Finite Group Databasebeta

← D16×D284 #32154106

Subgroups — D16×D284 #32154106

Order 18176.

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×D16×D71C212yesmaximal, complemented
2D8×D284C212yesmaximal, complemented
3#22590590C211yesmaximal, characteristic, complemented
4#22590427C212yesmaximal, complemented
5#22590375C212yesmaximal, complemented
6#22590253C214yesmaximal, complemented
7C16×D284C211yesmaximal, characteristic, complemented
8C4×D16×C71C211yesmaximal, characteristic, complemented
9C2×D8×D71C2214yescomplemented
10D4×D284—22no—
11C2×D1136C2212yescomplemented
12C2×D1136C2212yescomplemented
13C2×#14556069C2214yescomplemented
14D16×D71—28no—
15C2×C16×D71C2212yescomplemented
16#17986376C2212yescomplemented
17#17986236C2214yescomplemented
18#17986194—22no—
19#17986134—24no—
20C8×D284C2211yescharacteristic
21C4⋊(C71⋊C16)C2211yescharacteristic, complemented
22#17985799C2214yescomplemented
23(C2×D71)⋊C16C2212yescomplemented
24C2×D16×C71C2211yescharacteristic
25C4×D8×C71C2212yescomplemented
26#366×C71C2211yescharacteristic, complemented
27#357×C71C2212yescomplemented
28C4×C16×C71C2211yescharacteristic, complemented
29C22×D284—42no—
30C2×D4×D71—24no—
31C2×D568—22no—
32C2×D568C2314yes—
33C2×#11765850—24no—
34D8×D71—28no—
35D8×D71—44no—
36C2×C8×D71C2312yes—
37#14556125—22no—
38#14556103—24no—
39#14556102—42no—
40#14556098—44no—
41C4×D284D411yescharacteristic
42D1136—24no—
43D1136—42no—
44#14556069—28no—
45C2×C71⋊C16C2312yes—
46C16×D71—24no—
47C4⋊(C71⋊C8)D411yescharacteristic
48#14556048—24no—
49(C2×D71)⋊C8D412yes—
50C2×D8×C71C2312yes—
51C4×D4×C71—22no—
52D16×C71D414yescomplemented
53C2×C16×C71C2311yescharacteristic
54C2×C16×C71C2311yescharacteristic
55#107×C71C2312yes—
56#102×C71—22no—
57C4×C8×C71C2311yescharacteristic
58C23×D71—44no—
59C2×D284—24no—
60C2×D284—44no—
61C2×D284—42no—
62C2×D284—42no—
63C2×D284—88no—
64C2×D284D811yescharacteristic
65C2×C22⋊D71—44no—
66D4×D71—48no—
67D4×D71—84no—
68C2×C4×D71C2×D412yes—
69D568—24no—
70D568—24no—
71D568—82no—
72#11765850—48no—
73C2×C71⋊C8C2×D412yes—
74C8×D71—22no—
75C8×D71—22no—
76C4⋊Dic71D811yescharacteristic
77(C2×D71)⋊C4—44no—
78(C2×D71)⋊C4D812yes—
79C71⋊C16—22no—
80C2×D4×C71—22no—
81C22×C4×C71—42no—
82D8×C71—22no—
83D8×C71C2×D414yescomplemented
84C2×C8×C71C2×D411yescharacteristic
85C2×C8×C71C2411yescharacteristic
86C4⋊C4×C71—22no—
87C22⋊C4×C71—42no—
88C42×C71C2×D411yescharacteristic
89C16×C71—21no—
90C16×C71C2×D412yescomplemented
91C23×C71—42no—
92C22×D71—44no—
93C22×D71—88no—
94C22×D71—88no—
95C22×D71—164no—
96C22×D71C2×D812yes—
97D4×C71—24no—
98D4×C71—42no—
99C2×C4×C71—42no—
100C2×C4×C71—84no—
101C2×C4×C71C2×D811yescharacteristic
102C2×C4×C71C2×D811yescharacteristic
103C2×C4×C71C22×D411yescharacteristic
104C22⋊D71—88no—
105C2×Dic71C2×D812yes—
106D284—44no—
107D284—44no—
108D284—88no—
109D284—84no—
110D284—162no—
111D284D1614yesdirect product factor
112C4×D71—22no—
113C4×D71—22no—
114C8×C71—21no—
115C8×C71C22×D411yescharacteristic
116C8×C71H(5,𝔽2)11yescharacteristic
117C71⋊C8—22no—
118C22×C71—44no—
119C22×C71—82no—
120C22×C71—82no—
121C22×C71C22×D811yescharacteristic
122C2×D71—22no—
123C2×D71—22no—
124C2×D71—84no—
125C2×D71—84no—
126C2×D71—84no—
127C2×D71—1616no—
128C2×D71C2×D1614yescomplemented
129C4×C71—21no—
130C4×C71—82no—
131C4×C71C2×D1612yescomplemented
132C4×C71D4211yescharacteristic
133C4×C71#57611yescharacteristic
134Dic71—22no—
135D4×D16—711nomaximal, Sylow
136C2×C71—84no—
137C2×C71D4×D811yescharacteristic
138C2×C71C22×D1611yescharacteristic
139C2×C71#341511yescharacteristic
140D71—24no—
141D71—164no—
142C22×D16—712no—
143D4×D8—712no—
144#2246—711no—
145#2215—712no—
146#2206—712no—
147#2184—714no—
148C4×D16D7111yescharacteristic, complemented
149D4×C16—711no—
150C71D4×D1611yescharacteristic, complemented, Sylow
151C22×D8—714no—
152D42—1422no—
153C2×D16—714no—
154C2×D16—712no—
155C2×D16—712no—
156C2×D16—1428no—
157C2×D16C2×D7111yescharacteristic
158C22×C16—712no—
159#493—712no—
160#466—714no—
161#459—1422no—
162#447—1424no—
163C4×D8C2×D7112yescomplemented
164C8×D4—711no—
165#366C2×D7111yescharacteristic, complemented
166C4⋊C16—711no—
167#357—714no—
168#357C2×D7112yescomplemented
169C22⋊C16—712no—
170C4×C16C2×D7111yescharacteristic, complemented
171C22×D4—2842no—
172C22×D4—1424no—
173C2×D8—2844no—
174C2×D8—714no—
175C2×D8—1424no—
176C2×D8—1428no—
177C2×D8—1422no—
178C2×D8C22×D7112yes—
179C22×C8—712no—
180#127—1422no—
181#121—2842no—
182#121—1424no—
183#120—2844no—
184C4×D4—22no—
185C4×D4—711no—
186D16—2842no—
187D16—1428no—
188D16—1424no—
189D16D28414yesdirect product factor
190C2×C16—712no—
191C2×C16—1424no—
192C2×C16C22×D7111yescharacteristic
193C2×C16C22×D7111yescharacteristic
194#107C22×D7112yes—
195C4⋊C8—711no—
196#102—22no—
197#102—1424no—
198C22⋊C8—712no—
199C4×C8C22×D7111yescharacteristic
200C24—2844no—
201C2×D4—22no—
202C2×D4—2844no—
203C2×D4—2844no—
204C2×D4—2848no—
205C2×D4—2842no—
206C2×D4—2842no—
207C2×D4—5688no—
208C2×D4—5684no—
209C2×D4—711no—
210C2×D4—1424no—
211C22×C4—42no—
212C22×C4—712no—
213D8—22no—
214D8—2848no—
215D8—5682no—
216D8—1424no—
217D8—1424no—
218D8C2×D28414yescomplemented
219C2×C8—712no—
220C2×C8—1422no—
221C2×C8—1422no—
222C2×C8D4×D7111yescharacteristic
223C2×C8C23×D7111yescharacteristic
224C4⋊C4—22no—
225C4⋊C4—711no—
226C22⋊C4—42no—
227C22⋊C4—2844no—
228C22⋊C4—712no—
229C42D4×D7111yescharacteristic
230C16—21no—
231C16—1422no—
232C16C2×D28412yescomplemented
233C23—42no—
234C23—2844no—
235C23—5688no—
236C23—5688no—
237C23—712no—
238C23—11364no—
239D4—24no—
240D4—42no—
241D4—2844no—
242D4—2844no—
243D4—5688no—
244D4—5688no—
245D4—5684no—
246D4—714no—
247D4—11362no—
248C2×C4—42no—
249C2×C4—84no—
250C2×C4—712no—
251C2×C4—1422no—
252C2×C4—1422no—
253C2×C4D8×D7111yescharacteristic
254C2×C4D8×D7111yescharacteristic
255C2×C4C2×D4×D7111yescharacteristic
256C8—21no—
257C8—1422no—
258C8C22×D28411yescharacteristic
259C8#1455617411yescharacteristic
260C22—44no—
261C22—82no—
262C22—82no—
263C22—5684no—
264C22—5684no—
265C22—5684no—
266C22—714no—
267C22—113616no—
268C22—1422no—
269C22—1422no—
270C22C2×D8×D7111yescharacteristic
271C4—21no—
272C4—82no—
273C4—1422no—
274C4D16×D7112yescomplemented
275C4D4×D28411yescharacteristic
276C4#1798680111yescharacteristic
277C2—84no—
278C2—11364no—
279C2—1424no—
280C2D8×D28411yescharacteristic
281C2C2×D16×D7111yescharacteristic
282C2#2260147811yescharacteristic
subgroupG/H
centerC22C2×D8×D71
commutator, cosocleC2×C8×C71C24
FrattiniC2×C8C23×D71
FittingC4×D16×C71C2
socleC22×C71C22×D8
hypercenterC4×D16D71
hypocenterC71D4×D16
LCSG ▷ C2×C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×D16

