Finite Group Databasebeta

← C3×#4983 #10592080

Subgroups — C3×#4983 #10592080

Order 576.

346 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 122 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×C32×C4⋊C4C211yesmaximal, characteristic
2C2×C3×Dic3⋊C4C211yesmaximal, characteristic
3C2×C3×Dic3⋊C4C212yesmaximal
4C3×C3⋊#95C212yesmaximal
5C3×C3⋊#95C211yesmaximal, characteristic
6C3×#398—31nomaximal
7#4983C311yesmaximal, characteristic, direct product factor
8C22×C32×C4C2212yes—
9C22×C32×C4C2211yescharacteristic
10C22×C3×Dic3C2211yescharacteristic
11C22×C3×Dic3C2211yescharacteristic
12C22×C3×Dic3C2212yes—
13C32×C4⋊C4—22no—
14C3×Dic3⋊C4—22no—
15C3×Dic3⋊C4—24no—
16C2×C3×C4⋊C4—21no—
17C2×C3×C4⋊C4—32no—
18C2×C3×C4⋊C4—31no—
19C2×C3×C4⋊C4D311yescharacteristic
20C2×C3×C4⋊C4C2×C311yescharacteristic
21C2×Dic3⋊C4C2×C311yescharacteristic
22C2×Dic3⋊C4C2×C312yes—
23C3×#95—31no—
24C3×#95—32no—
25C3⋊#95C2×C312yes—
26C3⋊#95C2×C311yescharacteristic
27C23×C32C2311yescharacteristic
28C2×C32×C4—22no—
29C2×C32×C4—22no—
30C2×C32×C4—22no—
31C2×C32×C4—22no—
32C2×C32×C4D412yes—
33C2×C3×Dic3—22no—
34C2×C3×Dic3—21no—
35C2×C3×Dic3—22no—
36C2×C3×Dic3—21no—
37C2×C3×Dic3—21no—
38C2×C3×Dic3—22no—
39C2×C3×Dic3D412yes—
40C2×C3×Dic3Q814yes—
41#398—31noSylow
42C22×C3×C4—21no—
43C22×C3×C4—22no—
44C22×C3×C4—32no—
45C22×C3×C4—31no—
46C22×C3×C4—31no—
47C22×C3×C4C2×D312yes—
48C22×C3×C4C2×D311yescharacteristic
49C22×C3×C4C22×C312yes—
50C22×C3×C4C22×C311yescharacteristic
51C22×Dic3C22×C311yescharacteristic
52C22×Dic3C22×C311yescharacteristic
53C22×Dic3C22×C312yes—
54C3×C4⋊C4—24no—
55C3×C4⋊C4—22no—
56C3×C4⋊C4—22no—
57C3×C4⋊C4—64no—
58C3×C4⋊C4—62no—
59Dic3⋊C4—22no—
60Dic3⋊C4—24no—
61C22×C32C2×D411yescharacteristic
62C22×C32C2×D411yescharacteristic
63C22×C32C2×Q812yes—
64C22×C32#4112yes—
65C22×C32#4111yescharacteristic
66C32×C4—22no—
67C32×C4—42no—
68C3×Dic3—22no—
69C3×Dic3—24no—
70C3×Dic3—41no—
71C2×C4⋊C4—32no—
72C2×C4⋊C4—31no—
73C2×C4⋊C4C3×D311yescharacteristic
74#95—31no—
75#95—32no—
76C23×C3—21no—
77C23×C3C22×D311yescharacteristic
78C23×C3C23×C311yescharacteristic
79C2×C3×C4—24no—
80C2×C3×C4—22no—
81C2×C3×C4—22no—
82C2×C3×C4—24no—
83C2×C3×C4—22no—
84C2×C3×C4—22no—
85C2×C3×C4—22no—
86C2×C3×C4—22no—
87C2×C3×C4—22no—
88C2×C3×C4—22no—
89C2×C3×C4—22no—
90C2×C3×C4—32no—
91C2×C3×C4—34no—
92C2×C3×C4—42no—
93C2×C3×C4—42no—
94C2×C3×C4—62no—
95C2×C3×C4—62no—
96C2×C3×C4—61no—
97C2×C3×C4—61no—
98C2×C3×C4—62no—
99C2×C3×C4—61no—
100C2×C3×C4#6712yes—
101C2×C3×C4C3×D412yes—
102C2×Dic3—22no—
