Finite Group Databasebeta

← #11799095

Subgroups — #11799095

Order 1152.

510 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C32×#493C211yesmaximal, characteristic, complemented
2#10592846C212yesmaximal, complemented
3#10592399C211yesmaximal, characteristic, complemented
4#10589429C212yesmaximal, complemented
5#10589329C211yesmaximal, characteristic, complemented
6#71295—34nomaximal
7C2×C32×D8—21no—
8C2×C32×D8C2212yes—
9C32×#127—21no—
10#64113C2211yescharacteristic
11#64110—21no—
12C32×C4×C8C2211yescharacteristic
13#63654—22no—
14#63653—22no—
15#63646C2211yescharacteristic
16#63639C2212yes—
17#63632—21no—
18C3×#493D314yescomplemented
19#5147—38no—
20#4700—34no—
21#4563—38no—
22#4463—34no—
23C2×C32×D4—22no—
24C2×C32×D4—42no—
25#3828—21no—
26C32×D8—22no—
27C32×D8—22no—
28C32×D8—41no—
29C32×D8—41no—
30C2×C32×C8D411yescharacteristic
31C2×C32×C8C2311yescharacteristic
32C32×C42D411yescharacteristic
33#3748—21no—
34#3746D411yescharacteristic, complemented
35#3745D411yescharacteristic, complemented
36#3744—21no—
37#3743—41no—
38C8×C3⋊D3—41no—
39C3⋊(C3⋊C16)—22no—
40#2213—91noSylow
41C2×C3×D8—24no—
42C2×C3×D8C2×D318yes—
43C3×#127—24no—
44#904—34no—
45#901—64no—
46C3×C4×C8C2×D314yes—
47#827—68no—
48#826—68no—
49#819—34no—
50#812—38no—
51#805—64no—
52C23×C32—42no—
53C32×D4—42no—
54C32×D4—42no—
55C32×D4—84no—
56C2×C32×C4—21no—
57C2×C32×C4C2×D411yescharacteristic
58#638—41no—
59C4⋊(C3⋊D3)—21no—
60C4×C3⋊D3—41no—
61#634—21no—
62C32×C8D811yescharacteristic
63C32×C8D811yescharacteristic
64C32×C8C2×D411yescharacteristic
65C32×C8#4111yescharacteristic
66C3⋊(C3⋊C8)—41no—
67#509—92no—
68#493C3⋊D311yescharacteristic, complemented
69#443—91no—
70#364—91no—
71#361—92no—
72C2×C3×D4—28no—
73C2×C3×D4—48no—
74#235—64no—
75C3×D8—28no—
76C3×D8—28no—
77C3×D8—44no—
78C3×D8—44no—
79C2×C3×C8#6714yes—
80C2×C3×C8C22×D314yes—
81C3×C42#6714yes—
82#208—64no—
83Dic12—34no—
84D24—34no—
85#204—64no—
86ΓL(1,𝔽25)—124no—
87D3×C8—124no—
88C3⋊C16—68no—
89C22×C32—84no—
90C22×C32—82no—
91C22×C32AGL(1,ℤ/8)11yescharacteristic
92C2×C3⋊D3—41no—
93C32×C4—22no—
94C32×C4#12111yescharacteristic
95C32×C4C2×D811yescharacteristic
96C3⋊Dic3—41no—
97#135—91no—
98C2×D8—21no—
99C2×D8C2×C3⋊D312yes—
100#131—181no—
101#127—21no—
102SD32—182no—
103D16—182no—
104M32—92no—
105#108—91no—
106#104—181no—
107C4×C8C2×C3⋊D311yescharacteristic
108C23×C3—48no—
109C3×D4—48no—
110C3×D4—48no—
111C3×D4—816no—
112C2×C3×C4—24no—
113C2×C3×C4C2×#6714yes—
114#67—124no—
115D12—64no—
116C4×D3—124no—
117Dic6—64no—
118C3×C8#21314yes—
119C3×C8#21314yes—
120C3×C8D3×D414yes—
121C3×C8#23714yes—
122C3⋊C8—124no—
123C2×C32—21no—
124C2×C32—162no—
125C2×C32#45911yescharacteristic
126C3⋊D3—81no—
127#41—181no—
128C2×D4—22no—
129C2×D4—42no—
130Q16—91no—
131SD16—181no—
132D8—22no—
133D8—22no—
134D8—41no—
135D8—41no—
136D8—91no—
137M16—181no—
138M16—361no—
139C2×C8—361no—
140C2×C8#63811yescharacteristic
141C2×C8C22×C3⋊D311yescharacteristic
142C42#63811yescharacteristic
143C16—182no—
144C22×C3—816no—
145C22×C3—88no—
146C22×C3#93214yes—
147C2×D3—124no—
148C3×C4—28no—
149C3×C4C2×#21314yes—
150C3×C4#93814yes—
151Dic3—124no—
152C32#221311yescharacteristic, complemented, Sylow
153C23—42no—
154Q8—181no—
155D4—42no—
156D4—42no—
157D4—84no—
158D4—181no—
159D4—361no—
160C2×C4—21no—
161C2×C4—361no—
162C2×C4C2×#63811yescharacteristic
163C8—361no—
164C8#375311yescharacteristic
165C8#375311yescharacteristic
166C8D4×C3⋊D311yescharacteristic
167C8#383011yescharacteristic
168C2×C3—24no—
169C2×C3—168no—
170C2×C3#507214yes—
171D3—244no—
172C22—84no—
173C22—82no—
174C22—361no—
175C22#6414111yescharacteristic
176C4—22no—
177C4—361no—
178C4C2×#375311yescharacteristic
179C4#6414711yescharacteristic
180C3#7129514yescomplemented
181C2—21no—
182C2—162no—
183C2—721no—
184C2#1059277111yescharacteristic
subgroupG/H
centerC2#10592771
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#493C2
socleC2×C32#459
hypercenter#493C3⋊D3
hypocenterC32#2213
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #493

Complements

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

NH ≅ G/Ntype
1. C32×#493C2semidirect
2. #10592846C2semidirect
3. #10592399C2semidirect
4. #10589429C2semidirect
5. #10589329C2semidirect
18. C3×#493D3semidirect
34. #3746D4semidirect
35. #3745D4semidirect
68. #493C3⋊D3semidirect
152. C32#2213semidirect
180. C3#71295semidirect

Maximal subgroups

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

subgroupindex
C32×#4932
#105928462
#105923992
#105894292
#105893292
#712953