Finite Group Databasebeta

← #14755180

Subgroups — #14755180

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
1C2×#10623343C211yesmaximal, characteristic, complemented
2C2×#10622846C211yesmaximal, characteristic
3C22×#66899C211yesmaximal, characteristic, complemented
4#13071208C211yesmaximal, characteristic
5#13068973C214yesmaximal, complemented
6#13068959C214yesmaximal, complemented
7#13068336C211yesmaximal, characteristic, complemented
8#13068314C211yesmaximal, 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
18#10623343—24no—
19#10623343—24no—
20C2×Q8×Dic11—22no—
21C2×Q8×Dic11C2214yes—
22C2×#66979—22no—
23C2×#66979C2211yescharacteristic
24C2×#66979C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C23×C11⋊C8C2211yescharacteristic
27#10622846—24no—
28#10622843C2212yes—
29C2×#66899—24no—
30C2×#66899C2214yes—
31C2×#66899C2212yes—
32#10622834C2212yes—
33#10622833—22no—
34C2×#66896C2212yes—
35#10622825—22no—
36#10622189C2214yes—
37#10622188C2214yes—
38C2×C11×#41—22no—
39C2×C11×#41—22no—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41C2×C414yes—
44C22×Q8×C11—21no—
45C22×Q8×C11—22no—
46C22×Q8×C11—22no—
47C22×Q8×C11—22no—
48C22×Q8×C11C2×C414yes—
49C22×Q8×C11D414yes—
50C22×Q8×C11D414yes—
51C22×Q8×C11C2311yescharacteristic
52C22×Q8×C11C2312yes—
53C22×D4×C11—21no—
54C22×D4×C11C2311yescharacteristic
55C23×C4×C11—21no—
56C23×C4×C11—21no—
57C23×C4×C11C2311yescharacteristic
58C23×Dic11—21no—
59C11×#137—232no—
60C2×C11×Q16—24no—
61C2×C11×Q16—24no—
62C2×C11×Q16C2×C418yescomplemented
63C2×C11×SD16—24no—
64C2×C11×SD16—24no—
65C2×C11×SD16C2×C418yescomplemented
66C2×C11×M16—22no—
67C2×C11×M16—22no—
68C2×C11×M16C2×C414yes—
69C22×C8×C11C2312yes—
70C2×C22⋊Dic11—21no—
71C2×C22⋊Dic11—24no—
72C2×C22⋊Dic11D412yes—
73Q8×Dic11—216no—
74Q8×Dic11—28no—
75Q8×Dic11—28no—
76#66979—216no—
77#66979—22no—
78#66979—22no—
79#66979—22no—
80#66979D414yes—
81C2×C4⋊Dic11—24no—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11D412yes—
86C2×C4⋊Dic11C2312yes—
87C2×C4⋊Dic11C2312yes—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—24no—
90C2×C4×Dic11C2312yes—
91C22×C11⋊C8—22no—
92C22×C11⋊C8—22no—
93C22×C11⋊C8—22no—
94C22×C11⋊C8C2312yes—
95#66899—28no—
96#66899—24no—
97#66896—24no—
98C11⋊#95—24no—
99#20930—111nomaximal, Sylow
100C24×C11—21no—
101C24×C11C2×D411yescharacteristic
102C11×#41—28no—
103C11×#41—28no—
104C11×#41—44no—
105C11×#41—44no—
106C2×Q8×C11—24no—
107C2×Q8×C11—28no—
108C2×Q8×C11—24no—
109C2×Q8×C11—24no—
110C2×Q8×C11—28no—
111C2×Q8×C11—28no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11C22⋊C4116yescomplemented
121C2×Q8×C11C22×C412yes—
122C2×Q8×C11C22×C414yes—
123C2×Q8×C11C2×D414yes—
124C2×Q8×C11C2×D414yes—
125C2×D4×C11—24no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—42no—
132C2×D4×C11—42no—
133C2×D4×C11C22×C412yes—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—22no—
138C22×C4×C11—21no—
139C22×C4×C11—24no—
140C22×C4×C11—42no—
141C22×C4×C11—42no—
142C22×C4×C11C22×C412yes—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D412yes—
147C22×C4×C11#4112yes—
148C22×C4×C11#4112yes—
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—42no—
153C22×Dic11—82no—
154C22×Dic11C2×D414yes—
155C11×Q16—216no—
156C11×SD16—216no—
157C11×M16—28no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C2×C8×C11C22×C414yes—
161C22⋊Dic11—24no—
162C22⋊Dic11—24no—
163C22⋊Dic11—84no—
164C4⋊Dic11—216no—
165C4⋊Dic11—24no—
166C4⋊Dic11—22no—
167C4⋊Dic11—22no—
168C4⋊Dic11—22no—
169C4⋊Dic11—42no—
170C4⋊Dic11C2×D414yes—
