Finite Group Databasebeta

← C11×#11980 #14589173

Subgroups — C11×#11980 #14589173

Order 2816.

314 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3168C211yesmaximal, characteristic
2C11×#2150C211yesmaximal, characteristic, complemented
3C11×#1566C211yesmaximal, characteristic, complemented
4C11×#1363C212yesmaximal, complemented
5C11×#1360C212yesmaximal, complemented
6C11×#529—21no—
7C2×C11×M32—21no—
8C11×#499C2211yescharacteristic
9C11×#495C2211yescharacteristic
10C11×#488—21no—
11C11×#467C411yescharacteristic
12C11×#466C411yescharacteristic
13C11×#465—21no—
14C4×C11×Q16C411yescharacteristic
15C4×C11×SD16—21no—
16C4×C11×D8C411yescharacteristic
17C11×#423—21no—
18C2×C4×C8×C11C2211yescharacteristic
19C11×C4⋊C16—21no—
20C11×C4⋊C16C2212yes—
21C11×#334—21no—
22C11×#334C2212yes—
23C2×C11×Q16C2×C411yescharacteristic
24C2×C11×SD16—21no—
25C2×C11×D8C2×C411yescharacteristic
26C2×C11×M16—41no—
27C22×C8×C11C2×C411yescharacteristic
28C22×C8×C11D411yescharacteristic
29C11×#126—41no—
30C11×#125—21no—
31C11×#124—21no—
32C11×#123—41no—
33C11×C22⋊Q8—21no—
34C11×#121—21no—
35C4×Q8×C11—21no—
36C4×D4×C11—21no—
37C4×D4×C11—41no—
38C11×#117—41no—
39C2×C42×C11D411yescharacteristic
40C11×M32—42no—
41C2×C11×C16—22no—
42C11×#107C2×C411yescharacteristic
43C11×#107C2×C411yescharacteristic
44C11×#106—21no—
45C11×C4⋊C8—22no—
46C11×C4⋊C8—41no—
47C11×#103—21no—
48C11×#103—21no—
49C11×#102—21no—
50C11×#102—21no—
51C4×C8×C11C2×C411yescharacteristic
52C4×C8×C11D411yescharacteristic
53C4×C8×C11D411yescharacteristic
54C4×C8×C11C2311yescharacteristic
55#11980C1111yesmaximal, characteristic, direct product factor, Sylow
56C2×Q8×C11—21no—
57C2×D4×C11—21no—
58C2×D4×C11—41no—
59C22×C4×C11—41no—
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11D811yescharacteristic
62C22×C4×C11SD1611yescharacteristic
63C11×Q16—41no—
64C11×SD16—41no—
65C11×SD16—41no—
66C11×D8—41no—
67C11×M16—82no—
68C2×C8×C11—21no—
69C2×C8×C11—21no—
70C2×C8×C11—41no—
71C2×C8×C11—42no—
72C2×C8×C11C22⋊C411yescharacteristic
73C2×C8×C11C22⋊C411yescharacteristic
74C2×C8×C11C22×C411yescharacteristic
75C2×C8×C11C2×D411yescharacteristic
76C11×C4⋊C4—21no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C22⋊C4—41no—
83C11×C22⋊C4—41no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—41no—
86C11×C22⋊C4—41no—
87C42×C11—41no—
88C42×C11C22⋊C411yescharacteristic
89C42×C11D811yescharacteristic
90C42×C11SD1611yescharacteristic
91C42×C11C2×D411yescharacteristic
92C11×C16—42no—
93#3168C2×C1111yescharacteristic
94#2150C2×C1111yescharacteristic, complemented
95#1566C2×C1111yescharacteristic, complemented
96#1363C2×C1112yescomplemented
97#1360C2×C1112yescomplemented
98C23×C11—41no—
99C23×C11#10211yescharacteristic
100Q8×C11—41no—
101Q8×C11—41no—
102D4×C11—41no—
103D4×C11—41no—
104D4×C11—82no—
105C2×C4×C11—22no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11—41no—
111C2×C4×C11—41no—
112C2×C4×C11—82no—
113C2×C4×C11#10211yescharacteristic
114C2×C4×C11#10211yescharacteristic
115C2×C4×C11#10211yescharacteristic
116C2×C4×C11C2×C22⋊C411yescharacteristic
117C2×C4×C11C2×D811yescharacteristic
118C2×C4×C11C2×SD1611yescharacteristic
119C8×C11—21no—
120C8×C11—21no—
121C8×C11—21no—
122C8×C11—82no—
123C8×C11AGL(1,ℤ/8)11yescharacteristic
124C8×C11#13711yescharacteristic
125#529—21no—
126C2×M32—21no—
127#499C22×C1111yescharacteristic
128#495C22×C1111yescharacteristic
129#488—21no—
130#467C4×C1111yescharacteristic
131#466C4×C1111yescharacteristic
132#465—21no—
133C4×Q16C4×C1111yescharacteristic
134C4×SD16—21no—
135C4×D8C4×C1111yescharacteristic
136#423—21no—
