Finite Group Databasebeta

← #10591580

Subgroups — #10591580

Order 576.

250 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 64 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#64153C211yesmaximal, characteristic
2C2×C3×#216C211yesmaximal, characteristic
3#63843C211yesmaximal, characteristic
4C2×#3719C211yesmaximal, characteristic
5C3×#835C211yesmaximal, characteristic
6#63572C211yesmaximal, characteristic
7#63567C211yesmaximal, characteristic
8#5182—31nomaximal
9#4795—31nomaximal
10C2×C32×Q8C2211yescharacteristic
11C2×#634C2211yescharacteristic
12C2×C3×Dic6C2211yescharacteristic
13#3750—21no—
14#3750—21no—
15C4×C3⋊Dic3C2211yescharacteristic
16C3×#216—22no—
17C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C3⋊C8C2211yescharacteristic
19C2×C3×C3⋊C8C2211yescharacteristic
20Dic3⋊Dic3—21no—
21Dic32—21no—
22#3719—22no—
23C2×C3×Q16—31no—
24Q8×Dic3—31no—
25#944—31no—
26#944—31no—
27#944—61no—
28C2×#216—31no—
29C2×#216D311yescharacteristic
30C2×Dic12—31no—
31#887—31no—
32C3×#103—31no—
33#835D311yescharacteristic
34#816—31no—
35Dic3⋊C8—31no—
36Dic3⋊C8—31no—
37#810—31no—
38C32×Q8—21no—
39C32×Q8—21no—
40C2×C32×C4—21no—
41C2×C32×C4C2311yescharacteristic
42C2×C3⋊Dic3—21no—
43C2×C3⋊Dic3D411yescharacteristic
44C2×C3⋊Dic3D411yescharacteristic
45#634—21no—
46#634—21no—
47C2×C3×Dic3—21no—
48C2×C3×Dic3—21no—
49C3×Dic6—21no—
50C3×Dic6D412yes—
51C3×C3⋊C8—21no—
52C3×C3⋊C8—21no—
53#462—91noSylow
54C2×C3×Q8—21no—
55C2×C3×Q8—31no—
56C2×C3×Q8C2×D311yescharacteristic
57C2×C3×Q8C2×D311yescharacteristic
58C2×Dic6—31no—
59C2×Dic6—31no—
60C2×Dic6—61no—
61C2×Dic6C2×D311yescharacteristic
62C3×Q16—62no—
63C2×C3×C8—31no—
64C2×C3×C8—31no—
65C3×C4⋊C4—31no—
66#216—22no—
67#216—62no—
68C4⋊Dic3—61no—
69C4⋊Dic3C2×D311yescharacteristic
70Dic3⋊C4—61no—
71Dic3⋊C4—61no—
72Dic3⋊C4—61no—
73Dic3⋊C4—61no—
74Dic3⋊C4—61no—
75Dic3⋊C4—62no—
76Dic3⋊C4—62no—
77C4×Dic3—31no—
78C4×Dic3—31no—
79C4×Dic3—61no—
80C4×Dic3—61no—
81C4×Dic3—61no—
82C2×C3⋊C8C2×D311yescharacteristic
83C2×C3⋊C8C2×D311yescharacteristic
84Dic12—62no—
85C22×C32C2×D411yescharacteristic
86C32×C4—41no—
87C32×C4C2×D411yescharacteristic
88C32×C4#4111yescharacteristic
89C3⋊Dic3—21no—
90C3⋊Dic3—41no—
91C3⋊Dic3Q1612yescomplemented
92C3×Dic3—22no—
93C3×Dic3—41no—
94C2×Q16—31no—
95C2×Q16—91no—
96C4⋊Q8—91no—
97C4×Q8—91no—
98C4⋊C8—91no—
99#103—31no—
100#103—91no—
101C3×Q8—21no—
102C3×Q8—21no—
103C3×Q8—21no—
104C3×Q8—21no—
105C3×Q8—32no—
106C3×Q8—41no—
107C3×Q8—41no—
108C3×Q8—61no—
109C2×C3×C4—22no—
110C2×C3×C4—21no—
111C2×C3×C4—21no—
112C2×C3×C4—21no—
113C2×C3×C4—61no—
114C2×C3×C4—61no—
