Finite Group Databasebeta

← #14649545

Subgroups — #14649545

Order 2816.

1024 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076895C211yesmaximal, characteristic
2C2×#10622280C211yesmaximal, characteristic, complemented
3#13068525C211yesmaximal, characteristic, complemented
4C2×#10622175C211yesmaximal, characteristic, complemented
5#13066496C211yesmaximal, characteristic, complemented
6#13066495C211yesmaximal, characteristic, complemented
7C2×C11×#327C211yesmaximal, characteristic, complemented
8C23×C4×D11C2211yescharacteristic
9C2×C11×#121C2211yescharacteristic
10C2×#66991C412yescomplemented
11C2×#66990—21no—
12C22×(C2×D11)⋊C4—21no—
13C22×Dic11⋊C4—21no—
14C2×C11×C22⋊C8C2211yescharacteristic
15C2×C11×#95C2211yescharacteristic
16#10622833—21no—
17#10622825C2211yescharacteristic
18C2×C11⋊#95C2211yescharacteristic
19C2×C22⋊(C11⋊C8)C2211yescharacteristic
20C2×(C2×D11)⋊C8—22no—
21#10622600C412yescomplemented
22#10622569—22no—
23#10622280—22no—
24#10622280—22no—
25C11×#327—22no—
26#10622175—22no—
27C24×D11D411yescharacteristic
28C22×D4×C11—21no—
29C22×D4×C11C2×C411yescharacteristic
30C23×C4×C11—21no—
31C23×C4×C11C2311yescharacteristic
32C22×C22⋊D11—22no—
33C23×Dic11—21no—
34C23×Dic11D411yescharacteristic
35C22×C4×D11—21no—
36C22×C4×D11—21no—
37C22×C4×D11—21no—
38C22×C4×D11—21no—
39C22×C4×D11—44no—
40C22×C4×D11C2×C412yes—
41C22×C4×D11D412yes—
42C22×C8×C11—21no—
43C11×#121—21no—
44C11×#121—21no—
45C11×#121—21no—
46C11×#121—21no—
47C2×C11×C4⋊C4C2×C411yescharacteristic
48C2×C11×C22⋊C4—21no—
49C2×C22⋊Dic11—21no—
50C2×C22⋊Dic11—22no—
51#66991—44no—
52#66990—42no—
53#66990—42no—
54C2×(C2×D11)⋊C4—24no—
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—42no—
57C2×(C2×D11)⋊C4—42no—
58C2×C4⋊Dic11C2×C412yes—
59C2×Dic11⋊C4—24no—
60C2×Dic11⋊C4—44no—
61C22×C11⋊C8—21no—
62C11×C22⋊C8—21no—
63C11×C22⋊C8—21no—
64C11×#95—21no—
65C11×#95D412yescomplemented
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—22no—
69C11⋊#95D412yescomplemented
70C22⋊(C11⋊C8)—21no—
71C22⋊(C11⋊C8)—21no—
72(C2×D11)⋊C8—44no—
73#9155—111nomaximal, Sylow
74C24×C11—21no—
75C24×C11C2×D411yescharacteristic
76C23×D11—21no—
77C23×D11—21no—
78C23×D11—21no—
79C23×D11—21no—
80C23×D11—42no—
81C23×D11—42no—
82C23×D11C22⋊C412yes—
83C23×D11D812yes—
84C23×D11SD1612yes—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—42no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—42no—
97C22×C4×C11—42no—
98C22×C4×C11—42no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11C22×C411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11#4111yescharacteristic
106C22×C4×C11#4111yescharacteristic
107C2×C22⋊D11—44no—
108C2×C22⋊D11—44no—
109C2×C22⋊D11—44no—
110C22×Dic11—24no—
111C22×Dic11—22no—
112C22×Dic11—21no—
113C22×Dic11—22no—
114C22×Dic11—21no—
115C22×Dic11—42no—
116C22×Dic11—42no—
117C22×Dic11—41no—
