Finite Group Databasebeta

← D8×SD16 #19969

Subgroups — D8×SD16 #19969

Order 256.

399 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 399 conjugacy classes of subgroups — too many to draw. Only its 119 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
1Q8×D8C211yesmaximal, characteristic, complemented
2D4×SD16C212yesmaximal, complemented
3D4×D8C211yesmaximal, characteristic
4#1706C211yesmaximal, characteristic, complemented
5#1673C211yesmaximal, characteristic, complemented
6#1668C211yesmaximal, characteristic, complemented
7#1665C212yesmaximal, complemented
8#1639C212yesmaximal, complemented
9#1627C212yesmaximal, complemented
10C8×SD16C211yesmaximal, characteristic, complemented
11C8×D8C211yesmaximal, characteristic, complemented
12C22×SD16—22no—
13C22×D8—21no—
14D4×Q8C2212yescomplemented
15D42C2212yes—
16#500—21no—
17#500C2211yescharacteristic, complemented
18#493C2211yescharacteristic
19#492C2212yescomplemented
20#486C2212yescomplemented
21#474—22no—
22#474C2212yescomplemented
23#466—21no—
24#465—22no—
25#461C2212yes—
26#460C2212yescomplemented
27#459C2212yes—
28#450—22no—
29#448—22no—
30#447—22no—
31C8×Q8C2211yescharacteristic, complemented
32C4×SD16C2211yescharacteristic
33C4×D8—21no—
34C4×D8C2211yescharacteristic
35C8×D4C2211yescharacteristic
36C8×D4C2212yescomplemented
37#335C2211yescharacteristic, complemented
38#334C2211yescharacteristic, complemented
39#332C2212yescomplemented
40#331C2212yescomplemented
41Q8⋊C8C2211yescharacteristic, complemented
42D4⋊C8C2211yescharacteristic
43D4⋊C8C2212yescomplemented
44C82C2211yescharacteristic, complemented
45C22×Q8—22no—
46C22×D4—22no—
47C22×D4—22no—
48C2×SD16—22no—
49C2×SD16—22no—
50C2×SD16—22no—
51C2×SD16—22no—
52C2×SD16—48no—
53C2×SD16D411yescharacteristic
54C2×D8—22no—
55C2×D8—21no—
56C2×D8—21no—
57C2×D8—44no—
58C2×D8D411yescharacteristic
59C22×C8—21no—
60C22×C8—22no—
61C4⋊Q8—22no—
62C4⋊Q8C2312yes—
63#127C2312yes—
64C22⋊Q8—22no—
65C22⋊Q8—42no—
66#121—22no—
67#121—22no—
68#120—42no—
69C4×Q8C2311yescharacteristic
70C4×D4—22no—
71C4×D4C2311yescharacteristic
72C4×D4C2312yes—
73#107—21no—
74#107—21no—
75#107—22no—
76#107D411yescharacteristic
77#106D411yescharacteristic
78C4⋊C8—21no—
79C4⋊C8C2311yescharacteristic
80C4⋊C8C2312yes—
81C4⋊C8C2311yescharacteristic
82#103—22no—
83#103D411yescharacteristic
84#102—22no—
85#102—22no—
86#102—22no—
87#102—42no—
88#102D412yes—
89#102D411yescharacteristic
90C22⋊C8—21no—
91C22⋊C8—22no—
92C4×C8—21no—
93C4×C8C2311yescharacteristic
94C4×C8C2311yescharacteristic
95C4×C8C2311yescharacteristic
96C24—42no—
97C2×Q8—22no—
98C2×Q8—42no—
99C2×Q8—44no—
100C2×Q8—82no—
101C2×Q8C2×D411yescharacteristic
102C2×D4—22no—
103C2×D4—22no—
104C2×D4—22no—
105C2×D4—42no—
106C2×D4—42no—
107C2×D4—44no—
108C2×D4—44no—
109C2×D4—82no—
110C2×D4—82no—
111C2×D4C2×D411yescharacteristic
112C2×D4C2×D412yes—
113C22×C4—21no—
114C22×C4—22no—
115C22×C4—42no—
