Finite Group Databasebeta

← #14910563

Subgroups — #14910563

Order 2816.

668 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081754C211yesmaximal, characteristic, complemented
2#13080413C212yesmaximal, complemented
3#13070864C211yesmaximal, characteristic, complemented
4#13070736C211yesmaximal, characteristic, complemented
5#13070733C211yesmaximal, characteristic, complemented
6#13070690C212yesmaximal, complemented
7#13070573C212yesmaximal, complemented
8#13070570C212yesmaximal, complemented
9#13070497C211yesmaximal, characteristic, complemented
10#13070451C211yesmaximal, characteristic, complemented
11C11×#3415C211yesmaximal, characteristic, complemented
12C11×#576C2212yescomplemented
13#10623366—22no—
14#10623300C2212yescomplemented
15C11×#509—22no—
16C11×#509C2212yescomplemented
17C11×#508—21no—
18C11×#508C2211yescharacteristic
19C2×C11×D16—21no—
20C2×C11×D16C2211yescharacteristic, complemented
21C11×#504C2211yescharacteristic, complemented
22#10622854—22no—
23#10622812—22no—
24#10622811—22no—
25#10622809C2212yescomplemented
26#10622806C2212yescomplemented
27#10622773C2212yescomplemented
28#10622764C2212yescomplemented
29C2×#66890C2212yescomplemented
30#10622757C2211yescharacteristic
31#10622755C2212yescomplemented
32#10622532—21no—
33#10622527—22no—
34D11×D16—21no—
35C2×D176C2211yescharacteristic, complemented
36#10622514C2211yescharacteristic, complemented
37#10622205C2212yescomplemented
38#10622201C2212yescomplemented
39#10622199C2211yescharacteristic, complemented
40#10622154C2212yescomplemented
41#10622153C2211yescharacteristic, complemented
42#10622149C2211yescharacteristic, complemented
43#10622144C2211yescharacteristic, complemented
44C16×Dic11C2211yescharacteristic, complemented
45C11×H(5,𝔽2)—22no—
46#67042—22no—
47C11×AGL(1,ℤ/8)—22no—
48C11×AGL(1,ℤ/8)—42no—
49C11×#135—22no—
50C11×#135C2312yes—
51C2×C11×D8—22no—
52C2×C11×D8C2312yes—
53C11×#131C2311yescharacteristic
54#67003—42no—
55#67003D411yescharacteristic
56#67002—22no—
57#67002—22no—
58#67002—42no—
59#67001—22no—
60#66993—22no—
61#66985—22no—
62#66985—42no—
63C2×#4323—22no—
64C2×#4323—42no—
65#66972—22no—
66#66967—42no—
67D8×D11—22no—
68C2×D88C2312yes—
69#66954C2311yescharacteristic
70C11×Q32D411yescharacteristic, complemented
71C11×SD32—22no—
72C11×SD32D412yescomplemented
73C11×D16—22no—
74C11×D16—21no—
75C11×D16—21no—
76C11×D16D411yescharacteristic, complemented
77C11×M32—21no—
78C11×M32C2311yescharacteristic
79C2×C11×C16—21no—
80C2×C11×C16C2311yescharacteristic
81#66901—22no—
82#66901D411yescharacteristic
83#66897—22no—
84#66892—22no—
85#66890—22no—
86#66890—42no—
87#66889D411yescharacteristic
88#66887—22no—
89#66886D411yescharacteristic
90#66883C2312yes—
91C8×Dic11C2311yescharacteristic
92#66876C2311yescharacteristic
93C2×C11⋊C16C2311yescharacteristic
94D176—21no—
95D176—21no—
96#66862—21no—
97C16×D11—21no—
98#33858—111nomaximal, Sylow
99C11×#41—22no—
100C11×#41—42no—
101C11×#41—42no—
102C11×#41C2×D411yescharacteristic
103C2×D4×C11—22no—
104C2×D4×C11—42no—
105C2×D4×C11—42no—
106C2×D4×C11—82no—
107C2×C22⋊D11—82no—
108#4343—42no—
109D4×D11—42no—
110D4×D11—82no—
111#4339—42no—
112#4339C2×D411yescharacteristic
113C2×D44—22no—
114C2×D44—42no—
115C11×Q16C2×D412yes—
116C11×SD16—22no—
117C11×SD16—42no—
118C11×D8—22no—
119C11×D8—22no—
120C11×D8—42no—
121C11×D8C2×D412yes—
122C11×M16—21no—
123C11×M16C2×D411yescharacteristic
124C2×C8×C11—21no—
125C2×C8×C11C2411yescharacteristic
126#4326D811yescharacteristic
127#4325—42no—
128#4325—42no—
129#4325D811yescharacteristic
130#4324—42no—
131#4324D811yescharacteristic
132#4323—42no—
133#4323—42no—
134#4323—42no—
135#4323—42no—
136#4323—42no—
137#4323D811yescharacteristic
138C4×Dic11C2×D411yescharacteristic
139#4318—22no—
140#4318—42no—
141#4318C2×D411yescharacteristic
142C2×C11⋊C8—42no—
143C2×C11⋊C8C2×D411yescharacteristic
144D88—22no—
145D88—22no—
146#4313—21no—
147C8×D11—21no—
148C11×C16—21no—
149C11×C16C2×D411yescharacteristic
150C11×C16C2×D411yescharacteristic
151C11⋊C16—21no—
152C11⋊C16—21no—
153#3415—111no—
154#3415D1111yescharacteristic, complemented
155#3292—112no—
156#2246—111no—
157#2221—111no—
158#2221—111no—
159#2213—112no—
160#2192—112no—
161#2192—112no—
162#2178—111no—
163#2170—111no—
164C23×C11—42no—
165C23×C11—82no—
166C22×D11—42no—
167C22×D11—82no—
168Q8×C11—22no—
169Q8×C11C2×D811yescharacteristic
170D4×C11—21no—
171D4×C11—22no—
172D4×C11—42no—
173D4×C11—42no—
174D4×C11—42no—
175D4×C11—82no—
176D4×C11—82no—
177D4×C11C2×D811yescharacteristic
178C2×C4×C11—21no—
179C2×C4×C11—42no—
180C2×C4×C11—82no—
181C2×C4×C11C22×D411yescharacteristic
