Finite Group Databasebeta

← C11×#33656 #14610849

Subgroups — C11×#33656 #14610849

Order 2816.

556 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3054C211yesmaximal, characteristic
2C2×C11×#430C211yesmaximal, characteristic, complemented
3C11×#2239C214yesmaximal, complemented
4C11×#2238C214yesmaximal, complemented
5C11×#2155C212yesmaximal, complemented
6C11×#2148C212yesmaximal, complemented
7C2×C11×#349C211yesmaximal, characteristic, complemented
8C2×C11×#135C2211yescharacteristic
9C22×C11×M16—21no—
10C22×C11×M16C2211yescharacteristic
11C11×#525—21no—
12C2×C11×M32C2212yes—
13C11×#470C2212yes—
14C11×#469C2212yes—
15C11×#468—22no—
16C11×#430—22no—
17C11×#430C2214yes—
18C2×C11×#108—21no—
19C2×C11×#108C2212yes—
20C11×#427C2211yescharacteristic
21C11×#416—21no—
22C11×#365C2218yescomplemented
23C11×#362C2214yescomplemented
24C11×#361C2214yescomplemented
25C11×#349C2214yes—
26C2×C11×#41—21no—
27C23×C4×C11D411yescharacteristic
28C11×#135—22no—
29C11×#135—22no—
30C2×C11×Q16C2311yescharacteristic
31C2×C11×SD16—21no—
32C2×C11×D8C2311yescharacteristic
33C2×C11×M16—22no—
34C2×C11×M16—22no—
35C2×C11×M16—24no—
36C2×C11×M16—22no—
37C2×C11×M16—42no—
38C2×C11×M16—41no—
39C2×C11×M16D412yes—
40C2×C11×M16C2312yes—
41C22×C8×C11—41no—
42C22×C8×C11D411yescharacteristic
43C22×C8×C11C2311yescharacteristic
44C11×#123—41no—
45C11×C22⋊Q8—22no—
46C11×#121—22no—
47C11×#120—41no—
48C4×D4×C11—42no—
49C11×#117—21no—
50C11×M32—22no—
51C11×M32C2314yes—
52C2×C11×C16—22no—
53C11×#108—24no—
54C11×#108—22no—
55C11×#108C2314yes—
56C11×#107—21no—
57C11×#106C2312yes—
58C11×#103—22no—
59C11×#102—22no—
60#33656C1111yesmaximal, characteristic, direct product factor, Sylow
61C24×C11SD1611yescharacteristic
62C11×#41—41no—
63C11×#41—41no—
64C11×#41—41no—
65C11×#41—41no—
66C2×Q8×C11—21no—
67C2×D4×C11—21no—
68C2×D4×C11—42no—
69C2×D4×C11—41no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—41no—
75C22×C4×C11SD1612yes—
76C22×C4×C11SD1611yescharacteristic
77C22×C4×C11C2×D412yes—
78C22×C4×C11C2×D411yescharacteristic
79C11×Q16—22no—
80C11×SD16—42no—
81C11×D8—22no—
82C11×M16—24no—
83C11×M16—24no—
84C11×M16—24no—
85C11×M16—44no—
86C11×M16—42no—
87C2×C8×C11—21no—
88C2×C8×C11—21no—
89C2×C8×C11—44no—
90C2×C8×C11—42no—
91C2×C8×C11C2×D412yes—
92C2×C8×C11C2×D411yescharacteristic
93C2×C8×C11#4112yes—
94C2×C8×C11#4112yes—
95C2×C8×C11C2411yescharacteristic
96C11×C4⋊C4—22no—
97C11×C4⋊C4—42no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—42no—
100C11×C22⋊C4—42no—
101C42×C11—41no—
102C11×C16—24no—
103#3054C2×C1111yescharacteristic
104C2×#430C2×C1111yescharacteristic, complemented
105#2239C2×C1114yescomplemented
106#2238C2×C1114yescomplemented
107#2155C2×C1112yescomplemented
108#2148C2×C1112yescomplemented
109C2×#349C2×C1111yescharacteristic, complemented
110C23×C11—21no—
111C23×C11—21no—
112C23×C11—41no—
113C23×C11—81no—
114C23×C11C2×SD1612yes—
115C23×C11C2×SD1611yescharacteristic
116Q8×C11—41no—
117Q8×C11—41no—
118D4×C11—41no—
119D4×C11—41no—
120D4×C11—84no—
121D4×C11—81no—
122D4×C11—81no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—42no—
130C2×C4×C11—41no—
131C2×C4×C11—81no—
132C2×C4×C11—81no—
133C2×C4×C11#12311yescharacteristic
134C2×C4×C11#12311yescharacteristic
135C2×C4×C11C2×SD1612yes—
136C2×C4×C11C2×SD1611yescharacteristic
137C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C11C22×D411yescharacteristic
140C8×C11—22no—
141C8×C11—44no—
142C8×C11#12312yes—
143C8×C11C2×#4112yes—
144C2×#135C22×C1111yescharacteristic
145C22×M16—21no—
146C22×M16C22×C1111yescharacteristic
147#525—21no—
148C2×M32C22×C1112yes—
149#470C22×C1112yes—
150#469C22×C1112yes—
151#468—22no—
152#430—22no—
153#430C22×C1114yes—
154C2×#108—21no—
155C2×#108C22×C1112yes—
156#427C22×C1111yescharacteristic
157#416—21no—
158#365C22×C1118yescomplemented
159#362C22×C1114yescomplemented
160#361C22×C1114yescomplemented
161#349C22×C1114yes—
162C22×C11—22no—
163C22×C11—41no—
164C22×C11—42no—
165C22×C11—42no—
166C22×C11—81no—
167C22×C11—82no—
