Finite Group Databasebeta

← #11799127

Subgroups — #11799127

Order 1152.

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

normal subgroups only

This group has 450 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×#494C211yesmaximal, characteristic, complemented
2#10592878C212yesmaximal
3#10592399C211yesmaximal, characteristic
4#10589431C212yesmaximal, complemented
5#10589329C211yesmaximal, characteristic, complemented
6#71317—34nomaximal
7C2×C32×Q16—21no—
8C2×C32×Q16C2212yes—
9C32×C4⋊Q8—21no—
10#64113C2211yescharacteristic
11#64110—21no—
12C32×C4×C8C2211yescharacteristic
13#63656—22no—
14#63655—22no—
15#63646C2211yescharacteristic
16#63639C2212yes—
17#63632—21no—
18C3×#494D314yescomplemented
19#5179—38no—
20#4700—34no—
21#4565—38no—
22#4463—34no—
23C2×C32×Q8—22no—
24#3828—21no—
25C32×Q16—22no—
26C32×Q16—22no—
27C32×Q16—41no—
28C32×Q16—41no—
29C2×C32×C8D411yescharacteristic
30C2×C32×C8C2311yescharacteristic
31C32×C4⋊C4—42no—
32C32×C42D411yescharacteristic
33#3748—21no—
34#3746D411yescharacteristic
35#3745D411yescharacteristic
36#3744—21no—
37#3743—41no—
38C8×C3⋊D3—41no—
39C3⋊(C3⋊C16)—22no—
40#2214—91noSylow
41C2×C3×Q16—24no—
42C2×C3×Q16C2×D318yes—
43C3×C4⋊Q8—24no—
44#904—34no—
45#901—64no—
46C3×C4×C8C2×D314yes—
47#829—68no—
48#828—68no—
49#819—34no—
50#812—38no—
51#805—64no—
52C32×Q8—42no—
53C32×Q8—42no—
54C2×C32×C4—21no—
55C2×C32×C4—42no—
56C2×C32×C4C2×D411yescharacteristic
57#638—41no—
58C4⋊(C3⋊D3)—21no—
59C4×C3⋊D3—41no—
60#634—21no—
61C32×C8D811yescharacteristic
62C32×C8D811yescharacteristic
63C32×C8C2×D411yescharacteristic
64C32×C8#4111yescharacteristic
65C3⋊(C3⋊C8)—41no—
66#510—92no—
67#494C3⋊D311yescharacteristic, complemented
68#443—91no—
69#364—91no—
70#362—92no—
71C2×C3×Q8—28no—
72#235—64no—
73C3×Q16—28no—
74C3×Q16—28no—
75C3×Q16—44no—
76C3×Q16—44no—
77C2×C3×C8#6714yes—
78C2×C3×C8C22×D314yes—
79C3×C4⋊C4—48no—
80C3×C42#6714yes—
81#208—64no—
82Dic12—34no—
83D24—34no—
84#204—64no—
85ΓL(1,𝔽25)—124no—
86D3×C8—124no—
87C3⋊C16—68no—
88C22×C32AGL(1,ℤ/8)11yescharacteristic
89C2×C3⋊D3—41no—
90C32×C4—22no—
91C32×C4—82no—
92C32×C4#12111yescharacteristic
93C32×C4C2×D811yescharacteristic
94C3⋊Dic3—41no—
95#135—91no—
96C2×Q16—21no—
97C2×Q16C2×C3⋊D312yes—
98#131—181no—
99C4⋊Q8—21no—
100Q32—182no—
101SD32—182no—
102M32—92no—
103#108—91no—
104#104—181no—
105C4×C8C2×C3⋊D311yescharacteristic
106C3×Q8—48no—
107C3×Q8—48no—
108C2×C3×C4—24no—
109C2×C3×C4—48no—
110C2×C3×C4C2×#6714yes—
111#67—124no—
112D12—64no—
113C4×D3—124no—
114Dic6—64no—
115C3×C8#21314yes—
116C3×C8#21314yes—
117C3×C8D3×D414yes—
118C3×C8#23714yes—
119C3⋊C8—124no—
120C2×C32—21no—
121C2×C32#45911yescharacteristic
122C3⋊D3—81no—
123#41—181no—
124C2×Q8—22no—
125Q16—22no—
126Q16—22no—
127Q16—41no—
128Q16—41no—
129Q16—91no—
130SD16—181no—
131D8—91no—
132M16—181no—
133M16—361no—
134C2×C8—361no—
135C2×C8#63811yescharacteristic
136C2×C8C22×C3⋊D311yescharacteristic
137C4⋊C4—42no—
138C42#63811yescharacteristic
139C16—182no—
140C22×C3#93214yes—
141C2×D3—124no—
142C3×C4—28no—
143C3×C4—88no—
144C3×C4C2×#21314yes—
145C3×C4#93814yes—
146Dic3—124no—
147C32#221411yescharacteristic, complemented, Sylow
148Q8—42no—
149Q8—42no—
150Q8—181no—
151D4—181no—
152D4—361no—
153C2×C4—21no—
154C2×C4—42no—
155C2×C4—361no—
156C2×C4C2×#63811yescharacteristic
157C8—361no—
158C8#375311yescharacteristic
159C8#375311yescharacteristic
160C8D4×C3⋊D311yescharacteristic
161C8#383011yescharacteristic
162C2×C3—24no—
163C2×C3#507214yes—
164D3—244no—
165C22—361no—
166C22#6414111yescharacteristic
167C4—22no—
168C4—82no—
169C4—361no—
170C4C2×#375311yescharacteristic
171C4#6414711yescharacteristic
172C3#7131714yescomplemented
173C2—21no—
174C2—721no—
175C2#1059277111yescharacteristic
subgroupG/H
centerC2#10592771
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#494C2
socleC2×C32#459
prime radical#64113C22
hypercenter#494C3⋊D3
hypocenterC32#2214
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #494

Complements

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

NH ≅ G/Ntype
1. C32×#494C2semidirect
4. #10589431C2semidirect
5. #10589329C2semidirect
18. C3×#494D3semidirect
67. #494C3⋊D3semidirect
147. C32#2214semidirect
172. C3#71317semidirect

Maximal subgroups

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

subgroupindex
C32×#4942
#105928782
#105923992
#105894312
#105893292
#713173