Finite Group Databasebeta

← #10593935

Subgroups — #10593935

Order 576.

482 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 144 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
1#64081C211yesmaximal, characteristic
2C3×C4×Dic6C212yesmaximal, complemented
3C4×#627C212yesmaximal, complemented
4#63895C212yesmaximal
5#63888C212yesmaximal
6C4×#624C211yesmaximal, characteristic
7#63874C211yesmaximal, characteristic
8#63847C212yesmaximal, complemented
9#63839C212yesmaximal, complemented
10#5578—32nomaximal
11C2×C4×C3⋊D3C2211yescharacteristic
12C2×C3×Dic6C2212yes—
13C2×#627C2212yes—
14C2×#624C2212yes—
15C32×C42C2211yescharacteristic
16#3752C2212yes—
17#3750C2212yes—
18C4×C3⋊Dic3C2211yescharacteristic
19C3×C4⋊Dic3C2212yes—
20C3×Dic3⋊C4C2212yes—
21C3×Dic3⋊C4C2212yes—
22C3×C4×Dic3C2212yes—
23C3×C4×Dic3C2212yes—
24#3724C2212yes—
25#3724C2212yes—
26Dic3⋊Dic3C2212yes—
27Dic3⋊Dic3C2212yes—
28#3722C2211yescharacteristic
29#3722C2211yescharacteristic
30Dic32C2211yescharacteristic
31Dic32C2211yescharacteristic
32C3×C4×Q8—32no—
33#946—32no—
34#944—32no—
35#897—32no—
36#896—32no—
37#896—32no—
38#889—32no—
39#889—32no—
40#888—32no—
41#872—32no—
42#872—32no—
43#872—61no—
44C42×D3—32no—
45C4×Dic6—32no—
46C4×Dic6—32no—
47C4×Dic6D312yescomplemented
48C22×C3⋊D3C2311yescharacteristic
49C2×C32×C4C2312yes—
50C2×C32×C4C2311yescharacteristic
51C2×C3⋊Dic3C2312yes—
52C2×C3⋊Dic3C2311yescharacteristic
53C4×C3⋊D3Q814yescomplemented
54C2×C3×Dic3C2312yes—
55C2×C3×Dic3C2312yes—
56C2×C3×Dic3C2312yes—
57C2×C3×Dic3C2312yes—
58C3×Dic6—24no—
59#627—24no—
60#624—24no—
61#533—91noSylow
62C2×C3×Q8—32no—
63C2×C4×D3—32no—
64C2×C4×D3—32no—
65C2×C4×D3—32no—
66C2×C4×D3—61no—
67C2×Dic6—32no—
68C2×Dic6—32no—
69C2×Dic6C2×D312yes—
70C3×C4⋊C4—32no—
71C3×C4⋊C4—32no—
72C3×C4⋊C4—32no—
73C3×C42—21no—
74C3×C42—32no—
75C3×C42—32no—
76C3×C42C2×D312yes—
77(C2×D3)⋊C4—32no—
78(C2×D3)⋊C4—32no—
79(C2×D3)⋊C4—32no—
80(C2×D3)⋊C4—32no—
81(C2×D3)⋊C4—62no—
82C4⋊Dic3—32no—
83C4⋊Dic3—32no—
84C4⋊Dic3C2×D312yes—
85Dic3⋊C4—32no—
86Dic3⋊C4—32no—
87Dic3⋊C4—32no—
88Dic3⋊C4—32no—
89Dic3⋊C4—32no—
90Dic3⋊C4—32no—
91Dic3⋊C4—32no—
92Dic3⋊C4—32no—
93Dic3⋊C4—62no—
94Dic3⋊C4C2×D312yes—
95Dic3⋊C4C2×D312yes—
96C4×Dic3—32no—
97C4×Dic3—32no—
98C4×Dic3—32no—
99C4×Dic3—61no—
100C4×Dic3C2×D312yes—
101C4×Dic3C2×D312yes—
102C22×C32C2411yescharacteristic
103C2×C3⋊D3—22no—
104C2×C3⋊D3C2×Q812yes—
105C32×C4—22no—
106C32×C4C2×Q812yes—
107C3⋊Dic3—22no—
108C3⋊Dic3C2×Q812yes—
109C3×Dic3—22no—
110C3×Dic3—22no—
111C3×Dic3—22no—
112C3×Dic3#4114yes—
113C4⋊Q8—92no—
114#125—92no—
115C22⋊Q8—92no—
116C22⋊Q8—92no—
117C4×Q8—32no—
