Finite Group Databasebeta

← C22×C11×#359 #14610576

Subgroups — C22×C11×#359 #14610576

Order 2816.

1174 conjugacy classes of subgroups.

The subgroup lattice has 288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#135C211yesmaximal, characteristic
2C23×C11×C16C211yesmaximal, characteristic, complemented
3C22×C11×#108C211yesmaximal, characteristic, complemented
4C2×C11×#359C2112yesmaximal, direct product factor
5C22×C11×#41—21no—
6C2×C11×#135—23no—
7C2×C11×#135—23no—
8C2×C11×#135C416yes—
9C2×C11×#135C2216yes—
10C22×C11×Q16C411yescharacteristic
11C22×C11×SD16—21no—
12C22×C11×D8C411yescharacteristic
13C22×C11×M16—21no—
14C23×C8×C11C2211yescharacteristic
15C22×C11×C16—21no—
16C22×C11×C16—23no—
17C22×C11×C16C2216yescomplemented
18C2×C11×#108—23no—
19C2×C11×#108C2216yescomplemented
20C11×#359C22116yesdirect product factor
21C2×C11×#41—26no—
22C2×C11×#41—26no—
23C2×C11×#41—43no—
24C2×C11×#41—43no—
25C22×Q8×C11—21no—
26C22×D4×C11—21no—
27C22×D4×C11—41no—
28C23×C4×C11—41no—
29C23×C4×C11D411yescharacteristic
30C11×#135—212no—
31C11×#135—26no—
32C11×#135—26no—
33C11×#135C2×C4112yes—
34C11×#135C2314yes—
35C2×C11×Q16—23no—
36C2×C11×Q16C2×C416yes—
37C2×C11×SD16—26no—
38C2×C11×SD16—26no—
39C2×C11×D8—23no—
40C2×C11×D8C2×C416yes—
41C2×C11×M16—26no—
42C2×C11×M16—43no—
43C22×C8×C11—41no—
44C22×C8×C11C2×C411yescharacteristic
45C22×C8×C11C2×C413yes—
46C22×C8×C11D413yes—
47C22×C8×C11D411yescharacteristic
48C22×C8×C11D413yes—
49C22×C8×C11C2313yes—
50C2×C11×C16—26no—
51C2×C11×C16—26no—
52C2×C11×C16C2314yescomplemented
53C11×#108—26no—
54C11×#108C2314yescomplemented
55C22×#359C1111yesmaximal, characteristic, direct product factor, Sylow
56C24×C11—41no—
57C24×C11SD1611yescharacteristic
58C11×#41—212no—
59C11×#41—24no—
60C11×#41—412no—
61C11×#41—46no—
62C11×#41—46no—
63C2×Q8×C11—26no—
64C2×Q8×C11—43no—
65C2×D4×C11—26no—
66C2×D4×C11—46no—
67C2×D4×C11—46no—
68C2×D4×C11—43no—
69C22×C4×C11—41no—
70C22×C4×C11—46no—
71C22×C4×C11—46no—
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C413yes—
74C22×C4×C11D813yes—
75C22×C4×C11D811yescharacteristic
76C22×C4×C11SD1613yes—
77C22×C4×C11C2×D413yes—
78C11×Q16—26no—
79C11×Q16C22×C414yes—
80C11×SD16—212no—
81C11×SD16—24no—
82C11×D8—26no—
83C11×D8C22×C414yes—
84C11×M16—24no—
85C11×M16—46no—
86C2×C8×C11—46no—
87C2×C8×C11C22⋊C413yes—
88C2×C8×C11C22⋊C413yes—
89C2×C8×C11C22⋊C416yes—
90C2×C8×C11C22×C413yes—
91C2×C8×C11C22×C413yes—
92C2×C8×C11C2×D413yes—
93C2×C8×C11C2×D413yes—
94C2×C8×C11C2×D413yes—
95C2×C8×C11C2411yescharacteristic
96C11×C16—24no—
97C22×#135C2×C1111yescharacteristic
98C23×C16C2×C1111yescharacteristic, complemented
