Finite Group Databasebeta

← #11920049

Subgroups — #11920049

Order 1152.

168 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 33 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
1#557⋊C9C211yesmaximal, characteristic
2C4⋊#3688C211yesmaximal, characteristic
3(Q8⋊C9)⋊C8C211yesmaximal, characteristic
4#71938—31nomaximal
5C2×#3688—21no—
6C4×Q8⋊C9—21no—
7C4×Q8⋊C9C2211yescharacteristic
8#63367—41nomaximal
9C3×#557D311yescharacteristic
10#5080—31no—
11#5031—31no—
12#5020—31no—
13#4547—31no—
14#4535—31no—
15#4535—31no—
16C2×Q8⋊C9D411yescharacteristic
17#3688—41no—
18C9×C4⋊C4—41no—
19C4⋊Dic9—41no—
20C2×C9⋊C8—41no—
21#1653—91noSylow
22C3×C4⋊Q8—31no—
23C3×#125—61no—
24C3×C4×Q8—21no—
25C3×C4×Q8—31no—
26C3×C4×Q8C2×D311yescharacteristic
27C2×#216—61no—
28#869—31no—
29#835—61no—
30#810—61no—
31#808—62no—
32#808—61no—
33C4⋊(C3⋊C8)—31no—
34C4⋊(C3⋊C8)—31no—
35C4×C3⋊C8—31no—
36C2×C4×C9—41no—
37C2×C4×C9—81no—
38C2×Dic9—81no—
39Q8⋊C9SD1611yescharacteristic
40C9⋊C8—42no—
41#557D911yescharacteristic
42#498—91no—
43#475—91no—
44#462—91no—
45#332—91no—
46Q8⋊C8—91no—
47Q8⋊C8—91no—
48C2×C3×Q8—31no—
49C2×C3×Q8#6711yescharacteristic
50C2×Dic6—61no—
51C3×C4⋊C4—31no—
52C3×C4⋊C4—32no—
53C3×C4⋊C4—61no—
54C3×C4⋊C4—61no—
55C3×C4⋊C4S411yescharacteristic
56C3×C42—31no—
57C3×C42—61no—
58#216—121no—
59#216—121no—
60C4⋊Dic3—61no—
61C4⋊Dic3—61no—
62C2×C3⋊C8—61no—
63C2×C3⋊C8—61no—
64C2×C3⋊C8—61no—
65C22×C9—41no—
66C4×C9—41no—
67C4×C9—41no—
68C4×C9—161no—
69Dic9—161no—
70C2×Q16—181no—
71C4⋊Q8—31no—
72C4⋊Q8—91no—
73#125—61no—
74C4×Q8—21no—
75C4×Q8—31no—
76C4×Q8C2×D911yescharacteristic
77#106—182no—
78#106—181no—
79C4⋊C8—91no—
80C4⋊C8—91no—
81#103—181no—
82#103—181no—
83C4×C8—91no—
84C3×Q8—31no—
85C3×Q8—61no—
86C3×Q8—61no—
87C3×Q8#21511yescharacteristic
88C2×C3×C4—21no—
89C2×C3×C4—31no—
90C2×C3×C4—31no—
91C2×C3×C4—61no—
92C2×C3×C4C2×S411yescharacteristic
93C2×Dic3—121no—
94Dic6—121no—
95Dic6—121no—
96C3⋊C8—62no—
97C3⋊C8—121no—
98C3⋊C8—121no—
99C2×C9—41no—
100C2×C9—41no—
101C2×C9—41no—
102C2×Q8—31no—
103C2×Q8—181no—
104C2×Q8#61111yescharacteristic
105Q16—361no—
106Q16—361no—
107C2×C8—181no—
108C2×C8—181no—
109C2×C8—181no—
110C4⋊C4—31no—
111C4⋊C4—32no—
112C4⋊C4—61no—
113C4⋊C4—61no—
114C4⋊C4—181no—
115C4⋊C4—181no—
116C4⋊C4(C22⋊C9)⋊C211yescharacteristic
117C42—31no—
118C42—61no—
119C22×C3GL(2,ℤ/4)11yescharacteristic
120C3×C4—31no—
121C3×C4—31no—
122C3×C4—41no—
123C3×C4—61no—
124C3×C4—121no—
125C3×C4#98411yescharacteristic
126C3×C4#98511yescharacteristic
127Dic3—241no—
128C9—41noSylow
129Q8—31no—
130Q8—61no—
131Q8—61no—
132Q8—361no—
133Q8—361no—
134Q8#367511yescharacteristic
135C2×C4—21no—
136C2×C4—31no—
137C2×C4—31no—
138C2×C4—61no—
139C2×C4—361no—
140C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
141C8—182no—
142C8—361no—
143C8—361no—
144C2×C3#541711yescharacteristic
145C2×C3#542511yescharacteristic
146C2×C3#543011yescharacteristic
147C22#6369411yescharacteristic
148C4—31no—
149C4—31no—
150C4—41no—
151C4—61no—
152C4—121no—
153C4—721no—
154C4#6369011yescharacteristic
155C4#6369111yescharacteristic
156C3#7309411yescharacteristic
157C2#1058951911yescharacteristic
158C2#1058952711yescharacteristic
159C2#1058953211yescharacteristic
subgroupG/H
centerC22#63694
commutator, cosocleC4×Q8⋊C9C22
FrattiniC2×C3×C4C2×S4
FittingC3×#557D3
socle, prime radicalC22×C3GL(2,ℤ/4)
hypercenterC4⋊C4(C22⋊C9)⋊C2
hypocenterQ8⋊C9SD16
LCSG ▷ C4×Q8⋊C9 ▷ C2×Q8⋊C9 ▷ Q8⋊C9
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Maximal subgroups

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

subgroupindex
#557⋊C92
C4⋊#36882
(Q8⋊C9)⋊C82
#719383
#633674