Finite Group Databasebeta

← #10591585

Subgroups — #10591585

Order 576.

282 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 66 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×#3755C211yesmaximal, characteristic, complemented
2C3×#946C211yesmaximal, characteristic, complemented
3#63909C211yesmaximal, characteristic
4C2×D3×C3⋊C8C211yesmaximal, characteristic, complemented
5C3×#835C211yesmaximal, characteristic, complemented
6#63574C211yesmaximal, characteristic, complemented
7#63564C211yesmaximal, characteristic, complemented
8#5048—31nomaximal
9#4807—31nomaximal
10C2×C32×Q8C2211yescharacteristic
11C2×C4⋊(C3⋊D3)C2211yescharacteristic
12C2×C3×C4×D3C2211yescharacteristic
13C2×#626—21no—
14#3755—22no—
15C2×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×(C2×D3)⋊C4—21no—
17C3×C4⋊Dic3C2211yescharacteristic
18C3×C4⋊Dic3C2211yescharacteristic
19C3×Dic3⋊C4—21no—
20C2×C3×C3⋊C8C2211yescharacteristic
21#3722—21no—
22D3×C3⋊C8—22no—
23C3×C22⋊Q8—31no—
24#946D311yescharacteristic, complemented
25C2×#215—31no—
26C2×#215—31no—
27C2×#215—61no—
28#930—31no—
29C22×C3⋊C8—31no—
30C2×D3×C8—31no—
31#895—31no—
32C3×#103—31no—
33#835D311yescharacteristic, complemented
34#821—31no—
35#809—31no—
36#808—31no—
37#808—31no—
38C22×C3⋊D3—21no—
39C22×C3×D3D411yescharacteristic
40C32×Q8—21no—
41C32×Q8—21no—
42C2×C32×C4—21no—
43C2×C32×C4C2311yescharacteristic
44C4⋊(C3⋊D3)—21no—
45C4⋊(C3⋊D3)—21no—
46C2×C3×Dic3—21no—
47C2×C3×Dic3—21no—
48C2×C3×Dic3D411yescharacteristic
49C3×C4×D3—21no—
50C3×C4×D3—21no—
51#626—42no—
52C3⋊(C3⋊C8)D412yescomplemented
53C3×C3⋊C8—21no—
54#465—91noSylow
55C2×C3×Q8—21no—
56C2×C3×Q8C2×D311yescharacteristic
57C2×C3×Q8C2×D311yescharacteristic
58C22×C3×C4—31no—
59C2×#67—61no—
60C2×D12—31no—
61C2×D12—31no—
62C2×D12—61no—
63C2×D12—61no—
64C2×C4×D3C2×D311yescharacteristic
65C2×C3×C8—31no—
66C3×C4⋊C4—31no—
67C3×C4⋊C4—31no—
68C3×C4⋊C4—61no—
69C3×C22⋊C4—61no—
70#215—62no—
71#215—62no—
72#215—64no—
73(C2×D3)⋊C4—21no—
74(C2×D3)⋊C4—61no—
75(C2×D3)⋊C4—61no—
76C4⋊Dic3C2×D311yescharacteristic
77C4⋊Dic3C2×D311yescharacteristic
78Dic3⋊C4—21no—
79C2×C3⋊C8—31no—
80C2×C3⋊C8—31no—
81C2×C3⋊C8—61no—
82C2×C3⋊C8—62no—
83C2×C3⋊C8C2×D311yescharacteristic
84D3×C8—62no—
85C22×C32C2×D411yescharacteristic
86C2×C3⋊D3—41no—
87C2×C3⋊D3—41no—
88C2×C3⋊D3—41no—
89C2×C3×D3—21no—
90C2×C3×D3—21no—
91C2×C3×D3SD1612yescomplemented
92C32×C4—41no—
93C32×C4C2×D411yescharacteristic
94C32×C4#4111yescharacteristic
95C3×Dic3—21no—
96C3×Dic3—41no—
97C3×Dic3—41no—
98C2×SD16—91no—
99C22×C8—91no—
100C22⋊Q8—31no—
101#121—91no—
102#106—91no—
103#103—31no—
104#102—91no—
105C23×C3—31no—
106C22×D3—61no—
107C22×D3—61no—
108C22×D3—121no—
109C22×D3#6711yescharacteristic
110C3×Q8—22no—
111C3×Q8—21no—
112C3×Q8—21no—
113C3×Q8—21no—
114C3×Q8—21no—
115C3×Q8—41no—
116C2×C3×C4—21no—
117C2×C3×C4—21no—
118C2×C3×C4—21no—
119C2×C3×C4—31no—
120C2×C3×C4—41no—
121C2×C3×C4—61no—
122C2×C3×C4—61no—
123C2×C3×C4—61no—
124C2×C3×C4—61no—
125C2×C3×C4C22×D311yescharacteristic
126C2×C3×C4C22×D311yescharacteristic
127#67—122no—
