Finite Group Databasebeta

← #14911915

Subgroups — #14911915

Order 2816.

466 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622525C211yesmaximal, characteristic, complemented
2D11×#508C211yesmaximal, characteristic, complemented
3#13070936C211yesmaximal, characteristic, complemented
4#13070933C211yesmaximal, characteristic, complemented
5#13070932C212yesmaximal, complemented
6#13070929C211yesmaximal, characteristic, complemented
7#13070927C212yesmaximal, complemented
8#13070924C212yesmaximal, complemented
9#13070922C212yesmaximal, complemented
10D11×M64C211yesmaximal, characteristic, complemented
11C11×#2263C211yesmaximal, characteristic, complemented
12D11×#135—21no—
13C2×#66965—21no—
14C11×#508C2211yescharacteristic
15C2×C11×D16C2211yescharacteristic, complemented
16#10622807—21no—
17C2×#66891—21no—
18#10622532C2211yescharacteristic, complemented
19D11×Q32C2211yescharacteristic, complemented
20#10622529—21no—
21D11×SD32—21no—
22#10622525—21no—
23#10622525—21no—
24#10622525C2212yes—
25#10622525C2211yescharacteristic, complemented
26#10622525C2212yescomplemented
27D11×D16C2211yescharacteristic, complemented
28C2×Dic88C2211yescharacteristic, complemented
29#10622517C2211yescharacteristic
30C2×C16×D11C2211yescharacteristic
31C11×SD64C2212yescomplemented
32C11×D32C2212yescomplemented
33C11×M64C2211yescharacteristic, complemented
34#10622160C2212yescomplemented
35#10622158C2212yescomplemented
36#10622158C2212yescomplemented
37#10622157C2212yescomplemented
38#10622137C2211yescharacteristic, complemented
39Dic176C2212yescomplemented
40#10622087C2212yescomplemented
41#10622085C2212yescomplemented
42D11×C32C2212yescomplemented
43#41×D11—41no—
44C2×#4341—41no—
45C11×#135—21no—
46C2×C11×D8—21no—
47#67003—41no—
48C2×#4324—41no—
49#66972—21no—
50Q16×D11—21no—
51#66969—41no—
52SD16×D11—41no—
53#66965—22no—
54#66965—22no—
55#66965—21no—
56#66965—41no—
57#66965—41no—
58D8×D11—21no—
59C2×Dic44—21no—
60#66957—21no—
61C2×C8×D11D411yescharacteristic
62C11×Q32C2311yescharacteristic
63C11×SD32—21no—
64C11×D16—21no—
65C11×D16C2312yes—
66C11×D16C2311yescharacteristic
67C2×C11×C16C2311yescharacteristic
68#66893—21no—
69#66892—21no—
70#66891—22no—
71#66891—22no—
72#66891—21no—
73#66890—21no—
74C2×C11⋊C16D411yescharacteristic
75Dic88—21no—
76Dic88C2311yescharacteristic
77Dic88C2312yes—
78#66864—21no—
79D176C2311yescharacteristic
80C16×D11D411yescharacteristic
81C16×D11D411yescharacteristic
82C16×D11C2311yescharacteristic
83C16×D11C2311yescharacteristic
84C11×C32C2312yes—
85C11⋊C32C2312yes—
86#33981—111nomaximal, Sylow
87C11×#41—41no—
88C2×D4×C11—41no—
89C2×C22⋊D11—81no—
90C22×Dic11—81no—
91#4343—41no—
92Q8×D11—41no—
93#4341—42no—
94#4341—42no—
95#4341—41no—
96#4341—81no—
97#4341—81no—
98#4341—81no—
99D4×D11—41no—
100D4×D11—81no—
101#4339—41no—
102#4339—81no—
103C2×C4×D11—81no—
104C2×C4×D11D811yescharacteristic
105C2×Dic22—41no—
106C11×Q16—21no—
107C11×SD16—41no—
108C11×D8—21no—
109C11×D8—22no—
110C11×D8—41no—
111C2×C8×C11C2×D411yescharacteristic
112#4326—41no—
113#4325—41no—
114#4324—42no—
115#4324—42no—
116#4324—41no—
117#4323—41no—
118C2×C11⋊C8D811yescharacteristic
119Dic44—21no—
120Dic44—22no—
121Dic44—41no—
122D88—21no—
123#4314—41no—
124C8×D11D811yescharacteristic
125C8×D11D811yescharacteristic
126C8×D11C2×D411yescharacteristic
127C8×D11C2×D411yescharacteristic
128C11×C16C2×D411yescharacteristic
129C11×C16C2411yescharacteristic
130C11⋊C16C2×D411yescharacteristic
131C11⋊C16C2×D411yescharacteristic
132C2×#508—111no—
133C2×#508—111no—
134#2264—111no—
135#2264—112no—
136#2264—111no—
137#2263—111no—
138#2263—112no—
139#2263D1111yescharacteristic, complemented
140#2262—112no—
141#2262—112no—
142C2×M64—111no—
143C23×C11—81no—
144C22×D11—81no—
145C22×D11D1611yescharacteristic
146Q8×C11—41no—
147D4×C11—41no—
148D4×C11—42no—
149D4×C11—81no—
150D4×C11—81no—
151C2×C4×C11—81no—
152C2×C4×C11C2×D811yescharacteristic
153C22⋊D11—81no—
154C22⋊D11—81no—
155C22⋊D11—82no—
156C22⋊D11—82no—
157C22⋊D11—81no—
158C2×Dic11—81no—
159C2×Dic11—81no—
160C2×Dic11—82no—
161C2×Dic11—82no—
162C2×Dic11D1611yescharacteristic
163D44—41no—
164D44—81no—
165C4×D11—81no—
166C4×D11—81no—
167C4×D11—81no—
