Finite Group Databasebeta

← #14755175

Subgroups — #14755175

Order 2816.

1738 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66995C211yesmaximal, characteristic
2C2×#10623343C211yesmaximal, characteristic, complemented
3C2×#10622726C211yesmaximal, characteristic
4#13071209C211yesmaximal, characteristic
5#13068969C214yesmaximal, complemented
6#13068955C214yesmaximal, complemented
7#13068335C211yesmaximal, characteristic, complemented
8#13068312C211yesmaximal, characteristic, complemented
9C22×C11×#103C211yesmaximal, characteristic, complemented
10C23×Q8×C11C2211yescharacteristic
11C22×#4339C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14#10623343—24no—
15#10623343—24no—
16C2×Q8×Dic11—22no—
17C2×Q8×Dic11C2214yes—
18C22×#4326C2212yes—
19C2×#66995—24no—
20C2×#66995—24no—
21C2×#66995C418yescomplemented
22C22×#4325C2212yes—
23C2×#66979—22no—
24C2×#66979C2211yescharacteristic
25C2×#66979C2211yescharacteristic
26C22×#4318C2211yescharacteristic
27C2×C11×#103—24no—
28C2×C11×#103C2214yes—
29#10622826—22no—
30#10622726—24no—
31C2×#66885C2212yes—
32C2×#66880C2212yes—
33#10622601C2212yes—
34#10622600—22no—
35#10622587C2212yes—
36#10622188C2214yes—
37#10622167C2214yes—
38C22×Q8×C11—21no—
39C22×Q8×C11—22no—
40C22×Q8×C11—22no—
41C22×Q8×C11—22no—
42C22×Q8×C11C2×C414yes—
43C22×Q8×C11D414yes—
44C22×Q8×C11D414yes—
45C22×Q8×C11C2312yes—
46C23×C4×C11—21no—
47C23×C4×C11—21no—
48C23×C4×C11C2311yescharacteristic
49C22×C22⋊D11—21no—
50C2×#4339—22no—
51C2×#4339—22no—
52C2×#4339—22no—
53C2×#4339—22no—
54C2×#4339—22no—
55C2×#4339C2×C414yes—
56C22×D44C2311yescharacteristic
57C22×C4×D11—21no—
58C22×Dic22C2311yescharacteristic
59C22×C8×C11—22no—
60C22×C8×C11—22no—
61C22×C8×C11—22no—
62C22×C8×C11C2312yes—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2312yes—
67C2×C22⋊Dic11—21no—
68C2×C22⋊Dic11D412yes—
69Q8×Dic11—216no—
70Q8×Dic11—28no—
71Q8×Dic11—28no—
72C2×#4326—24no—
73C2×#4326—24no—
74C2×#4326C2×C418yescomplemented
75#66995—232no—
76C2×#4325—24no—
77C2×#4325—24no—
78C2×#4325C2×C418yescomplemented
79C2×(C2×D11)⋊C4—24no—
80#66979—216no—
81#66979—22no—
82#66979—22no—
83#66979—22no—
84#66979D414yes—
85C2×C4⋊Dic11—24no—
86C2×C4⋊Dic11D412yes—
87C2×C4⋊Dic11C2312yes—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—24no—
90C2×C4×Dic11C2312yes—
91C2×#4318—22no—
92C2×#4318—22no—
93C2×#4318C2×C414yes—
94C22×C11⋊C8C2312yes—
95C11×#103—28no—
96C11⋊#95—24no—
97#66885—24no—
98#66880—24no—
99#20930—111nomaximal, Sylow
100C24×C11C2×D411yescharacteristic
101C23×D11—21no—
102C2×Q8×C11—24no—
103C2×Q8×C11—28no—
104C2×Q8×C11—24no—
105C2×Q8×C11—24no—
106C2×Q8×C11—28no—
107C2×Q8×C11—28no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11C22⋊C4116yescomplemented
112C2×Q8×C11C22×C414yes—
113C2×Q8×C11C2×D414yes—
114C2×Q8×C11C2×D414yes—
115C22×C4×C11—24no—
116C22×C4×C11—24no—
117C22×C4×C11—24no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—42no—
