Finite Group Databasebeta

← #14810799

Subgroups — #14810799

Order 2816.

1176 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623110C211yesmaximal, characteristic, complemented
2C2×#10622684C211yesmaximal, characteristic, complemented
3C2×#10622685C211yesmaximal, characteristic
4#13069762C212yesmaximal, complemented
5#13069752C212yesmaximal, complemented
6#13069573C211yesmaximal, characteristic, complemented
7#13069557C211yesmaximal, characteristic, complemented
8#13068967C212yesmaximal, complemented
9#13068967C212yesmaximal, complemented
10#13068444C211yesmaximal, characteristic, complemented
11C11×#2548C211yesmaximal, characteristic, complemented
12C2×C11×#127C2211yescharacteristic
13C2×C11×#124—21no—
14C2×C4×Q8×C11C2211yescharacteristic
15C2×#66999—21no—
16C22×#4323C2212yes—
17#10623110—24no—
18#10623110—24no—
19C2×#66949—21no—
20C2×#66949—21no—
21C2×C4⋊C4×D11—21no—
22C2×C4×D44C2211yescharacteristic
23C2×C4×D44C2211yescharacteristic
24C2×C4×D44C2211yescharacteristic
25C2×#66923C2211yescharacteristic
26C2×#66923C2211yescharacteristic
27C2×#66922C2211yescharacteristic
28C11×#394—21no—
29C11×#394—21no—
30C11×#390—21no—
31C11×#390C2212yes—
32C11×#390C2212yes—
33C4×C11×C4⋊C4C2211yescharacteristic
34C2×#66896C2212yes—
35C2×#66896C2212yes—
36C2×#66896C2212yes—
37#10622685—24no—
38#10622684—24no—
39C2×#66873C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45#10622162C2212yes—
46#10622162C2212yes—
47C22×Q8×C11D411yescharacteristic
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11C2312yes—
51C22×D44C2311yescharacteristic
52C22×C4×D11—21no—
53C22×C4×D11—21no—
54C22×C4×D11—21no—
55C22×Dic22—21no—
56C11×#127—22no—
57C11×#127—22no—
58C11×#124—44no—
59C4×Q8×C11—22no—
60C4×Q8×C11—22no—
61C2×C11×C4⋊C4D411yescharacteristic
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C42×C11—21no—
70C2×C42×C11C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73#66999—28no—
74C2×#4323—24no—
75C2×#4323—24no—
76C2×#4323—24no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C22×C11⋊C8C2312yes—
89C22×C11⋊C8C2312yes—
90#66949—28no—
91#66949—28no—
92C4⋊C4×D11—28no—
93C4×D44—22no—
94C4×D44—22no—
95C4×D44—22no—
96C4×D44—22no—
97C4×D44—22no—
98C4×D44D414yes—
99#66923—22no—
100#66923—22no—
101#66923—22no—
102#66923D414yes—
103#66922—22no—
104#66922—22no—
105C11×#95—21no—
106#66896—24no—
107#66896—24no—
108#66896—24no—
109#66873—24no—
110C4⋊(C11⋊C8)—22no—
111#66867—22no—
112#25946—111nomaximal, Sylow
113C24×C11—22no—
114C23×D11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—41no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—42no—
125C2×D4×C11—42no—
126C2×D4×C11—42no—
127C2×D4×C11—42no—
128C2×D4×C11—82no—
129C22×C4×C11—22no—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C2×D44—21no—
141C2×D44—22no—
142C2×D44C2×D412yes—
143C2×D44#4114yes—
144C2×C4×D11—24no—
145C2×C4×D11—24no—
146C2×C4×D11—24no—
147C2×C4×D11—42no—
148C2×C4×D11—42no—
149C2×C4×D11—82no—
150C2×C4×D11—82no—
151C2×Dic22—24no—
152C2×Dic22—82no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C22⋊C4—44no—
159C11×C22⋊C4—44no—
160C11×C22⋊C4—82no—
161C11×C22⋊C4—82no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11—21no—
166C42×C11—42no—
167C42×C11C2×D412yes—
168C42×C11C2×D412yes—
169#4323—48no—
170(C2×D11)⋊C4—24no—
171(C2×D11)⋊C4—24no—
172(C2×D11)⋊C4—24no—
173C4⋊Dic11—24no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11C2×D412yes—
178C4⋊Dic11C2×D412yes—
179C4⋊Dic11C2×D412yes—
180Dic11⋊C4—24no—
181Dic11⋊C4—24no—
182Dic11⋊C4—24no—
183Dic11⋊C4—24no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—22no—
190C2×#554—111no—
