Finite Group Databasebeta

← #10591358

Subgroups — #10591358

Order 576.

346 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 106 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×C3×C4⋊Dic3C211yesmaximal, characteristic
3C2×Dic3⋊Dic3C212yesmaximal
4C3×C3⋊#95C211yesmaximal, characteristic
5#63579C212yesmaximal
6#4983—31nomaximal
7#4661—31nomaximal
8C22×C32×C4C2211yescharacteristic
9C22×C3⋊Dic3C2211yescharacteristic
10C22×C3⋊Dic3C2211yescharacteristic
11C22×C3×Dic3C2212yes—
12C22×C3×Dic3C2212yes—
13#3750—22no—
14C3×C4⋊Dic3—22no—
15Dic3⋊Dic3—24no—
16C2×C3×C4⋊C4—31no—
17C2×C4⋊Dic3—32no—
18C2×C4⋊Dic3D311yescharacteristic
19C2×Dic3⋊C4—31no—
20C2×Dic3⋊C4—31no—
21C2×Dic3⋊C4—32no—
22C2×Dic3⋊C4—61no—
23C3×#95—31no—
24C3⋊#95—32no—
25C3⋊#95—32no—
26C3⋊#95D311yescharacteristic
27C23×C32C2311yescharacteristic
28C2×C32×C4—22no—
29C2×C32×C4D412yes—
30C2×C3⋊Dic3—21no—
31C2×C3⋊Dic3—21no—
32C2×C3⋊Dic3—21no—
33C2×C3⋊Dic3—22no—
34C2×C3⋊Dic3D412yes—
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—91noSylow
42C22×C3×C4—21no—
43C22×C3×C4—32no—
44C22×C3×C4—32no—
45C22×C3×C4C2×D311yescharacteristic
46C22×C3×C4C2×D311yescharacteristic
47C22×Dic3—31no—
48C22×Dic3—31no—
49C22×Dic3—31no—
50C22×Dic3—31no—
51C22×Dic3—61no—
52C22×Dic3—61no—
53C22×Dic3C2×D312yes—
54C22×Dic3C2×D312yes—
55C3×C4⋊C4—62no—
56C4⋊Dic3—22no—
57C4⋊Dic3—64no—
58Dic3⋊C4—64no—
59Dic3⋊C4—64no—
60Dic3⋊C4—62no—
61Dic3⋊C4—62no—
62C22×C32C2×D411yescharacteristic
63C22×C32C2×D411yescharacteristic
64C22×C32C2×Q812yes—
65C22×C32#4112yes—
66C22×C32#4111yescharacteristic
67C32×C4—22no—
68C3⋊Dic3—22no—
69C3⋊Dic3—41no—
70C3×Dic3—24no—
71C3×Dic3—42no—
72C2×C4⋊C4—31no—
73C2×C4⋊C4—92no—
74C2×C4⋊C4—91no—
75#95—31no—
76#95—92no—
77C23×C3—21no—
78C23×C3C22×D311yescharacteristic
79C23×C3C22×D311yescharacteristic
80C2×C3×C4—22no—
81C2×C3×C4—22no—
82C2×C3×C4—22no—
83C2×C3×C4—34no—
84C2×C3×C4—42no—
85C2×C3×C4—62no—
86C2×C3×C4—62no—
87C2×C3×C4—62no—
88C2×C3×C4—62no—
89C2×C3×C4—62no—
90C2×C3×C4D1212yes—
91C2×C3×C4#6712yes—
92C2×Dic3—22no—
93C2×Dic3—22no—
94C2×Dic3—22no—
95C2×Dic3—22no—
96C2×Dic3—22no—
97C2×Dic3—32no—
98C2×Dic3—32no—
99C2×Dic3—62no—
100C2×Dic3—62no—
101C2×Dic3—62no—
102C2×Dic3—61no—
103C2×Dic3—61no—
104C2×Dic3—61no—
105C2×Dic3—61no—
106C2×Dic3—62no—
107C2×Dic3—61no—
108C2×Dic3—62no—
109C2×Dic3—62no—
110C2×Dic3—61no—
111C2×Dic3—122no—
112C2×Dic3Dic614yes—
113C2×C32#12111yescharacteristic
114C2×C32C22⋊Q812yes—
115C2×C32#12311yescharacteristic
116C2×C32#12512yes—
117C2×C32C4⋊Q811yescharacteristic
118C22×C4—32no—
119C22×C4—32no—
120C22×C4—91no—
121C22×C4—91no—
122C22×C4D3211yescharacteristic
123C4⋊C4—62no—
124C4⋊C4—184no—
125C4⋊C4—182no—
126C22×C3—22no—
127C22×C3—21no—
128C22×C3—21no—
129C22×C3—22no—
130C22×C3—21no—
131C22×C3C2×Dic612yes—
132C22×C3C2×D1211yescharacteristic
133C22×C3#23512yes—
134C22×C3D3×D411yescharacteristic
135C22×C3D3×D411yescharacteristic
136C22×C3#23711yescharacteristic
137C22×C3#23712yes—
138C22×C3D3×Q812yes—
139C22×C3#23911yescharacteristic
140C22×C3C2×#6711yescharacteristic
141C3×C4—22no—
142C3×C4—22no—
143C3×C4—42no—
144C3×C4—64no—
145C3×C4—122no—
146Dic3—24no—
147Dic3—42no—
148Dic3—64no—
149Dic3—62no—
150Dic3—62no—
151Dic3—122no—
152Dic3—121no—
153Dic3—121no—
154C32#39811yescharacteristic, complemented, Sylow
155C23C2×D3211yescharacteristic
156C2×C4—22no—
157C2×C4—34no—
158C2×C4—62no—
159C2×C4—62no—
160C2×C4—62no—
161C2×C4—62no—
162C2×C4—62no—
163C2×C4—92no—
164C2×C4—181no—
165C2×C4—181no—
166C2×C4—182no—
167C2×C4—181no—
168C2×C4#62612yes—
169C2×C3—22no—
170C2×C3—21no—
171C2×C3—22no—
172C2×C3—21no—
173C2×C3—21no—
174C2×C3#86911yescharacteristic
175C2×C3#87812yes—
176C2×C3#88611yescharacteristic
177C2×C3#88912yes—
178C2×C3#89012yes—
179C2×C3#89511yescharacteristic
180C2×C3#89612yes—
181C2×C3#92911yescharacteristic
182C2×C3#93811yescharacteristic
183C2×C3#94411yescharacteristic
184C22D3×Dic612yes—
185C22#379611yescharacteristic
186C22#380211yescharacteristic
187C22#380412yes—
188C22C2×#62611yescharacteristic
189C4—22no—
190C4—64no—
191C4—122no—
192C4—182no—
193C4—361no—
194C3—21no—
195C3#466111yescharacteristic, complemented
196C3#498311yescharacteristic, complemented
197C2#6384612yes—
198C2#6386611yescharacteristic
199C2#6389912yes—
200C2#6391611yescharacteristic
201C2#6396611yescharacteristic
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
154. C32#398semidirect
195. C3#4661semidirect
196. C3#4983semidirect

Maximal subgroups

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

subgroupindex
C2×#37502
C2×C3×C4⋊Dic32
C2×Dic3⋊Dic32
C3×C3⋊#952
#635792
#49833
#46613