Finite Group Databasebeta

← #11780669

Subgroups — #11780669

Order 1152.

588 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 105 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#10596171C211yesmaximal, characteristic
2C32×#491C211yesmaximal, characteristic, complemented
3#10592788C212yesmaximal, complemented
4#10589409C211yesmaximal, characteristic, complemented
5#10589330C212yesmaximal, complemented
6#71251—34nomaximal
7C32×C4⋊Q8C2211yescharacteristic
8C32×#125C2211yescharacteristic
9#64105—22no—
10#64104—22no—
11#64103—22no—
12#64084C2212yes—
13C32×#103—22no—
14C32×#97C2211yescharacteristic
15#63637—22no—
16#63636—22no—
17#63630C2212yes—
18#5700—34no—
19C3×#491D314yescomplemented
20#5089—38no—
21#4543—34no—
22#4464—38no—
23C2×C32×Q8—21no—
24C2×C4⋊(C3⋊D3)—22no—
25C2×C4⋊(C3⋊D3)D412yes—
26C2×C4×C3⋊D3—22no—
27C2×#634D412yes—
28C2×C32×C8—21no—
29C32×C4⋊C4—22no—
30C32×C4⋊C4—22no—
31C32×C4⋊C4D412yes—
32C32×C42C2311yescharacteristic
33#3752—22no—
34#3752—22no—
35#3752—22no—
36#3750—22no—
37C2×C3⋊(C3⋊C8)—22no—
38#1662—91noSylow
39C3×C4⋊Q8C2×D314yes—
40C3×#125C2×D314yes—
41#896—68no—
42#895—68no—
43#894—68no—
44#875—38no—
45C3×#103—28no—
46C3×#97C2×D314yes—
47#810—68no—
48#809—68no—
49#803—38no—
50C22×C3⋊D3—22no—
51C32×Q8—42no—
52C2×C32×C4—22no—
53C2×C32×C4—41no—
54C2×C32×C4C2×D412yes—
55C2×C32×C4C2×D411yescharacteristic
56C2×C3⋊Dic3—22no—
57C4⋊(C3⋊D3)—42no—
58C4⋊(C3⋊D3)—82no—
59C4×C3⋊D3—82no—
60#634—42no—
61C32×C8—41no—
62C3⋊(C3⋊C8)—42no—
63#562—91no—
64#491C3⋊D311yescharacteristic, complemented
65#489—92no—
66#330—91no—
67#329—92no—
68C2×C3×Q8—24no—
69C2×D12—38no—
70C2×D12—68no—
71C2×C4×D3—68no—
72C2×Dic6—38no—
73C2×C3×C8—24no—
74C3×C4⋊C4—28no—
75C3×C4⋊C4—28no—
76C3×C4⋊C4#6718yes—
77C3×C42C22×D314yes—
78(C2×D3)⋊C4—68no—
79(C2×D3)⋊C4—68no—
80(C2×D3)⋊C4—68no—
81Dic3⋊C4—68no—
82C2×C3⋊C8—68no—
83C22×C32#12011yescharacteristic
84C2×C3⋊D3—42no—
85C2×C3⋊D3—42no—
86C2×C3⋊D3—42no—
87C32×C4—21no—
88C32×C4—22no—
89C32×C4—42no—
90C32×C4—81no—
91C3⋊Dic3—42no—
92C4⋊Q8C2×C3⋊D311yescharacteristic
93#125C2×C3⋊D311yescharacteristic
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×C3⋊D311yescharacteristic
103C22×D3—68no—
104C3×Q8—48no—
105C2×C3×C4—28no—
106C2×C3×C4—44no—
107C2×C3×C4D3×D418yes—
108C2×C3×C4C2×#6714yes—
109C2×Dic3—68no—
110D12—128no—
111D12—248no—
112C4×D3—248no—
113Dic6—128no—
114C3×C8—44no—
115C3⋊C8—128no—
116C2×C32#45411yescharacteristic
117C2×C32#45512yes—
118C3⋊D3—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#63812yes—
130C22⋊C4—182no—
131C22⋊C4—182no—
132C22⋊C4—182no—
133C42C22×C3⋊D311yescharacteristic
134C22×C3#93714yes—
135C2×D3—128no—
136C2×D3—128no—
137C2×D3—128no—
138C3×C4—28no—
139C3×C4—24no—
140C3×C4—48no—
141C3×C4—84no—
142Dic3—128no—
143C32#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×C3⋊D312yes—
154C2×C4C2×#63811yescharacteristic
155C8—41no—
156C8—362no—
157C2×C3#506214yes—
158C2×C3#520218yes—
159D3—248no—
160C22—362no—
161C22—362no—
162C22—362no—
163C22#6414611yescharacteristic
164C4—22no—
165C4—21no—
166C4—42no—
167C4—81no—
168C4—362no—
169C3#7125114yescomplemented
170C2—722no—
171C2#1059276111yescharacteristic
172C2#1059290112yes—
subgroupG/H
centerC22#64146
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#491C2
socleC22×C32#120
prime radical#10596171C2
hypercenter#491C3⋊D3
hypocenterC32#1662
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. C32×#491C2semidirect
3. #10592788C2semidirect
4. #10589409C2semidirect
5. #10589330C2semidirect
19. C3×#491D3semidirect
64. #491C3⋊D3semidirect
143. C32#1662semidirect
169. C3#71251semidirect

Maximal subgroups

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

subgroupindex
#105961712
C32×#4912
#105927882
#105894092
#105893302
#712513