Finite Group Databasebeta

← #10591388

Subgroups — #10591388

Order 576.

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

normal subgroups only

This group has 522 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
1C22×#625C211yesmaximal, characteristic
2C2×#3750C211yesmaximal, characteristic, complemented
3C2×C3×(C2×D3)⋊C4C212yesmaximal, complemented
4C2×(C2×D3)⋊Dic3C212yesmaximal, complemented
5#63579C211yesmaximal, characteristic, complemented
6#4959—32nomaximal
7C23×C3×D3C2212yes—
8C22×C32×C4C2211yescharacteristic
9C22×C3⋊Dic3C2211yescharacteristic
10C22×C3⋊Dic3C2211yescharacteristic
11C22×C3×Dic3C2212yes—
12C2×#625—24no—
13C2×#625—22no—
14#3750—22no—
15C3×(C2×D3)⋊C4—24no—
16(C2×D3)⋊Dic3—24no—
17C22×#67—32no—
18C2×C3×C22⋊C4—32no—
19C2×#217—32no—
20C2×(C2×D3)⋊C4—32no—
21C2×(C2×D3)⋊C4D312yescomplemented
22C2×Dic3⋊C4—32no—
23C2×Dic3⋊C4—61no—
24C3⋊#95—32no—
25C23×C32C2311yescharacteristic
26C22×C3×D3—22no—
27C22×C3×D3—22no—
28C22×C3×D3—22no—
29C22×C3×D3—22no—
30C22×C3×D3—22no—
31C22×C3×D3—22no—
32C22×C3×D3D414yes—
33C2×C32×C4—21no—
34C2×C32×C4—22no—
35C2×C3⋊Dic3—21no—
36C2×C3⋊Dic3—21no—
37C2×C3⋊Dic3—22no—
38C2×C3⋊Dic3D412yes—
39C2×C3⋊Dic3D412yescomplemented
40C2×C3×Dic3—22no—
41C2×C3×Dic3—22no—
42C2×C3×Dic3—22no—
43#625—28no—
44#394—91noSylow
45C24×C3—32no—
46C23×D3C2×D312yes—
47C22×C3×C4—21no—
48C22×C3×C4—32no—
49C22×C3×C4C2×D312yes—
50C2×#67—64no—
51C2×#67—64no—
52C2×#67—64no—
53C22×Dic3—32no—
54C22×Dic3—32no—
55C22×Dic3—61no—
56C22×Dic3—61no—
57C22×Dic3C2×D312yes—
58C3×C22⋊C4—64no—
59#217—64no—
60(C2×D3)⋊C4—24no—
61(C2×D3)⋊C4—64no—
62Dic3⋊C4—64no—
63Dic3⋊C4—64no—
64C22×C32C2×D411yescharacteristic
65C22×C32C2×D411yescharacteristic
66C22×C32C2×D412yes—
67C22×C32#4111yescharacteristic
68C22×C32#4112yes—
69C2×C3×D3—24no—
70C2×C3×D3—24no—
71C2×C3×D3—24no—
72C2×C3×D3—42no—
73C2×C3×D3—42no—
74C2×C3×D3—42no—
75C2×C3×D3—42no—
76C32×C4—41no—
77C3⋊Dic3—22no—
78C3⋊Dic3—22no—
79C3×Dic3—42no—
80C22×D4—91no—
81C2×C4⋊C4—91no—
82C2×C22⋊C4—32no—
83C2×C22⋊C4—92no—
84#95—91no—
85C23×C3—21no—
86C23×C3—34no—
87C23×C3—62no—
88C23×C3—62no—
89C23×C3—62no—
90C23×C3—62no—
91C23×C3—62no—
92C23×C3—62no—
93C23×C3C22×D312yes—
94C22×D3—22no—
95C22×D3—22no—
96C22×D3—22no—
97C22×D3—22no—
98C22×D3—22no—
99C22×D3—22no—
100C22×D3#6714yes—
101C2×C3×C4—22no—
102C2×C3×C4—22no—
103C2×C3×C4—22no—
104C2×C3×C4—22no—
105C2×C3×C4—42no—
106C2×C3×C4—62no—
107C2×C3×C4—62no—
108C2×C3×C4—62no—
109#67—616no—
110C2×Dic3—22no—
111C2×Dic3—22no—
112C2×Dic3—22no—
113C2×Dic3—34no—
114C2×Dic3—34no—
115C2×Dic3—62no—
116C2×Dic3—62no—
117C2×Dic3—62no—
118C2×Dic3—62no—
119C2×Dic3—62no—
