Finite Group Databasebeta

← #11777058

Subgroups — #11777058

Order 1152.

204 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 55 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#10593731C211yesmaximal, characteristic
2#10593727C211yesmaximal, characteristic
3#10593725C211yesmaximal, characteristic
4#10590089C212yesmaximal, complemented
5#10590088C212yesmaximal, complemented
6C42×C3⋊D3C2211yescharacteristic
7#63779C2212yes—
8#63779C2212yes—
9#63778—21no—
10#63778—21no—
11#63778C412yes—
12#63777—21no—
13C4⋊#622C412yes—
14C4×#622—21no—
15C4×#622C2211yescharacteristic
16C4×#622C2211yescharacteristic
17C2×C4×C3⋊D3C2×C411yescharacteristic
18C2×C4×C3⋊D3D411yescharacteristic
19C2×C4×C3⋊D3Q811yescharacteristic
20C2×#622—22no—
21C2×#622—22no—
22C2×#622C2×C412yes—
23C2×#622C2×C412yes—
24C32×C42Q811yescharacteristic
25C4×C3⋊Dic3C2×C411yescharacteristic
26C4×C3⋊Dic3D411yescharacteristic
27C4×C3⋊Dic3C2311yescharacteristic
28#1572—91nomaximal, Sylow
29C42×D3—121no—
30C22×C3⋊D3C4⋊C411yescharacteristic
31C2×C32×C4C4⋊C411yescharacteristic
32C2×C32×C4C4⋊C411yescharacteristic
33C2×C32×C4C2×Q811yescharacteristic
34C2×C3⋊Dic3C4⋊C411yescharacteristic
35C2×C3⋊Dic3C22×C411yescharacteristic
36C2×C3⋊Dic3C2×D411yescharacteristic
37C4×C3⋊D3—22no—
38C4×C3⋊D3—22no—
39C4×C3⋊D3—41no—
40#622—22no—
41#622—22no—
42#622—42no—
43#622—42no—
44#432—91no—
45#431—91no—
46#431—91no—
47#335—92no—
48#334—92no—
49C2×C4×D3—121no—
50C2×C4×D3—121no—
51C2×C4×D3—121no—
52C3×C42—41no—
53C4×Dic3—121no—
54C4×Dic3—121no—
55C4×Dic3—121no—
56C22×C32C2×C4⋊C411yescharacteristic
57C2×C3⋊D3—21no—
58C2×C3⋊D3—21no—
59C2×C3⋊D3—21no—
60C32×C4—21no—
61C32×C4—21no—
62C32×C4—21no—
63C3⋊Dic3—21no—
64C3⋊Dic3#13112yes—
65C3⋊Dic3#13512yes—
66C2×C42—91no—
67C4⋊C8—92no—
68C4⋊C8—92no—
69C4⋊C8—92no—
70C22⋊C8—92no—
71C22⋊C8—181no—
72C22⋊C8—181no—
73#97—181no—
74C4×C8—91no—
75C4×C8—91no—
76C4×C8—181no—
77C22×D3—121no—
78C2×C3×C4—41no—
79C2×C3×C4—41no—
80C2×C3×C4—41no—
81C2×Dic3—121no—
82C2×Dic3—121no—
83C2×Dic3—121no—
84C4×D3—124no—
85C4×D3—124no—
86C4×D3—124no—
87C2×C32#42411yescharacteristic
88C2×C32#42711yescharacteristic
89C2×C32#43011yescharacteristic
90C3⋊D3—41no—
91C22×C4—91no—
92C22×C4—91no—
93C22×C4—91no—
94C2×C8—92no—
95C2×C8—92no—
96C2×C8—182no—
97C2×C8—182no—
98C42—91no—
99C42—91no—
100C42—91no—
101C42PSU(3,𝔽2)11yescharacteristic
102C22×C3—41no—
103C2×D3—122no—
104C2×D3—122no—
105C2×D3—122no—
106C3×C4—42no—
107C3×C4—42no—
108C3×C4—42no—
109Dic3—122no—
110Dic3—122no—
111Dic3—122no—
112C32#157211yescharacteristic, complemented, Sylow
113C23—91no—
114C2×C4—91no—
115C2×C4—91no—
116C2×C4—91no—
117C2×C4—182no—
118C2×C4—182no—
119C2×C4—361no—
120C2×C4#377711yescharacteristic
121C2×C4#377711yescharacteristic
122C2×C4C2×PSU(3,𝔽2)11yescharacteristic
123C8—182no—
124C8—182no—
125C8—362no—
126C8—362no—
127C2×C3—41no—
128C2×C3—41no—
129C2×C3—41no—
130D3—124no—
131C22—181no—
132C22—181no—
133C22—181no—
134C22C2×#377711yescharacteristic
135C4—21no—
136C4—21no—
137C4—21no—
138C4—92no—
139C4—92no—
140C4—181no—
141C3—41no—
142C2—361no—
143C2#1059354011yescharacteristic
144C2#1059354311yescharacteristic
145C2#1059354711yescharacteristic
subgroupG/H
centerC22C2×#3777
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×PSU(3,𝔽2)
FittingC32×C42Q8
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C4⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC42PSU(3,𝔽2)
hypocenterC32#1572
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #10590089C2semidirect
5. #10590088C2semidirect
112. C32#1572semidirect

Maximal subgroups

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

subgroupindex
#105937312
#105937272
#105937252
#105900892
#105900882
#15729