Finite Group Databasebeta

← #14643747

Subgroups — #14643747

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622339C211yesmaximal, characteristic
2D11×#407C211yesmaximal, characteristic
3D11×#407C211yesmaximal, characteristic
4#13066493C211yesmaximal, characteristic, complemented
5#13066492C211yesmaximal, characteristic, complemented
6#13066492C211yesmaximal, characteristic, complemented
7C11×#1293C211yesmaximal, characteristic, complemented
8C23×C4×D11C2211yescharacteristic
9C2×M16×D11—21no—
10C2×M16×D11—21no—
11C22×#4313C412yes—
12C11×#407C2211yescharacteristic
13C11×#407C2211yescharacteristic
14C2×C11×C22⋊C8C2211yescharacteristic
15#10622820C2211yescharacteristic
16#10622820C2211yescharacteristic
17C2×C22⋊(C11⋊C8)C2211yescharacteristic
18#10622739—21no—
19#10622739—21no—
20C2×(C2×D11)⋊C8C412yes—
21#10622339—21no—
22#10622339—21no—
23#10622339—21no—
24#10622339—21no—
25#10622339—21no—
26#10622339—21no—
27#10622339C412yes—
28#10622339C412yes—
29D11×C22⋊C8—21no—
30D11×C22⋊C8—21no—
31D11×C22⋊C8C412yes—
32D11×C22⋊C8C412yes—
33C24×D11Q811yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×Dic11Q811yescharacteristic
36C22×C4×D11—44no—
37C22×C4×D11C2×C411yescharacteristic
38C22×C4×D11C2×C411yescharacteristic
39C22×C4×D11C2×C411yescharacteristic
40C22×C4×D11C2×C411yescharacteristic
41C22×C4×D11C2×C411yescharacteristic
42C22×C4×D11C2×C411yescharacteristic
43C22×C4×D11D411yescharacteristic
44C22×C4×D11D411yescharacteristic
45C22×C4×D11D411yescharacteristic
46C22×C4×D11D411yescharacteristic
47C22×C4×D11D411yescharacteristic
48C22×C4×D11D411yescharacteristic
49C2×C11×M16—21no—
50C2×C11×M16—21no—
51C22×C8×C11C2×C412yes—
52C2×#4318—21no—
53C2×#4318—21no—
54C22×C11⋊C8C2×C412yes—
55M16×D11—44no—
56M16×D11—44no—
57C2×#4313—22no—
58C2×#4313—22no—
59C2×#4313—22no—
60C2×#4313—22no—
61C2×#4313—44no—
62C2×C8×D11—22no—
63C2×C8×D11—22no—
64C11×C22⋊C8—21no—
65C11×C22⋊C8—21no—
66C11×C22⋊C8—21no—
67C11×C22⋊C8—21no—
68C11×C22⋊C8C2×C412yes—
69C11×C22⋊C8C2×C412yes—
70C22⋊(C11⋊C8)—21no—
71C22⋊(C11⋊C8)—21no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)C2×C412yes—
75C22⋊(C11⋊C8)C2×C412yes—
76(C2×D11)⋊C8—22no—
77(C2×D11)⋊C8—22no—
78(C2×D11)⋊C8—22no—
79(C2×D11)⋊C8—22no—
80(C2×D11)⋊C8—22no—
81(C2×D11)⋊C8—22no—
82#8009—111nomaximal, Sylow
83C24×C11C2×Q811yescharacteristic
84C23×D11—42no—
85C23×D11—42no—
86C23×D11—42no—
87C23×D11C4⋊C411yescharacteristic
88C23×D11C4⋊C411yescharacteristic
89C23×D11C4⋊C411yescharacteristic
90C23×D11C4⋊C411yescharacteristic
91C23×D11C4⋊C411yescharacteristic
92C23×D11C4⋊C411yescharacteristic
93C22×C4×C11—42no—
94C22×C4×C11C22×C411yescharacteristic
95C22×C4×C11C22×C411yescharacteristic
96C22×C4×C11C22×C411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×Dic11—42no—
101C22×Dic11C4⋊C411yescharacteristic
102C22×Dic11C4⋊C411yescharacteristic
103C22×Dic11C4⋊C411yescharacteristic
104C22×Dic11C4⋊C411yescharacteristic
