Finite Group Databasebeta

← #11772802

Subgroups — #11772802

Order 1152.

252 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 20 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#10592773C211yesmaximal, characteristic
2#10590145C211yesmaximal, characteristic, complemented
3#10590143C211yesmaximal, characteristic, complemented
4C32×#127C411yescharacteristic, complemented
5C2×#3754—21no—
6C2×#3753—21no—
7#64084C2211yescharacteristic
8#63780—21no—
9#63774—21no—
10#63630C411yescharacteristic, complemented
11#5074—62no—
12C2×C32×D4—21no—
13C2×C32×D4—41no—
14C2×C4⋊(C3⋊D3)D411yescharacteristic
15C2×#634D411yescharacteristic
16C22⋊#157—41no—
17#3792—41no—
18C32×C42C2×C411yescharacteristic
19#3754—42no—
20#3753—42no—
21#3752—41no—
22C2×C3⋊(C3⋊C8)—21no—
23#1406—91nomaximal, Sylow
24C3×#127—22no—
25C2×#214—64no—
26C2×#213—64no—
27#875—62no—
28#803—62no—
29C23×C32—41no—
30C22×C3⋊D3—21no—
31C2×#157—81no—
32C32×D4—41no—
33C32×D4—41no—
34C32×D4—82no—
35C2×C32×C4—21no—
36C2×C32×C4C22⋊C411yescharacteristic
37C2×C3⋊Dic3—21no—
38C4⋊(C3⋊D3)—41no—
39#634—41no—
40#622—81no—
41C3⋊(C3⋊C8)—22no—
42#496—91no—
43#355—91no—
44#354—91no—
45C2×C3×D4—24no—
46C2×C3×D4—44no—
47C2×D12—62no—
48C2×Dic6—62no—
49C3×C42—22no—
50#214—128no—
51#213—128no—
52(C2×D3)⋊C4—124no—
53C2×C3⋊C8—64no—
54C22×C32—82no—
55C22×C32—81no—
56C22×C32#9911yescharacteristic
57C2×C3⋊D3—41no—
58C2×C3⋊D3—81no—
59#157—161no—
60C32×C4—21no—
61C32×C4—41no—
62C3⋊Dic3—41no—
63C2×SD16—181no—
64C2×D8—181no—
65#127#15711yescharacteristic, complemented
66#124—91no—
67#101—181no—
68#99—181no—
69#97—91no—
70C23×C3—44no—
71C22×D3—122no—
72C3×D4—44no—
73C3×D4—44no—
74C3×D4—88no—
75C2×C3×C4—24no—
76C2×C3×C4—22no—
77C2×Dic3—122no—
78D12—124no—
79Dic6—124no—
80C3⋊C8—68no—
81C2×C32—21no—
82C2×C32—161no—
83C2×C32#35311yescharacteristic
84C3⋊D3—81no—
85C2×Q8—91no—
86C2×D4—21no—
87C2×D4—41no—
88C2×D4—91no—
89SD16—362no—
90D8—362no—
91M16—361no—
92C2×C8—181no—
93C22⋊C4—361no—
94C22⋊C4—361no—
95C42C2×#15711yescharacteristic
96C22×C3—22no—
97C22×C3—84no—
98C22×C3—88no—
99C2×D3—242no—
100C2×D3—244no—
101C3×C4—24no—
102C3×C4—44no—
103Dic3—242no—
104C32#140611yescharacteristic, complemented, Sylow
105C23—41no—
106C23—181no—
107Q8—361no—
108D4—41no—
109D4—41no—
110D4—82no—
111D4—361no—
112C2×C4—21no—
113C2×C4—181no—
114C2×C4—721no—
115C2×C4C22⋊#15711yescharacteristic
116C8—182no—
117C8—721no—
118C2×C3—24no—
119C2×C3—22no—
120C2×C3—164no—
121D3—482no—
122C22—82no—
123C22—81no—
124C22—361no—
125C22—721no—
126C22#6378611yescharacteristic
127C4—21no—
128C4—41no—
129C4—361no—
130C4—1441no—
131C3—22no—
132C2—21no—
133C2—161no—
134C2—721no—
135C2#1059021111yescharacteristic
subgroupG/H
centerC2#10590211
commutatorC32×C42C2×C4
FrattiniC42C2×#157
FittingC32×#127C4
socleC2×C32#353
prime radical#10592773C2
cosocle#64084C22
hypercenter#127#157
hypocenterC32#1406
LCSG ▷ C32×C42 ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #10590145C2semidirect
3. #10590143C2semidirect
4. C32×#127C4semidirect
10. #63630C4semidirect
65. #127#157semidirect
104. C32#1406semidirect

Maximal subgroups

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

subgroupindex
#105927732
#105901452
#105901432
#14069