Finite Group Databasebeta

← #14910565

Subgroups — #14910565

Order 2816.

668 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081755C212yesmaximal, complemented
2#13080416C211yesmaximal, characteristic, complemented
3#13070865C211yesmaximal, characteristic, complemented
4#13070734C212yesmaximal, complemented
5#13070692C211yesmaximal, characteristic, complemented
6#13070689C211yesmaximal, characteristic, complemented
7#13070573C212yesmaximal, complemented
8#13070571C212yesmaximal, complemented
9#13070495C211yesmaximal, characteristic, complemented
10#13070453C211yesmaximal, characteristic, complemented
11C11×#3292C211yesmaximal, characteristic, complemented
12C11×#576—21no—
13C11×#576C2212yescomplemented
14#10623300—21no—
15#10623283C2212yescomplemented
16C11×#493C2211yescharacteristic, complemented
17C11×#472—21no—
18C11×#472C2212yescomplemented
19C11×#453—22no—
20C11×#443C2211yescharacteristic
21C11×#443C2211yescharacteristic, complemented
22#10622807—22no—
23#10622807C2211yescharacteristic
24#10622806—22no—
25#10622806C2212yescomplemented
26#10622760—22no—
27#10622760C2212yescomplemented
28C2×#66890—22no—
29C2×#66890C2212yescomplemented
30C2×#66890C2212yescomplemented
31#10622755C2212yescomplemented
32#10622753C2212yescomplemented
33#10622510—21no—
34#10622435—22no—
35#10622313C2211yescharacteristic, complemented
36#10622308C2211yescharacteristic, complemented
37#10622205C2211yescharacteristic, complemented
38#10622201C2212yescomplemented
39#10622199C2212yescomplemented
40#10622135C2211yescharacteristic, complemented
41#10622133C2212yescomplemented
42#10622131C2211yescharacteristic, complemented
43#10622101C2211yescharacteristic, complemented
44C4×C11⋊C16C2211yescharacteristic, complemented
45C11×H(5,𝔽2)—22no—
46#67042—22no—
47C11×AGL(1,ℤ/8)—22no—
48C11×AGL(1,ℤ/8)—22no—
49C11×AGL(1,ℤ/8)—42no—
50C11×AGL(1,ℤ/8)—42no—
51C11×#135—22no—
52C11×#135—41no—
53C11×#135D411yescharacteristic
54C11×#135C2311yescharacteristic
55C2×C11×D8—22no—
56C2×C11×D8—21no—
57C2×C11×D8—41no—
58C2×C11×D8C2312yes—
59C11×#131—21no—
60C11×#131C2312yes—
61C11×#127—21no—
62#67002—22no—
63#66972—41no—
64#66967—42no—
65D8×D11—41no—
66#66961—22no—
67#66961—42no—
68#66957—22no—
69#66957C2311yescharacteristic
70C2×D88—22no—
71C2×D88—21no—
72C2×D88C2312yes—
73#66954—21no—
74#66927—21no—
75C11×#108D411yescharacteristic
76C11×#108C2311yescharacteristic
77C11×#104—21no—
78C11×#104D412yes—
79C11×#100—22no—
80C4×C8×C11C2311yescharacteristic
81#66893D411yescharacteristic, complemented
82#66892—22no—
83#66892D411yescharacteristic, complemented
84#66891—22no—
85#66891D411yescharacteristic, complemented
86#66890—22no—
87#66890—22no—
88#66890—22no—
89#66890—22no—
90#66890—42no—
91#66890D411yescharacteristic, complemented
92#66887—22no—
93#66883C2311yescharacteristic
94#66876—22no—
95#66876C2312yes—
96C2×C11⋊C16—22no—
97C2×C11⋊C16C2311yescharacteristic
98C2×C11⋊C16C2311yescharacteristic
99#66869—21no—
100#33858—111nomaximal, Sylow
101C11×#41—21no—
102C11×#41—42no—
103C11×#41—42no—
104C11×#41C2×D412yes—
105C2×D4×C11—22no—
106C2×D4×C11—42no—
107C2×D4×C11—42no—
108C2×D4×C11—81no—
109C2×D4×C11—82no—
110#4343—42no—
111D4×D11—42no—
112D4×D11—82no—
113#4339—21no—
114#4339—42no—
115C2×D44—22no—
116C2×D44—42no—
117C2×D44—81no—
118C11×Q16D811yescharacteristic
119C11×Q16C2×D411yescharacteristic
120C11×SD16—21no—
121C11×SD16—42no—
122C11×SD16—42no—
123C11×SD16D812yes—
124C11×D8—22no—
125C11×D8—22no—
126C11×D8—42no—
127C11×D8—41no—
128C11×D8—41no—
129C11×D8—42no—
130C11×D8D811yescharacteristic
131C11×D8C2×D411yescharacteristic
132C11×M16—22no—
133C11×M16—21no—
134C11×M16—41no—
135C11×M16C2×D412yes—
136C2×C8×C11—22no—
137C2×C8×C11—41no—
138C2×C8×C11C2×D411yescharacteristic
139C2×C8×C11C2411yescharacteristic
140C42×C11C2×D411yescharacteristic
141#4325—42no—
142#4323—42no—
143#4318—21no—
144Dic44C2×D411yescharacteristic
145D88—22no—
146D88—22no—
147D88—42no—
148D88—41no—
149D88—41no—
150D88C2×D411yescharacteristic
151#4314—21no—
152#4314—42no—
153#4313—41no—
154C8×D11—41no—
155C11⋊C16—22no—
156C11⋊C16—21no—
157C11⋊C16C2×D411yescharacteristic
158C11⋊C16C2×D411yescharacteristic
159#3415—112no—
160#3292—111no—
161#3292D1111yescharacteristic, complemented
162#2246—111no—
163#2221—112no—
164#2213—111no—
165#2213—111no—
166#2192—112no—
167#2192—112no—
168#2178—111no—
169#2170—111no—
170C23×C11—42no—
171C23×C11—82no—
172C22×D11—42no—
173C22×D11—82no—
174Q8×C11—21no—
175Q8×C11C2×D812yes—
176D4×C11—22no—
177D4×C11—21no—
178D4×C11—41no—
179D4×C11—42no—
180D4×C11—42no—
181D4×C11—82no—
182D4×C11—82no—
183D4×C11—162no—
184D4×C11C2×D812yes—
185C2×C4×C11—21no—
186C2×C4×C11—22no—
187C2×C4×C11—41no—
188C2×C4×C11—82no—
