Finite Group Databasebeta

← D4×SD64 #513166

Subgroups — D4×SD64 #513166

Order 512.

465 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 465 conjugacy classes of subgroups — too many to draw. Only its 130 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
1C22×SD64C212yesmaximal, complemented
2D4×Q32C211yesmaximal, characteristic, complemented
3D4×D16C211yesmaximal, characteristic
4#13727C211yesmaximal, characteristic, complemented
5#13696C212yesmaximal, complemented
6#13687C211yesmaximal, characteristic, complemented
7#13686C211yesmaximal, characteristic, complemented
8#13664C212yesmaximal, complemented
9#13662C212yesmaximal, complemented
10C4×SD64C211yesmaximal, characteristic, complemented
11D4×C32C211yesmaximal, characteristic, complemented
12C22×Q32C2212yescomplemented
13C22×D16C2212yes—
14D4×Q16—21no—
15D4×D8—21no—
16C2×SD64—28no—
17C2×SD64C2212yes—
18C2×SD64C2211yescharacteristic
19C2×SD64C2212yescomplemented
20C2×SD64C2212yescomplemented
21C2×SD64C2212yescomplemented
22C22×C32C2212yescomplemented
23#2247C2211yescharacteristic, complemented
24#2246C2211yescharacteristic
25#2216C2212yescomplemented
26#2215C2212yes—
27#2209—21no—
28#2206—21no—
29#2188—22no—
30#2184—22no—
31C4×Q32C2211yescharacteristic, complemented
32C4×D16C2211yescharacteristic
33D4×C16C2211yescharacteristic
34#1424C2211yescharacteristic, complemented
35C4⋊C32C2211yescharacteristic, complemented
36#1416C2211yescharacteristic, complemented
37#1416C2212yescomplemented
38#1415C2211yescharacteristic
39#1415C2212yescomplemented
40C22⋊C32C2212yescomplemented
41C4×C32C2211yescharacteristic, complemented
42C22×Q16—22no—
43C22×D8—22no—
44D4×Q8—41no—
45D42—41no—
46C2×Q32—24no—
47C2×Q32—22no—
48C2×Q32—21no—
49C2×Q32—42no—
50C2×Q32C2312yes—
51C2×Q32C2311yescharacteristic
52C2×D16—24no—
53C2×D16—22no—
54C2×D16—21no—
55C2×D16—42no—
56C2×D16C2312yes—
57C2×D16C2311yescharacteristic
58C22×C16C2312yes—
59#494—21no—
60#493—21no—
61#467—22no—
62#466—22no—
63#462—41no—
64#459—41no—
65#451—42no—
66#447—42no—
67C4×Q16—21no—
68C4×D8—21no—
69C8×D4D411yescharacteristic
70SD64—24no—
71SD64—24no—
72SD64—24no—
73SD64—42no—
74SD64D414yesdirect product factor
75C2×C32—24no—
76C2×C32C2311yescharacteristic
77C2×C32C2312yes—
78C2×C32C2311yescharacteristic
79#366C2311yescharacteristic
80#366C2311yescharacteristic
81C4⋊C16D411yescharacteristic
82#358—21no—
83#358—22no—
84#357—21no—
85#357—22no—
86C22⋊C16D412yes—
87C4×C16C2311yescharacteristic
88C22×Q8—42no—
89C22×D4—42no—
90C22×D4—81no—
91C2×Q16—21no—
92C2×Q16—22no—
93C2×Q16—44no—
94C2×Q16—42no—
95C2×Q16—41no—
96C2×Q16—82no—
97C2×D8—21no—
98C2×D8—22no—
99C2×D8—44no—
100C2×D8—42no—
101C2×D8—41no—
102C2×D8—82no—
103C22×C8C2×D412yes—
104C4⋊Q8—41no—
105C4⋊Q8—81no—
106#127—41no—
107C22⋊Q8—42no—
108C22⋊Q8—82no—
109#121—42no—
110#121—81no—
111#120—82no—
112C4×Q8—41no—
113C4×D4—41no—
114C4×D4—81no—
115C4×D4D811yescharacteristic
116Q32—22no—
117Q32—21no—
118Q32—22no—
119Q32—44no—
120Q32—81no—
121Q32C2×D412yescomplemented
122D16—22no—
123D16—21no—
124D16—22no—
125D16—44no—
126D16—81no—
127D16C2×D412yes—
128C2×C16—22no—
129C2×C16—22no—
130C2×C16C2×D411yescharacteristic
131C2×C16C2×D412yes—
132C2×C16C2411yescharacteristic
133#107—21no—
134#107—21no—
135C4⋊C8D811yescharacteristic
136#103—41no—
137#103—42no—
138#102—41no—
