Finite Group Databasebeta

← D16×D172 #25253251

Subgroups — D16×D172 #25253251

Order 11008.

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×D43C212yesmaximal, complemented
2D8×D172C212yesmaximal, complemented
3#19136845C211yesmaximal, characteristic, complemented
4#19136682C212yesmaximal, complemented
5#19136630C212yesmaximal, complemented
6#19136508C214yesmaximal, complemented
7C16×D172C211yesmaximal, characteristic, complemented
8C4×D16×C43C211yesmaximal, characteristic, complemented
9C2×D8×D43C2214yescomplemented
10D4×D172—22no—
11C2×D688C2212yescomplemented
12C2×D688C2212yescomplemented
13C2×#13063266C2214yescomplemented
14D16×D43—28no—
15C2×C16×D43C2212yescomplemented
16#14583276C2212yescomplemented
17#14583136C2214yescomplemented
18#14583094—22no—
19#14583034—24no—
20C8×D172C2211yescharacteristic
21C4⋊(C43⋊C16)C2211yescharacteristic, complemented
22#14582699C2214yescomplemented
23(C2×D43)⋊C16C2212yescomplemented
24C2×D16×C43C2211yescharacteristic
25C4×D8×C43C2212yescomplemented
26C43×#366C2211yescharacteristic, complemented
27C43×#357C2212yescomplemented
28C4×C16×C43C2211yescharacteristic, complemented
29C22×D172—42no—
30C2×D4×D43—24no—
31C2×D344—22no—
32C2×D344C2314yes—
33C2×#10621882—24no—
34D8×D43—28no—
35D8×D43—44no—
36C2×C8×D43C2312yes—
37#13063322—22no—
38#13063300—24no—
39#13063299—42no—
40#13063295—44no—
41C4×D172D411yescharacteristic
42D688—24no—
43D688—42no—
44#13063266—28no—
45C2×C43⋊C16C2312yes—
46C16×D43—24no—
47C4⋊(C43⋊C8)D411yescharacteristic
48#13063245—24no—
49(C2×D43)⋊C8D412yes—
50C2×D8×C43C2312yes—
51C4×D4×C43—22no—
52D16×C43D414yescomplemented
53C2×C16×C43C2311yescharacteristic
54C2×C16×C43C2311yescharacteristic
55#107×C43C2312yes—
56#102×C43—22no—
57C4×C8×C43C2311yescharacteristic
58C23×D43—44no—
59C2×D4×C43—22no—
60C22×C4×C43—42no—
61C2×C22⋊D43—44no—
62D4×D43—48no—
63D4×D43—84no—
64C2×D172—24no—
65C2×D172—42no—
66C2×D172—42no—
67C2×D172—44no—
68C2×D172—88no—
69C2×D172D811yescharacteristic
70C2×C4×D43C2×D412yes—
71D8×C43—22no—
72D8×C43C2×D414yescomplemented
73C2×C8×C43C2×D411yescharacteristic
74C2×C8×C43C2411yescharacteristic
75C4⋊C4×C43—22no—
76C22⋊C4×C43—42no—
77C42×C43C2×D411yescharacteristic
78#10621882—48no—
79(C2×D43)⋊C4—44no—
80(C2×D43)⋊C4D812yes—
81C4⋊Dic43D811yescharacteristic
82C2×C43⋊C8C2×D412yes—
83D344—24no—
84D344—24no—
85D344—82no—
86C8×D43—22no—
87C8×D43—22no—
88C16×C43—21no—
89C16×C43C2×D412yescomplemented
90C43⋊C16—22no—
91C23×C43—42no—
92C22×D43—44no—
93C22×D43—88no—
94C22×D43—88no—
95C22×D43—164no—
96C22×D43C2×D812yes—
97D4×C43—24no—
98D4×C43—42no—
99C2×C4×C43—42no—
100C2×C4×C43—84no—
101C2×C4×C43C2×D811yescharacteristic
102C2×C4×C43C2×D811yescharacteristic
103C2×C4×C43C22×D411yescharacteristic
104C22⋊D43—88no—
105C2×Dic43C2×D812yes—
106D172—44no—
107D172—44no—
108D172—88no—
109D172—84no—
110D172—162no—
111D172D1614yesdirect product factor
112C4×D43—22no—
113C4×D43—22no—
114C8×C43—21no—
115C8×C43C22×D411yescharacteristic
116C8×C43H(5,𝔽2)11yescharacteristic
117C43⋊C8—22no—
118D4×D16—431nomaximal, Sylow
119C22×C43—44no—
120C22×C43—82no—
121C22×C43—82no—
122C22×C43C22×D811yescharacteristic
123C2×D43—22no—
124C2×D43—22no—
125C2×D43—84no—
126C2×D43—84no—
127C2×D43—84no—
128C2×D43—1616no—
129C2×D43C2×D1614yescomplemented
130C4×C43—21no—
131C4×C43—82no—
132C4×C43C2×D1612yescomplemented
133C4×C43D4211yescharacteristic
134C4×C43#57611yescharacteristic
135Dic43—22no—
136C22×D16—432no—
137D4×D8—432no—
138#2246—431no—
139#2215—432no—
140#2206—432no—
141#2184—434no—
142C4×D16D4311yescharacteristic, complemented
143D4×C16—431no—
144C2×C43—84no—
145C2×C43D4×D811yescharacteristic
146C2×C43C22×D1611yescharacteristic
147C2×C43#341511yescharacteristic
148D43—24no—
149D43—164no—
150C22×D8—434no—
151D42—862no—
152C2×D16—434no—
153C2×D16—432no—
154C2×D16—432no—
155C2×D16—868no—
156C2×D16C2×D4311yescharacteristic
157C22×C16—432no—
158#493—432no—
159#466—434no—
160#459—862no—
161#447—864no—
162C4×D8C2×D4312yescomplemented
163C8×D4—431no—
164#366C2×D4311yescharacteristic, complemented
165C4⋊C16—431no—
166#357—434no—
167#357C2×D4312yescomplemented
168C22⋊C16—432no—
169C4×C16C2×D4311yescharacteristic, complemented
170C43D4×D1611yescharacteristic, complemented, Sylow
171C22×D4—864no—
172C22×D4—1722no—
173C2×D8—434no—
174C2×D8—864no—
175C2×D8—868no—
176C2×D8—862no—
177C2×D8—1724no—
178C2×D8C22×D4312yes—
179C22×C8—432no—
180#127—862no—
181#121—864no—
182#121—1722no—
183#120—1724no—
184C4×D4—22no—
185C4×D4—431no—
186D16—868no—
187D16—864no—
188D16—1722no—
189D16D17214yesdirect product factor
190C2×C16—432no—
191C2×C16—864no—
192C2×C16C22×D4311yescharacteristic
193C2×C16C22×D4311yescharacteristic
194#107C22×D4312yes—
195C4⋊C8—431no—
196#102—22no—
197#102—864no—
198C22⋊C8—432no—
199C4×C8C22×D4311yescharacteristic
200C24—1724no—
201C2×D4—22no—
202C2×D4—431no—
203C2×D4—864no—
204C2×D4—3448no—
205C2×D4—3444no—
206C2×D4—1724no—
207C2×D4—1724no—
208C2×D4—1728no—
209C2×D4—1722no—
210C2×D4—1722no—
211C22×C4—42no—
212C22×C4—432no—
213D8—22no—
214D8—864no—
215D8—864no—
216D8—3442no—
217D8—1728no—
218D8C2×D17214yescomplemented
219C2×C8—432no—
220C2×C8—862no—
221C2×C8—862no—
222C2×C8D4×D4311yescharacteristic
223C2×C8C23×D4311yescharacteristic
224C4⋊C4—22no—
225C4⋊C4—431no—
226C22⋊C4—42no—
227C22⋊C4—432no—
228C22⋊C4—1724no—
229C42D4×D4311yescharacteristic
230C16—21no—
231C16—862no—
232C16C2×D17212yescomplemented
233C23—42no—
234C23—432no—
235C23—3448no—
236C23—3448no—
237C23—1724no—
238C23—6884no—
239D4—24no—
240D4—42no—
241D4—434no—
242D4—3448no—
243D4—3448no—
244D4—3444no—
245D4—1724no—
246D4—1724no—
247D4—6882no—
248C2×C4—42no—
249C2×C4—84no—
250C2×C4—432no—
251C2×C4—862no—
252C2×C4—862no—
253C2×C4D8×D4311yescharacteristic
254C2×C4D8×D4311yescharacteristic
255C2×C4C2×D4×D4311yescharacteristic
256C8—21no—
257C8—862no—
258C8C22×D17211yescharacteristic
259C8#1306337111yescharacteristic
260C22—44no—
261C22—82no—
262C22—82no—
263C22—434no—
264C22—862no—
265C22—862no—
266C22—3444no—
267C22—3444no—
268C22—3444no—
269C22—68816no—
270C22C2×D8×D4311yescharacteristic
271C4—21no—
272C4—82no—
273C4—862no—
274C4D16×D4312yescomplemented
275C4D4×D17211yescharacteristic
276C4#1458370111yescharacteristic
277C2—84no—
278C2—864no—
279C2—6884no—
280C2D8×D17211yescharacteristic
281C2C2×D16×D4311yescharacteristic
282C2#1914773311yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC4×D16×C43C2
socleC22×C43C22×D8
hypercenterC4×D16D43
hypocenterC43D4×D16
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×D16