99C22×#108C2×C1111yescharacteristic, complemented
100C2×#359C2×C11112yesdirect product factor
101C23×C11—24no—
102C23×C11—46no—
103C23×C11—84no—
104C23×C11#10213yes—
105C23×C11#10211yescharacteristic
106C23×C11C2×SD1613yes—
107Q8×C11—24no—
108Q8×C11—46no—
109D4×C11—24no—
110D4×C11—44no—
111D4×C11—412no—
112D4×C11—46no—
113C2×C4×C11—46no—
114C2×C4×C11—44no—
115C2×C4×C11—412no—
116C2×C4×C11#10213yes—
117C2×C4×C11#10213yes—
118C2×C4×C11#10216yes—
119C2×C4×C11C2×C22⋊C413yes—
120C2×C4×C11C2×C22⋊C413yes—
121C2×C4×C11C2×D813yes—
122C2×C4×C11C2×D813yes—
123C2×C4×C11C2×SD1613yes—
124C2×C4×C11C22×D411yescharacteristic
125C8×C11—44no—
126C8×C11C2×C22⋊C413yes—
127C8×C11C2×C22⋊C413yes—
128C8×C11C23×C411yescharacteristic
129C8×C11C22×D411yescharacteristic
130C22×#41—21no—
131C2×#135—23no—
132C2×#135—23no—
133C2×#135C4×C1116yes—
134C2×#135C22×C1116yes—
135C22×Q16C4×C1111yescharacteristic
136C22×SD16—21no—
137C22×D8C4×C1111yescharacteristic
138C22×M16—21no—
139C23×C8C22×C1111yescharacteristic
140C22×C16—21no—
141C22×C16—23no—
142C22×C16C22×C1116yescomplemented
143C2×#108—23no—
144C2×#108C22×C1116yescomplemented
145#359C22×C11116yesdirect product factor
146C22×C11—26no—
147C22×C11—26no—
148C22×C11—44no—
149C22×C11—812no—
150C22×C11#35914yesdirect product factor
151C22×C11C2×#10213yes—
152C22×C11C2×#10213yes—
153C22×C11C22×SD1611yescharacteristic
154C4×C11—44no—
155C4×C11C2×#10213yes—
156C4×C11C2×#10213yes—
157C4×C11C22×C22⋊C411yescharacteristic
158C4×C11C22×D811yescharacteristic
159C2×#41—26no—
160C2×#41—26no—
161C2×#41—43no—
162C2×#41—43no—
163C22×Q8—21no—
164C22×D4—21no—
165C22×D4—41no—
166C23×C4—41no—
167C23×C4D4×C1111yescharacteristic
168#135—212no—
169#135—26no—
170#135—26no—
171#135C2×C4×C11112yes—
172#135C23×C1114yes—
173C2×Q16—23no—
174C2×Q16C2×C4×C1116yes—
175C2×SD16—26no—
176C2×SD16—26no—
177C2×D8—23no—
178C2×D8C2×C4×C1116yes—
179C2×M16—26no—
180C2×M16—43no—
181C22×C8—41no—
182C22×C8C2×C4×C1111yescharacteristic
183C22×C8C2×C4×C1113yes—
184C22×C8D4×C1113yes—
185C22×C8D4×C1111yescharacteristic
186C22×C8D4×C1113yes—
187C22×C8C23×C1113yes—
188C2×C16—26no—
189C2×C16—26no—
190C2×C16C23×C1114yescomplemented
191#108—26no—
192#108C23×C1114yescomplemented
193C2×C11—21no—
194C2×C11—23no—
195C2×C11—84no—
196C2×C11C2×#35916yesdirect product factor
197C2×C11C22×#10211yescharacteristic
198C24—41no—
199C24C11×SD1611yescharacteristic
200#41—212no—
201#41—24no—
202#41—412no—
203#41—46no—
204#41—46no—
205C2×Q8—26no—
206C2×Q8—43no—
207C2×D4—26no—
208C2×D4—46no—
209C2×D4—46no—
210C2×D4—43no—
211C22×C4—41no—
212C22×C4—46no—
213C22×C4—46no—
