Finite Group Databasebeta

← C22×C11×#360 #14610579

Subgroups — C22×C11×#360 #14610579

Order 2816.

1214 conjugacy classes of subgroups.

The subgroup lattice has 294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#135C211yesmaximal, characteristic
2C22×C11×M32C211yesmaximal, characteristic, complemented
3C22×C11×#106C211yesmaximal, characteristic, complemented
4C2×C11×#360C2112yesmaximal, direct product factor
5C22×C11×#41—21no—
6C2×C11×#135—23no—
7C2×C11×#135—23no—
8C2×C11×#135C416yescomplemented
9C2×C11×#135C2216yes—
10C22×C11×Q16C411yescharacteristic, complemented
11C22×C11×SD16—21no—
12C22×C11×D8C411yescharacteristic, complemented
13C23×C8×C11C2211yescharacteristic
14C22×C11×C4⋊C4—21no—
15C2×C11×M32—23no—
16C2×C11×M32C2216yescomplemented
17C22×C11×C16—21no—
18C2×C11×#106—23no—
19C2×C11×#106C2216yescomplemented
20C11×#360C22116yesdirect 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×C11—41no—
30C23×C4×C11D411yescharacteristic
31C11×#135—212no—
32C11×#135—26no—
33C11×#135—26no—
34C11×#135C2×C4112yescomplemented
35C11×#135C2314yes—
36C2×C11×Q16—23no—
37C2×C11×Q16C2×C416yescomplemented
38C2×C11×SD16—26no—
39C2×C11×SD16—26no—
40C2×C11×D8—23no—
41C2×C11×D8C2×C416yescomplemented
42C22×C8×C11C2×C411yescharacteristic
43C22×C8×C11C2×C413yes—
44C22×C8×C11D413yes—
45C22×C8×C11D411yescharacteristic
46C22×C8×C11D413yes—
47C22×C8×C11C2313yes—
48C2×C11×C4⋊C4—26no—
49C2×C11×C4⋊C4—43no—
50C11×M32—26no—
51C11×M32C2314yescomplemented
52C2×C11×C16—26no—
53C11×#106—26no—
54C11×#106C2314yescomplemented
55C22×#360C1111yesmaximal, characteristic, direct product factor, Sylow
56C24×C11—41no—
57C24×C11D811yescharacteristic
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×C11—46no—
73C22×C4×C11—84no—
74C22×C4×C11C22⋊C413yes—
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11D813yes—
77C22×C4×C11SD1613yes—
78C22×C4×C11SD1611yescharacteristic
79C22×C4×C11C2×D413yes—
80C11×Q16—26no—
81C11×Q16C22×C414yescomplemented
82C11×SD16—212no—
83C11×SD16—24no—
84C11×D8—26no—
85C11×D8C22×C414yescomplemented
86C2×C8×C11C22⋊C413yes—
87C2×C8×C11C22⋊C413yes—
88C2×C8×C11C22⋊C416yes—
89C2×C8×C11C22×C413yes—
90C2×C8×C11C22×C413yes—
91C2×C8×C11C2×D413yes—
92C2×C8×C11C2×D413yes—
93C2×C8×C11C2×D413yes—
94C2×C8×C11C2411yescharacteristic
95C11×C4⋊C4—24no—
96C11×C4⋊C4—46no—
97C11×C16—24no—
98C22×#135C2×C1111yescharacteristic
99C22×M32C2×C1111yescharacteristic, complemented
100C22×#106C2×C1111yescharacteristic, complemented
101C2×#360C2×C11112yesdirect product factor
102C23×C11—24no—
103C23×C11—46no—
104C23×C11—84no—
105C23×C11#10213yes—
106C23×C11#10211yescharacteristic
107C23×C11C2×D813yes—
108Q8×C11—24no—
109Q8×C11—46no—
110D4×C11—24no—
111D4×C11—44no—
112D4×C11—412no—
113D4×C11—46no—
