Finite Group Databasebeta

← #11797390

Subgroups — #11797390

Order 1152.

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

normal subgroups only

This group has 270 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
1C4×#3743C211yesmaximal, characteristic
2#10590180C212yesmaximal
3#10590179C212yesmaximal, complemented
4#10590150C212yesmaximal, complemented
5C2×#3743C411yescharacteristic
6C2×#3743C2211yescharacteristic
7C42×C3⋊D3C411yescharacteristic
8#63773C2214yes—
9C32×C4×C8C411yescharacteristic
10#63642C411yescharacteristic
11#63642C2211yescharacteristic
12C4×C3⋊(C3⋊C8)C2211yescharacteristic
13C4×ΓL(1,𝔽25)—62no—
14C2×C4×C3⋊D3—21no—
15C2×C4×C3⋊D3C2×C411yescharacteristic
16C2×C32×C8C2×C411yescharacteristic
17C2×C32×C8C2×C411yescharacteristic
18C32×C42C2×C411yescharacteristic
19C4×C3⋊Dic3—21no—
20C4×C3⋊Dic3C2×C411yescharacteristic
21C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
22C2×C3⋊(C3⋊C8)C2311yescharacteristic
23#3743—22no—
24#3743—22no—
25#3708—24no—
26#2165—91nomaximal, Sylow
27C2×ΓL(1,𝔽25)—62no—
28C2×ΓL(1,𝔽25)—62no—
29C42×D3—62no—
30C3×C4×C8—22no—
31#815—62no—
32#815—62no—
33C4×C3⋊C8—62no—
34C22×C3⋊D3M1611yescharacteristic
35C2×C32×C4—21no—
36C2×C32×C4C22×C411yescharacteristic
37C2×C3⋊Dic3—21no—
38C2×C3⋊Dic3M1611yescharacteristic
39C4×C3⋊D3—21no—
40C4×C3⋊D3—21no—
41C4×C3⋊D3—42no—
42C32×C8—21no—
43C32×C8—21no—
44C3⋊(C3⋊C8)M1612yes—
45C3⋊(C3⋊C8)#4112yes—
46C4×M16—91no—
47#364—92no—
48#349—92no—
49#347—92no—
50C2×C4×D3—62no—
51C2×C4×D3—64no—
52C2×C3×C8—22no—
53C2×C3×C8—22no—
54C3×C42—22no—
55C4×Dic3—62no—
56C4×Dic3—64no—
57C2×C3⋊C8—62no—
58C2×C3⋊C8—62no—
59ΓL(1,𝔽25)—68no—
60ΓL(1,𝔽25)—68no—
61C22×C32C2×M1611yescharacteristic
62C2×C3⋊D3—21no—
63C2×C3⋊D3—41no—
64C32×C4—22no—
65C32×C4#11711yescharacteristic
66C32×C4C2×M1611yescharacteristic
67C3⋊Dic3—21no—
68C3⋊Dic3—41no—
69C2×M16—91no—
70C2×M16—91no—
71C2×C42—91no—
72M32—94no—
73#97—91no—
74#97—91no—
75C4×C8—91no—
76C4×C8#15711yescharacteristic
77C22×D3—62no—
78C2×C3×C4—24no—
79C2×C3×C4—22no—
80C2×Dic3—62no—
81C2×Dic3—64no—
82C4×D3—64no—
83C4×D3—64no—
84C4×D3—128no—
85C3×C8—24no—
86C3×C8—24no—
87C3⋊C8—64no—
88C3⋊C8—64no—
89C2×C32—21no—
90C2×C32#43211yescharacteristic
91C3⋊D3—41no—
92C22×C4—91no—
93C22×C4—181no—
94M16—182no—
95M16—182no—
96C2×C8—91no—
97C2×C8—91no—
98C2×C8C2×#15711yescharacteristic
99C2×C8C2×#15711yescharacteristic
100C42—91no—
101C42—181no—
102C42C2×#15711yescharacteristic
103C16—184no—
104C22×C3—22no—
105C2×D3—64no—
106C2×D3—124no—
107C3×C4—28no—
108C3×C4—22no—
109C3×C4—22no—
110Dic3—64no—
111Dic3—124no—
112C32#216511yescharacteristic, complemented, Sylow
113C23—91no—
114C2×C4—21no—
115C2×C4—91no—
116C2×C4—181no—
117C2×C4—181no—
118C2×C4—181no—
119C2×C4—362no—
120C2×C4C22×#15711yescharacteristic
121C8—21no—
122C8—21no—
123C8—92no—
124C8—92no—
125C2×C3—24no—
126C2×C3—22no—
127D3—124no—
128C22—181no—
129C22—361no—
130C22#6428311yescharacteristic
131C4—22no—
132C4—181no—
133C4—361no—
134C4#6428311yescharacteristic
135C4#6428611yescharacteristic
136C3—22no—
137C2—21no—
138C2—361no—
139C2#1059373111yescharacteristic
subgroupG/H
centerC4#64286
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C4×C8C4
socleC2×C32#432
prime radicalC22×C3⋊D3M16
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC4×C8#157
hypocenterC32#2165
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C8 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
3. #10590179C2semidirect
4. #10590150C2semidirect
112. C32#2165semidirect

Maximal subgroups

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

subgroupindex
C4×#37432
#105901802
#105901792
#105901502
#21659