Finite Group Databasebeta

← C11×#11946 #14589139

Subgroups — C11×#11946 #14589139

Order 2816.

302 conjugacy classes of subgroups.

The subgroup lattice has 274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3168C211yesmaximal, characteristic
2C11×#2163C211yesmaximal, characteristic, complemented
3C11×#1564C211yesmaximal, 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
16C11×#431—21no—
17C2×C4×C8×C11C2211yescharacteristic
18C11×C4⋊C16C2212yes—
19C11×C22⋊C16—21no—
20C11×#346—21no—
21C11×#335—21no—
22C11×#334C2212yes—
23C2×C11×Q16C2×C411yescharacteristic
24C2×C11×SD16—21no—
25C2×C11×D8C2×C411yescharacteristic
26C22×C8×C11C2×C411yescharacteristic
27C22×C8×C11D411yescharacteristic
28C11×#126—41no—
29C11×#125—21no—
30C11×#124—21no—
31C11×#123—41no—
32C11×C22⋊Q8—21no—
33C11×#121—21no—
34C4×Q8×C11—21no—
35C4×D4×C11—21no—
36C4×D4×C11—41no—
37C11×#117—41no—
38C2×C42×C11D411yescharacteristic
39C2×C11×C16—22no—
40C11×#107C2×C411yescharacteristic
41C11×#107C2×C411yescharacteristic
42C11×#106—21no—
43C11×C4⋊C8—22no—
44C11×#103—21no—
45C11×#103—21no—
46C11×#102—21no—
47C11×#102—21no—
48C11×C22⋊C8—41no—
49C4×C8×C11—41no—
50C4×C8×C11C2×C411yescharacteristic
51C4×C8×C11D411yescharacteristic
52C4×C8×C11D411yescharacteristic
53C4×C8×C11C2311yescharacteristic
54#11946C1111yesmaximal, 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×C11C22⋊C411yescharacteristic
69C2×C8×C11C22⋊C411yescharacteristic
70C2×C8×C11C22×C411yescharacteristic
71C2×C8×C11C2×D411yescharacteristic
72C11×C4⋊C4—21no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C22⋊C4—41no—
79C11×C22⋊C4—41no—
80C11×C22⋊C4—41no—
81C11×C22⋊C4—41no—
82C11×C22⋊C4—41no—
83C42×C11—41no—
84C42×C11C22⋊C411yescharacteristic
85C42×C11D811yescharacteristic
86C42×C11SD1611yescharacteristic
87C42×C11C2×D411yescharacteristic
88C11×C16—42no—
89#3168C2×C1111yescharacteristic
90#2163C2×C1111yescharacteristic, complemented
91#1564C2×C1111yescharacteristic, complemented
92#1363C2×C1112yescomplemented
93#1360C2×C1112yescomplemented
94C23×C11—41no—
95C23×C11#10211yescharacteristic
96Q8×C11—41no—
97Q8×C11—41no—
98D4×C11—41no—
99D4×C11—41no—
100D4×C11—82no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—41no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11—82no—
109C2×C4×C11#10211yescharacteristic
110C2×C4×C11#10211yescharacteristic
111C2×C4×C11#10211yescharacteristic
112C2×C4×C11C2×C22⋊C411yescharacteristic
113C2×C4×C11C2×D811yescharacteristic
114C2×C4×C11C2×SD1611yescharacteristic
115C8×C11—21no—
116C8×C11—21no—
117C8×C11—21no—
118C8×C11—82no—
119C8×C11#13512yes—
120#529—21no—
121#499C22×C1111yescharacteristic
122#495C22×C1111yescharacteristic
123#488—21no—
124#467C4×C1111yescharacteristic
125#466C4×C1111yescharacteristic
126#465—21no—
127C4×Q16C4×C1111yescharacteristic
128C4×SD16—21no—
129C4×D8C4×C1111yescharacteristic
130#431—21no—
131C2×C4×C8C22×C1111yescharacteristic
132C4⋊C16C22×C1112yes—
133C22⋊C16—21no—
134#346—21no—
135#335—21no—
136#334C22×C1112yes—
137C22×C11—21no—
138C22×C11—21no—
139C22×C11—21no—
140C22×C11—81no—
141C22×C11—81no—
142C22×C11—81no—