105C22×Dic11C4⋊C411yescharacteristic
106C22×Dic11C4⋊C411yescharacteristic
107C2×C4×D11—24no—
108C2×C4×D11—24no—
109C2×C4×D11—24no—
110C2×C4×D11—42no—
111C2×C4×D11—42no—
112C2×C4×D11—42no—
113C2×C4×D11—42no—
114C2×C4×D11—42no—
115C2×C4×D11—42no—
116C2×C4×D11—42no—
117C2×C4×D11—42no—
118C2×C4×D11—42no—
119C2×C4×D11C4211yescharacteristic
120C2×C4×D11C4211yescharacteristic
121C2×C4×D11C4211yescharacteristic
122C2×C4×D11C4211yescharacteristic
123C2×C4×D11C22⋊C411yescharacteristic
124C2×C4×D11C22⋊C411yescharacteristic
125C2×C4×D11C22⋊C411yescharacteristic
126C2×C4×D11C22⋊C411yescharacteristic
127C2×C4×D11C22⋊C411yescharacteristic
128C2×C4×D11C22⋊C411yescharacteristic
129C2×C4×D11C22⋊C411yescharacteristic
130C2×C4×D11C22⋊C411yescharacteristic
131C2×C4×D11C22⋊C411yescharacteristic
132C2×C4×D11C22⋊C411yescharacteristic
133C2×C4×D11C22⋊C411yescharacteristic
134C2×C4×D11C22⋊C411yescharacteristic
135C11×M16—42no—
136C11×M16—42no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—42no—
141#4318—42no—
142#4318—42no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—42no—
147#4313—44no—
148#4313—44no—
149#4313—44no—
150#4313—44no—
151C8×D11—44no—
152C8×D11—44no—
153C2×#407—111no—
154C2×#407—111no—
155C2×#407—111no—
156#1293—111no—
157#1293—111no—
158#1293—111no—
159#1293D1111yescharacteristic, complemented
160C23×C11—22no—
161C23×C11—41no—
162C23×C11—41no—
163C23×C11C2×C4⋊C411yescharacteristic
164C23×C11C2×C4⋊C411yescharacteristic
165C23×C11C2×C4⋊C411yescharacteristic
166C22×D11—22no—
167C22×D11—22no—
168C22×D11—22no—
169C22×D11—22no—
170C22×D11—22no—
171C22×D11—22no—
172C22×D11—22no—
173C22×D11—22no—
174C22×D11—41no—
175C22×D11—41no—
176C22×D11—41no—
177C22×D11—41no—
178C22×D11—41no—
179C22×D11—41no—
180C22×D11—41no—
181C22×D11—41no—
182C22×D11—41no—
183C22×D11—41no—
184C22×D11—416no—
185C22×D11#9511yescharacteristic
186C22×D11#9511yescharacteristic
187C22×D11#9511yescharacteristic
188C22×D11#9511yescharacteristic
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11C2×C4211yescharacteristic
196C2×C4×C11C2×C22⋊C411yescharacteristic
197C2×C4×C11C2×C22⋊C411yescharacteristic
198C2×C4×C11C2×C22⋊C411yescharacteristic
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11#9511yescharacteristic
206C2×Dic11#9511yescharacteristic
207C2×Dic11#9511yescharacteristic
208C2×Dic11#9511yescharacteristic
209C4×D11—22no—
210C4×D11—22no—
211C4×D11—22no—
212C4×D11—22no—
213C4×D11—22no—
214C4×D11—22no—
215C4×D11—22no—
216C4×D11—22no—
217C4×D11—22no—
218C4×D11—41no—
219C4×D11—41no—
220C4×D11—41no—
221C4×D11—41no—
222C4×D11—41no—
223C4×D11—41no—
224C4×D11#9914yes—
225C8×C11—42no—
226C8×C11—42no—
227C8×C11—42no—
228C11⋊C8—42no—
229C11⋊C8—42no—
230C11⋊C8—42no—
231C24×C4—111no—
232C22×M16—112no—
233C22×M16—221no—
234C22×M16—221no—
235#407—111no—
236#407—111no—
237#407—112no—
238#407—112no—
239#407—221no—
240#407—221no—
241#407—221no—
