Finite Group Databasebeta

← #14724111

Subgroups — #14724111

Order 2816.

680 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#13077591C211yesmaximal, characteristic, complemented
3#13067504C212yesmaximal, complemented
4#13067499C212yesmaximal, complemented
5#13067492C212yesmaximal, complemented
6#13067478C212yesmaximal, complemented
7#13067399C211yesmaximal, characteristic, complemented
8#13067059C211yesmaximal, characteristic, complemented
9#13067027C211yesmaximal, characteristic, complemented
10C8×#4318C211yesmaximal, characteristic, complemented
11C2×C11×#436C211yesmaximal, characteristic, complemented
12C22×C11×M16—21no—
13C2×C4×D4×C11C2211yescharacteristic
14#10623010C2211yescharacteristic
15C11×#436—21no—
16C11×#436—21no—
17C11×#436C2212yes—
18C11×#436C2212yes—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C22⋊C8—21no—
21C2×C4×C8×C11C2211yescharacteristic
22#10622831C411yescharacteristic
23#10622830C411yescharacteristic
24#10622724—21no—
25C8×C22⋊D11—21no—
26C4×#4324C2212yes—
27#10622629C412yes—
28C4×#4323C2212yes—
29#10622622C412yes—
30#10622583C411yescharacteristic
31#10622581C411yescharacteristic
32#10622539C2211yescharacteristic
33#10622538C2211yescharacteristic
34C4×#4318C2211yescharacteristic
35#10622303—21no—
36#10622302—21no—
37#10622301C2211yescharacteristic, complemented
38C8×D44C2211yescharacteristic, complemented
39#10622292C2211yescharacteristic, complemented
40C8×Dic22C2211yescharacteristic, complemented
41D4⋊(C11⋊C8)C2212yes—
42D4⋊(C11⋊C8)C2212yes—
43#10622122C2212yescomplemented
44#10622121C2212yescomplemented
45#10622118C2212yescomplemented
46#10622117C2212yescomplemented
47#10622092C2212yescomplemented
48C8×C11⋊C8C2212yescomplemented
49C22×D4×C11C2×C411yescharacteristic
50C23×C4×C11—21no—
51C2×C11×M16—22no—
52C2×C11×M16—22no—
53C2×C11×M16—44no—
54C22×C8×C11—21no—
55C22×C8×C11D411yescharacteristic
56C22×C8×C11D411yescharacteristic
57C4×D4×C11—21no—
58C4×D4×C11—21no—
59C4×D4×C11C2×C412yes—
60C4×D4×C11C2312yes—
61C2×C11×C4⋊C4C2×C411yescharacteristic
62C2×C11×C22⋊C4—21no—
63C2×C42×C11C2311yescharacteristic
64C2×#4324C2×C412yes—
65C2×#4323C2×C412yes—
66#66983C2×C411yescharacteristic
67#66982—21no—
68C4×C22⋊D11—21no—
69#66977C2×C411yescharacteristic
70C2×#4318—21no—
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⋊C8—21no—
80C11×C4⋊C8C2312yes—
81C11×C22⋊C8—22no—
82C11×C22⋊C8—22no—
83C4×C8×C11D411yescharacteristic
84C4×C8×C11D411yescharacteristic
85C4×C8×C11C2311yescharacteristic
86C4×C8×C11C2311yescharacteristic
87#66896C2×C412yes—
88#66896C2×C412yes—
89C22⋊(C11⋊C8)—21no—
90C22⋊(C11⋊C8)C2×C411yescharacteristic
91C22⋊(C11⋊C8)C2×C411yescharacteristic
92(C2×D11)⋊C8—21no—
93(C2×D11)⋊C8—21no—
94#66879—21no—
95Dic11⋊C8—21no—
96Dic11⋊C8—21no—
97C8×Dic11—21no—
98#66874C2×C412yes—
99#66873C2×C412yes—
100#66872C2×C412yes—
101#66871C2×C412yes—
102C4⋊(C11⋊C8)C2×C412yes—
103C4⋊(C11⋊C8)C2311yescharacteristic
104C4⋊(C11⋊C8)C2311yescharacteristic
105#66867—21no—
106#66867—21no—
107C4×C11⋊C8C2312yes—
108C4×C11⋊C8C2312yes—
109#17942—111nomaximal, Sylow
