Finite Group Databasebeta

← C11×#13138 #14590331

Subgroups — C11×#13138 #14590331

Order 2816.

354 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
1C2×C11×#365C211yesmaximal, characteristic, complemented
2C2×C11×#361C211yesmaximal, characteristic
3C2×C11×#361C211yesmaximal, characteristic
4C11×#1972C211yesmaximal, characteristic
5C11×#1778C211yesmaximal, characteristic, complemented
6C11×#1383C211yesmaximal, characteristic, complemented
7C11×#1377C211yesmaximal, characteristic, complemented
8C22×C11×D8C2211yescharacteristic
9C2×C11×M32C2211yescharacteristic
10C2×C11×M32C2211yescharacteristic
11C2×C11×#108C2211yescharacteristic
12C2×C11×#108C2211yescharacteristic
13C2×C11×#106C2211yescharacteristic
14C2×C11×#102—21no—
15C4×C11×M16—21no—
16C2×C11×#97C2211yescharacteristic
17C11×#390—21no—
18C11×#365—22no—
19C11×#361—22no—
20C11×#361C414yescomplemented
21C11×#341—21no—
22C22×D4×C11—21no—
23C2×C11×D8—21no—
24C2×C11×D8—21no—
25C2×C11×D8—21no—
26C2×C11×D8—21no—
27C2×C11×D8—21no—
28C2×C11×D8C2×C412yes—
29C2×C11×M16—21no—
30C2×C11×M16—21no—
31C22×C8×C11D411yescharacteristic
32C22×C8×C11C2311yescharacteristic
33C2×C11×C4⋊C4—21no—
34C2×C11×C22⋊C4—42no—
35C2×C42×C11D411yescharacteristic
36C11×M32—21no—
37C11×M32—21no—
38C11×M32—21no—
39C11×M32C2×C412yes—
40C2×C11×C16—21no—
41C2×C11×C16—21no—
42C11×#108—21no—
43C11×#108—21no—
44C11×#108C2×C412yes—
45C11×#108D412yes—
46C11×#106—21no—
47C11×#106—21no—
48C11×#102—42no—
49C11×#97—21no—
50C11×#97—21no—
51C11×#97—41no—
52C4×C8×C11—41no—
53#13138C1111yesmaximal, characteristic, direct product factor, Sylow
54C24×C11—41no—
55C2×D4×C11—22no—
56C2×D4×C11—41no—
57C2×D4×C11—41no—
58C2×D4×C11—41no—
59C2×D4×C11—41no—
60C2×D4×C11—41no—
61C22×C4×C11—41no—
62C22×C4×C11SD1612yes—
63C22×C4×C11C2×D411yescharacteristic
64C11×D8—22no—
65C11×D8—22no—
66C11×D8—41no—
67C11×D8—41no—
68C11×M16—22no—
69C11×M16—22no—
70C11×M16—41no—
71C11×M16—41no—
72C2×C8×C11—21no—
73C2×C8×C11—21no—
74C2×C8×C11—21no—
75C2×C8×C11—41no—
76C2×C8×C11—41no—
77C2×C8×C11C22×C411yescharacteristic
78C2×C8×C11C2×D411yescharacteristic
79C2×C8×C11#4111yescharacteristic
80C2×C8×C11#4111yescharacteristic
81C2×C8×C11#4111yescharacteristic
82C2×C8×C11#4111yescharacteristic
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C22⋊C4—84no—
86C42×C11—21no—
87C42×C11—21no—
88C11×C16—22no—
89C11×C16—41no—
90C2×#365C2×C1111yescharacteristic, complemented
91C2×#361C2×C1111yescharacteristic
92C2×#361C2×C1111yescharacteristic
93#1972C2×C1111yescharacteristic
94#1778C2×C1111yescharacteristic, complemented
95#1383C2×C1111yescharacteristic, complemented
96#1377C2×C1111yescharacteristic, complemented
97C23×C11—42no—
98C23×C11—82no—
99C23×C11—82no—
100C23×C11—81no—
101C23×C11—81no—
102C23×C11C2×SD1611yescharacteristic
103D4×C11—42no—
104D4×C11—42no—
105D4×C11—81no—
106D4×C11—81no—
107C2×C4×C11—22no—
108C2×C4×C11—42no—
109C2×C4×C11—82no—
110C2×C4×C11—81no—
111C2×C4×C11C4×D411yescharacteristic
112C2×C4×C11#12111yescharacteristic
113C2×C4×C11#12311yescharacteristic
114C2×C4×C11#13511yescharacteristic
115C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
116C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
117C8×C11—42no—
118C8×C11—42no—
119C8×C11—41no—
120C8×C11#11711yescharacteristic
121C8×C11C4×D411yescharacteristic
122C8×C11#12411yescharacteristic
123C8×C11#12611yescharacteristic
124C22×D8C22×C1111yescharacteristic
125C2×M32C22×C1111yescharacteristic
126C2×M32C22×C1111yescharacteristic
127C2×#108C22×C1111yescharacteristic
128C2×#108C22×C1111yescharacteristic
129C2×#106C22×C1111yescharacteristic
130C2×#102—21no—
131C4×M16—21no—
