Finite Group Databasebeta

← #14649520

Subgroups — #14649520

Order 2816.

1088 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076895C211yesmaximal, characteristic
2C2×#10622279C211yesmaximal, 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×C4×Dic11—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#10622279—22no—
24#10622279—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—28no—
56C2×(C2×D11)⋊C4—22no—
57C2×C4⋊Dic11C2×C412yes—
58C2×C4×Dic11—24no—
59C2×C4×Dic11—44no—
60C22×C11⋊C8—21no—
61C11×C22⋊C8—21no—
62C11×C22⋊C8—21no—
63C11×#95—21no—
64C11×#95D412yescomplemented
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—22no—
68C11⋊#95D412yescomplemented
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)—21no—
71(C2×D11)⋊C8—44no—
72#9150—111nomaximal, Sylow
73C24×C11—21no—
74C24×C11C2×D411yescharacteristic
75C23×D11—21no—
76C23×D11—21no—
77C23×D11—24no—
78C23×D11—21no—
79C23×D11—21no—
80C23×D11—21no—
81C23×D11—21no—
82C23×D11—42no—
83C23×D11C22⋊C412yes—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—42no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C22×C4×C11—24no—
94C22×C4×C11—22no—
95C22×C4×C11—21no—
96C22×C4×C11—42no—
97C22×C4×C11—42no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11C22×C411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11#4111yescharacteristic
105C22×C4×C11#4111yescharacteristic
106C2×C22⋊D11—44no—
107C2×C22⋊D11—44no—
108C2×C22⋊D11—44no—
109C22×Dic11—24no—
110C22×Dic11—24no—
111C22×Dic11—22no—
112C22×Dic11—21no—
113C22×Dic11—22no—
114C22×Dic11—21no—
115C22×Dic11—42no—
116C22×Dic11—41no—
117C22×Dic11—41no—
118C22×Dic11C22⋊C412yes—
119C2×C4×D11—24no—
120C2×C4×D11—24no—
121C2×C4×D11—22no—
122C2×C4×D11—22no—
123C2×C4×D11—22no—
124C2×C4×D11—22no—
125C2×C4×D11—42no—
126C2×C4×D11—42no—
127C2×C4×D11—44no—
128C2×C4×D11—44no—
129C2×C4×D11—44no—
130C2×C4×D11—44no—
131C2×C8×C11—42no—
132C2×C8×C11—41no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C22⋊C4—41no—
136C11×C22⋊C4—41no—
137C22⋊Dic11—44no—
138C22⋊Dic11—41no—
139C22⋊Dic11—41no—
140(C2×D11)⋊C4—216no—
141(C2×D11)⋊C4—44no—
142C4⋊Dic11—42no—
143C4×Dic11—48no—
144C2×C11⋊C8—42no—
145C2×C11⋊C8—41no—
146#2847—111no—
147C2×C4×C22⋊C4—111no—
148#1779—111no—
149C2×#327—111no—
150C2×#327D1111yescharacteristic, complemented
151#1294—111no—
152#1294—111no—
153C23×C11—22no—
154C23×C11—22no—
155C23×C11—41no—
156C23×C11—42no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—42no—
160C23×C11C2×C22⋊C411yescharacteristic
161C23×C11#12011yescharacteristic
162C23×C11#12311yescharacteristic
163C23×C11#13511yescharacteristic
164C23×C11#13511yescharacteristic
165C23×C11AGL(1,ℤ/8)11yescharacteristic
166C23×C11AGL(1,ℤ/8)11yescharacteristic
167C22×D11—24no—
168C22×D11—24no—
169C22×D11—22no—
170C22×D11—22no—
171C22×D11—22no—
172C22×D11—22no—
173C22×D11—22no—
174C22×D11—22no—
175C22×D11—44no—
176C22×D11—44no—
177C22×D11—44no—
178C22×D11—44no—
179C22×D11—42no—
180C22×D11—42no—
181C22×D11—41no—
182C22×D11—41no—
183C22×D11—41no—
184C22×D11—41no—
185C22×D11#10414yes—
186D4×C11—81no—
187D4×C11—81no—
188D4×C11—81no—
189D4×C11—81no—
190D4×C11—81no—
191D4×C11—81no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—24no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—42no—
200C2×C4×C11—44no—
201C2×C4×C11—44no—
202C2×C4×C11—42no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11C4×D411yescharacteristic
207C2×C4×C11C4×D411yescharacteristic
