Finite Group Databasebeta

← #108×C22⋊C9 #11919565

Subgroups — #108×C22⋊C9 #11919565

Order 1152.

230 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 60 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
1M16×C22⋊C9C212yesmaximal
2C2×C8×C22⋊C9C211yesmaximal, characteristic
3C22×C3×#108C311yesmaximal, characteristic
4C2×C4×C22⋊C9C2211yescharacteristic
5C8×C22⋊C9—22no—
6C8×C22⋊C9C412yes—
7C9×#108—41nomaximal
8C22×C3×M16C2×C312yes—
9C23×C3×C8C2×C311yescharacteristic
10C2×C3×#108—31no—
11C2×C3×#108—32no—
12C2×C3×#108—31no—
13C22×C22⋊C9Q811yescharacteristic
14C4×C22⋊C9C2×C411yescharacteristic
15C4×C22⋊C9D411yescharacteristic
16C9×M16—42no—
17C2×C8×C9—41no—
18C22×#108C911yescharacteristic, complemented, Sylow
19C23×C3×C4C22×C311yescharacteristic
20C2×C3×M16—32no—
21C2×C3×M16—32no—
22C2×C3×M16—62no—
23C22×C3×C8—22no—
24C22×C3×C8—31no—
25C22×C3×C8—32no—
26C22×C3×C8—31no—
27C22×C3×C8C3×C412yes—
28C3×#108—32no—
29C3×#108—32no—
30C3×#108—31no—
31C3×#108A411yescharacteristic
32C2×C22⋊C9—21no—
33C2×C22⋊C9C4⋊C411yescharacteristic
34C2×C4×C9—41no—
35C8×C9—42no—
36C8×C9—82no—
37C22×M16C2×C912yes—
38C23×C8C2×C911yescharacteristic
39C2×#108—31no—
40C2×#108—32no—
41C2×#108—31no—
42C24×C3C3×Q811yescharacteristic
43C22×C3×C4—31no—
44C22×C3×C4—31no—
45C22×C3×C4—31no—
46C22×C3×C4—31no—
47C22×C3×C4C2×C3×C411yescharacteristic
48C22×C3×C4C3×D411yescharacteristic
49C3×M16—32no—
50C3×M16—62no—
51C3×M16—62no—
52C3×M16C2×A412yes—
53C2×C3×C8—32no—
54C2×C3×C8—31no—
55C2×C3×C8—32no—
56C2×C3×C8—32no—
57C2×C3×C8—32no—
58C2×C3×C8—62no—
59C2×C3×C8—62no—
60C2×C3×C8C2×A411yescharacteristic
61C22×C9—41no—
62C22⋊C9#10811yescharacteristic, direct product factor
63C4×C9—41no—
64C4×C9—41no—
65C23×C4C22×C911yescharacteristic
66C2×M16—32no—
67C2×M16—32no—
68C2×M16—62no—
69C22×C8—22no—
70C22×C8—31no—
71C22×C8—31no—
72C22×C8—32no—
73C22×C8C4×C912yes—
74#108—32no—
75#108—32no—
76#108—31no—
77#108C22⋊C911yescharacteristic, direct product factor
78C23×C3—21no—
79C23×C3—31no—
80C23×C3—31no—
81C23×C3—61no—
82C23×C3C3×C4⋊C411yescharacteristic
83C2×C3×C4—32no—
84C2×C3×C4—31no—
85C2×C3×C4—31no—
86C2×C3×C4—31no—
87C2×C3×C4—31no—
88C2×C3×C4—31no—
89C2×C3×C4—31no—
90C2×C3×C4—31no—
91C2×C3×C4C22×A411yescharacteristic
92C3×C8—22no—
93C3×C8—32no—
94C3×C8—62no—
95C3×C8C4×A412yes—
96C2×C9—41no—
97C2×C9—81no—
98C24Q8×C911yescharacteristic
99C22×C4—31no—
100C22×C4—31no—
101C22×C4—31no—
102C22×C4—31no—
103C22×C4C2×C4×C911yescharacteristic
104C22×C4D4×C911yescharacteristic
105M16—32no—
106M16—62no—
107M16—62no—
108M16C2×C22⋊C912yes—
109C2×C8—32no—
110C2×C8—31no—
111C2×C8—32no—
112C2×C8—32no—
113C2×C8—32no—
114C2×C8—62no—
115C2×C8—62no—
116C2×C8C2×C22⋊C911yescharacteristic
117C22×C3—31no—
118C22×C3—31no—
119C22×C3—31no—
120C22×C3—61no—
121C22×C3—61no—
122C22×C3—61no—
123C22×C3—61no—
124C22×C3C3×#10811yescharacteristic
125C22×C3Q8×A411yescharacteristic
126C3×C4—31no—
127C3×C4—31no—
128C3×C4C2×C4×A411yescharacteristic
129C3×C4D4×A411yescharacteristic
130C9—41noSylow
131C23—21no—
132C23—31no—
133C23—31no—
134C23—61no—
135C23C9×C4⋊C411yescharacteristic
136C2×C4—32no—
137C2×C4—31no—
138C2×C4—31no—
139C2×C4—31no—
140C2×C4—31no—
141C2×C4—31no—
142C2×C4—31no—
143C2×C4—31no—
144C2×C4C22×C22⋊C911yescharacteristic
145C8—22no—
146C8—32no—
147C8—62no—
148C8C4×C22⋊C912yes—
149C2×C3—21no—
150C2×C3—31no—
151C2×C3—31no—
152C2×C3—61no—
153C2×C3A4×C4⋊C411yescharacteristic
154C22—31no—
155C22—31no—
156C22—31no—
157C22—61no—
158C22—61no—
159C22—61no—
160C22—61no—
161C22C9×#10811yescharacteristic, complemented
162C22Q8×C22⋊C911yescharacteristic
163C4—31no—
164C4—31no—
165C4C2×C4×C22⋊C911yescharacteristic
166C4D4×C22⋊C911yescharacteristic
167C3A4×#10811yescharacteristic
168C2—21no—
169C2—31no—
170C2—31no—
171C2—61no—
172C2C4⋊C4×C22⋊C911yescharacteristic
subgroupG/H
centerC3×C4D4×A4
commutatorC22×C4C2×C4×C9
FrattiniC2×C3×C4C22×A4
FittingC22×C3×#108C3
socleC23×C3C3×C4⋊C4
prime radicalC24×C3C3×Q8
cosocleC23×C3×C4C22×C3
hypercenterC3×#108A4
hypocenterC22C9×#108
LCSG ▷ C22×C4 ▷ C23 ▷ C22
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C3×#108

Complements

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

NH ≅ G/Ntype
18. C22×#108C9semidirect
62. C22⋊C9#108direct (N × H)
77. #108C22⋊C9direct (N × H)
161. C22C9×#108semidirect

Maximal subgroups

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

subgroupindex
M16×C22⋊C92
C2×C8×C22⋊C92
C22×C3×#1083
C9×#1084