Finite Group Databasebeta

← #10593443

Subgroups — #10593443

Order 576.

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

normal subgroups only

This group has 196 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×#3776C212yesmaximal, complemented
2C2×#3775C212yesmaximal
3#63919C211yesmaximal, characteristic, complemented
4#63915C211yesmaximal, characteristic
5#63777C211yesmaximal, characteristic, complemented
6C2×#627C2211yescharacteristic
7C2×#627C2212yes—
8C2×#625C2211yescharacteristic
9C2×#622C2212yes—
10#3776—24no—
11#3775—24no—
12C4×C3⋊Dic3C2211yescharacteristic
13C3×(C2×D3)⋊C4—21no—
14C3×C4⋊Dic3—21no—
15#3724—21no—
16(C2×D3)⋊Dic3—21no—
17#888—61no—
18#885—61no—
19C22×C3×D3—21no—
20C2×C32×C4D411yescharacteristic
21C2×C3⋊Dic3D411yescharacteristic
22C2×C3⋊Dic3C2311yescharacteristic
23C2×C3×Dic3—21no—
24C2×C3×Dic3—22no—
25#627—22no—
26#627—22no—
27#627—22no—
28#625—22no—
29#622D414yes—
30#497—91nomaximal, Sylow
31C2×#67—61no—
32C2×Dic6—61no—
33C2×Dic6—62no—
34C3×C4⋊C4—61no—
35C3×C22⋊C4—61no—
36#217—61no—
37(C2×D3)⋊C4—21no—
38(C2×D3)⋊C4—61no—
39C4⋊Dic3—21no—
40Dic3⋊C4—62no—
41C4×Dic3—61no—
42C4×Dic3—61no—
43C22×C32C2×D411yescharacteristic
44C2×C3×D3—41no—
45C2×C3×D3—41no—
46C2×C3×D3—41no—
47C32×C4—21no—
48C3⋊Dic3—21no—
49C3⋊Dic3C2×D412yes—
50C3×Dic3—42no—
51C3×Dic3—41no—
52C2×Q16—92no—
53C2×SD16—92no—
54C4⋊Q8—91no—
55#124—91no—
56#97—91no—
57C23×C3—61no—
58C22×D3—21no—
59C2×C3×C4—21no—
60C2×C3×C4—21no—
61C2×C3×C4—62no—
62C2×C3×C4—61no—
63#67—122no—
64C2×Dic3—22no—
65C2×Dic3—21no—
66C2×Dic3—61no—
67C2×Dic3—61no—
68C2×Dic3—61no—
69C2×Dic3—61no—
70Dic6—122no—
71Dic6—122no—
72Dic6—122no—
73C2×C32#12711yescharacteristic
74C2×C32#13711yescharacteristic
75C2×C32#13711yescharacteristic
76C3×D3—81no—
77C2×Q8—91no—
78C2×Q8—92no—
79C2×D4—91no—
80Q16—184no—
81SD16—184no—
82C2×C8—92no—
83C4⋊C4—61no—
84C4⋊C4—181no—
85C22⋊C4—61no—
86C22⋊C4—181no—
87C42—91no—
88C22×C3—21no—
89C22×C3—21no—
90C22×C3—121no—
91C22×C3—121no—
92C22×C3—121no—
93C2×D3—41no—
94C2×D3—41no—
95C2×D3—41no—
96C3×C4—22no—
97C3×C4—41no—
98C3×C4—122no—
99C3×C4—121no—
100Dic3—42no—
101Dic3—41no—
102Dic3—62no—
103Dic3—62no—
104Dic3—62no—
105Dic3—121no—
106C32#49711yescharacteristic, complemented, Sylow
107C23—61no—
108Q8—182no—
109Q8—182no—
110Q8—182no—
111D4—182no—
112C2×C4—61no—
113C2×C4—62no—
114C2×C4—91no—
115C2×C4—91no—
116C2×C4GO+(4,𝔽2)11yescharacteristic
117C8—94no—
118C2×C3—21no—
119C2×C3—21no—
120C2×C3—21no—
121C2×C3—21no—
122C2×C3—21no—
123C2×C3—21no—
124C2×C3—241no—
125D3—81no—
126C22—121no—
127C22—121no—
128C22—121no—
129C22C2×GO+(4,𝔽2)11yescharacteristic
130C4—21no—
131C4—92no—
132C4—121no—
133C4—122no—
134C4—181no—
135C3—21no—
136C3—21no—
137C2—241no—
138C2#6422611yescharacteristic
139C2#6423111yescharacteristic
140C2#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#497
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
1. C2×#3776C2semidirect
3. #63919C2semidirect
5. #63777C2semidirect
106. C32#497semidirect

Maximal subgroups

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

subgroupindex
C2×#37762
C2×#37752
#639192
#639152
#637772
#4979