Finite Group Databasebeta

← #10591214

Subgroups — #10591214

Order 576.

338 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 104 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×C3×C4⋊Dic3C211yesmaximal, characteristic
2C2×C3×Dic3⋊C4C211yesmaximal, characteristic
3C2×#3724C212yesmaximal
4#63658C211yesmaximal, characteristic
5#63579C212yesmaximal
6#4983—31nomaximal
7#4981—31nomaximal
8C22×C32×C4C2211yescharacteristic
9C22×C3⋊Dic3C2212yes—
10C22×C3×Dic3C2211yescharacteristic
11C22×C3×Dic3C2212yes—
12C22×C3×Dic3C2211yescharacteristic
13C3×C4⋊Dic3—22no—
14C3×Dic3⋊C4—22no—
15#3724—24no—
16C2×C3×C4⋊C4—31no—
17C2×C3×C4⋊C4—31no—
18C2×C4⋊Dic3D311yescharacteristic
19C2×Dic3⋊C4—32no—
20C2×Dic3⋊C4—32no—
21C2×Dic3⋊C4D311yescharacteristic
22C3⋊#95—31no—
23C3⋊#95—31no—
24C3⋊#95—32no—
25C3⋊#95—32no—
26C3⋊#95—61no—
27C23×C32C2311yescharacteristic
28C2×C32×C4—22no—
29C2×C32×C4D412yes—
30C2×C3⋊Dic3—22no—
31C2×C3⋊Dic3—22no—
32C2×C3⋊Dic3Q814yes—
33C2×C3×Dic3—21no—
34C2×C3×Dic3—21no—
35C2×C3×Dic3—22no—
36C2×C3×Dic3—21no—
37C2×C3×Dic3—22no—
38C2×C3×Dic3—22no—
39C2×C3×Dic3—22no—
40C2×C3×Dic3D412yes—
41#398—91noSylow
42C22×C3×C4—21no—
43C22×C3×C4—31no—
44C22×C3×C4—31no—
45C22×C3×C4—32no—
46C22×C3×C4C2×D311yescharacteristic
47C22×C3×C4C2×D311yescharacteristic
48C22×Dic3—32no—
49C22×Dic3—32no—
50C22×Dic3—62no—
51C22×Dic3C2×D311yescharacteristic
52C22×Dic3C2×D312yes—
53C22×Dic3C2×D311yescharacteristic
54C3×C4⋊C4—62no—
55C3×C4⋊C4—62no—
56C4⋊Dic3—22no—
57Dic3⋊C4—22no—
58Dic3⋊C4—64no—
59Dic3⋊C4—64no—
60C22×C32C2×D411yescharacteristic
61C22×C32C2×D411yescharacteristic
62C22×C32C2×Q812yes—
63C22×C32#4111yescharacteristic
64C22×C32#4112yes—
65C32×C4—22no—
66C3⋊Dic3—24no—
67C3×Dic3—22no—
68C3×Dic3—42no—
69C3×Dic3—41no—
70C2×C4⋊C4—31no—
71C2×C4⋊C4—31no—
72C2×C4⋊C4—92no—
73#95—92no—
74#95—91no—
75C23×C3—21no—
76C23×C3C22×D311yescharacteristic
77C23×C3C22×D311yescharacteristic
78C2×C3×C4—22no—
79C2×C3×C4—22no—
80C2×C3×C4—22no—
81C2×C3×C4—32no—
82C2×C3×C4—42no—
83C2×C3×C4—61no—
84C2×C3×C4—61no—
85C2×C3×C4—62no—
86C2×C3×C4—62no—
87C2×C3×C4—62no—
88C2×C3×C4—61no—
89C2×C3×C4—62no—
90C2×C3×C4#6712yes—
91C2×C3×C4#6712yes—
92C2×Dic3—21no—
93C2×Dic3—21no—
94C2×Dic3—22no—
95C2×Dic3—22no—
96C2×Dic3—22no—
97C2×Dic3—21no—
98C2×Dic3—22no—
99C2×Dic3—34no—
100C2×Dic3—34no—
101C2×Dic3—64no—
102C2×Dic3—62no—
103C2×Dic3—62no—
104C2×Dic3—62no—
105C2×Dic3—62no—
106C2×Dic3—122no—
107C2×Dic3—122no—
108C2×Dic3D1212yes—
109C2×C32#12111yescharacteristic
110C2×C32C22⋊Q812yes—
111C2×C32#12311yescharacteristic
112C2×C32#12512yes—
113C2×C32C4⋊Q811yescharacteristic
114C22×C4—31no—
115C22×C4—31no—
116C22×C4—32no—
117C22×C4—92no—
118C22×C4D3211yescharacteristic
119C4⋊C4—62no—
120C4⋊C4—62no—
121C4⋊C4—184no—
122C22×C3—21no—
123C22×C3—22no—
124C22×C3—21no—
125C22×C3—22no—
126C22×C3—21no—
127C22×C3C2×D1211yescharacteristic
128C22×C3#23511yescharacteristic
129C22×C3#23512yes—
130C22×C3D3×D411yescharacteristic
131C22×C3#23711yescharacteristic
132C22×C3#23712yes—
133C22×C3D3×Q812yes—
134C22×C3D3×Q812yes—
135C22×C3C2×#6711yescharacteristic
136C22×C3C2×#6711yescharacteristic
137C3×C4—22no—
138C3×C4—22no—
139C3×C4—42no—
140C3×C4—62no—
141C3×C4—121no—
142C3×C4—122no—
143Dic3—22no—
144Dic3—41no—
145Dic3—42no—
146Dic3—64no—
147Dic3—64no—
148Dic3—124no—
149C32#39811yescharacteristic, complemented, Sylow
150C23C2×D3211yescharacteristic
151C2×C4—22no—
152C2×C4—32no—
153C2×C4—61no—
154C2×C4—61no—
155C2×C4—62no—
156C2×C4—62no—
157C2×C4—62no—
158C2×C4—62no—
159C2×C4—61no—
160C2×C4—94no—
161C2×C4—182no—
162C2×C4—182no—
163C2×C4#62512yes—
164C2×C3—22no—
165C2×C3—21no—
166C2×C3—22no—
167C2×C3—21no—
168C2×C3—21no—
169C2×C3#88912yes—
170C2×C3#88912yes—
171C2×C3#89612yes—
172C2×C3#89712yes—
173C2×C3#92911yescharacteristic
174C2×C3#93011yescharacteristic
175C2×C3#93511yescharacteristic
176C2×C3#93811yescharacteristic
177C2×C3#94411yescharacteristic
178C2×C3#94411yescharacteristic
179C22#379511yescharacteristic
180C22#379712yes—
181C22D3×D1211yescharacteristic
182C22#380412yes—
183C22C2×#62511yescharacteristic
184C4—22no—
185C4—62no—
186C4—122no—
187C4—121no—
188C4—184no—
189C3—21no—
190C3#498111yescharacteristic, complemented
191C3#498311yescharacteristic, complemented
192C2#6384712yes—
193C2#6387311yescharacteristic
194C2#6389512yes—
195C2#6390811yescharacteristic
196C2#6396111yescharacteristic
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
149. C32#398semidirect
190. C3#4981semidirect
191. C3#4983semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4⋊Dic32
C2×C3×Dic3⋊C42
C2×#37242
#636582
#635792
#49833
#49813