Finite Group Databasebeta

← D16×D44 #14910427

Subgroups — D16×D44 #14910427

Order 2816.

812 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 159 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×D16C212yesmaximal, complemented
2D8×D44C212yesmaximal, complemented
3#13070866C211yesmaximal, characteristic, complemented
4#13070703C212yesmaximal, complemented
5#13070651C212yesmaximal, complemented
6#13070529C214yesmaximal, complemented
7C16×D44C211yesmaximal, characteristic, complemented
8C4×C11×D16C211yesmaximal, characteristic, complemented
9C2×D8×D11C2214yescomplemented
10D4×D44—22no—
11C2×C11×D16C2211yescharacteristic
12C4×C11×D8C2212yescomplemented
13C2×#66890C2214yescomplemented
14#10622628—22no—
15D11×D16—28no—
16C2×D176C2212yescomplemented
17C2×D176C2212yescomplemented
18C2×C16×D11C2212yescomplemented
19#10622496C2214yescomplemented
20#10622386—24no—
21#10622308C2212yescomplemented
22C8×D44C2211yescharacteristic
23C11×#366C2211yescharacteristic, complemented
24C11×#357C2212yescomplemented
25C4×C11×C16C2211yescharacteristic, complemented
26(C2×D11)⋊C16C2212yescomplemented
27#10622129C2214yescomplemented
28C4⋊(C11⋊C16)C2211yescharacteristic, complemented
29C2×D4×D11—24no—
30C22×D44—42no—
31C2×C11×D8C2312yes—
32C4×D4×C11—22no—
33C2×#4323—24no—
34#66983—42no—
35D8×D11—28no—
36D8×D11—44no—
37C2×D88—22no—
38C2×D88C2314yes—
39C2×C8×D11C2312yes—
40#66948—24no—
41#66935—44no—
42#66927—22no—
43C4×D44D411yescharacteristic
44C11×D16D414yescomplemented
45C2×C11×C16C2311yescharacteristic
46C2×C11×C16C2311yescharacteristic
47C11×#107C2312yes—
48C11×#102—22no—
49C4×C8×C11C2311yescharacteristic
50#66890—28no—
51(C2×D11)⋊C8D412yes—
52C2×C11⋊C16C2312yes—
53#66873—24no—
54C4⋊(C11⋊C8)D411yescharacteristic
55D176—24no—
56D176—42no—
57C16×D11—24no—
58D4×D16—111nomaximal, Sylow
59C23×D11—44no—
60C2×D4×C11—22no—
61C22×C4×C11—42no—
62C2×C22⋊D11—44no—
63D4×D11—48no—
64D4×D11—84no—
65C2×D44—24no—
66C2×D44—44no—
67C2×D44—42no—
68C2×D44—42no—
69C2×D44—88no—
70C2×D44D811yescharacteristic
71C2×C4×D11C2×D412yes—
72C11×D8—22no—
73C11×D8C2×D414yescomplemented
74C2×C8×C11C2×D411yescharacteristic
75C2×C8×C11C2411yescharacteristic
76C11×C4⋊C4—22no—
77C11×C22⋊C4—42no—
78C42×C11C2×D411yescharacteristic
79#4323—48no—
80(C2×D11)⋊C4—44no—
81(C2×D11)⋊C4D812yes—
82C4⋊Dic11D811yescharacteristic
83C2×C11⋊C8C2×D412yes—
84D88—24no—
85D88—24no—
86D88—82no—
87C8×D11—22no—
88C8×D11—22no—
89C11×C16—21no—
90C11×C16C2×D412yescomplemented
91C11⋊C16—22no—
92C22×D16—112no—
93D4×D8—112no—
94#2246—111no—
95#2215—112no—
96#2206—112no—
97#2184—114no—
98C4×D16D1111yescharacteristic, complemented
99D4×C16—111no—
100C23×C11—42no—
101C22×D11—44no—
102C22×D11—88no—
103C22×D11—88no—
104C22×D11—164no—
105C22×D11C2×D812yes—
106D4×C11—24no—
107D4×C11—42no—
108C2×C4×C11—42no—
109C2×C4×C11—84no—
110C2×C4×C11C2×D811yescharacteristic
111C2×C4×C11C2×D811yescharacteristic
112C2×C4×C11C22×D411yescharacteristic
113C22⋊D11—88no—
114C2×Dic11C2×D812yes—
115D44—44no—
116D44—44no—
117D44—88no—
118D44—84no—
119D44—162no—
120D44D1614yesdirect product factor
121C4×D11—22no—
122C4×D11—22no—
123C8×C11—21no—
124C8×C11C22×D411yescharacteristic
125C8×C11H(5,𝔽2)11yescharacteristic
126C11⋊C8—22no—
127C22×D8—114no—
128D42—222no—
129C2×D16—114no—
130C2×D16—112no—
131C2×D16—112no—
132C2×D16—228no—
133C2×D16C2×D1111yescharacteristic
134C22×C16—112no—
135#493—112no—
136#466—114no—
137#459—222no—
138#447—224no—
139C4×D8C2×D1112yescomplemented
140C8×D4—111no—
141#366C2×D1111yescharacteristic, complemented
142C4⋊C16—111no—
143#357—114no—
144#357C2×D1112yescomplemented
145C22⋊C16—112no—
146C4×C16C2×D1111yescharacteristic, complemented
147C22×C11—44no—
148C22×C11—82no—
149C22×C11—82no—
150C22×C11C22×D811yescharacteristic
151C2×D11—22no—
152C2×D11—22no—
153C2×D11—84no—
154C2×D11—84no—
155C2×D11—84no—
156C2×D11—1616no—
157C2×D11C2×D1614yescomplemented
158C4×C11—21no—
159C4×C11—82no—
160C4×C11C2×D1612yescomplemented
161C4×C11D4211yescharacteristic
162C4×C11#57611yescharacteristic
163Dic11—22no—
164C22×D4—224no—
165C22×D4—442no—
166C2×D8—114no—
167C2×D8—224no—
168C2×D8—228no—
169C2×D8—222no—
170C2×D8—444no—
171C2×D8C22×D1112yes—
172C22×C8—112no—
173#127—222no—
174#121—224no—
175#121—442no—
176#120—444no—
177C4×D4—22no—
178C4×D4—111no—
179D16—228no—
180D16—224no—
181D16—442no—
182D16D4414yesdirect product factor
183C2×C16—112no—
184C2×C16—224no—
185C2×C16C22×D1111yescharacteristic
186C2×C16C22×D1111yescharacteristic
187#107C22×D1112yes—
188C4⋊C8—111no—
189#102—22no—
190#102—224no—
191C22⋊C8—112no—
192C4×C8C22×D1111yescharacteristic
193C2×C11—84no—
194C2×C11D4×D811yescharacteristic
195C2×C11C22×D1611yescharacteristic
196C2×C11#341511yescharacteristic
197D11—24no—
198D11—164no—
199C24—444no—
200C2×D4—22no—
201C2×D4—111no—
202C2×D4—224no—
203C2×D4—444no—
204C2×D4—444no—
205C2×D4—448no—
206C2×D4—442no—
207C2×D4—442no—
208C2×D4—888no—
209C2×D4—884no—
210C22×C4—42no—
211C22×C4—112no—
212D8—22no—
213D8—224no—
214D8—224no—
215D8—448no—
216D8—882no—
217D8C2×D4414yescomplemented
218C2×C8—112no—
219C2×C8—222no—
220C2×C8—222no—
221C2×C8D4×D1111yescharacteristic
222C2×C8C23×D1111yescharacteristic
223C4⋊C4—22no—
224C4⋊C4—111no—
225C22⋊C4—42no—
226C22⋊C4—112no—
227C22⋊C4—444no—
228C42D4×D1111yescharacteristic
229C16—21no—
230C16—222no—
231C16C2×D4412yescomplemented
232C11D4×D1611yescharacteristic, complemented, Sylow
233C23—42no—
234C23—112no—
235C23—444no—
236C23—888no—
237C23—888no—
238C23—1764no—
239D4—24no—
240D4—42no—
241D4—114no—
242D4—444no—
243D4—444no—
244D4—888no—
245D4—888no—
246D4—884no—
247D4—1762no—
248C2×C4—42no—
249C2×C4—84no—
250C2×C4—112no—
251C2×C4—222no—
252C2×C4—222no—
253C2×C4D8×D1111yescharacteristic
254C2×C4D8×D1111yescharacteristic
255C2×C4C2×D4×D1111yescharacteristic
256C8—21no—
257C8—222no—
258C8C22×D4411yescharacteristic
259C8#6704211yescharacteristic
260C22—44no—
261C22—82no—
262C22—82no—
263C22—114no—
264C22—222no—
265C22—222no—
266C22—884no—
267C22—884no—
268C22—884no—
269C22—17616no—
270C22C2×D8×D1111yescharacteristic
271C4—21no—
272C4—82no—
273C4—222no—
274C4D11×D1612yescomplemented
275C4D4×D4411yescharacteristic
276C4#1062330011yescharacteristic
277C2—84no—
278C2—224no—
279C2—1764no—
280C2D8×D4411yescharacteristic
281C2C2×D11×D1611yescharacteristic
282C2#1308175411yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×D16C2
socleC22×C11C22×D8
hypercenterC4×D16D11
hypocenterC11D4×D16
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×D16