114C2×C4×C11—46no—
115C2×C4×C11—44no—
116C2×C4×C11—412no—
117C2×C4×C11—44no—
118C2×C4×C11—812no—
119C2×C4×C11#10213yes—
120C2×C4×C11#10213yes—
121C2×C4×C11#10216yes—
122C2×C4×C11C2×C22⋊C413yes—
123C2×C4×C11C2×C22⋊C413yes—
124C2×C4×C11C2×D813yes—
125C2×C4×C11C2×SD1613yes—
126C2×C4×C11C2×SD1613yes—
127C2×C4×C11C22×D411yescharacteristic
128C8×C11C2×C22⋊C413yes—
129C8×C11C2×C22⋊C413yes—
130C8×C11C23×C411yescharacteristic
131C8×C11C22×D411yescharacteristic
132C22×#41—21no—
133C2×#135—23no—
134C2×#135—23no—
135C2×#135C4×C1116yescomplemented
136C2×#135C22×C1116yes—
137C22×Q16C4×C1111yescharacteristic, complemented
138C22×SD16—21no—
139C22×D8C4×C1111yescharacteristic, complemented
140C23×C8C22×C1111yescharacteristic
141C22×C4⋊C4—21no—
142C2×M32—23no—
143C2×M32C22×C1116yescomplemented
144C22×C16—21no—
145C2×#106—23no—
146C2×#106C22×C1116yescomplemented
147#360C22×C11116yesdirect product factor
148C22×C11—26no—
149C22×C11—26no—
150C22×C11—44no—
151C22×C11—812no—
152C22×C11#36014yesdirect product factor
153C22×C11C2×#10213yes—
154C22×C11C2×#10213yes—
155C22×C11C22×D811yescharacteristic
156C4×C11—44no—
157C4×C11—84no—
158C4×C11C2×#10213yes—
159C4×C11C2×#10213yes—
160C4×C11C22×C22⋊C411yescharacteristic
161C4×C11C22×SD1611yescharacteristic
162C2×#41—26no—
163C2×#41—26no—
164C2×#41—43no—
165C2×#41—43no—
166C22×Q8—21no—
167C22×D4—21no—
168C22×D4—41no—
169C23×C4—41no—
170C23×C4—41no—
171C23×C4D4×C1111yescharacteristic
172#135—212no—
173#135—26no—
174#135—26no—
175#135C2×C4×C11112yescomplemented
176#135C23×C1114yes—
177C2×Q16—23no—
178C2×Q16C2×C4×C1116yescomplemented
179C2×SD16—26no—
180C2×SD16—26no—
181C2×D8—23no—
182C2×D8C2×C4×C1116yescomplemented
183C22×C8C2×C4×C1111yescharacteristic
184C22×C8C2×C4×C1113yes—
185C22×C8D4×C1113yes—
186C22×C8D4×C1111yescharacteristic
187C22×C8D4×C1113yes—
188C22×C8C23×C1113yes—
189C2×C4⋊C4—26no—
190C2×C4⋊C4—43no—
191M32—26no—
192M32C23×C1114yescomplemented
193C2×C16—26no—
194#106—26no—
195#106C23×C1114yescomplemented
196C2×C11—21no—
197C2×C11—23no—
198C2×C11—84no—
199C2×C11C2×#36016yesdirect product factor
200C2×C11C22×#10211yescharacteristic
201C24—41no—
202C24C11×D811yescharacteristic
203#41—212no—
204#41—24no—
205#41—412no—
206#41—46no—
207#41—46no—
208C2×Q8—26no—
209C2×Q8—43no—
210C2×D4—26no—
211C2×D4—46no—
212C2×D4—46no—
213C2×D4—43no—
214C22×C4—41no—
215C22×C4—46no—
216C22×C4—46no—
217C22×C4—46no—
218C22×C4—84no—
219C22×C4C11×C22⋊C411yescharacteristic
220C22×C4C11×C22⋊C413yes—
221C22×C4C11×D813yes—
222C22×C4C11×SD1611yescharacteristic
223C22×C4C11×SD1613yes—
224C22×C4C2×D4×C1113yes—
225Q16—26no—
226Q16C22×C4×C1114yescomplemented
227SD16—212no—
228SD16—24no—
229D8—26no—
230D8C22×C4×C1114yescomplemented
231C2×C8C11×C22⋊C413yes—
232C2×C8C11×C22⋊C413yes—
