Finite Group Databasebeta

← #14723739

Subgroups — #14723739

Order 2816.

720 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078663C211yesmaximal, characteristic
2#13077585C211yesmaximal, characteristic, complemented
3C2×D4×C11⋊C8C211yesmaximal, characteristic, complemented
4#13067477C212yesmaximal, complemented
5#13067470C212yesmaximal, complemented
6#13067419C212yesmaximal, complemented
7#13067408C212yesmaximal, complemented
8#13067402C211yesmaximal, characteristic, complemented
9#13067030C211yesmaximal, characteristic, complemented
10M16×C11⋊C8C211yesmaximal, characteristic, complemented
11C11×#1490C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C23×C11⋊C8—21no—
14#10623010C2211yescharacteristic
15C11×#432C2211yescharacteristic
16C4×C11×M16C2211yescharacteristic
17#10622831C411yescharacteristic
18#10622830C411yescharacteristic
19C2×C22⋊(C11⋊C8)—21no—
20C4×#4324C2212yes—
21#10622629C412yes—
22C4×#4323C2212yes—
23D4×C11⋊C8—21no—
24D4×C11⋊C8—21no—
25D4×C11⋊C8C2212yes—
26D4×C11⋊C8C2212yes—
27#10622622C412yes—
28#10622583C411yescharacteristic
29#10622581C411yescharacteristic
30#10622538C2211yescharacteristic
31C2×C4⋊(C11⋊C8)C2211yescharacteristic
32C2×C4×C11⋊C8C2211yescharacteristic
33#10622451C2211yescharacteristic, complemented
34#10622447C2211yescharacteristic, complemented
35#10622444C2211yescharacteristic, complemented
36#10622443C2211yescharacteristic, complemented
37#10622343—21no—
38(C22⋊D11)⋊C8—21no—
39#10622322—21no—
40#10622321—21no—
41C11×D4⋊C8C2212yes—
42C11×D4⋊C8C2212yes—
43#10622118C2212yescomplemented
44#10622117C2212yescomplemented
45#10622097C2212yescomplemented
46#10622094C2212yescomplemented
47#10622093C2212yescomplemented
48C8×C11⋊C8C2212yescomplemented
49C22×D4×C11C2×C411yescharacteristic
50C23×C4×C11—21no—
51C2×C11×M16—21no—
52C4×D4×C11—21no—
53C4×D4×C11—21no—
54C4×D4×C11C2×C412yes—
55C4×D4×C11C2312yes—
56C2×C11×C4⋊C4C2×C411yescharacteristic
57C2×C11×C22⋊C4—21no—
58C2×C42×C11C2311yescharacteristic
59C2×#4324C2×C412yes—
60C2×#4323C2×C412yes—
61#66983C2×C411yescharacteristic
62#66982—21no—
63C4×C22⋊D11—21no—
64#66977C2×C411yescharacteristic
65C22×C11⋊C8—21no—
66C22×C11⋊C8—22no—
67C22×C11⋊C8—22no—
68C22×C11⋊C8—44no—
69C22×C11⋊C8D411yescharacteristic
70C22×C11⋊C8D411yescharacteristic
71C2×#4313—21no—
72C2×C8×D11—21no—
73#66929—21no—
74#66928C2×C411yescharacteristic
75C4×D44C2311yescharacteristic
76#66925—21no—
77#66923C2×C411yescharacteristic
78C4×Dic22C2311yescharacteristic
79C11×C4⋊C8C2311yescharacteristic
80C11×C4⋊C8C2311yescharacteristic
81C11×C22⋊C8—21no—
82C11×#97—21no—
83C11×#97—21no—
84C4×C8×C11C2312yes—
85#66896C2×C412yes—
86#66896C2×C412yes—
87C22⋊(C11⋊C8)—22no—
88C22⋊(C11⋊C8)—22no—
89C22⋊(C11⋊C8)C2×C411yescharacteristic
90C22⋊(C11⋊C8)C2×C411yescharacteristic
91(C2×D11)⋊C8—21no—
92(C2×D11)⋊C8—21no—
93#66879—21no—
94Dic11⋊C8—21no—