128C2×Dic3—21no—
129C2×Dic3—21no—
130C2×Dic3#6711yescharacteristic
131D12—62no—
132D12—61no—
133D12—61no—
134D12—61no—
135D12—61no—
136D12—121no—
137D12—122no—
138C4×D3—21no—
139C4×D3—21no—
140C3×C8—61no—
141C3⋊C8—21no—
142C3⋊C8—32no—
143C3⋊C8—32no—
144C3⋊C8—62no—
145C2×C32#12111yescharacteristic
146C2×C32C2×SD1611yescharacteristic
147C2×C32#13511yescharacteristic
148C3⋊D3—81no—
149C3×D3—22no—
150C2×Q8D3211yescharacteristic
151C2×D4—91no—
152C2×D4—181no—
153C22×C4—31no—
154SD16—182no—
155C2×C8—31no—
156C2×C8—91no—
157C2×C8—182no—
158C4⋊C4—31no—
159C4⋊C4—31no—
160C4⋊C4—61no—
161C22⋊C4—61no—
162C22⋊C4—181no—
163C22×C3—21no—
164C22×C3—32no—
165C22×C3—61no—
166C22×C3—61no—
167C22×C3D3×D411yescharacteristic
168C22×C3C2×#6711yescharacteristic
169C2×D3—21no—
170C2×D3—21no—
171C2×D3—122no—
172C2×D3—121no—
173C2×D3—121no—
174C2×D3—121no—
175C2×D3—121no—
176C2×D3—121no—
177C2×D3—121no—
178C2×D3—241no—
179C2×D3—241no—
180C2×D3#21512yescomplemented
181C3×C4—21no—
182C3×C4—21no—
183C3×C4—42no—
184C3×C4—41no—
185C3×C4—41no—
186C3×C4—61no—
187C3×C4—121no—
188C3×C4—121no—
189C3×C4#23511yescharacteristic
190C3×C4D3×D411yescharacteristic
191C3×C4D3×D411yescharacteristic
192C3×C4#23711yescharacteristic
193Dic3—21no—
194Dic3—41no—
195Dic3—41no—
196C32#46511yescharacteristic, complemented, Sylow
197C23—31no—
198C23—181no—
199Q8—21no—
200Q8—21no—
201D4—181no—
202D4—181no—
203D4—362no—
204C2×C4—21no—
205C2×C4—31no—
206C2×C4—61no—
207C2×C4—61no—
208C2×C4—61no—
209C2×C4—61no—
210C2×C4C2×D3211yescharacteristic
211C8—61no—
212C8—92no—
213C2×C3—21no—
214C2×C3—21no—
215C2×C3—21no—
216C2×C3—62no—
217C2×C3#88411yescharacteristic
218C2×C3D3×SD1611yescharacteristic
219C2×C3#91911yescharacteristic
220C2×C3#93911yescharacteristic
221C2×C3C2×#21511yescharacteristic
222C2×C3#95011yescharacteristic
223D3—22no—
224D3—242no—
225D3—241no—
226D3—241no—
227C22—32no—
228C22—61no—
229C22—61no—
230C22—361no—
231C22—361no—
232C22—361no—
233C22D3×#6711yescharacteristic
234C4—41no—
235C4—61no—
236C4—121no—
237C4—121no—
238C4#380411yescharacteristic
239C4#381111yescharacteristic
240C3—21no—
241C3#480711yescharacteristic, complemented
242C3#504811yescharacteristic, complemented
243C2—62no—
244C2—721no—
245C2D3×#21511yescharacteristic
246C2#6394911yescharacteristic
247C2#6397111yescharacteristic
subgroupG/H
centerC22D3×#67
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
FittingC2×C32×Q8C22
socleC22×C32C2×D4
prime radical#63909C2
hypercenterC2×Q8D32
hypocenterC32#465
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#3755C2semidirect
2. C3×#946C2semidirect
4. C2×D3×C3⋊C8C2semidirect
5. C3×#835C2semidirect
6. #63574C2semidirect
7. #63564C2semidirect
24. #946D3semidirect
33. #835D3semidirect
52. C3⋊(C3⋊C8)D4semidirect
91. C2×C3×D3SD16semidirect
180. C2×D3#215semidirect
196. C32#465semidirect
241. C3#4807semidirect
242. C3#5048semidirect

Maximal subgroups

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

subgroupindex
C2×#37552
C3×#9462
#639092
C2×D3×C3⋊C82
C3×#8352
#635742
#635642
#50483
#48073