Finite Group Databasebeta

← #14649485

Subgroups — #14649485

Order 2816.

1270 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076900C211yesmaximal, characteristic
2C2×D11×#95C211yesmaximal, characteristic
3#13068525C211yesmaximal, characteristic
4C2×#10622176C211yesmaximal, characteristic, complemented
5#13066496C211yesmaximal, characteristic, complemented
6#13066495C211yesmaximal, characteristic, complemented
7C2×C11×#328C211yesmaximal, characteristic, complemented
8C23×C4×D11—21no—
9C23×C4×D11C2211yescharacteristic
10C2×C11×C22⋊Q8C2211yescharacteristic
11C2×#66999C412yescomplemented
12C2×C11×C22⋊C8C2211yescharacteristic
13C2×C11×#95C2211yescharacteristic
14#10622825C2211yescharacteristic
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2211yescharacteristic
17C2×C22⋊(C11⋊C8)C2211yescharacteristic
18C2×(C2×D11)⋊C8—22no—
19#10622602—22no—
20#10622600C412yescomplemented
21#10622568—21no—
22#10622559—21no—
23D11×#95—22no—
24D11×#95—22no—
25C11×#328—22no—
26#10622176—22no—
27C24×D11D411yescharacteristic
28C22×Q8×C11C2×C411yescharacteristic, complemented
29C23×C4×C11—21no—
30C23×C4×C11C2311yescharacteristic
31C23×Dic11—21no—
32C23×Dic11D411yescharacteristic
33C22×C4×D11—24no—
34C22×C4×D11—28no—
35C22×C4×D11—21no—
36C22×C4×D11—21no—
37C22×C4×D11—21no—
38C22×C4×D11—21no—
39C22×C4×D11—44no—
40C22×C4×D11—44no—
41C22×C4×D11—42no—
42C22×C4×D11—42no—
43C22×C4×D11C2×C412yes—
44C22×C4×D11D412yes—
45C22×C8×C11—21no—
46C11×C22⋊Q8—21no—
47C11×C22⋊Q8—21no—
48C11×C22⋊Q8—21no—
49C11×C22⋊Q8—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
52C2×C11×C22⋊C4—21no—
53C2×C22⋊Dic11—21no—
54#66999—44no—
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—22no—
57C2×C4⋊Dic11C2×C412yescomplemented
58C2×Dic11⋊C4—22no—
59C22×C11⋊C8—21no—
60C11×C22⋊C8—21no—
61C11×C22⋊C8—21no—
62C11×#95—21no—
63C11×#95D412yes—
64C11⋊#95—24no—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—22no—
68C11⋊#95D412yes—
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)—21no—
71(C2×D11)⋊C8—44no—
72#9143—111nomaximal, Sylow
73C24×C11C2×D411yescharacteristic
74C23×D11—21no—
75C23×D11—21no—
76C23×D11—21no—
77C23×D11—21no—
78C23×D11—24no—
79C23×D11—24no—
80C23×D11C22⋊C412yes—
81C23×D11SD1612yes—
82C23×D11Q1612yes—
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—42no—
86C22×C4×C11—24no—
87C22×C4×C11—22no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—42no—
91C22×C4×C11—42no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11C22×C411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11#4111yescharacteristic
99C22×C4×C11#4111yescharacteristic
100C22×Dic11—24no—
101C22×Dic11—22no—
102C22×Dic11—21no—
103C22×Dic11—22no—
104C22×Dic11—21no—
105C22×Dic11—42no—
106C22×Dic11—42no—
107C22×Dic11—41no—
108C22×Dic11—41no—
109C22×Dic11C22⋊C412yes—
110C2×C4×D11—216no—
111C2×C4×D11—24no—
112C2×C4×D11—24no—
113C2×C4×D11—22no—
114C2×C4×D11—22no—
115C2×C4×D11—22no—
116C2×C4×D11—22no—
117C2×C4×D11—42no—
118C2×C4×D11—42no—
119C2×C4×D11—44no—
120C2×C4×D11—44no—
121C2×C4×D11—44no—
122C2×C4×D11—44no—
123C2×C4×D11—48no—
124C2×C4×D11—416no—
125C2×C4×D11—416no—
126C2×C4×D11—48no—
127C2×C8×C11—42no—
128C2×C8×C11—41no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—41no—
132C11×C4⋊C4—41no—
133C11×C22⋊C4—41no—
134C11×C22⋊C4—41no—
135C22⋊Dic11—41no—
136C22⋊Dic11—41no—
137(C2×D11)⋊C4—44no—
138(C2×D11)⋊C4—44no—
139C4⋊Dic11—42no—
140Dic11⋊C4—44no—
141C2×C11⋊C8—42no—
142C2×C11⋊C8—41no—
143#2848—111no—
144C22×#95—111no—
145#1779—111no—
146C2×#328—111no—
147C2×#328D1111yescharacteristic, complemented
148#1294—111no—
149#1294—111no—
150C23×C11—22no—
151C23×C11—22no—
152C23×C11C2×C22⋊C411yescharacteristic
153C23×C11#12011yescharacteristic
154C23×C11#12311yescharacteristic
155C23×C11C2×SD1611yescharacteristic