168C22×C11—81no—
169C22×C11#48111yescharacteristic
170C22×C11#48111yescharacteristic
171C22×C11C22×SD1611yescharacteristic
172C4×C11—22no—
173C4×C11—82no—
174C4×C11—81no—
175C4×C11#48111yescharacteristic
176C4×C11#48111yescharacteristic
177C4×C11C2×#12311yescharacteristic
178C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
179C2×#41—21no—
180C23×C4D4×C1111yescharacteristic
181#135—22no—
182#135—22no—
183C2×Q16C23×C1111yescharacteristic
184C2×SD16—21no—
185C2×D8C23×C1111yescharacteristic
186C2×M16—22no—
187C2×M16—22no—
188C2×M16—22no—
189C2×M16—24no—
190C2×M16—42no—
191C2×M16—41no—
192C2×M16D4×C1112yes—
193C2×M16C23×C1112yes—
194C22×C8—41no—
195C22×C8D4×C1111yescharacteristic
196C22×C8C23×C1111yescharacteristic
197#123—41no—
198C22⋊Q8—22no—
199#121—22no—
200#120—41no—
201C4×D4—42no—
202#117—21no—
203M32—22no—
204M32C23×C1114yes—
205C2×C16—22no—
206#108—24no—
207#108—22no—
208#108C23×C1114yes—
209#107—21no—
210#106C23×C1112yes—
211#103—22no—
212#102—22no—
213C2×C11—21no—
214C2×C11—21no—
215C2×C11—21no—
216C2×C11—42no—
217C2×C11—161no—
218C2×C11C2×#48111yescharacteristic
219C24C11×SD1611yescharacteristic
220#41—41no—
221#41—41no—
222#41—41no—
223#41—41no—
224C2×Q8—21no—
225C2×D4—21no—
226C2×D4—42no—
227C2×D4—41no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—41no—
233C22×C4C11×SD1612yes—
234C22×C4C11×SD1611yescharacteristic
235C22×C4C2×D4×C1112yes—
236C22×C4C2×D4×C1111yescharacteristic
237Q16—22no—
238SD16—42no—
239D8—22no—
240M16—24no—
241M16—24no—
242M16—24no—
243M16—44no—
244M16—42no—
245C2×C8—21no—
246C2×C8—21no—
247C2×C8—44no—
248C2×C8—42no—
249C2×C8C2×D4×C1112yes—
250C2×C8C2×D4×C1111yescharacteristic
251C2×C8C11×#4112yes—
252C2×C8C11×#4112yes—
253C2×C8C24×C1111yescharacteristic
254C4⋊C4—22no—
255C4⋊C4—42no—
256C22⋊C4—41no—
257C22⋊C4—42no—
258C22⋊C4—42no—
259C42—41no—
260C16—24no—
261C11#3365611yescharacteristic, direct product factor, Sylow
262C23—21no—
263C23—21no—
264C23—41no—
265C23—81no—
266C23C2×C11×SD1612yes—
267C23C2×C11×SD1611yescharacteristic
268Q8—41no—
269Q8—41no—
270D4—41no—
271D4—41no—
272D4—84no—
273D4—81no—
274D4—81no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—42no—
282C2×C4—41no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4C11×#12311yescharacteristic
286C2×C4C11×#12311yescharacteristic
287C2×C4C2×C11×SD1612yes—
288C2×C4C2×C11×SD1611yescharacteristic
289C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
290C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
291C2×C4C22×D4×C1111yescharacteristic
292C8—22no—
293C8—44no—
294C8C11×#12312yes—
295C8C2×C11×#4112yes—
296C22—22no—
297C22—41no—
298C22—42no—
299C22—42no—
300C22—81no—
301C22—82no—
302C22—81no—
303C22C11×#48111yescharacteristic
304C22C11×#48111yescharacteristic
305C22C22×C11×SD1611yescharacteristic
306C4—22no—
307C4—82no—
308C4—81no—
309C4C11×#48111yescharacteristic
310C4C11×#48111yescharacteristic
311C4C2×C11×#12311yescharacteristic
312C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
313C2—21no—
314C2—21no—
315C2—21no—
316C2—42no—
317C2—161no—
318C2C2×C11×#48111yescharacteristic
subgroupG/H
centerC4×C11#481
commutator, Frattini, cosocleC2×C8C24×C11
socleC2×C11C2×#481
prime radicalC11×#3054C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C11 ◁ C22×C4×C11 ◁ C22×C11×M16 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#430C2semidirect
3. C11×#2239C2semidirect
4. C11×#2238C2semidirect
5. C11×#2155C2semidirect
6. C11×#2148C2semidirect
7. C2×C11×#349C2semidirect
22. C11×#365C22semidirect
23. C11×#362C22semidirect
24. C11×#361C22semidirect
60. #33656C11direct (N × H)
104. C2×#430C2×C11semidirect
105. #2239C2×C11semidirect
106. #2238C2×C11semidirect
107. #2155C2×C11semidirect
108. #2148C2×C11semidirect
109. C2×#349C2×C11semidirect
158. #365C22×C11semidirect
159. #362C22×C11semidirect
160. #361C22×C11semidirect
261. C11#33656direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30542
C2×C11×#4302
C11×#22392
C11×#22382
C11×#21552
C11×#21482
C2×C11×#3492
#3365611