118C22×Dic11—41no—
119C22×Dic11C22⋊C412yes—
120C2×C4×D11—24no—
121C2×C4×D11—24no—
122C2×C4×D11—22no—
123C2×C4×D11—22no—
124C2×C4×D11—22no—
125C2×C4×D11—22no—
126C2×C4×D11—42no—
127C2×C4×D11—42no—
128C2×C4×D11—44no—
129C2×C4×D11—44no—
130C2×C4×D11—44no—
131C2×C4×D11—44no—
132C2×C8×C11—42no—
133C2×C8×C11—41no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C22⋊C4—41no—
137C11×C22⋊C4—41no—
138C22⋊Dic11—44no—
139C22⋊Dic11—41no—
140C22⋊Dic11—41no—
141(C2×D11)⋊C4—48no—
142(C2×D11)⋊C4—44no—
143C4⋊Dic11—42no—
144Dic11⋊C4—48no—
145C2×C11⋊C8—42no—
146C2×C11⋊C8—41no—
147#2847—111no—
148C2×#380—111no—
149#1779—111no—
150C2×#327—111no—
151C2×#327D1111yescharacteristic, complemented
152#1294—111no—
153#1294—111no—
154C23×C11—22no—
155C23×C11—22no—
156C23×C11—41no—
157C23×C11—42no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—42no—
161C23×C11C2×C22⋊C411yescharacteristic
162C23×C11#12011yescharacteristic
163C23×C11#12311yescharacteristic
164C23×C11C2×D811yescharacteristic
165C23×C11C2×SD1611yescharacteristic
166C23×C11AGL(1,ℤ/8)11yescharacteristic
167C23×C11#13711yescharacteristic
168C22×D11—22no—
169C22×D11—22no—
170C22×D11—22no—
171C22×D11—22no—
172C22×D11—22no—
173C22×D11—22no—
174C22×D11—22no—
175C22×D11—22no—
176C22×D11—22no—
177C22×D11—22no—
178C22×D11—44no—
179C22×D11—44no—
180C22×D11—42no—
181C22×D11—42no—
182C22×D11—42no—
183C22×D11—42no—
184C22×D11—44no—
185C22×D11—44no—
186C22×D11#10214yes—
187D4×C11—81no—
188D4×C11—81no—
189D4×C11—81no—
190D4×C11—81no—
191D4×C11—81no—
192D4×C11—81no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—42no—
205C2×C4×C11—82no—
206C2×C4×C11—82no—
207C2×C4×C11C4×D411yescharacteristic
208C2×C4×C11C4×D411yescharacteristic
209C2×C4×C11#12111yescharacteristic
210C2×C4×C11#12111yescharacteristic
211C22⋊D11—88no—
212C2×Dic11—24no—
213C2×Dic11—24no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—82no—
223C2×Dic11—82no—
224C2×Dic11#9914yes—
225C4×D11—44no—
226C4×D11—44no—
227C4×D11—44no—
228C4×D11—44no—
229C8×C11—81no—
230C11⋊C8—81no—
231C24×C4—111no—
232C2×#121—112no—
233C2×#121C2×D1111yescharacteristic
234C2×#120—221no—
235C22×C4⋊C4—221no—
236C22×C22⋊C4—221no—
237C2×C22⋊C8—111no—
238C2×C22⋊C8—222no—
239C2×C22⋊C8C2×D1111yescharacteristic
240#386—222no—
241#386—221no—
242#380—111no—
243#380—112no—
244#380—222no—
245#380—222no—
246C2×#95—111no—
247C2×#95C2×D1111yescharacteristic
248#327—22no—
249#327—222no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11—21no—
254C22×C11—22no—
255C22×C11—22no—
256C22×C11—22no—
257C22×C11—22no—
258C22×C11—81no—
259C22×C11—81no—
260C22×C11—81no—
261C22×C11—82no—
262C22×C11—82no—
263C22×C11#38611yescharacteristic
264C22×C11C2×#9912yes—
265C22×C11C2×#10211yescharacteristic
266C22×C11#41711yescharacteristic
267C22×C11#42112yes—
268C22×C11#44711yescharacteristic
