Finite Group Databasebeta

← #14909770

Subgroups — #14909770

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#13079188C211yesmaximal, characteristic, complemented
2D11×#493C211yesmaximal, characteristic, complemented
3#13070882C211yesmaximal, characteristic, complemented
4#13070880C211yesmaximal, characteristic, complemented
5#13070859C211yesmaximal, characteristic, complemented
6#13070655C212yesmaximal, complemented
7#13070650C212yesmaximal, complemented
8#13070546C212yesmaximal, complemented
9#13070529C212yesmaximal, complemented
10#13070417C211yesmaximal, characteristic, complemented
11C11×#2244C211yesmaximal, characteristic, complemented
12C2×D8×D11—21no—
13C2×D8×D11C2212yes—
14D11×#127—21no—
15#10623222—21no—
16C11×#499C2211yescharacteristic, complemented
17C11×#493C2211yescharacteristic
18#10622764—21no—
19#10622764C2212yes—
20C2×#66891C2212yescomplemented
21C2×#66890C2212yescomplemented
22#10622686—21no—
23#10622681—21no—
24C2×#66864C2212yescomplemented
25C2×D176C2212yescomplemented
26#10622500C2211yescharacteristic
27#10622496C2211yescharacteristic
28#10622486C2211yescharacteristic, complemented
29#10622485C2211yescharacteristic, complemented
30#10622477—21no—
31#10622465—21no—
32#10622309C2211yescharacteristic, complemented
33#10622308C2211yescharacteristic
34C4×C8×D11C2211yescharacteristic
35C11×#357C2212yescomplemented
36C11×#357C2212yescomplemented
37C11×#346C2211yescharacteristic, complemented
38(C2×D11)⋊C16C2212yes—
39Dic11⋊C16C2212yescomplemented
40#10622129C2212yescomplemented
41#10622129C2212yescomplemented
42#10622099C2211yescharacteristic, complemented
43C2×D4×D11—22no—
44C2×D4×D11—41no—
45C2×D4×D11—41no—
46C2×C11×D8—21no—
47C2×C11×D8C2312yes—
48C11×#127—21no—
49C11×#125—21no—
50#66993—22no—
51#66993—41no—
52#66993—41no—
53C2×#4323—22no—
54C2×#4323—22no—
55D8×D11—42no—
56D8×D11—42no—
57D8×D11—44no—
58C2×Dic44C2311yescharacteristic
59C2×D88—21no—
60C2×D88C2311yescharacteristic
61C2×D88C2312yes—
62C2×#4314—21no—
63C2×C8×D11D411yescharacteristic
64C2×C8×D11C2311yescharacteristic
65#66951—41no—
66#66950—21no—
67#66948—21no—
68#66947—41no—
69#66946—21no—
70#66946—41no—
71#66945—41no—
72#66940—21no—
73#66928—21no—
74#66927—21no—
75C42×D11D411yescharacteristic
76C2×C11×C16C2312yes—
77C11×#107C2311yescharacteristic
78C11×#107C2311yescharacteristic
79C11×#106—21no—
80C4×C8×C11C2311yescharacteristic
81#66891—42no—
82#66890—42no—
83C8×Dic11D411yescharacteristic
84C8×Dic11C2311yescharacteristic
85C2×C11⋊C16C2312yes—
86#66874—21no—
87#66874—21no—
88#66873—21no—
89#66873—21no—
90C4×C11⋊C8D411yescharacteristic
91#66864—42no—
92D176—42no—
93#33783—111nomaximal, Sylow
94C23×D11—42no—
95C2×D4×C11—22no—
96C2×D4×C11—41no—
97C2×D4×C11—41no—
98C2×C22⋊D11—42no—
99C2×C22⋊D11—42no—
100C2×C22⋊D11—42no—
101D4×D11—44no—
102D4×D11—44no—
103D4×D11—84no—
104D4×D11—84no—
105C2×D44—21no—
106C2×D44—22no—
107C2×D44—41no—
108C2×D44—41no—
109C2×D44—41no—
110C2×C4×D11—41no—
111C2×C4×D11D811yescharacteristic
112C2×C4×D11D811yescharacteristic
113C2×C4×D11C2×D411yescharacteristic
114C2×Dic22—21no—
115C11×D8—22no—
116C11×D8—22no—
