Finite Group Databasebeta

← C2×C11×#3416 #14639826

Subgroups — C2×C11×#3416 #14639826

Order 2816.

2074 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#578C211yesmaximal, characteristic, complemented
2C2×C11×#576C211yesmaximal, characteristic, complemented
3C11×#3416C2116yesmaximal, direct product factor
4C2×C11×#510C213yesmaximal, complemented
5C2×C11×#509C213yesmaximal, complemented
6C2×C11×#508C213yesmaximal, complemented
7C22×C11×SD32C213yesmaximal, complemented
8C2×C11×#504C211yesmaximal, characteristic, complemented
9C2×C11×2−1+4—21no—
10C2×C11×H(5,𝔽2)—21no—
11C11×#578—24no—
12C11×#578C2218yescomplemented
13C11×#576—24no—
14C11×#576C2218yescomplemented
15C2×C11×#137—23no—
16C2×C11×AGL(1,ℤ/8)—23no—
17C2×C11×#135C2213yes—
18C2×C11×#135C2213yescomplemented
19C22×C11×Q16C2213yescomplemented
20C22×C11×D8C2213yes—
21C2×C11×#131C2211yescharacteristic
22C11×#510C22124yescomplemented
23C11×#509C22124yescomplemented
24C11×#508C22124yescomplemented
25C2×C11×Q32C2213yescomplemented
26C2×C11×SD32C2213yescomplemented
27C2×C11×SD32C2216yescomplemented
28C2×C11×SD32C2211yescharacteristic, complemented
29C2×C11×SD32C22124yescomplemented
30C2×C11×D16C2213yescomplemented
31C11×#504C2218yescomplemented
32C2×C11×M32C2213yescomplemented
33C22×C11×C16C2213yescomplemented
34C11×2−1+4—28no—
35C11×2−1+4—44no—
36C11×H(5,𝔽2)—28no—
37C11×H(5,𝔽2)—44no—
38C2×C11×#41—23no—
39C2×C11×#41—23no—
40C2×C11×#41—41no—
41C2×C11×#41—43no—
42C2×C11×#41D411yescharacteristic
43C22×Q8×C11—23no—
44C22×Q8×C11—41no—
45C22×D4×C11—23no—
46C22×D4×C11—43no—
47C11×#137—224no—
48C11×AGL(1,ℤ/8)—224no—
49C11×#135—26no—
50C11×#135—26no—
51C11×#135C23112yes—
52C11×#135C23112yescomplemented
53C2×C11×Q16—23no—
54C2×C11×Q16—26no—
55C2×C11×Q16C2313yes—
56C2×C11×Q16C2311yescharacteristic
57C2×C11×Q16C23112yescomplemented
58C2×C11×SD16—23no—
59C2×C11×SD16—23no—
60C2×C11×D8—23no—
61C2×C11×D8—26no—
62C2×C11×D8C2311yescharacteristic
63C2×C11×D8C2313yes—
64C2×C11×D8C23112yes—
65C11×#131D414yes—
66C11×#131C2314yes—
67C2×C11×M16D413yes—
68C22×C8×C11C2313yes—
69C11×Q32C23112yescomplemented
70C11×SD32C23112yescomplemented
71C11×SD32C23124yescomplemented
72C11×SD32C2314yescomplemented
73C11×D16C23112yescomplemented
74C11×M32C23112yescomplemented
75C2×C11×C16C2311yescharacteristic
76C2×C11×C16C2313yes—
77C2×C11×C16C23112yescomplemented
78C2×#3416C1111yesmaximal, characteristic, direct product factor, Sylow
79C24×C11—43no—
80C11×#41—212no—
81C11×#41—212no—
82C11×#41—48no—
83C11×#41—424no—
84C11×#41—46no—
85C11×#41—46no—
86C11×#41D814yes—
87C11×#41C2×D414yes—
88C2×Q8×C11—21no—
89C2×Q8×C11—23no—
90C2×Q8×C11—212no—
91C2×Q8×C11—48no—
92C2×Q8×C11—43no—
