Finite Group Databasebeta

← C11×#21314 #14598507

Subgroups — C11×#21314 #14598507

Order 2816.

1174 conjugacy classes of subgroups.

The subgroup lattice has 256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#125C211yesmaximal, characteristic
2C2×C11×#423C211yesmaximal, characteristic
3C4×C11×#117C211yesmaximal, characteristic
4C11×#1989C218yesmaximal, complemented
5C11×#1736C214yesmaximal
6C22×C11×M16C2212yes—
7C2×C11×#125—21no—
8C2×C11×#125—21no—
9C2×C11×#125—24no—
10C2×C11×#125C418yescomplemented
11C2×C11×#125C2214yes—
12C2×C11×#117C2212yes—
13C22×C11×C4⋊C4—22no—
14C22×C11×C4⋊C4C2212yes—
15C22×C42×C11C2211yescharacteristic
16C11×#423—24no—
17C2×C11×C4⋊C8C2214yes—
18C4×C11×C4⋊C4C2214yes—
19C4×C11×C22⋊C4—22no—
20C11×#376—21no—
21C43×C11—21no—
22C11×#340C22116yes—
23C23×C4×C11—22no—
24C23×C4×C11D412yes—
25C23×C4×C11C2311yescharacteristic
26C2×C11×M16—24no—
27C2×C11×M16—28no—
28C22×C8×C11C2314yes—
29C11×#125—28no—
30C11×#125—28no—
31C11×#125—28no—
32C11×#125C2×C4116yes—
33C11×#117—24no—
34C11×#117Q818yes—
35C2×C11×C4⋊C4—216no—
36C2×C11×C4⋊C4—24no—
37C2×C11×C4⋊C4—24no—
38C2×C11×C4⋊C4—22no—
39C2×C11×C4⋊C4—24no—
40C2×C11×C4⋊C4C2×C418yes—
41C2×C11×C4⋊C4C2314yes—
42C2×C11×C4⋊C4C2314yes—
43C2×C11×C22⋊C4—22no—
44C2×C42×C11—22no—
45C2×C42×C11—24no—
46C2×C42×C11C2×C414yes—
47C2×C42×C11D411yescharacteristic
48C2×C42×C11D411yescharacteristic
49C2×C42×C11D414yes—
50C2×C42×C11C2312yes—
51C11×C4⋊C8—28no—
52C11×#95—24no—
53#21314C1111yesmaximal, characteristic, direct product factor, Sylow
54C24×C11C2×D411yescharacteristic
55C22×C4×C11—28no—
56C22×C4×C11—24no—
57C22×C4×C11—24no—
58C22×C4×C11—44no—
59C22×C4×C11—48no—
60C22×C4×C11C22⋊C418yes—
61C22×C4×C11C22×C412yes—
62C22×C4×C11C2×D412yes—
63C22×C4×C11C2×D412yes—
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D412yes—
66C22×C4×C11C2×Q814yes—
67C22×C4×C11#4114yes—
68C22×C4×C11C2411yescharacteristic
69C11×M16—48no—
70C2×C8×C11—24no—
71C2×C8×C11—28no—
72C11×C4⋊C4—216no—
73C11×C4⋊C4—216no—
74C11×C4⋊C4—28no—
75C11×C4⋊C4—24no—
76C11×C4⋊C4—24no—
77C11×C4⋊C4C22×C418yes—
78C11×C4⋊C4C2×Q818yes—
79C11×C22⋊C4—28no—
80C42×C11—28no—
81C42×C11—48no—
82C42×C11C22⋊C414yes—
83C42×C11C22⋊C414yes—
84C42×C11C22×C414yes—
85C42×C11C2×D414yes—
86C22×#125C2×C1111yescharacteristic
87C2×#423C2×C1111yescharacteristic
88C4×#117C2×C1111yescharacteristic
89#1989C2×C1118yescomplemented
90#1736C2×C1114yes—
91C23×C11—24no—
92C23×C11C2×C22⋊C412yes—
93C23×C11C22⋊Q814yes—
94C23×C11C22×D411yescharacteristic
95C2×C4×C11—24no—
96C2×C4×C11—24no—
97C2×C4×C11—28no—
98C2×C4×C11—28no—
99C2×C4×C11—48no—
100C2×C4×C11—416no—
101C2×C4×C11—48no—
102C2×C4×C11—48no—
103C2×C4×C11C2×C22⋊C414yes—
104C2×C4×C11C2×C22⋊C414yes—
105C2×C4×C11C2×C22⋊C412yes—
106C2×C4×C11C4×Q818yes—
107C2×C4×C11C22⋊Q814yes—
108C2×C4×C11#12414yes—
109C2×C4×C11C4⋊Q814yes—
110C2×C4×C11C23×C411yescharacteristic
111C2×C4×C11C22×D411yescharacteristic
112C2×C4×C11C22×Q812yes—
113C2×C4×C11C2×#4112yes—
114C8×C11—44no—
115C22×M16C22×C1112yes—
116C2×#125—21no—
117C2×#125—21no—
118C2×#125—24no—
119C2×#125C4×C1118yescomplemented
120C2×#125C22×C1114yes—
121C2×#117C22×C1112yes—
122C22×C4⋊C4—22no—
123C22×C4⋊C4C22×C1112yes—
124C22×C42C22×C1111yescharacteristic
