Finite Group Databasebeta

← #11771834

Subgroups — #11771834

Order 1152.

372 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 105 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
1C32×#398C211yesmaximal, characteristic
2#10589396C211yesmaximal, characteristic
3#10589394C211yesmaximal, characteristic
4#67650—34nomaximal
5C2×C32×C4⋊C4—21no—
6C2×C32×C4⋊C4C411yescharacteristic
7C2×C32×C4⋊C4C2211yescharacteristic
8C2×#3748—21no—
9C32×#95—21no—
10C32×#95C411yescharacteristic
11#63657—21no—
12C3×#398D314yes—
13#4530—34no—
14#4528—34no—
15C22×C32×C4—21no—
16C22×C32×C4—21no—
17C22×C32×C4C2×C411yescharacteristic
18C22×C32×C4D411yescharacteristic
19C22×C32×C4D411yescharacteristic
20C32×C4⋊C4—41no—
21C32×C4⋊C4—41no—
22C32×C4⋊C4—41no—
23C32×C4⋊C4—41no—
24#3748—22no—
25#3748—41no—
26C2×C3⋊(C3⋊C8)—41no—
27C2×C3⋊(C3⋊C8)—41no—
28#1346—91noSylow
29C2×C3×C4⋊C4—24no—
30C2×C3×C4⋊C4Dic314yes—
31C2×C3×C4⋊C4C2×D314yes—
32C2×#208—64no—
33C3×#95—24no—
34C3×#95Dic314yes—
35#830—64no—
36C23×C32C22⋊C411yescharacteristic
37C2×C32×C4—21no—
38C2×C32×C4—21no—
39C2×C32×C4—22no—
40C2×C32×C4—21no—
41C2×C32×C4—21no—
42C2×C32×C4—41no—
43C2×C32×C4—41no—
44C2×C32×C4—41no—
45C2×C32×C4—41no—
46C2×C32×C4—41no—
47C2×C32×C4—41no—
48C2×C32×C4—41no—
49C2×C32×C4D811yescharacteristic
50C2×C32×C4SD1611yescharacteristic
51C3⋊(C3⋊C8)—42no—
52C3⋊(C3⋊C8)—81no—
53#398C3⋊D311yescharacteristic
54#343—91no—
55#324—91no—
56C22×C3×C4—24no—
57C22×C3×C4—24no—
58C22×C3×C4C2×Dic314yes—
59C22×C3×C4#6714yes—
60C22×C3×C4#6714yes—
61C3×C4⋊C4—44no—
62C3×C4⋊C4—44no—
63C3×C4⋊C4—44no—
64C3×C4⋊C4—44no—
65#208—68no—
66#208—124no—
67C2×C3⋊C8—124no—
68C2×C3⋊C8—124no—
69C22×C32—21no—
70C22×C32—21no—
71C22×C32#9911yescharacteristic
72C22×C32#10211yescharacteristic
73C22×C32#10411yescharacteristic
74C32×C4—21no—
75C32×C4—21no—
76C32×C4—42no—
77C32×C4—41no—
78C32×C4—41no—
79C32×C4—81no—
80C2×M16—181no—
81C2×C4⋊C4—21no—
82C2×C4⋊C4C3⋊Dic311yescharacteristic
83C2×C4⋊C4C2×C3⋊D311yescharacteristic
84C22⋊C8—181no—
85#95—21no—
86#95C3⋊Dic311yescharacteristic
87C23×C3#21714yes—
88C2×C3×C4—24no—
89C2×C3×C4—24no—
90C2×C3×C4—28no—
91C2×C3×C4—24no—
92C2×C3×C4—24no—
93C2×C3×C4—44no—
94C2×C3×C4—44no—
95C2×C3×C4—44no—
96C2×C3×C4—44no—
97C2×C3×C4—44no—
98C2×C3×C4—44no—
99C2×C3×C4—44no—
100C2×C3×C4#21314yes—
101C2×C3×C4#21414yes—
102C3⋊C8—128no—
103C3⋊C8—244no—
104C2×C32—21no—
105C2×C32—21no—
106C2×C32#32711yescharacteristic
107C2×C32#35211yescharacteristic
108C2×C32#35611yescharacteristic
109C22×C4—21no—
110C22×C4—21no—
111C22×C4C2×C3⋊Dic311yescharacteristic
112C22×C4#63811yescharacteristic
113C22×C4#63811yescharacteristic
114M16—182no—
115M16—361no—
116C2×C8—361no—
117C2×C8—361no—
118C4⋊C4—41no—
119C4⋊C4—41no—
120C4⋊C4—41no—
121C4⋊C4—41no—
122C22×C3—24no—
123C22×C3—24no—
124C22×C3#83214yes—
125C22×C3#83414yes—
126C22×C3#83714yes—
127C3×C4—24no—
128C3×C4—24no—
129C3×C4—48no—
130C3×C4—44no—
131C3×C4—44no—
132C3×C4—84no—
133C32#134611yescharacteristic, complemented, Sylow
134C23#375711yescharacteristic
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—22no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4#375311yescharacteristic
148C2×C4#375411yescharacteristic
149C8—362no—
150C8—721no—
151C2×C3—24no—
152C2×C3—24no—
153C2×C3#453714yes—
154C2×C3#453914yes—
155C2×C3#454814yes—
156C22—21no—
157C22—21no—
158C22#6365911yescharacteristic
159C22#6366111yescharacteristic
160C22#6366411yescharacteristic
161C4—21no—
162C4—21no—
163C4—42no—
164C4—41no—
165C4—41no—
166C4—81no—
167C3#6765014yescomplemented
168C2—21no—
169C2—21no—
170C2#1058940311yescharacteristic
171C2#1058940511yescharacteristic
172C2#1058941411yescharacteristic
subgroupG/H
centerC22#63661
commutatorC22×C32×C4C2×C4
FrattiniC2×C4⋊C4C2×C3⋊D3
FittingC32×#398C2
socleC22×C32#99
prime radicalC23×C32C22⋊C4
cosocleC2×C32×C4⋊C4C22
hypercenter#398C3⋊D3
hypocenterC32#1346
LCSG ▷ C22×C32×C4 ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #398

Complements

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

NH ≅ G/Ntype
133. C32#1346semidirect
167. C3#67650semidirect

Maximal subgroups

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

subgroupindex
C32×#3982
#105893962
#105893942
#676503