93C2×Q8×C11—46no—
94C2×Q8×C11D811yescharacteristic
95C2×D4×C11—23no—
96C2×D4×C11—212no—
97C2×D4×C11—21no—
98C2×D4×C11—43no—
99C2×D4×C11—43no—
100C2×D4×C11—424no—
101C2×D4×C11—43no—
102C2×D4×C11—46no—
103C2×D4×C11D813yes—
104C22×C4×C11—43no—
105C22×C4×C11—43no—
106C22×C4×C11—43no—
107C22×C4×C11C2×D413yes—
108C11×Q16—23no—
109C11×Q16—212no—
110C11×Q16—21no—
111C11×Q16C2416yes—
112C11×Q16C2412yes—
113C11×SD16—212no—
114C11×SD16—212no—
115C11×D8—23no—
116C11×D8—212no—
117C11×D8—21no—
118C11×D8C2412yes—
119C11×D8C2416yes—
120C11×M16C2×D4112yes—
121C2×C8×C11C2×D413yes—
122C2×C8×C11C2×D416yes—
123C2×C8×C11C2411yescharacteristic
124C2×C8×C11C2416yes—
125C11×C16C2412yes—
126C11×C16C2416yes—
127C2×#578C2×C1111yescharacteristic, complemented
128C2×#576C2×C1111yescharacteristic, complemented
129#3416C2×C11116yesdirect product factor
130C2×#510C2×C1113yescomplemented
131C2×#509C2×C1113yescomplemented
132C2×#508C2×C1113yescomplemented
133C22×SD32C2×C1113yescomplemented
134C2×#504C2×C1111yescharacteristic, complemented
135C23×C11—41no—
136C23×C11—43no—
137C23×C11—412no—
138C23×C11—166no—
139C23×C11C2×D813yes—
140Q8×C11—22no—
141Q8×C11—26no—
142Q8×C11—412no—
143Q8×C11—43no—
144Q8×C11—41no—
145Q8×C11C2×D814yes—
146D4×C11—26no—
147D4×C11—22no—
148D4×C11—412no—
149D4×C11—412no—
150D4×C11—412no—
151D4×C11—43no—
152D4×C11—41no—
153D4×C11C2×D8112yes—
154C2×C4×C11—412no—
155C2×C4×C11—41no—
156C2×C4×C11—43no—
157C2×C4×C11—412no—
158C2×C4×C11—412no—
159C2×C4×C11C2×D816yes—
160C2×C4×C11C2×D813yes—
161C2×C4×C11C22×D416yes—
162C2×C4×C11C22×D411yescharacteristic
163C8×C11C22×D411yescharacteristic
164C8×C11C22×D416yes—
165C8×C11C2511yescharacteristic
166C2×2−1+4—21no—
167C2×H(5,𝔽2)—21no—
168#578—24no—
169#578C22×C1118yescomplemented
170#576—24no—
171#576C22×C1118yescomplemented
172C2×#137—23no—
173C2×AGL(1,ℤ/8)—23no—
174C2×#135C22×C1113yes—
175C2×#135C22×C1113yescomplemented
176C22×Q16C22×C1113yescomplemented
177C22×D8C22×C1113yes—
178C2×#131C22×C1111yescharacteristic
179#510C22×C11124yescomplemented
180#509C22×C11124yescomplemented
181#508C22×C11124yescomplemented
182C2×Q32C22×C1113yescomplemented
183C2×SD32C22×C1113yescomplemented
184C2×SD32C22×C1116yescomplemented
185C2×SD32C22×C1111yescharacteristic, complemented
186C2×SD32C22×C11124yescomplemented
187C2×D16C22×C1113yescomplemented
188#504C22×C1118yescomplemented
189C2×M32C22×C1113yescomplemented
190C22×C16C22×C1113yescomplemented
191C22×C11—26no—
192C22×C11—42no—
193C22×C11—46no—
194C22×C11—82no—
195C22×C11—86no—
196C22×C11—1612no—
197C22×C11C22×D816yes—
198C22×C11C22×D811yescharacteristic
199C4×C11—42no—
200C4×C11—46no—
201C4×C11C22×D816yes—
202C4×C11C22×D811yescharacteristic
