Finite Group Databasebeta

← #14755172

Subgroups — #14755172

Order 2816.

1954 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
1C22×#67002C211yesmaximal, characteristic
2C2×#10623052C211yesmaximal, characteristic, complemented
3C2×#10622846C211yesmaximal, characteristic, complemented
4C22×#66873C211yesmaximal, characteristic, complemented
5#13068967C214yesmaximal, complemented
6#13068953C214yesmaximal, complemented
7#13068335C211yesmaximal, characteristic, complemented
8#13068313C211yesmaximal, characteristic, complemented
9C11×#2311C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C23×D44C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C2×#67002—24no—
15C2×#67002—24no—
16C2×#67002C418yescomplemented
17C22×#4325C2212yes—
18C22×#4323C2212yes—
19C2×#66979C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22#10623052—24no—
23#10623052—24no—
24C2×#66946—22no—
25C2×C22⋊C4×D11—22no—
26C2×C4×D44C2214yes—
27C11×#391C2212yescomplemented
28C11×#390C2212yescomplemented
29C11×#386—22no—
30C11×#380—22no—
31#10622846—24no—
32C2×#66899C2212yescomplemented
33C2×#66896C2212yescomplemented
34C2×#66873—24no—
35C2×#66873C2214yes—
36#10622167C2214yescomplemented
37#10622162C2214yescomplemented
38C24×D11—21no—
39C2×C11×#41—22no—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41C2×C414yescomplemented
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11—21no—
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11—21no—
49C23×C4×C11—21no—
50C23×C4×C11C2311yescharacteristic
51C22×D44—21no—
52C22×D44—22no—
53C22×D44—22no—
54C22×D44—22no—
55C22×D44C2×C414yes—
56C22×D44D414yes—
57C22×D44D414yes—
58C22×D44C2312yes—
59C22×C4×D11—24no—
60C11×#117—22no—
61C11×#117—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4D412yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C22⋊C4—24no—
68C2×C11×C22⋊C4D412yes—
69C2×C42×C11C2312yes—
70C2×C22⋊Dic11—21no—
71#67002—232no—
72C2×#4325—24no—
73C2×#4325—24no—
74C2×#4325C2×C418yescomplemented
75C2×#4323—24no—
76C2×#4323—24no—
77C2×#4323C2×C418yescomplemented
78C2×(C2×D11)⋊C4—24no—
79#66979—22no—
80#66979D414yes—
81C2×C4⋊Dic11C2312yes—
82C2×C4×Dic11—21no—
83C2×#4318—22no—
84C2×#4318—22no—
85C2×#4318C2×C414yescomplemented
86C22×C11⋊C8—22no—
87C22×C11⋊C8—22no—
88C22×C11⋊C8—22no—
89C22×C11⋊C8C2312yes—
90C22×C11⋊C8C2312yes—
91#66946—216no—
92C22⋊C4×D11—216no—
93C4×D44—28no—
94C4×D44—28no—
95C11×#95—24no—
96#66899—24no—
97#66896—24no—
98#66873—28no—
99#20929—111nomaximal, Sylow
100C24×C11—21no—
101C24×C11C2×D411yescharacteristic
102C23×D11—22no—
103C23×D11—24no—
104C23×D11—24no—
105C23×D11—24no—
106C23×D11—82no—
107C23×D11—82no—
108C11×#41—28no—
109C11×#41—28no—
110C11×#41—44no—
111C11×#41—44no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11C22×C412yes—
118C2×D4×C11—24no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—42no—
125C2×D4×C11—42no—
126C2×D4×C11C22×C412yes—
127C22×C4×C11—21no—
128C22×C4×C11—24no—
