Finite Group Databasebeta

← #10593742

Subgroups — #10593742

Order 576.

216 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 46 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
1C2×#3792C211yesmaximal, characteristic, complemented
2C2×#3788C211yesmaximal, characteristic, complemented
3#64090C211yesmaximal, characteristic
4C22⋊#622C211yesmaximal, characteristic, complemented
5#63779C211yesmaximal, characteristic, complemented
6#63778C211yesmaximal, characteristic, complemented
7C4×#622C211yesmaximal, characteristic, complemented
8C2×#638C411yescharacteristic
9C22×C3⋊Dic3C2211yescharacteristic
10C2×C4×C3⋊D3C2211yescharacteristic
11#3792—22no—
12C2×#622C2211yescharacteristic
13C2×#622C2211yescharacteristic
14C2×#622C2211yescharacteristic
15C2×#622C2211yescharacteristic
16#3788—22no—
17C32×C22⋊C4C411yescharacteristic
18#3752C411yescharacteristic
19#3750C411yescharacteristic
20C4×C3⋊Dic3C2211yescharacteristic
21#67⋊C4—62no—
22C23×C32C2×C411yescharacteristic
23C22×C3⋊D3C2×C411yescharacteristic
24C2×C32×C4C2×C411yescharacteristic
25C2×C32×C4C2×C411yescharacteristic
26#638—22no—
27C2×C3⋊Dic3—21no—
28C2×C3⋊Dic3—21no—
29C2×C3⋊Dic3C2×C411yescharacteristic
30C2×C3⋊Dic3C2×C411yescharacteristic
31C2×C3⋊Dic3C2311yescharacteristic
32C4×C3⋊D3—21no—
33C4×C3⋊D3—21no—
34#622—21no—
35#622—21no—
36#622—21no—
37#622D412yescomplemented
38#436—91nomaximal, Sylow
39C2×#67—62no—
40C22×Dic3—62no—
41C2×C4×D3—62no—
42C3×C22⋊C4—22no—
43(C2×D3)⋊C4—62no—
44Dic3⋊C4—62no—
45C4×Dic3—62no—
46C22×C32—21no—
47C22×C32—21no—
48C22×C32—21no—
49C22×C32C22×C411yescharacteristic
50C2×C3⋊D3—21no—
51C2×C3⋊D3—21no—
52C2×C3⋊D3—21no—
53C32×C4—21no—
54C32×C4—21no—
55C3⋊Dic3—21no—
56C3⋊Dic3M1612yescomplemented
57C3⋊Dic3C2×D411yescharacteristic
58C3⋊Dic3#4111yescharacteristic
59C2×M16—91no—
60C2×M16—91no—
61C4×D4—91no—
62C4⋊C8—91no—
63C22⋊C8—91no—
64C22⋊C8—91no—
65C4×C8—91no—
66C23×C3—22no—
67C22×D3—62no—
68C2×C3×C4—22no—
69C2×C3×C4—22no—
70#67—68no—
71C2×Dic3—62no—
72C2×Dic3—62no—
73C2×Dic3—62no—
74C2×Dic3—122no—
75C2×Dic3—122no—
76C4×D3—122no—
77C4×D3—122no—
78C2×C32—41no—
79C2×C32C4×D411yescharacteristic
80C2×C32C2×M1611yescharacteristic
81C2×C32#13111yescharacteristic
82C3⋊D3—41no—
83C2×D4—91no—
84C22×C4—91no—
85C22×C4—91no—
86M16—182no—
87M16—182no—
88C2×C8—91no—
89C2×C8—91no—
90C2×C8—91no—
91C2×C8—91no—
92C4⋊C4—91no—
93C22⋊C4—91no—
94C22⋊C4#15711yescharacteristic
95C42—91no—
96C22×C3—24no—
97C22×C3—22no—
98C22×C3—42no—
99C22×C3—42no—
100C2×D3—64no—
101C2×D3—122no—
102C2×D3—122no—
103C3×C4—42no—
104C3×C4—42no—
105Dic3—62no—
106Dic3—62no—
107Dic3—64no—
108Dic3—122no—
109C32#43611yescharacteristic, complemented, Sylow
110C23—91no—
111C23C2×#15711yescharacteristic
112D4—182no—
113C2×C4—91no—
114C2×C4—91no—
115C2×C4—91no—
116C2×C4—181no—
117C2×C4—181no—
118C2×C4—181no—
119C2×C4—181no—
120C2×C4C2×#15711yescharacteristic
121C2×C4C2×#15711yescharacteristic
122C8—92no—
123C8—181no—
124C8—181no—
125C8—181no—
126C2×C3—22no—
127C2×C3—22no—
128C2×C3—22no—
129C2×C3—44no—
130D3—124no—
131C22—21no—
132C22—21no—
133C22—21no—
134C22—181no—
135C22—181no—
136C22—181no—
137C22C22×#15711yescharacteristic
138C4—21no—
139C4—21no—
140C4—92no—
141C4—91no—
142C4—91no—
143C4—181no—
144C3—22no—
145C2—41no—
146C2—361no—
147C2#6428311yescharacteristic
148C2#6428711yescharacteristic
149C2D4×#15711yescharacteristic
subgroupG/H
center, FrattiniC22C22×#157
commutator, socleC22×C32C22×C4
FittingC32×C22⋊C4C4
prime radicalC2×#638C4
cosocleC2×C3⋊Dic3C23
hypercenterC22⋊C4#157
hypocenterC32#436
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#3792C2semidirect
2. C2×#3788C2semidirect
4. C22⋊#622C2semidirect
5. #63779C2semidirect
6. #63778C2semidirect
7. C4×#622C2semidirect
37. #622D4semidirect
56. C3⋊Dic3M16semidirect
109. C32#436semidirect

Maximal subgroups

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

subgroupindex
C2×#37922
C2×#37882
#640902
C22⋊#6222
#637792
#637782
C4×#6222
#4369