Finite Group Databasebeta

← #14909765

Subgroups — #14909765

Order 2816.

688 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079183C211yesmaximal, characteristic, complemented
2D11×#493C211yesmaximal, characteristic, complemented
3#13070883C211yesmaximal, characteristic, complemented
4#13070858C211yesmaximal, characteristic, complemented
5#13070857C211yesmaximal, characteristic, complemented
6#13070654C212yesmaximal, complemented
7#13070649C212yesmaximal, complemented
8#13070543C212yesmaximal, complemented
9#13070526C212yesmaximal, complemented
10#13070417C211yesmaximal, characteristic, complemented
11C11×#2250C211yesmaximal, characteristic, complemented
12C2×D8×D11—21no—
13C2×D8×D11C2212yes—
14D11×#127—21no—
15#10623211—21no—
16C2×C11×SD32C2212yescomplemented
17C2×C11×D16C2212yescomplemented
18C11×#495C2211yescharacteristic, complemented
19C11×#493C2211yescharacteristic
20#10622801C2211yescharacteristic
21Q16×Dic11C2211yescharacteristic, complemented
22C2×#66892C2212yescomplemented
23#10622784—21no—
24SD16×Dic11—21no—
25#10622770C2211yescharacteristic
26#10622764—21no—
27#10622764C2212yes—
28D8×Dic11C2211yescharacteristic, complemented
29C2×#66890C2212yescomplemented
30#10622686—21no—
31#10622669—21no—
32#10622308C2211yescharacteristic
33C4×C8×D11C2211yescharacteristic
34#10622296C2211yescharacteristic, complemented
35C11×#346C2211yescharacteristic, complemented
36#10622200C2212yescomplemented
37#10622200C2212yescomplemented
38#10622147C2212yescomplemented
39#10622147C2212yescomplemented
40(C2×D11)⋊C16C2212yes—
41Dic11⋊C16C2212yescomplemented
42#10622099C2211yescharacteristic, complemented
43C2×D4×D11—22no—
44C2×D4×D11—41no—
45C2×D4×D11—41no—
46C2×C11×Q16C2311yescharacteristic
47C2×C11×SD16—21no—
48C2×C11×D8—21no—
49C2×C11×D8C2312yes—
50C2×C11×D8C2311yescharacteristic
51C11×#127—21no—
52C11×#124—21no—
53#66999—21no—
54Q8×Dic11—21no—
55#66993—22no—
56#66993—41no—
57#66993—41no—
58#66991—21no—
59D4×Dic11—21no—
60C2×#4323—22no—
61C2×#4323—22no—
62D8×D11—42no—
63D8×D11—42no—
64D8×D11—44no—
65C2×D88—21no—
66C2×D88C2312yes—
67C2×C8×D11D411yescharacteristic
68C2×C8×D11C2311yescharacteristic
69#66936—41no—
70(C22⋊D11)⋊C4—41no—
71#66932—41no—
72#66930—41no—
73#66927—21no—
74C42×D11D411yescharacteristic
75#66923—21no—
76C11×SD32—42no—
77C11×D16—42no—
78C2×C11×C16C2312yes—
79C4×C8×C11C2311yescharacteristic
80#66899—21no—
81#66899—21no—
82#66896—21no—
83#66896—21no—
84#66892—42no—
85#66890—42no—
86#66882C2311yescharacteristic
87#66882C2311yescharacteristic
88#66881—21no—
89C8×Dic11D411yescharacteristic
90C8×Dic11C2311yescharacteristic
91C2×C11⋊C16C2312yes—
92C4×C11⋊C8D411yescharacteristic
93#33783—111nomaximal, Sylow
94C23×D11—42no—
95C2×Q8×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—22no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C2×C22⋊D11—42no—
101C2×C22⋊D11—42no—
102C2×C22⋊D11—42no—
103C2×C22⋊D11—41no—
104C22×Dic11—41no—
105D4×D11—44no—
106D4×D11—44no—
107D4×D11—84no—
108D4×D11—84no—
109C2×D44—22no—
110C2×D44—41no—
111C2×D44—41no—
112C2×C4×D11D811yescharacteristic
113C2×C4×D11D811yescharacteristic
114C2×C4×D11C2×D411yescharacteristic
115C11×Q16—22no—
116C11×SD16—42no—
117C11×D8—22no—
118C11×D8—22no—
119C11×D8—22no—
120C11×D8—42no—
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2411yescharacteristic
123C11×C22⋊C4—41no—
124C11×C22⋊C4—41no—
125C42×C11C2×D411yescharacteristic
126C22⋊Dic11—41no—
127C22⋊Dic11—41no—
128#4323—44no—
129#4323—44no—
130(C2×D11)⋊C4—41no—
131C4⋊Dic11—21no—
132C4⋊Dic11—21no—
133C4⋊Dic11—41no—
134Dic11⋊C4—41no—
135Dic11⋊C4—41no—
136Dic11⋊C4—41no—
137C4×Dic11—41no—
138C4×Dic11D811yescharacteristic
139C4×Dic11D811yescharacteristic
140C4×Dic11C2×D411yescharacteristic
141C2×C11⋊C8C2×D411yescharacteristic
142C2×C11⋊C8C2×D411yescharacteristic
143D88—22no—
144D88—22no—
145D88—42no—
146C8×D11—22no—
147C8×D11—22no—
148C11×C16—22no—
149C11⋊C16—22no—
150#3168—111no—
151C2×#493—111no—
152#2250—111no—
153#2250D1111yescharacteristic, complemented
154#2244—111no—
155#2244—111no—
156#2207—112no—
157#2206—112no—
158#2187—112no—
159#2184—112no—
160#2163—111no—
161C23×C11—41no—
162C23×C11—42no—
163C22×D11—42no—
164C22×D11—84no—
165C22×D11—84no—
166C22×D11—84no—
167C22×D11C2×D811yescharacteristic
168Q8×C11—41no—
169Q8×C11—41no—
170D4×C11—42no—
171D4×C11—41no—
172D4×C11—42no—
173D4×C11—41no—
174D4×C11—82no—
175D4×C11—82no—
176C2×C4×C11—41no—
177C2×C4×C11C2×D811yescharacteristic
178C2×C4×C11C2×D811yescharacteristic
179C2×C4×C11C22×D411yescharacteristic
180C22⋊D11—84no—
181C22⋊D11—84no—
182C22⋊D11—82no—
183C22⋊D11—84no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—82no—
187C2×Dic11C2×D811yescharacteristic
188C2×Dic11C2×D811yescharacteristic
