Finite Group Databasebeta

← C11×#11945 #14589138

Subgroups — C11×#11945 #14589138

Order 2816.

312 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3168C211yesmaximal, characteristic
2C11×#2163C211yesmaximal, characteristic, complemented
3C2×C11×#334C211yesmaximal, characteristic, complemented
4C11×#1363C212yesmaximal, complemented
5C11×#1360C212yesmaximal, complemented
6C11×#529—21no—
7C11×#499C2211yescharacteristic
8C11×#495C2211yescharacteristic
9C11×#488—21no—
10C11×#467C411yescharacteristic
11C11×#466C411yescharacteristic
12C11×#465—21no—
13C4×C11×Q16C411yescharacteristic
14C4×C11×SD16—21no—
15C4×C11×D8C411yescharacteristic
16C2×C11×C4⋊C8—21no—
17C2×C4×C8×C11C2211yescharacteristic
18C11×C4⋊C16C2212yes—
19C11×C22⋊C16—21no—
20C11×#346—21no—
21C11×#334—21no—
22C11×#334C2212yes—
23C2×C11×Q16C2×C411yescharacteristic
24C2×C11×SD16—21no—
25C2×C11×D8C2×C411yescharacteristic
26C22×C8×C11—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
40C2×C11×C16—22no—
41C11×#107C2×C411yescharacteristic
42C11×#107C2×C411yescharacteristic
43C11×#106—21no—
44C11×C4⋊C8—22no—
45C11×C4⋊C8—41no—
46C11×#103—21no—
47C11×#103—21no—
48C11×#102—21no—
49C11×#102—21no—
50C4×C8×C11C2×C411yescharacteristic
51C4×C8×C11D411yescharacteristic
52C4×C8×C11D411yescharacteristic
53C4×C8×C11C2311yescharacteristic
54#11945C1111yesmaximal, characteristic, direct product factor, Sylow
55C2×Q8×C11—21no—
56C2×D4×C11—21no—
57C2×D4×C11—41no—
58C22×C4×C11—41no—
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11D811yescharacteristic
61C22×C4×C11SD1611yescharacteristic
62C11×Q16—41no—
63C11×SD16—42no—
64C11×D8—41no—
65C2×C8×C11—22no—
66C2×C8×C11—41no—
67C2×C8×C11—42no—
68C2×C8×C11—82no—
69C2×C8×C11C22⋊C411yescharacteristic
70C2×C8×C11C22⋊C411yescharacteristic
71C2×C8×C11C22×C411yescharacteristic
72C2×C8×C11C2×D411yescharacteristic
73C11×C4⋊C4—21no—
74C11×C4⋊C4—21no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C22⋊C4—41no—
80C11×C22⋊C4—41no—
81C11×C22⋊C4—41no—
82C11×C22⋊C4—41no—
83C11×C22⋊C4—41no—
84C42×C11—41no—
85C42×C11C22⋊C411yescharacteristic
86C42×C11D811yescharacteristic
87C42×C11SD1611yescharacteristic
88C42×C11C2×D411yescharacteristic
89C11×C16—42no—
90#3168C2×C1111yescharacteristic
91#2163C2×C1111yescharacteristic, complemented
92C2×#334C2×C1111yescharacteristic, complemented
93#1363C2×C1112yescomplemented
94#1360C2×C1112yescomplemented
95C23×C11—41no—
96C23×C11#10211yescharacteristic
97Q8×C11—41no—
98Q8×C11—41no—
99D4×C11—41no—
100D4×C11—41no—
101D4×C11—82no—
102C2×C4×C11—22no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11—41no—
109C2×C4×C11—82no—
110C2×C4×C11#10211yescharacteristic
111C2×C4×C11#10211yescharacteristic
112C2×C4×C11#10211yescharacteristic
113C2×C4×C11C2×C22⋊C411yescharacteristic
114C2×C4×C11C2×D811yescharacteristic
115C2×C4×C11C2×SD1611yescharacteristic
116C8×C11—21no—
117C8×C11—21no—
118C8×C11—21no—
119C8×C11—82no—
120C8×C11#13512yes—
121#529—21no—
122#499C22×C1111yescharacteristic
123#495C22×C1111yescharacteristic
124#488—21no—
125#467C4×C1111yescharacteristic
126#466C4×C1111yescharacteristic
127#465—21no—
128C4×Q16C4×C1111yescharacteristic
129C4×SD16—21no—
130C4×D8C4×C1111yescharacteristic
131C2×C4⋊C8—21no—
132C2×C4×C8C22×C1111yescharacteristic
133C4⋊C16C22×C1112yes—
134C22⋊C16—21no—
135#346—21no—
