Finite Group Databasebeta

← #11780668

Subgroups — #11780668

Order 1152.

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

normal subgroups only

This group has 294 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
1#10589802C211yesmaximal, characteristic
2C9×#491C211yesmaximal, characteristic, complemented
3#10588774C212yesmaximal, complemented
4#10588220C211yesmaximal, characteristic, complemented
5#10588142C212yesmaximal, complemented
6#71251—31nomaximal
7C9×C4⋊Q8C2211yescharacteristic
8C9×#125C2211yescharacteristic
9#63458—22no—
10#63457—22no—
11#63456—22no—
12#63437C2212yes—
13C9×#103—22no—
14C9×#97C2211yescharacteristic
15#63369—22no—
16#63368—22no—
17#63362C2212yes—
18#5700—31no—
19C3×#491D311yescharacteristic
20#5089—32no—
21#4543—31no—
22#4464—32no—
23C2×Q8×C9—21no—
24C2×D36—22no—
25C2×D36D412yes—
26C2×C4×D9—22no—
27C2×Dic18D412yes—
28C2×C8×C9—21no—
29C9×C4⋊C4—22no—
30C9×C4⋊C4—22no—
31C9×C4⋊C4D412yes—
32C42×C9C2311yescharacteristic
33(C2×D9)⋊C4—22no—
34(C2×D9)⋊C4—22no—
35(C2×D9)⋊C4—22no—
36Dic9⋊C4—22no—
37C2×C9⋊C8—22no—
38#1662—91noSylow
39C3×C4⋊Q8C2×D311yescharacteristic
40C3×#125C2×D311yescharacteristic
41#896—62no—
42#895—62no—
43#894—62no—
44#875—32no—
45C3×#103—22no—
46C3×#97C2×D311yescharacteristic
47#810—62no—
48#809—62no—
49#803—32no—
50C22×D9—22no—
51Q8×C9—42no—
52C2×C4×C9—22no—
53C2×C4×C9—41no—
54C2×C4×C9C2×D412yes—
55C2×C4×C9C2×D411yescharacteristic
56C2×Dic9—22no—
57D36—42no—
58D36—82no—
59C4×D9—82no—
60Dic18—42no—
61C8×C9—41no—
62C9⋊C8—42no—
63#562—91no—
64#491D911yescharacteristic, complemented
65#489—92no—
66#330—91no—
67#329—92no—
68C2×C3×Q8—21no—
69C2×D12—32no—
70C2×D12—62no—
71C2×C4×D3—62no—
72C2×Dic6—32no—
73C2×C3×C8—21no—
74C3×C4⋊C4—22no—
75C3×C4⋊C4—22no—
76C3×C4⋊C4#6712yes—
77C3×C42C22×D311yescharacteristic
78(C2×D3)⋊C4—62no—
79(C2×D3)⋊C4—62no—
80(C2×D3)⋊C4—62no—
81Dic3⋊C4—62no—
82C2×C3⋊C8—62no—
83C22×C9#12011yescharacteristic
84C2×D9—42no—
85C2×D9—42no—
86C2×D9—42no—
87C4×C9—21no—
88C4×C9—22no—
89C4×C9—42no—
90C4×C9—81no—
91Dic9—42no—
92C4⋊Q8C2×D911yescharacteristic
93#125C2×D911yescharacteristic
94#124—92no—
95#123—182no—
96C22⋊Q8—182no—
97#121—182no—
98#103—22no—
99#103—182no—
100#102—182no—
101#97—92no—
102#97C2×D911yescharacteristic
103C22×D3—62no—
104C3×Q8—42no—
105C2×C3×C4—22no—
106C2×C3×C4—41no—
107C2×C3×C4D3×D412yes—
108C2×C3×C4C2×#6711yescharacteristic
109C2×Dic3—62no—
110D12—122no—
111D12—242no—
112C4×D3—242no—
113Dic6—122no—
114C3×C8—41no—
115C3⋊C8—122no—
116C2×C9#45411yescharacteristic
117C2×C9#45512yes—
118D9—82no—
119C2×Q8—21no—
120C2×Q8—92no—
121C2×D4—92no—
122C2×D4—182no—
123C22×C4—182no—
124C2×C8—21no—
125C2×C8—182no—
126C4⋊C4—22no—
127C4⋊C4—22no—
128C4⋊C4—182no—
129C4⋊C4#61112yes—
130C22⋊C4—182no—
131C22⋊C4—182no—
132C22⋊C4—182no—
133C42C22×D911yescharacteristic
134C22×C3#93711yescharacteristic
135C2×D3—122no—
136C2×D3—122no—
137C2×D3—122no—
138C3×C4—22no—
139C3×C4—21no—
140C3×C4—42no—
141C3×C4—81no—
142Dic3—122no—
143C9#166211yescharacteristic, complemented, Sylow
144C23—182no—
145Q8—42no—
146Q8—362no—
147D4—362no—
148D4—722no—
149C2×C4—22no—
150C2×C4—41no—
151C2×C4—182no—
152C2×C4—722no—
153C2×C4D4×D912yes—
154C2×C4C2×#61111yescharacteristic
155C8—41no—
156C8—362no—
157C2×C3#506211yescharacteristic
158C2×C3#520212yes—
159D3—242no—
160C22—362no—
161C22—362no—
162C22—362no—
163C22#6349911yescharacteristic
164C4—21no—
165C4—22no—
166C4—42no—
167C4—81no—
168C4—362no—
169C3#7125111yescharacteristic
170C2—722no—
171C2#1058874211yescharacteristic
172C2#1058888312yes—
subgroupG/H
centerC22#63499
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#491C2
socleC22×C3#937
prime radical#10589802C2
hypercenter#491D9
hypocenterC9#1662
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. C9×#491C2semidirect
3. #10588774C2semidirect
4. #10588220C2semidirect
5. #10588142C2semidirect
64. #491D9semidirect
143. C9#1662semidirect

Maximal subgroups

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

subgroupindex
#105898022
C9×#4912
#105887742
#105882202
#105881422
#712513