Finite Group Databasebeta

← #10591356

Subgroups — #10591356

Order 576.

346 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 100 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
3C2×Dic3⋊Dic3C212yesmaximal
4C3×C3⋊#95C212yesmaximal
5#63579C211yesmaximal, characteristic
6#4657—32nomaximal
7C22×C32×C4C2211yescharacteristic
8C22×C3⋊Dic3C2211yescharacteristic
9C22×C3⋊Dic3C2211yescharacteristic
10C22×C3×Dic3C2212yes—
11C22×C3×Dic3C2212yes—
12#3750—22no—
13#3724—22no—
14Dic3⋊Dic3—24no—
15C2×C4⋊Dic3—32no—
16C2×Dic3⋊C4—32no—
17C2×Dic3⋊C4—32no—
18C2×Dic3⋊C4—32no—
19C2×Dic3⋊C4—61no—
20C3×#95—32no—
21C3⋊#95—32no—
22C3⋊#95D312yes—
23C23×C32C2311yescharacteristic
24C2×C32×C4—21no—
25C2×C32×C4—22no—
26C2×C3⋊Dic3—21no—
27C2×C3⋊Dic3—21no—
28C2×C3⋊Dic3—22no—
29C2×C3⋊Dic3D412yes—
30C2×C3⋊Dic3D412yes—
31C2×C3×Dic3—22no—
32C2×C3×Dic3—22no—
33C2×C3×Dic3—22no—
34C2×C3×Dic3—22no—
35C2×C3×Dic3—22no—
36C2×C3×Dic3Q814yes—
37#398—91noSylow
38C22×C3×C4—21no—
39C22×C3×C4—32no—
40C22×C3×C4—32no—
41C22×C3×C4C2×D312yes—
42C22×Dic3—32no—
43C22×Dic3—32no—
44C22×Dic3—61no—
45C22×Dic3—61no—
46C22×Dic3C2×D312yes—
47C22×Dic3C2×D312yes—
48C4⋊Dic3—64no—
49Dic3⋊C4—64no—
50Dic3⋊C4—64no—
51Dic3⋊C4—64no—
52Dic3⋊C4—64no—
53C22×C32C2×D411yescharacteristic
54C22×C32C2×D411yescharacteristic
55C22×C32C2×Q812yes—
56C22×C32#4111yescharacteristic
57C22×C32#4112yes—
58C32×C4—41no—
59C3⋊Dic3—22no—
60C3⋊Dic3—22no—
61C3×Dic3—24no—
62C3×Dic3—42no—
63C2×C4⋊C4—91no—
64C2×C4⋊C4—92no—
65C2×C4⋊C4—91no—
66#95—32no—
67#95—91no—
68C23×C3—21no—
69C23×C3C22×D312yes—
70C2×C3×C4—22no—
71C2×C3×C4—22no—
72C2×C3×C4—22no—
73C2×C3×C4—22no—
74C2×C3×C4—34no—
75C2×C3×C4—42no—
76C2×C3×C4—62no—
77C2×C3×C4—62no—
78C2×C3×C4—62no—
79C2×C3×C4—62no—
80C2×C3×C4—62no—
81C2×Dic3—22no—
82C2×Dic3—22no—
83C2×Dic3—22no—
84C2×Dic3—22no—
85C2×Dic3—22no—
86C2×Dic3—34no—
87C2×Dic3—34no—
88C2×Dic3—62no—
89C2×Dic3—62no—
90C2×Dic3—62no—
91C2×Dic3—62no—
92C2×Dic3—62no—
93C2×Dic3—62no—
94C2×Dic3—62no—
95C2×Dic3—62no—
96C2×Dic3—122no—
97C2×Dic3Dic614yes—
98C2×C32#12111yescharacteristic
99C2×C32C22⋊Q812yes—
100C2×C32#12311yescharacteristic
101C2×C32#12512yes—
102C2×C32C4⋊Q811yescharacteristic
103C22×C4—32no—
104C22×C4—32no—
105C22×C4—91no—
106C22×C4—91no—
107C22×C4D3211yescharacteristic
108C4⋊C4—182no—
109C4⋊C4—182no—
110C4⋊C4—184no—
111C22×C3—22no—
112C22×C3—21no—
113C22×C3—21no—
114C22×C3—22no—
115C22×C3—21no—
116C22×C3C2×Dic612yes—
117C22×C3#23512yes—
118C22×C3#23512yes—
119C22×C3D3×D412yes—
120C22×C3D3×D412yes—
121C22×C3#23712yes—
122C22×C3D3×Q812yes—
123C3×C4—42no—
124C3×C4—42no—
125C3×C4—64no—
126C3×C4—122no—
127Dic3—24no—
128Dic3—42no—
129Dic3—64no—
130Dic3—64no—
131Dic3—64no—
132Dic3—122no—
133C32#39811yescharacteristic, complemented, Sylow
134C23C2×D3211yescharacteristic
135C2×C4—22no—
136C2×C4—21no—
137C2×C4—34no—
138C2×C4—62no—
139C2×C4—62no—
140C2×C4—62no—
141C2×C4—62no—
142C2×C4—62no—
143C2×C4—92no—
144C2×C4—92no—
145C2×C4—181no—
146C2×C4—182no—
147C2×C4—181no—
148C2×C3—21no—
149C2×C3—22no—
150C2×C3—22no—
151C2×C3—21no—
152C2×C3—21no—
153C2×C3#87012yes—
154C2×C3#87812yes—
155C2×C3#88312yes—
156C2×C3#88412yes—
157C2×C3#88812yes—
158C2×C3#88912yes—
159C2×C3#89612yes—
160C22D3×Dic612yes—
161C22#379811yescharacteristic
162C22#380211yescharacteristic
163C22#380412yes—
164C22#381111yescharacteristic
165C4—41no—
166C4—64no—
167C4—122no—
168C4—182no—
169C4—182no—
170C3—21no—
171C3#465712yescomplemented
172C2#6384011yescharacteristic
173C2#6386712yes—
174C2#6389912yes—
175C2#6391211yescharacteristic
176C2#6397511yescharacteristic
subgroupG/H
center, FrattiniC23C2×D32
commutator, socle, prime radical, cosocleC23×C32C23
FittingC22×C32×C4C22
hypercenterC22×C4D32
hypocenterC32#398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
133. C32#398semidirect
171. C3#4657semidirect

Maximal subgroups

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

subgroupindex
C2×#37502
C2×#37242
C2×Dic3⋊Dic32
C3×C3⋊#952
#635792
#46573