Finite Group Databasebeta

← #11779300

Subgroups — #11779300

Order 1152.

942 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 942 conjugacy classes of subgroups — too many to draw. Only its 133 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#10596188C211yesmaximal, characteristic
2#10592775C211yesmaximal, characteristic, complemented
3#10592541C212yesmaximal, complemented
4C32×#331C211yesmaximal, characteristic, complemented
5#10589349C212yesmaximal, complemented
6#68391—34nomaximal
7C2×D4×C3⋊D3—22no—
8C32×#127C2211yescharacteristic
9#64147—22no—
10#64146—22no—
11C2×#3754—22no—
12C4×C4⋊(C3⋊D3)C2212yes—
13#64078C2211yescharacteristic, complemented
14C32×C4⋊C8C2212yescomplemented
15#63648—22no—
16#63644—22no—
17C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
18#5717—34no—
19#5076—34no—
20#4842—38no—
21C3×#331D314yescomplemented
22#4483—38no—
23C23×C3⋊D3—22no—
24C2×C32×D4—22no—
25C2×C32×D4D412yes—
26C2×#638—24no—
27D4×C3⋊D3—44no—
28D4×C3⋊D3—44no—
29C2×C4⋊(C3⋊D3)D412yes—
30C2×C4×C3⋊D3—22no—
31C2×#634—21no—
32C2×C32×C8—22no—
33C32×C42C2311yescharacteristic
34#3757—22no—
35#3754—44no—
36#3752—22no—
37C4⋊(C3⋊Dic3)—22no—
38C4⋊(C3⋊Dic3)D412yes—
39C2×C3⋊(C3⋊C8)—21no—
40#1629—91noSylow
41C2×D3×D4—68no—
42C3×#127C2×D314yes—
43#938—68no—
44#937—68no—
45C2×#214—68no—
46C4×D12—38no—
47#869—34no—
48C3×C4⋊C8C2×D318yescomplemented
49#821—68no—
50#817—68no—
51C4×C3⋊C8—34no—
52C23×C32—22no—
53C22×C3⋊D3—22no—
54C22×C3⋊D3—48no—
55C22×C3⋊D3—82no—
56C32×D4—42no—
57C32×D4—42no—
58C32×D4—42no—
59C2×C32×C4C2×D411yescharacteristic
60C2×C32×C4C2×D412yes—
61#638—48no—
62C2×C3⋊Dic3—22no—
63C2×C3⋊Dic3—41no—
64C4⋊(C3⋊D3)—22no—
65C4⋊(C3⋊D3)SD1614yescomplemented
66C4×C3⋊D3—42no—
67C4×C3⋊D3—42no—
68#634—42no—
69C32×C8—42no—
70C3⋊(C3⋊C8)—22no—
71D42—91no—
72#492—91no—
73#476—92no—
74#331C3⋊D311yescharacteristic, complemented
75D4⋊C8—92no—
76C23×D3—68no—
77C2×C3×D4—28no—
78C2×C3×D4D1218yes—
79C2×#67—616no—
80D3×D4—1216no—
81D3×D4—1216no—
82C2×D12—38no—
83C2×C4×D3—68no—
84C2×Dic6—64no—
85C2×C3×C8—28no—
86C3×C42C22×D314yes—
87#217—68no—
88#214—1216no—
89(C2×D3)⋊C4—68no—
90C4⋊Dic3—38no—
91C4⋊Dic3—68no—
92C2×C3⋊C8—64no—
93C22×C32—44no—
94C22×C32—42no—
95C22×C32#12011yescharacteristic
96C2×C3⋊D3—24no—
97C2×C3⋊D3—42no—
98C2×C3⋊D3—42no—
99C2×C3⋊D3—88no—
100C32×C4—21no—
101C32×C4C2×SD1612yes—
102C32×C4AGL(1,ℤ/8)12yes—
103C3⋊Dic3—42no—
104C3⋊Dic3—81no—
105C22×D4—182no—
106C2×SD16—182no—
107C4⋊Q8—91no—
108#127C2×C3⋊D311yescharacteristic
109#121—182no—