117C11×D8—42no—
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2411yescharacteristic
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C42×C11C2×D411yescharacteristic
125#4323—44no—
126#4323—44no—
127(C2×D11)⋊C4—41no—
128(C2×D11)⋊C4—41no—
129(C2×D11)⋊C4—41no—
130(C2×D11)⋊C4—41no—
131(C2×D11)⋊C4—41no—
132C4⋊Dic11—41no—
133Dic11⋊C4—41no—
134C4×Dic11—41no—
135C4×Dic11D811yescharacteristic
136C4×Dic11D811yescharacteristic
137C4×Dic11C2×D411yescharacteristic
138C2×C11⋊C8C2×D411yescharacteristic
139C2×C11⋊C8C2×D411yescharacteristic
140Dic44—22no—
141D88—22no—
142D88—22no—
143D88—22no—
144D88—42no—
145#4314—42no—
146C8×D11—22no—
147C8×D11—22no—
148C11×C16—22no—
149C11⋊C16—22no—
150#3168—111no—
151C2×#493—111no—
152#2250—111no—
153#2250—111no—
154#2244—111no—
155#2244D1111yescharacteristic, complemented
156#2207—112no—
157#2206—112no—
158#2187—112no—
159#2184—112no—
160#2163—111no—
161C23×C11—42no—
162C22×D11—41no—
163C22×D11—42no—
164C22×D11—84no—
165C22×D11—84no—
166C22×D11—84no—
167C22×D11C2×D811yescharacteristic
168D4×C11—42no—
169D4×C11—42no—
170D4×C11—82no—
171D4×C11—82no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11C2×D811yescharacteristic
175C2×C4×C11C2×D811yescharacteristic
176C2×C4×C11C22×D411yescharacteristic
177C22⋊D11—84no—
178C22⋊D11—84no—
179C22⋊D11—84no—
180C2×Dic11—41no—
181C2×Dic11C2×D811yescharacteristic
182C2×Dic11C2×D811yescharacteristic
183C2×Dic11C2×D811yescharacteristic
184D44—42no—
185D44—41no—
186D44—41no—
187D44—42no—
188D44—82no—
189D44—82no—
190D44—82no—
191C4×D11—22no—
192C4×D11—21no—
193C4×D11—21no—
194C4×D11—22no—
195C4×D11—82no—
196Dic22—41no—
197Dic22—41no—
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×SD32—112no—
208C2×D16—112no—
209C2×D16—112no—
210#499C2×D1111yescharacteristic, complemented
211#495—111no—
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#357C2×D1112yescomplemented
229#357C2×D1112yescomplemented
230C22⋊C16—112no—
231#346—111no—
232#346C2×D1111yescharacteristic, complemented
233C22×C11—82no—
234C22×C11—82no—
235C22×C11—82no—
236C22×C11C22×D811yescharacteristic
237C2×D11—21no—
238C2×D11—21no—
239C2×D11—82no—
240C2×D11—82no—
241C2×D11—81no—
242C2×D11—81no—
243C2×D11—82no—
244C2×D11—81no—
245C2×D11—168no—
246C2×D11#50912yes—
247C4×C11—21no—
248C4×C11—21no—
249C4×C11—81no—
250C4×C11—81no—
251C4×C11#53511yescharacteristic
252C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
253Dic11—21no—
254Dic11—21no—
255Dic11—81no—
256Dic11#50912yes—
257C22×D4—222no—
258C22×D4—441no—
259C22×D4—441no—
260C2×Q16—111no—
261C2×SD16—221no—
262C2×D8—21no—
263C2×D8—112no—
264C2×D8—111no—
265C2×D8—222no—
266C2×D8—222no—
267C2×D8—221no—
268C2×D8—442no—
269C2×D8—442no—
270C2×D8—444no—
271C2×D8C22×D1112yes—
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—21no—
281#124—221no—
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—442no—
291SD32—442no—
292D16—442no—
293D16—442no—
294C2×C16—112no—
295C2×C16C22×D1112yes—
296#107C22×D1111yescharacteristic
297#107C22×D1111yescharacteristic
298#106—21no—
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#320511yescharacteristic
