Finite Group Databasebeta

← #10590043

Subgroups — #10590043

Order 576.

210 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 49 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×#3787C211yesmaximal, characteristic
2C4×#624C211yesmaximal, characteristic
3C2×#3710C211yesmaximal, characteristic
4C2×C4×C3⋊D3C2211yescharacteristic
5C2×#624C412yes—
6C2×#622—21no—
7#3787—21no—
8#3787C412yescomplemented
9C3×C4×Dic3—21no—
10C2×C3×C3⋊C8—21no—
11Dic32—21no—
12#3710—21no—
13#3710C412yescomplemented
14C2×D3×C8—61no—
15C42×D3—61no—
16C22×C3⋊D3C2×C411yescharacteristic
17C2×C32×C4D411yescharacteristic
18C2×C3⋊Dic3D411yescharacteristic
19C4×C3⋊D3C2×C411yescharacteristic
20C4×C3⋊D3C2×C411yescharacteristic
21C4×C3⋊D3D411yescharacteristic
22C4×C3⋊D3Q811yescharacteristic
23C2×C3×Dic3—22no—
24#624—22no—
25#624C814yescomplemented
26#622—22no—
27C3×C3⋊C8—22no—
28#336—91nomaximal, Sylow
29C2×C4×D3—62no—
30C2×C4×D3—61no—
31C2×C4×D3—61no—
32C2×C3×C8—61no—
33C3×C42—61no—
34C4×Dic3—21no—
35C4×Dic3—62no—
36C2×C3⋊C8—21no—
37D3×C8—62no—
38D3×C8—62no—
39C22×C32C22⋊C411yescharacteristic
40C2×C3⋊D3C4211yescharacteristic
41C2×C3⋊D3C4⋊C411yescharacteristic
42C2×C3⋊D3C2×C812yes—
43C2×C3⋊D3M1612yes—
44C32×C4C22⋊C411yescharacteristic
45C32×C4C4⋊C411yescharacteristic
46C3⋊Dic3C22⋊C411yescharacteristic
47C3⋊Dic3C4⋊C411yescharacteristic
48C3×Dic3—24no—
49C22×C8—91no—
50C22×C8—91no—
51C2×C42—91no—
52C22×D3—61no—
53C22×D3—61no—
54C2×C3×C4—21no—
55C2×C3×C4—21no—
56C2×C3×C4—62no—
57C2×Dic3—22no—
58C2×Dic3—61no—
59C2×Dic3—61no—
60C4×D3—64no—
61C4×D3—61no—
62C4×D3—61no—
63C4×D3—61no—
64C4×D3—61no—
65C4×D3—61no—
66C4×D3—61no—
67C4×D3—61no—
68C4×D3—61no—
69C4×D3—64no—
70C3×C8—62no—
71C3⋊C8—22no—
72C2×C32#9511yescharacteristic
73C2×C32C22⋊C812yes—
74C3⋊D3C4×C811yescharacteristic
75C3⋊D3#9711yescharacteristic
76C3⋊D3C4⋊C812yes—
77C22×C4—92no—
78C22×C4—91no—
79C2×C8—61no—
80C2×C8—92no—
81C2×C8—92no—
82C2×C8—181no—
83C2×C8—181no—
84C2×C8—181no—
85C42—61no—
86C42—181no—
87C22×C3—21no—
88C22×C3—21no—
89C2×D3—61no—
90C2×D3—61no—
91C2×D3—61no—
92C2×D3—61no—
93C2×D3—62no—
94C2×D3—62no—
95C2×D3—62no—
96C2×D3—62no—
97C3×C4—21no—
98C3×C4—21no—
99C3×C4—21no—
100C3×C4—21no—
101C3×C4—64no—
102Dic3—24no—
103Dic3—61no—
104Dic3—61no—
105Dic3—61no—
106Dic3—61no—
107C32#33611yescharacteristic, complemented, Sylow
108C23—91no—
109C2×C4—62no—
110C2×C4—94no—
111C2×C4—91no—
112C2×C4—91no—
113C2×C4—91no—
114C2×C4—91no—
115C2×C4—91no—
116C2×C4—182no—
117C2×C4GO+(4,𝔽2)11yescharacteristic
118C8—62no—
119C8—182no—
120C2×C3—22no—
121C2×C3—22no—
122C2×C3—21no—
123C2×C3—21no—
124D3—61no—
125D3—61no—
126D3—61no—
127D3—61no—
128D3—62no—
129D3—62no—
130C22—92no—
131C22—92no—
132C22—91no—
133C22—91no—
134C22D32⋊C411yescharacteristic
135C4—64no—
136C4—91no—
137C4—91no—
138C4D32⋊C411yescharacteristic
139C4#377311yescharacteristic
140C3—21no—
141C3—21no—
142C2—91no—
143C2—92no—
144C2—91no—
145C2D32⋊C812yes—
146C2#6373711yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2×C4GO+(4,𝔽2)
commutatorC3⋊D3C4×C8
FittingC2×C32×C4D4
socleC22×C32C22⋊C4
prime radicalC22×C3⋊D3C2×C4
cosocleC2×C4×C3⋊D3C22
hypocenterC32#336
LCSG ▷ C3⋊D3 ▷ C32
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
8. #3787C4semidirect
13. #3710C4semidirect
25. #624C8semidirect
107. C32#336semidirect

Maximal subgroups

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

subgroupindex
C2×#37872
C4×#6242
C2×#37102
#3369