Finite Group Databasebeta

← #14755144

Subgroups — #14755144

Order 2816.

1802 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×Q8×Dic11C211yesmaximal, characteristic, complemented
2C2×#10622845C211yesmaximal, characteristic
3C2×#10622838C211yesmaximal, characteristic, complemented
4#13071107C211yesmaximal, characteristic
5#13068973C214yesmaximal, complemented
6#13068959C214yesmaximal, complemented
7#13068336C211yesmaximal, characteristic, complemented
8#13068309C211yesmaximal, characteristic, complemented
9C22×C11×#137C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C23×Q8×C11C2211yescharacteristic
12C2×C11×#137—24no—
13C2×C11×#137—24no—
14C2×C11×#137C418yescomplemented
15C22×C11×Q16C2212yes—
16C22×C11×SD16C2212yes—
17C22×C11×M16C2211yescharacteristic
18C2×Q8×Dic11—24no—
19C2×Q8×Dic11—24no—
20C2×Q8×Dic11—22no—
21C2×Q8×Dic11C2214yes—
22C2×#66979C2211yescharacteristic
23C22×C4⋊Dic11—21no—
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4×Dic11—21no—
26C22×C4×Dic11C2211yescharacteristic
27C22×#4318C2211yescharacteristic
28#10622845—24no—
29#10622843C2212yes—
30#10622838—24no—
31C2×#66899C2214yes—
32C2×#66899C2212yes—
33#10622834C2212yes—
34#10622833—21no—
35#10622833—21no—
36C2×#66896C2212yes—
37C4×C22⋊Dic11—22no—
38#10622189C2214yes—
39#10622188C2214yes—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41C2×C414yes—
46C22×Q8×C11—22no—
47C22×Q8×C11—21no—
48C22×Q8×C11—22no—
49C22×Q8×C11—22no—
50C22×Q8×C11C2×C414yes—
51C22×Q8×C11D414yes—
52C22×Q8×C11D414yes—
53C22×Q8×C11C2311yescharacteristic
54C22×Q8×C11C2312yes—
55C22×D4×C11—21no—
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C23×C4×C11—21no—
59C23×C4×C11C2311yescharacteristic
60C23×Dic11—21no—
61C23×Dic11D411yescharacteristic
62C23×Dic11D411yescharacteristic
63C11×#137—232no—
64C2×C11×Q16—24no—
65C2×C11×Q16—24no—
66C2×C11×Q16C2×C418yescomplemented
67C2×C11×SD16—24no—
68C2×C11×SD16—24no—
69C2×C11×SD16C2×C418yescomplemented
70C2×C11×M16—22no—
71C2×C11×M16—22no—
72C2×C11×M16C2×C414yes—
73C22×C8×C11C2312yes—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—22no—
76C2×C22⋊Dic11—22no—
77Q8×Dic11—216no—
78Q8×Dic11—28no—
79Q8×Dic11—28no—
80#66979—22no—
81#66979—22no—
82C2×C4⋊Dic11—28no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—24no—
86C2×C4⋊Dic11D414yes—
87C2×C4⋊Dic11C2312yes—
88C2×C4⋊Dic11C2312yes—
89C2×C4×Dic11—28no—
90C2×C4×Dic11—22no—
91C2×C4×Dic11—22no—
92C2×C4×Dic11—24no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11D412yes—
95C2×C4×Dic11C2312yes—
96C2×#4318—22no—
97C2×#4318—22no—
98C2×#4318—22no—
99C22×C11⋊C8C2312yes—
100#66899—28no—
101#66899—24no—
102#66896—24no—
103C11⋊#95—22no—
104C11⋊#95—22no—
105#20926—111nomaximal, Sylow
106C24×C11—21no—
107C24×C11C2×D411yescharacteristic
108C11×#41—28no—
109C11×#41—28no—
110C11×#41—44no—
111C11×#41—44no—
112C2×Q8×C11—24no—
113C2×Q8×C11—28no—
114C2×Q8×C11—24no—
115C2×Q8×C11—24no—
116C2×Q8×C11—28no—
117C2×Q8×C11—28no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11C22⋊C4116yescomplemented