182C22⋊D11—21no—
183C22⋊D11—82no—
184C22⋊D11—164no—
185C2×Dic11—21no—
186D44—42no—
187D44—42no—
188D44—82no—
189D44C2×D811yescharacteristic
190C4×D11—21no—
191C4×D11—82no—
192Dic22C2×D811yescharacteristic
193C8×C11—21no—
194C8×C11C22×D411yescharacteristic
195C8×C11H(5,𝔽2)11yescharacteristic
196C11⋊C8—21no—
197C11⋊C8—42no—
198C11⋊C8C2×D811yescharacteristic
199C11⋊C8C2×D811yescharacteristic
200#576—112no—
201#576—222no—
202#576C2×D1112yescomplemented
203#509—22no—
204#509—112no—
205#509—222no—
206#509C2×D1112yescomplemented
207#508—21no—
208#508—221no—
209#508C2×D1111yescharacteristic
210C2×D16—21no—
211C2×D16—112no—
212C2×D16—111no—
213C2×D16—221no—
214C2×D16C2×D1111yescharacteristic, complemented
215#504—111no—
216#504C2×D1111yescharacteristic, complemented
217#493—112no—
218#472—112no—
219#472—112no—
220#472—222no—
221#453—222no—
222#453—222no—
223#443—111no—
224#443—112no—
225#368—111no—
226#364—111no—
227#361—112no—
228#361—112no—
229#359—112no—
230#350—111no—
231#350—111no—
232C4×C16—111no—
233C22×C11—21no—
234C22×C11—42no—
235C22×C11—82no—
236C22×C11—162no—
237C22×C11—322no—
238C22×C11#57611yescharacteristic
239C2×D11—21no—
240C2×D11—82no—
241C2×D11—162no—
242C2×D11—322no—
243C4×C11—21no—
244C4×C11—42no—
245C4×C11D4211yescharacteristic
246C4×C11C22×D811yescharacteristic
247Dic11—22no—
248Dic11—21no—
249H(5,𝔽2)—22no—
250H(5,𝔽2)—222no—
251AGL(1,ℤ/8)—22no—
252AGL(1,ℤ/8)—42no—
253AGL(1,ℤ/8)—222no—
254AGL(1,ℤ/8)—222no—
255AGL(1,ℤ/8)—222no—
256AGL(1,ℤ/8)—442no—
257AGL(1,ℤ/8)—442no—
258AGL(1,ℤ/8)—442no—
259#135—22no—
260#135—111no—
261#135—222no—
262#135—442no—
263#135C22×D1112yes—
264C2×D8—22no—
265C2×D8—112no—
266C2×D8—222no—
267C2×D8—222no—
268C2×D8—442no—
269C2×D8C22×D1112yes—
270#131—111no—
271#131—222no—
272#131C22×D1111yescharacteristic
273#127—222no—
274Q32C22⋊D1111yescharacteristic, complemented
275SD32—22no—
276SD32—222no—
277SD32C22⋊D1112yescomplemented
278D16—22no—
279D16—21no—
280D16—21no—
281D16—222no—
282D16—221no—
283D16—221no—
284D16—442no—
285D16C22⋊D1111yescharacteristic, complemented
286M32—21no—
287M32—111no—
288M32—221no—
289M32C22×D1111yescharacteristic
290C2×C16—21no—
291C2×C16—111no—
292C2×C16—221no—
293C2×C16C22×D1111yescharacteristic
294#108—111no—
295#108—112no—
296#104—111no—
297#104—111no—
298#104—222no—
299#100—222no—
300#100—222no—
301C4×C8—111no—
302C2×C11—21no—
303C2×C11—41no—
304C2×C11—82no—
305C2×C11—162no—
306C2×C11D4×D811yescharacteristic
307D11—41no—
308D11—162no—
309#41—22no—
310#41—42no—
311#41—42no—
312#41—111no—
313#41—442no—
314#41—442no—
315#41D4×D1111yescharacteristic
316C2×D4—22no—
317C2×D4—42no—
318C2×D4—42no—
319C2×D4—82no—
320C2×D4—222no—
321C2×D4—442no—
322C2×D4—442no—
323C2×D4—882no—
324C2×D4—882no—
325Q16—111no—
326Q16C2×C22⋊D1112yes—
327SD16—22no—
328SD16—42no—
329SD16—111no—
330SD16—111no—
331SD16—442no—
332SD16—442no—
333SD16—442no—
334D8—22no—
335D8—22no—
336D8—42no—
337D8—111no—
338D8—222no—
339D8—222no—
340D8—442no—
341D8—442no—
342D8—442no—
343D8—442no—
344D8—442no—
345D8C2×C22⋊D1112yes—
346M16—21no—
347M16—111no—
348M16—221no—
349M16—222no—
350M16—442no—
351M16D4×D1111yescharacteristic
352C2×C8—21no—
353C2×C8—111no—
354C2×C8—221no—
355C2×C8—442no—
356C2×C8C23×D1111yescharacteristic
357C42—111no—
358C16—21no—
359C16—221no—
360C16—221no—
361C16C2×C22⋊D1111yescharacteristic
362C16C2×C22⋊D1111yescharacteristic
363C11#3385811yescharacteristic, complemented, Sylow
364C23—42no—
365C23—82no—
366C23—442no—
367C23—882no—
368Q8—22no—
369Q8—111no—
370Q8D8×D1111yescharacteristic
371D4—21no—
372D4—22no—
373D4—42no—
374D4—42no—
375D4—42no—
376D4—82no—
377D4—82no—
378D4—111no—
379D4—221no—
380D4—442no—
381D4—442no—
382D4—882no—
383D4—882no—
384D4—1764no—
385D4D8×D1111yescharacteristic
386C2×C4—21no—
387C2×C4—42no—
388C2×C4—82no—
389C2×C4—221no—
390C2×C4—221no—
391C2×C4—882no—
392C2×C4C2×D4×D1111yescharacteristic
393C8—21no—
394C8—111no—
395C8—111no—
396C8—221no—
397C8—442no—
398C8#6703711yescharacteristic
399C8C22×C22⋊D1111yescharacteristic
400C22—21no—
401C22—42no—
402C22—82no—
403C22—162no—
404C22—221no—
405C22—322no—
406C22—882no—
407C22—3522no—
408C22—1762no—
409C22#1062328811yescharacteristic
410C4—21no—
411C4—42no—
412C4—222no—
413C4—221no—
414C4C2×D8×D1111yescharacteristic
415C4D4×C22⋊D1111yescharacteristic
416C2—21no—
417C2—41no—
418C2—82no—
419C2—162no—
420C2—441no—
421C2—1762no—
422C2D8×C22⋊D1111yescharacteristic
subgroupG/H
centerC2D8×C22⋊D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3415C2
socleC2×C11D4×D8
hypercenter#3415D11
hypocenterC11#33858
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #3415