116SD16—44no—
117SD16—44no—
118SD16—44no—
119SD16—82no—
120SD16D814yesdirect product factor
121D8—44no—
122D8—42no—
123D8—81no—
124D8SD1614yesdirect product factor
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—22no—
128C2×C8—21no—
129C2×C8—44no—
130C2×C8—42no—
131C2×C8C2×D411yescharacteristic
132C2×C8C2×D411yescharacteristic
133C2×C8C2×D411yescharacteristic
134C2×C8C2×D411yescharacteristic
135C4⋊C4—21no—
136C4⋊C4—22no—
137C4⋊C4—22no—
138C4⋊C4—42no—
139C4⋊C4C2×D411yescharacteristic
140C4⋊C4C2×D412yes—
141C4⋊C4C2×D411yescharacteristic
142C22⋊C4—21no—
143C22⋊C4—22no—
144C22⋊C4—42no—
145C22⋊C4—42no—
146C42—21no—
147C42C2411yescharacteristic
148C23—22no—
149C23—21no—
150C23—42no—
151C23—84no—
152C23—84no—
153C23—162no—
154Q8—21no—
155Q8—42no—
156Q8—42no—
157Q8—84no—
158Q8C2×D812yescomplemented
159D4—21no—
160D4—22no—
161D4—42no—
162D4—42no—
163D4—42no—
164D4—42no—
165D4—82no—
166D4—84no—
167D4—84no—
168D4C2×D812yes—
169D4C2×SD1614yescomplemented
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—41no—
176C2×C4—42no—
177C2×C4—41no—
178C2×C4—42no—
179C2×C4—84no—
180C2×C4C22×D411yescharacteristic
181C2×C4C22×D411yescharacteristic
182C2×C4H(5,𝔽2)11yescharacteristic
183C8—21no—
184C8—21no—
185C8—41no—
186C8—42no—
187C8—41no—
188C8—41no—
189C8C2×D812yescomplemented
190C8C2×SD1612yescomplemented
191C22—22no—
192C22—24no—
193C22—42no—
194C22—41no—
195C22—42no—
196C22—41no—
197C22—82no—
198C22—82no—
199C22—82no—
200C22—168no—
201C22D4211yescharacteristic
202C4—22no—
203C4—21no—
204C4—42no—
205C4—41no—
206C4—41no—
207C4—82no—
208C4C22×D811yescharacteristic
209C4C22×SD1611yescharacteristic
210C4#57611yescharacteristic
211C4#57711yescharacteristic
212C2—44no—
213C2—42no—
214C2—162no—
215C2D4×D811yescharacteristic
216C2D4×SD1611yescharacteristic
217C2#329011yescharacteristic
subgroupG/H
center, socleC22D42
commutator, Frattini, cosocleC42C24
prime radicalD4×D8C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C42 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. Q8×D8C2semidirect
2. D4×SD16C2semidirect
4. #1706C2semidirect
5. #1673C2semidirect
6. #1668C2semidirect
7. #1665C2semidirect
8. #1639C2semidirect
9. #1627C2semidirect
10. C8×SD16C2semidirect
11. C8×D8C2semidirect
14. D4×Q8C22semidirect
17. #500C22semidirect
19. #492C22semidirect
20. #486C22semidirect
22. #474C22semidirect
26. #460C22semidirect
31. C8×Q8C22semidirect
36. C8×D4C22semidirect
37. #335C22semidirect
38. #334C22semidirect
39. #332C22semidirect
40. #331C22semidirect
41. Q8⋊C8C22semidirect
43. D4⋊C8C22semidirect
44. C82C22semidirect
120. SD16D8direct (N × H)
124. D8SD16direct (N × H)
158. Q8C2×D8semidirect
169. D4C2×SD16semidirect
189. C8C2×D8semidirect
190. C8C2×SD16semidirect

Maximal subgroups

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

subgroupindex
Q8×D82
D4×SD162
D4×D82
#17062
#16732
#16682
#16652
#16392
#16272
C8×SD162
C8×D82