95Dic11⋊C8—21no—
96C8×Dic11—21no—
97#66874C2×C412yes—
98#66873C2×C412yes—
99#66872C2×C412yes—
100#66871C2×C412yes—
101C4⋊(C11⋊C8)—21no—
102C4⋊(C11⋊C8)C2×C412yes—
103C4⋊(C11⋊C8)C2312yes—
104C4×C11⋊C8D411yescharacteristic
105C4×C11⋊C8D411yescharacteristic
106C4×C11⋊C8C2312yes—
107C4×C11⋊C8C2311yescharacteristic
108C4×C11⋊C8C2311yescharacteristic
109#17910—111nomaximal, Sylow
110C24×C11—21no—
111C2×D4×C11—24no—
112C2×D4×C11—21no—
113C2×D4×C11C22×C412yes—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11C22×C411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11#4111yescharacteristic
122C2×C22⋊D11—21no—
123C2×D44C22×C411yescharacteristic
124C2×C4×D11—21no—
125C2×Dic22C22×C411yescharacteristic
126C11×M16—24no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11—22no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4C22×C412yes—
132C11×C22⋊C4—22no—
133C11×C22⋊C4—22no—
134C42×C11C22×C411yescharacteristic
135C42×C11C2×D411yescharacteristic
136C42×C11#4111yescharacteristic
137C42×C11C2411yescharacteristic
138C22⋊Dic11—21no—
139#4324—24no—
140#4323—24no—
141(C2×D11)⋊C4—21no—
142(C2×D11)⋊C4—21no—
143(C2×D11)⋊C4—21no—
144(C2×D11)⋊C4—21no—
145C4⋊Dic11C22×C411yescharacteristic
146C4⋊Dic11C22×C411yescharacteristic
147Dic11⋊C4—21no—
148Dic11⋊C4—21no—
149Dic11⋊C4—21no—
150Dic11⋊C4—21no—
151C4×Dic11—21no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—41no—
155C2×C11⋊C8—42no—
156C2×C11⋊C8—44no—
157C2×C11⋊C8—44no—
158C2×C11⋊C8C22×C412yes—
159C2×C11⋊C8C22×C412yes—
160C2×C11⋊C8C2×D411yescharacteristic
161C2×C11⋊C8C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163C2×C11⋊C8C2×D411yescharacteristic
164#4313—42no—
165C8×D11—42no—
166#3105—111no—
167#2966—111no—
168C2×C8×D4—111no—
169#1586—112no—
170#1585—112no—
171C8×SD16—112no—
172C8×D8—112no—
173#1573—111no—
174#1490D1111yescharacteristic, complemented
175#1483—111no—
176C8×M16—111no—
177C23×C11—24no—
178C23×C11—22no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11C4×D411yescharacteristic
182C22×D11—21no—
183D4×C11—24no—
184D4×C11—22no—
185D4×C11#13114yes—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—22no—
191C2×C4×C11—44no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11C4×D411yescharacteristic
196C2×C4×C11C4×D411yescharacteristic
197C2×C4×C11C4×D411yescharacteristic
198C2×C4×C11C23×C411yescharacteristic
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C22⋊D11—42no—
202C2×Dic11—21no—
203C2×Dic11—21no—
204C2×Dic11—21no—
205D44—22no—
206C4×D11—41no—
207C4×D11—41no—
208Dic22—22no—
209C8×C11—24no—
210C8×C11—41no—
211C8×C11—41no—
212C11⋊C8—22no—
213C11⋊C8—22no—
214C11⋊C8—21no—
215C11⋊C8—21no—
216C11⋊C8—21no—
217C11⋊C8—42no—
218C11⋊C8AGL(1,ℤ/8)12yes—
219C23×C8—221no—
220#529—111no—
221C2×C4×D4C2×D1111yescharacteristic
222#484—111no—
223#481—111no—
224#478—112no—
225#463—112no—
226#450—111no—