115C2×C3×C4C22×D311yescharacteristic
116C2×C3×C4C22×D311yescharacteristic
117C2×Dic3—21no—
118C2×Dic3—21no—
119C2×Dic3—31no—
120C2×Dic3—31no—
121C2×Dic3—31no—
122C2×Dic3—31no—
123C2×Dic3—61no—
124C2×Dic3—61no—
125C2×Dic3—62no—
126C2×Dic3—61no—
127C2×Dic3—61no—
128Dic6—21no—
129Dic6—61no—
130Dic6—61no—
131Dic6—61no—
132Dic6—61no—
133Dic6—121no—
134Dic6—121no—
135Dic6#6712yes—
136C3×C8—61no—
137C3×C8—61no—
138C3⋊C8—21no—
139C3⋊C8—21no—
140C2×C32#12111yescharacteristic
141C2×C32C2×Q1611yescharacteristic
142C2×C32#13711yescharacteristic
143C2×Q8—31no—
144C2×Q8—91no—
145C2×Q8D3211yescharacteristic
146Q16—62no—
147Q16—182no—
148C2×C8—31no—
149C2×C8—31no—
150C4⋊C4—31no—
151C4⋊C4—181no—
152C4⋊C4—181no—
153C4⋊C4—181no—
154C42—91no—
155C42—181no—
156C22×C3—21no—
157C22×C3D3×D411yescharacteristic
158C22×C3D3×D411yescharacteristic
159C3×C4—21no—
160C3×C4—21no—
161C3×C4—42no—
162C3×C4—41no—
163C3×C4—41no—
164C3×C4—62no—
165C3×C4—121no—
166C3×C4#23511yescharacteristic
167C3×C4D3×D411yescharacteristic
168C3×C4#23711yescharacteristic
169C3×C4C2×#6711yescharacteristic
170Dic3—22no—
171Dic3—32no—
172Dic3—32no—
173Dic3—41no—
174Dic3—62no—
175Dic3—62no—
176Dic3—61no—
177Dic3—61no—
178Dic3—122no—
179Dic3—121no—
180Dic3—121no—
181C32#46211yescharacteristic, complemented, Sylow
182Q8—21no—
183Q8—21no—
184Q8—32no—
185Q8—61no—
186Q8—181no—
187Q8—181no—
188C2×C4—21no—
189C2×C4—61no—
190C2×C4—61no—
191C2×C4—91no—
192C2×C4—91no—
193C2×C4—181no—
194C2×C4C2×D3211yescharacteristic
195C8—61no—
196C8—61no—
197C2×C3—21no—
198C2×C3—21no—
199C2×C3—21no—
200C2×C3#88411yescharacteristic
201C2×C3#91511yescharacteristic
202C2×C3D3×Q1611yescharacteristic
203C2×C3D3×Q1611yescharacteristic
204C2×C3#91811yescharacteristic
205C2×C3#93911yescharacteristic
206C22#381111yescharacteristic
207C4—41no—
208C4—62no—
209C4—92no—
210C4—121no—
211C4—181no—
212C4—361no—
213C4#380411yescharacteristic
214C4D3×#6711yescharacteristic
215C3—21no—
216C3#479511yescharacteristic, complemented
217C3#518211yescharacteristic, complemented
218C2#6394411yescharacteristic
219C2#6395111yescharacteristic
220C2#6397111yescharacteristic
subgroupG/H
centerC22#3811
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
FittingC2×C32×Q8C22
socle, prime radicalC22×C32C2×D4
hypercenterC2×Q8D32
hypocenterC32#462
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
91. C3⋊Dic3Q16semidirect
181. C32#462semidirect
216. C3#4795semidirect
217. C3#5182semidirect

Maximal subgroups

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

subgroupindex
#641532
C2×C3×#2162
#638432
C2×#37192
C3×#8352
#635722
#635672
#51823
#47953