Finite Group Databasebeta

← C11×#13142 #14590335

Subgroups — C11×#13142 #14590335

Order 2816.

356 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
1C2×C11×#365C211yesmaximal, characteristic, complemented
2C2×C11×#361C211yesmaximal, characteristic
3C11×#2140C211yesmaximal, characteristic
4C11×#1972C211yesmaximal, characteristic
5C11×#1773C211yesmaximal, characteristic, complemented
6C11×#1386C211yesmaximal, characteristic, complemented
7C11×#1375C211yesmaximal, characteristic, complemented
8C22×C11×D8C2211yescharacteristic
9C2×C11×M32C2211yescharacteristic
10C2×C11×M32C2211yescharacteristic
11C2×C11×#108C2211yescharacteristic
12C11×#427C2211yescharacteristic
13C2×C11×#106C2211yescharacteristic
14C2×C11×#102—21no—
15C11×#405—21no—
16C2×C11×#97C2211yescharacteristic
17C11×#390—21no—
18C11×#365—22no—
19C11×#361—22no—
20C11×#357C414yescomplemented
21C11×#339—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—
30C22×C8×C11D411yescharacteristic
31C22×C8×C11C2311yescharacteristic
32C11×#117—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C22⋊C4—42no—
35C2×C42×C11D411yescharacteristic
36C11×M32—21no—
37C11×M32—21no—
38C11×M32—21no—
39C11×M32—21no—
40C2×C11×C16—21no—
41C2×C11×C16C2×C412yes—
42C11×#108—21no—
43C11×#108D412yes—
44C11×#107C2×C412yes—
45C11×#106—21no—
46C11×#106—21no—
47C11×#106—21no—
48C11×#102—42no—
49C11×#97—21no—
50C11×#97—21no—
51C11×#97—41no—
52C4×C8×C11—41no—
53#13142C1111yesmaximal, 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—21no—
62C22×C4×C11—41no—
63C22×C4×C11C2×D411yescharacteristic
64C11×D8—22no—
65C11×D8—22no—
66C11×D8—41no—
67C11×D8—41no—
68C11×M16—22no—
69C11×M16—41no—
70C2×C8×C11—21no—
71C2×C8×C11—21no—
72C2×C8×C11—41no—
73C2×C8×C11SD1612yes—
74C2×C8×C11C22×C411yescharacteristic
75C2×C8×C11C2×D411yescharacteristic
76C2×C8×C11#4111yescharacteristic
77C2×C8×C11#4111yescharacteristic
78C2×C8×C11#4111yescharacteristic
79C2×C8×C11#4111yescharacteristic
80C11×C4⋊C4—22no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C22⋊C4—41no—
84C11×C22⋊C4—84no—
85C42×C11—21no—
86C42×C11—21no—
87C42×C11—41no—
88C11×C16—22no—
89C11×C16—41no—
90C2×#365C2×C1111yescharacteristic, complemented
91C2×#361C2×C1111yescharacteristic
92#2140C2×C1111yescharacteristic
93#1972C2×C1111yescharacteristic
94#1773C2×C1111yescharacteristic, complemented
95#1386C2×C1111yescharacteristic, complemented
96#1375C2×C1111yescharacteristic, complemented
97C23×C11—42no—
98C23×C11—82no—
99C23×C11—82no—
100C23×C11—81no—
101C23×C11—81no—
102C23×C11AGL(1,ℤ/8)11yescharacteristic
103D4×C11—42no—
104D4×C11—42no—
105D4×C11—81no—
106D4×C11—81no—
107C2×C4×C11—42no—
108C2×C4×C11—42no—
109C2×C4×C11—41no—
110C2×C4×C11—82no—
111C2×C4×C11—81no—
112C2×C4×C11C4×D411yescharacteristic
113C2×C4×C11#12111yescharacteristic
114C2×C4×C11#12311yescharacteristic
115C2×C4×C11C2×SD1611yescharacteristic
116C2×C4×C11#13511yescharacteristic
117C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
118C8×C11—22no—
119C8×C11—42no—
120C8×C11#11711yescharacteristic
121C8×C11C4×D411yescharacteristic
122C8×C11#12411yescharacteristic
123C8×C11#12611yescharacteristic
124C22×D8C22×C1111yescharacteristic
125C2×M32C22×C1111yescharacteristic
126C2×M32C22×C1111yescharacteristic
127C2×#108C22×C1111yescharacteristic
128#427C22×C1111yescharacteristic
129C2×#106C22×C1111yescharacteristic
130C2×#102—21no—
131#405—21no—
132C2×#97C22×C1111yescharacteristic
133#390—21no—
134#365—22no—
135#361—22no—
