Finite Group Databasebeta

← #10593438

Subgroups — #10593438

Order 576.

201 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 201 conjugacy classes of subgroups — too many to draw. Only its 35 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×#3775C212yesmaximal
2#63919C211yesmaximal, characteristic, complemented
3#63902C211yesmaximal, characteristic
4#63779C211yesmaximal, characteristic, complemented
5#63740C212yesmaximal, complemented
6C2×#627C2212yes—
7C2×#625C2211yescharacteristic
8C2×D3×Dic3—21no—
9C2×#622C2212yes—
10#3775—24no—
11C4×C3⋊Dic3C2211yescharacteristic
12C3×(C2×D3)⋊C4—21no—
13C3×C4⋊Dic3—21no—
14#3724—21no—
15#3724C2211yescharacteristic
16#888—61no—
17#67⋊C4—61no—
18C22×C3×D3—21no—
19C2×C32×C4D411yescharacteristic
20C2×C3⋊Dic3D411yescharacteristic
21C2×C3⋊Dic3C2311yescharacteristic
22C2×C3×Dic3—22no—
23C2×C3×Dic3—21no—
24#627—22no—
25#627—22no—
26#625—21no—
27#625D412yes—
28D3×Dic3—42no—
29#622—22no—
30#461—91nomaximal, Sylow
31C2×#67—61no—
32C22×Dic3—61no—
33C2×C4×D3—61no—
34C2×Dic6—62no—
35C3×C4⋊C4—61no—
36C3×C22⋊C4—61no—
37(C2×D3)⋊C4—21no—
38C4⋊Dic3—21no—
39Dic3⋊C4—61no—
40Dic3⋊C4—62no—
41C4×Dic3—61no—
42C4×Dic3—61no—
43C22×C32C2×D411yescharacteristic
44C2×C3×D3—22no—
45C2×C3×D3—41no—
46C2×C3×D3—41no—
47C32×C4—21no—
48C3⋊Dic3SD1612yescomplemented
49C3⋊Dic3C2×D411yescharacteristic
50C3⋊Dic3#4111yescharacteristic
51C3×Dic3—42no—
52C3×Dic3—41no—
53C2×SD16—92no—
54C4⋊Q8—91no—
55C4×D4—91no—
56C4⋊C8—91no—
57#103—92no—
58C23×C3—61no—
59C22×D3—21no—
60C2×C3×C4—21no—
61C2×C3×C4—21no—
62C2×C3×C4—61no—
63C2×C3×C4—62no—
64#67—62no—
65#67—62no—
66C2×Dic3—22no—
67C2×Dic3—21no—
68C2×Dic3—61no—
69C2×Dic3—61no—
70C2×Dic3—61no—
71C2×Dic3—61no—
72C2×Dic3—122no—
73C4×D3—122no—
74Dic6—122no—
75Dic6—122no—
76C2×C32#12111yescharacteristic
77C2×C32C2×SD1611yescharacteristic
78C2×C32#13711yescharacteristic
79C3×D3—42no—
80C2×Q8—92no—
81C2×D4—91no—
82C22×C4—181no—
83SD16—184no—
84C2×C8—92no—
85C4⋊C4—61no—
86C4⋊C4—91no—
87C4⋊C4—181no—
88C22⋊C4—61no—
89C42—91no—
90C22×C3—21no—
91C22×C3—21no—
92C22×C3—62no—
93C22×C3—121no—
94C22×C3—121no—
95C2×D3—22no—
96C2×D3—41no—
97C2×D3—41no—
98C3×C4—22no—
99C3×C4—41no—
100C3×C4—122no—
101C3×C4—121no—
102Dic3—42no—
103Dic3—41no—
104Dic3—61no—
105Dic3—61no—
106Dic3—62no—
107Dic3—61no—
108Dic3—61no—
109Dic3—62no—
110C32#46111yescharacteristic, complemented, Sylow
111C23—61no—
112Q8—182no—
113Q8—182no—
114D4—92no—
115D4—181no—
116C2×C4—61no—
117C2×C4—62no—
118C2×C4—91no—
119C2×C4—91no—
120C2×C4—362no—
121C2×C4GO+(4,𝔽2)11yescharacteristic
122C8—182no—
123C2×C3—21no—
124C2×C3—21no—
125C2×C3—21no—
126C2×C3—21no—
127C2×C3—21no—
128C2×C3—21no—
129C2×C3—122no—
130D3—42no—
131C22—62no—
132C22—121no—
133C22—121no—
134C22C2×GO+(4,𝔽2)11yescharacteristic
135C4—21no—
136C4—92no—
137C4—91no—
138C4—91no—
139C4—121no—
140C4—122no—
141C3—21no—
142C3—21no—
143C2—122no—
144C2#6422711yescharacteristic
145C2#6423011yescharacteristic
146C2#6423911yescharacteristic
subgroupG/H
center, FrattiniC22C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C23
FittingC2×C32×C4D4
socleC22×C32C2×D4
prime radicalC2×#625C22
hypercenterC2×C4GO+(4,𝔽2)
hypocenterC32#461
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #63919C2semidirect
4. #63779C2semidirect
5. #63740C2semidirect
48. C3⋊Dic3SD16semidirect
110. C32#461semidirect

Maximal subgroups

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

subgroupindex
C2×#37752
#639192
#639022
#637792
#637402
#4619