Finite Group Databasebeta

← #10594030

Subgroups — #10594030

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#64086C211yesmaximal, characteristic
2C3×#878C212yesmaximal
3#63964C212yesmaximal
4#63957C211yesmaximal, characteristic
5C2×Dic32C211yesmaximal, characteristic
6#63847C212yesmaximal, complemented
7#63843C212yesmaximal, complemented
8#63839C212yesmaximal, complemented
9#63838C212yesmaximal, complemented
10#5622—32nomaximal
11C22×C3⋊Dic3C2211yescharacteristic
12C22×C3×Dic3C2212yes—
13C2×C3×Dic6C2212yes—
14C2×#627C2212yes—
15C32×C22⋊C4C2211yescharacteristic
16#3757C2211yescharacteristic
17#3750C2212yes—
18C4×C3⋊Dic3C2212yes—
19C3×#217C2212yes—
20C3×C4⋊Dic3C2212yes—
21C3×Dic3⋊C4C2212yes—
22C3×Dic3⋊C4C2212yes—
23#3724C2212yes—
24#3724C2212yes—
25Dic3⋊Dic3C2212yes—
26Dic3⋊Dic3C2212yes—
27Dic32C2211yescharacteristic
28Dic32C2212yes—
29Dic32C2211yescharacteristic
30Dic32C2211yescharacteristic
31Dic32C2211yescharacteristic
32C3×C22⋊Q8—32no—
33Q8×Dic3—32no—
34#944—32no—
35#924—32no—
36C2×C4×Dic3—32no—
37#889—32no—
38#889—32no—
39#888—32no—
40#887—32no—
41#887—32no—
42#887—32no—
43#878—32no—
44#878D312yes—
45#877—32no—
46#877—32no—
47#877—61no—
48C23×C32C2311yescharacteristic
49C2×C32×C4C2312yes—
50C2×C3⋊Dic3Q814yescomplemented
51C2×C3⋊Dic3C2312yes—
52C2×C3⋊Dic3C2311yescharacteristic
53C2×C3⋊Dic3C2311yescharacteristic
54C2×C3×Dic3—24no—
55C2×C3×Dic3C2312yes—
56C2×C3×Dic3C2312yes—
57C2×C3×Dic3C2312yes—
58C2×C3×Dic3C2312yes—
59C3×Dic6—24no—
60#627—24no—
61#533—91noSylow
62C2×C3×Q8—32no—
63C22×C3×C4—32no—
64C22×Dic3—32no—
65C22×Dic3—61no—
66C22×Dic3C2×D312yes—
67C2×Dic6—32no—
68C2×Dic6—32no—
69C2×Dic6C2×D312yes—
70C3×C4⋊C4—32no—
71C3×C4⋊C4—32no—
72C3×C4⋊C4—32no—
73C3×C22⋊C4—21no—
74C3×C22⋊C4—32no—
75C3×C22⋊C4C2×D312yes—
76#217—32no—
77#217—61no—
78#217C2×D312yes—
79C4⋊Dic3—32no—
80C4⋊Dic3—32no—
81C4⋊Dic3C2×D312yes—
82Dic3⋊C4—32no—
83Dic3⋊C4—32no—
84Dic3⋊C4—32no—
85Dic3⋊C4—32no—
86Dic3⋊C4—32no—
87Dic3⋊C4—32no—
88Dic3⋊C4—32no—
89Dic3⋊C4—32no—
90Dic3⋊C4—62no—
91Dic3⋊C4C2×D312yes—
92Dic3⋊C4C2×D312yes—
93C4×Dic3—32no—
94C4×Dic3—32no—
95C4×Dic3—32no—
96C4×Dic3—32no—
97C4×Dic3—32no—
98C4×Dic3—32no—
99C4×Dic3—32no—
100C4×Dic3—32no—
101C4×Dic3—62no—
102C22×C32—22no—
103C22×C32C2×Q812yes—
104C22×C32C2411yescharacteristic
105C32×C4—22no—
106C3⋊Dic3—22no—
107C3⋊Dic3C2×Q812yes—
108C3⋊Dic3C2×Q812yes—
109C3×Dic3—22no—
110C3×Dic3—22no—
111C3×Dic3—22no—
112C3×Dic3#4114yes—
113C4⋊Q8—92no—
114#125—92no—
115C22⋊Q8—32no—
116C22⋊Q8—92no—
