
#130686142
C11×#18752
#2186911