121C22×C4×C11—82no—
122C22×C4×C11C22×C412yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D412yes—
127C22×C4×C11#4112yes—
128C22×C4×C11#4112yes—
129C22×C4×C11C2411yescharacteristic
130C2×C22⋊D11—24no—
131C2×C22⋊D11—42no—
132C2×C22⋊D11—42no—
133C22×Dic11—21no—
134C22×Dic11—22no—
135C22×Dic11C2×D414yes—
136#4339—28no—
137#4339—28no—
138#4339—44no—
139#4339—44no—
140C2×D44—21no—
141C2×D44—21no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44C22×C412yes—
146C2×C4×D11—24no—
147C2×C4×D11—42no—
148C2×C4×D11—42no—
149C2×Dic22—21no—
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22C22×C412yes—
155C2×C8×C11—22no—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C2×C8×C11—44no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—42no—
162C22⋊Dic11—24no—
163C22⋊Dic11—24no—
164#4326—216no—
165#4325—216no—
166(C2×D11)⋊C4—84no—
167C4⋊Dic11—216no—
168C4⋊Dic11—24no—
169C4⋊Dic11—22no—
170C4⋊Dic11C2×D414yes—
171C4×Dic11—216no—
172C4×Dic11—24no—
173C4×Dic11—22no—
174C4×Dic11—22no—
175#4318—28no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8C22×C414yes—
179C22×#137—111no—
180C2×#519—111no—
181C2×#416—111no—
182C22×#103D1111yescharacteristic, complemented
183#2311—111no—
184#1880—114no—
185#1878—114no—
186#1736—111no—
187#1729—111no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11C4×D412yes—
191C23×C11#12012yes—
192C23×C11#12112yes—
193C23×C11C22×D411yescharacteristic
194C22×D11—22no—
195C22×D11—41no—
196C22×D11—41no—
197C22×D11—42no—
198C22×D11—42no—
199Q8×C11—24no—
200Q8×C11—24no—
201Q8×C11—24no—
202Q8×C11—216no—
203Q8×C11C2×C22⋊C418yes—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—216no—
208C2×C4×C11—42no—
209C2×C4×C11—44no—
210C2×C4×C11—84no—
211C2×C4×C11C2×C22⋊C414yes—
212C2×C4×C11C4×D414yes—
213C2×C4×C11C4×D412yes—
214C2×C4×C11#12012yes—
215C2×C4×C11#12114yes—
216C2×C4×C11#12112yes—
217C2×C4×C11#12314yes—
218C2×C4×C11C23×C411yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C22⋊D11—48no—
225C2×Dic11—22no—
226C2×Dic11—24no—
227C2×Dic11—24no—
228C2×Dic11—24no—
229C2×Dic11—24no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234D44—22no—
235D44—22no—
236D44—41no—
237D44—41no—
238C4×D11—48no—
239Dic22—22no—
240Dic22—22no—
241Dic22—41no—
242Dic22—41no—
243C8×C11—42no—
244C11⋊C8—24no—
245C22×#41—111no—
246C23×Q8C2×D1111yescharacteristic
247C2×#137—118no—
248C2×#137—224no—
249C2×#137—224no—
250C22×Q16—112no—
251C22×SD16—112no—
252C22×M16—111no—
253C23×C8C2×D1111yescharacteristic
254#519—224no—
255#519—224no—
256C2×C4×Q8—114no—
257C2×C4×Q8—222no—
258C2×#117—111no—
259C2×#117—111no—
260C2×#117—222no—
261C22×C4⋊C4C2×D1111yescharacteristic
262#416—224no—
263C2×#103—24no—
264C2×#103—112no—
265C2×#103C2×D1114yes—
266C2×#102—112no—
267#391—112no—
268#390—112no—
269#386—222no—
270#380—222no—
271#340—114no—
272#336—114no—
273C22×C11—24no—
274C22×C11—24no—