191C2×#490—111no—
192C2×#459—111no—
193#2548D1111yescharacteristic, complemented
194#2025—112no—
195#2023—112no—
196#1989—111no—
197#1985—111no—
198#1879—112no—
199#1879—112no—
200#1762—111no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11C22×D411yescharacteristic
209C22×D11—22no—
210C22×D11—24no—
211C22×D11—41no—
212C22×D11—41no—
213C22×D11—42no—
214Q8×C11—44no—
215D4×C11—42no—
216D4×C11—42no—
217D4×C11—42no—
218D4×C11—42no—
219D4×C11—84no—
220D4×C11—84no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—22no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11#12012yes—
237C2×C4×C11#12012yes—
238C2×C4×C11AGL(1,ℤ/8)12yes—
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C2×#4112yes—
242C2×C4×C112−1+412yes—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250D44—22no—
251D44—24no—
252D44#12414yescomplemented
253C4×D11—48no—
254C4×D11—84no—
255C4×D11—84no—
256Dic22—84no—
257C11⋊C8—42no—
258C11⋊C8—42no—
259C22×D8—112no—
260#554—224no—
261#554—224no—
262C2×C4⋊Q8—111no—
263C2×#127C2×D1111yescharacteristic
264C2×#125—111no—
265C2×#125—111no—
266C2×#124—21no—
267C2×C22⋊Q8—221no—
268C2×C22⋊Q8—221no—
269C2×C22⋊Q8—221no—
270C2×C4×Q8C2×D1111yescharacteristic
271C2×C4×D4—111no—
272C2×C4×D4—111no—
273C2×C4×D4—111no—
274C22×C4⋊C4—221no—
275#490—224no—
276#459—224no—
277C2×C4⋊C8—111no—
278C2×#102—112no—
279C2×#102—112no—
280C2×#102—112no—
281C2×#102—112no—
282C2×#97—111no—
283#394—21no—
284#394—21no—
285#390—21no—
286#390C2×D1112yes—
287#390C2×D1112yes—
288C4×C4⋊C4C2×D1111yescharacteristic
289#340—112no—
290#340—112no—
291#340—112no—
292#336—112no—
293#336—112no—
294C22×C11—82no—
295C22×C11—82no—
296C22×C11—82no—
297C22×C11—82no—
298C22×C11—82no—
299C22×C11—82no—
300C22×C11—82no—
301C22×C11C2×#12011yescharacteristic
302C22×C11#54812yes—
303C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
304C22×C11#57511yescharacteristic
305C22×C11#57612yes—
306C2×D11—24no—
307C2×D11—44no—
308C2×D11—44no—
309C2×D11—42no—
310C2×D11—42no—
311C4×C11—22no—
312C4×C11—22no—
313C4×C11—22no—
314C4×C11—41no—
315C4×C11—41no—
316C4×C11—41no—
317C4×C11—82no—
318C4×C11C2×#12411yescharacteristic
319C4×C11#53611yescharacteristic
320C4×C11#54812yes—
321Dic11—42no—
322Dic11—42no—
323Dic11—42no—
324C22×Q8—221no—
325C22×Q8C22⋊D1111yescharacteristic
326C22×D4—21no—
327C22×D4—21no—
328C22×D4—111no—
329C22×D4C22×D1112yes—
330C23×C4—221no—
331C23×C4—221no—
332C23×C4—221no—
333C2×D8—224no—
334C2×D8—224no—
335C2×D8—224no—
336C22×C8—112no—
337C22×C8—112no—
338C4⋊Q8—222no—
339C4⋊Q8—222no—
340#127—22no—
341#127—22no—
342#125—114no—
343#125—222no—
344#125—222no—
345#125—222no—
346#124—44no—
347C22⋊Q8—228no—
348C22⋊Q8—228no—
349C22⋊Q8—228no—
350C4×Q8—22no—
351C4×Q8—22no—
352C4×D4—114no—
353C4×D4—222no—
354C4×D4—222no—
355C4×D4—222no—
356C4×D4—222no—
357C4×D4—222no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—228no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4C22⋊D1111yescharacteristic
368C2×C4⋊C4C22⋊D1111yescharacteristic
369C2×C4⋊C4C22⋊D1111yescharacteristic
370C2×C4⋊C4C22×D1112yes—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—221no—
376C2×C22⋊C4—221no—
377C2×C22⋊C4—221no—
378C2×C42—21no—
379C2×C42C22×D1111yescharacteristic
380C2×C42C22×D1111yescharacteristic
381C2×C42C22×D1111yescharacteristic
382C4⋊C8—222no—
383#102—224no—
384#102—224no—
385#102—224no—
386#102—224no—
387#97—222no—
388#95—21no—
389C2×C11—162no—
390C2×C11#243611yescharacteristic
391C2×C11#300611yescharacteristic
392C2×C11#300811yescharacteristic
393C2×C11#336612yes—
394C2×C11#337012yes—
395D11—44no—
396C24—22no—
397C24—221no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—41no—
