Finite Group Databasebeta

← SD16×Q8⋊C9 #11919607

Subgroups — SD16×Q8⋊C9 #11919607

Order 1152.

226 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 65 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×Q8⋊C9C211yesmaximal, characteristic, complemented
2D4×Q8⋊C9C211yesmaximal, characteristic
3C8×Q8⋊C9C211yesmaximal, characteristic, complemented
4C3×Q8×SD16C311yesmaximal, characteristic
5C22×Q8⋊C9—21no—
6C2×C9×SD16—41nomaximal
7C4×Q8⋊C9—21no—
8C4×Q8⋊C9C2211yescharacteristic
9C3×Q82C2×C311yescharacteristic
10C3×D4×Q8C2×C311yescharacteristic
11C3×#498—31no—
12C3×#476—31no—
13C3×#475—31no—
14C3×C8×Q8C2×C311yescharacteristic
15C3×C4×SD16—31no—
16C2×Q8×C9—41no—
17C2×D4×C9—41no—
18C2×Q8⋊C9—41no—
19C2×Q8⋊C9D411yescharacteristic
20C9×SD16—44no—
21C2×C8×C9—41no—
22Q8×SD16C911yescharacteristic, complemented, Sylow
23C22×C3×Q8—21no—
24C2×C3×SD16A411yescharacteristic
25C3×C4⋊Q8—31no—
26C3×C4⋊Q8—31no—
27C3×C4⋊Q8—61no—
28C3×C22⋊Q8—61no—
29C3×C4×Q8—21no—
30C3×C4×Q8—31no—
31C3×C4×Q8C22×C311yescharacteristic
32C3×C4×D4—31no—
33C3×#106—32no—
34C3×#106—31no—
35C3×C4⋊C8—31no—
36C3×#103—31no—
37C3×#102—31no—
38C3×C4×C8—31no—
39C23×C9—81no—
40Q8×C9—42no—
41Q8×C9—81no—
42D4×C9—42no—
43D4×C9—81no—
44C2×C4×C9—41no—
45C2×C4×C9—81no—
46Q8⋊C9SD1611yescharacteristic, direct product factor
47C8×C9—42no—
48Q82C2×C911yescharacteristic, complemented
49D4×Q8C2×C911yescharacteristic
50#498—31no—
51#476—31no—
52#475—31no—
53C8×Q8C2×C911yescharacteristic, complemented
54C4×SD16—31no—
55C2×C3×Q8—41no—
56C2×C3×Q8—61no—
57C2×C3×Q8—61no—
58C2×C3×Q8—121no—
59C2×C3×Q8C3×D411yescharacteristic
60C2×C3×Q8C2×A411yescharacteristic
61C2×C3×D4C2×A411yescharacteristic
62C22×C3×C4—61no—
63C3×SD16SL(2,𝔽3)14yes—
64C2×C3×C8—31no—
65C2×C3×C8C2×A411yescharacteristic
66C3×C4⋊C4—31no—
67C3×C4⋊C4—31no—
68C3×C4⋊C4—31no—
69C3×C4⋊C4—61no—
70C3×C4⋊C4—61no—
71C3×C4⋊C4—61no—
72C3×C22⋊C4—61no—
73C3×C42—31no—
74C3×C42—61no—
75C22×C9—41no—
76C22×C9—82no—
77C22×C9—161no—
78C22×C9—161no—
79C4×C9—41no—
80C4×C9—41no—
81C4×C9—82no—
82C22×Q8—21no—
83C2×SD16C22⋊C911yescharacteristic
84C4⋊Q8—31no—
85C4⋊Q8—31no—
86C4⋊Q8—61no—
87C22⋊Q8—61no—
88C4×Q8—21no—
89C4×Q8—31no—
90C4×Q8C22×C911yescharacteristic
91C4×D4—31no—
92#106—32no—
93#106—31no—
94C4⋊C8—31no—
95#103—31no—
96#102—31no—
97C4×C8—31no—
98C23×C3—21no—
99C3×Q8—21no—
100C3×Q8—31no—
101C3×Q8—121no—
102C3×Q8—121no—
103C3×Q8—241no—
104C3×Q8C3×SD1611yescharacteristic
105C3×Q8C2×SL(2,𝔽3)12yes—
106C3×D4—21no—
107C3×D4C2×SL(2,𝔽3)12yes—
108C2×C3×C4—21no—
109C2×C3×C4—31no—