117C4×Q8—92no—
118C4×Q8—92no—
119#117—91no—
120#117—91no—
121C2×C42—91no—
122C23×C3—21no—
123C23×C3C22×D312yes—
124C3×Q8—64no—
125C2×C3×C4—22no—
126C2×C3×C4—32no—
127C2×C3×C4—32no—
128C2×C3×C4—32no—
129C2×C3×C4—32no—
130C2×C3×C4—64no—
131C2×C3×C4C22×D312yes—
132C2×C3×C4C22×D312yes—
133C2×Dic3—24no—
134C2×Dic3—38no—
135C2×Dic3—32no—
136C2×Dic3—32no—
137C2×Dic3—32no—
138C2×Dic3—32no—
139C2×Dic3—64no—
140C2×Dic3—61no—
141C2×Dic3—61no—
142C2×Dic3—62no—
143C2×Dic3C22×D312yes—
144C2×Dic3C22×D312yes—
145C2×Dic3C22×D312yes—
146C2×Dic3C22×D312yes—
147Dic6—24no—
148Dic6—64no—
149Dic6—64no—
150C2×C32—22no—
151C2×C32C22×Q811yescharacteristic
152C2×C32C2×#4112yes—
153C2×Q8—32no—
154C2×Q8—92no—
155C22×C4—32no—
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—32no—
166C22⋊C4—91no—
167C22⋊C4D3211yescharacteristic
168C42—92no—
169C42—91no—
170C42—91no—
171C42—91no—
172C42—91no—
173C42—92no—
174C22×C3—22no—
175C22×C3—22no—
176C22×C3—21no—
177C22×C3—22no—
178C22×C3—42no—
179C22×C3D3×Q814yes—
180C22×C3C23×D312yes—
181C3×C4—22no—
182C3×C4—22no—
183C3×C4—34no—
184C3×C4—42no—
185C3×C4—62no—
186C3×C4—62no—
187C3×C4—62no—
188Dic3—22no—
189Dic3—22no—
190Dic3—22no—
191Dic3—34no—
192Dic3—34no—
193Dic3—62no—
194Dic3—62no—
195Dic3—62no—
196Dic3—62no—
197Dic3—122no—
198Dic3#23714yes—
199C32#53311yescharacteristic, complemented, Sylow
200C23C2×D3211yescharacteristic
201Q8—64no—
202Q8—184no—
203C2×C4—32no—
204C2×C4—32no—
205C2×C4—32no—
206C2×C4—32no—
207C2×C4—64no—
208C2×C4—91no—
209C2×C4—91no—
210C2×C4—94no—
211C2×C4—92no—
212C2×C4C2×D3212yes—
213C2×C3—24no—
214C2×C3—21no—
215C2×C3—22no—
216C2×C3—42no—
217C2×C3C2×#23712yes—
218C2×C3C2×D3×Q812yes—
219C2×C3D3×#4112yes—
220C22—22no—
221C22#379712yes—
222C22C22×D3211yescharacteristic
223C4—22no—
224C4—34no—
225C4—62no—
226C4—62no—
227C4—62no—
228C4—92no—
229C4—92no—
230C4—182no—
231C3—21no—
232C3#562212yescomplemented
233C2—22no—
234C2C2×#379711yescharacteristic
235C2D3×#23712yes—
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC32×C22⋊C4C22
prime radicalC23×C32C23
hypercenterC22⋊C4D32
hypocenterC32#533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
6. #63847C2semidirect
7. #63843C2semidirect
8. #63839C2semidirect
9. #63838C2semidirect
50. C2×C3⋊Dic3Q8semidirect
199. C32#533semidirect
232. C3#5622semidirect

Maximal subgroups

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

subgroupindex
#640862
C3×#8782
#639642
#639572
C2×Dic322
#638472
#638432
#638392
#638382
#56223