233C2×C8C11×C22⋊C416yes—
234C2×C8C22×C4×C1113yes—
235C2×C8C22×C4×C1113yes—
236C2×C8C2×D4×C1113yes—
237C2×C8C2×D4×C1113yes—
238C2×C8C2×D4×C1113yes—
239C2×C8C24×C1111yescharacteristic
240C4⋊C4—24no—
241C4⋊C4—46no—
242C16—24no—
243C11C22×#36011yescharacteristic, direct product factor, Sylow
244C23—24no—
245C23—46no—
246C23—84no—
247C23C11×#10213yes—
248C23C11×#10211yescharacteristic
249C23C2×C11×D813yes—
250Q8—24no—
251Q8—46no—
252D4—24no—
253D4—412no—
254D4—44no—
255D4—46no—
256C2×C4—46no—
257C2×C4—412no—
258C2×C4—44no—
259C2×C4—44no—
260C2×C4—812no—
261C2×C4C11×#10213yes—
262C2×C4C11×#10213yes—
263C2×C4C11×#10216yes—
264C2×C4C2×C11×C22⋊C413yes—
265C2×C4C2×C11×C22⋊C413yes—
266C2×C4C2×C11×D813yes—
267C2×C4C2×C11×SD1613yes—
268C2×C4C2×C11×SD1613yes—
269C2×C4C22×D4×C1111yescharacteristic
270C8C2×C11×C22⋊C413yes—
271C8C2×C11×C22⋊C413yes—
272C8C23×C4×C1111yescharacteristic
273C8C22×D4×C1111yescharacteristic
274C22—26no—
275C22—26no—
276C22—44no—
277C22—812no—
278C22C11×#36014yesdirect product factor
279C22C2×C11×#10213yes—
280C22C2×C11×#10213yes—
281C22C22×C11×D811yescharacteristic
282C4—44no—
283C4—84no—
284C4C2×C11×#10213yes—
285C4C2×C11×#10213yes—
286C4C22×C11×C22⋊C411yescharacteristic
287C4C22×C11×SD1611yescharacteristic
288C2—21no—
289C2—23no—
290C2—84no—
291C2C2×C11×#36016yesdirect product factor
292C2C22×C11×#10211yescharacteristic
subgroupG/H
center, socleC23×C11#102
commutatorC8C23×C4×C11
Frattini, cosocleC2×C8C24×C11
prime radicalC22×C11×#135C2
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×M32C2semidirect
3. C22×C11×#106C2semidirect
4. C2×C11×#360C2direct (N × H)
8. C2×C11×#135C4semidirect
10. C22×C11×Q16C4semidirect
12. C22×C11×D8C4semidirect
16. C2×C11×M32C22semidirect
19. C2×C11×#106C22semidirect
20. C11×#360C22direct (N × H)
34. C11×#135C2×C4semidirect
37. C2×C11×Q16C2×C4semidirect
41. C2×C11×D8C2×C4semidirect
51. C11×M32C23semidirect
54. C11×#106C23semidirect
55. C22×#360C11direct (N × H)
81. C11×Q16C22×C4semidirect
85. C11×D8C22×C4semidirect
99. C22×M32C2×C11semidirect
100. C22×#106C2×C11semidirect
101. C2×#360C2×C11direct (N × H)
135. C2×#135C4×C11semidirect
137. C22×Q16C4×C11semidirect
139. C22×D8C4×C11semidirect
143. C2×M32C22×C11semidirect
146. C2×#106C22×C11semidirect
147. #360C22×C11direct (N × H)
152. C22×C11#360direct (N × H)
175. #135C2×C4×C11semidirect
178. C2×Q16C2×C4×C11semidirect
182. C2×D8C2×C4×C11semidirect
192. M32C23×C11semidirect
195. #106C23×C11semidirect
199. C2×C11C2×#360direct (N × H)
226. Q16C22×C4×C11semidirect
230. D8C22×C4×C11semidirect
243. C11C22×#360direct (N × H)
278. C22C11×#360direct (N × H)
291. C2C2×C11×#360direct (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
C22×C11×M322
C22×C11×#1062
C2×C11×#3602
C22×#36011