118C4×Q8—92no—
119#117—91no—
120#117—91no—
121C2×C42—91no—
122C22×D3—32no—
123C22×D3—61no—
124C3×Q8—64no—
125C2×C3×C4—22no—
126C2×C3×C4—21no—
127C2×C3×C4—32no—
128C2×C3×C4—32no—
129C2×C3×C4—32no—
130C2×C3×C4—32no—
131C2×C3×C4C22×D312yes—
132C2×C3×C4C22×D312yes—
133C2×C3×C4C22×D312yes—
134C2×Dic3—32no—
135C2×Dic3—32no—
136C2×Dic3—32no—
137C2×Dic3—61no—
138C2×Dic3—62no—
139C2×Dic3C22×D312yes—
140C2×Dic3C22×D312yes—
141C2×Dic3C22×D312yes—
142C2×Dic3C22×D312yes—
143C4×D3—38no—
144C4×D3—64no—
145C4×D3—64no—
146C4×D3—64no—
147Dic6—24no—
148Dic6—64no—
149Dic6—64no—
150C2×C32C22×Q811yescharacteristic
151C2×C32C2×#4112yes—
152C3⋊D3—22no—
153C2×Q8—32no—
154C2×Q8—92no—
155C22×C4—92no—
156C22×C4—91no—
157C4⋊C4—32no—
158C4⋊C4—32no—
159C4⋊C4—32no—
160C4⋊C4—92no—
161C4⋊C4—92no—
162C4⋊C4—92no—
163C4⋊C4—92no—
164C4⋊C4—92no—
165C22⋊C4—91no—
166C22⋊C4—91no—
167C22⋊C4—92no—
168C42—32no—
169C42—32no—
170C42—91no—
171C42—91no—
172C42—91no—
173C42D3211yescharacteristic
174C22×C3—21no—
175C22×C3C23×D312yes—
176C2×D3—34no—
177C2×D3—62no—
178C2×D3—62no—
179C2×D3—62no—
180C2×D3—122no—
181C3×C4—22no—
182C3×C4—22no—
183C3×C4—22no—
184C3×C4—34no—
185C3×C4—42no—
186C3×C4—62no—
187C3×C4—62no—
188C3×C4—62no—
189C3×C4D3×Q814yes—
190Dic3—22no—
191Dic3—22no—
192Dic3—22no—
193Dic3—34no—
194Dic3—62no—
195Dic3—62no—
196Dic3—62no—
197Dic3—122no—
198Dic3#23514yes—
199C32#53311yescharacteristic, complemented, Sylow
200C23—91no—
201Q8—64no—
202Q8—184no—
203C2×C4—32no—
204C2×C4—32no—
205C2×C4—32no—
206C2×C4—32no—
207C2×C4—91no—
208C2×C4—94no—
209C2×C4—92no—
210C2×C4—184no—
211C2×C4C2×D3212yes—
212C2×C4C2×D3211yescharacteristic
213C2×C3—21no—
214C2×C3—22no—
215C2×C3C2×#23512yes—
216C2×C3C2×D3×Q812yes—
217C2×C3D3×#4112yes—
218D3—64no—
219D3—122no—
220C22—92no—
221C22—182no—
222C22C22×D3211yescharacteristic
223C4—22no—
224C4—34no—
225C4—62no—
226C4—62no—
227C4—62no—
228C4—92no—
229C4—182no—
230C4#379712yes—
231C3—21no—
232C3#557812yescomplemented
233C2—182no—
234C2C2×#379711yescharacteristic
235C2D3×#23512yes—
subgroupG/H
centerC2×C4C2×D32
commutator, socle, cosocleC22×C32C24
FrattiniC22C22×D32
FittingC32×C42C22
prime radicalC22×C3⋊D3C23
hypercenterC42D32
hypocenterC32#533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C3×C4×Dic6C2semidirect
3. C4×#627C2semidirect
8. #63847C2semidirect
9. #63839C2semidirect
47. C4×Dic6D3semidirect
53. C4×C3⋊D3Q8semidirect
199. C32#533semidirect
232. C3#5578semidirect

Maximal subgroups

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

subgroupindex
#640812
C3×C4×Dic62
C4×#6272
#638952
#638882
C4×#6242
#638742
#638472
#638392
#55783