401C2×Q8—224no—
402C2×Q8—882no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—42no—
410C2×D4—42no—
411C2×D4—42no—
412C2×D4—42no—
413C2×D4—82no—
414C2×D4—112no—
415C2×D4—114no—
416C2×D4—221no—
417C2×D4—222no—
418C22×C4—22no—
419C22×C4—224no—
420C22×C4—224no—
421C22×C4—221no—
422C22×C4—221no—
423C22×C4—221no—
424C22×C4—224no—
425C22×C4—442no—
426C22×C4—442no—
427C22×C4—882no—
428C22×C4—882no—
429C22×C4C2×C22⋊D1111yescharacteristic
430C22×C4C2×C22⋊D1111yescharacteristic
431C22×C4C2×C22⋊D1111yescharacteristic
432C22×C4C2×C22⋊D1111yescharacteristic
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C2×C22⋊D1111yescharacteristic
435C22×C4C23×D1111yescharacteristic
436D8—448no—
437C2×C8—222no—
438C2×C8—222no—
439C2×C8—222no—
440C2×C8—222no—
441C2×C8—222no—
442C2×C8—222no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—112no—
449C4⋊C4—112no—
450C4⋊C4—112no—
451C4⋊C4—224no—
452C4⋊C4—224no—
453C4⋊C4—224no—
454C4⋊C4—224no—
455C4⋊C4—224no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C22⋊C4—44no—
460C22⋊C4—44no—
461C22⋊C4—82no—
462C22⋊C4—82no—
463C22⋊C4—224no—
464C22⋊C4—224no—
465C22⋊C4—224no—
466C42—21no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—42no—
471C42D4×D1112yes—
472C42D4×D1112yes—
473C11#2594611yescharacteristic, complemented, Sylow
474C23—42no—
475C23—42no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23—42no—
481C23—222no—
482C23—224no—
483C23—441no—
484C23—441no—
485C23—442no—
486C23C22×C22⋊D1111yescharacteristic
487Q8—44no—
488Q8—884no—
489D4—42no—
490D4—42no—
491D4—42no—
492D4—42no—
493D4—84no—
494D4—84no—
495D4—114no—
496D4—222no—
497D4—224no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—222no—
514C2×C4—222no—
515C2×C4—222no—
516C2×C4—448no—
517C2×C4—441no—
518C2×C4—441no—
519C2×C4—442no—
520C2×C4—442no—
521C2×C4—884no—
522C2×C4—884no—
523C2×C4#6698512yes—
524C2×C4#6699012yes—
525C2×C4#6699012yes—
526C2×C4C2×D4×D1111yescharacteristic
527C2×C4C2×D4×D1111yescharacteristic
528C2×C4#41×D1112yes—
529C2×C4#6704312yes—
530C8—442no—
531C8—442no—
532C22—82no—
533C22—82no—
534C22—82no—
535C22—82no—
536C22—82no—
537C22—82no—
538C22—82no—
539C22—224no—
540C22—444no—
541C22—442no—
542C22—442no—
543C22—444no—
544C22C2×#6698511yescharacteristic
545C22C2×#6699011yescharacteristic
546C22#1062335311yescharacteristic
547C22#1062336212yes—
548C22#1062336612yes—
549C4—22no—
550C4—22no—
551C4—22no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—82no—
556C4—442no—
557C4—442no—
558C4—442no—
559C4D11×#12411yescharacteristic
560C4#1062320611yescharacteristic
561C4#1062320812yes—
562C2—162no—
563C2—444no—
564C2#1307227111yescharacteristic
565C2#1307786611yescharacteristic
566C2#1307788211yescharacteristic
567C2#1308131912yes—
568C2#1308136312yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2548C2
socleC23×C11C22×D4
prime radicalC2×#10622685C2
hypercenter#2548D11
hypocenterC11#25946
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2548

Complements

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

NH ≅ G/Ntype
1. C2×#10623110C2semidirect
2. C2×#10622684C2semidirect
4. #13069762C2semidirect
5. #13069752C2semidirect
6. #13069573C2semidirect
7. #13069557C2semidirect
8. #13068967C2semidirect
9. #13068967C2semidirect
10. #13068444C2semidirect
11. C11×#2548C2semidirect
193. #2548D11semidirect
252. D44#124semidirect
473. C11#25946semidirect

Maximal subgroups

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

subgroupindex
C2×#106231102
C2×#106226842
C2×#106226852
#130697622
#130697522
#130695732
#130695572
#130689672
#130684442
C11×#25482
#2594611