309C2×C11C2×#50911yescharacteristic
310C2×C11C2×#50911yescharacteristic
311D11—22no—
312D11—161no—
313D11—162no—
314C24—442no—
315C2×Q8—221no—
316C2×D4—22no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—221no—
320C2×D4—222no—
321C2×D4—441no—
322C2×D4—442no—
323C2×D4—442no—
324C2×D4—442no—
325C2×D4—444no—
326C2×D4—444no—
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—222no—
336SD16—442no—
337D8—22no—
338D8—22no—
339D8—42no—
340D8—222no—
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—21no—
353C4⋊C4—21no—
354C4⋊C4—41no—
355C4⋊C4—41no—
356C4⋊C4—441no—
357C4⋊C4—441no—
358C22⋊C4—441no—
359C22⋊C4—441no—
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—42no—
372C23—111no—
373C23—441no—
374C23—442no—
375C23—884no—
376C23—884no—
377C23—884no—
378Q8—441no—
379Q8—441no—
380D4—42no—
381D4—42no—
382D4—82no—
383D4—82no—
384D4—442no—
385D4—441no—
386D4—442no—
387D4—441no—
388D4—882no—
389D4—882no—
390D4—882no—
391D4—884no—
392D4—884no—
393D4—884no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—111no—
397C2×C4—111no—
398C2×C4—111no—
399C2×C4—222no—
400C2×C4—222no—
401C2×C4—221no—
402C2×C4—221no—
403C2×C4—441no—
404C2×C4—882no—
405C2×C4D8×D1111yescharacteristic
406C2×C4D8×D1111yescharacteristic
407C2×C4C2×D4×D1111yescharacteristic
408C8—221no—
409C8—221no—
410C8#6696712yes—
411C8#6704212yes—
412C22—82no—
413C22—82no—
414C22—82no—
415C22—112no—
416C22—221no—
417C22—221no—
418C22—881no—
419C22—882no—
420C22—882no—
421C22—881no—
422C22—882no—
423C22—881no—
424C22—1768no—
425C22C2×D8×D1111yescharacteristic
426C4—21no—
427C4—21no—
428C4—81no—
429C4—81no—
430C4—112no—
431C4—221no—
432C4—221no—
433C4—881no—
434C4#1062320511yescharacteristic
435C4C2×#6696711yescharacteristic
436C2—162no—
437C2—222no—
438C2—1762no—
439C2—1761no—
440C2#1307953511yescharacteristic
441C2D11×#50911yescharacteristic
442C2D11×#50911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2244C2
socleC22×C11C22×D8
hypercenter#2244D11
hypocenterC11#33783
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2244

Complements

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

NH ≅ G/Ntype
1. #13079188C2semidirect
2. D11×#493C2semidirect
3. #13070882C2semidirect
4. #13070880C2semidirect
5. #13070859C2semidirect
6. #13070655C2semidirect
7. #13070650C2semidirect
8. #13070546C2semidirect
9. #13070529C2semidirect
10. #13070417C2semidirect
11. C11×#2244C2semidirect
16. C11×#499C22semidirect
20. C2×#66891C22semidirect
21. C2×#66890C22semidirect
24. C2×#66864C22semidirect
25. C2×D176C22semidirect
28. #10622486C22semidirect
29. #10622485C22semidirect
32. #10622309C22semidirect
35. C11×#357C22semidirect
36. C11×#357C22semidirect
37. C11×#346C22semidirect
39. Dic11⋊C16C22semidirect
40. #10622129C22semidirect
41. #10622129C22semidirect
42. #10622099C22semidirect
155. #2244D11semidirect
210. #499C2×D11semidirect
228. #357C2×D11semidirect
229. #357C2×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
#130791882
D11×#4932
#130708822
#130708802
#130708592
#130706552
#130706502
#130705462
#130705292
#130704172
C11×#22442
#3378311