Finite Group Databasebeta

← #14649562

Subgroups — #14649562

Order 2816.

980 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076899C211yesmaximal, characteristic
2C2×#10622277C211yesmaximal, characteristic, complemented
3#13068525C211yesmaximal, characteristic, complemented
4C2×#10622108C211yesmaximal, characteristic, complemented
5C2×#10622089C211yesmaximal, characteristic, complemented
6#13066494C211yesmaximal, characteristic, complemented
7C11×#1294C211yesmaximal, characteristic, complemented
8C23×C4×D11C2211yescharacteristic
9C2×#66983C2211yescharacteristic
10C22×(C2×D11)⋊C4—21no—
11C2×#66948C412yescomplemented
12C2×#66935—21no—
13C2×C11×C22⋊C8C2211yescharacteristic
14C11×#380C2211yescharacteristic
15C2×C11×#95C2211yescharacteristic
16C2×C11⋊#95—21no—
17C2×C11⋊#95C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19C2×(C2×D11)⋊C8—22no—
20#10622600C412yescomplemented
21#10622571—21no—
22#10622278—22no—
23#10622277—22no—
24#10622277—22no—
25#10622108—22no—
26#10622089—22no—
27C24×D11D411yescharacteristic
28C23×C4×C11—21no—
29C23×C4×C11C2311yescharacteristic
30C22×C22⋊D11—21no—
31C23×Dic11—21no—
32C23×Dic11D411yescharacteristic
33C22×D44—22no—
34C22×D44C2×C411yescharacteristic
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—
43C2×C11×C4⋊C4C2×C412yes—
44C2×C11×C22⋊C4—21no—
45#66983—21no—
46#66983—21no—
47#66983—21no—
48#66983—21no—
49C2×(C2×D11)⋊C4—24no—
50C2×(C2×D11)⋊C4—22no—
51C2×(C2×D11)⋊C4—21no—
52C2×(C2×D11)⋊C4—22no—
53C2×(C2×D11)⋊C4—44no—
54C2×C4⋊Dic11C2×C411yescharacteristic
55C22×C11⋊C8—21no—
56#66948—44no—
57#66935—42no—
58#66935—42no—
59C11×C22⋊C8—21no—
60C11×C22⋊C8—21no—
61C11×#95—21no—
62C11×#95—21no—
63C11×#95D412yescomplemented
64C11⋊#95—24no—
65C11⋊#95—21no—
66C11⋊#95—22no—
67C11⋊#95D412yescomplemented
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70(C2×D11)⋊C8—44no—
71#9158—111nomaximal, Sylow
72C24×C11C2×D411yescharacteristic
73C23×D11—21no—
74C23×D11—21no—
75C23×D11—24no—
76C23×D11—21no—
77C23×D11—21no—
78C23×D11—21no—
79C23×D11—21no—
80C23×D11—21no—
81C23×D11—42no—
82C23×D11C22⋊C412yes—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—42no—
86C22×C4×C11—42no—
87C22×C4×C11—42no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11C22×C411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C22×C4×C11#4111yescharacteristic
96C2×C22⋊D11—41no—
97C2×C22⋊D11—41no—
98C2×C22⋊D11—41no—
99C2×C22⋊D11—41no—
100C2×C22⋊D11—41no—
101C2×C22⋊D11—41no—
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11—22no—
105C22×Dic11—21no—
106C22×Dic11—42no—
107C22×Dic11—42no—
108C22×Dic11—42no—
109C22×Dic11—41no—
110C22×Dic11—41no—
111C22×Dic11C22⋊C412yes—
112C2×D44—21no—
113C2×D44—21no—
114C2×D44—42no—
115C2×D44—44no—
116C2×D44—44no—
117C2×D44—44no—
118C2×C4×D11—24no—
119C2×C4×D11—24no—
120C2×C4×D11—22no—
121C2×C4×D11—22no—
122C2×C4×D11—22no—
123C2×C4×D11—22no—
124C2×C4×D11—42no—
125C2×C4×D11—42no—
126C2×C4×D11—44no—
127C2×C4×D11—44no—
128C2×C4×D11—44no—
129C2×C4×D11—44no—
130C2×C8×C11—42no—
131C2×C8×C11—41no—
132C11×C4⋊C4—42no—
133C11×C22⋊C4—41no—
134C11×C22⋊C4—41no—
135(C2×D11)⋊C4—44no—
136(C2×D11)⋊C4—48no—
137(C2×D11)⋊C4—44no—
138(C2×D11)⋊C4—41no—
139(C2×D11)⋊C4—41no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142C2×C11⋊C8—42no—
143C2×C11⋊C8—41no—
144#2847—111no—
145C2×#381—111no—
146#1779—111no—
147C2×#327—111no—
148C2×#327—111no—
149#1294—111no—
150#1294D1111yescharacteristic, complemented
151C23×C11—22no—
152C23×C11—22no—
153C23×C11C2×C22⋊C411yescharacteristic
154C23×C11#12011yescharacteristic
155C23×C11#12311yescharacteristic
156C23×C11#13511yescharacteristic
157C23×C11#13511yescharacteristic
158C23×C11AGL(1,ℤ/8)11yescharacteristic