129C22×C4×C11—22no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11—82no—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C2×D414yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D412yes—
140C22×C4×C11#4112yes—
141C22×C4×C11#4112yes—
142C22×C4×C11C2411yescharacteristic
143C22×Dic11—22no—
144C2×D44—28no—
145C2×D44—24no—
146C2×D44—24no—
147C2×D44—28no—
148C2×D44—24no—
149C2×D44—28no—
150C2×D44—22no—
151C2×D44—22no—
152C2×D44—22no—
153C2×D44C22⋊C4116yescomplemented
154C2×D44C22×C414yes—
155C2×D44C2×D414yes—
156C2×D44C2×D414yes—
157C2×C4×D11—216no—
158C2×C4×D11—84no—
159C2×C4×D11—84no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—42no—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—84no—
166C42×C11—22no—
167C42×C11—22no—
168C22⋊Dic11—24no—
169#4325—216no—
170#4323—216no—
171(C2×D11)⋊C4—216no—
172C4⋊Dic11—22no—
173C4⋊Dic11C2×D414yes—
174C4×Dic11—24no—
175#4318—28no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—44no—
182C2×C11⋊C8C22×C414yes—
183C22×AGL(1,ℤ/8)—111no—
184C2×#518—111no—
185C2×#416—111no—
186C22×#102—111no—
187#2311D1111yescharacteristic, complemented
188#1879—114no—
189#1877—114no—
190#1736—111no—
191#1729—111no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11C4×D412yes—
200C23×C11#12012yes—
201C23×C11#12112yes—
202C23×C11C22×D411yescharacteristic
203C22×D11—24no—
204C22×D11—24no—
205C22×D11—24no—
206C22×D11—216no—
207C22×D11—44no—
208C22×D11—44no—
209C22×D11—88no—
210C22×D11—88no—
211C22×D11—84no—
212C22×D11—84no—
213Q8×C11—22no—
214Q8×C11—22no—
215Q8×C11—41no—
216Q8×C11—41no—
217D4×C11—22no—
218D4×C11—22no—
219D4×C11—48no—
220D4×C11—41no—
221D4×C11—41no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—48no—
229C2×C4×C11—42no—
230C2×C4×C11—44no—
231C2×C4×C11—84no—
232C2×C4×C11C2×C22⋊C414yes—
233C2×C4×C11C4×D414yes—
234C2×C4×C11C4×D412yes—
235C2×C4×C11#12012yes—
236C2×C4×C11#12114yes—
237C2×C4×C11#12112yes—
238C2×C4×C11#12314yes—
239C2×C4×C11C23×C411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×Dic11—24no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248D44—24no—
249D44—24no—
250D44—24no—
251D44—216no—
252D44C2×C22⋊C418yes—
253C4×D11—816no—
254C11⋊C8—24no—
255C11⋊C8—42no—
256C22×#41C2×D1111yescharacteristic
257C23×D4—111no—
258C2×AGL(1,ℤ/8)—118no—
259C2×AGL(1,ℤ/8)—224no—
260C2×AGL(1,ℤ/8)—224no—
261C22×SD16—112no—
262C22×D8—112no—
263C22×M16—111no—
264C23×C8—111no—
265#518—224no—
266#518—224no—
267C2×C4×D4—114no—
268C2×C4×D4—222no—
269C2×#117—111no—
270C2×#117C2×D1111yescharacteristic
271C22×C4⋊C4C2×D1111yescharacteristic
272C22×C22⋊C4—222no—
273#416—224no—
274C2×#103—112no—
275C2×#102—112no—
276C2×#102—114no—
277C2×#102—224no—
278#391C2×D1112yescomplemented
279#390C2×D1112yescomplemented
280#386—22no—
281#380—22no—
282#340—114no—
283#336—114no—
284C22×C11—24no—
285C22×C11—24no—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—44no—
289C22×C11—42no—
290C22×C11—82no—
291C22×C11—81no—
292C22×C11—81no—
293C22×C11#38614yes—
294C22×C11C2×C4×D411yescharacteristic
295C22×C11C2×#12011yescharacteristic
296C22×C11C2×#12111yescharacteristic
297C22×C11#57612yes—
298C22×C11#57712yes—