103C2×Dic3—21no—
104C2×Dic3—22no—
105C2×Dic3—21no—
106C2×Dic3—21no—
107C2×Dic3—22no—
108C2×Dic3C3×D412yes—
109C2×Dic3C3×Q814yes—
110C2×C32#12111yescharacteristic
111C2×C32C22⋊Q812yes—
112C2×C32#12311yescharacteristic
113C2×C32#12512yes—
114C2×C32C4⋊Q811yescharacteristic
115C22×C4—32no—
116C22×C4—31no—
117C22×C4—31no—
118C22×C4C2×C3×D312yes—
119C22×C4C2×C3×D311yescharacteristic
120C4⋊C4—22no—
121C4⋊C4—64no—
122C4⋊C4—62no—
123C22×C3—22no—
124C22×C3—21no—
125C22×C3—21no—
126C22×C3—22no—
127C22×C3—21no—
128C22×C3#23512yes—
129C22×C3D3×D411yescharacteristic
130C22×C3#23711yescharacteristic
131C22×C3D3×Q812yes—
132C22×C3C2×#6711yescharacteristic
133C22×C3C2×C3×D411yescharacteristic
134C22×C3C2×C3×D411yescharacteristic
135C22×C3C2×C3×Q812yes—
136C22×C3C3×#4112yes—
137C22×C3C3×#4111yescharacteristic
138C3×C4—24no—
139C3×C4—22no—
140C3×C4—22no—
141C3×C4—44no—
142C3×C4—42no—
143C3×C4—42no—
144C3×C4—64no—
145C3×C4—62no—
146C3×C4—121no—
147Dic3—22no—
148Dic3—24no—
149Dic3—41no—
150C32#39811yescharacteristic, complemented, Sylow
151C23C22×C3×D311yescharacteristic
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—32no—
157C2×C4—34no—
158C2×C4—62no—
159C2×C4—62no—
160C2×C4—61no—
161C2×C4—61no—
162C2×C4—62no—
163C2×C4—61no—
164C2×C4C3×#6712yes—
165C2×C3—22no—
166C2×C3—22no—
167C2×C3—21no—
168C2×C3—21no—
169C2×C3—21no—
170C2×C3#88912yes—
171C2×C3#89612yes—
172C2×C3#92911yescharacteristic
173C2×C3#93811yescharacteristic
174C2×C3#94411yescharacteristic
175C2×C3C3×#12111yescharacteristic
176C2×C3C3×C22⋊Q812yes—
177C2×C3C3×#12311yescharacteristic
178C2×C3C3×#12512yes—
179C2×C3C3×C4⋊Q811yescharacteristic
180C22C3×#23512yes—
181C22C3×D3×D411yescharacteristic
182C22C3×#23711yescharacteristic
183C22C3×D3×Q812yes—
184C22C2×C3×#6711yescharacteristic
185C4—22no—
186C4—42no—
187C4—64no—
188C4—62no—
189C4—121no—
190C3—21no—
191C3#498311yescharacteristic, direct product factor
192C3C3×#39811yescharacteristic, complemented
193C2C3×#88912yes—
194C2C3×#89612yes—
195C2C3×#92911yescharacteristic
196C2C3×#93811yescharacteristic
197C2C3×#94411yescharacteristic
subgroupG/H
centerC23×C3C22×D3
commutator, cosocleC23×C3C23×C3
FrattiniC23C22×C3×D3
FittingC2×C32×C4⋊C4C2
socle, prime radicalC23×C32C23
hypercenterC2×C3×C4⋊C4D3
hypocenterC3C3×#398
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
7. #4983C3direct (N × H)
150. C32#398semidirect
191. C3#4983direct (N × H)
192. C3C3×#398semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4⋊C42
C2×C3×Dic3⋊C42
C3×C3⋊#952
C3×#3983
#49833