171C4×Dic11—216no—
172C4×Dic11—24no—
173C4×Dic11—22no—
174C4×Dic11—22no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—44no—
179C22×#137D1111yescharacteristic
180C2×#519—111no—
181C2×#416—111no—
182C22×#103—111no—
183#2311—111no—
184#1880—114no—
185#1878—114no—
186#1736—111no—
187#1729—111no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11C4×D412yes—
196C23×C11#12012yes—
197C23×C11#12112yes—
198C23×C11C22×D411yescharacteristic
199Q8×C11—24no—
200Q8×C11—24no—
201Q8×C11—24no—
202Q8×C11—216no—
203Q8×C11—22no—
204Q8×C11—22no—
205Q8×C11—41no—
206Q8×C11—41no—
207Q8×C11C2×C22⋊C418yes—
208D4×C11—22no—
209D4×C11—22no—
210D4×C11—48no—
211D4×C11—41no—
212D4×C11—41no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—216no—
217C2×C4×C11—22no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—48no—
221C2×C4×C11C2×C22⋊C414yes—
222C2×C4×C11C4×D414yes—
223C2×C4×C11C4×D412yes—
224C2×C4×C11#12012yes—
225C2×C4×C11#12114yes—
226C2×C4×C11#12112yes—
227C2×C4×C11#12314yes—
228C2×C4×C11C23×C411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C2×Dic11—24no—
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—44no—
242C2×Dic11—84no—
243C8×C11—24no—
244C11⋊C8—42no—
245C22×#41C2×D1111yescharacteristic
246C23×Q8C2×D1111yescharacteristic
247C2×#137—24no—
248C2×#137—24no—
249C2×#137Dic1118yescomplemented
250C22×Q16C2×D1112yes—
251C22×SD16C2×D1112yes—
252C22×M16C2×D1111yescharacteristic
253C23×C8—111no—
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⋊C4—111no—
262#416—224no—
263C2×#103—114no—
264C2×#103—112no—
265C2×#103—224no—
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—44no—
278C22×C11—42no—
279C22×C11—82no—
280C22×C11—81no—
281C22×C11—81no—
282C22×C11#38614yes—
283C22×C11C2×C4×D411yescharacteristic
284C22×C11C2×#12011yescharacteristic
285C22×C11C2×#12111yescharacteristic
286C22×C11#57712yes—
287C22×C11#57812yes—
288C4×C11—28no—
289C4×C11—42no—
290C4×C11#38614yes—
291C4×C11C22×C22⋊C411yescharacteristic
292C4×C11C2×C4×D411yescharacteristic
293C4×C11C2×#12111yescharacteristic
294C4×C11C2×#12311yescharacteristic
295Dic11—44no—
296Dic11—44no—
297Dic11—82no—
298C2×#41—22no—
299C2×#41—22no—
300C2×#41—22no—
301C2×#41—22no—
302C2×#41—22no—
303C2×#41C2×Dic1114yes—
304C22×Q8—21no—
305C22×Q8—22no—
306C22×Q8—22no—
307C22×Q8—22no—
308C22×Q8C2×Dic1114yes—
309C22×Q8C22⋊D1114yes—
310C22×Q8C22⋊D1114yes—
311C22×Q8C22×D1111yescharacteristic
312C22×Q8C22×D1112yes—
313C22×D4—21no—
314C22×D4C22×D1111yescharacteristic
315C23×C4—21no—
316C23×C4—21no—
317C23×C4—221no—
318C23×C4C22×D1111yescharacteristic
319#137—232no—
320C2×Q16—24no—
321C2×Q16—24no—
322C2×Q16C2×Dic1118yescomplemented
323C2×SD16—24no—
324C2×SD16—24no—
325C2×SD16C2×Dic1118yescomplemented
326C2×M16—22no—
327C2×M16—22no—
328C2×M16C2×Dic1114yes—
329C22×C8—112no—
330C22×C8—222no—
331C22×C8—222no—
332C22×C8—222no—
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—112no—
343C2×C4⋊C4—112no—
344C2×C4⋊C4—112no—
345C2×C4⋊C4—224no—
346C2×C4⋊C4—222no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4—221no—
349C2×C22⋊C4—112no—
350C2×C22⋊C4—221no—
351C2×C22⋊C4—224no—
352C2×C42—112no—
353C2×C42—224no—
354C2×C42—221no—
355#103—224no—
356#103—228no—
357#102—224no—
358#95—224no—
359C2×C11—24no—
360C2×C11—82no—
361C2×C11C2×#38611yescharacteristic
362C2×C11#294712yes—
363C2×C11#301312yes—
364C2×C11#304311yescharacteristic
365C2×C11#304411yescharacteristic
366C24—21no—
367C24D4×D1111yescharacteristic
368#41—28no—
369#41—28no—
370#41—44no—
371#41—44no—
372C2×Q8—24no—
373C2×Q8—28no—
