Finite Group Databasebeta

← #11771956

Subgroups — #11771956

Order 1152.

348 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 95 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#10592685C211yesmaximal, characteristic
2C32×#324C211yesmaximal, characteristic
3#10589396C211yesmaximal, characteristic
4#67459—34nomaximal
5C2×C32×C4⋊C4C2211yescharacteristic
6C2×C4⋊(C3⋊Dic3)C411yescharacteristic
7C2×#3748—21no—
8C32×C22⋊C8—21no—
9#63658—21no—
10#63658—21no—
11#63658C411yescharacteristic
12#4986—34no—
13C3×#324D314yes—
14#4530—34no—
15C22×C32×C4C2×C411yescharacteristic
16C22×C32×C4D411yescharacteristic
17C22×C32×C4D411yescharacteristic
18C22×C3⋊Dic3—21no—
19C22×C3⋊Dic3—21no—
20C2×C32×C8—41no—
21C32×C4⋊C4—41no—
22C4⋊(C3⋊Dic3)—41no—
23#3748—22no—
24#3748—41no—
25C2×C3⋊(C3⋊C8)—41no—
26#1353—91noSylow
27C2×C3×C4⋊C4C2×D314yes—
28C2×C4⋊Dic3—34no—
29C2×#208—64no—
30C3×C22⋊C8—24no—
31C3⋊#95—34no—
32C3⋊#95—64no—
33C3⋊#95—64no—
34C23×C32C22⋊C411yescharacteristic
35C2×C32×C4—21no—
36C2×C32×C4—21no—
37C2×C32×C4—21no—
38C2×C32×C4—21no—
39C2×C32×C4—41no—
40C2×C32×C4—41no—
41C2×C32×C4SD1611yescharacteristic
42C2×C32×C4Q1611yescharacteristic
43C2×C3⋊Dic3—41no—
44C2×C3⋊Dic3—41no—
45C2×C3⋊Dic3—42no—
46C2×C3⋊Dic3—41no—
47C2×C3⋊Dic3—41no—
48C32×C8—81no—
49C3⋊(C3⋊C8)—42no—
50#400—91no—
51#343—91no—
52#324C3⋊D311yescharacteristic
53C22×C3×C4C4×D314yes—
54C22×C3×C4D1214yes—
55C22×C3×C4#6714yes—
56C22×Dic3—64no—
57C22×Dic3—64no—
58C2×C3×C8—44no—
59C3×C4⋊C4—44no—
60C4⋊Dic3—124no—
61#208—68no—
62#208—124no—
63C2×C3⋊C8—124no—
64C22×C32—21no—
65C22×C32—21no—
66C22×C32#9911yescharacteristic
67C22×C32#10311yescharacteristic
68C22×C32#10411yescharacteristic
69C32×C4—21no—
70C32×C4—21no—
71C32×C4—41no—
72C32×C4—41no—
73C3⋊Dic3—81no—
74C3⋊Dic3—81no—
75C2×M16—181no—
76C2×C4⋊C4—91no—
77C2×C4⋊C4C2×C3⋊D311yescharacteristic
78C22⋊C8—21no—
79#95—91no—
80#95—181no—
81#95—181no—
82C23×C3(C2×D3)⋊C414yes—
83C2×C3×C4—24no—
84C2×C3×C4—24no—
85C2×C3×C4—24no—
86C2×C3×C4—24no—
87C2×C3×C4—44no—
88C2×C3×C4—44no—
89C2×C3×C4#20414yes—
90C2×C3×C4Dic1214yes—
91C2×Dic3—124no—
92C2×Dic3—124no—
93C2×Dic3—128no—
94C2×Dic3—124no—
95C2×Dic3—124no—
96C3×C8—84no—
97C3⋊C8—128no—
98C2×C32—21no—
99C2×C32—21no—
100C2×C32#32811yescharacteristic
101C2×C32#35211yescharacteristic
102C2×C32#35511yescharacteristic
103C22×C4—181no—
104C22×C4—181no—
105C22×C4C4×C3⋊D311yescharacteristic
106C22×C4C4⋊(C3⋊D3)11yescharacteristic
107C22×C4#63811yescharacteristic
108M16—182no—
109M16—361no—
110C2×C8—41no—
111C2×C8—361no—
112C4⋊C4—41no—
113C4⋊C4—361no—
114C22×C3—24no—
115C22×C3—24no—
116C22×C3#80614yes—
117C22×C3#81614yes—
118C22×C3#82514yes—
119C3×C4—24no—
120C3×C4—24no—
121C3×C4—44no—
122C3×C4—44no—
123Dic3—244no—
124Dic3—244no—
125C32#135311yescharacteristic, complemented, Sylow
126C23#375211yescharacteristic
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—361no—
134C2×C4—361no—
135C2×C4—362no—
136C2×C4—361no—
137C2×C4—361no—
138C2×C4#374411yescharacteristic
139C2×C4#374611yescharacteristic
140C8—81no—
141C8—362no—
142C2×C3—24no—
143C2×C3—24no—
144C2×C3#446714yes—
145C2×C3#447214yes—
146C2×C3#447714yes—
147C22—21no—
148C22—21no—
149C22#6363311yescharacteristic
150C22#6364311yescharacteristic
151C22#6365211yescharacteristic
152C4—21no—
153C4—21no—
154C4—41no—
155C4—41no—
156C4—721no—
157C4—721no—
158C3#6745914yescomplemented
159C2—21no—
160C2—21no—
161C2#1058933311yescharacteristic
162C2#1058933811yescharacteristic
163C2#1058934311yescharacteristic
subgroupG/H
centerC22#63633
commutatorC22×C32×C4C2×C4
FrattiniC2×C4⋊C4C2×C3⋊D3
FittingC32×#324C2
socleC22×C32#99
prime radicalC23×C32C22⋊C4
cosocleC2×C32×C4⋊C4C22
hypercenter#324C3⋊D3
hypocenterC32#1353
LCSG ▷ C22×C32×C4 ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #324

Complements

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

NH ≅ G/Ntype
125. C32#1353semidirect
158. C3#67459semidirect

Maximal subgroups

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

subgroupindex
#105926852
C32×#3242
#105893962
#674593