189C2×Dic11C2×D811yescharacteristic
190D44—42no—
191D44—42no—
192D44—82no—
193D44—82no—
194C4×D11—22no—
195C4×D11—21no—
196C4×D11—21no—
197C4×D11—22no—
198C8×C11AGL(1,ℤ/8)12yes—
199C8×C11H(5,𝔽2)12yes—
200C11⋊C8—21no—
201C11⋊C8—21no—
202C22×D8—112no—
203C22×D8—221no—
204C2×#127—221no—
205#529—221no—
206C2×SD32—112no—
207C2×SD32C2×D1112yescomplemented
208C2×D16—112no—
209C2×D16C2×D1112yescomplemented
210#499—111no—
211#495C2×D1111yescharacteristic, complemented
212#493—112no—
213#493—111no—
214#493—221no—
215#493—221no—
216#493C2×D1111yescharacteristic
217#488—221no—
218#467—111no—
219#466—111no—
220#465—221no—
221C4×Q16—111no—
222C4×SD16—221no—
223C4×D8—111no—
224C2×C4×C8—111no—
225C4⋊C16—112no—
226#357—112no—
227#357—112no—
228#357—112no—
229#357—112no—
230C22⋊C16—112no—
231#346—111no—
232#346C2×D1111yescharacteristic, complemented
233C22×C11—82no—
234C22×C11—82no—
235C22×C11—81no—
236C22×C11—81no—
237C22×C11—82no—
238C22×C11—81no—
239C22×C11C22×D811yescharacteristic
240C2×D11—21no—
241C2×D11—21no—
242C2×D11—82no—
243C2×D11—82no—
244C2×D11—82no—
245C2×D11—168no—
246C2×D11#50912yes—
247C4×C11—21no—
248C4×C11—21no—
249C4×C11—81no—
250C4×C11#53511yescharacteristic
251C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
252Dic11—21no—
253Dic11—21no—
254Dic11—81no—
255Dic11—81no—
256Dic11#50912yes—
257C22×D4—222no—
258C22×D4—441no—
259C22×D4—441no—
260C2×Q16C22×D1111yescharacteristic
261C2×SD16—21no—
262C2×D8—21no—
263C2×D8—112no—
264C2×D8—222no—
265C2×D8—222no—
266C2×D8—221no—
267C2×D8—442no—
268C2×D8—442no—
269C2×D8—444no—
270C2×D8C22×D1112yes—
271C2×D8C22×D1111yescharacteristic
272C22×C8—111no—
273C22×C8—111no—
274#127—21no—
275#127—222no—
276#127—221no—
277#127—441no—
278#127—441no—
279#126—441no—
280#125—221no—
281#124—21no—
282#123—441no—
283C22⋊Q8—221no—
284#121—221no—
285C4×Q8—221no—
286C4×D4—221no—
287C4×D4—441no—
288#117—441no—
289C2×C42—111no—
290SD32—42no—
291SD32—442no—
292D16—42no—
293D16—442no—
294C2×C16—112no—
295C2×C16C22×D1112yes—
296#107—111no—
297#107—111no—
298#106—221no—
299#103—221no—
300#103—221no—
301#102—221no—
302#102—221no—
303C4×C8—111no—
304C4×C8—111no—
305C4×C8—111no—
306C4×C8C22×D1111yescharacteristic
307C2×C11—162no—
308C2×C11—161no—
309C2×C11#320511yescharacteristic
310C2×C11C2×#50911yescharacteristic
311C2×C11C2×#50911yescharacteristic
312D11—22no—
313D11—162no—
314C24—442no—
315C2×Q8—21no—
316C2×D4—21no—
317C2×D4—22no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—222no—
321C2×D4—442no—
322C2×D4—442no—
323C2×D4—442no—
324C2×D4—444no—
325C2×D4—444no—
326C2×D4—441no—
327C2×D4—441no—
328C2×D4—441no—
329C2×D4—884no—
330C2×D4—884no—
331C22×C4—111no—
332C22×C4—111no—
333C22×C4—111no—
334C22×C4—441no—
335Q16—22no—
336SD16—42no—
337D8—22no—
338D8—22no—
339D8—22no—
340D8—42no—
341D8—222no—
342D8—222no—
343D8—444no—
344D8—444no—
345D8—442no—
346C2×C8—111no—
347C2×C8—111no—
348C2×C8—222no—
349C2×C8—222no—
350C2×C8D4×D1111yescharacteristic
351C2×C8C23×D1111yescharacteristic
352C4⋊C4—221no—
353C4⋊C4—221no—
354C4⋊C4—441no—
355C4⋊C4—441no—
356C4⋊C4—441no—
357C4⋊C4—441no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—441no—
361C22⋊C4—441no—
362C22⋊C4—441no—
363C42—111no—
364C42—111no—
365C42—111no—
366C42—441no—
367C42D4×D1111yescharacteristic
368C16—22no—
369C16—222no—
370C11#3378311yescharacteristic, complemented, Sylow
371C23—41no—
372C23—42no—
373C23—111no—
374C23—442no—
375C23—884no—
376C23—884no—
377C23—884no—
378Q8—41no—
379Q8—41no—
380D4—42no—
381D4—41no—
382D4—42no—
383D4—41no—
384D4—82no—
385D4—82no—
386D4—442no—
387D4—442no—
388D4—882no—
389D4—882no—
390D4—884no—
391D4—884no—
392D4—884no—
393D4—882no—
394C2×C4—41no—
395C2×C4—111no—
396C2×C4—111no—
397C2×C4—111no—
398C2×C4—222no—
399C2×C4—222no—
400C2×C4—221no—
401C2×C4—221no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4—882no—
405C2×C4D8×D1111yescharacteristic
406C2×C4D8×D1111yescharacteristic
407C2×C4C2×D4×D1111yescharacteristic
408C8—221no—
409C8—221no—
410C8#6696412yes—
411C8#6703712yes—
412C22—81no—
413C22—82no—
414C22—82no—
415C22—81no—
416C22—82no—
417C22—81no—
418C22—112no—
419C22—221no—
420C22—221no—
421C22—882no—
422C22—882no—
423C22—882no—
424C22—1768no—
425C22C2×D8×D1111yescharacteristic
426C4—21no—
427C4—21no—
428C4—81no—
429C4—112no—
430C4—221no—
431C4—221no—
432C4—881no—
433C4—881no—
434C4#1062324611yescharacteristic
435C4C2×#6696411yescharacteristic
436C2—162no—
437C2—161no—
438C2—222no—
439C2—1762no—
440C2#1307953011yescharacteristic
441C2D11×#50911yescharacteristic
442C2D11×#50911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2250C2
socleC22×C11C22×D8
hypercenter#2250D11
hypocenterC11#33783
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2250