127C2×Q8×C11C22×C412yes—
128C2×Q8×C11C22×C414yes—
129C2×Q8×C11C2×D414yes—
130C2×Q8×C11C2×D414yes—
131C2×D4×C11—24no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—42no—
138C2×D4×C11—42no—
139C2×D4×C11C22×C412yes—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—24no—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11—24no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11C22×C412yes—
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D412yes—
153C22×C4×C11#4112yes—
154C22×C4×C11#4112yes—
155C22×C4×C11C2411yescharacteristic
156C22×Dic11—24no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—24no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—42no—
163C22×Dic11—44no—
164C22×Dic11C2×D412yes—
165C22×Dic11C2×D412yes—
166C11×Q16—216no—
167C11×SD16—216no—
168C11×M16—28no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11C22×C414yes—
172C22⋊Dic11—44no—
173C22⋊Dic11—44no—
174C22⋊Dic11—42no—
175C4⋊Dic11—216no—
176C4⋊Dic11—24no—
177C4⋊Dic11—22no—
178C4⋊Dic11—22no—
179C4⋊Dic11—22no—
180C4⋊Dic11C2×D414yes—
181C4×Dic11—216no—
182C4×Dic11—24no—
183C4×Dic11—22no—
184C4×Dic11—22no—
185C4×Dic11—42no—
186#4318—44no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—22no—
190C22×#137D1111yescharacteristic
191C22×C4×Q8—111no—
192C2×#417—111no—
193C2×#419—111no—
194#2297—111no—
195#1880—114no—
196#1878—114no—
197#1736—111no—
198#1728—111no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11C4×D412yes—
207C23×C11#12012yes—
208C23×C11#12112yes—
209C23×C11C22×D411yescharacteristic
210Q8×C11—24no—
211Q8×C11—24no—
212Q8×C11—24no—
213Q8×C11—216no—
214Q8×C11—22no—
215Q8×C11—22no—
216Q8×C11—41no—
217Q8×C11—41no—
218Q8×C11C2×C22⋊C418yes—
219D4×C11—22no—
220D4×C11—22no—
221D4×C11—48no—
222D4×C11—41no—
223D4×C11—41no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—216no—
228C2×C4×C11—22no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—48no—
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—28no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—24no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—44no—
253C2×Dic11—48no—
254C2×Dic11—44no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11#13714yescomplemented
259C8×C11—24no—
260C11⋊C8—42no—
261C22×#41C2×D1111yescharacteristic
262C23×Q8C2×D1111yescharacteristic
263C2×#137—24no—
264C2×#137—24no—
265C2×#137Dic1118yescomplemented
266C22×Q16C2×D1112yes—
267C22×SD16C2×D1112yes—
268C22×M16—111no—
269C22×M16C2×D1111yescharacteristic
270C2×C4×Q8—114no—
271C2×C4×Q8—222no—
272C2×C4×Q8—224no—
273C2×C4×Q8—224no—
274C2×#117—111no—
275C22×C4⋊C4—111no—
276C22×C4⋊C4—221no—
277C22×C42—111no—
278C22×C42—221no—
279#419—224no—
280#417—224no—
281C2×#103—114no—
282C2×#103—112no—
283C2×#102—112no—
284#391—112no—
285#390—112no—
286#386—221no—
287#386—221no—
288C4×C22⋊C4—222no—
289#340—114no—
290#336—114no—
291C22×C11—24no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—24no—
295C22×C11—44no—
296C22×C11—42no—
297C22×C11—81no—
298C22×C11—81no—