374C2×Q8—28no—
375C2×Q8—24no—
376C2×Q8—24no—
377C2×Q8—28no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8C22⋊Dic11116yescomplemented
387C2×Q8C22×Dic1112yes—
388C2×Q8C22×Dic1114yes—
389C2×Q8C2×C22⋊D1114yes—
390C2×Q8C2×C22⋊D1114yes—
391C2×D4—24no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4C22×Dic1112yes—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—24no—
406C22×C4—42no—
407C22×C4—42no—
408C22×C4—114no—
409C22×C4—222no—
410C22×C4—222no—
411C22×C4—442no—
412C22×C4—882no—
413C22×C4D4×D1111yescharacteristic
414C22×C4D4×D1112yes—
415C22×C4#434112yes—
416C22×C4#434112yes—
417C22×C4C22×Dic1112yes—
418C22×C4C2×C22⋊D1112yes—
419C22×C4C2×C22⋊D1112yes—
420C22×C4C23×D1111yescharacteristic
421Q16—216no—
422SD16—216no—
423M16—28no—
424C2×C8—22no—
425C2×C8—22no—
426C2×C8—222no—
427C2×C8—222no—
428C2×C8—222no—
429C2×C8—444no—
430C2×C8C22×Dic1114yes—
431C4⋊C4—114no—
432C4⋊C4—2216no—
433C4⋊C4—224no—
434C4⋊C4—222no—
435C4⋊C4—222no—
436C4⋊C4—222no—
437C4⋊C4—442no—
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—22no—
449C23—42no—
450C23—42no—
451C23—41no—
452C23—41no—
453C23D4×Dic1112yes—
454C23#6699012yes—
455C23#6699212yes—
456C23C2×D4×D1111yescharacteristic
457Q8—24no—
458Q8—24no—
459Q8—24no—
460Q8—216no—
461Q8—22no—
462Q8—22no—
463Q8—41no—
464Q8—41no—
465Q8C2×C22⋊Dic1118yes—
466D4—22no—
467D4—22no—
468D4—48no—
469D4—41no—
470D4—41no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—216no—
475C2×C4—22no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—48no—
479C2×C4—224no—
480C2×C4—224no—
481C2×C4—224no—
482C2×C4—224no—
483C2×C4—442no—
484C2×C4—442no—
485C2×C4—444no—
486C2×C4—442no—
487C2×C4—884no—
488C2×C4D4×Dic1114yes—
489C2×C4D4×Dic1112yes—
490C2×C4#6698814yes—
491C2×C4#6699012yes—
492C2×C4#6699214yes—
493C2×C4#6699212yes—
494C2×C4C2×C22⋊Dic1114yes—
495C2×C4C2×D4×D1111yescharacteristic
496C2×C4C2×#434111yescharacteristic
497C2×C4C2×#434111yescharacteristic
498C2×C4C23×Dic1111yescharacteristic
499C2×C4C22×C22⋊D1111yescharacteristic
500C2×C4C22×C22⋊D1111yescharacteristic
501C8—24no—
502C8—442no—
503C22—22no—
504C22—22no—
505C22—24no—
506C22—24no—
507C22—42no—
508C22—44no—
509C22—81no—
510C22—81no—
511C22—82no—
512C22#1062283314yes—
513C22#1062330912yes—
514C22#1062331012yes—
515C22C2×D4×Dic1111yescharacteristic
516C22C2×#6699011yescharacteristic
517C22C2×#6699211yescharacteristic
518C4—28no—
519C4—42no—
520C4—444no—
521C4—444no—
522C4—882no—
523C4#1062283314yes—
524C4C2×D4×Dic1111yescharacteristic
525C4C2×#6698811yescharacteristic
526C4C2×#6699211yescharacteristic
527C4C22×C22⋊Dic1111yescharacteristic
528C2—24no—
529C2—82no—
530C2C2×#1062283311yescharacteristic
531C2#1307746012yes—
532C2#1307793012yes—
533C2#1307813911yescharacteristic
534C2#1307814811yescharacteristic
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#20930
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. C2×#10623343C2semidirect
3. C22×#66899C2semidirect
5. #13068973C2semidirect
6. #13068959C2semidirect
7. #13068336C2semidirect
8. #13068314C2semidirect
14. C2×C11×#137C4semidirect
62. C2×C11×Q16C2×C4semidirect
65. C2×C11×SD16C2×C4semidirect
120. C2×Q8×C11C22⋊C4semidirect
249. C2×#137Dic11semidirect
322. C2×Q16C2×Dic11semidirect
325. C2×SD16C2×Dic11semidirect
386. C2×Q8C22⋊Dic11semidirect
445. C11#20930semidirect

Maximal subgroups

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

subgroupindex
C2×#106233432
C2×#106228462
C22×#668992
#130712082
#130689732
#130689592
#130683362
#130683142
C22×C11×#1372
#2093011