203C4×C11C23×D411yescharacteristic
2042−1+4—28no—
2052−1+4—44no—
206H(5,𝔽2)—28no—
207H(5,𝔽2)—44no—
208C2×#41—23no—
209C2×#41—23no—
210C2×#41—41no—
211C2×#41—43no—
212C2×#41D4×C1111yescharacteristic
213C22×Q8—23no—
214C22×Q8—41no—
215C22×D4—23no—
216C22×D4—43no—
217#137—224no—
218AGL(1,ℤ/8)—224no—
219#135—26no—
220#135—26no—
221#135C23×C11112yes—
222#135C23×C11112yescomplemented
223C2×Q16—23no—
224C2×Q16—26no—
225C2×Q16C23×C1113yes—
226C2×Q16C23×C1111yescharacteristic
227C2×Q16C23×C11112yescomplemented
228C2×SD16—23no—
229C2×SD16—23no—
230C2×D8—23no—
231C2×D8—26no—
232C2×D8C23×C1113yes—
233C2×D8C23×C11112yes—
234C2×D8C23×C1111yescharacteristic
235#131D4×C1114yes—
236#131C23×C1114yes—
237C2×M16D4×C1113yes—
238C22×C8C23×C1113yes—
239Q32C23×C11112yescomplemented
240SD32C23×C11112yescomplemented
241SD32C23×C11124yescomplemented
242SD32C23×C1114yescomplemented
243D16C23×C11112yescomplemented
244M32C23×C11112yescomplemented
245C2×C16C23×C1111yescharacteristic
246C2×C16C23×C1113yes—
247C2×C16C23×C11112yescomplemented
248C2×C11—26no—
249C2×C11—82no—
250C2×C11—86no—
251C2×C11#341612yesdirect product factor
252C2×C11C23×D811yescharacteristic
253C24—43no—
254#41—212no—
255#41—212no—
256#41—48no—
257#41—424no—
258#41—46no—
259#41—46no—
260#41C11×D814yes—
261#41C2×D4×C1114yes—
262C2×Q8—21no—
263C2×Q8—23no—
264C2×Q8—212no—
265C2×Q8—48no—
266C2×Q8—43no—
267C2×Q8—46no—
268C2×Q8C11×D811yescharacteristic
269C2×D4—23no—
270C2×D4—212no—
271C2×D4—21no—
272C2×D4—43no—
273C2×D4—43no—
274C2×D4—424no—
275C2×D4—43no—
276C2×D4—46no—
277C2×D4C11×D813yes—
278C22×C4—43no—
279C22×C4—43no—
280C22×C4—43no—
281C22×C4C2×D4×C1113yes—
282Q16—23no—
283Q16—212no—
284Q16—21no—
285Q16C24×C1116yes—
286Q16C24×C1112yes—
287SD16—212no—
288SD16—212no—
289D8—23no—
290D8—212no—
291D8—21no—
292D8C24×C1112yes—
293D8C24×C1116yes—
294M16C2×D4×C11112yes—
295C2×C8C2×D4×C1113yes—
296C2×C8C2×D4×C1116yes—
297C2×C8C24×C1111yescharacteristic
298C2×C8C24×C1116yes—
299C16C24×C1112yes—
300C16C24×C1116yes—
301C11C2×#341611yescharacteristic, direct product factor, Sylow
302C23—41no—
303C23—43no—
304C23—412no—
305C23—166no—
306C23C2×C11×D813yes—
307Q8—22no—
308Q8—26no—
309Q8—412no—
310Q8—43no—
311Q8—41no—
312Q8C2×C11×D814yes—
313D4—26no—
314D4—22no—
315D4—412no—
316D4—412no—
317D4—412no—
318D4—43no—
319D4—41no—
320D4C2×C11×D8112yes—
321C2×C4—41no—
322C2×C4—43no—
323C2×C4—412no—
324C2×C4—412no—
325C2×C4—412no—
326C2×C4C2×C11×D813yes—
327C2×C4C2×C11×D816yes—
328C2×C4C22×D4×C1111yescharacteristic
329C2×C4C22×D4×C1116yes—
330C8C22×D4×C1111yescharacteristic
331C8C22×D4×C1116yes—
332C8C25×C1111yescharacteristic
333C22—26no—
334C22—42no—