110C24×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—42no—
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—44no—
127C11×M16—44no—
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C2×C8×C11—41no—
131C2×C8×C11—42no—
132C2×C8×C11C2×D411yescharacteristic
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11C2×D411yescharacteristic
135C2×C8×C11C2×D411yescharacteristic
136C11×C4⋊C4—21no—
137C11×C4⋊C4C22×C412yes—
138C11×C22⋊C4—22no—
139C11×C22⋊C4—22no—
140C42×C11C22×C411yescharacteristic
141C42×C11C2×D411yescharacteristic
142C42×C11#4111yescharacteristic
143C42×C11C2411yescharacteristic
144C22⋊Dic11—21no—
145#4324—42no—
146#4323—42no—
147(C2×D11)⋊C4—21no—
148(C2×D11)⋊C4—21no—
149(C2×D11)⋊C4—21no—
150(C2×D11)⋊C4—21no—
151C4⋊Dic11C22×C411yescharacteristic
152C4⋊Dic11C22×C411yescharacteristic
153Dic11⋊C4—21no—
154Dic11⋊C4—21no—
155Dic11⋊C4—21no—
156Dic11⋊C4—21no—
157C4×Dic11—21no—
158#4318—24no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8C22×C412yes—
163C2×C11⋊C8C22×C412yes—
164#4313—42no—
165C8×D11—42no—
166#3105—111no—
167#2966—111no—
168C2×#436D1111yescharacteristic, complemented
169#1590—112no—
170#1589—112no—
171#1588—112no—
172#1586—112no—
173#1573—111no—
174#1490—111no—
175#1483—111no—
176C8×M16—111no—
177C23×C11—22no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11C4×D411yescharacteristic
182C22×D11—21no—
183D4×C11—22no—
184D4×C11—22no—
185D4×C11—42no—
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—21no—
210C8×C11—21no—
211C8×C11—21no—
212C8×C11—42no—
213C8×C11AGL(1,ℤ/8)12yes—
214C11⋊C8—24no—
215C11⋊C8—22no—
216C11⋊C8—22no—
217C11⋊C8—41no—
218C11⋊C8—41no—
219C22×M16—21no—
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—21no—
233#436—21no—
234#436—111no—
235#436C2×D1112yes—
236#436C2×D1112yes—
237#435—221no—
238C8×D4—111no—
239C8×D4—221no—
240#433—221no—
241#432—111no—
242#431—111no—
243C2×C4⋊C8C2×D1111yescharacteristic
244C2×C22⋊C8—21no—
245#405—221no—
246C4×M16—111no—
247C2×C4×C8C2×D1111yescharacteristic
248#335—112no—
249#334—112no—
250Q8⋊C8—112no—
251D4⋊C8—112no—
252D4⋊C8—112no—
253D4⋊C8—112no—
254#322—112no—
255C82—112no—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11—84no—
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×C11#56812yes—
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—22no—
283C2×M16—22no—
284C2×M16—44no—
285C2×M16—221no—
286C2×M16—221no—
287C22×C8—21no—
288C22×C8—221no—
289C22×C8C22⋊D1111yescharacteristic
290C22×C8C22⋊D1111yescharacteristic
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—21no—
311C4⋊C8—112no—
312C4⋊C8—111no—
313C4⋊C8—111no—
314C4⋊C8—221no—
315C4⋊C8—221no—
316C4⋊C8C22×D1112yes—
317#103—112no—
318#102—112no—
319#102—112no—
320#102—112no—
321C22⋊C8—22no—
322C22⋊C8—22no—
323C22⋊C8—111no—
324C22⋊C8—111no—
325C22⋊C8—221no—
326C22⋊C8—221no—
327C22⋊C8—221no—
328#97—221no—
329#97—221no—
330#97—221no—
331C4×C8—112no—
332C4×C8—112no—
333C4×C8—221no—
334C4×C8C22⋊D1111yescharacteristic
335C4×C8C22⋊D1111yescharacteristic
336C4×C8C22×D1111yescharacteristic
337C4×C8C22×D1111yescharacteristic