208C2×C4×C11#12111yescharacteristic
209C2×C4×C11#12111yescharacteristic
210C22⋊D11—88no—
211C2×Dic11—24no—
212C2×Dic11—24no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—24no—
216C2×Dic11—42no—
217C2×Dic11—44no—
218C2×Dic11—44no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11#9914yes—
224C4×D11—44no—
225C4×D11—44no—
226C4×D11—44no—
227C4×D11—44no—
228C8×C11—81no—
229C11⋊C8—81no—
230C24×C4—111no—
231C2×#121—112no—
232C2×#121C2×D1111yescharacteristic
233C2×#120—221no—
234C22×C22⋊C4—221no—
235C22×C42—221no—
236C2×C22⋊C8—111no—
237C2×C22⋊C8—222no—
238C2×C22⋊C8C2×D1111yescharacteristic
239#386—222no—
240#386—221no—
241#380—111no—
242#380—112no—
243C4×C22⋊C4—222no—
244C4×C22⋊C4—222no—
245C2×#95—111no—
246C2×#95C2×D1111yescharacteristic
247#327—22no—
248#327—222no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11—22no—
254C22×C11—22no—
255C22×C11—22no—
256C22×C11—22no—
257C22×C11—81no—
258C22×C11—81no—
259C22×C11—81no—
260C22×C11—82no—
261C22×C11—82no—
262C22×C11#38611yescharacteristic
263C22×C11C2×#9912yes—
264C22×C11#41611yescharacteristic
265C22×C11#41811yescharacteristic
266C22×C11C2×#10412yes—
267C22×C11#44911yescharacteristic
268C22×C11#44911yescharacteristic
269C22×C11#48211yescharacteristic
270C22×C11#48211yescharacteristic
271C2×D11—24no—
272C2×D11—24no—
273C2×D11—24no—
274C2×D11—44no—
275C2×D11—44no—
276C2×D11—44no—
277C2×D11—44no—
278C2×D11—42no—
279C2×D11—42no—
280C2×D11—42no—
281C2×D11—42no—
282C4×C11—21no—
283C4×C11—21no—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—44no—
287C4×C11—81no—
288Dic11—24no—
289Dic11—44no—
290Dic11—82no—
291C25—111no—
292C22×D4—21no—
293C22×D4—222no—
294C22×D4C4×D1111yescharacteristic
295C23×C4—21no—
296C23×C4—111no—
297C23×C4—112no—
298C23×C4—112no—
299C23×C4—221no—
300C23×C4—221no—
301C23×C4—221no—
302C23×C4—221no—
303C23×C4—221no—
304C23×C4—444no—
305C23×C4C22×D1111yescharacteristic
306C22×C8—21no—
307C22×C8—221no—
308#121—21no—
309#121—21no—
310#121—21no—
311#121—21no—
312#121—444no—
313#120—442no—
314#120—442no—
315C2×C4⋊C4—112no—
316C2×C4⋊C4C4×D1111yescharacteristic
317C2×C22⋊C4—21no—
318C2×C22⋊C4—224no—
319C2×C22⋊C4—228no—
320C2×C22⋊C4—222no—
321C2×C22⋊C4—222no—
322C2×C22⋊C4—221no—
323C2×C42—224no—
324C2×C42—444no—
325C22⋊C8—21no—
326C22⋊C8—21no—
327C22⋊C8—221no—
328C22⋊C8—221no—
329C22⋊C8—444no—
330#95—21no—
331#95—112no—
332#95—222no—
333#95—221no—
334#95—221no—
335#95C22⋊D1112yescomplemented
336C2×C11—21no—
337C2×C11—21no—
338C2×C11—21no—
339C2×C11—21no—
340C2×C11—161no—
341C2×C11#150112yes—
342C2×C11#150712yes—
343C2×C11#187511yescharacteristic
344C2×C11#189611yescharacteristic
345C2×C11#189811yescharacteristic
346D11—44no—
347C24—21no—
348C24—112no—
349C24—224no—
350C24—221no—
351C24—221no—
352C24—221no—
353C24—221no—
354C24—221no—
355C24—221no—
356C24—442no—
357C24D4×D1111yescharacteristic
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—42no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—444no—
368C2×D4—444no—
369C2×D4—444no—
370C22×C4—24no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—42no—
374C22×C4—42no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—112no—
378C22×C4—224no—
379C22×C4—224no—
380C22×C4—224no—
381C22×C4—221no—
382C22×C4—221no—
383C22×C4—224no—
384C22×C4—222no—
385C22×C4—222no—
386C22×C4—222no—
387C22×C4—222no—
388C22×C4—222no—
389C22×C4—222no—
390C22×C4—442no—
391C22×C4—442no—
392C22×C4—444no—
393C22×C4—444no—
394C22×C4—444no—
395C22×C4—444no—
