Finite Group Databasebeta

← #14763731

Subgroups — #14763731

Order 2816.

1118 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623131C211yesmaximal, characteristic
2C2×#10622731C211yesmaximal, characteristic, complemented
3#13071011C211yesmaximal, characteristic, complemented
4#13069570C212yesmaximal, complemented
5#13069547C212yesmaximal, complemented
6#13069055C211yesmaximal, characteristic
7#13069049C211yesmaximal, characteristic, complemented
8#13069047C211yesmaximal, characteristic, complemented
9#13068630C212yesmaximal, complemented
10#13068624C212yesmaximal, complemented
11C11×#1895C211yesmaximal, characteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#121C2211yescharacteristic
14C2×#66989C2211yescharacteristic
15C2×#66988—21no—
16C2×D4×Dic11—21no—
17C2×D4×Dic11C2211yescharacteristic
18C2×#66977C2211yescharacteristic
19C22×C4×Dic11C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21#10623131—24no—
22#10623131C418yescomplemented
23C2×#66943C2211yescharacteristic
24C2×#66940C2211yescharacteristic
25C2×#66932—21no—
26C2×#66930—21no—
27C2×C11×#102C2212yes—
28C11×#380C2211yescharacteristic
29C2×#66896C2212yes—
30#10622825C2211yescharacteristic
31#10622731—24no—
32C2×#66880C2212yes—
33C2×Dic11⋊C8C2212yes—
34C2×Dic11⋊C8C2212yes—
35#10622590C2212yes—
36C4⋊C4×Dic11C2212yes—
37C2×#66874C2212yes—
38#10622556—21no—
39C22⋊C4×Dic11—21no—
40#10622264—21no—
41#10622261—21no—
42C11×#340C2212yes—
43#10622189C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C22×D4×C11—21no—
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×Dic11—21no—
50C23×Dic11D411yescharacteristic
51C23×Dic11D411yescharacteristic
52C22×Dic22C2311yescharacteristic
53C2×C11×M16—22no—
54C2×C11×M16—42no—
55C22×C8×C11C2312yes—
56C11×#121—22no—
57C11×#121C2×C414yes—
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C22⋊C4—21no—
61C2×C11×C22⋊C4—21no—
62C2×C22⋊Dic11—21no—
63C2×C22⋊Dic11—21no—
64C2×C22⋊Dic11—21no—
65C2×C22⋊Dic11—21no—
66C2×C22⋊Dic11—21no—
67#66989—22no—
68#66989C2×C414yes—
69#66988—28no—
70D4×Dic11—28no—
71D4×Dic11—22no—
72D4×Dic11C2×C414yes—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11C2312yes—
75C2×C4⋊Dic11C2311yescharacteristic
76#66977—22no—
77#66977C2×C414yes—
78C2×Dic11⋊C4—21no—
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×C4×Dic11—21no—
82C2×C4×Dic11—22no—
83C2×C4×Dic11C2×C414yes—
84C2×C4×Dic11D411yescharacteristic
85C2×C4×Dic11D411yescharacteristic
86C2×C4×Dic11D414yes—
87C2×C4×Dic11C2311yescharacteristic
88C2×C4×Dic11C2311yescharacteristic
89C2×#4318—22no—
90C2×#4318—42no—
91C22×C11⋊C8C2312yes—
92#66943—22no—
93#66943C2×C414yes—
94#66940—22no—
95#66940C2×C414yes—
96#66932—28no—
97#66930—28no—
98C11×#102—42no—
99C11×#95—21no—
100#66896—42no—
101C11⋊#95—21no—
102C11⋊#95—22no—
103C11⋊#95—22no—
104C11⋊#95—22no—
105#66880—42no—
106Dic11⋊C8—24no—
107Dic11⋊C8—24no—
108#66874—42no—
