Finite Group Databasebeta

← #11772441

Subgroups — #11772441

Order 1152.

246 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 48 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#10593768C211yesmaximal, characteristic
2#10593762C211yesmaximal, characteristic
3#10592559C211yesmaximal, characteristic
4#64286—21no—
5C2×C8×C3⋊D3C2211yescharacteristic
6#64101—21no—
7#63773—21no—
8#63769—21no—
9#63768C412yescomplemented
10#63765—21no—
11#63764C412yescomplemented
12C32×#106C411yescharacteristic, complemented
13#63644C411yescharacteristic, complemented
14#63634—21no—
15#4860—62no—
16C2×C4×C3⋊D3D411yescharacteristic
17C22⋊#157—41no—
18C4⋊#157—22no—
19C4×#157—41no—
20C2×C32×C8C2×C411yescharacteristic
21C32×C4⋊C4—21no—
22#3752—41no—
23C4⋊(C3⋊Dic3)—21no—
24C4×C3⋊Dic3—41no—
25C2×C3⋊(C3⋊C8)D411yescharacteristic
26C8×C3⋊D3C2×C411yescharacteristic
27C8×C3⋊D3C2×C411yescharacteristic
28C8×C3⋊D3D411yescharacteristic
29C8×C3⋊D3Q811yescharacteristic
30#3708—22no—
31#1384—91nomaximal, Sylow
32C2×D3×C8—62no—
33#892—64no—
34C3×#106—22no—
35#817—62no—
36#807—64no—
37C22×C3⋊D3D811yescharacteristic
38C2×#157—42no—
39C2×C32×C4—41no—
40C2×C32×C4C22⋊C411yescharacteristic
41C2×C3⋊Dic3—41no—
42C2×C3⋊Dic3SD1611yescharacteristic
43C4×C3⋊D3C22⋊C411yescharacteristic
44C4×C3⋊D3C4⋊C411yescharacteristic
45C4×C3⋊D3SD1611yescharacteristic
46C4×C3⋊D3Q1611yescharacteristic
47C32×C8C4211yescharacteristic
48C32×C8C4⋊C411yescharacteristic
49C3⋊(C3⋊C8)C22⋊C411yescharacteristic
50C3⋊(C3⋊C8)C4⋊C411yescharacteristic
51C2×M32—91no—
52#427—91no—
53#427—91no—
54C2×C4×D3—62no—
55C2×C3×C8—22no—
56C3×C4⋊C4—24no—
57(C2×D3)⋊C4—124no—
58C4⋊Dic3—64no—
59C4×Dic3—124no—
60C2×C3⋊C8—62no—
61D3×C8—62no—
62D3×C8—62no—
63D3×C8—62no—
64D3×C8—62no—
65C22×C32#10211yescharacteristic
66C2×C3⋊D3—41no—
67C2×C3⋊D3#10211yescharacteristic
68C2×C3⋊D3#10711yescharacteristic
69#157—82no—
70C32×C4—81no—
71C32×C4#9511yescharacteristic
72C32×C4#10311yescharacteristic
73C3⋊Dic3—81no—
74C3⋊Dic3#10311yescharacteristic
75C3⋊Dic3#10611yescharacteristic
76C22×C8—91no—
77#117—181no—
78#117—181no—
79M32—181no—
80M32—181no—
81C2×C16—92no—
82#107—181no—
83#107—181no—
84#106—92no—
85#106—91no—
86#106#15711yescharacteristic, complemented
87C22×D3—62no—
88C2×C3×C4—22no—
89C2×C3×C4—44no—
90C2×Dic3—62no—
91C2×Dic3—124no—
92C4×D3—62no—
93C4×D3—62no—
94C4×D3—62no—
95C4×D3—62no—
96C3×C8—22no—
97C3×C8—22no—
98C3⋊C8—62no—
99C3⋊C8—62no—
100C2×C32—21no—
101C2×C32#34011yescharacteristic
102C3⋊D3—21no—
103C3⋊D3—21no—
104C22×C4—91no—
105C2×C8—91no—
106C2×C8—91no—
107C2×C8—91no—
108C2×C8—91no—
109C2×C8—91no—
110C2×C8C2×#15711yescharacteristic
111C4⋊C4—21no—
112C4⋊C4—182no—
113C4⋊C4—181no—
114C22⋊C4—361no—
115C22⋊C4—361no—
116C42—361no—
117C42—361no—
118C16—182no—
119C22×C3—22no—
120C2×D3—62no—
121C2×D3—62no—
122C2×D3—124no—
123C3×C4—22no—
124C3×C4—22no—
125C3×C4—84no—
126Dic3—62no—
127Dic3—62no—
128Dic3—244no—
129C32#138411yescharacteristic, complemented, Sylow
130C23—91no—
131C2×C4—41no—
132C2×C4—91no—
133C2×C4—91no—
134C2×C4—91no—
135C2×C4—91no—
136C2×C4—91no—
137C2×C4—362no—
138C2×C4—361no—
139C2×C4C22⋊#15711yescharacteristic
140C8—91no—
141C8—91no—
142C8C4×#15711yescharacteristic
143C8C4⋊#15711yescharacteristic
144C2×C3—24no—
145C2×C3—22no—
146D3—122no—
147D3—122no—
148C22—91no—
149C22—91no—
150C22—361no—
151C22#6378211yescharacteristic
152C4—81no—
153C4—91no—
154C4—91no—
155C4—721no—
156C4—722no—
157C4#6378111yescharacteristic
158C4#6378411yescharacteristic
159C3—22no—
160C2—21no—
161C2—181no—
162C2—181no—
163C2#1059016311yescharacteristic
subgroupG/H
centerC2#10590163
commutatorC32×C8C42
FrattiniC2×C8C2×#157
FittingC32×#106C4
socleC2×C32#340
prime radicalC22×C3⋊D3D8
cosocleC2×C8×C3⋊D3C22
hypercenter#106#157
hypocenterC32#1384
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #106

Complements

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

NH ≅ G/Ntype
9. #63768C4semidirect
11. #63764C4semidirect
12. C32×#106C4semidirect
13. #63644C4semidirect
86. #106#157semidirect
129. C32#1384semidirect

Maximal subgroups

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

subgroupindex
#105937682
#105937622
#105925592
#13849