275C22×C11—22no—
276C22×C11—22no—
277C22×C11#38614yes—
278C22×C11C2×C4×D411yescharacteristic
279C22×C11C2×#12011yescharacteristic
280C22×C11C2×#12111yescharacteristic
281C22×C11#57712yes—
282C22×C11#57812yes—
283C2×D11—44no—
284C2×D11—42no—
285C2×D11—82no—
286C2×D11—81no—
287C2×D11—81no—
288C4×C11—28no—
289C4×C11—82no—
290C4×C11#38614yes—
291C4×C11C22×C22⋊C411yescharacteristic
292C4×C11C2×C4×D411yescharacteristic
293C4×C11C2×#12111yescharacteristic
294C4×C11C2×#12311yescharacteristic
295Dic11—44no—
296Dic11—44no—
297Dic11—42no—
298C2×#41—114no—
299C2×#41—222no—
300C2×#41—222no—
301C2×#41—222no—
302C2×#41—222no—
303C2×#41—222no—
304C22×Q8—21no—
305C22×Q8—22no—
306C22×Q8—22no—
307C22×Q8—22no—
308C22×Q8—111no—
309C22×Q8C4×D1114yes—
310C22×Q8D4414yes—
311C22×Q8C22⋊D1114yes—
312C22×Q8C22×D1112yes—
313C22×D4—111no—
314C22×D4—221no—
315C23×C4—21no—
316C23×C4—21no—
317C23×C4—221no—
318C23×C4C22×D1111yescharacteristic
319#137—2232no—
320C2×Q16—118no—
321C2×Q16—224no—
322C2×Q16—224no—
323C2×SD16—118no—
324C2×SD16—224no—
325C2×SD16—224no—
326C2×M16—114no—
327C2×M16—222no—
328C2×M16—222no—
329C22×C8—22no—
330C22×C8—22no—
331C22×C8—22no—
332C22×C8—112no—
333C22×C8C22×D1112yes—
334C4×Q8—228no—
335C4×Q8—2216no—
336C4×Q8—228no—
337#117—114no—
338#117—2216no—
339#117—222no—
340#117—222no—
341#117—222no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—112no—
346C2×C4⋊C4—112no—
347C2×C4⋊C4—224no—
348C2×C4⋊C4C22×D1112yes—
349C2×C22⋊C4—112no—
350C2×C22⋊C4—221no—
351C2×C22⋊C4—224no—
352C2×C42—112no—
353C2×C42—224no—
354C2×C42—221no—
355#103—28no—
356#103—224no—
357#102—224no—
358#95—224no—
359C2×C11—24no—
360C2×C11C2×#38611yescharacteristic
361C2×C11#294712yes—
362C2×C11#301312yes—
363C2×C11#304311yescharacteristic
364C2×C11#304411yescharacteristic
365D11—82no—
366C24—221no—
367C24D4×D1111yescharacteristic
368#41—228no—
369#41—228no—
370#41—444no—
371#41—444no—
372C2×Q8—24no—
373C2×Q8—28no—
374C2×Q8—24no—
375C2×Q8—28no—
376C2×Q8—24no—
377C2×Q8—28no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—112no—
382C2×Q8—221no—
383C2×Q8—221no—
384C2×Q8—221no—
385C2×Q8—221no—
386C2×Q8—221no—
387C2×Q8(C2×D11)⋊C4116yescomplemented
388C2×Q8C2×C4×D1114yes—
389C2×Q8C2×D4414yes—
390C2×Q8C2×C22⋊D1114yes—
391C2×D4—112no—
392C2×D4—224no—
393C2×D4—221no—
394C2×D4—221no—
395C2×D4—221no—
396C2×D4—221no—
397C2×D4—221no—
398C2×D4—442no—
399C2×D4—442no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—42no—
406C22×C4—82no—
407C22×C4—114no—
408C22×C4—221no—
409C22×C4—222no—
410C22×C4—224no—
411C22×C4—442no—
412C22×C4—442no—
413C22×C4C2×C4×D1112yes—
414C22×C4C2×D4412yes—
415C22×C4D4×D1111yescharacteristic
416C22×C4D4×D1112yes—
417C22×C4#434112yes—
418C22×C4#434112yes—
419C22×C4C2×C22⋊D1112yes—
420C22×C4C23×D1111yescharacteristic
421Q16—2216no—
422SD16—2216no—
423M16—228no—
424C2×C8—22no—
425C2×C8—22no—
426C2×C8—22no—
427C2×C8—44no—