Complements

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

NH ≅ G/Ntype
1. C2×D16×D71C2semidirect
2. D8×D284C2semidirect
3. #22590590C2semidirect
4. #22590427C2semidirect
5. #22590375C2semidirect
6. #22590253C2semidirect
7. C16×D284C2semidirect
8. C4×D16×C71C2semidirect
9. C2×D8×D71C22semidirect
11. C2×D1136C22semidirect
12. C2×D1136C22semidirect
13. C2×#14556069C22semidirect
15. C2×C16×D71C22semidirect
16. #17986376C22semidirect
17. #17986236C22semidirect
21. C4⋊(C71⋊C16)C22semidirect
22. #17985799C22semidirect
23. (C2×D71)⋊C16C22semidirect
25. C4×D8×C71C22semidirect
26. #366×C71C22semidirect
27. #357×C71C22semidirect
28. C4×C16×C71C22semidirect
52. D16×C71D4semidirect
83. D8×C71C2×D4semidirect
90. C16×C71C2×D4semidirect
111. D284D16direct (N × H)
128. C2×D71C2×D16semidirect
131. C4×C71C2×D16semidirect
148. C4×D16D71semidirect
150. C71D4×D16semidirect
163. C4×D8C2×D71semidirect
165. #366C2×D71semidirect
168. #357C2×D71semidirect
170. C4×C16C2×D71semidirect
189. D16D284direct (N × H)
218. D8C2×D284semidirect
232. C16C2×D284semidirect
274. C4D16×D71semidirect

Maximal subgroups

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

subgroupindex
C2×D16×D712
D8×D2842
#225905902
#225904272
#225903752
#225902532
C16×D2842
C4×D16×C712
D4×D1671