Finite Group Databasebeta

← #11771125

Subgroups — #11771125

Order 1152.

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

normal subgroups only

This group has 276 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#10593801C211yesmaximal, characteristic
2C4×#3792C211yesmaximal, characteristic
3#10592817C211yesmaximal, characteristic
4C2×#3792—21no—
5C2×C32×M16C411yescharacteristic
6C2×C4×C3⋊Dic3C2211yescharacteristic
7C2×#3748C411yescharacteristic
8C22⋊#622—21no—
9#63779C412yes—
10#63777C412yes—
11C4×#622—21no—
12C4×#622—21no—
13#63641—21no—
14#63641—21no—
15#5118—62no—
16C22×C32×C4C2×C411yescharacteristic
17C22×C3⋊Dic3D411yescharacteristic
18C22×C3⋊Dic3Q811yescharacteristic
19#3792—24no—
20C2×#622—22no—
21C2×#622—22no—
22C32×M16—41no—
23C2×C32×C8—21no—
24C4×C3⋊Dic3C2×C411yescharacteristic
25C4×C3⋊Dic3C2×C411yescharacteristic
26C4×C3⋊Dic3D411yescharacteristic
27C4×C3⋊Dic3D411yescharacteristic
28#3748—41no—
29C2×C3⋊(C3⋊C8)—21no—
30#1299—91nomaximal, Sylow
31C2×C3×M16—22no—
32C2×C4×Dic3—62no—
33C2×#208—62no—
34Dic3⋊C8—64no—
35Dic3⋊C8—64no—
36C23×C32C4⋊C411yescharacteristic
37C2×C32×C4—21no—
38C2×C32×C4—21no—
39C2×C32×C4C4211yescharacteristic
40C2×C32×C4C22⋊C411yescharacteristic
41C2×C3⋊Dic3—22no—
42C2×C3⋊Dic3—22no—
43C2×C3⋊Dic3C22⋊C411yescharacteristic
44C2×C3⋊Dic3C22⋊C411yescharacteristic
45C2×C3⋊Dic3C4⋊C411yescharacteristic
46C2×C3⋊Dic3C4⋊C411yescharacteristic
47#622—24no—
48#622—42no—
49C32×C8—41no—
50C3⋊(C3⋊C8)—41no—
51#431—91no—
52#423—91no—
53C4×M16—91no—
54C22×C3×C4—22no—
55C22×Dic3—62no—
56C22×Dic3—62no—
57C3×M16—44no—
58C2×C3×C8—24no—
59C4×Dic3—62no—
60C4×Dic3—62no—
61C4×Dic3—62no—
62C4×Dic3—62no—
63#208—124no—
64C2×C3⋊C8—64no—
65C22×C32—21no—
66C22×C32—21no—
67C22×C32—21no—
68C22×C32#9511yescharacteristic
69C32×C4—21no—
70C32×C4#10011yescharacteristic
71C32×C4#10111yescharacteristic
72C3⋊Dic3—21no—
73C3⋊Dic3—21no—
74C3⋊Dic3#10412yes—
75C3⋊Dic3#10812yes—
76C2×M16—91no—
77C2×M16—181no—
78C2×M16#15711yescharacteristic
79C2×C42—91no—
80C4⋊C8—92no—
81C4⋊C8—181no—
82C4⋊C8—181no—
83C22⋊C8—181no—
84#97—92no—
85C4×C8—181no—
86C4×C8—181no—
87C23×C3—22no—
88C2×C3×C4—24no—
89C2×C3×C4—24no—
90C2×C3×C4—22no—
91C2×C3×C4—22no—
92C2×Dic3—62no—
93C2×Dic3—62no—
94C2×Dic3—62no—
95C2×Dic3—62no—
96C2×Dic3—124no—
97C2×Dic3—124no—
98C3×C8—44no—
99C3⋊C8—124no—
100C2×C32—41no—
101C2×C32#33911yescharacteristic
102C2×C32#34111yescharacteristic
103C2×C32#34311yescharacteristic
104C22×C4—91no—
105C22×C4—91no—
106C22×C4C2×#15711yescharacteristic
107M16—41no—
108M16—184no—
109M16—361no—
110C2×C8—21no—
111C2×C8—182no—
112C2×C8—182no—
113C2×C8—181no—
114C42—91no—
115C42—91no—
116C42—91no—
117C42—91no—
118C22×C3—24no—
119C22×C3—22no—
120C22×C3—42no—
121C22×C3—42no—
122C3×C4—24no—
123C3×C4—22no—
124C3×C4—22no—
125Dic3—64no—
126Dic3—64no—
127Dic3—122no—
128Dic3—122no—
129C32#129911yescharacteristic, complemented, Sylow
130C23C4⋊#15711yescharacteristic
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—91no—
134C2×C4—91no—
135C2×C4—91no—
136C2×C4—91no—
137C2×C4—182no—
138C2×C4—182no—
139C2×C4C4×#15711yescharacteristic
140C2×C4C22⋊#15711yescharacteristic
141C8—41no—
142C8—184no—
143C8—362no—
144C8—361no—
145C2×C3—22no—
146C2×C3—22no—
147C2×C3—22no—
148C2×C3—44no—
149C22—21no—
150C22—21no—
151C22—21no—
152C22#6378111yescharacteristic
153C4—21no—
154C4—92no—
155C4—92no—
156C4—181no—
157C4—181no—
158C4#6378011yescharacteristic
159C4#6378811yescharacteristic
160C3—22no—
161C2—41no—
162C2#1059018911yescharacteristic
163C2#1059019011yescharacteristic
164C2#1059020811yescharacteristic
subgroupG/H
centerC2×C4C22⋊#157
commutatorC2×C32×C4C42
FrattiniC22×C4C2×#157
FittingC2×C32×M16C4
socleC22×C32#95
prime radicalC23×C32C4⋊C4
cosocleC2×C4×C3⋊Dic3C22
hypercenterC2×M16#157
hypocenterC32#1299
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
129. C32#1299semidirect

Maximal subgroups

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

subgroupindex
#105938012
C4×#37922
#105928172
#12999