136#334—21no—
137#334C22×C1112yes—
138C22×C11—21no—
139C22×C11—21no—
140C22×C11—81no—
141C22×C11—81no—
142C22×C11—81no—
143C22×C11#36012yes—
144C22×C11C2×#10211yescharacteristic
145C4×C11—21no—
146C4×C11—21no—
147C4×C11—21no—
148C4×C11—21no—
149C4×C11—21no—
150C4×C11—81no—
151C4×C11—81no—
152C4×C11—81no—
153C4×C11#41311yescharacteristic
154C4×C11#41611yescharacteristic
155C2×Q16C2×C4×C1111yescharacteristic
156C2×SD16—21no—
157C2×D8C2×C4×C1111yescharacteristic
158C22×C8—41no—
159C22×C8C2×C4×C1111yescharacteristic
160C22×C8D4×C1111yescharacteristic
161#126—41no—
162#125—21no—
163#124—21no—
164#123—41no—
165C22⋊Q8—21no—
166#121—21no—
167C4×Q8—21no—
168C4×D4—21no—
169C4×D4—41no—
170#117—41no—
171C2×C42D4×C1111yescharacteristic
172C2×C16—22no—
173#107C2×C4×C1111yescharacteristic
174#107C2×C4×C1111yescharacteristic
175#106—21no—
176C4⋊C8—22no—
177C4⋊C8—41no—
178#103—21no—
179#103—21no—
180#102—21no—
181#102—21no—
182C4×C8C2×C4×C1111yescharacteristic
183C4×C8D4×C1111yescharacteristic
184C4×C8D4×C1111yescharacteristic
185C4×C8C23×C1111yescharacteristic
186C2×C11—22no—
187C2×C11—161no—
188C2×C11#154011yescharacteristic
189C2×C11#214311yescharacteristic
190C2×C11C2×#36011yescharacteristic
191C2×Q8—21no—
192C2×D4—21no—
193C2×D4—41no—
194C22×C4—41no—
195C22×C4C11×C22⋊C411yescharacteristic
196C22×C4C11×D811yescharacteristic
197C22×C4C11×SD1611yescharacteristic
198Q16—41no—
199SD16—42no—
200D8—41no—
201C2×C8—22no—
202C2×C8—41no—
203C2×C8—42no—
204C2×C8—82no—
205C2×C8C11×C22⋊C411yescharacteristic
206C2×C8C11×C22⋊C411yescharacteristic
207C2×C8C22×C4×C1111yescharacteristic
208C2×C8C2×D4×C1111yescharacteristic
209C4⋊C4—21no—
210C4⋊C4—21no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C22⋊C4—41no—
216C22⋊C4—41no—
217C22⋊C4—41no—
218C22⋊C4—41no—
219C22⋊C4—41no—
220C42—41no—
221C42C11×C22⋊C411yescharacteristic
222C42C11×D811yescharacteristic
223C42C11×SD1611yescharacteristic
224C42C2×D4×C1111yescharacteristic
225C16—42no—
226C11#1194511yescharacteristic, direct product factor, Sylow
227C23—41no—
228C23C11×#10211yescharacteristic
229Q8—41no—
230Q8—41no—
231D4—41no—
232D4—41no—
233D4—82no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—82no—
242C2×C4C11×#10211yescharacteristic
243C2×C4C11×#10211yescharacteristic
244C2×C4C11×#10211yescharacteristic
245C2×C4C2×C11×C22⋊C411yescharacteristic
246C2×C4C2×C11×D811yescharacteristic
247C2×C4C2×C11×SD1611yescharacteristic
248C8—21no—
249C8—21no—
250C8—21no—
251C8—82no—
252C8C11×#13512yes—
253C22—21no—
254C22—21no—
255C22—81no—
256C22—81no—
257C22—81no—
258C22C11×#36012yes—
259C22C2×C11×#10211yescharacteristic
260C4—21no—
261C4—21no—
262C4—21no—
263C4—21no—
264C4—21no—
265C4—81no—
266C4—81no—
267C4—81no—
268C4C11×#41311yescharacteristic
269C4C11×#41611yescharacteristic
270C2—22no—
271C2—161no—
272C2C11×#154011yescharacteristic
273C2C11×#214311yescharacteristic
274C2C2×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×#2163C2semidirect
3. C2×C11×#334C2semidirect
4. C11×#1363C2semidirect
5. C11×#1360C2semidirect
54. #11945C11direct (N × H)
91. #2163C2×C11semidirect
92. C2×#334C2×C11semidirect
93. #1363C2×C11semidirect
94. #1360C2×C11semidirect
226. C11#11945direct (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×#21632
C2×C11×#3342
C11×#13632
C11×#13602
#1194511