125#423—24no—
126C2×C4⋊C8C22×C1114yes—
127C4×C4⋊C4C22×C1114yes—
128C4×C22⋊C4—22no—
129#376—21no—
130C43—21no—
131#340C22×C11116yes—
132C22×C11—28no—
133C22×C11—24no—
134C22×C11#39114yes—
135C22×C11C22×C22⋊C411yescharacteristic
136C22×C11C2×C22⋊Q812yes—
137C22×C11#57514yes—
138C4×C11—24no—
139C4×C11—24no—
140C4×C11—48no—
141C4×C11—48no—
142C4×C11#39114yes—
143C4×C11C2×C4×Q812yes—
144C4×C11C2×#12411yescharacteristic
145C4×C11C2×C4⋊Q811yescharacteristic
146C23×C4—22no—
147C23×C4D4×C1112yes—
148C23×C4C23×C1111yescharacteristic
149C2×M16—24no—
150C2×M16—28no—
151C22×C8C23×C1114yes—
152#125—28no—
153#125—28no—
154#125—28no—
155#125C2×C4×C11116yes—
156#117—24no—
157#117Q8×C1118yes—
158C2×C4⋊C4—216no—
159C2×C4⋊C4—24no—
160C2×C4⋊C4—24no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—24no—
163C2×C4⋊C4C2×C4×C1118yes—
164C2×C4⋊C4C23×C1114yes—
165C2×C4⋊C4C23×C1114yes—
166C2×C22⋊C4—22no—
167C2×C42—22no—
168C2×C42—24no—
169C2×C42C2×C4×C1114yes—
170C2×C42D4×C1111yescharacteristic
171C2×C42D4×C1111yescharacteristic
172C2×C42D4×C1114yes—
173C2×C42C23×C1112yes—
174C4⋊C8—28no—
175#95—24no—
176C2×C11—24no—
177C2×C11C2×#39111yescharacteristic
178C2×C11#289612yes—
179C2×C11#308014yes—
180C24C2×D4×C1111yescharacteristic
181C22×C4—28no—
182C22×C4—24no—
183C22×C4—24no—
184C22×C4—44no—
185C22×C4—48no—
186C22×C4C11×C22⋊C418yes—
187C22×C4C22×C4×C1112yes—
188C22×C4C2×D4×C1112yes—
189C22×C4C2×D4×C1112yes—
190C22×C4C2×D4×C1111yescharacteristic
191C22×C4C2×D4×C1112yes—
192C22×C4C2×Q8×C1114yes—
193C22×C4C11×#4114yes—
194C22×C4C24×C1111yescharacteristic
195M16—48no—
196C2×C8—24no—
197C2×C8—28no—
198C4⋊C4—216no—
199C4⋊C4—216no—
200C4⋊C4—28no—
201C4⋊C4—24no—
202C4⋊C4—24no—
203C4⋊C4C22×C4×C1118yes—
204C4⋊C4C2×Q8×C1118yes—
205C22⋊C4—28no—
206C42—28no—
207C42—48no—
208C42C11×C22⋊C414yes—
209C42C11×C22⋊C414yes—
210C42C22×C4×C1114yes—
211C42C2×D4×C1114yes—
212C11#2131411yescharacteristic, direct product factor, Sylow
213C23—24no—
214C23C2×C11×C22⋊C412yes—
215C23C11×C22⋊Q814yes—
216C23C22×D4×C1111yescharacteristic
217C2×C4—24no—
218C2×C4—24no—
219C2×C4—28no—
220C2×C4—28no—
221C2×C4—48no—
222C2×C4—416no—
223C2×C4—48no—
224C2×C4—48no—
225C2×C4C2×C11×C22⋊C414yes—
226C2×C4C2×C11×C22⋊C414yes—
227C2×C4C2×C11×C22⋊C412yes—
228C2×C4C4×Q8×C1118yes—
229C2×C4C11×C22⋊Q814yes—
230C2×C4C11×#12414yes—
231C2×C4C11×C4⋊Q814yes—
232C2×C4C23×C4×C1111yescharacteristic
233C2×C4C22×D4×C1111yescharacteristic
234C2×C4C22×Q8×C1112yes—
235C2×C4C2×C11×#4112yes—
236C8—44no—
237C22—24no—
238C22—28no—
239C22C11×#39114yes—
240C22C22×C11×C22⋊C411yescharacteristic
241C22C2×C11×C22⋊Q812yes—
242C22C11×#57514yes—
243C4—24no—
244C4—24no—
245C4—48no—
246C4—48no—
247C4C11×#39114yes—
248C4C2×C4×Q8×C1112yes—
249C4C2×C11×#12411yescharacteristic
250C4C2×C11×C4⋊Q811yescharacteristic
251C2—24no—
252C2C2×C11×#39111yescharacteristic
253C2C11×#289612yes—
254C2C11×#308014yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1989C2semidirect
10. C2×C11×#125C4semidirect
53. #21314C11direct (N × H)
89. #1989C2×C11semidirect
119. C2×#125C4×C11semidirect
212. C11#21314direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1252
C2×C11×#4232
C4×C11×#1172
C11×#19892
C11×#17362
#2131411