Finite Group Databasebeta

← #11772425

Subgroups — #11772425

Order 1152.

242 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 50 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
1C2×#63768C211yesmaximal, characteristic
2#10593762C211yesmaximal, characteristic
3C3⋊D3×#108C211yesmaximal, characteristic
4C2×C4⋊#157—21no—
5M16×C3⋊D3—21no—
6C2×C8×C3⋊D3C2211yescharacteristic
7#63773—21no—
8#63768—21no—
9#63768C412yes—
10#63765—21no—
11#63764C412yescomplemented
12C32×#108C411yescharacteristic, complemented
13#63649—21no—
14#63646C411yescharacteristic, complemented
15D3×#108—62no—
16C22×#157—41no—
17C2×C4×C3⋊D3D411yescharacteristic
18C4⋊#157—22no—
19C4⋊#157—41no—
20C32×M16—21no—
21C2×C32×C8C2×C411yescharacteristic
22#3748—21no—
23C2×C3⋊(C3⋊C8)D411yescharacteristic
24#3743—41no—
25C8×C3⋊D3—41no—
26C8×C3⋊D3C2×C411yescharacteristic
27C8×C3⋊D3C2×C411yescharacteristic
28C8×C3⋊D3D411yescharacteristic
29C8×C3⋊D3Q811yescharacteristic
30#3708—22no—
31#1383—91nomaximal, Sylow
32D3×M16—64no—
33C2×D3×C8—62no—
34C3×#108—22no—
35#822—64no—
36#819—62no—
37C22×C3⋊D3SD1611yescharacteristic
38C2×#157—42no—
39C2×#157—82no—
40C2×C32×C4C22⋊C411yescharacteristic
41C2×C3⋊Dic3Q1611yescharacteristic
42C4×C3⋊D3C22⋊C411yescharacteristic
43C4×C3⋊D3C4⋊C411yescharacteristic
44C4×C3⋊D3D811yescharacteristic
45C4×C3⋊D3SD1611yescharacteristic
46C32×C8—41no—
47C32×C8C4211yescharacteristic
48C32×C8C4⋊C411yescharacteristic
49C3⋊(C3⋊C8)—41no—
50C3⋊(C3⋊C8)C22⋊C411yescharacteristic
51C3⋊(C3⋊C8)C4⋊C411yescharacteristic
52C2×M32—91no—
53C2×#108—91no—
54C2×#106—91no—
55C2×C4×D3—62no—
56C3×M16—24no—
57C2×C3×C8—22no—
58#208—64no—
59C2×C3⋊C8—62no—
60ΓL(1,𝔽25)—124no—
61D3×C8—62no—
62D3×C8—62no—
63D3×C8—62no—
64D3×C8—62no—
65D3×C8—124no—
66C22×C32#10311yescharacteristic
67C2×C3⋊D3—22no—
68C2×C3⋊D3#10211yescharacteristic
69C2×C3⋊D3#10611yescharacteristic
70#157—82no—
71C32×C4#9511yescharacteristic
72C32×C4#10211yescharacteristic
73C3⋊Dic3#10311yescharacteristic
74C3⋊Dic3#10711yescharacteristic
75C2×M16—181no—
76C22×C8—91no—
77C2×C4⋊C4—181no—
78M32—181no—
79M32—181no—
80C2×C16—92no—
81#108—91no—
82#108—181no—
83#108#15711yescharacteristic, complemented
84#106—92no—
85#106—181no—
86C22×D3—62no—
87C2×C3×C4—22no—
88C2×Dic3—62no—
89C4×D3—62no—
90C4×D3—62no—
91C4×D3—62no—
92C4×D3—62no—
93C3×C8—22no—
94C3×C8—22no—
95C3×C8—44no—
96C3⋊C8—62no—
97C3⋊C8—62no—
98C3⋊C8—124no—
99C2×C32—21no—
100C2×C32#34011yescharacteristic
101C3⋊D3—21no—
102C3⋊D3#36512yes—
103C22×C4—91no—
104C22×C4—361no—
105M16—21no—
106M16—181no—
107M16—361no—
108C2×C8—91no—
109C2×C8—91no—
110C2×C8—91no—
111C2×C8—91no—
112C2×C8—91no—
113C2×C8—361no—
114C2×C8C2×#15711yescharacteristic
115C4⋊C4—182no—
116C4⋊C4—361no—
117C16—182no—
118C22×C3—22no—
119C2×D3—62no—
120C2×D3—62no—
121C2×D3—124no—
122C3×C4—22no—
123C3×C4—22no—
124Dic3—62no—
125Dic3—62no—
126C32#138311yescharacteristic, complemented, Sylow
127C23—91no—
128C2×C4—91no—
129C2×C4—91no—
130C2×C4—91no—
131C2×C4—91no—
132C2×C4—91no—
133C2×C4—362no—
134C2×C4—722no—
135C2×C4C22⋊#15711yescharacteristic
136C8—41no—
137C8—91no—
138C8—91no—
139C8—361no—
140C8C4×#15711yescharacteristic
141C8C4⋊#15711yescharacteristic
142C2×C3—22no—
143C2×C3—42no—
144D3—64no—
145D3—122no—
146C22—91no—
147C22—91no—
148C22—182no—
149C22#6378411yescharacteristic
150C4—91no—
151C4—91no—
152C4—722no—
153C4#6378111yescharacteristic
154C4#6378211yescharacteristic
155C3—22no—
156C2—21no—
157C2—92no—
158C2—181no—
159C2#1059016311yescharacteristic
subgroupG/H
centerC2#10590163
commutatorC32×C8C42
FrattiniC2×C8C2×#157
FittingC32×#108C4
socleC2×C32#340
prime radicalC22×C3⋊D3SD16
cosocleC2×C8×C3⋊D3C22
hypercenter#108#157
hypocenterC32#1383
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #108

Complements

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

NH ≅ G/Ntype
11. #63764C4semidirect
12. C32×#108C4semidirect
14. #63646C4semidirect
83. #108#157semidirect
126. C32#1383semidirect

Maximal subgroups

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

subgroupindex
C2×#637682
#105937622
C3⋊D3×#1082
#13839