269C22×C11#44811yescharacteristic
270C22×C11#48011yescharacteristic
271C22×C11#48111yescharacteristic
272C2×D11—24no—
273C2×D11—24no—
274C2×D11—24no—
275C2×D11—44no—
276C2×D11—44no—
277C2×D11—44no—
278C2×D11—44no—
279C2×D11—42no—
280C2×D11—42no—
281C2×D11—42no—
282C2×D11—42no—
283C4×C11—21no—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—21no—
287C4×C11—82no—
288C4×C11—81no—
289Dic11—24no—
290Dic11—82no—
291Dic11—82no—
292C25—111no—
293C22×D4—21no—
294C22×D4—222no—
295C22×D4C4×D1111yescharacteristic
296C23×C4—21no—
297C23×C4—111no—
298C23×C4—112no—
299C23×C4—112no—
300C23×C4—221no—
301C23×C4—221no—
302C23×C4—221no—
303C23×C4—221no—
304C23×C4—221no—
305C23×C4—444no—
306C23×C4C22×D1111yescharacteristic
307C22×C8—21no—
308C22×C8—221no—
309#121—21no—
310#121—21no—
311#121—21no—
312#121—21no—
313#121—444no—
314#120—442no—
315#120—442no—
316C2×C4⋊C4—112no—
317C2×C4⋊C4—224no—
318C2×C4⋊C4—444no—
319C2×C4⋊C4C4×D1111yescharacteristic
320C2×C22⋊C4—21no—
321C2×C22⋊C4—222no—
322C2×C22⋊C4—224no—
323C2×C22⋊C4—222no—
324C2×C22⋊C4—221no—
325C2×C22⋊C4—442no—
326C2×C22⋊C4—442no—
327C22⋊C8—21no—
328C22⋊C8—21no—
329C22⋊C8—221no—
330C22⋊C8—221no—
331C22⋊C8—444no—
332#95—21no—
333#95—112no—
334#95—222no—
335#95—221no—
336#95—221no—
337#95C22⋊D1112yescomplemented
338C2×C11—21no—
339C2×C11—21no—
340C2×C11—21no—
341C2×C11—21no—
342C2×C11—161no—
343C2×C11#151312yes—
344C2×C11#151912yes—
345C2×C11#187411yescharacteristic
346C2×C11#189711yescharacteristic
347C2×C11#189811yescharacteristic
348D11—44no—
349C24—21no—
350C24—112no—
351C24—112no—
352C24—112no—
353C24—221no—
354C24—221no—
355C24—221no—
356C24—221no—
357C24—442no—
358C24—442no—
359C24D4×D1111yescharacteristic
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—42no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—444no—
370C2×D4—444no—
371C2×D4—444no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—112no—
380C22×C4—224no—
381C22×C4—224no—
382C22×C4—224no—
383C22×C4—221no—
384C22×C4—221no—
385C22×C4—222no—
386C22×C4—222no—
387C22×C4—222no—
388C22×C4—222no—
389C22×C4—222no—
390C22×C4—222no—
391C22×C4—442no—
392C22×C4—442no—
393C22×C4—444no—
394C22×C4—444no—
395C22×C4—444no—
396C22×C4—444no—
397C22×C4—442no—
398C22×C4—442no—
399C22×C4—441no—
400C22×C4—441no—
401C22×C4C2×C4×D1111yescharacteristic
402C22×C4#433911yescharacteristic
403C22×C4D4×D1111yescharacteristic
404C22×C4D4×D1111yescharacteristic
405C22×C4#434111yescharacteristic
406C22×C4C2×C22⋊D1111yescharacteristic
407C2×C8—42no—
408C2×C8—41no—
409C2×C8—442no—
410C2×C8—441no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—442no—
414C4⋊C4—448no—
415C22⋊C4—41no—
416C22⋊C4—41no—
417C22⋊C4—444no—
418C22⋊C4—448no—
419C22⋊C4—444no—
420C22⋊C4—441no—
421C22⋊C4—441no—
422C11#915511yescharacteristic, complemented, Sylow
423C23—22no—
424C23—22no—
425C23—41no—