396C22×C4—442no—
397C22×C4—441no—
398C22×C4—441no—
399C22×C4C2×C4×D1111yescharacteristic
400C22×C4#433911yescharacteristic
401C22×C4D4×D1111yescharacteristic
402C22×C4D4×D1111yescharacteristic
403C22×C4#434111yescharacteristic
404C22×C4C2×C22⋊D1111yescharacteristic
405C2×C8—42no—
406C2×C8—41no—
407C2×C8—442no—
408C2×C8—441no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—442no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C22⋊C4—2216no—
415C22⋊C4—444no—
416C22⋊C4—444no—
417C22⋊C4—441no—
418C22⋊C4—441no—
419C42—448no—
420C11#915011yescharacteristic, complemented, Sylow
421C23—22no—
422C23—22no—
423C23—41no—
424C23—42no—
425C23—41no—
426C23—41no—
427C23—42no—
428C23—114no—
429C23—224no—
430C23—224no—
431C23—222no—
432C23—222no—
433C23—222no—
434C23—222no—
435C23—222no—
436C23—222no—
437C23—444no—
438C23—444no—
439C23—444no—
440C23—444no—
441C23—442no—
442C23—442no—
443C23—441no—
444C23—441no—
445C23—441no—
446C23—441no—
447C23C22⋊C4×D1111yescharacteristic
448C23#6693611yescharacteristic
449C23#6696411yescharacteristic
450C23#6696511yescharacteristic
451C23#6696711yescharacteristic
452C23#6696911yescharacteristic
453C23#6699011yescharacteristic
454D4—81no—
455D4—81no—
456D4—81no—
457D4—81no—
458D4—81no—
459D4—81no—
460D4—888no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—24no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—42no—
469C2×C4—44no—
470C2×C4—44no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—114no—
476C2×C4—224no—
477C2×C4—224no—
478C2×C4—222no—
479C2×C4—222no—
480C2×C4—224no—
481C2×C4—444no—
482C2×C4—444no—
483C2×C4—444no—
484C2×C4—444no—
485C2×C4—442no—
486C2×C4—444no—
487C2×C4—444no—
488C2×C4—442no—
489C2×C4—442no—
490C2×C4—442no—
491C2×C4—442no—
492C2×C4(C22⋊D11)⋊C411yescharacteristic
493C2×C4#6693711yescharacteristic
494C2×C4C4×C22⋊D1111yescharacteristic
495C2×C4#6699111yescharacteristic
496C8—81no—
497C8—881no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—22no—
503C22—22no—
504C22—22no—
505C22—22no—
506C22—81no—
507C22—81no—
508C22—82no—
509C22—82no—
510C22—81no—
511C22—224no—
512C22—224no—
513C22—224no—
514C22—444no—
515C22—444no—
516C22—444no—
517C22—444no—
518C22—442no—
519C22—442no—
520C22—442no—
521C22—442no—
522C22D11×#9912yes—
523C22#1062238311yescharacteristic
524C22#1062238511yescharacteristic
525C22#1062239211yescharacteristic
526C22#1062239711yescharacteristic
527C22D11×#10412yes—
528C22#1062256911yescharacteristic
529C22#1062277111yescharacteristic
530C22#1062278511yescharacteristic
531C4—21no—
532C4—21no—
533C4—21no—
534C4—21no—
535C4—44no—
536C4—81no—
537C4—224no—
538C4—444no—
539C4—882no—
540C2—21no—
541C2—21no—
542C2—21no—
543C2—21no—
544C2—161no—
545C2—444no—
546C2#1306710412yes—
547C2#1306713012yes—
548C2#1306893511yescharacteristic
549C2#1306905611yescharacteristic
550C2#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#9150
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×#10622279C2semidirect
3. #13068525C2semidirect
4. C2×#10622175C2semidirect
5. #13066496C2semidirect
6. #13066495C2semidirect
7. C2×C11×#327C2semidirect
10. C2×#66991C4semidirect
21. #10622600C4semidirect
64. C11×#95D4semidirect
68. C11⋊#95D4semidirect
150. C2×#327D11semidirect
335. #95C22⋊D11semidirect
420. C11#9150semidirect

Maximal subgroups

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

subgroupindex
#130768952
C2×#106222792
#130685252
C2×#106221752
#130664962
#130664952
C2×C11×#3272
#915011