109#21895—111nomaximal, Sylow
110C24×C11—21no—
111C24×C11C2×D411yescharacteristic
112C2×D4×C11—24no—
113C2×D4×C11—21no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—44no—
117C2×D4×C11C22×C412yes—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11C22×C412yes—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2411yescharacteristic
126C22×Dic11—24no—
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—22no—
130C22×Dic11—41no—
131C22×Dic11—41no—
132C22×Dic11—42no—
133C22×Dic11—42no—
134C22×Dic11—42no—
135C22×Dic11C22⋊C414yes—
136C22×Dic11C22⋊C414yes—
137C22×Dic11C2×D411yescharacteristic
138C22×Dic11C2×D411yescharacteristic
139C22×Dic11C2×D411yescharacteristic
140C22×Dic11C2×D411yescharacteristic
141C2×Dic22—21no—
142C2×Dic22—22no—
143C2×Dic22—22no—
144C2×Dic22C22×C412yes—
145C11×M16—44no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4C22×C412yes—
153C11×C22⋊C4—24no—
154C11×C22⋊C4—42no—
155C22⋊Dic11—24no—
156C22⋊Dic11—24no—
157C22⋊Dic11—24no—
158C22⋊Dic11—24no—
159C22⋊Dic11—42no—
160C4⋊Dic11—24no—
161C4⋊Dic11—21no—
162C4⋊Dic11—22no—
163C4⋊Dic11—22no—
164C4⋊Dic11C22×C412yes—
165Dic11⋊C4—24no—
166Dic11⋊C4—24no—
167Dic11⋊C4—24no—
168C4×Dic11—24no—
169C4×Dic11—44no—
170C4×Dic11C22⋊C414yes—
171C4×Dic11C22⋊C414yes—
172C4×Dic11C22×C412yes—
173C4×Dic11C22×C412yes—
174C4×Dic11C2×D412yes—
175C4×Dic11C2×D412yes—
176#4318—44no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×#529—111no—
181C2×#423—111no—
182#2283—111no—
183#1989—112no—
184#1983—112no—
185#1895—111no—
186#1895D1111yescharacteristic
187#1894—111no—
188#1894—111no—
189#1805—112no—
190#1804—112no—
191C23×C11—22no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—42no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—42no—
200C23×C11C2×C22⋊C412yes—
201C23×C11C22×D411yescharacteristic
202D4×C11—24no—
203D4×C11—48no—
204D4×C11—41no—
205D4×C11—41no—
206C2×C4×C11—22no—
207C2×C4×C11—24no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11C2×C22⋊C412yes—
216C2×C4×C11C23×C411yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11H(5,𝔽2)12yes—
219C2×C4×C112−1+412yes—
220C2×Dic11—22no—
221C2×Dic11—21no—
222C2×Dic11—21no—
223C2×Dic11—22no—
224C2×Dic11—21no—
225C2×Dic11—21no—
226C2×Dic11—22no—
227C2×Dic11—22no—
228C2×Dic11—44no—
229C2×Dic11—44no—
230C2×Dic11—48no—
231C2×Dic11—42no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11C2×C22⋊C412yes—
238C2×Dic11C2×C22⋊C412yes—
239C2×Dic11C2×C22⋊C412yes—
240C2×Dic11C2×C22⋊C412yes—
241Dic22—24no—
242Dic22—41no—
243Dic22—41no—
244C8×C11—42no—
245C11⋊C8—42no—
246C22×M16—111no—
247C22×M16C2×D1111yescharacteristic
248#529—118no—
249#529—224no—
250C2×#126—221no—
251C2×#125—111no—
252C2×#124—111no—
253C2×#123—221no—
254C2×C22⋊Q8—111no—
255C2×#121C2×D1111yescharacteristic
256C2×C4×Q8—111no—
257C2×C4×D4—111no—
258C2×C4×D4—221no—
259C2×#117—221no—
260C22×C42—111no—
261#423—224no—