156C23×C11C2×Q1611yescharacteristic
157C23×C11AGL(1,ℤ/8)11yescharacteristic
158C23×C11#13711yescharacteristic
159C22×D11—24no—
160C22×D11—24no—
161C22×D11—24no—
162C22×D11—28no—
163C22×D11—24no—
164C22×D11—28no—
165C22×D11—22no—
166C22×D11—22no—
167C22×D11—22no—
168C22×D11—22no—
169C22×D11—22no—
170C22×D11—22no—
171C22×D11—22no—
172C22×D11—22no—
173C22×D11—28no—
174C22×D11—28no—
175C22×D11#9914yes—
176C22×D11#10314yes—
177C22×D11#10414yes—
178Q8×C11—81no—
179Q8×C11—81no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—24no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—42no—
188C2×C4×C11—44no—
189C2×C4×C11—44no—
190C2×C4×C11—42no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11C4×D411yescharacteristic
196C2×C4×C11C4×D411yescharacteristic
197C2×C4×C11#12111yescharacteristic
198C2×C4×C11#12111yescharacteristic
199C2×Dic11—24no—
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—42no—
204C2×Dic11—44no—
205C2×Dic11—44no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C4×D11—44no—
213C4×D11—44no—
214C4×D11—44no—
215C4×D11—44no—
216C4×D11—432no—
217C8×C11—81no—
218C11⋊C8—81no—
219C24×C4—111no—
220C24×C4—221no—
221C2×C22⋊Q8—112no—
222C2×C22⋊Q8C2×D1111yescharacteristic
223C2×C22⋊C8—111no—
224C2×C22⋊C8—222no—
225C2×C22⋊C8C2×D1111yescharacteristic
226#385—221no—
227#385—222no—
228#380—111no—
229#380—112no—
230#379—221no—
231C2×#95—111no—
232C2×#95—222no—
233C2×#95—221no—
234C2×#95—222no—
235C2×#95C2×D1111yescharacteristic
236#328—22no—
237#328—222no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—22no—
243C22×C11—22no—
244C22×C11—22no—
245C22×C11—22no—
246C22×C11#38611yescharacteristic
247C22×C11C2×#9912yes—
248C22×C11C2×#10311yescharacteristic
249C22×C11#41711yescharacteristic
250C22×C11C2×#10412yes—
251C22×C11#45011yescharacteristic
252C22×C11#45111yescharacteristic
253C22×C11#48311yescharacteristic
254C22×C11#48411yescharacteristic
255C2×D11—28no—
256C2×D11—28no—
257C2×D11—28no—
258C2×D11—28no—
259C2×D11—24no—
260C2×D11—24no—
261C2×D11—24no—
262C2×D11—24no—
263C2×D11—24no—
264C2×D11—24no—
265C2×D11#32818yescomplemented
266C4×C11—21no—
267C4×C11—21no—
268C4×C11—21no—
269C4×C11—21no—
270C4×C11—44no—
271C4×C11—81no—
272C4×C11—81no—
273Dic11—44no—
274Dic11—42no—
275Dic11—82no—
276C25—111no—
277C22×Q8C4×D1111yescharacteristic, complemented
278C23×C4—21no—
279C23×C4—111no—
280C23×C4—112no—
281C23×C4—112no—
282C23×C4—224no—
283C23×C4—228no—
284C23×C4—221no—
285C23×C4—221no—
286C23×C4—221no—
287C23×C4—221no—
288C23×C4—221no—
289C23×C4—444no—
290C23×C4—442no—
291C23×C4—444no—
292C23×C4—442no—
293C23×C4C22×D1111yescharacteristic
294C22×C8—21no—
295C22×C8—221no—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C22⋊Q8—444no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—112no—
303C2×C4⋊C4—222no—
304C2×C4⋊C4C4×D1111yescharacteristic, complemented
305C2×C22⋊C4—21no—
306C2×C22⋊C4—222no—
307C2×C22⋊C4—222no—
308C2×C22⋊C4—221no—
309C22⋊C8—21no—
310C22⋊C8—21no—
311C22⋊C8—221no—
312C22⋊C8—221no—
313C22⋊C8—444no—
314#95—21no—
315#95—112no—
316#95—222no—
317#95—224no—
318#95—221no—
319#95—221no—
320#95C22⋊D1112yes—
321C2×C11—21no—
322C2×C11—21no—
323C2×C11—21no—
324C2×C11—21no—
325C2×C11C2×#32812yes—
326C2×C11#150412yes—
327C2×C11#187211yescharacteristic
328C2×C11#189611yescharacteristic
329C2×C11#189811yescharacteristic
330D11—28no—
331C24—112no—
332C24—112no—
333C24—112no—
334C24—224no—
335C24—224no—
336C24—221no—
337C24—221no—
338C24—221no—
339C24—221no—
340C24D4×D1111yescharacteristic
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8—42no—
344C22×C4—24no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—112no—
353C22×C4—224no—
354C22×C4—224no—
355C22×C4—2216no—
356C22×C4—224no—
357C22×C4—221no—
358C22×C4—222no—