299C22×C11—82no—
300C22×C11#38614yes—
301C22×C11C2×C4×D411yescharacteristic
302C22×C11C2×#12011yescharacteristic
303C22×C11C2×#12111yescharacteristic
304C22×C11C2×#13712yes—
305C22×C11#57512yes—
306C4×C11—28no—
307C4×C11—42no—
308C4×C11#38614yes—
309C4×C11C22×C22⋊C411yescharacteristic
310C4×C11C2×C4×D411yescharacteristic
311C4×C11C2×#12111yescharacteristic
312C4×C11C2×#12311yescharacteristic
313Dic11—24no—
314Dic11—42no—
315Dic11—44no—
316Dic11—82no—
317C2×#41—22no—
318C2×#41—22no—
319C2×#41—22no—
320C2×#41—22no—
321C2×#41—22no—
322C2×#41C2×Dic1114yes—
323C22×Q8—22no—
324C22×Q8—21no—
325C22×Q8—22no—
326C22×Q8—22no—
327C22×Q8C2×Dic1114yes—
328C22×Q8C22⋊D1114yes—
329C22×Q8C22⋊D1114yes—
330C22×Q8C22×D1111yescharacteristic
331C22×Q8C22×D1112yes—
332C22×D4—21no—
333C22×D4C22×D1111yescharacteristic
334C23×C4—21no—
335C23×C4—21no—
336C23×C4—111no—
337C23×C4—111no—
338C23×C4—221no—
339C23×C4C22×D1111yescharacteristic
340#137—232no—
341C2×Q16—24no—
342C2×Q16—24no—
343C2×Q16C2×Dic1118yescomplemented
344C2×SD16—24no—
345C2×SD16—24no—
346C2×SD16C2×Dic1118yescomplemented
347C2×M16—22no—
348C2×M16—22no—
349C2×M16—222no—
350C2×M16—222no—
351C2×M16—222no—
352C2×M16C2×Dic1114yes—
353C22×C8—112no—
354C22×C8C22×D1112yes—
355C4×Q8—228no—
356C4×Q8—2216no—
357C4×Q8—228no—
358#117—222no—
359#117—222no—
360C2×C4⋊C4—114no—
361C2×C4⋊C4—112no—
362C2×C4⋊C4—112no—
363C2×C4⋊C4—224no—
364C2×C4⋊C4—228no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—222no—
367C2×C22⋊C4—222no—
368C2×C22⋊C4—222no—
369C2×C22⋊C4—221no—
370C2×C42—112no—
371C2×C42—112no—
372C2×C42—224no—
373C2×C42—228no—
374C2×C42—222no—
375C2×C42—222no—
376C2×C42—221no—
377#103—224no—
378#103—228no—
379#102—224no—
380#95—222no—
381#95—222no—
382C2×C11—24no—
383C2×C11—82no—
384C2×C11C2×#38611yescharacteristic
385C2×C11C4×#13712yes—
386C2×C11#300411yescharacteristic
387C2×C11#300511yescharacteristic
388C2×C11#303712yes—
389C24—21no—
390C24D4×D1111yescharacteristic
391#41—28no—
392#41—28no—
393#41—44no—
394#41—44no—
395C2×Q8—24no—
396C2×Q8—28no—
397C2×Q8—28no—
398C2×Q8—24no—
399C2×Q8—24no—
400C2×Q8—28no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8C22⋊Dic11116yescomplemented
410C2×Q8C22×Dic1112yes—
411C2×Q8C22×Dic1114yes—
412C2×Q8C2×C22⋊D1114yes—
413C2×Q8C2×C22⋊D1114yes—
414C2×D4—24no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—42no—
421C2×D4—42no—
422C2×D4C22×Dic1112yes—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—24no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—112no—
432C22×C4—112no—
433C22×C4—224no—
434C22×C4—222no—
435C22×C4—224no—
436C22×C4—222no—
437C22×C4—222no—
438C22×C4—222no—
439C22×C4—442no—
440C22×C4—444no—
441C22×C4D4×D1111yescharacteristic
442C22×C4D4×D1112yes—
443C22×C4#434112yes—
444C22×C4#434112yes—
445C22×C4C22×Dic1112yes—
446C22×C4C2×C22⋊D1112yes—
447C22×C4C2×C22⋊D1112yes—
448C22×C4C23×D1111yescharacteristic
449Q16—216no—
450SD16—216no—
451M16—28no—
452M16—444no—
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—222no—