168C4×D11D1611yescharacteristic
169C4×D11D1611yescharacteristic
170C4×D11C2×D811yescharacteristic
171C4×D11C2×D811yescharacteristic
172Dic22—41no—
173Dic22—42no—
174Dic22—81no—
175Dic22—81no—
176C8×C11C2×D811yescharacteristic
177C8×C11C22×D411yescharacteristic
178C11⋊C8C2×D811yescharacteristic
179C11⋊C8C2×D811yescharacteristic
180C2×#135—221no—
181C2×#135—221no—
182#508—111no—
183#508—112no—
184#508—112no—
185#508—111no—
186#508—111no—
187#508—221no—
188#508—221no—
189#508—221no—
190#508—221no—
191#508C2×D1111yescharacteristic
192C2×Q32—111no—
193C2×Q32—111no—
194C2×SD32—221no—
195C2×SD32—221no—
196C2×D16—111no—
197C2×D16C2×D1111yescharacteristic, complemented
198C22×C16—111no—
199Q64—112no—
200Q64—112no—
201SD64—112no—
202SD64—112no—
203SD64—112no—
204SD64C2×D1112yescomplemented
205D32—112no—
206D32C2×D1112yescomplemented
207M64—111no—
208M64—112no—
209M64C2×D1111yescharacteristic, complemented
210C2×C32—112no—
211C22×C11—81no—
212C22×C11—82no—
213C22×C11—162no—
214C22×C11C2×D1611yescharacteristic
215C2×D11—41no—
216C2×D11—81no—
217C2×D11—162no—
218C2×D11C2×D1611yescharacteristic
219C2×D11C2×D1611yescharacteristic
220C4×C11—81no—
221C4×C11C2×D1611yescharacteristic
222C4×C11C22×D811yescharacteristic
223Dic11—81no—
224Dic11—82no—
225Dic11C2×D1611yescharacteristic
226Dic11C2×D1611yescharacteristic
227C2×#41—441no—
228C2×#41—441no—
229#135—21no—
230#135—222no—
231#135—222no—
232#135—221no—
233#135—221no—
234#135—221no—
235#135—441no—
236#135—441no—
237#135—441no—
238#135—441no—
239C2×Q16—221no—
240C2×Q16—221no—
241C2×SD16—441no—
242C2×SD16—441no—
243C2×D8—21no—
244C2×D8—221no—
245C22×C8—111no—
246Q32—111no—
247Q32—112no—
248Q32—221no—
249Q32—221no—
250Q32C22×D1111yescharacteristic
251SD32—21no—
252SD32—222no—
253SD32—222no—
254SD32—221no—
255SD32—221no—
256SD32—221no—
257D16—21no—
258D16—111no—
259D16—221no—
260D16C22×D1112yes—
261D16C22×D1111yescharacteristic
262C2×C16—111no—
263C2×C16—111no—
264C2×C16—111no—
265C2×C16—111no—
266C2×C16—111no—
267C2×C16C22×D1111yescharacteristic
268C32—112no—
269C32C22×D1112yes—
270C2×C11—21no—
271C2×C11—161no—
272C2×C11—162no—
273C2×C11C22×D1611yescharacteristic
274D11—21no—
275D11—21no—
276D11—161no—
277#41—41no—
278#41—442no—
279#41—442no—
280#41—441no—
281#41—441no—
282#41—441no—
283#41—881no—
284#41—881no—
285#41—881no—
286#41—881no—
287C2×Q8—441no—
288C2×Q8—441no—
289C2×D4—41no—
290C2×D4—441no—
291C2×D4—881no—
292C2×D4—881no—
293C22×C4—111no—
294C22×C4—881no—
295C22×C4—881no—
296Q16—21no—
297Q16—222no—
298Q16—221no—
299Q16—441no—
300Q16—441no—
301SD16—41no—
302SD16—442no—
303SD16—442no—
304SD16—441no—
305SD16—441no—
306SD16—441no—
307D8—22no—
308D8—21no—
309D8—41no—
310D8—221no—
311D8—441no—
312C2×C8—111no—
313C2×C8—111no—
314C2×C8—111no—
315C2×C8—111no—
316C2×C8—111no—
317C2×C8D4×D1111yescharacteristic
318C16—111no—
319C16—111no—
320C16D4×D1111yescharacteristic
321C16C23×D1111yescharacteristic
322C11#3398111yescharacteristic, complemented, Sylow
323C23—81no—
324C23—111no—
325C23—881no—
326Q8—41no—
327Q8—442no—
328Q8—441no—
329Q8—881no—
330Q8—881no—
331D4—42no—
332D4—41no—
333D4—81no—
334D4—81no—
335D4—441no—
336D4—881no—
337D4—881no—
338D4—881no—
339D4—882no—
340D4—882no—
341D4—881no—
342C2×C4—81no—
343C2×C4—111no—
344C2×C4—111no—
345C2×C4—111no—
346C2×C4—111no—
347C2×C4—111no—
348C2×C4—881no—
349C2×C4—881no—
350C2×C4—881no—
351C2×C4—882no—
352C2×C4—882no—
353C2×C4—881no—
354C2×C4—881no—
355C2×C4D8×D1111yescharacteristic
356C8—111no—
357C8—111no—
358C8D8×D1111yescharacteristic
359C8C2×D4×D1111yescharacteristic
360C22—81no—
361C22—82no—
362C22—111no—
363C22—111no—
364C22—162no—
365C22—441no—
366C22—881no—
367C22—1762no—
368C22D11×D1611yescharacteristic
369C4—81no—
370C4—111no—
371C4—111no—
372C4—881no—
373C4—882no—
374C4D11×D1611yescharacteristic
375C4C2×D8×D1111yescharacteristic
376C2—21no—
377C2—162no—
378C2—161no—
379C2—221no—
380C2—221no—
381C2—1761no—
382C2C2×D11×D1611yescharacteristic
subgroupG/H
centerC2C2×D11×D16
commutator, cosocleC11×C16C24
FrattiniC16C23×D11
FittingC11×#2263C2
socleC2×C11C22×D16
hypercenter#2263D11
hypocenterC11#33981
LCSG ▷ C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #2263