242#407—221no—
243#407—221no—
244#407—221no—
245#407—221no—
246#407—221no—
247#407C2×D1111yescharacteristic
248#407C2×D1111yescharacteristic
249C2×C22⋊C8—112no—
250C2×C22⋊C8—112no—
251C2×C22⋊C8—111no—
252C2×C22⋊C8—112no—
253C2×C22⋊C8—221no—
254C2×C22⋊C8—221no—
255C2×C22⋊C8C2×D1111yescharacteristic
256C22×C11—21no—
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—21no—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—44no—
265C22×C11C2×#9511yescharacteristic
266C22×C11#43012yes—
267C2×D11—21no—
268C2×D11—21no—
269C2×D11—21no—
270C2×D11—21no—
271C2×D11—21no—
272C2×D11—21no—
273C2×D11—21no—
274C2×D11—21no—
275C2×D11—21no—
276C2×D11—21no—
277C2×D11—44no—
278C2×D11—44no—
279C2×D11—44no—
280C2×D11—44no—
281C2×D11—44no—
282C2×D11—44no—
283C2×D11#33812yes—
284C2×D11#34212yes—
285C4×C11—21no—
286C4×C11—21no—
287C4×C11—21no—
288C4×C11C2×#9912yes—
289Dic11—21no—
290Dic11—21no—
291Dic11—21no—
292Dic11#34212yes—
293C25—111no—
294C23×C4—111no—
295C23×C4—111no—
296C23×C4—111no—
297C23×C4—111no—
298C23×C4—111no—
299C23×C4—111no—
300C23×C4—111no—
301C23×C4—111no—
302C23×C4—111no—
303C23×C4—111no—
304C23×C4—111no—
305C23×C4—111no—
306C23×C4—111no—
307C23×C4—444no—
308C23×C4C22×D1111yescharacteristic
309C2×M16—21no—
310C2×M16—21no—
311C2×M16—222no—
312C2×M16—222no—
313C2×M16—222no—
314C2×M16—222no—
315C2×M16—221no—
316C2×M16—221no—
317C2×M16—444no—
318C2×M16—444no—
319C2×M16—444no—
320C22×C8—112no—
321C22×C8—222no—
322C22×C8—222no—
323C22×C8C4×D1112yes—
324C22⋊C8—21no—
325C22⋊C8—21no—
326C22⋊C8—21no—
327C22⋊C8—21no—
328C22⋊C8—112no—
329C22⋊C8—112no—
330C22⋊C8—222no—
331C22⋊C8—222no—
332C22⋊C8—222no—
333C22⋊C8—222no—
334C22⋊C8—222no—
335C22⋊C8—222no—
336C22⋊C8—221no—
337C22⋊C8—221no—
338C22⋊C8—221no—
339C22⋊C8—221no—
340C22⋊C8C4×D1112yes—
341C22⋊C8C4×D1112yes—
342C2×C11—22no—
343C2×C11—41no—
344C2×C11—41no—
345C2×C11C2×#33811yescharacteristic
346C2×C11#173811yescharacteristic
347C2×C11C2×#34211yescharacteristic
348D11—22no—
349D11—22no—
350D11—41no—
351D11—41no—
352C24—111no—
353C24—111no—
354C24—111no—
355C24—111no—
356C24—111no—
357C24—111no—
358C24—442no—
359C24—442no—
360C24—442no—
361C24Q8×D1111yescharacteristic
362C22×C4—42no—
363C22×C4—111no—
364C22×C4—111no—
365C22×C4—111no—
366C22×C4—111no—
367C22×C4—111no—
368C22×C4—111no—
369C22×C4—111no—
370C22×C4—111no—
371C22×C4—111no—
372C22×C4—111no—
373C22×C4—111no—
374C22×C4—111no—
375C22×C4—111no—
376C22×C4—111no—
377C22×C4—111no—
378C22×C4—111no—
379C22×C4—111no—
380C22×C4—111no—
381C22×C4—111no—
382C22×C4—111no—
383C22×C4—111no—
384C22×C4—111no—
385C22×C4—224no—
386C22×C4—224no—
387C22×C4—224no—
388C22×C4—442no—
389C22×C4—442no—
390C22×C4—442no—
391C22×C4—442no—
392C22×C4—442no—
393C22×C4—442no—
394C22×C4—442no—
395C22×C4—442no—
396C22×C4—442no—
397C22×C4—442no—
398C22×C4C2×C4×D1111yescharacteristic
399C22×C4C2×C4×D1111yescharacteristic
400C22×C4C2×C4×D1111yescharacteristic
