Finite Group Databasebeta

← SD32×C22⋊C9 #11919627

Subgroups — SD32×C22⋊C9 #11919627

Order 1152.

194 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 40 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
1Q16×C22⋊C9C211yesmaximal, characteristic, complemented
2D8×C22⋊C9C211yesmaximal, characteristic
3C16×C22⋊C9C211yesmaximal, characteristic, complemented
4C22×C3×SD32C311yesmaximal, characteristic
5Q8×C22⋊C9—21no—
6D4×C22⋊C9—21no—
7C8×C22⋊C9C2211yescharacteristic
8C9×SD32—41nomaximal
9C22×C3×Q16C2×C311yescharacteristic
10C22×C3×D8C2×C311yescharacteristic
11C2×C3×SD32—31no—
12C2×C3×SD32—31no—
13C2×C3×SD32—31no—
14C2×C3×SD32—31no—
15C22×C3×C16C2×C311yescharacteristic
16C22×C22⋊C9—41no—
17C4×C22⋊C9—41no—
18C4×C22⋊C9D411yescharacteristic
19C9×Q16—41no—
20C9×D8—41no—
21C9×C16—41no—
22C22×SD32C911yescharacteristic, complemented, Sylow
23C22×C3×Q8—21no—
24C22×C3×D4—21no—
25C2×C3×Q16—31no—
26C2×C3×Q16—31no—
27C2×C3×Q16—61no—
28C2×C3×D8—31no—
29C2×C3×D8—31no—
30C2×C3×D8—61no—
31C22×C3×C8C22×C311yescharacteristic
32C3×SD32—32no—
33C3×SD32—31no—
34C3×SD32—31no—
35C3×SD32—31no—
36C3×SD32A411yescharacteristic
37C2×C3×C16—31no—
38C2×C3×C16—31no—
39C2×C22⋊C9—81no—
40C2×C22⋊C9D811yescharacteristic
41Q8×C9—81no—
42D4×C9—81no—
43C8×C9—41no—
44C22×Q16C2×C911yescharacteristic, complemented
45C22×D8C2×C911yescharacteristic
46C2×SD32—31no—
47C2×SD32—31no—
48C2×SD32—31no—
49C2×SD32—31no—
50C22×C16C2×C911yescharacteristic, complemented
51C24×C3—41no—
52C2×C3×Q8—61no—
53C2×C3×Q8—61no—
54C2×C3×Q8—121no—
55C2×C3×D4—61no—
56C2×C3×D4—61no—
57C2×C3×D4—121no—
58C22×C3×C4—41no—
59C22×C3×C4C3×D411yescharacteristic
60C3×Q16—31no—
61C3×Q16—61no—
62C3×Q16—61no—
63C3×Q16C2×A411yescharacteristic
64C3×D8—31no—
65C3×D8—61no—
66C3×D8—61no—
67C3×D8C2×A411yescharacteristic
68C2×C3×C8—31no—
69C2×C3×C8—31no—
70C3×C16—31no—
71C3×C16C2×A411yescharacteristic
72C22×C9—161no—
73C22⋊C9SD3211yescharacteristic, direct product factor
74C4×C9—41no—
75C4×C9—161no—
76C22×Q8—21no—
77C22×D4—21no—
78C2×Q16—31no—
79C2×Q16—31no—
80C2×Q16—61no—
81C2×D8—31no—
82C2×D8—31no—
83C2×D8—61no—
84C22×C8C22×C911yescharacteristic
85SD32—32no—
86SD32—31no—
87SD32—31no—
88SD32—31no—
89SD32C22⋊C911yescharacteristic, direct product factor
90C2×C16—31no—
91C2×C16—31no—
92C23×C3—81no—
93C23×C3—121no—
94C23×C3—121no—
95C23×C3—241no—
96C23×C3C3×D811yescharacteristic
97C3×Q8—21no—
98C3×Q8—61no—
99C3×Q8—121no—
100C3×Q8—121no—
101C3×D4—21no—
102C3×D4—61no—
103C3×D4—121no—
104C3×D4—121no—
105C2×C3×C4—31no—
106C2×C3×C4—31no—
107C2×C3×C4—121no—
108C2×C3×C4—121no—
109C3×C8—31no—
110C3×C8C22×A411yescharacteristic
111C2×C9—41no—
112C2×C9—321no—
113C24—41no—
114C2×Q8—61no—
115C2×Q8—61no—
116C2×Q8—121no—
117C2×D4—61no—
118C2×D4—61no—
119C2×D4—121no—
120C22×C4—41no—
121C22×C4D4×C911yescharacteristic
122Q16—31no—
123Q16—61no—
124Q16—61no—
125Q16C2×C22⋊C911yescharacteristic, complemented
126D8—31no—
127D8—61no—
128D8—61no—
129D8C2×C22⋊C911yescharacteristic
130C2×C8—31no—
131C2×C8—31no—
132C16—31no—
133C16C2×C22⋊C911yescharacteristic, complemented
134C22×C3—31no—
135C22×C3—31no—
136C22×C3—41no—
137C22×C3—121no—
138C22×C3—241no—
139C22×C3—241no—
140C22×C3—241no—
141C22×C3—241no—
142C22×C3C3×SD3211yescharacteristic
143C3×C4—31no—
144C3×C4—41no—
145C3×C4—121no—
146C3×C4D4×A411yescharacteristic
147C9—41noSylow
148C23—81no—
149C23—121no—
150C23—121no—
151C23—241no—
152C23C9×D811yescharacteristic
153Q8—21no—
154Q8—61no—
155Q8—121no—
156Q8—121no—
157D4—21no—
158D4—61no—
159D4—121no—
160D4—121no—
161C2×C4—31no—
162C2×C4—31no—
163C2×C4—121no—
164C2×C4—121no—
165C8—31no—
166C8C22×C22⋊C911yescharacteristic
167C2×C3—31no—
168C2×C3—31no—
169C2×C3—81no—
170C2×C3—241no—
171C2×C3A4×D811yescharacteristic
172C22—31no—
173C22—31no—
174C22—41no—
175C22—121no—
176C22—241no—
177C22—241no—
178C22—241no—
179C22—241no—
180C22C9×SD3211yescharacteristic, complemented
181C4—31no—
182C4—41no—
183C4—121no—
184C4D4×C22⋊C911yescharacteristic
185C3A4×SD3211yescharacteristic
186C2—31no—
187C2—31no—
188C2—81no—
189C2—241no—
190C2D8×C22⋊C911yescharacteristic
subgroupG/H
centerC2×C3A4×D8
commutatorC22×C8C22×C9
FrattiniC3×C8C22×A4
FittingC22×C3×SD32C3
socleC23×C3C3×D8
prime radicalC22×C3×D8C2×C3
cosocleC22×C3×C8C22×C3
hypercenterC3×SD32A4
hypocenterC22C9×SD32
LCSG ▷ C22×C8 ▷ C22×C4 ▷ C23 ▷ C22
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8 ◁ C3×SD32

Complements

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

NH ≅ G/Ntype
1. Q16×C22⋊C9C2semidirect
3. C16×C22⋊C9C2semidirect
22. C22×SD32C9semidirect
44. C22×Q16C2×C9semidirect
50. C22×C16C2×C9semidirect
73. C22⋊C9SD32direct (N × H)
89. SD32C22⋊C9direct (N × H)
125. Q16C2×C22⋊C9semidirect
133. C16C2×C22⋊C9semidirect
180. C22C9×SD32semidirect

Maximal subgroups

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

subgroupindex
Q16×C22⋊C92
D8×C22⋊C92
C16×C22⋊C92
C22×C3×SD323
C9×SD324