Finite Group Databasebeta

← #10591497

Subgroups — #10591497

Order 576.

287 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 287 conjugacy classes of subgroups — too many to draw. Only its 68 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
1D4×C3⋊Dic3C211yesmaximal, characteristic
2C2×C3×#214C212yesmaximal
3#63873C211yesmaximal, characteristic, complemented
4#63572C211yesmaximal, characteristic, complemented
5#63566C212yesmaximal, complemented
6#5162—32nomaximal
7C2×C32×D4C2211yescharacteristic
8C22×C3⋊Dic3—21no—
9C2×C3×Dic6C2212yes—
10#3757—21no—
11C4⋊(C3⋊Dic3)C2211yescharacteristic
12C4×C3⋊Dic3C2211yescharacteristic
13C3×#214—24no—
14C2×C3×C3⋊C8C2212yes—
15#3724—21no—
16#3724—21no—
17C2×C3×SD16—32no—
18#944—32no—
19D4×Dic3—32no—
20D4×Dic3—61no—
21C2×#214D312yes—
22#835—32no—
23#816—32no—
24Dic3⋊C8—32no—
25C23×C32—21no—
26C32×D4—21no—
27C32×D4D412yes—
28C2×C32×C4C2311yescharacteristic
29C2×C3⋊Dic3—21no—
30C2×C3⋊Dic3—42no—
31C2×C3⋊Dic3D411yescharacteristic
32C2×C3⋊Dic3D411yescharacteristic
33C2×C3×Dic3—22no—
34C3×Dic6—22no—
35C3×Dic6—22no—
36C3×C3⋊C8—22no—
37#461—91noSylow
38C2×C3×Q8—32no—
39C2×C3×D4—21no—
40C2×C3×D4C2×D312yes—
41C22×Dic3—62no—
42C22×Dic3—62no—
43C2×Dic6C2×D312yes—
44C3×SD16—64no—
45C2×C3×C8—32no—
46#217—62no—
47#217—62no—
48#214—24no—
49C4⋊Dic3—32no—
50C4⋊Dic3—61no—
51Dic3⋊C4—62no—
52Dic3⋊C4—62no—
53C4×Dic3—32no—
54C4×Dic3—61no—
55C2×C3⋊C8C2×D312yes—
56C22×C32—22no—
57C22×C32—41no—
58C22×C32—41no—
59C22×C32C2×D411yescharacteristic
60C32×C4C2×D411yescharacteristic
61C32×C4#4111yescharacteristic
62C3⋊Dic3—21no—
63C3⋊Dic3—41no—
64C3⋊Dic3SD1612yescomplemented
65C3×Dic3—42no—
66C2×SD16—32no—
67C4⋊Q8—91no—
68C4×D4—91no—
69C4⋊C8—91no—
70#103—92no—
71C23×C3—22no—
72C23×C3—22no—
73C3×Q8—62no—
74C3×Q8—62no—
75C3×D4—22no—
76C3×D4—22no—
77C3×D4—22no—
78C3×D4#6714yes—
79C2×C3×C4—21no—
80C2×C3×C4—62no—
81C2×C3×C4C22×D312yes—
82C2×Dic3—22no—
83C2×Dic3—32no—
84C2×Dic3—32no—
85C2×Dic3—61no—
86C2×Dic3—61no—
87C2×Dic3—62no—
88C2×Dic3—62no—
89C2×Dic3—124no—
90C2×Dic3—124no—
91Dic6—22no—
92Dic6—22no—
93C3×C8—62no—
94C3⋊C8—22no—
95C2×C32—42no—
96C2×C32#12111yescharacteristic
97C2×C32C2×SD1611yescharacteristic
98C2×C32#13711yescharacteristic
99C2×Q8—32no—
100C2×D4D3211yescharacteristic
101C22×C4—181no—
102SD16—64no—
103C2×C8—32no—
104C4⋊C4—91no—
105C4⋊C4—181no—
106C4⋊C4—181no—
107C22⋊C4—181no—
108C42—91no—
109C22×C3—24no—
110C22×C3—24no—
111C22×C3—21no—
112C22×C3—42no—
113C22×C3—42no—
114C22×C3—42no—
115C22×C3—42no—
116C22×C3D3×D412yes—
117C3×C4—21no—
118C3×C4—21no—
119C3×C4—122no—
120C3×C4#23712yes—
121C3×C4C2×#6712yes—
122Dic3—34no—
123Dic3—42no—
124Dic3—62no—
125Dic3—62no—
126Dic3—121no—
127Dic3—122no—
128Dic3—122no—
129C32#46111yescharacteristic, complemented, Sylow
130C23—21no—
131Q8—62no—
132Q8—62no—
133D4—21no—
134D4#62512yes—
135C2×C4—62no—
136C2×C4—91no—
137C2×C4—91no—
138C2×C4—181no—
139C2×C4—362no—
140C2×C4C2×D3211yescharacteristic
141C8—62no—
142C2×C3—21no—
143C2×C3—21no—
144C2×C3—21no—
145C2×C3—44no—
146C2×C3—44no—
147C2×C3D3×SD1612yes—
148C2×C3#91512yes—
149C2×C3#93912yes—
150C22—22no—
151C22—41no—
152C22—41no—
153C22#381111yescharacteristic
154C4—92no—
155C4—122no—
156C4—181no—
157C4—361no—
158C4#380511yescharacteristic
159C4C2×#62511yescharacteristic
160C3—21no—
161C3#516212yescomplemented
162C2—42no—
163C2#6393011yescharacteristic
164C2#6393111yescharacteristic
165C2#6398011yescharacteristic
subgroupG/H
centerC22#3811
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
Fitting, prime radicalC2×C32×D4C22
socleC22×C32C2×D4
hypercenterC2×D4D32
hypocenterC32#461
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
3. #63873C2semidirect
4. #63572C2semidirect
5. #63566C2semidirect
64. C3⋊Dic3SD16semidirect
129. C32#461semidirect
161. C3#5162semidirect

Maximal subgroups

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

subgroupindex
D4×C3⋊Dic32
C2×C3×#2142
#638732
#635722
#635662
#51623