143C22×C11C2×#10211yescharacteristic
144C4×C11—21no—
145C4×C11—21no—
146C4×C11—21no—
147C4×C11—21no—
148C4×C11—21no—
149C4×C11—81no—
150C4×C11—81no—
151C4×C11—81no—
152C4×C11#41311yescharacteristic
153C4×C11#41611yescharacteristic
154C2×Q16C2×C4×C1111yescharacteristic
155C2×SD16—21no—
156C2×D8C2×C4×C1111yescharacteristic
157C22×C8C2×C4×C1111yescharacteristic
158C22×C8D4×C1111yescharacteristic
159#126—41no—
160#125—21no—
161#124—21no—
162#123—41no—
163C22⋊Q8—21no—
164#121—21no—
165C4×Q8—21no—
166C4×D4—21no—
167C4×D4—41no—
168#117—41no—
169C2×C42D4×C1111yescharacteristic
170C2×C16—22no—
171#107C2×C4×C1111yescharacteristic
172#107C2×C4×C1111yescharacteristic
173#106—21no—
174C4⋊C8—22no—
175#103—21no—
176#103—21no—
177#102—21no—
178#102—21no—
179C22⋊C8—41no—
180C4×C8—41no—
181C4×C8C2×C4×C1111yescharacteristic
182C4×C8D4×C1111yescharacteristic
183C4×C8D4×C1111yescharacteristic
184C4×C8C23×C1111yescharacteristic
185C2×C11—41no—
186C2×C11—161no—
187C2×C11#154011yescharacteristic
188C2×C11#214311yescharacteristic
189C2×C11#214511yescharacteristic
190C2×Q8—21no—
191C2×D4—21no—
192C2×D4—41no—
193C22×C4—41no—
194C22×C4C11×C22⋊C411yescharacteristic
195C22×C4C11×D811yescharacteristic
196C22×C4C11×SD1611yescharacteristic
197Q16—41no—
198SD16—42no—
199D8—41no—
200C2×C8—22no—
201C2×C8—41no—
202C2×C8—42no—
203C2×C8C11×C22⋊C411yescharacteristic
204C2×C8C11×C22⋊C411yescharacteristic
205C2×C8C22×C4×C1111yescharacteristic
206C2×C8C2×D4×C1111yescharacteristic
207C4⋊C4—21no—
208C4⋊C4—21no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C22⋊C4—41no—
214C22⋊C4—41no—
215C22⋊C4—41no—
216C22⋊C4—41no—
217C22⋊C4—41no—
218C42—41no—
219C42C11×C22⋊C411yescharacteristic
220C42C11×D811yescharacteristic
221C42C11×SD1611yescharacteristic
222C42C2×D4×C1111yescharacteristic
223C16—42no—
224C11#1194611yescharacteristic, direct product factor, Sylow
225C23—41no—
226C23C11×#10211yescharacteristic
227Q8—41no—
228Q8—41no—
229D4—41no—
230D4—41no—
231D4—82no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—82no—
240C2×C4C11×#10211yescharacteristic
241C2×C4C11×#10211yescharacteristic
242C2×C4C11×#10211yescharacteristic
243C2×C4C2×C11×C22⋊C411yescharacteristic
244C2×C4C2×C11×D811yescharacteristic
245C2×C4C2×C11×SD1611yescharacteristic
246C8—21no—
247C8—21no—
248C8—21no—
249C8—82no—
250C8C11×#13512yes—
251C22—21no—
252C22—21no—
253C22—21no—
254C22—81no—
255C22—81no—
256C22—81no—
257C22C2×C11×#10211yescharacteristic
258C4—21no—
259C4—21no—
260C4—21no—
261C4—21no—
262C4—21no—
263C4—81no—
264C4—81no—
265C4—81no—
266C4C11×#41311yescharacteristic
267C4C11×#41611yescharacteristic
268C2—41no—
269C2—161no—
270C2C11×#154011yescharacteristic
271C2C11×#214311yescharacteristic
272C2C11×#214511yescharacteristic
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. C11×#1564C2semidirect
4. C11×#1363C2semidirect
5. C11×#1360C2semidirect
54. #11946C11direct (N × H)
90. #2163C2×C11semidirect
91. #1564C2×C11semidirect
92. #1363C2×C11semidirect
93. #1360C2×C11semidirect
224. C11#11946direct (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
C11×#15642
C11×#13632
C11×#13602
#1194611