359C22×C4—221no—
360C22×C4—222no—
361C22×C4—222no—
362C22×C4—222no—
363C22×C4—222no—
364C22×C4—222no—
365C22×C4—442no—
366C22×C4—442no—
367C22×C4—444no—
368C22×C4—444no—
369C22×C4—444no—
370C22×C4—444no—
371C22×C4—4416no—
372C22×C4—448no—
373C22×C4—4416no—
374C22×C4—448no—
375C22×C4—442no—
376C22×C4—442no—
377C22×C4—441no—
378C22×C4—441no—
379C22×C4C2×C4×D1111yescharacteristic
380C22×C4#433911yescharacteristic
381C22×C4D4×D1111yescharacteristic
382C22×C4D4×D1111yescharacteristic
383C22×C4#434111yescharacteristic
384C22×C4C2×C22⋊D1111yescharacteristic
385C2×C8—42no—
386C2×C8—41no—
387C2×C8—442no—
388C2×C8—441no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—41no—
392C4⋊C4—41no—
393C4⋊C4—442no—
394C4⋊C4—444no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—444no—
398C22⋊C4—444no—
399C22⋊C4—441no—
400C22⋊C4—441no—
401C11#914311yescharacteristic, complemented, Sylow
402C23—22no—
403C23—22no—
404C23—114no—
405C23—114no—
406C23—114no—
407C23—228no—
408C23—228no—
409C23—224no—
410C23—224no—
411C23—224no—
412C23—228no—
413C23—224no—
414C23—228no—
415C23—222no—
416C23—222no—
417C23—222no—
418C23—222no—
419C23—222no—
420C23—222no—
421C23—222no—
422C23—222no—
423C23C22⋊C4×D1111yescharacteristic
424C23#6693611yescharacteristic
425C23SD16×D1111yescharacteristic
426C23#6696711yescharacteristic
427C23Q16×D1111yescharacteristic
428C23#6697111yescharacteristic
429C23#6699011yescharacteristic
430Q8—81no—
431Q8—81no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—24no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—44no—
441C2×C4—44no—
442C2×C4—42no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—224no—
448C2×C4—222no—
449C2×C4—222no—
450C2×C4—222no—
451C2×C4—444no—
452C2×C4—444no—
453C2×C4—444no—
454C2×C4—444no—
455C2×C4—4432no—
456C2×C4—442no—
457C2×C4—444no—
458C2×C4—444no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4—442no—
463C2×C4—442no—
464C2×C4—442no—
465C2×C4(C22⋊D11)⋊C411yescharacteristic
466C2×C4#6693711yescharacteristic
467C2×C4C4×C22⋊D1111yescharacteristic
468C2×C4#6699111yescharacteristic
469C8—81no—
470C8—881no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—22no—
476C22—22no—
477C22—22no—
478C22—22no—
479C22—118no—
480C22—228no—
481C22—228no—
482C22—228no—
483C22—228no—
484C22—224no—
485C22—224no—
486C22—224no—
487C22—224no—
488C22—224no—
489C22—224no—
490C22D11×#9912yes—
491C22D11×#10311yescharacteristic
492C22#1062241611yescharacteristic
493C22#1062241811yescharacteristic
494C22#1062242211yescharacteristic
495C22D11×#10412yes—
496C22#1062256911yescharacteristic
497C22#1062278211yescharacteristic
498C22#1062279911yescharacteristic
499C4—21no—
500C4—21no—
501C4—21no—
502C4—21no—
503C4—44no—
504C4—81no—
505C4—81no—
506C4—444no—
507C4—442no—
508C4—882no—
509C2—21no—
510C2—21no—
511C2—21no—
512C2—21no—
513C2—228no—
514C2D11×#32812yes—
515C2#1306711912yes—
516C2#1306892011yescharacteristic
517C2#1306905611yescharacteristic
518C2#1306906611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#328C2
socleC23×C11C2×C22⋊C4
prime radicalC24×D11D4
cosocleC23×C4×C11C23
hypercenterC2×#328D11
hypocenterC11#9143
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
4. C2×#10622176C2semidirect
5. #13066496C2semidirect
6. #13066495C2semidirect
7. C2×C11×#328C2semidirect
11. C2×#66999C4semidirect
20. #10622600C4semidirect
28. C22×Q8×C11C2×C4semidirect
51. C2×C11×C4⋊C4C2×C4semidirect
57. C2×C4⋊Dic11C2×C4semidirect
147. C2×#328D11semidirect
265. C2×D11#328semidirect
277. C22×Q8C4×D11semidirect
304. C2×C4⋊C4C4×D11semidirect
401. C11#9143semidirect

Maximal subgroups

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

subgroupindex
#130769002
C2×D11×#952
#130685252
C2×#106221762
#130664962
#130664952
C2×C11×#3282
#914311