159C23×C11AGL(1,ℤ/8)11yescharacteristic
160C22×D11—24no—
161C22×D11—24no—
162C22×D11—22no—
163C22×D11—22no—
164C22×D11—22no—
165C22×D11—22no—
166C22×D11—22no—
167C22×D11—22no—
168C22×D11—44no—
169C22×D11—44no—
170C22×D11—44no—
171C22×D11—44no—
172C22×D11—42no—
173C22×D11—42no—
174C22×D11—41no—
175C22×D11—41no—
176C22×D11—41no—
177C22×D11—41no—
178C22×D11—41no—
179C22×D11—42no—
180C22×D11—41no—
181C22×D11—41no—
182C22×D11—42no—
183C22×D11#9914yes—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—82no—
197C2×C4×C11—82no—
198C2×C4×C11C4×D411yescharacteristic
199C2×C4×C11C4×D411yescharacteristic
200C2×C4×C11#12111yescharacteristic
201C2×C4×C11#12111yescharacteristic
202C22⋊D11—81no—
203C22⋊D11—81no—
204C22⋊D11—81no—
205C22⋊D11—81no—
206C2×Dic11—22no—
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—42no—
217C2×Dic11—82no—
218C2×Dic11—82no—
219D44—81no—
220D44—81no—
221D44—88no—
222C4×D11—44no—
223C4×D11—44no—
224C4×D11—44no—
225C4×D11—44no—
226C8×C11—81no—
227C11⋊C8—81no—
228C24×C4—111no—
229C2×#121—111no—
230C2×#121—112no—
231C2×#120—221no—
232C22×C22⋊C4—221no—
233C2×C22⋊C8—111no—
234C2×C22⋊C8—222no—
235C2×C22⋊C8C2×D1111yescharacteristic
236#386—222no—
237#386—221no—
238#381—222no—
239#381—222no—
240#380—112no—
241#380C2×D1111yescharacteristic
242C2×#95—111no—
243C2×#95—221no—
244C2×#95C2×D1111yescharacteristic
245#327—222no—
246#327—222no—
247C22×C11—21no—
248C22×C11—21no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11—22no—
252C22×C11—22no—
253C22×C11—22no—
254C22×C11—22no—
255C22×C11#38611yescharacteristic
256C22×C11C2×#9912yes—
257C22×C11#41611yescharacteristic
258C22×C11#41811yescharacteristic
259C22×C11#42112yes—
260C22×C11#44911yescharacteristic
261C22×C11#44911yescharacteristic
262C22×C11#48211yescharacteristic
263C22×C11#48211yescharacteristic
264C2×D11—24no—
265C2×D11—24no—
266C2×D11—24no—
267C2×D11—44no—
268C2×D11—44no—
269C2×D11—44no—
270C2×D11—44no—
271C2×D11—42no—
272C2×D11—42no—
273C2×D11—42no—
274C2×D11—42no—
275C2×D11—81no—
276C2×D11—81no—
277C2×D11—81no—
278C2×D11—82no—
279C2×D11—82no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—21no—
284C4×C11—82no—
285C4×C11—82no—
286Dic11—42no—
287Dic11—82no—
288Dic11—81no—
289C25—111no—
290C22×D4—111no—
291C22×D4—222no—
292C22×D4—221no—
293C23×C4—21no—
294C23×C4—111no—
295C23×C4—112no—
296C23×C4—112no—
297C23×C4—221no—
298C23×C4—221no—
299C23×C4—221no—
300C23×C4—221no—
301C23×C4—221no—
302C23×C4—444no—
303C23×C4C22×D1111yescharacteristic
304C22×C8—21no—
305C22×C8—221no—
306#121—221no—
307#121—221no—
308#121—221no—
309#121—221no—
310#121—444no—
311#120—442no—
312#120—442no—
313C2×C4⋊C4—111no—
314C2×C4⋊C4C4×D1112yes—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—222no—
317C2×C22⋊C4—222no—
318C2×C22⋊C4—224no—
319C2×C22⋊C4—221no—
320C2×C22⋊C4—444no—
321C22⋊C8—21no—
322C22⋊C8—21no—
323C22⋊C8—221no—
324C22⋊C8—221no—
325C22⋊C8—444no—
326#95—21no—
327#95—21no—
328#95—112no—
329#95—222no—
330#95—224no—
331#95—221no—
332#95D4412yescomplemented
333C2×C11—21no—
334C2×C11—21no—
335C2×C11—21no—
336C2×C11—21no—
337C2×C11#151012yes—
338C2×C11#151612yes—
339C2×C11#187511yescharacteristic
340C2×C11#189711yescharacteristic
341C2×C11#189811yescharacteristic
342D11—44no—
343D11—161no—
344C24—112no—
345C24—224no—
346C24—221no—
347C24—221no—
348C24—221no—
349C24—221no—
350C24—221no—
351C24—221no—
352C24—221no—
353C24—442no—
354C24D4×D1111yescharacteristic
355C2×D4—221no—
356C2×D4—221no—
357C2×D4—442no—
358C2×D4—444no—
359C2×D4—444no—
360C2×D4—444no—
361C2×D4—441no—
362C2×D4—441no—
363C2×D4—441no—
364C2×D4—441no—
365C2×D4—441no—
366C2×D4—441no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—112no—
375C22×C4—224no—
376C22×C4—224no—