132C2×#97C22×C1111yescharacteristic
133#390—21no—
134#365—22no—
135#361—22no—
136#361C4×C1114yescomplemented
137#341—21no—
138C22×C11—22no—
139C22×C11—84no—
140C22×C11—82no—
141C22×C11—161no—
142C22×C11—161no—
143C22×C11—162no—
144C22×C11C4×SD1611yescharacteristic
145C22×C11#46011yescharacteristic
146C22×C11#48111yescharacteristic
147C4×C11—42no—
148C4×C11—161no—
149C4×C11#38811yescharacteristic
150C4×C11#44211yescharacteristic
151C4×C11#46311yescharacteristic
152C4×C11#48211yescharacteristic
153C22×D4—21no—
154C2×D8—21no—
155C2×D8—21no—
156C2×D8—21no—
157C2×D8—21no—
158C2×D8—21no—
159C2×D8C2×C4×C1112yes—
160C2×M16—21no—
161C2×M16—21no—
162C22×C8D4×C1111yescharacteristic
163C22×C8C23×C1111yescharacteristic
164C2×C4⋊C4—21no—
165C2×C22⋊C4—42no—
166C2×C42D4×C1111yescharacteristic
167M32—21no—
168M32—21no—
169M32—21no—
170M32C2×C4×C1112yes—
171C2×C16—21no—
172C2×C16—21no—
173#108—21no—
174#108—21no—
175#108C2×C4×C1112yes—
176#108D4×C1112yes—
177#106—21no—
178#106—21no—
179#102—42no—
180#97—21no—
181#97—21no—
182#97—41no—
183C4×C8—41no—
184C2×C11—21no—
185C2×C11—21no—
186C2×C11—162no—
187C2×C11#192611yescharacteristic
188C2×C11#223812yes—
189C24—41no—
190C2×D4—22no—
191C2×D4—41no—
192C2×D4—41no—
193C2×D4—41no—
194C2×D4—41no—
195C2×D4—41no—
196C22×C4—41no—
197C22×C4C11×SD1612yes—
198C22×C4C2×D4×C1111yescharacteristic
199D8—22no—
200D8—22no—
201D8—41no—
202D8—41no—
203M16—22no—
204M16—22no—
205M16—41no—
206M16—41no—
207C2×C8—21no—
208C2×C8—21no—
209C2×C8—21no—
210C2×C8—41no—
211C2×C8—41no—
212C2×C8C22×C4×C1111yescharacteristic
213C2×C8C2×D4×C1111yescharacteristic
214C2×C8C11×#4111yescharacteristic
215C2×C8C11×#4111yescharacteristic
216C2×C8C11×#4111yescharacteristic
217C2×C8C11×#4111yescharacteristic
218C4⋊C4—41no—
219C4⋊C4—41no—
220C22⋊C4—84no—
221C42—21no—
222C42—21no—
223C16—22no—
224C16—41no—
225C11#1313811yescharacteristic, direct product factor, Sylow
226C23—42no—
227C23—82no—
228C23—82no—
229C23—81no—
230C23—81no—
231C23C2×C11×SD1611yescharacteristic
232D4—42no—
233D4—42no—
234D4—81no—
235D4—81no—
236C2×C4—22no—
237C2×C4—42no—
238C2×C4—82no—
239C2×C4—81no—
240C2×C4C4×D4×C1111yescharacteristic
241C2×C4C11×#12111yescharacteristic
242C2×C4C11×#12311yescharacteristic
243C2×C4C11×#13511yescharacteristic
244C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
245C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
246C8—42no—
247C8—42no—
248C8—41no—
249C8C11×#11711yescharacteristic
250C8C4×D4×C1111yescharacteristic
251C8C11×#12411yescharacteristic
252C8C11×#12611yescharacteristic
253C22—22no—
254C22—84no—
255C22—82no—
256C22—161no—
257C22—161no—
258C22—162no—
259C22C4×C11×SD1611yescharacteristic
260C22C11×#46011yescharacteristic
261C22C11×#48111yescharacteristic
262C4—42no—
263C4—161no—
264C4C11×#38811yescharacteristic
265C4C11×#44211yescharacteristic
266C4C11×#46311yescharacteristic
267C4C11×#48211yescharacteristic
268C2—21no—
269C2—21no—
270C2—162no—
271C2C11×#192611yescharacteristic
272C2C11×#223812yes—
subgroupG/H
center, socleC22×C11#481
commutatorC2×C8C22×C4×C11
Frattini, cosocleC22×C8C23×C11
prime radicalC22×C11×D8C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C11×#97 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#365C2semidirect
5. C11×#1778C2semidirect
6. C11×#1383C2semidirect
7. C11×#1377C2semidirect
20. C11×#361C4semidirect
53. #13138C11direct (N × H)
90. C2×#365C2×C11semidirect
94. #1778C2×C11semidirect
95. #1383C2×C11semidirect
96. #1377C2×C11semidirect
136. #361C4×C11semidirect
225. C11#13138direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3652
C2×C11×#3612
C11×#19722
C11×#17782
C11×#13832
C11×#13772
#1313811