Finite Group Databasebeta

← C11×#11979 #14589172

Subgroups — C11×#11979 #14589172

Order 2816.

306 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3168C211yesmaximal, characteristic
2C11×#2150C211yesmaximal, characteristic, complemented
3C11×#1568C211yesmaximal, 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×#432—21no—
18C2×C4×C8×C11C2211yescharacteristic
19C11×C4⋊C16—21no—
20C11×C4⋊C16C2212yes—
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
39C11×M32—42no—
40C2×C11×C16—22no—
41C11×#107C2×C411yescharacteristic
42C11×#107C2×C411yescharacteristic
43C11×#106—21no—
44C11×C4⋊C8—22no—
45C11×#103—21no—
46C11×#103—21no—
47C11×#102—21no—
48C11×#102—21no—
49C11×C22⋊C8—41no—
50C11×#97—41no—
51C4×C8×C11C2×C411yescharacteristic
52C4×C8×C11D411yescharacteristic
53C4×C8×C11D411yescharacteristic
54C4×C8×C11C2311yescharacteristic
55#11979C1111yesmaximal, 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—
67C2×C8×C11—21no—
68C2×C8×C11—21no—
69C2×C8×C11—41no—
70C2×C8×C11—42no—
71C2×C8×C11C22⋊C411yescharacteristic
72C2×C8×C11C22⋊C411yescharacteristic
73C2×C8×C11C22×C411yescharacteristic
74C2×C8×C11C2×D411yescharacteristic
75C11×C4⋊C4—21no—
76C11×C4⋊C4—21no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C22⋊C4—41no—
82C11×C22⋊C4—41no—
83C11×C22⋊C4—41no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—41no—
86C42×C11—41no—
87C42×C11C22⋊C411yescharacteristic
88C42×C11D811yescharacteristic
89C42×C11SD1611yescharacteristic
90C42×C11C2×D411yescharacteristic
91C11×C16—42no—
92#3168C2×C1111yescharacteristic
93#2150C2×C1111yescharacteristic, complemented
94#1568C2×C1111yescharacteristic, complemented
95#1363C2×C1112yescomplemented
96#1360C2×C1112yescomplemented
97C23×C11—41no—
98C23×C11#10211yescharacteristic
99Q8×C11—41no—
100Q8×C11—41no—
101D4×C11—41no—
102D4×C11—41no—
103D4×C11—82no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11—41no—
111C2×C4×C11—82no—
112C2×C4×C11#10211yescharacteristic
113C2×C4×C11#10211yescharacteristic
114C2×C4×C11#10211yescharacteristic
115C2×C4×C11C2×C22⋊C411yescharacteristic
116C2×C4×C11C2×D811yescharacteristic
117C2×C4×C11C2×SD1611yescharacteristic
118C8×C11—21no—
119C8×C11—21no—
120C8×C11—21no—
121C8×C11—82no—
122C8×C11AGL(1,ℤ/8)11yescharacteristic
123C8×C11#13711yescharacteristic
124#529—21no—
125C2×M32—21no—
126#499C22×C1111yescharacteristic
127#495C22×C1111yescharacteristic
128#488—21no—
129#467C4×C1111yescharacteristic
130#466C4×C1111yescharacteristic
131#465—21no—
132C4×Q16C4×C1111yescharacteristic
133C4×SD16—21no—
134C4×D8C4×C1111yescharacteristic
135#432—21no—
136C2×C4×C8C22×C1111yescharacteristic
137C4⋊C16—21no—
138C4⋊C16C22×C1112yes—
139#335—21no—
140#334C22×C1112yes—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11—21no—
144C22×C11—81no—
145C22×C11—81no—
146C22×C11—81no—
147C22×C11C2×#10211yescharacteristic
148C4×C11—21no—
149C4×C11—21no—
150C4×C11—21no—
151C4×C11—21no—
152C4×C11—21no—
153C4×C11—81no—
154C4×C11—81no—
155C4×C11—81no—
156C4×C11#41311yescharacteristic