227#447—111no—
228#446—111no—
229C8×Q8—111no—
230C4×SD16—112no—
231C4×D8—112no—
232#436—111no—
233#435—221no—
234C8×D4—112no—
235C8×D4—112no—
236C8×D4—111no—
237C8×D4—221no—
238C8×D4—221no—
239C8×D4—221no—
240#433—221no—
241#432C2×D1111yescharacteristic
242#431—111no—
243C2×C4⋊C8—111no—
244C2×C22⋊C8—221no—
245#405—221no—
246C4×M16C2×D1111yescharacteristic
247C2×C4×C8—111no—
248#335—112no—
249#334—112no—
250Q8⋊C8—112no—
251D4⋊C8—112no—
252D4⋊C8C2×D1112yes—
253D4⋊C8C2×D1112yes—
254#322—112no—
255C82—112no—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11—24no—
259C22×C11—48no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11#44312yes—
263C22×C11C2×C4×D411yescharacteristic
264C2×D11—41no—
265C2×D11—41no—
266C2×D11—41no—
267C4×C11—21no—
268C4×C11—21no—
269C4×C11—21no—
270C4×C11—21no—
271C4×C11—42no—
272C4×C11C2×#13112yes—
273C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
274C4×C11#57511yescharacteristic
275Dic11—41no—
276Dic11—41no—
277Dic11—41no—
278C22×D4C4×D1111yescharacteristic
279C23×C4—21no—
280C2×SD16—112no—
281C2×D8—112no—
282C2×M16—21no—
283C2×M16—221no—
284C22×C8—111no—
285C22×C8—111no—
286C22×C8—221no—
287C22×C8—222no—
288C22×C8—222no—
289C22×C8—221no—
290C22×C8—444no—
291#126—221no—
292#125—111no—
293#124—111no—
294#123—221no—
295C22⋊Q8—111no—
296#121—111no—
297C4×Q8—111no—
298C4×D4—21no—
299C4×D4—21no—
300C4×D4—111no—
301C4×D4—221no—
302C4×D4C4×D1112yes—
303C4×D4C22×D1112yes—
304#117—221no—
305C2×C4⋊C4C4×D1111yescharacteristic
306C2×C22⋊C4—21no—
307C2×C42C22×D1111yescharacteristic
308#107—112no—
309#106—112no—
310C4⋊C8—112no—
311C4⋊C8—112no—
312C4⋊C8—221no—
313C4⋊C8—221no—
314C4⋊C8—221no—
315C4⋊C8C22×D1111yescharacteristic
316C4⋊C8C22×D1111yescharacteristic
317#103—112no—
318#102—112no—
319#102—112no—
320#102—112no—
321C22⋊C8—21no—
322C22⋊C8—111no—
323C22⋊C8—111no—
324C22⋊C8—221no—
325C22⋊C8—221no—
326C22⋊C8—222no—
327C22⋊C8—222no—
328#97—21no—
329#97—21no—
330#97—221no—
331C4×C8—111no—
332C4×C8—111no—
333C4×C8—111no—
334C4×C8—112no—
335C4×C8—111no—
336C4×C8—221no—
337C4×C8C22×D1112yes—
338C2×C11—22no—
339C2×C11—44no—
340C2×C11#292911yescharacteristic
341C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
342C2×C11C2×#44311yescharacteristic
343D11—81no—
344C24—21no—
345C2×Q8—111no—
346C2×D4—24no—
347C2×D4—21no—
348C2×D4—111no—
349C2×D4—221no—
350C2×D4C2×C4×D1112yes—
351C22×C4—21no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—221no—
357C22×C4C2×C4×D1111yescharacteristic
358C22×C4D4×D1111yescharacteristic
359C22×C4#434111yescharacteristic
360SD16—224no—
361D8—224no—
362M16—24no—
363M16—442no—
364C2×C8—22no—
365C2×C8—21no—
366C2×C8—21no—
367C2×C8—111no—
368C2×C8—112no—
369C2×C8—112no—
370C2×C8—111no—
371C2×C8—111no—
372C2×C8—111no—
373C2×C8—222no—
374C2×C8—222no—
375C2×C8—442no—
376C2×C8—444no—
377C2×C8—441no—
378C2×C8—444no—