120C2×Dic3—62no—
121C2×Dic3—62no—
122C2×Dic3—62no—
123C2×Dic3—122no—
124C2×C32#12011yescharacteristic
125C2×C32#12111yescharacteristic
126C2×C32#12112yes—
127C2×C32#12312yes—
128C2×C32#12411yescharacteristic
129C3×D3—44no—
130C24—32no—
131C2×D4—182no—
132C2×D4—184no—
133C22×C4—32no—
134C22×C4—91no—
135C22×C4—91no—
136C22×C4D3211yescharacteristic
137C4⋊C4—182no—
138C22⋊C4—64no—
139C22⋊C4—184no—
140C22×C3—22no—
141C22×C3—21no—
142C22×C3—21no—
143C22×C3—22no—
144C22×C3—21no—
145C22×C3—64no—
146C22×C3—64no—
147C22×C3—64no—
148C22×C3—122no—
149C22×C3—122no—
150C22×C3—122no—
151C22×C3—122no—
152C22×C3#23512yes—
153C22×C3#23512yes—
154C22×C3D3×D412yes—
155C22×C3D3×D412yes—
156C22×C3D3×D412yes—
157C22×C3#23712yes—
158C22×C3C2×#6712yes—
159C2×D3—24no—
160C2×D3—24no—
161C2×D3—24no—
162C2×D3—42no—
163C2×D3—42no—
164C2×D3—42no—
165C2×D3—42no—
166C3×C4—42no—
167C3×C4—42no—
168C3×C4—122no—
169Dic3—42no—
170Dic3—64no—
171Dic3—64no—
172Dic3—64no—
173Dic3—122no—
174C32#39411yescharacteristic, complemented, Sylow
175C23—34no—
176C23—62no—
177C23—62no—
178C23—62no—
179C23—62no—
180C23—62no—
181C23—62no—
182C23C2×D3211yescharacteristic
183D4—188no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—62no—
187C2×C4—62no—
188C2×C4—62no—
189C2×C4—92no—
190C2×C4—92no—
191C2×C4—181no—
192C2×C4—182no—
193C2×C4—181no—
194C2×C3—22no—
195C2×C3—22no—
196C2×C3—21no—
197C2×C3—21no—
198C2×C3—21no—
199C2×C3—124no—
200C2×C3#88312yes—
201C2×C3#88412yes—
202C2×C3#88412yes—
203C2×C3#88512yes—
204C2×C3#92912yes—
205C2×C3#93712yes—
206C2×C3#93912yes—
207D3—44no—
208C22—64no—
209C22—64no—
210C22—64no—
211C22—122no—
212C22—122no—
213C22—122no—
214C22—122no—
215C22#379512yes—
216C22#379811yescharacteristic
217C22#380211yescharacteristic
218C22D3×#6712yes—
219C22#381111yescharacteristic
220C4—41no—
221C4—122no—
222C4—182no—
223C4—182no—
224C3—21no—
225C3#495912yescomplemented
226C2—124no—
227C2#6388512yes—
228C2#6390512yes—
229C2#6391211yescharacteristic
230C2#6391311yescharacteristic
231C2#6398311yescharacteristic
subgroupG/H
center, FrattiniC23C2×D32
commutator, socle, cosocleC23×C32C23
FittingC22×C32×C4C22
prime radicalC22×#625C2
hypercenterC22×C4D32
hypocenterC32#394
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#3750C2semidirect
3. C2×C3×(C2×D3)⋊C4C2semidirect
4. C2×(C2×D3)⋊Dic3C2semidirect
5. #63579C2semidirect
21. C2×(C2×D3)⋊C4D3semidirect
39. C2×C3⋊Dic3D4semidirect
174. C32#394semidirect
225. C3#4959semidirect

Maximal subgroups

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

subgroupindex
C22×#6252
C2×#37502
C2×C3×(C2×D3)⋊C42
C2×(C2×D3)⋊Dic32
#635792
#49593