Finite Group Databasebeta

← #11920051

Subgroups — #11920051

Order 1152.

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

normal subgroups only

This group has 191 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, complemented
2C4⋊#3689C211yesmaximal, characteristic
3(Q8⋊C9)⋊C8C211yesmaximal, characteristic, complemented
4#71935—31nomaximal
5C2×#3689—21no—
6C4×Q8⋊C9—21no—
7C4×Q8⋊C9C2211yescharacteristic
8#63369—41nomaximal
9C3×#557D311yescharacteristic
10#5088—31no—
11#5027—31no—
12#5027—31no—
13#4547—31no—
14#4535—31no—
15#4535—31no—
16C2×D36—41no—
17C2×Q8⋊C9D411yescharacteristic
18#3689—41no—
19C9×C4⋊C4—41no—
20C2×C9⋊C8—41no—
21#1626—91noSylow
22C3×C4⋊Q8—31no—
23C3×#125—61no—
24C3×C4×Q8—21no—
25C3×C4×Q8—31no—
26C3×C4×Q8C2×D311yescharacteristic
27C2×#215—61no—
28C2×#215—61no—
29#874—31no—
30#809—61no—
31#809—62no—
32#809—61no—
33C4⋊(C3⋊C8)—31no—
34C4⋊(C3⋊C8)—31no—
35C4×C3⋊C8—31no—
36C22×D9—81no—
37C2×C4×C9—41no—
38C2×C4×C9—81no—
39D36—42no—
40D36—81no—
41Q8⋊C9SD1611yescharacteristic, complemented
42C9⋊C8—81no—
43#557D911yescharacteristic, complemented
44#486—91no—
45#460—91no—
46#460—91no—
47#332—91no—
48Q8⋊C8—91no—
49Q8⋊C8—91no—
50C2×C3×Q8—31no—
51C2×C3×Q8#6711yescharacteristic
52C2×D12—61no—
53C2×D12—61no—
54C2×D12—61no—
55C3×C4⋊C4—31no—
56C3×C4⋊C4—32no—
57C3×C4⋊C4—61no—
58C3×C4⋊C4—61no—
59C3×C4⋊C4S411yescharacteristic
60C3×C42—31no—
61C3×C42—61no—
62#215—121no—
63#215—122no—
64#215—121no—
65C2×C3⋊C8—61no—
66C2×C3⋊C8—61no—
67C2×C3⋊C8—61no—
68C22×C9—41no—
69C2×D9—82no—
70C2×D9—161no—
71C2×D9—161no—
72C4×C9—41no—
73C4×C9—41no—
74C4×C9—161no—
75C2×SD16—181no—
76C2×SD16—181no—
77C4⋊Q8—31no—
78#127—91no—
79#125—61no—
80C4×Q8—21no—
81C4×Q8—31no—
82C4×Q8C2×D911yescharacteristic
83C4⋊C8—91no—
84C4⋊C8—91no—
85#102—181no—
86#102—182no—
87#102—181no—
88C4×C8—91no—
89C22×D3—121no—
90C3×Q8—31no—
91C3×Q8—61no—
92C3×Q8—61no—
93C3×Q8#21511yescharacteristic
94C2×C3×C4—21no—
95C2×C3×C4—31no—
96C2×C3×C4—31no—
97C2×C3×C4—61no—
98C2×C3×C4C2×S411yescharacteristic
99D12—121no—
100D12—121no—
101D12—122no—
102D12—121no—
103D12—121no—
104C3⋊C8—121no—
105C3⋊C8—121no—
106C3⋊C8—121no—
107C2×C9—41no—
108C2×C9—41no—
109C2×C9—41no—
110D9—162no—
111C2×Q8—31no—
112C2×Q8#61111yescharacteristic
113C2×D4—181no—
114C2×D4—181no—
115C2×D4—181no—
116SD16—361no—
117SD16—362no—
118SD16—361no—
119C2×C8—181no—
120C2×C8—181no—
121C2×C8—181no—
122C4⋊C4—31no—
123C4⋊C4—32no—
124C4⋊C4—61no—
125C4⋊C4—61no—
126C4⋊C4(C22⋊C9)⋊C211yescharacteristic
127C42—31no—
128C42—61no—
129C22×C3GL(2,ℤ/4)11yescharacteristic
130C2×D3—241no—
131C2×D3—241no—
132C2×D3—241no—
133C3×C4—31no—
134C3×C4—31no—
135C3×C4—41no—
136C3×C4—61no—
137C3×C4—121no—
138C3×C4#98511yescharacteristic
139C3×C4#98611yescharacteristic
140C9—41noSylow
141C23—361no—
142Q8—31no—
143Q8—61no—
144Q8—61no—
145Q8#367511yescharacteristic
146D4—361no—
147D4—361no—
148D4—362no—
149D4—361no—
150D4—361no—
151C2×C4—21no—
152C2×C4—31no—
153C2×C4—31no—
154C2×C4—61no—
155C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
156C8—361no—
157C8—361no—
158C8—361no—
159C2×C3#541711yescharacteristic
160C2×C3#542711yescharacteristic
161C2×C3#543111yescharacteristic
162D3—481no—
163C22—721no—
164C22—721no—
165C22—721no—
166C22#6369411yescharacteristic
167C4—31no—
168C4—31no—
169C4—41no—
170C4—61no—
171C4—121no—
172C4#6369111yescharacteristic
173C4#6369211yescharacteristic
174C3#7309611yescharacteristic
175C2—1441no—
176C2#1058951911yescharacteristic
177C2#1058952911yescharacteristic
178C2#1058953311yescharacteristic
subgroupG/H
centerC22#63694
commutator, cosocleC4×Q8⋊C9C22
FrattiniC2×C3×C4C2×S4
FittingC3×#557D3
socleC22×C3GL(2,ℤ/4)
prime radicalC4⋊#3689C2
hypercenterC4⋊C4(C22⋊C9)⋊C2
hypocenterQ8⋊C9SD16
LCSG ▷ C4×Q8⋊C9 ▷ C2×Q8⋊C9 ▷ Q8⋊C9
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #557⋊C9C2semidirect
3. (Q8⋊C9)⋊C8C2semidirect
41. Q8⋊C9SD16semidirect
43. #557D9semidirect

Maximal subgroups

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

subgroupindex
#557⋊C92
C4⋊#36892
(Q8⋊C9)⋊C82
#719353
#633694