262C2×C4⋊C8—112no—
263C2×C4⋊C8—112no—
264C2×#103—112no—
265C2×#103—112no—
266C2×#102—112no—
267C2×#102C2×D1112yes—
268#383—221no—
269#382—112no—
270#381—221no—
271#380—111no—
272#380C2×D1111yescharacteristic
273C4×C4⋊C4—112no—
274C4×C22⋊C4—221no—
275#376—221no—
276#340—112no—
277#340—112no—
278#340—112no—
279#340C2×D1112yes—
280C22×C11—22no—
281C22×C11—22no—
282C22×C11—22no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—82no—
289C22×C11—82no—
290C22×C11C22×C22⋊C411yescharacteristic
291C22×C11#53712yes—
292C22×C11#57512yes—
293C22×C11#57511yescharacteristic
294C22×C11#57511yescharacteristic
295C4×C11—22no—
296C4×C11—42no—
297C4×C11—82no—
298C4×C11#52012yes—
299C4×C11#53511yescharacteristic
300C4×C11#53611yescharacteristic
301Dic11—22no—
302Dic11—22no—
303Dic11—22no—
304Dic11—22no—
305Dic11—42no—
306Dic11—42no—
307Dic11—82no—
308C22×Q8—111no—
309C22×D4—21no—
310C22×D4C22×D1111yescharacteristic
311C23×C4—111no—
312C23×C4—111no—
313C23×C4—221no—
314C23×C4C22×D1111yescharacteristic
315C2×M16—22no—
316C2×M16—42no—
317C2×M16—222no—
318C2×M16—442no—
319C22×C8—112no—
320C22×C8C22×D1112yes—
321#126—228no—
322#125—114no—
323#125—222no—
324#124—114no—
325#124—222no—
326#123—228no—
327C22⋊Q8—114no—
328C22⋊Q8—222no—
329#121—22no—
330#121C4×D1114yes—
331C4×Q8—114no—
332C4×Q8—222no—
333C4×D4—114no—
334C4×D4—222no—
335C4×D4—228no—
336#117—228no—
337C2×C4⋊C4—111no—
338C2×C4⋊C4—112no—
339C2×C4⋊C4—221no—
340C2×C4⋊C4—221no—
341C2×C4⋊C4—221no—
342C2×C4⋊C4—221no—
343C2×C4⋊C4C22×D1112yes—
344C2×C4⋊C4C22×D1111yescharacteristic
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—221no—
348C2×C22⋊C4—221no—
349C2×C22⋊C4—221no—
350C2×C22⋊C4—221no—
351C2×C22⋊C4—221no—
352C2×C42—114no—
353C2×C42—111no—
354C2×C42—111no—
355C2×C42—114no—
356C2×C42—111no—
357C2×C42—111no—
358C2×C42—221no—
359C2×C42—222no—
360C4⋊C8—224no—
361C4⋊C8—224no—
362#103—442no—
363#103—442no—
364#102—42no—
365#102—442no—
366#95—21no—
367#95—222no—
368#95—222no—
369#95—222no—
370#95—221no—
371C2×C11—42no—
372C2×C11—82no—
373C2×C11#231111yescharacteristic
374C2×C11#289611yescharacteristic
375C2×C11#289611yescharacteristic
376C2×C11#325612yes—
377C2×C11#325612yes—
378C24—21no—
379C24D4×D1111yescharacteristic
380C2×Q8—112no—
381C2×Q8—221no—
382C2×Q8—222no—
383C2×Q8—222no—
384C2×D4—24no—
385C2×D4—21no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—44no—
389C2×D4C2×C4×D1112yes—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—111no—
395C22×C4—111no—
396C22×C4—111no—
397C22×C4—111no—
398C22×C4—114no—
399C22×C4—114no—
400C22×C4—224no—
401C22×C4—221no—
402C22×C4—221no—
403C22×C4—222no—
404C22×C4—442no—
405C22×C4—441no—
406C22×C4—441no—
407C22×C4—442no—
408C22×C4—442no—
409C22×C4C2×C4×D1112yes—
410C22×C4D4×D1111yescharacteristic
411C22×C4D4×D1112yes—
412C22×C4C23×D1111yescharacteristic
413M16—44no—
414M16—444no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—222no—