428C2×C8—114no—
429C2×C8—222no—
430C2×C8—222no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—42no—
434C4⋊C4—114no—
435C4⋊C4—2216no—
436C4⋊C4—224no—
437C4⋊C4—222no—
438C22⋊C4—224no—
439C22⋊C4—224no—
440C22⋊C4—884no—
441C42—2216no—
442C42—224no—
443C42—222no—
444C42—222no—
445C11#2093011yescharacteristic, complemented, Sylow
446C23—22no—
447C23—22no—
448C23—222no—
449C23—441no—
450C23—442no—
451C23—442no—
452C23—441no—
453C23(C22⋊D11)⋊C412yes—
454C23#6693512yes—
455C23#6699212yes—
456C23C2×D4×D1111yescharacteristic
457Q8—24no—
458Q8—24no—
459Q8—24no—
460Q8—216no—
461Q8—222no—
462Q8—222no—
463Q8—441no—
464Q8—441no—
465Q8C2×(C2×D11)⋊C418yes—
466D4—222no—
467D4—222no—
468D4—448no—
469D4—441no—
470D4—441no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—216no—
475C2×C4—44no—
476C2×C4—42no—
477C2×C4—84no—
478C2×C4—222no—
479C2×C4—224no—
480C2×C4—224no—
481C2×C4—224no—
482C2×C4—224no—
483C2×C4—441no—
484C2×C4—442no—
485C2×C4—442no—
486C2×C4—441no—
487C2×C4—448no—
488C2×C4(C22⋊D11)⋊C414yes—
489C2×C4(C22⋊D11)⋊C412yes—
490C2×C4#6693512yes—
491C2×C4#6693914yes—
492C2×C4C2×(C2×D11)⋊C414yes—
493C2×C4#6699214yes—
494C2×C4#6699212yes—
495C2×C4C22×C4×D1111yescharacteristic
496C2×C4C22×D4411yescharacteristic
497C2×C4C2×D4×D1111yescharacteristic
498C2×C4C2×#434111yescharacteristic
499C2×C4C2×#434111yescharacteristic
500C2×C4C22×C22⋊D1111yescharacteristic
501C8—42no—
502C8—224no—
503C22—22no—
504C22—22no—
505C22—24no—
506C22—24no—
507C22—442no—
508C22—444no—
509C22—881no—
510C22—881no—
511C22—882no—
512C22#1062257114yes—
513C22C2×(C22⋊D11)⋊C411yescharacteristic
514C22C2×#6693511yescharacteristic
515C22#1062329312yes—
516C22#1062329712yes—
517C22C2×#6699211yescharacteristic
518C4—28no—
519C4—82no—
520C4—444no—
521C4—444no—
522C4—442no—
523C4#1062257114yes—
524C4C2×(C22⋊D11)⋊C411yescharacteristic
525C4C2×#6693911yescharacteristic
526C4C22×(C2×D11)⋊C411yescharacteristic
527C4C2×#6699211yescharacteristic
528C2—24no—
529C2—882no—
530C2C2×#1062257111yescharacteristic
531C2#1307745312yes—
532C2#1307793612yes—
533C2#1307813411yescharacteristic
534C2#1307814311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#103C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenterC22×#103D11
hypocenterC11#20930
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
2. C2×#10623343C2semidirect
5. #13068969C2semidirect
6. #13068955C2semidirect
7. #13068335C2semidirect
8. #13068312C2semidirect
9. C22×C11×#103C2semidirect
21. C2×#66995C4semidirect
74. C2×#4326C2×C4semidirect
78. C2×#4325C2×C4semidirect
111. C2×Q8×C11C22⋊C4semidirect
182. C22×#103D11semidirect
387. C2×Q8(C2×D11)⋊C4semidirect
445. C11#20930semidirect

Maximal subgroups

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

subgroupindex
C22×#669952
C2×#106233432
C2×#106227262
#130712092
#130689692
#130689552
#130683352
#130683122
C22×C11×#1032
#2093011