299C2×D11—28no—
300C2×D11—48no—
301C2×D11—48no—
302C2×D11—44no—
303C2×D11—44no—
304C2×D11—816no—
305C4×C11—44no—
306C4×C11—42no—
307C4×C11—82no—
308C4×C11#38614yes—
309C4×C11C22×C22⋊C411yescharacteristic
310C4×C11C2×C4×D411yescharacteristic
311C4×C11C2×#12111yescharacteristic
312C4×C11C2×#12311yescharacteristic
313Dic11—44no—
314C25—221no—
315C2×#41—22no—
316C2×#41—22no—
317C2×#41—22no—
318C2×#41—22no—
319C2×#41—22no—
320C2×#41C4×D1114yescomplemented
321C22×Q8C22×D1111yescharacteristic
322C22×D4—21no—
323C22×D4—114no—
324C22×D4—114no—
325C22×D4—114no—
326C22×D4—112no—
327C22×D4—222no—
328C22×D4—222no—
329C22×D4—222no—
330C22×D4—221no—
331C22×D4C22×D1111yescharacteristic
332C23×C4—21no—
333C23×C4—21no—
334C23×C4—224no—
335C23×C4C22×D1111yescharacteristic
336AGL(1,ℤ/8)—2232no—
337C2×SD16—118no—
338C2×SD16—224no—
339C2×SD16—224no—
340C2×D8—118no—
341C2×D8—224no—
342C2×D8—224no—
343C2×M16—114no—
344C2×M16—222no—
345C2×M16—222no—
346C22×C8—112no—
347C22×C8—112no—
348C22×C8—222no—
349C22×C8—222no—
350C22×C8—222no—
351C4×D4—228no—
352C4×D4—228no—
353C4×D4—2216no—
354#117—22no—
355#117—22no—
356#117—114no—
357#117—222no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—112no—
362C2×C4⋊C4C22⋊D1112yes—
363C2×C4⋊C4C22×D1112yes—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—2216no—
366C2×C22⋊C4—221no—
367C2×C22⋊C4—224no—
368C2×C22⋊C4C22⋊D1112yes—
369C2×C42—221no—
370C2×C42C22×D1112yes—
371#103—224no—
372#102—228no—
373#102—224no—
374#95—24no—
375C2×C11—24no—
376C2×C11—82no—
377C2×C11C2×#38611yescharacteristic
378C2×C11#294612yes—
379C2×C11#301212yes—
380C2×C11#304111yescharacteristic
381C2×C11#304211yescharacteristic
382D11—48no—
383C24—21no—
384C24—222no—
385C24—224no—
386C24—224no—
387C24—224no—
388C24—882no—
389C24—882no—
390C24C2×C22⋊D1111yescharacteristic
391#41—28no—
392#41—28no—
393#41—44no—
394#41—44no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8C2×C4×D1112yes—
401C2×D4—24no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—42no—
408C2×D4—42no—
409C2×D4—1116no—
410C2×D4—114no—
411C2×D4—114no—
412C2×D4—114no—
413C2×D4—228no—
414C2×D4—228no—
415C2×D4—228no—
416C2×D4—224no—
417C2×D4—224no—
418C2×D4—224no—
419C2×D4—222no—
420C2×D4—222no—
421C2×D4—222no—
422C2×D4C2×C4×D1112yes—
423C22×C4—21no—
424C22×C4—24no—
425C22×C4—22no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—82no—
430C22×C4—2216no—
431C22×C4—222no—
432C22×C4—884no—
433C22×C4—884no—
434C22×C4C2×C4×D1112yes—
435C22×C4#433912yes—
436C22×C4D4×D1112yes—
437C22×C4D4×D1112yes—
438C22×C4D4×D1112yes—
439C22×C4#434112yes—
440C22×C4C2×C22⋊D1114yes—
441C22×C4C2×C22⋊D1111yescharacteristic
442C22×C4C23×D1111yescharacteristic
443SD16—2216no—
444D8—2216no—
445M16—228no—
446C2×C8—114no—
447C2×C8—222no—
448C2×C8—222no—
449C2×C8—222no—
450C2×C8—222no—
451C2×C8—222no—
452C2×C8—444no—
453C4⋊C4—24no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—42no—
457C4⋊C4—114no—
458C4⋊C4—222no—
459C22⋊C4—24no—
460C22⋊C4—84no—
461C22⋊C4—2216no—
462C22⋊C4—224no—
463C42—22no—
464C42—22no—