335C22—46no—
336C22—86no—
337C22—82no—
338C22—1612no—
339C22C22×C11×D816yes—
340C22C22×C11×D811yescharacteristic
341C4—42no—
342C4—46no—
343C4C22×C11×D816yes—
344C4C22×C11×D811yescharacteristic
345C4C23×D4×C1111yescharacteristic
346C2—26no—
347C2—86no—
348C2—82no—
349C2C11×#341612yesdirect product factor
350C2C23×C11×D811yescharacteristic
subgroupG/H
center, socleC22×C11C22×D8
commutator, Frattini, cosocleC8C25×C11
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C11×#41 ◁ C2×C11×#131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#578C2semidirect
2. C2×C11×#576C2semidirect
3. C11×#3416C2direct (N × H)
4. C2×C11×#510C2semidirect
5. C2×C11×#509C2semidirect
6. C2×C11×#508C2semidirect
7. C22×C11×SD32C2semidirect
8. C2×C11×#504C2semidirect
12. C11×#578C22semidirect
14. C11×#576C22semidirect
18. C2×C11×#135C22semidirect
19. C22×C11×Q16C22semidirect
22. C11×#510C22semidirect
23. C11×#509C22semidirect
24. C11×#508C22semidirect
25. C2×C11×Q32C22semidirect
26. C2×C11×SD32C22semidirect
27. C2×C11×SD32C22semidirect
28. C2×C11×SD32C22semidirect
29. C2×C11×SD32C22semidirect
30. C2×C11×D16C22semidirect
31. C11×#504C22semidirect
32. C2×C11×M32C22semidirect
33. C22×C11×C16C22semidirect
52. C11×#135C23semidirect
57. C2×C11×Q16C23semidirect
69. C11×Q32C23semidirect
70. C11×SD32C23semidirect
71. C11×SD32C23semidirect
72. C11×SD32C23semidirect
73. C11×D16C23semidirect
74. C11×M32C23semidirect
77. C2×C11×C16C23semidirect
78. C2×#3416C11direct (N × H)
127. C2×#578C2×C11semidirect
128. C2×#576C2×C11semidirect
129. #3416C2×C11direct (N × H)
130. C2×#510C2×C11semidirect
131. C2×#509C2×C11semidirect
132. C2×#508C2×C11semidirect
133. C22×SD32C2×C11semidirect
134. C2×#504C2×C11semidirect
169. #578C22×C11semidirect
171. #576C22×C11semidirect
175. C2×#135C22×C11semidirect
176. C22×Q16C22×C11semidirect
179. #510C22×C11semidirect
180. #509C22×C11semidirect
181. #508C22×C11semidirect
182. C2×Q32C22×C11semidirect
183. C2×SD32C22×C11semidirect
184. C2×SD32C22×C11semidirect
185. C2×SD32C22×C11semidirect
186. C2×SD32C22×C11semidirect
187. C2×D16C22×C11semidirect
188. #504C22×C11semidirect
189. C2×M32C22×C11semidirect
190. C22×C16C22×C11semidirect
222. #135C23×C11semidirect
227. C2×Q16C23×C11semidirect
239. Q32C23×C11semidirect
240. SD32C23×C11semidirect
241. SD32C23×C11semidirect
242. SD32C23×C11semidirect
243. D16C23×C11semidirect
244. M32C23×C11semidirect
247. C2×C16C23×C11semidirect
251. C2×C11#3416direct (N × H)
301. C11C2×#3416direct (N × H)
349. C2C11×#3416direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5782
C2×C11×#5762
C11×#34162
C2×C11×#5102
C2×C11×#5092
C2×C11×#5082
C22×C11×SD322
C2×C11×#5042
C2×#341611