Finite Group Databasebeta

← D4×SD32 #33847

Subgroups — D4×SD32 #33847

Order 256.

369 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 369 conjugacy classes of subgroups — too many to draw. Only its 117 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×SD32C212yesmaximal, complemented
2D4×Q16C211yesmaximal, characteristic, complemented
3D4×D8C211yesmaximal, characteristic
4#2248C211yesmaximal, characteristic, complemented
5#2217C212yesmaximal, complemented
6#2208C211yesmaximal, characteristic, complemented
7#2207C211yesmaximal, characteristic, complemented
8#2187C212yesmaximal, complemented
9#2185C212yesmaximal, complemented
10C4×SD32C211yesmaximal, characteristic, complemented
11D4×C16C211yesmaximal, characteristic, complemented
12C22×Q16C2212yescomplemented
13C22×D8C2212yes—
14D4×Q8—21no—
15D42—21no—
16C2×SD32—28no—
17C2×SD32C2212yes—
18C2×SD32C2211yescharacteristic
19C2×SD32C2212yescomplemented
20C2×SD32C2212yescomplemented
21C2×SD32C2212yescomplemented
22C22×C16C2212yescomplemented
23#494C2211yescharacteristic, complemented
24#493C2211yescharacteristic
25#467C2212yescomplemented
26#466C2212yes—
27#462—21no—
28#459—21no—
29#451—22no—
30#447—22no—
31C4×Q16C2211yescharacteristic, complemented
32C4×D8C2211yescharacteristic
33C8×D4C2211yescharacteristic
34#367C2211yescharacteristic, complemented
35C4⋊C16C2211yescharacteristic, complemented
36#358C2211yescharacteristic, complemented
37#358C2212yescomplemented
38#357C2211yescharacteristic
39#357C2212yescomplemented
40C22⋊C16C2212yescomplemented
41C4×C16C2211yescharacteristic, complemented
42C22×Q8—22no—
43C22×D4—22no—
44C22×D4—41no—
45C2×Q16—24no—
46C2×Q16—22no—
47C2×Q16—21no—
48C2×Q16—42no—
49C2×Q16C2312yes—
50C2×Q16C2311yescharacteristic
51C2×D8—24no—
52C2×D8—22no—
53C2×D8—21no—
54C2×D8—42no—
55C2×D8C2312yes—
56C2×D8C2311yescharacteristic
57C22×C8C2312yes—
58C4⋊Q8—21no—
59C4⋊Q8—41no—
60#127—21no—
61C22⋊Q8—22no—
62C22⋊Q8—42no—
63#121—22no—
64#121—41no—
65#120—42no—
66C4×Q8—21no—
67C4×D4—21no—
68C4×D4—41no—
69C4×D4D411yescharacteristic
70SD32—24no—
71SD32—24no—
72SD32—24no—
73SD32—42no—
74SD32D414yesdirect product factor
75C2×C16—24no—
76C2×C16C2311yescharacteristic
77C2×C16C2312yes—
78C2×C16C2311yescharacteristic
79#107C2311yescharacteristic
80#107C2311yescharacteristic
81C4⋊C8D411yescharacteristic
82#103—21no—
83#103—22no—
84#102—21no—
85#102—22no—
86C22⋊C8D412yes—
87C4×C8C2311yescharacteristic
88C24—42no—
89C2×Q8—21no—
90C2×Q8—22no—
91C2×Q8—44no—
92C2×Q8—42no—
93C2×Q8—82no—
94C2×D4—21no—
95C2×D4—22no—
96C2×D4—44no—
97C2×D4—42no—
98C2×D4—42no—
99C2×D4—41no—
100C2×D4—41no—
101C2×D4—82no—
102C2×D4—84no—
103C2×D4D811yescharacteristic
104C22×C4—42no—
105C22×C4—41no—
106C22×C4C2×D412yes—
107Q16—22no—
108Q16—21no—
109Q16—22no—
110Q16—44no—
111Q16—81no—
112Q16C2×D412yescomplemented
113D8—22no—
114D8—21no—
115D8—22no—
116D8—44no—
117D8—81no—
118D8C2×D412yes—
119C2×C8—22no—
120C2×C8—22no—
121C2×C8C2×D411yescharacteristic
122C2×C8C2×D412yes—
123C2×C8C2411yescharacteristic
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—41no—
127C4⋊C4—41no—
128C4⋊C4—42no—
129C4⋊C4—41no—
130C4⋊C4D811yescharacteristic
131C22⋊C4—42no—
132C22⋊C4—41no—
133C22⋊C4—42no—
134C22⋊C4D812yes—
135C42—41no—
136C42C2×D411yescharacteristic
137C16—22no—
138C16—21no—
139C16C2×D412yescomplemented
140C23—41no—
141C23—42no—
142C23—84no—
143C23—84no—
144C23—162no—
145C23C2×D812yes—
146Q8—22no—
147Q8—41no—
148Q8—42no—
149Q8—42no—
150Q8—84no—
151D4—22no—
152D4—42no—
153D4—41no—
154D4—42no—
155D4—84no—
156D4—84no—
157D4—82no—
158D4—161no—
159D4SD3214yesdirect product factor
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—42no—
166C2×C4—84no—
167C2×C4—82no—
168C2×C4C2×D811yescharacteristic
169C2×C4C2×D812yes—
170C2×C4C2×D811yescharacteristic
171C2×C4C22×D411yescharacteristic
172C8—22no—
173C8—21no—
174C8C22×D411yescharacteristic
175C8H(5,𝔽2)11yescharacteristic
176C22—22no—
177C22—22no—
178C22—42no—
179C22—81no—
180C22—81no—
181C22—82no—
182C22—82no—
183C22—82no—
184C22—168no—
185C22C2×SD3214yescomplemented
186C22C22×D811yescharacteristic
187C4—21no—
188C4—22no—
189C4—42no—
190C4—81no—
191C4—81no—
192C4—82no—
193C4C2×SD3212yescomplemented
194C4D4211yescharacteristic
195C4#57611yescharacteristic
196C2—24no—
197C2—82no—
198C2—162no—
199C2D4×D811yescharacteristic
200C2C22×SD3211yescharacteristic
201C2#341611yescharacteristic
subgroupG/H
center, socleC22C22×D8
commutator, Frattini, cosocleC2×C8C24
prime radicalD4×D8C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ G
LECSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×SD32C2semidirect
2. D4×Q16C2semidirect
4. #2248C2semidirect
5. #2217C2semidirect
6. #2208C2semidirect
7. #2207C2semidirect
8. #2187C2semidirect
9. #2185C2semidirect
10. C4×SD32C2semidirect
11. D4×C16C2semidirect
12. C22×Q16C22semidirect
19. C2×SD32C22semidirect
20. C2×SD32C22semidirect
21. C2×SD32C22semidirect
22. C22×C16C22semidirect
23. #494C22semidirect
25. #467C22semidirect
31. C4×Q16C22semidirect
34. #367C22semidirect
35. C4⋊C16C22semidirect
36. #358C22semidirect
37. #358C22semidirect
39. #357C22semidirect
40. C22⋊C16C22semidirect
41. C4×C16C22semidirect
74. SD32D4direct (N × H)
112. Q16C2×D4semidirect
139. C16C2×D4semidirect
159. D4SD32direct (N × H)
185. C22C2×SD32semidirect
193. C4C2×SD32semidirect

Maximal subgroups

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

subgroupindex
C22×SD322
D4×Q162
D4×D82
#22482
#22172
#22082
#22072
#21872
#21852
C4×SD322
D4×C162