189C2×C4×C11C22×D411yescharacteristic
190C22⋊D11—41no—
191C22⋊D11—82no—
192D44—21no—
193D44—42no—
194D44—42no—
195D44—82no—
196D44—162no—
197C4×D11—41no—
198C4×D11—82no—
199Dic22—21no—
200C8×C11—22no—
201C8×C11—41no—
202C8×C11C2×D811yescharacteristic
203C8×C11C2×D811yescharacteristic
204C8×C11C22×D411yescharacteristic
205C8×C11H(5,𝔽2)11yescharacteristic
206C11⋊C8—41no—
207#576—21no—
208#576—112no—
209#576—221no—
210#576C2×D1112yescomplemented
211#509—112no—
212#509—112no—
213#509—222no—
214#509—222no—
215#508—111no—
216#508—222no—
217C2×D16—112no—
218C2×D16—112no—
219C2×D16—222no—
220#504—112no—
221#493—111no—
222#493C2×D1111yescharacteristic, complemented
223#472—21no—
224#472—112no—
225#472—221no—
226#472C2×D1112yescomplemented
227#453—22no—
228#453—222no—
229#443—111no—
230#443C2×D1111yescharacteristic
231#443C2×D1111yescharacteristic, complemented
232#368—111no—
233#364—111no—
234#361—112no—
235#361—112no—
236#359—111no—
237#359—111no—
238#350—112no—
239C4×C16—111no—
240C22×C11—22no—
241C22×C11—41no—
242C22×C11—82no—
243C22×C11—162no—
244C22×C11—322no—
245C22×C11#57611yescharacteristic
246C2×D11—41no—
247C2×D11—82no—
248C2×D11—162no—
249C2×D11—322no—
250C4×C11—22no—
251C4×C11—22no—
252C4×C11—41no—
253C4×C11D4211yescharacteristic
254C4×C11C22×D811yescharacteristic
255Dic11—41no—
256H(5,𝔽2)—22no—
257H(5,𝔽2)—222no—
258AGL(1,ℤ/8)—22no—
259AGL(1,ℤ/8)—22no—
260AGL(1,ℤ/8)—42no—
261AGL(1,ℤ/8)—42no—
262AGL(1,ℤ/8)—222no—
263AGL(1,ℤ/8)—222no—
264AGL(1,ℤ/8)—442no—
265AGL(1,ℤ/8)—442no—
266#135—22no—
267#135—41no—
268#135—111no—
269#135—222no—
270#135—441no—
271#135C22⋊D1111yescharacteristic
272#135C22×D1111yescharacteristic
273C2×D8—22no—
274C2×D8—21no—
275C2×D8—41no—
276C2×D8—112no—
277C2×D8—222no—
278C2×D8—221no—
279C2×D8—441no—
280C2×D8C22×D1112yes—
281#131—21no—
282#131—221no—
283#131C22×D1112yes—
284#127—21no—
285#127—221no—
286Q32—111no—
287SD32—111no—
288SD32—111no—
289SD32—222no—
290SD32—222no—
291D16—111no—
292D16—222no—
293D16—222no—
294D16—222no—
295D16—222no—
296D16—442no—
297M32—112no—
298M32—222no—
299C2×C16—111no—
300C2×C16—111no—
301C2×C16—222no—
302#108—111no—
303#108C22⋊D1111yescharacteristic
304#108C22×D1111yescharacteristic
305#104—21no—
306#104—221no—
307#104C22⋊D1112yes—
308#100—22no—
309#100—222no—
310C4×C8C22×D1111yescharacteristic
311C2×C11—21no—
312C2×C11—42no—
313C2×C11—81no—
314C2×C11—162no—
315C2×C11D4×D811yescharacteristic
316D11—81no—
317D11—162no—
318#41—21no—
319#41—42no—
320#41—42no—
321#41—221no—
322#41—442no—
323#41—442no—
324#41C2×C22⋊D1112yes—
325C2×D4—22no—
326C2×D4—42no—
327C2×D4—42no—
328C2×D4—81no—
329C2×D4—82no—
330C2×D4—222no—
331C2×D4—442no—
332C2×D4—442no—
333C2×D4—881no—
334C2×D4—882no—
335Q16—111no—
336Q16#432311yescharacteristic
337Q16D4×D1111yescharacteristic
338SD16—21no—
339SD16—42no—
340SD16—42no—
341SD16—221no—
342SD16—442no—
343SD16—442no—
344SD16#432312yes—
345D8—22no—
346D8—22no—
347D8—42no—
348D8—42no—
349D8—41no—
350D8—41no—
351D8—111no—
352D8—222no—
353D8—222no—
354D8—442no—
355D8—442no—
356D8—441no—
357D8—441no—
358D8#432311yescharacteristic
359D8D4×D1111yescharacteristic
360M16—22no—
361M16—21no—
362M16—41no—
363M16—221no—
364M16—441no—
365M16C2×C22⋊D1112yes—
366C2×C8—22no—
367C2×C8—41no—
368C2×C8—441no—
369C2×C8C2×C22⋊D1111yescharacteristic
370C2×C8C23×D1111yescharacteristic
371C42C2×C22⋊D1111yescharacteristic
372C16—111no—
373C16—111no—
374C16—222no—
375C16—221no—
376C11#3385811yescharacteristic, complemented, Sylow
377C23—42no—
378C23—82no—
379C23—442no—
380C23—882no—
381Q8—21no—
382Q8—221no—
383Q8C2×#432312yes—
384D4—22no—
385D4—21no—
386D4—41no—
387D4—42no—
388D4—42no—
389D4—82no—
390D4—82no—
391D4—162no—
392D4—221no—
393D4—441no—
394D4—442no—
395D4—442no—
396D4—882no—
397D4—882no—
398D4—1762no—
399D4C2×#432312yes—
400C2×C4—21no—
401C2×C4—22no—
402C2×C4—41no—
403C2×C4—82no—
404C2×C4—441no—
405C2×C4—882no—
406C2×C4C22×C22⋊D1111yescharacteristic
407C8—22no—
408C8—41no—
409C8—441no—
410C8C2×#432311yescharacteristic
411C8C2×#432311yescharacteristic
412C8C2×D4×D1111yescharacteristic
413C8#6703711yescharacteristic
414C22—22no—
415C22—41no—
416C22—82no—
417C22—162no—
418C22—322no—
419C22—441no—
420C22—882no—
421C22—3522no—
422C22—1762no—
423C22#1062336611yescharacteristic
424C4—22no—
425C4—22no—
426C4—41no—
427C4—441no—
428C4C22×#432311yescharacteristic
429C4D4×C22⋊D1111yescharacteristic
430C2—21no—
431C2—42no—
432C2—81no—
433C2—162no—
434C2—881no—
435C2—1762no—
436C2D4×#432311yescharacteristic
subgroupG/H
centerC2D4×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3292C2
socleC2×C11D4×D8
hypercenter#3292D11
hypocenterC11#33858
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443 ◁ #3292