Complements

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

NH ≅ G/Ntype
1. #13081754C2semidirect
2. #13080413C2semidirect
3. #13070864C2semidirect
4. #13070736C2semidirect
5. #13070733C2semidirect
6. #13070690C2semidirect
7. #13070573C2semidirect
8. #13070570C2semidirect
9. #13070497C2semidirect
10. #13070451C2semidirect
11. C11×#3415C2semidirect
12. C11×#576C22semidirect
14. #10623300C22semidirect
16. C11×#509C22semidirect
20. C2×C11×D16C22semidirect
21. C11×#504C22semidirect
25. #10622809C22semidirect
26. #10622806C22semidirect
27. #10622773C22semidirect
28. #10622764C22semidirect
29. C2×#66890C22semidirect
31. #10622755C22semidirect
35. C2×D176C22semidirect
36. #10622514C22semidirect
37. #10622205C22semidirect
38. #10622201C22semidirect
39. #10622199C22semidirect
40. #10622154C22semidirect
41. #10622153C22semidirect
42. #10622149C22semidirect
43. #10622144C22semidirect
44. C16×Dic11C22semidirect
70. C11×Q32D4semidirect
72. C11×SD32D4semidirect
76. C11×D16D4semidirect
154. #3415D11semidirect
202. #576C2×D11semidirect
206. #509C2×D11semidirect
214. C2×D16C2×D11semidirect
216. #504C2×D11semidirect
274. Q32C22⋊D11semidirect
277. SD32C22⋊D11semidirect
285. D16C22⋊D11semidirect
363. C11#33858semidirect

Maximal subgroups

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

subgroupindex
#130817542
#130804132
#130708642
#130707362
#130707332
#130706902
#130705732
#130705702
#130704972
#130704512
C11×#34152
#3385811