Complements

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

NH ≅ G/Ntype
1. C2×D16×D43C2semidirect
2. D8×D172C2semidirect
3. #19136845C2semidirect
4. #19136682C2semidirect
5. #19136630C2semidirect
6. #19136508C2semidirect
7. C16×D172C2semidirect
8. C4×D16×C43C2semidirect
9. C2×D8×D43C22semidirect
11. C2×D688C22semidirect
12. C2×D688C22semidirect
13. C2×#13063266C22semidirect
15. C2×C16×D43C22semidirect
16. #14583276C22semidirect
17. #14583136C22semidirect
21. C4⋊(C43⋊C16)C22semidirect
22. #14582699C22semidirect
23. (C2×D43)⋊C16C22semidirect
25. C4×D8×C43C22semidirect
26. C43×#366C22semidirect
27. C43×#357C22semidirect
28. C4×C16×C43C22semidirect
52. D16×C43D4semidirect
72. D8×C43C2×D4semidirect
89. C16×C43C2×D4semidirect
111. D172D16direct (N × H)
129. C2×D43C2×D16semidirect
132. C4×C43C2×D16semidirect
142. C4×D16D43semidirect
162. C4×D8C2×D43semidirect
164. #366C2×D43semidirect
167. #357C2×D43semidirect
169. C4×C16C2×D43semidirect
170. C43D4×D16semidirect
189. D16D172direct (N × H)
218. D8C2×D172semidirect
232. C16C2×D172semidirect
274. C4D16×D43semidirect

Maximal subgroups

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

subgroupindex
C2×D16×D432
D8×D1722
#191368452
#191366822
#191366302
#191365082
C16×D1722
C4×D16×C432
D4×D1643