419C2×C8—222no—
420C2×C8—222no—
421C4⋊C4—21no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—112no—
425C4⋊C4—224no—
426C4⋊C4—224no—
427C4⋊C4—224no—
428C4⋊C4—224no—
429C4⋊C4—221no—
430C4⋊C4—222no—
431C4⋊C4—222no—
432C4⋊C4C2×C4×D1112yes—
433C22⋊C4—24no—
434C22⋊C4—42no—
435C22⋊C4—224no—
436C22⋊C4—224no—
437C22⋊C4—224no—
438C22⋊C4—224no—
439C22⋊C4—442no—
440C42—114no—
441C42—114no—
442C42—112no—
443C42—112no—
444C42—112no—
445C42—112no—
446C42—224no—
447C42—444no—
448C11#2189511yescharacteristic, complemented, Sylow
449C23—21no—
450C23—22no—
451C23—21no—
452C23—22no—
453C23—22no—
454C23—41no—
455C23—42no—
456C23—41no—
457C23—42no—
458C23C22⋊C4×D1112yes—
459C23C2×D4×D1111yescharacteristic
460Q8—224no—
461Q8—441no—
462Q8—441no—
463D4—24no—
464D4—48no—
465D4—41no—
466D4—41no—
467C2×C4—22no—
468C2×C4—24no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—112no—
477C2×C4—112no—
478C2×C4—112no—
479C2×C4—112no—
480C2×C4—222no—
481C2×C4—221no—
482C2×C4—222no—
483C2×C4—221no—
484C2×C4—221no—
485C2×C4—221no—
486C2×C4—222no—
487C2×C4—222no—
488C2×C4—444no—
489C2×C4—444no—
490C2×C4—448no—
491C2×C4—441no—
492C2×C4—441no—
493C2×C4—442no—
494C2×C4—442no—
495C2×C4—442no—
496C2×C4—442no—
497C2×C4C22⋊C4×D1112yes—
498C2×C4C22×C4×D1111yescharacteristic
499C2×C4C2×D4×D1111yescharacteristic
500C2×C4#6703712yes—
501C2×C4#6704312yes—
502C8—42no—
503C8—442no—
504C22—22no—
505C22—22no—
506C22—22no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22—42no—
512C22—82no—
513C22—82no—
514C22C2×C22⋊C4×D1111yescharacteristic
515C22#1062312812yes—
516C22#1062330412yes—
517C22#1062330411yescharacteristic
518C22#1062330811yescharacteristic
519C4—22no—
520C4—42no—
521C4—82no—
522C4—222no—
523C4—222no—
524C4—222no—
525C4—222no—
526C4—442no—
527C4—442no—
528C4—882no—
529C4#1062307712yes—
530C4#1062312311yescharacteristic
531C4#1062317911yescharacteristic
532C2—42no—
533C2—82no—
534C2#1307120311yescharacteristic
535C2#1307713011yescharacteristic
536C2#1307713211yescharacteristic
537C2#1308001112yes—
538C2#1308001312yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1895C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
cosocleC22×C4×C11C24
hypercenter#1895D11
hypocenterC11#21895
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1895

Complements

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

NH ≅ G/Ntype
2. C2×#10622731C2semidirect
3. #13071011C2semidirect
4. #13069570C2semidirect
5. #13069547C2semidirect
7. #13069049C2semidirect
8. #13069047C2semidirect
9. #13068630C2semidirect
10. #13068624C2semidirect
22. #10623131C4semidirect
448. C11#21895semidirect

Maximal subgroups

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

subgroupindex
C2×#106231312
C2×#106227312
#130710112
#130695702
#130695472
#130690552
#130690492
#130690472
#130686302
#130686242
C11×#18952
#2189511