110#120—182no—
111C4×D4—92no—
112#106—182no—
113C4⋊C8C2×C3⋊D312yescomplemented
114#102—182no—
115C4×C8—91no—
116C23×C3—28no—
117C22×D3—68no—
118C22×D3—1232no—
119C22×D3—248no—
120C3×D4—48no—
121C3×D4—48no—
122C3×D4—48no—
123C2×C3×C4C2×D1214yes—
124C2×C3×C4D3×D418yes—
125#67—1232no—
126C2×Dic3—68no—
127C2×Dic3—124no—
128D12—316no—
129D12—68no—
130C4×D3—128no—
131C4×D3—128no—
132Dic6—128no—
133C3×C8—48no—
134C3⋊C8—68no—
135C2×C32—82no—
136C2×C32#45012yes—
137C2×C32#45311yescharacteristic
138C3⋊D3—44no—
139C24—182no—
140C2×Q8—181no—
141C2×D4—22no—
142C2×D4—92no—
143C2×D4—184no—
144C2×D4—364no—
145C2×D4—364no—
146C2×D4C4⋊(C3⋊D3)12yes—
147C22×C4—182no—
148SD16—364no—
149C2×C8—22no—
150C2×C8—181no—
151C4⋊C4—92no—
152C4⋊C4—182no—
153C22⋊C4—182no—
154C22⋊C4—182no—
155C42C22×C3⋊D311yescharacteristic
156C22×C3—48no—
157C22×C3—416no—
158C22×C3#88214yes—
159C2×D3—616no—
160C2×D3—128no—
161C2×D3—128no—
162C2×D3—2432no—
163C3×C4—24no—
164C3×C4#91118yes—
165C3×C4D3×SD1618yes—
166Dic3—128no—
167Dic3—244no—
168C32#162911yescharacteristic, complemented, Sylow
169C23—22no—
170C23—182no—
171C23—368no—
172C23—722no—
173Q8—362no—
174D4—42no—
175D4—42no—
176D4—42no—
177D4—94no—
178D4—182no—
179D4—368no—
180C2×C4—182no—
181C2×C4—362no—
182C2×C4—362no—
183C2×C4—361no—
184C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
185C2×C4D4×C3⋊D312yes—
186C8—42no—
187C8—182no—
188C2×C3—88no—
189C2×C3#474714yes—
190C2×C3#477618yes—
191D3—1216no—
192C22—42no—
193C22—44no—
194C22—184no—
195C22—362no—
196C22—362no—
197C22—728no—
198C22#6409111yescharacteristic
199C4—21no—
200C4—362no—
201C4—721no—
202C4#6412012yes—
203C4SD16×C3⋊D312yes—
204C3#6839114yescomplemented
205C2—82no—
206C2—364no—
207C2#1059244611yescharacteristic
208C2#1059247512yes—
subgroupG/H
centerC22#64091
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#331C2
socleC22×C32#120
prime radical#10596188C2
hypercenter#331C3⋊D3
hypocenterC32#1629
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #10592775C2semidirect
3. #10592541C2semidirect
4. C32×#331C2semidirect
5. #10589349C2semidirect
13. #64078C22semidirect
14. C32×C4⋊C8C22semidirect
17. C4×C3⋊(C3⋊C8)C22semidirect
21. C3×#331D3semidirect
48. C3×C4⋊C8C2×D3semidirect
65. C4⋊(C3⋊D3)SD16semidirect
74. #331C3⋊D3semidirect
113. C4⋊C8C2×C3⋊D3semidirect
168. C32#1629semidirect
204. C3#68391semidirect

Maximal subgroups

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

subgroupindex
#105961882
#105927752
#105925412
C32×#3312
#105893492
#683913