Finite Group Databasebeta

← #11920042

Subgroups — #11920042

Order 1152.

208 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 37 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
1D4×Q8⋊C9C211yesmaximal, characteristic
2#10589488C211yesmaximal, characteristic, complemented
3(Q8⋊C9)⋊C8C211yesmaximal, characteristic, complemented
4#71917—31nomaximal
5C22×Q8⋊C9—21no—
6C2×#3672—41nomaximal
7C4×Q8⋊C9C2211yescharacteristic
8#63421—21no—
9C3×D4×Q8D311yescharacteristic
10#5080—31no—
11#5020—31no—
12#5019—31no—
13#4547—31no—
14#4535—31no—
15D4⋊(C3⋊C8)—31no—
16C2×D4×C9—41no—
17C2×Dic18—41no—
18C2×Q8⋊C9—41no—
19C2×Q8⋊C9D411yescharacteristic
20#3672—44no—
21C2×C9⋊C8—41no—
22#1651—91noSylow
23C22×C3×Q8—21no—
24C3×C4⋊Q8—31no—
25C3×C22⋊Q8—61no—
26C3×C4×Q8C2×D311yescharacteristic
27C3×C4×D4—31no—
28C2×#214—61no—
29#869—31no—
30#835—61no—
31#810—61no—
32#808—61no—
33#808—62no—
34C4⋊(C3⋊C8)—31no—
35C4⋊(C3⋊C8)—31no—
36C4×C3⋊C8—31no—
37C23×C9—81no—
38D4×C9—42no—
39D4×C9—81no—
40C2×C4×C9—41no—
41C2×Dic9—81no—
42Dic18—42no—
43Dic18—81no—
44Q8⋊C9SD1611yescharacteristic, complemented
45C9⋊C8—42no—
46D4×Q8D911yescharacteristic
47#498—91no—
48#475—91no—
49#461—91no—
50#332—91no—
51Q8⋊C8—91no—
52D4⋊C8—91no—
53C2×C3×Q8—41no—
54C2×C3×Q8—61no—
55C2×C3×Q8—121no—
56C2×C3×Q8#6711yescharacteristic
57C2×C3×D4S411yescharacteristic
58C22×C3×C4—61no—
59C2×Dic6—61no—
60C3×C4⋊C4—31no—
61C3×C4⋊C4—32no—
62C3×C4⋊C4—31no—
63C3×C22⋊C4—61no—
64C3×C42—31no—
65#214—122no—
66C4⋊Dic3—61no—
67C4⋊Dic3—61no—
68C2×C3⋊C8—61no—
69C2×C3⋊C8—61no—
70C2×C3⋊C8—61no—
71C22×C9—41no—
72C22×C9—82no—
73C22×C9—161no—
74C22×C9—161no—
75C4×C9—41no—
76C4×C9—41no—
77Dic9—82no—
78C22×Q8—21no—
79C2×SD16—181no—
80C4⋊Q8—31no—
81C4⋊Q8—91no—
82C22⋊Q8—61no—
83C4×Q8C2×D911yescharacteristic
84C4×D4—31no—
85#106—181no—
86#106—182no—
87C4⋊C8—91no—
88C4⋊C8—91no—
89#103—181no—
90#103—181no—
91C4×C8—91no—
92C23×C3—21no—
93C3×Q8—31no—
94C3×Q8—121no—
95C3×Q8—121no—
96C3×Q8#21411yescharacteristic
97C3×D4—21no—
98C3×D4GL(2,𝔽3)12yes—
99C2×C3×C4—31no—
100C2×C3×C4—31no—
101C2×C3×C4—61no—
102C2×C3×C4—121no—
103C2×C3×C4—121no—
104C2×C3×C4C2×S411yescharacteristic
105C2×Dic3—121no—
106Dic6—121no—
107Dic6—121no—
108C3⋊C8—62no—
109C3⋊C8—121no—
110C3⋊C8—121no—
111C2×C9—41no—
112C2×C9—41no—
113C2×C9—41no—
114C2×C9—162no—
115C2×Q8—41no—
116C2×Q8—61no—
117C2×Q8—121no—
118C2×Q8—181no—
119C2×Q8#61111yescharacteristic
120C2×D4(C22⋊C9)⋊C211yescharacteristic
121C22×C4—61no—
122SD16—362no—
123C2×C8—181no—
124C2×C8—181no—
125C2×C8—181no—
126C4⋊C4—31no—
127C4⋊C4—32no—
128C4⋊C4—31no—
129C4⋊C4—181no—
130C4⋊C4—181no—
131C22⋊C4—61no—
132C42—31no—
133C22×C3—22no—
134C22×C3—41no—
135C22×C3—41no—
136C22×C3GL(2,ℤ/4)11yescharacteristic
137C3×C4—31no—
138C3×C4—31no—
139C3×C4—61no—
140C3×C4—121no—
141C3×C4C2×GL(2,𝔽3)11yescharacteristic
142C3×C4#98311yescharacteristic
143Dic3—241no—
144C9—41noSylow
145C23—21no—
146Q8—31no—
147Q8—121no—
148Q8—121no—
149Q8—361no—
150Q8—361no—
151Q8#367211yescharacteristic, complemented
152D4—21no—
153D4#368912yes—
154C2×C4—31no—
155C2×C4—31no—
156C2×C4—61no—
157C2×C4—121no—
158C2×C4—121no—
159C2×C4—361no—
160C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
161C8—182no—
162C8—361no—
163C8—361no—
164C2×C3—42no—
165C2×C3#541411yescharacteristic
166C2×C3#542111yescharacteristic
167C2×C3#543011yescharacteristic
168C22—22no—
169C22—41no—
170C22—41no—
171C22#6369411yescharacteristic
172C4—31no—
173C4—31no—
174C4—61no—
175C4—121no—
176C4—721no—
177C4C2×#368911yescharacteristic
178C4#6368911yescharacteristic
179C3#7308711yescharacteristic
180C2—42no—
181C2#1058951611yescharacteristic
182C2#1058952311yescharacteristic
183C2#1058953211yescharacteristic
subgroupG/H
centerC22#63694
commutator, cosocleC4×Q8⋊C9C22
FrattiniC2×C3×C4C2×S4
FittingC3×D4×Q8D3
socleC22×C3GL(2,ℤ/4)
prime radicalC2×C3×D4S4
hypercenterC2×D4(C22⋊C9)⋊C2
hypocenterQ8⋊C9SD16
LCSG ▷ C4×Q8⋊C9 ▷ C2×Q8⋊C9 ▷ Q8⋊C9
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #10589488C2semidirect
3. (Q8⋊C9)⋊C8C2semidirect
44. Q8⋊C9SD16semidirect
151. Q8#3672semidirect

Maximal subgroups

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

subgroupindex
D4×Q8⋊C92
#105894882
(Q8⋊C9)⋊C82
#719173
C2×#36724