139#102—42no—
140C22⋊C8D812yes—
141C4×C8C2×D411yescharacteristic
142C32—22no—
143C32—21no—
144C32C2×D412yescomplemented
145C24—82no—
146C2×Q8—41no—
147C2×Q8—42no—
148C2×Q8—84no—
149C2×Q8—82no—
150C2×Q8—162no—
151C2×D4—41no—
152C2×D4—42no—
153C2×D4—84no—
154C2×D4—82no—
155C2×D4—82no—
156C2×D4—81no—
157C2×D4—81no—
158C2×D4—162no—
159C2×D4—164no—
160C2×D4D1611yescharacteristic
161C22×C4—82no—
162C22×C4—81no—
163C22×C4C2×D812yes—
164Q16—22no—
165Q16—42no—
166Q16—41no—
167Q16—42no—
168Q16—84no—
169Q16—161no—
170D8—22no—
171D8—42no—
172D8—41no—
173D8—42no—
174D8—84no—
175D8—161no—
176C2×C8—22no—
177C2×C8—22no—
178C2×C8C2×D811yescharacteristic
179C2×C8C2×D812yes—
180C2×C8C22×D411yescharacteristic
181C4⋊C4—41no—
182C4⋊C4—41no—
183C4⋊C4—81no—
184C4⋊C4—81no—
185C4⋊C4—82no—
186C4⋊C4—81no—
187C4⋊C4D1611yescharacteristic
188C22⋊C4—82no—
189C22⋊C4—81no—
190C22⋊C4—82no—
191C22⋊C4D1612yes—
192C42—81no—
193C42C2×D811yescharacteristic
194C16—22no—
195C16—21no—
196C16C22×D411yescharacteristic
197C16H(5,𝔽2)11yescharacteristic
198C23—81no—
199C23—82no—
200C23—164no—
201C23—164no—
202C23—322no—
203C23C2×D1612yes—
204Q8—42no—
205Q8—81no—
206Q8—82no—
207Q8—82no—
208Q8—164no—
209D4—42no—
210D4—81no—
211D4—82no—
212D4—82no—
213D4—164no—
214D4—164no—
215D4—162no—
216D4—321no—
217D4SD6414yesdirect product factor
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—81no—
221C2×C4—81no—
222C2×C4—81no—
223C2×C4—82no—
224C2×C4—164no—
225C2×C4—162no—
226C2×C4C2×D1611yescharacteristic
227C2×C4C2×D1612yes—
228C2×C4C2×D1611yescharacteristic
229C2×C4C22×D811yescharacteristic
230C8—21no—
231C8—22no—
232C8D4211yescharacteristic
233C8#57611yescharacteristic
234C22—22no—
235C22—22no—
236C22—82no—
237C22—161no—
238C22—161no—
239C22—162no—
240C22—162no—
241C22—162no—
242C22—328no—
243C22C2×SD6414yescomplemented
244C22C22×D1611yescharacteristic
245C4—22no—
246C4—21no—
247C4—82no—
248C4—162no—
249C4—161no—
250C4—161no—
251C4C2×SD6412yescomplemented
252C4D4×D811yescharacteristic
253C4#341511yescharacteristic
254C2—24no—
255C2—162no—
256C2—322no—
257C2D4×D1611yescharacteristic
258C2C22×SD6411yescharacteristic
259C2#3398311yescharacteristic
subgroupG/H
center, socleC22C22×D16
commutator, Frattini, cosocleC2×C16C24
prime radicalD4×D16C2
LCSG ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ D4×C16 ◁ G
LECSG ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×SD64C2semidirect
2. D4×Q32C2semidirect
4. #13727C2semidirect
5. #13696C2semidirect
6. #13687C2semidirect
7. #13686C2semidirect
8. #13664C2semidirect
9. #13662C2semidirect
10. C4×SD64C2semidirect
11. D4×C32C2semidirect
12. C22×Q32C22semidirect
19. C2×SD64C22semidirect
20. C2×SD64C22semidirect
21. C2×SD64C22semidirect
22. C22×C32C22semidirect
23. #2247C22semidirect
25. #2216C22semidirect
31. C4×Q32C22semidirect
34. #1424C22semidirect
35. C4⋊C32C22semidirect
36. #1416C22semidirect
37. #1416C22semidirect
39. #1415C22semidirect
40. C22⋊C32C22semidirect
41. C4×C32C22semidirect
74. SD64D4direct (N × H)
121. Q32C2×D4semidirect
144. C32C2×D4semidirect
217. D4SD64direct (N × H)
243. C22C2×SD64semidirect
251. C4C2×SD64semidirect

Maximal subgroups

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

subgroupindex
C22×SD642
D4×Q322
D4×D162
#137272
#136962
#136872
#136862
#136642
#136622
C4×SD642
D4×C322