137C2×C4×C8C22×C1111yescharacteristic
138C4⋊C16—21no—
139C4⋊C16C22×C1112yes—
140#334—21no—
141#334C22×C1112yes—
142C22×C11—21no—
143C22×C11—21no—
144C22×C11—21no—
145C22×C11—81no—
146C22×C11—81no—
147C22×C11—81no—
148C22×C11C2×#10211yescharacteristic
149C4×C11—21no—
150C4×C11—21no—
151C4×C11—21no—
152C4×C11—21no—
153C4×C11—81no—
154C4×C11—81no—
155C4×C11—81no—
156C4×C11#36012yes—
157C4×C11#41311yescharacteristic
158C4×C11#41711yescharacteristic
159C2×Q16C2×C4×C1111yescharacteristic
160C2×SD16—21no—
161C2×D8C2×C4×C1111yescharacteristic
162C2×M16—41no—
163C22×C8C2×C4×C1111yescharacteristic
164C22×C8D4×C1111yescharacteristic
165#126—41no—
166#125—21no—
167#124—21no—
168#123—41no—
169C22⋊Q8—21no—
170#121—21no—
171C4×Q8—21no—
172C4×D4—21no—
173C4×D4—41no—
174#117—41no—
175C2×C42D4×C1111yescharacteristic
176M32—42no—
177C2×C16—22no—
178#107C2×C4×C1111yescharacteristic
179#107C2×C4×C1111yescharacteristic
180#106—21no—
181C4⋊C8—22no—
182C4⋊C8—41no—
183#103—21no—
184#103—21no—
185#102—21no—
186#102—21no—
187C4×C8C2×C4×C1111yescharacteristic
188C4×C8D4×C1111yescharacteristic
189C4×C8D4×C1111yescharacteristic
190C4×C8C23×C1111yescharacteristic
191C2×C11—41no—
192C2×C11—161no—
193C2×C11#154711yescharacteristic
194C2×C11#214311yescharacteristic
195C2×C11C2×#36011yescharacteristic
196C2×Q8—21no—
197C2×D4—21no—
198C2×D4—41no—
199C22×C4—41no—
200C22×C4C11×C22⋊C411yescharacteristic
201C22×C4C11×D811yescharacteristic
202C22×C4C11×SD1611yescharacteristic
203Q16—41no—
204SD16—41no—
205SD16—41no—
206D8—41no—
207M16—82no—
208C2×C8—21no—
209C2×C8—21no—
210C2×C8—41no—
211C2×C8—42no—
212C2×C8C11×C22⋊C411yescharacteristic
213C2×C8C11×C22⋊C411yescharacteristic
214C2×C8C22×C4×C1111yescharacteristic
215C2×C8C2×D4×C1111yescharacteristic
216C4⋊C4—21no—
217C4⋊C4—21no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C22⋊C4—41no—
223C22⋊C4—41no—
224C22⋊C4—41no—
225C22⋊C4—41no—
226C22⋊C4—41no—
227C42—41no—
228C42C11×C22⋊C411yescharacteristic
229C42C11×D811yescharacteristic
230C42C11×SD1611yescharacteristic
231C42C2×D4×C1111yescharacteristic
232C16—42no—
233C11#1198011yescharacteristic, direct product factor, Sylow
234C23—41no—
235C23C11×#10211yescharacteristic
236Q8—41no—
237Q8—41no—
238D4—41no—
239D4—41no—
240D4—82no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—82no—
249C2×C4C11×#10211yescharacteristic
250C2×C4C11×#10211yescharacteristic
251C2×C4C11×#10211yescharacteristic
252C2×C4C2×C11×C22⋊C411yescharacteristic
253C2×C4C2×C11×D811yescharacteristic
254C2×C4C2×C11×SD1611yescharacteristic
255C8—21no—
256C8—21no—
257C8—21no—
258C8—82no—
259C8C11×AGL(1,ℤ/8)11yescharacteristic
260C8C11×#13711yescharacteristic
261C22—21no—
262C22—21no—
263C22—21no—
264C22—81no—
265C22—81no—
266C22—81no—
267C22C2×C11×#10211yescharacteristic
268C4—21no—
269C4—21no—
270C4—21no—
271C4—21no—
272C4—81no—
273C4—81no—
274C4—81no—
275C4C11×#36012yes—
276C4C11×#41311yescharacteristic
277C4C11×#41711yescharacteristic
278C2—41no—
279C2—161no—
280C2C11×#154711yescharacteristic
281C2C11×#214311yescharacteristic
282C2C2×C11×#36011yescharacteristic
subgroupG/H
center, socleC22×C11C2×#102
commutatorC2×C8C22×C4×C11
Frattini, cosocleC4×C8C23×C11
prime radicalC11×#466C4
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2150C2semidirect
3. C11×#1566C2semidirect
4. C11×#1363C2semidirect
5. C11×#1360C2semidirect
55. #11980C11direct (N × H)
94. #2150C2×C11semidirect
95. #1566C2×C11semidirect
96. #1363C2×C11semidirect
97. #1360C2×C11semidirect
233. C11#11980direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31682
C11×#21502
C11×#15662
C11×#13632
C11×#13602
#1198011