Complements

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

NH ≅ G/Ntype
1. C2×D11×D16C2semidirect
2. D8×D44C2semidirect
3. #13070866C2semidirect
4. #13070703C2semidirect
5. #13070651C2semidirect
6. #13070529C2semidirect
7. C16×D44C2semidirect
8. C4×C11×D16C2semidirect
9. C2×D8×D11C22semidirect
12. C4×C11×D8C22semidirect
13. C2×#66890C22semidirect
16. C2×D176C22semidirect
17. C2×D176C22semidirect
18. C2×C16×D11C22semidirect
19. #10622496C22semidirect
21. #10622308C22semidirect
23. C11×#366C22semidirect
24. C11×#357C22semidirect
25. C4×C11×C16C22semidirect
26. (C2×D11)⋊C16C22semidirect
27. #10622129C22semidirect
28. C4⋊(C11⋊C16)C22semidirect
44. C11×D16D4semidirect
73. C11×D8C2×D4semidirect
90. C11×C16C2×D4semidirect
98. C4×D16D11semidirect
120. D44D16direct (N × H)
139. C4×D8C2×D11semidirect
141. #366C2×D11semidirect
144. #357C2×D11semidirect
146. C4×C16C2×D11semidirect
157. C2×D11C2×D16semidirect
160. C4×C11C2×D16semidirect
182. D16D44direct (N × H)
217. D8C2×D44semidirect
231. C16C2×D44semidirect
232. C11D4×D16semidirect
274. C4D11×D16semidirect

Maximal subgroups

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

subgroupindex
C2×D11×D162
D8×D442
#130708662
#130707032
#130706512
#130705292
C16×D442
C4×C11×D162
D4×D1611