136#357C4×C1114yescomplemented
137#339—21no—
138C22×C11—22no—
139C22×C11—84no—
140C22×C11—82no—
141C22×C11—162no—
142C22×C11—161no—
143C22×C11—161no—
144C22×C11#44211yescharacteristic
145C22×C11#46011yescharacteristic
146C22×C11#48211yescharacteristic
147C4×C11—81no—
148C4×C11—82no—
149C4×C11—161no—
150C4×C11#38811yescharacteristic
151C4×C11C4×SD1611yescharacteristic
152C4×C11#46311yescharacteristic
153C4×C11#48111yescharacteristic
154C22×D4—21no—
155C2×D8—21no—
156C2×D8—21no—
157C2×D8—21no—
158C2×D8—21no—
159C2×D8—21no—
160C2×D8C2×C4×C1112yes—
161C2×M16—21no—
162C22×C8D4×C1111yescharacteristic
163C22×C8C23×C1111yescharacteristic
164#117—21no—
165C2×C4⋊C4—21no—
166C2×C22⋊C4—42no—
167C2×C42D4×C1111yescharacteristic
168M32—21no—
169M32—21no—
170M32—21no—
171M32—21no—
172C2×C16—21no—
173C2×C16C2×C4×C1112yes—
174#108—21no—
175#108D4×C1112yes—
176#107C2×C4×C1112yes—
177#106—21no—
178#106—21no—
179#106—21no—
180#102—42no—
181#97—21no—
182#97—21no—
183#97—41no—
184C4×C8—41no—
185C2×C11—21no—
186C2×C11—21no—
187C2×C11—162no—
188C2×C11#192611yescharacteristic
189C2×C11AGL(1,ℤ/16)12yes—
190C24—41no—
191C2×D4—22no—
192C2×D4—41no—
193C2×D4—41no—
194C2×D4—41no—
195C2×D4—41no—
196C2×D4—41no—
197C22×C4—21no—
198C22×C4—41no—
199C22×C4C2×D4×C1111yescharacteristic
200D8—22no—
201D8—22no—
202D8—41no—
203D8—41no—
204M16—22no—
205M16—41no—
206C2×C8—21no—
207C2×C8—21no—
208C2×C8—41no—
209C2×C8C11×SD1612yes—
210C2×C8C22×C4×C1111yescharacteristic
211C2×C8C2×D4×C1111yescharacteristic
212C2×C8C11×#4111yescharacteristic
213C2×C8C11×#4111yescharacteristic
214C2×C8C11×#4111yescharacteristic
215C2×C8C11×#4111yescharacteristic
216C4⋊C4—22no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C22⋊C4—41no—
220C22⋊C4—84no—
221C42—21no—
222C42—21no—
223C42—41no—
224C16—22no—
225C16—41no—
226C11#1314211yescharacteristic, direct product factor, Sylow
227C23—42no—
228C23—82no—
229C23—82no—
230C23—81no—
231C23—81no—
232C23C11×AGL(1,ℤ/8)11yescharacteristic
233D4—42no—
234D4—42no—
235D4—81no—
236D4—81no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—41no—
240C2×C4—82no—
241C2×C4—81no—
242C2×C4C4×D4×C1111yescharacteristic
243C2×C4C11×#12111yescharacteristic
244C2×C4C11×#12311yescharacteristic
245C2×C4C2×C11×SD1611yescharacteristic
246C2×C4C11×#13511yescharacteristic
247C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
248C8—22no—
249C8—42no—
250C8C11×#11711yescharacteristic
251C8C4×D4×C1111yescharacteristic
252C8C11×#12411yescharacteristic
253C8C11×#12611yescharacteristic
254C22—22no—
255C22—84no—
256C22—82no—
257C22—162no—
258C22—161no—
259C22—161no—
260C22C11×#44211yescharacteristic
261C22C11×#46011yescharacteristic
262C22C11×#48211yescharacteristic
263C4—81no—
264C4—82no—
265C4—161no—
266C4C11×#38811yescharacteristic
267C4C4×C11×SD1611yescharacteristic
268C4C11×#46311yescharacteristic
269C4C11×#48111yescharacteristic
270C2—21no—
271C2—21no—
272C2—162no—
273C2C11×#192611yescharacteristic
274C2C11×AGL(1,ℤ/16)12yes—
subgroupG/H
center, socleC22×C11#442
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×#1773C2semidirect
6. C11×#1386C2semidirect
7. C11×#1375C2semidirect
20. C11×#357C4semidirect
53. #13142C11direct (N × H)
90. C2×#365C2×C11semidirect
94. #1773C2×C11semidirect
95. #1386C2×C11semidirect
96. #1375C2×C11semidirect
136. #357C4×C11semidirect
226. C11#13142direct (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×#21402
C11×#19722
C11×#17732
C11×#13862
C11×#13752
#1314211