157C4×C11#41711yescharacteristic
158C2×Q16C2×C4×C1111yescharacteristic
159C2×SD16—21no—
160C2×D8C2×C4×C1111yescharacteristic
161C22×C8C2×C4×C1111yescharacteristic
162C22×C8D4×C1111yescharacteristic
163#126—41no—
164#125—21no—
165#124—21no—
166#123—41no—
167C22⋊Q8—21no—
168#121—21no—
169C4×Q8—21no—
170C4×D4—21no—
171C4×D4—41no—
172#117—41no—
173C2×C42D4×C1111yescharacteristic
174M32—42no—
175C2×C16—22no—
176#107C2×C4×C1111yescharacteristic
177#107C2×C4×C1111yescharacteristic
178#106—21no—
179C4⋊C8—22no—
180#103—21no—
181#103—21no—
182#102—21no—
183#102—21no—
184C22⋊C8—41no—
185#97—41no—
186C4×C8C2×C4×C1111yescharacteristic
187C4×C8D4×C1111yescharacteristic
188C4×C8D4×C1111yescharacteristic
189C4×C8C23×C1111yescharacteristic
190C2×C11—41no—
191C2×C11—161no—
192C2×C11#154711yescharacteristic
193C2×C11#214311yescharacteristic
194C2×C11#214511yescharacteristic
195C2×Q8—21no—
196C2×D4—21no—
197C2×D4—41no—
198C22×C4—41no—
199C22×C4C11×C22⋊C411yescharacteristic
200C22×C4C11×D811yescharacteristic
201C22×C4C11×SD1611yescharacteristic
202Q16—41no—
203SD16—41no—
204SD16—41no—
205D8—41no—
206C2×C8—21no—
207C2×C8—21no—
208C2×C8—41no—
209C2×C8—42no—
210C2×C8C11×C22⋊C411yescharacteristic
211C2×C8C11×C22⋊C411yescharacteristic
212C2×C8C22×C4×C1111yescharacteristic
213C2×C8C2×D4×C1111yescharacteristic
214C4⋊C4—21no—
215C4⋊C4—21no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C22⋊C4—41no—
221C22⋊C4—41no—
222C22⋊C4—41no—
223C22⋊C4—41no—
224C22⋊C4—41no—
225C42—41no—
226C42C11×C22⋊C411yescharacteristic
227C42C11×D811yescharacteristic
228C42C11×SD1611yescharacteristic
229C42C2×D4×C1111yescharacteristic
230C16—42no—
231C11#1197911yescharacteristic, direct product factor, Sylow
232C23—41no—
233C23C11×#10211yescharacteristic
234Q8—41no—
235Q8—41no—
236D4—41no—
237D4—41no—
238D4—82no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—82no—
247C2×C4C11×#10211yescharacteristic
248C2×C4C11×#10211yescharacteristic
249C2×C4C11×#10211yescharacteristic
250C2×C4C2×C11×C22⋊C411yescharacteristic
251C2×C4C2×C11×D811yescharacteristic
252C2×C4C2×C11×SD1611yescharacteristic
253C8—21no—
254C8—21no—
255C8—21no—
256C8—82no—
257C8C11×AGL(1,ℤ/8)11yescharacteristic
258C8C11×#13711yescharacteristic
259C22—21no—
260C22—21no—
261C22—21no—
262C22—81no—
263C22—81no—
264C22—81no—
265C22C2×C11×#10211yescharacteristic
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—21no—
271C4—81no—
272C4—81no—
273C4—81no—
274C4C11×#41311yescharacteristic
275C4C11×#41711yescharacteristic
276C2—41no—
277C2—161no—
278C2C11×#154711yescharacteristic
279C2C11×#214311yescharacteristic
280C2C11×#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×#2150C2semidirect
3. C11×#1568C2semidirect
4. C11×#1363C2semidirect
5. C11×#1360C2semidirect
55. #11979C11direct (N × H)
93. #2150C2×C11semidirect
94. #1568C2×C11semidirect
95. #1363C2×C11semidirect
96. #1360C2×C11semidirect
231. C11#11979direct (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×#15682
C11×#13632
C11×#13602
#1197911