Finite Group Databasebeta

← D8×D16 #492519

Subgroups — D8×D16 #492519

Order 512.

608 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 134 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
1D4×D16C212yesmaximal, complemented
2D82C212yesmaximal, complemented
3#12515C211yesmaximal, characteristic, complemented
4#12430C212yesmaximal, complemented
5#12424C212yesmaximal, complemented
6#12316C214yesmaximal, complemented
7C8×D16C211yesmaximal, characteristic, complemented
8C16×D8C211yesmaximal, characteristic, complemented
9C22×D16—22no—
10D4×D8—22no—
11D4×D8C2214yescomplemented
12#2246C2212yescomplemented
13#2246C2212yescomplemented
14#2215—22no—
15#2206C2214yescomplemented
16#2184—24no—
17C4×D16C2211yescharacteristic
18D4×C16C2212yescomplemented
19#1712C2212yescomplemented
20#1667—22no—
21#1667C2214yescomplemented
22#1619—24no—
23C8×D8C2211yescharacteristic
24C8×D8C2212yescomplemented
25#1371C2211yescharacteristic, complemented
26#1370C2211yescharacteristic, complemented
27#1361C2214yescomplemented
28#1331C2212yescomplemented
29D4⋊C16C2212yescomplemented
30C8×C16C2211yescharacteristic, complemented
31C22×D8—24no—
32C22×D8—42no—
33D42—24no—
34C2×D16—24no—
35C2×D16—22no—
36C2×D16—22no—
37C2×D16—42no—
38C2×D16—48no—
39C2×D16D411yescharacteristic
40C22×C16—22no—
41#493—22no—
42#493—22no—
43#493C2314yes—
44#466—24no—
45#466—42no—
46#459—24no—
47#459—24no—
48#447—44no—
49#447—44no—
50C4×D8D411yescharacteristic
51C4×D8C2312yes—
52C8×D4—22no—
53C8×D4C2312yes—
54#366D411yescharacteristic
55C4⋊C16C2312yes—
56#357—24no—
57#357D412yes—
58C22⋊C16—22no—
59C4×C16C2311yescharacteristic
60C4×C16C2311yescharacteristic
61#335D411yescharacteristic
62#335C2312yes—
63#331—24no—
64D4⋊C8—22no—
65D4⋊C8D412yes—
66C82C2311yescharacteristic
67C22×D4—44no—
68C22×D4—44no—
69C2×D8—24no—
70C2×D8—24no—
71C2×D8—44no—
72C2×D8—48no—
73C2×D8—44no—
74C2×D8—42no—
75C2×D8—42no—
76C2×D8—82no—
77C2×D8—84no—
78C2×D8—88no—
79C2×D8D811yescharacteristic
80C2×D8C2×D412yes—
81C22×C8—22no—
82C22×C8—42no—
83#127—24no—
84#121—44no—
85#121—44no—
86#120—84no—
87C4×D4—22no—
88C4×D4C2×D412yes—
89D16—48no—
90D16—44no—
91D16—82no—
92D16—84no—
93D16D814yesdirect product factor
94C2×C16—21no—
95C2×C16—22no—
96C2×C16—44no—
97C2×C16C2×D411yescharacteristic
98C2×C16C2×D411yescharacteristic
99#107D811yescharacteristic
100#107C2×D412yes—
101C4⋊C8—22no—
102C4⋊C8C2×D412yes—
103#102—22no—
104#102—44no—
105#102—44no—
106#102D812yes—
107C22⋊C8—22no—
108C22⋊C8—42no—
109C4×C8C2×D411yescharacteristic
110C4×C8C2×D411yescharacteristic
111C4×C8C2411yescharacteristic
112C24—84no—
113C2×D4—22no—
114C2×D4—44no—
115C2×D4—44no—
116C2×D4—44no—
117C2×D4—84no—
118C2×D4—88no—
119C2×D4—84no—
120C2×D4—88no—
121C2×D4—164no—
122C2×D4—164no—
123C2×D4C2×D812yes—
124C22×C4—22no—
125C22×C4—42no—
126D8—22no—
127D8—44no—
128D8—44no—
129D8—84no—
130D8—88no—
131D8—88no—
132D8—84no—
133D8—162no—
134D8—164no—
135D8D1614yesdirect product factor
136D8C2×D814yescomplemented
137C2×C8—21no—
138C2×C8—22no—
139C2×C8—42no—
140C2×C8—42no—
141C2×C8—42no—
142C2×C8—84no—
143C2×C8C2×D811yescharacteristic
144C2×C8C2×D811yescharacteristic
145C2×C8C22×D411yescharacteristic
146C2×C8H(5,𝔽2)11yescharacteristic
147C4⋊C4—22no—
148C4⋊C4C2×D812yes—
149C22⋊C4—22no—
150C22⋊C4—42no—
151C22⋊C4—84no—
152C42C22×D411yescharacteristic
153C16—22no—
154C16—21no—
155C16—42no—
156C16C2×D812yescomplemented
157C23—22no—
158C23—42no—
159C23—84no—
160C23—168no—
161C23—168no—
162C23—324no—
163D4—22no—
164D4—24no—
165D4—42no—
166D4—84no—
167D4—84no—
168D4—84no—
169D4—84no—
170D4—164no—
171D4—168no—
172D4—168no—
173D4C2×D1614yescomplemented
174C2×C4—22no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—82no—
179C2×C4—82no—
180C2×C4D4211yescharacteristic
181C2×C4C22×D811yescharacteristic
182C2×C4#57611yescharacteristic
183C8—22no—
184C8—21no—
185C8—21no—
186C8—42no—
187C8—82no—
188C8C2×D1612yescomplemented
189C8C22×D811yescharacteristic
190C8#57611yescharacteristic
191C22—24no—
192C22—42no—
193C22—42no—
194C22—44no—
195C22—82no—
196C22—82no—
197C22—164no—
198C22—164no—
199C22—164no—
200C22—3216no—
201C22D4×D811yescharacteristic
202C4—21no—
203C4—42no—
204C4—82no—
205C4D4×D811yescharacteristic
206C4#329211yescharacteristic
207C4C22×D1611yescharacteristic
208C4#341511yescharacteristic
209C2—44no—
210C2—84no—
211C2—324no—
212C2D8211yescharacteristic
213C2D4×D1611yescharacteristic
214C2#3385811yescharacteristic
subgroupG/H
center, socleC22D4×D8
commutator, Frattini, cosocleC4×C8C24
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C42 ◁ C8×D8 ◁ G
LECSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. D4×D16C2semidirect
2. D82C2semidirect
3. #12515C2semidirect
4. #12430C2semidirect
5. #12424C2semidirect
6. #12316C2semidirect
7. C8×D16C2semidirect
8. C16×D8C2semidirect
11. D4×D8C22semidirect
12. #2246C22semidirect
13. #2246C22semidirect
15. #2206C22semidirect
18. D4×C16C22semidirect
19. #1712C22semidirect
21. #1667C22semidirect
24. C8×D8C22semidirect
25. #1371C22semidirect
26. #1370C22semidirect
27. #1361C22semidirect
28. #1331C22semidirect
29. D4⋊C16C22semidirect
30. C8×C16C22semidirect
93. D16D8direct (N × H)
135. D8D16direct (N × H)
136. D8C2×D8semidirect
156. C16C2×D8semidirect
173. D4C2×D16semidirect
188. C8C2×D16semidirect

Maximal subgroups

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

subgroupindex
D4×D162
D822
#125152
#124302
#124242
#123162
C8×D162
C16×D82