Finite Group Databasebeta

← #10591217

Subgroups — #10591217

Order 576.

314 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 92 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×#3750C211yesmaximal, characteristic
2C2×#3724C211yesmaximal, characteristic
3C3×C3⋊#95C212yesmaximal
4#63579C211yesmaximal, characteristic
5#63579C212yesmaximal
6#4658—32nomaximal
7C22×C32×C4C2211yescharacteristic
8C22×C3⋊Dic3C2211yescharacteristic
9C22×C3⋊Dic3C2211yescharacteristic
10C22×C3×Dic3C2212yes—
11C22×C3×Dic3C2212yes—
12#3750—22no—
13#3724—22no—
14C2×Dic3⋊C4—32no—
15C2×Dic3⋊C4—32no—
16C2×Dic3⋊C4—61no—
17C3×#95—32no—
18C3⋊#95—32no—
19C3⋊#95—32no—
20C3⋊#95—32no—
21C3⋊#95D312yes—
22C23×C32C2311yescharacteristic
23C2×C32×C4—21no—
24C2×C32×C4—22no—
25C2×C3⋊Dic3—21no—
26C2×C3⋊Dic3—21no—
27C2×C3⋊Dic3—22no—
28C2×C3⋊Dic3D412yes—
29C2×C3⋊Dic3Q812yes—
30C2×C3×Dic3—22no—
31C2×C3×Dic3—22no—
32C2×C3×Dic3—22no—
33C2×C3×Dic3—22no—
34C2×C3×Dic3—22no—
35C2×C3×Dic3—22no—
36#400—91noSylow
37C22×C3×C4—21no—
38C22×C3×C4—32no—
39C22×C3×C4—32no—
40C22×C3×C4C2×D312yes—
41C22×Dic3—32no—
42C22×Dic3—32no—
43C22×Dic3—61no—
44C22×Dic3—61no—
45C22×Dic3C2×D312yes—
46C22×Dic3C2×D312yes—
47Dic3⋊C4—64no—
48Dic3⋊C4—64no—
49Dic3⋊C4—64no—
50C22×C32C2×D411yescharacteristic
51C22×C32C2×Q811yescharacteristic
52C22×C32#4111yescharacteristic
53C22×C32#4112yes—
54C22×C32#4112yes—
55C32×C4—41no—
56C3⋊Dic3—22no—
57C3⋊Dic3—22no—
58C3×Dic3—42no—
59C3×Dic3—42no—
60C2×C4⋊C4—91no—
61C2×C4⋊C4—91no—
62#95—32no—
63#95—91no—
64#95—92no—
65C23×C3—21no—
66C23×C3C22×D312yes—
67C2×C3×C4—22no—
68C2×C3×C4—22no—
69C2×C3×C4—22no—
70C2×C3×C4—22no—
71C2×C3×C4—42no—
72C2×C3×C4—62no—
73C2×C3×C4—62no—
74C2×C3×C4—62no—
75C2×C3×C4—62no—
76C2×C3×C4—62no—
77C2×C3×C4—62no—
78C2×Dic3—22no—
79C2×Dic3—22no—
80C2×Dic3—22no—
81C2×Dic3—22no—
82C2×Dic3—22no—
83C2×Dic3—22no—
84C2×Dic3—34no—
85C2×Dic3—34no—
86C2×Dic3—62no—
87C2×Dic3—62no—
88C2×Dic3—62no—
89C2×Dic3—62no—
90C2×Dic3—62no—
91C2×Dic3—62no—
92C2×Dic3—62no—
93C2×Dic3—62no—
94C2×Dic3—122no—
95C2×C32C22⋊Q811yescharacteristic
96C2×C32#12311yescharacteristic
97C2×C32#12411yescharacteristic
98C2×C32#12512yes—
99C2×C32#12612yes—
100C22×C4—32no—
101C22×C4—32no—
102C22×C4—91no—
103C22×C4—91no—
104C22×C4D3211yescharacteristic
105C4⋊C4—182no—
106C4⋊C4—182no—
107C22×C3—22no—
108C22×C3—21no—
109C22×C3—21no—
110C22×C3—22no—
111C22×C3—21no—
112C22×C3#23512yes—
113C22×C3#23512yes—
114C22×C3#23512yes—
115C22×C3D3×D412yes—
116C22×C3#23712yes—
117C22×C3#23712yes—
118C22×C3D3×Q812yes—
119C3×C4—42no—
120C3×C4—42no—
121C3×C4—122no—
122C3×C4—122no—
123Dic3—42no—
124Dic3—42no—
125Dic3—64no—
126Dic3—64no—
127Dic3—64no—
128Dic3—122no—
129C32#40011yescharacteristic, complemented, Sylow
130C23C2×D3211yescharacteristic
131C2×C4—22no—
132C2×C4—21no—
133C2×C4—62no—
134C2×C4—62no—
135C2×C4—62no—
136C2×C4—62no—
137C2×C4—62no—
138C2×C4—62no—
139C2×C4—92no—
140C2×C4—92no—
141C2×C4—181no—
142C2×C4—182no—
143C2×C4—181no—
144C2×C3—22no—
145C2×C3—22no—
146C2×C3—21no—
147C2×C3—21no—
148C2×C3—21no—
149C2×C3#87612yes—
150C2×C3#87912yes—
151C2×C3#88312yes—
152C2×C3#88512yes—
153C2×C3#88912yes—
154C2×C3#88912yes—
155C2×C3#89612yes—
156C22#379512yes—
157C22#379711yescharacteristic
158C22#379811yescharacteristic
159C22#380412yes—
160C22#381111yescharacteristic
161C4—41no—
162C4—122no—
163C4—122no—
164C4—182no—
165C4—182no—
166C3—21no—
167C3#465812yescomplemented
168C2#6384712yes—
169C2#6385912yes—
170C2#6386511yescharacteristic
171C2#6391311yescharacteristic
172C2#6397511yescharacteristic
subgroupG/H
center, FrattiniC23C2×D32
commutator, socle, prime radical, cosocleC23×C32C23
FittingC22×C32×C4C22
hypercenterC22×C4D32
hypocenterC32#400
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
129. C32#400semidirect
167. C3#4658semidirect

Maximal subgroups

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

subgroupindex
C2×#37502
C2×#37242
C3×C3⋊#952
#635792
#46583