456C2×C8—222no—
457C2×C8—222no—
458C2×C8C22×Dic1114yes—
459C4⋊C4—114no—
460C4⋊C4—2216no—
461C4⋊C4—224no—
462C4⋊C4—222no—
463C4⋊C4—222no—
464C4⋊C4—222no—
465C22⋊C4—444no—
466C22⋊C4—444no—
467C22⋊C4—442no—
468C42—2216no—
469C42—224no—
470C42—222no—
471C42—222no—
472C42—442no—
473C11#2092611yescharacteristic, complemented, Sylow
474C23—22no—
475C23—22no—
476C23—22no—
477C23—42no—
478C23—42no—
479C23—41no—
480C23—41no—
481C23D4×Dic1112yes—
482C23#6699012yes—
483C23#6699212yes—
484C23C2×D4×D1111yescharacteristic
485Q8—24no—
486Q8—24no—
487Q8—24no—
488Q8—216no—
489Q8—22no—
490Q8—22no—
491Q8—41no—
492Q8—41no—
493Q8C2×C22⋊Dic1118yes—
494D4—22no—
495D4—22no—
496D4—48no—
497D4—41no—
498D4—41no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—216no—
503C2×C4—22no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—48no—
507C2×C4—114no—
508C2×C4—228no—
509C2×C4—222no—
510C2×C4—222no—
511C2×C4—222no—
512C2×C4—222no—
513C2×C4—224no—
514C2×C4—222no—
515C2×C4—444no—
516C2×C4—448no—
517C2×C4—444no—
518C2×C4—442no—
519C2×C4—442no—
520C2×C4—442no—
521C2×C4D4×Dic1114yes—
522C2×C4D4×Dic1112yes—
523C2×C4#6698814yes—
524C2×C4#6699012yes—
525C2×C4#6699214yes—
526C2×C4#6699212yes—
527C2×C4C2×C22⋊Dic1114yes—
528C2×C4C2×D4×D1111yescharacteristic
529C2×C4C2×#434111yescharacteristic
530C2×C4C2×#434111yescharacteristic
531C2×C4C23×Dic1111yescharacteristic
532C2×C4C22×C22⋊D1111yescharacteristic
533C2×C4C22×C22⋊D1111yescharacteristic
534C8—24no—
535C8—442no—
536C22—24no—
537C22—22no—
538C22—22no—
539C22—24no—
540C22—42no—
541C22—44no—
542C22—82no—
543C22—81no—
544C22—81no—
545C22#1062283314yes—
546C22D11×#13712yes—
547C22#1062330812yes—
548C22C2×D4×Dic1111yescharacteristic
549C22C2×#6699011yescharacteristic
550C22C2×#6699211yescharacteristic
551C4—28no—
552C4—42no—
553C4—224no—
554C4—442no—
555C4—444no—
556C4—882no—
557C4#1062283314yes—
558C4C2×D4×Dic1111yescharacteristic
559C4C2×#6698811yescharacteristic
560C4C2×#6699211yescharacteristic
561C4C22×C22⋊Dic1111yescharacteristic
562C2—24no—
563C2—82no—
564C2C2×#1062283311yescharacteristic
565C2#137×Dic1112yes—
566C2#1307784811yescharacteristic
567C2#1307785711yescharacteristic
568C2#1307808512yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#137C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenterC22×#137D11
hypocenterC11#20926
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
1. C22×Q8×Dic11C2semidirect
3. C2×#10622838C2semidirect
5. #13068973C2semidirect
6. #13068959C2semidirect
7. #13068336C2semidirect
8. #13068309C2semidirect
14. C2×C11×#137C4semidirect
66. C2×C11×Q16C2×C4semidirect
69. C2×C11×SD16C2×C4semidirect
126. C2×Q8×C11C22⋊C4semidirect
258. C2×Dic11#137semidirect
265. C2×#137Dic11semidirect
343. C2×Q16C2×Dic11semidirect
346. C2×SD16C2×Dic11semidirect
409. C2×Q8C22⋊Dic11semidirect
473. C11#20926semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×Dic112
C2×#106228452
C2×#106228382
#130711072
#130689732
#130689592
#130683362
#130683092
C22×C11×#1372
#2092611