110C2×C3×C4—31no—
111C2×C3×C4—61no—
112C2×C3×C4—61no—
113C2×C3×C4—121no—
114C2×C3×C4—121no—
115C2×C3×C4C22×A411yescharacteristic
116C3×C8—61no—
117C3×C8C2×SL(2,𝔽3)12yes—
118C2×C9—41no—
119C2×C9—41no—
120C2×C9—41no—
121C2×C9—162no—
122C2×Q8—41no—
123C2×Q8—61no—
124C2×Q8—61no—
125C2×Q8—121no—
126C2×Q8D4×C911yescharacteristic
127C2×Q8C2×C22⋊C911yescharacteristic
128C2×D4C2×C22⋊C911yescharacteristic
129C22×C4—61no—
130SD16Q8⋊C914yesdirect product factor
131C2×C8—31no—
132C2×C8C2×C22⋊C911yescharacteristic
133C4⋊C4—31no—
134C4⋊C4—31no—
135C4⋊C4—31no—
136C4⋊C4—61no—
137C4⋊C4—61no—
138C4⋊C4—61no—
139C22⋊C4—61no—
140C42—31no—
141C42—61no—
142C22×C3—22no—
143C22×C3—41no—
144C22×C3—41no—
145C22×C3D4×A411yescharacteristic
146C3×C4—22no—
147C3×C4—31no—
148C3×C4—31no—
149C3×C4—61no—
150C3×C4—121no—
151C3×C4—121no—
152C3×C4C22×SL(2,𝔽3)11yescharacteristic
153C3×C42−1+4⋊C311yescharacteristic
154C9—41noSylow
155C23—21no—
156Q8—21no—
157Q8—31no—
158Q8—121no—
159Q8—121no—
160Q8—241no—
161Q8C9×SD1611yescharacteristic, complemented
162Q8C2×Q8⋊C912yescomplemented
163D4—21no—
164D4C2×Q8⋊C912yes—
165C2×C4—21no—
166C2×C4—31no—
167C2×C4—31no—
168C2×C4—61no—
169C2×C4—61no—
170C2×C4—121no—
171C2×C4—121no—
172C2×C4C22×C22⋊C911yescharacteristic
173C8—61no—
174C8C2×Q8⋊C912yescomplemented
175C2×C3—42no—
176C2×C3D4×SL(2,𝔽3)11yescharacteristic
177C2×C3A4×SD1611yescharacteristic
178C2×C3#577⋊C311yescharacteristic
179C22—22no—
180C22—41no—
181C22—41no—
182C22D4×C22⋊C911yescharacteristic
183C4—22no—
184C4—31no—
185C4—31no—
186C4—61no—
187C4—121no—
188C4—121no—
189C4C22×Q8⋊C911yescharacteristic
190C42−1+4⋊C911yescharacteristic
191C3SD16×SL(2,𝔽3)11yescharacteristic
192C2—42no—
193C2D4×Q8⋊C911yescharacteristic
194C2SD16×C22⋊C911yescharacteristic
195C2#577⋊C911yescharacteristic
subgroupG/H
center, socleC22×C3D4×A4
commutatorC4×Q8C22×C9
FrattiniC2×C3×C4C22×A4
FittingC3×Q8×SD16C3
prime radicalC2×C3×D4C2×A4
cosocleC3×C4×Q8C22×C3
hypercenterC2×C3×SD16A4
hypocenterQ8C9×SD16
LCSG ▷ C4×Q8 ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×SD16

Complements

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

NH ≅ G/Ntype
1. Q8×Q8⋊C9C2semidirect
3. C8×Q8⋊C9C2semidirect
22. Q8×SD16C9semidirect
46. Q8⋊C9SD16direct (N × H)
48. Q82C2×C9semidirect
53. C8×Q8C2×C9semidirect
130. SD16Q8⋊C9direct (N × H)
161. Q8C9×SD16semidirect
162. Q8C2×Q8⋊C9semidirect
174. C8C2×Q8⋊C9semidirect

Maximal subgroups

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

subgroupindex
Q8×Q8⋊C92
D4×Q8⋊C92
C8×Q8⋊C92
C3×Q8×SD163
C2×C9×SD164