Finite Group Databasebeta

← C3×#4981 #10592078

Subgroups — C3×#4981 #10592078

Order 576.

346 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 126 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×C4⋊Dic3C211yesmaximal, characteristic
3C2×C3×Dic3⋊C4C212yesmaximal
4C3×C3⋊#95C212yesmaximal
5C3×C3⋊#95C211yesmaximal, characteristic
6C3×#398—31nomaximal
7#4981C311yesmaximal, characteristic, direct product factor
8C22×C32×C4C2211yescharacteristic
9C22×C32×C4C2211yescharacteristic
10C22×C32×C4C2211yescharacteristic
11C22×C3×Dic3C2212yes—
12C22×C3×Dic3C2212yes—
13C32×C4⋊C4—22no—
14C3×C4⋊Dic3—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×C4⋊Dic3C2×C311yescharacteristic
22C2×Dic3⋊C4C2×C312yes—
23C3×#95—31no—
24C3×#95—32no—
25C3⋊#95C2×C312yes—
26C3⋊#95C2×C311yescharacteristic
27C23×C32C2311yescharacteristic
28C2×C32×C4—21no—
29C2×C32×C4—21no—
30C2×C32×C4—21no—
31C2×C32×C4—22no—
32C2×C32×C4—22no—
33C2×C32×C4D412yes—
34C2×C32×C4D412yes—
35C2×C3×Dic3—22no—
36C2×C3×Dic3—22no—
37C2×C3×Dic3—22no—
38C2×C3×Dic3—22no—
39C2×C3×Dic3—22no—
40C2×C3×Dic3Q814yes—
41#398—31noSylow
42C22×C3×C4—21no—
43C22×C3×C4—21no—
44C22×C3×C4—21no—
45C22×C3×C4—32no—
46C22×C3×C4—32no—
47C22×C3×C4C2×D311yescharacteristic
48C22×C3×C4C2×D311yescharacteristic
49C22×C3×C4C2×D311yescharacteristic
50C22×C3×C4C22×C311yescharacteristic
51C22×C3×C4C22×C311yescharacteristic
52C22×C3×C4C22×C311yescharacteristic
53C22×Dic3C22×C312yes—
54C22×Dic3C22×C312yes—
55C3×C4⋊C4—24no—
56C3×C4⋊C4—22no—
57C3×C4⋊C4—22no—
58C3×C4⋊C4—64no—
59C3×C4⋊C4—62no—
60C4⋊Dic3—22no—
61Dic3⋊C4—24no—
62C22×C32C2×D411yescharacteristic
63C22×C32C2×D411yescharacteristic
64C22×C32C2×Q812yes—
65C22×C32#4111yescharacteristic
66C22×C32#4112yes—
67C32×C4—22no—
68C32×C4—22no—
69C32×C4—41no—
70C3×Dic3—24no—
71C3×Dic3—42no—
72C2×C4⋊C4—32no—
73C2×C4⋊C4—31no—
74C2×C4⋊C4C3×D311yescharacteristic
75#95—31no—
76#95—32no—
77C23×C3—21no—
78C23×C3C22×D311yescharacteristic
79C23×C3C23×C311yescharacteristic
80C2×C3×C4—22no—
81C2×C3×C4—22no—
82C2×C3×C4—21no—
83C2×C3×C4—22no—
84C2×C3×C4—21no—
85C2×C3×C4—21no—
86C2×C3×C4—21no—
87C2×C3×C4—22no—
88C2×C3×C4—22no—
89C2×C3×C4—22no—
90C2×C3×C4—21no—
91C2×C3×C4—21no—
92C2×C3×C4—22no—
93C2×C3×C4—22no—
94C2×C3×C4—22no—
95C2×C3×C4—34no—
96C2×C3×C4—42no—
97C2×C3×C4—42no—
98C2×C3×C4—62no—
99C2×C3×C4—62no—
100C2×C3×C4—62no—
101C2×C3×C4—62no—
102C2×C3×C4—62no—
103C2×C3×C4D1212yes—
104C2×C3×C4#6712yes—
105C2×C3×C4C3×D412yes—
106C2×C3×C4C3×D412yes—
107C2×Dic3—22no—
108C2×Dic3—22no—
109C2×Dic3—22no—
110C2×Dic3—22no—
111C2×Dic3—22no—
112C2×Dic3C3×Q814yes—
113C2×C32#12111yescharacteristic
114C2×C32C22⋊Q812yes—
115C2×C32#12311yescharacteristic
116C2×C32#12512yes—
117C2×C32C4⋊Q811yescharacteristic
118C22×C4—32no—
119C22×C4—32no—
120C22×C4C2×C3×D311yescharacteristic
121C22×C4C2×C3×D311yescharacteristic
122C22×C4C2×C3×D311yescharacteristic
123C4⋊C4—22no—
124C4⋊C4—64no—
125C4⋊C4—62no—
126C22×C3—21no—
127C22×C3—21no—
128C22×C3—22no—
129C22×C3—22no—
130C22×C3—21no—
131C22×C3C2×D1211yescharacteristic
132C22×C3#23511yescharacteristic
133C22×C3#23712yes—
134C22×C3D3×Q812yes—
135C22×C3C2×#6711yescharacteristic
136C22×C3C2×C3×D411yescharacteristic
137C22×C3C2×C3×D411yescharacteristic
138C22×C3C2×C3×Q812yes—
139C22×C3C3×#4111yescharacteristic
140C22×C3C3×#4112yes—
141C3×C4—24no—
142C3×C4—22no—
143C3×C4—22no—
144C3×C4—22no—
145C3×C4—22no—
146C3×C4—42no—
147C3×C4—42no—
148C3×C4—41no—
149C3×C4—41no—
150C3×C4—64no—
151C3×C4—122no—
152Dic3—24no—
153Dic3—42no—
154C32#39811yescharacteristic, complemented, Sylow
155C23C22×C3×D311yescharacteristic
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—34no—
162C2×C4—62no—
163C2×C4—62no—
164C2×C4—62no—
165C2×C4—62no—
166C2×C4—62no—
167C2×C4C3×D1212yes—
168C2×C4C3×#6712yes—
169C2×C3—22no—
170C2×C3—22no—
171C2×C3—21no—
172C2×C3—21no—
173C2×C3—21no—
174C2×C3#88912yes—
175C2×C3#89712yes—
176C2×C3#93011yescharacteristic
177C2×C3#93511yescharacteristic
178C2×C3#94411yescharacteristic
179C2×C3C3×#12111yescharacteristic
180C2×C3C3×C22⋊Q812yes—
181C2×C3C3×#12311yescharacteristic
182C2×C3C3×#12512yes—
183C2×C3C3×C4⋊Q811yescharacteristic
184C22C2×C3×D1211yescharacteristic
185C22C3×#23511yescharacteristic
186C22C3×#23712yes—
187C22C3×D3×Q812yes—
188C22C2×C3×#6711yescharacteristic
189C4—22no—
190C4—22no—
191C4—41no—
192C4—64no—
193C4—122no—
194C3—21no—
195C3#498111yescharacteristic, direct product factor
196C3C3×#39811yescharacteristic, complemented
197C2C3×#88912yes—
198C2C3×#89712yes—
199C2C3×#93011yescharacteristic
200C2C3×#93511yescharacteristic
201C2C3×#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. #4981C3direct (N × H)
154. C32#398semidirect
195. C3#4981direct (N × H)
196. 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×C4⋊Dic32
C2×C3×Dic3⋊C42
C3×C3⋊#952
C3×#3983
#49813