379C2×C8—442no—
380C4⋊C4—21no—
381C4⋊C4—111no—
382C4⋊C4—111no—
383C4⋊C4—221no—
384C4⋊C4—221no—
385C4⋊C4—221no—
386C4⋊C4—221no—
387C4⋊C4C2×C4×D1112yes—
388C22⋊C4—22no—
389C22⋊C4—22no—
390C22⋊C4—221no—
391C22⋊C4—221no—
392C22⋊C4—221no—
393C22⋊C4—221no—
394C22⋊C4—221no—
395C42—221no—
396C42C2×C4×D1111yescharacteristic
397C42D4×D1111yescharacteristic
398C42#434111yescharacteristic
399C42C23×D1111yescharacteristic
400C11#1791011yescharacteristic, complemented, Sylow
401C23—24no—
402C23—22no—
403C23—42no—
404C23—42no—
405C23—221no—
406C23(C22⋊D11)⋊C411yescharacteristic
407Q8—222no—
408D4—24no—
409D4—22no—
410D4—222no—
411D4—442no—
412D4#6696014yes—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—22no—
418C2×C4—44no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—221no—
423C2×C4—221no—
424C2×C4—221no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4(C22⋊D11)⋊C411yescharacteristic
428C2×C4(C22⋊D11)⋊C411yescharacteristic
429C2×C4(C22⋊D11)⋊C411yescharacteristic
430C2×C4C22×C4×D1111yescharacteristic
431C2×C4C2×D4×D1111yescharacteristic
432C2×C4C2×#434111yescharacteristic
433C8—24no—
434C8—41no—
435C8—41no—
436C8—112no—
437C8—222no—
438C8—222no—
439C8—221no—
440C8—221no—
441C8—221no—
442C8—442no—
443C22—21no—
444C22—21no—
445C22—24no—
446C22—48no—
447C22—42no—
448C22—42no—
449C22—441no—
450C22—441no—
451C22—441no—
452C22#1062243712yes—
453C22C2×(C22⋊D11)⋊C411yescharacteristic
454C4—21no—
455C4—21no—
456C4—21no—
457C4—21no—
458C4—42no—
459C4—441no—
460C4—441no—
461C4—441no—
462C4C2×#6696012yes—
463C4D11×AGL(1,ℤ/8)11yescharacteristic
464C4#1062330411yescharacteristic
465C2—22no—
466C2—44no—
467C2—881no—
468C2#1307730611yescharacteristic
469C2#1307742011yescharacteristic
470C2C2×#1062243711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1490C2
socleC22×C11C2×C4×D4
prime radical#10622830C4
cosocleC42×C11C24
hypercenter#1490D11
hypocenterC11#17910
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1490

Complements

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

NH ≅ G/Ntype
2. #13077585C2semidirect
3. C2×D4×C11⋊C8C2semidirect
4. #13067477C2semidirect
5. #13067470C2semidirect
6. #13067419C2semidirect
7. #13067408C2semidirect
8. #13067402C2semidirect
9. #13067030C2semidirect
10. M16×C11⋊C8C2semidirect
11. C11×#1490C2semidirect
33. #10622451C22semidirect
34. #10622447C22semidirect
35. #10622444C22semidirect
36. #10622443C22semidirect
43. #10622118C22semidirect
44. #10622117C22semidirect
45. #10622097C22semidirect
46. #10622094C22semidirect
47. #10622093C22semidirect
48. C8×C11⋊C8C22semidirect
174. #1490D11semidirect
400. C11#17910semidirect

Maximal subgroups

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

subgroupindex
#130786632
#130775852
C2×D4×C11⋊C82
#130674772
#130674702
#130674192
#130674082
#130674022
#130670302
M16×C11⋊C82
C11×#14902
#1791011