426C23—42no—
427C23—41no—
428C23—41no—
429C23—42no—
430C23—114no—
431C23—222no—
432C23—222no—
433C23—222no—
434C23—222no—
435C23—222no—
436C23—222no—
437C23—222no—
438C23—222no—
439C23—222no—
440C23—222no—
441C23—444no—
442C23—444no—
443C23—442no—
444C23—442no—
445C23—442no—
446C23—442no—
447C23—444no—
448C23—444no—
449C23C22⋊C4×D1111yescharacteristic
450C23#6693611yescharacteristic
451C23D8×D1111yescharacteristic
452C23#6696411yescharacteristic
453C23SD16×D1111yescharacteristic
454C23#6696811yescharacteristic
455C23#6699011yescharacteristic
456D4—81no—
457D4—81no—
458D4—81no—
459D4—81no—
460D4—81no—
461D4—81no—
462D4—888no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—82no—
476C2×C4—82no—
477C2×C4—114no—
478C2×C4—224no—
479C2×C4—224no—
480C2×C4—222no—
481C2×C4—222no—
482C2×C4—444no—
483C2×C4—444no—
484C2×C4—444no—
485C2×C4—444no—
486C2×C4—442no—
487C2×C4—442no—
488C2×C4—442no—
489C2×C4—442no—
490C2×C4—442no—
491C2×C4—442no—
492C2×C4—882no—
493C2×C4—882no—
494C2×C4(C22⋊D11)⋊C411yescharacteristic
495C2×C4#6693711yescharacteristic
496C2×C4C4×C22⋊D1111yescharacteristic
497C2×C4#6699111yescharacteristic
498C8—81no—
499C8—881no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—22no—
505C22—22no—
506C22—22no—
507C22—22no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—82no—
512C22—82no—
513C22—224no—
514C22—224no—
515C22—224no—
516C22—444no—
517C22—444no—
518C22—444no—
519C22—444no—
520C22—442no—
521C22—442no—
522C22—442no—
523C22—442no—
524C22D11×#9912yes—
525C22D11×#10211yescharacteristic
526C22#1062238411yescharacteristic
527C22#1062238711yescharacteristic
528C22#1062239011yescharacteristic
529C22#1062243412yes—
530C22#1062256911yescharacteristic
531C22#1062276911yescharacteristic
532C22#1062278311yescharacteristic
533C4—21no—
534C4—21no—
535C4—21no—
536C4—21no—
537C4—82no—
538C4—81no—
539C4—224no—
540C4—882no—
541C4—882no—
542C2—21no—
543C2—21no—
544C2—21no—
545C2—21no—
546C2—161no—
547C2—444no—
548C2#1306715612yes—
549C2#1306718212yes—
550C2#1306893011yescharacteristic
551C2#1306906111yescharacteristic
552C2#1306906611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#327C2
socleC23×C11C2×C22⋊C4
prime radical#13076895C2
cosocleC23×C4×C11C23
hypercenterC2×#327D11
hypocenterC11#9155
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C2×#10622280C2semidirect
3. #13068525C2semidirect
4. C2×#10622175C2semidirect
5. #13066496C2semidirect
6. #13066495C2semidirect
7. C2×C11×#327C2semidirect
10. C2×#66991C4semidirect
21. #10622600C4semidirect
65. C11×#95D4semidirect
69. C11⋊#95D4semidirect
151. C2×#327D11semidirect
337. #95C22⋊D11semidirect
422. C11#9155semidirect

Maximal subgroups

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

subgroupindex
#130768952
C2×#106222802
#130685252
C2×#106221752
#130664962
#130664952
C2×C11×#3272
#915511