401C22×C4D4×D1111yescharacteristic
402C22×C4D4×D1111yescharacteristic
403C22×C4D4×D1111yescharacteristic
404M16—42no—
405M16—42no—
406M16—444no—
407M16—444no—
408M16—444no—
409M16—444no—
410M16—442no—
411M16—442no—
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—42no—
416C2×C8—222no—
417C2×C8—222no—
418C2×C8—222no—
419C2×C8—444no—
420C2×C8—444no—
421C2×C8—442no—
422C11#800911yescharacteristic, complemented, Sylow
423C23—22no—
424C23—41no—
425C23—41no—
426C23—111no—
427C23—111no—
428C23—111no—
429C23—111no—
430C23—222no—
431C23—222no—
432C23—222no—
433C23—222no—
434C23—222no—
435C23—222no—
436C23—222no—
437C23—222no—
438C23—441no—
439C23—441no—
440C23—441no—
441C23—441no—
442C23—441no—
443C23—441no—
444C23—441no—
445C23—441no—
446C23—441no—
447C23—441no—
448C23—4416no—
449C23C4⋊C4×D1111yescharacteristic
450C23C4⋊C4×D1111yescharacteristic
451C23C4⋊C4×D1111yescharacteristic
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—111no—
459C2×C4—114no—
460C2×C4—111no—
461C2×C4—111no—
462C2×C4—111no—
463C2×C4—222no—
464C2×C4—222no—
465C2×C4—222no—
466C2×C4—222no—
467C2×C4—222no—
468C2×C4—222no—
469C2×C4—222no—
470C2×C4—222no—
471C2×C4—222no—
472C2×C4—222no—
473C2×C4—222no—
474C2×C4—222no—
475C2×C4—441no—
476C2×C4—441no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—441no—
481C2×C4—441no—
482C2×C4—441no—
483C2×C4—441no—
484C2×C4C42×D1111yescharacteristic
485C2×C4C22⋊C4×D1111yescharacteristic
486C2×C4C22⋊C4×D1111yescharacteristic
487C2×C4C22⋊C4×D1111yescharacteristic
488C8—42no—
489C8—42no—
490C8—42no—
491C8—442no—
492C8—442no—
493C8—442no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—44no—
503C22—112no—
504C22—112no—
505C22—221no—
506C22—221no—
507C22—221no—
508C22—221no—
509C22—221no—
510C22—221no—
511C22—221no—
512C22—221no—
513C22—221no—
514C22—221no—
515C22—444no—
516C22—444no—
517C22—444no—
518C22—444no—
519C22—444no—
520C22—444no—
521C22D11×#9511yescharacteristic
522C22#1062250612yes—
523C4—21no—
524C4—21no—
525C4—21no—
526C4—112no—
527C4—221no—
528C4—221no—
529C4—221no—
530C4D11×#9912yes—
531C2—22no—
532C2—41no—
533C2—41no—
534C2—222no—
535C2—222no—
536C2—441no—
537C2—441no—
538C2D11×#33811yescharacteristic
539C2#1306834111yescharacteristic
540C2D11×#34211yescharacteristic
subgroupG/H
centerC22D11×#95
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC11×#1293C2
socleC22×C11C2×#95
prime radicalC24×D11Q8
cosocleC23×C4×C11C23
hypercenter#1293D11
hypocenterC11#8009
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1293

Complements

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

NH ≅ G/Ntype
4. #13066493C2semidirect
5. #13066492C2semidirect
6. #13066492C2semidirect
7. C11×#1293C2semidirect
159. #1293D11semidirect
422. C11#8009semidirect

Maximal subgroups

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

subgroupindex
C2×#106223392
D11×#4072
#130664932
#130664922
C11×#12932
#800911