338C2×C11—22no—
339C2×C11—82no—
340C2×C11#293011yescharacteristic
341C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
342C2×C11C2×#44311yescharacteristic
343D11—81no—
344C24—21no—
345C2×Q8—111no—
346C2×D4—21no—
347C2×D4—42no—
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×C4#433911yescharacteristic
359C22×C4C2×C22⋊D1111yescharacteristic
360SD16—442no—
361D8—442no—
362M16—44no—
363M16—44no—
364M16—224no—
365M16—442no—
366C2×C8—22no—
367C2×C8—22no—
368C2×C8—41no—
369C2×C8—42no—
370C2×C8—112no—
371C2×C8—112no—
372C2×C8—222no—
373C2×C8—221no—
374C2×C8—221no—
375C2×C8—442no—
376C2×C8C2×C22⋊D1111yescharacteristic
377C2×C8C2×C22⋊D1111yescharacteristic
378C2×C8C2×C22⋊D1111yescharacteristic
379C2×C8C2×C22⋊D1111yescharacteristic
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
397C42#433911yescharacteristic
398C42C2×C22⋊D1111yescharacteristic
399C42C23×D1111yescharacteristic
400C11#1794211yescharacteristic, complemented, Sylow
401C23—22no—
402C23—42no—
403C23—42no—
404C23—42no—
405C23—221no—
406C23C4×C22⋊D1111yescharacteristic
407Q8—222no—
408D4—22no—
409D4—22no—
410D4—42no—
411D4—222no—
412D4—442no—
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×C4C4×C22⋊D1111yescharacteristic
428C2×C4C4×C22⋊D1111yescharacteristic
429C2×C4C4×C22⋊D1111yescharacteristic
430C2×C4C22×C4×D1111yescharacteristic
431C2×C4C2×#433911yescharacteristic
432C2×C4C22×C22⋊D1111yescharacteristic
433C8—21no—
434C8—21no—
435C8—21no—
436C8—42no—
437C8—224no—
438C8—222no—
439C8—222no—
440C8—441no—
441C8—441no—
442C8#6698512yes—
443C22—21no—
444C22—21no—
445C22—42no—
446C22—42no—
447C22—42no—
448C22—84no—
449C22—441no—
450C22—441no—
451C22—441no—
452C22#1062275712yes—
453C22C2×C4×C22⋊D1111yescharacteristic
454C4—21no—
455C4—21no—
456C4—21no—
457C4—21no—
458C4—42no—
459C4—441no—
460C4—441no—
461C4—441no—
462C4#1062327612yes—
463C4C2×#6698511yescharacteristic
464C4#1062335311yescharacteristic
465C2—22no—
466C2—82no—
467C2—881no—
468C2#1307731911yescharacteristic
469C2C4×#6698511yescharacteristic
470C2C2×#1062275711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC2×C11×#436C2
socleC22×C11C2×C4×D4
prime radical#10622830C4
cosocleC42×C11C24
hypercenterC2×#436D11
hypocenterC11#17942
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
2. #13077591C2semidirect
3. #13067504C2semidirect
4. #13067499C2semidirect
5. #13067492C2semidirect
6. #13067478C2semidirect
7. #13067399C2semidirect
8. #13067059C2semidirect
9. #13067027C2semidirect
10. C8×#4318C2semidirect
11. C2×C11×#436C2semidirect
37. #10622301C22semidirect
38. C8×D44C22semidirect
39. #10622292C22semidirect
40. C8×Dic22C22semidirect
43. #10622122C22semidirect
44. #10622121C22semidirect
45. #10622118C22semidirect
46. #10622117C22semidirect
47. #10622092C22semidirect
48. C8×C11⋊C8C22semidirect
168. C2×#436D11semidirect
400. C11#17942semidirect

Maximal subgroups

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

subgroupindex
#130786632
#130775912
#130675042
#130674992
#130674922
#130674782
#130673992
#130670592
#130670272
C8×#43182
C2×C11×#4362
#1794211