Complements

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

NH ≅ G/Ntype
1. C2×#10622525C2semidirect
2. D11×#508C2semidirect
3. #13070936C2semidirect
4. #13070933C2semidirect
5. #13070932C2semidirect
6. #13070929C2semidirect
7. #13070927C2semidirect
8. #13070924C2semidirect
9. #13070922C2semidirect
10. D11×M64C2semidirect
11. C11×#2263C2semidirect
15. C2×C11×D16C22semidirect
18. #10622532C22semidirect
19. D11×Q32C22semidirect
25. #10622525C22semidirect
26. #10622525C22semidirect
27. D11×D16C22semidirect
28. C2×Dic88C22semidirect
31. C11×SD64C22semidirect
32. C11×D32C22semidirect
33. C11×M64C22semidirect
34. #10622160C22semidirect
35. #10622158C22semidirect
36. #10622158C22semidirect
37. #10622157C22semidirect
38. #10622137C22semidirect
39. Dic176C22semidirect
40. #10622087C22semidirect
41. #10622085C22semidirect
42. D11×C32C22semidirect
139. #2263D11semidirect
197. C2×D16C2×D11semidirect
204. SD64C2×D11semidirect
206. D32C2×D11semidirect
209. M64C2×D11semidirect
322. C11#33981semidirect

Maximal subgroups

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

subgroupindex
C2×#106225252
D11×#5082
#130709362
#130709332
#130709322
#130709292
#130709272
#130709242
#130709222
D11×M642
C11×#22632
#3398111