Finite Group Databasebeta

← #11799760

Subgroups — #11799760

Order 1152.

151 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 151 conjugacy classes of subgroups — too many to draw. Only its 35 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#10593779C211yesmaximal, characteristic
2#10593533C211yesmaximal, characteristic, complemented
3#10590192C212yesmaximal
4#10590084C212yesmaximal, complemented
5#10590083C211yesmaximal, characteristic, complemented
6#64287—21no—
7#64243—21no—
8#64121C2211yescharacteristic
9#63783—21no—
10#63771C2211yescharacteristic
11#63768C2212yes—
12C8×#157C2211yescharacteristic
13#63765C2212yes—
14#63746—21no—
15#3830—21no—
16#3792—41no—
17C2×#622—41no—
18C4⋊#157—22no—
19C4×#157D411yescharacteristic
20#3788—21no—
21#3787D411yescharacteristic
22#3777—42no—
23C32×D8Q811yescharacteristic
24#3754—21no—
25#3746Q811yescharacteristic
26C8×C3⋊D3C2311yescharacteristic
27#3708—22no—
28#2231—91nomaximal, Sylow
29#912—121no—
30C2×#157—21no—
31C2×#157—42no—
32C32×D4—21no—
33#638—41no—
34C2×C3⋊Dic3—41no—
35C4×C3⋊D3C2×D411yescharacteristic
36#634—21no—
37#622—41no—
38#622SD1611yescharacteristic
39#622SD1611yescharacteristic
40C32×C8C2×Q811yescharacteristic
41C3⋊(C3⋊C8)#4111yescharacteristic
42#499—91no—
43#443—91no—
44#365—92no—
45#364—91no—
46#360—92no—
47#237—122no—
48C3×D8—41no—
49#214—122no—
50Dic12—121no—
51D3×C8—121no—
52C22×C32—41no—
53C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
54#157—41no—
55#157—82no—
56C32×C4C22⋊Q811yescharacteristic
57C3⋊Dic3—41no—
58C3⋊Dic3C2×SD1611yescharacteristic
59#135—91no—
60#131—181no—
61#125—181no—
62M32—92no—
63#108—91no—
64#107—181no—
65#106—92no—
66#104—181no—
67C4×C8—91no—
68C3×D4—42no—
69#67—242no—
70C2×Dic3—242no—
71C4×D3—121no—
72Dic6—122no—
73C3×C8—41no—
74C3⋊C8—121no—
75C2×C32—81no—
76C2×C32#47611yescharacteristic
77C3⋊D3—21no—
78#41—181no—
79Q16—91no—
80SD16—181no—
81D8PSU(3,𝔽2)11yescharacteristic
82M16—181no—
83M16—361no—
84C2×C8—91no—
85C2×C8—91no—
86C2×C8—361no—
87C4⋊C4—182no—
88C4⋊C4—362no—
89C42—91no—
90C16—182no—
91C22×C3—82no—
92C2×D3—121no—
93C3×C4—41no—
94Dic3—121no—
95Dic3—242no—
96C32#223111yescharacteristic, complemented, Sylow
97Q8—181no—
98D4—21no—
99D4—361no—
100C2×C4—91no—
101C2×C4—181no—
102C2×C4—361no—
103C2×C4—362no—
104C8—91no—
105C8—91no—
106C8—91no—
107C8—361no—
108C8C2×PSU(3,𝔽2)11yescharacteristic
109C2×C3—41no—
110C2×C3—162no—
111D3—241no—
112C22—41no—
113C22—91no—
114C4—91no—
115C4—361no—
116C4—361no—
117C4—722no—
118C4C22⋊PSU(3,𝔽2)11yescharacteristic
119C3—41no—
120C2—81no—
121C2—181no—
122C2#1059355911yescharacteristic
subgroupG/H
centerC2#10593559
commutator, cosocleC8×C3⋊D3C23
FrattiniC8C2×PSU(3,𝔽2)
FittingC32×D8Q8
socleC2×C32#476
prime radical#64121C22
hypercenterD8PSU(3,𝔽2)
hypocenterC32#2231
LCSG ▷ C8×C3⋊D3 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ D8

Complements

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

NH ≅ G/Ntype
2. #10593533C2semidirect
4. #10590084C2semidirect
5. #10590083C2semidirect
96. C32#2231semidirect

Maximal subgroups

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

subgroupindex
#105937792
#105935332
#105901922
#105900842
#105900832
#22319