214C22×C4C11×C22⋊C411yescharacteristic
215C22×C4C11×C22⋊C413yes—
216C22×C4C11×D811yescharacteristic
217C22×C4C11×D813yes—
218C22×C4C11×SD1613yes—
219C22×C4C2×D4×C1113yes—
220Q16—26no—
221Q16C22×C4×C1114yes—
222SD16—212no—
223SD16—24no—
224D8—26no—
225D8C22×C4×C1114yes—
226M16—24no—
227M16—46no—
228C2×C8—46no—
229C2×C8C11×C22⋊C413yes—
230C2×C8C11×C22⋊C413yes—
231C2×C8C11×C22⋊C416yes—
232C2×C8C22×C4×C1113yes—
233C2×C8C22×C4×C1113yes—
234C2×C8C2×D4×C1113yes—
235C2×C8C2×D4×C1113yes—
236C2×C8C2×D4×C1113yes—
237C2×C8C24×C1111yescharacteristic
238C16—24no—
239C11C22×#35911yescharacteristic, direct product factor, Sylow
240C23—24no—
241C23—46no—
242C23—84no—
243C23C11×#10213yes—
244C23C11×#10211yescharacteristic
245C23C2×C11×SD1613yes—
246Q8—24no—
247Q8—46no—
248D4—24no—
249D4—412no—
250D4—44no—
251D4—46no—
252C2×C4—46no—
253C2×C4—412no—
254C2×C4—44no—
255C2×C4C11×#10213yes—
256C2×C4C11×#10213yes—
257C2×C4C11×#10216yes—
258C2×C4C2×C11×C22⋊C413yes—
259C2×C4C2×C11×C22⋊C413yes—
260C2×C4C2×C11×D813yes—
261C2×C4C2×C11×D813yes—
262C2×C4C2×C11×SD1613yes—
263C2×C4C22×D4×C1111yescharacteristic
264C8—44no—
265C8C2×C11×C22⋊C413yes—
266C8C2×C11×C22⋊C413yes—
267C8C23×C4×C1111yescharacteristic
268C8C22×D4×C1111yescharacteristic
269C22—26no—
270C22—26no—
271C22—44no—
272C22—812no—
273C22C11×#35914yesdirect product factor
274C22C2×C11×#10213yes—
275C22C2×C11×#10213yes—
276C22C22×C11×SD1611yescharacteristic
277C4—44no—
278C4C2×C11×#10213yes—
279C4C2×C11×#10213yes—
280C4C22×C11×C22⋊C411yescharacteristic
281C4C22×C11×D811yescharacteristic
282C2—23no—
283C2—21no—
284C2—84no—
285C2C2×C11×#35916yesdirect product factor
286C2C22×C11×#10211yescharacteristic
subgroupG/H
centerC22×C4×C11D8
commutatorC8C23×C4×C11
Frattini, cosocleC2×C8C24×C11
socleC23×C11#102
prime radicalC22×C11×#135C2
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C11×C16C2semidirect
3. C22×C11×#108C2semidirect
4. C2×C11×#359C2direct (N × H)
17. C22×C11×C16C22semidirect
19. C2×C11×#108C22semidirect
20. C11×#359C22direct (N × H)
52. C2×C11×C16C23semidirect
54. C11×#108C23semidirect
55. C22×#359C11direct (N × H)
98. C23×C16C2×C11semidirect
99. C22×#108C2×C11semidirect
100. C2×#359C2×C11direct (N × H)
142. C22×C16C22×C11semidirect
144. C2×#108C22×C11semidirect
145. #359C22×C11direct (N × H)
150. C22×C11#359direct (N × H)
190. C2×C16C23×C11semidirect
192. #108C23×C11semidirect
196. C2×C11C2×#359direct (N × H)
239. C11C22×#359direct (N × H)
273. C22C11×#359direct (N × H)
285. C2C2×C11×#359direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1352
C23×C11×C162
C22×C11×#1082
C2×C11×#3592
C22×#35911