465C42—224no—
466C11#2092911yescharacteristic, complemented, Sylow
467C23—22no—
468C23—22no—
469C23—22no—
470C23—41no—
471C23—41no—
472C23—42no—
473C23—42no—
474C23—224no—
475C23—224no—
476C23—224no—
477C23—2216no—
478C23—444no—
479C23—444no—
480C23—884no—
481C23—884no—
482C23—888no—
483C23—888no—
484C23C4×C22⋊D1112yes—
485C23#6699012yes—
486C23#6699112yes—
487C23C22×C22⋊D1111yescharacteristic
488Q8—22no—
489Q8—22no—
490Q8—41no—
491Q8—41no—
492D4—22no—
493D4—22no—
494D4—48no—
495D4—41no—
496D4—41no—
497D4—118no—
498D4—224no—
499D4—224no—
500D4—224no—
501D4—2216no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—48no—
509C2×C4—42no—
510C2×C4—44no—
511C2×C4—84no—
512C2×C4—224no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—8816no—
516C2×C4C22⋊C4×D1114yes—
517C2×C4(C22⋊D11)⋊C414yes—
518C2×C4#6693614yes—
519C2×C4#6693714yes—
520C2×C4C4×C22⋊D1112yes—
521C2×C4#6699012yes—
522C2×C4#6699112yes—
523C2×C4C22×C4×D1111yescharacteristic
524C2×C4C2×#433911yescharacteristic
525C2×C4C2×D4×D1111yescharacteristic
526C2×C4C2×D4×D1111yescharacteristic
527C2×C4C2×D4×D1111yescharacteristic
528C2×C4C2×#434111yescharacteristic
529C8—224no—
530C8—442no—
531C22—22no—
532C22—22no—
533C22—24no—
534C22—24no—
535C22—42no—
536C22—44no—
537C22—81no—
538C22—81no—
539C22—82no—
540C22—228no—
541C22—444no—
542C22—444no—
543C22—448no—
544C22—448no—
545C22—8816no—
546C22#1062256914yes—
547C22C2×C4×C22⋊D1111yescharacteristic
548C22C2×#6699011yescharacteristic
549C22C2×#6699111yescharacteristic
550C22#1062336612yes—
551C22#1062336812yes—
552C4—44no—
553C4—42no—
554C4—82no—
555C4—444no—
556C4#1062256914yes—
557C4C2×C22⋊C4×D1111yescharacteristic
558C4C2×(C22⋊D11)⋊C411yescharacteristic
559C4C2×#6693611yescharacteristic
560C4C2×#6693711yescharacteristic
561C2—24no—
562C2—82no—
563C2—448no—
564C2C2×#1062256911yescharacteristic
565C2#1307744412yes—
566C2#1307791712yes—
567C2#1307811511yescharacteristic
568C2#1307812411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2311C2
socleC23×C11C22×D4
prime radicalC22×#67002C2
cosocleC22×C4×C11C24
hypercenter#2311D11
hypocenterC11#20929
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. C2×#10623052C2semidirect
3. C2×#10622846C2semidirect
4. C22×#66873C2semidirect
5. #13068967C2semidirect
6. #13068953C2semidirect
7. #13068335C2semidirect
8. #13068313C2semidirect
9. C11×#2311C2semidirect
16. C2×#67002C4semidirect
27. C11×#391C22semidirect
28. C11×#390C22semidirect
32. C2×#66899C22semidirect
33. C2×#66896C22semidirect
36. #10622167C22semidirect
37. #10622162C22semidirect
44. C2×C11×#41C2×C4semidirect
74. C2×#4325C2×C4semidirect
77. C2×#4323C2×C4semidirect
85. C2×#4318C2×C4semidirect
153. C2×D44C22⋊C4semidirect
187. #2311D11semidirect
278. #391C2×D11semidirect
279. #390C2×D11semidirect
320. C2×#41C4×D11semidirect
466. C11#20929semidirect

Maximal subgroups

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

subgroupindex
C22×#670022
C2×#106230522
C2×#106228462
C22×#668732
#130689672
#130689532
#130683352
#130683132
C11×#23112
#2092911