Finite Group Databasebeta

← #11771021

Subgroups — #11771021

Order 1152.

290 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 56 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#10593805C212yesmaximal
2C2×#63641C211yesmaximal, characteristic
3C2×#3792—22no—
4C22×C32×C8C411yescharacteristic
5C2×C4×C3⋊Dic3C2211yescharacteristic
6C22×C3⋊(C3⋊C8)C411yescharacteristic
7#63779C414yes—
8C4⋊#622—22no—
9#63641—22no—
10C2×Dic3⋊C8—62no—
11C22×C32×C4C2×C411yescharacteristic
12C22×C3⋊Dic3D411yescharacteristic
13C22×C3⋊Dic3Q811yescharacteristic
14#3792—42no—
15#3792—42no—
16C2×#622—24no—
17C2×C32×C8—21no—
18C2×C32×C8—41no—
19C4×C3⋊Dic3C2×C412yes—
20C4×C3⋊Dic3D412yes—
21C2×C3⋊(C3⋊C8)—21no—
22C2×C3⋊(C3⋊C8)—41no—
23#1292—91nomaximal, Sylow
24C22×C3×C8—22no—
25C2×C4×Dic3—62no—
26C22×C3⋊C8—62no—
27Dic3⋊C8—68no—
28C23×C32C4⋊C411yescharacteristic
29C2×C32×C4—21no—
30C2×C32×C4—21no—
31C2×C32×C4C4211yescharacteristic
32C2×C32×C4C22⋊C411yescharacteristic
33C2×C3⋊Dic3—41no—
34C2×C3⋊Dic3C22⋊C412yes—
35C2×C3⋊Dic3C4⋊C412yes—
36C2×C3⋊Dic3D811yescharacteristic
37C2×C3⋊Dic3SD1612yes—
38C2×C3⋊Dic3Q1611yescharacteristic
39#622—44no—
40C32×C8—41no—
41C3⋊(C3⋊C8)—41no—
42#423—92no—
43C2×C4⋊C8—91no—
44C22×C3×C4—22no—
45C22×Dic3—62no—
46C22×Dic3—62no—
47C2×C3×C8—24no—
48C2×C3×C8—44no—
49C4×Dic3—64no—
50C4×Dic3—64no—
51C2×C3⋊C8—64no—
52C2×C3⋊C8—124no—
53C22×C32—21no—
54C22×C32—21no—
55C22×C32#9511yescharacteristic
56C22×C32#10611yescharacteristic
57C22×C32#10711yescharacteristic
58C32×C4—21no—
59C32×C4#10011yescharacteristic
60C32×C4#10111yescharacteristic
61C3⋊Dic3—22no—
62C3⋊Dic3#10212yes—
63C3⋊Dic3#10312yes—
64C2×M16—182no—
65C22×C8—91no—
66C22×C8#15711yescharacteristic
67C2×C42—91no—
68C4⋊C8—94no—
69C4⋊C8—182no—
70C4⋊C8—182no—
71C23×C3—22no—
72C2×C3×C4—24no—
73C2×C3×C4—24no—
74C2×C3×C4—22no—
75C2×C3×C4—22no—
76C2×Dic3—64no—
77C2×Dic3—62no—
78C2×Dic3—64no—
79C2×Dic3—62no—
80C2×Dic3—64no—
81C2×Dic3—124no—
82C3×C8—44no—
83C3⋊C8—124no—
84C2×C32—21no—
85C2×C32—21no—
86C2×C32#33811yescharacteristic
87C2×C32#34011yescharacteristic
88C2×C32#34311yescharacteristic
89C22×C4—91no—
90C22×C4—91no—
91C22×C4C2×#15711yescharacteristic
92M16—362no—
93M16—362no—
94C2×C8—21no—
95C2×C8—41no—
96C2×C8—184no—
97C2×C8—181no—
98C2×C8—361no—
99C42—92no—
100C42—92no—
101C22×C3—24no—
102C22×C3—24no—
103C22×C3—22no—
104C22×C3—22no—
105C22×C3—22no—
106C3×C4—24no—
107C3×C4—22no—
108C3×C4—22no—
109Dic3—64no—
110Dic3—64no—
111Dic3—124no—
112C32#129211yescharacteristic, complemented, Sylow
113C23C4⋊#15711yescharacteristic
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—92no—
117C2×C4—91no—
118C2×C4—91no—
119C2×C4—92no—
120C2×C4—92no—
121C2×C4—361no—
122C2×C4C4×#15711yescharacteristic
123C2×C4C22⋊#15711yescharacteristic
124C8—41no—
125C8—364no—
126C8—361no—
127C2×C3—24no—
128C2×C3—24no—
129C2×C3—22no—
130C2×C3—22no—
131C2×C3—22no—
132C22—21no—
133C22—21no—
134C22#6376811yescharacteristic
135C22#6376911yescharacteristic
136C22#6378111yescharacteristic
137C4—21no—
138C4—92no—
139C4—92no—
140C4—182no—
141C4#6378011yescharacteristic
142C4#6378811yescharacteristic
143C3—22no—
144C2—21no—
145C2—21no—
146C2#1059018211yescharacteristic
147C2#1059018611yescharacteristic
148C2#1059020811yescharacteristic
subgroupG/H
centerC22#63781
commutatorC2×C32×C4C42
FrattiniC22×C4C2×#157
FittingC22×C32×C8C4
socleC22×C32#95
prime radicalC23×C32C4⋊C4
cosocleC2×C4×C3⋊Dic3C22
hypercenterC22×C8#157
hypocenterC32#1292
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
112. C32#1292semidirect

Maximal subgroups

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

subgroupindex
#105938052
C2×#636412
#12929