377C22×C4—221no—
378C22×C4—221no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—222no—
382C22×C4—222no—
383C22×C4—221no—
384C22×C4—222no—
385C22×C4—442no—
386C22×C4—442no—
387C22×C4—444no—
388C22×C4—444no—
389C22×C4—444no—
390C22×C4—444no—
391C22×C4—442no—
392C22×C4—442no—
393C22×C4—442no—
394C22×C4—441no—
395C22×C4—441no—
396C22×C4C2×C4×D1111yescharacteristic
397C22×C4C2×D4411yescharacteristic
398C22×C4#433911yescharacteristic
399C22×C4D4×D1111yescharacteristic
400C22×C4D4×D1111yescharacteristic
401C22×C4#434311yescharacteristic
402C2×C8—42no—
403C2×C8—41no—
404C2×C8—442no—
405C2×C8—441no—
406C4⋊C4—42no—
407C4⋊C4—221no—
408C4⋊C4—221no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C22⋊C4—444no—
412C22⋊C4—448no—
413C22⋊C4—444no—
414C22⋊C4—441no—
415C22⋊C4—441no—
416C11#915811yescharacteristic, complemented, Sylow
417C23—22no—
418C23—22no—
419C23—114no—
420C23—224no—
421C23—224no—
422C23—222no—
423C23—222no—
424C23—222no—
425C23—222no—
426C23—222no—
427C23—222no—
428C23—444no—
429C23—444no—
430C23—444no—
431C23—444no—
432C23—442no—
433C23—442no—
434C23—441no—
435C23—441no—
436C23—441no—
437C23—441no—
438C23—441no—
439C23—442no—
440C23—441no—
441C23—441no—
442C23—442no—
443C23C22⋊C4×D1111yescharacteristic
444C23#6693511yescharacteristic
445C23#6694711yescharacteristic
446C23#6696411yescharacteristic
447C23#6696711yescharacteristic
448C23#6696911yescharacteristic
449C23#6697211yescharacteristic
450D4—881no—
451D4—881no—
452D4—888no—
453D4—881no—
454D4—881no—
455D4—881no—
456D4—881no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—82no—
470C2×C4—82no—
471C2×C4—222no—
472C2×C4—222no—
473C2×C4—222no—
474C2×C4—444no—
475C2×C4—444no—
476C2×C4—444no—
477C2×C4—444no—
478C2×C4—442no—
479C2×C4—442no—
480C2×C4—442no—
481C2×C4—442no—
482C2×C4—441no—
483C2×C4—441no—
484C2×C4—441no—
485C2×C4—442no—
486C2×C4—882no—
487C2×C4—882no—
488C2×C4C4×D4411yescharacteristic
489C2×C4#6693711yescharacteristic
490C2×C4#6694611yescharacteristic
491C2×C4#6694811yescharacteristic
492C8—81no—
493C8—881no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—22no—
499C22—22no—
500C22—22no—
501C22—22no—
502C22—224no—
503C22—224no—
504C22—224no—
505C22—444no—
506C22—444no—
507C22—444no—
508C22—444no—
509C22—442no—
510C22—442no—
511C22—442no—
512C22—442no—
513C22—881no—
514C22—881no—
515C22—882no—
516C22—881no—
517C22—882no—
518C22#1062227811yescharacteristic
519C22D11×#9912yes—
520C22#1062238311yescharacteristic
521C22#1062239411yescharacteristic
522C22#1062241711yescharacteristic
523C22#1062242411yescharacteristic
524C22#1062243412yes—
525C22#1062247911yescharacteristic
526C22#1062249811yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—82no—
532C4—82no—
533C4—442no—
534C4—882no—
535C4—881no—
536C2—21no—
537C2—21no—
538C2—21no—
539C2—21no—
540C2—444no—
541C2—1761no—
542C2#1306714312yes—
543C2#1306717112yes—
544C2#1306893711yescharacteristic
545C2#1306906311yescharacteristic
546C2#1306906811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1294C2
socleC23×C11C2×C22⋊C4
prime radical#13076899C2
cosocleC23×C4×C11C23
hypercenter#1294D11
hypocenterC11#9158
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
2. C2×#10622277C2semidirect
3. #13068525C2semidirect
4. C2×#10622108C2semidirect
5. C2×#10622089C2semidirect
6. #13066494C2semidirect
7. C11×#1294C2semidirect
11. C2×#66948C4semidirect
20. #10622600C4semidirect
63. C11×#95D4semidirect
67. C11⋊#95D4semidirect
150. #1294D11semidirect
332. #95D44semidirect
416. C11#9158semidirect

Maximal subgroups

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

subgroupindex
#130768992
C2×#106222772
#130685252
C2×#106221082
C2×#106220892
#130664942
C11×#12942
#915811