Complements

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

NH ≅ G/Ntype
1. #13079183C2semidirect
2. D11×#493C2semidirect
3. #13070883C2semidirect
4. #13070858C2semidirect
5. #13070857C2semidirect
6. #13070654C2semidirect
7. #13070649C2semidirect
8. #13070543C2semidirect
9. #13070526C2semidirect
10. #13070417C2semidirect
11. C11×#2250C2semidirect
16. C2×C11×SD32C22semidirect
17. C2×C11×D16C22semidirect
18. C11×#495C22semidirect
21. Q16×Dic11C22semidirect
22. C2×#66892C22semidirect
28. D8×Dic11C22semidirect
29. C2×#66890C22semidirect
34. #10622296C22semidirect
35. C11×#346C22semidirect
36. #10622200C22semidirect
37. #10622200C22semidirect
38. #10622147C22semidirect
39. #10622147C22semidirect
41. Dic11⋊C16C22semidirect
42. #10622099C22semidirect
153. #2250D11semidirect
207. C2×SD32C2×D11semidirect
209. C2×D16C2×D11semidirect
211. #495C2×D11semidirect
232. #346C2×D11semidirect
370. C11#33783semidirect

Maximal subgroups

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

subgroupindex
#130791832
D11×#4932
#130708832
#130708582
#130708572
#130706542
#130706492
#130705432
#130705262
#130704172
C11×#22502
#3378311