Complements

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

NH ≅ G/Ntype
1. #13081755C2semidirect
2. #13080416C2semidirect
3. #13070865C2semidirect
4. #13070734C2semidirect
5. #13070692C2semidirect
6. #13070689C2semidirect
7. #13070573C2semidirect
8. #13070571C2semidirect
9. #13070495C2semidirect
10. #13070453C2semidirect
11. C11×#3292C2semidirect
13. C11×#576C22semidirect
15. #10623283C22semidirect
16. C11×#493C22semidirect
18. C11×#472C22semidirect
21. C11×#443C22semidirect
25. #10622806C22semidirect
27. #10622760C22semidirect
29. C2×#66890C22semidirect
30. C2×#66890C22semidirect
31. #10622755C22semidirect
32. #10622753C22semidirect
35. #10622313C22semidirect
36. #10622308C22semidirect
37. #10622205C22semidirect
38. #10622201C22semidirect
39. #10622199C22semidirect
40. #10622135C22semidirect
41. #10622133C22semidirect
42. #10622131C22semidirect
43. #10622101C22semidirect
44. C4×C11⋊C16C22semidirect
81. #66893D4semidirect
83. #66892D4semidirect
85. #66891D4semidirect
91. #66890D4semidirect
161. #3292D11semidirect
210. #576C2×D11semidirect
222. #493C2×D11semidirect
226. #472C2×D11semidirect
231. #443C2×D11semidirect
376. C11#33858semidirect

Maximal subgroups

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

subgroupindex
#130817552
#130804162
#130708652
#130707342
#130706922
#130706892
#130705732
#130705712
#130704952
#130704532
C11×#32922
#3385811