Finite Group Databasebeta

← #10590529

Subgroups — #10590529

Order 576.

254 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 60 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
1C4⋊C4×C3⋊D3C211yesmaximal, characteristic
2#63871C211yesmaximal, characteristic
3C3×#810C211yesmaximal, characteristic, complemented
4C3×#808C211yesmaximal, characteristic, complemented
5#63573C211yesmaximal, characteristic, complemented
6#63566C211yesmaximal, characteristic, complemented
7#63557C211yesmaximal, characteristic
8#4862—31nomaximal
9#4805—31nomaximal
10C2×C4×C3⋊D3—21no—
11C2×C4×C3⋊D3C2211yescharacteristic
12C2×C3×Dic6C2211yescharacteristic
13C32×C4⋊C4C2211yescharacteristic
14C4⋊(C3⋊Dic3)C2211yescharacteristic
15#3750—21no—
16C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C3⋊C8C2211yescharacteristic
18C2×C3×C3⋊C8C2211yescharacteristic
19Dic3⋊Dic3—21no—
20#3722—21no—
21#946—31no—
22#897—31no—
23D3×C4⋊C4—31no—
24D3×C4⋊C4—31no—
25D3×C4⋊C4—61no—
26C3×#106—31no—
27C3×#103—31no—
28#835—31no—
29(C2×D3)⋊C8—31no—
30(C2×D3)⋊C8—31no—
31#817—31no—
32#816—31no—
33#810D311yescharacteristic, complemented
34#808—31no—
35#808D311yescharacteristic, complemented
36C22×C3⋊D3D411yescharacteristic
37C2×C32×C4—21no—
38C2×C32×C4C2311yescharacteristic
39C2×C3⋊Dic3—21no—
40C2×C3⋊Dic3D411yescharacteristic
41C4×C3⋊D3—21no—
42C4×C3⋊D3—21no—
43C4×C3⋊D3—42no—
44C2×C3×Dic3—21no—
45C2×C3×Dic3—21no—
46C3×Dic6—21no—
47C3×Dic6—21no—
48C3×C3⋊C8—21no—
49C3×C3⋊C8—21no—
50#483—91noSylow
51C2×C3×Q8—31no—
52C2×C4×D3—31no—
53C2×C4×D3—31no—
54C2×C4×D3—61no—
55C2×C4×D3—61no—
56C2×C4×D3—61no—
57C2×C4×D3—62no—
58C2×Dic6C2×D311yescharacteristic
59C2×C3×C8—31no—
60C2×C3×C8—31no—
61C3×C4⋊C4—21no—
62C3×C4⋊C4—31no—
63C3×C4⋊C4C2×D311yescharacteristic
64C3×C4⋊C4C2×D311yescharacteristic
65(C2×D3)⋊C4—61no—
66(C2×D3)⋊C4—61no—
67C4⋊Dic3—31no—
68C4⋊Dic3—31no—
69C4⋊Dic3—61no—
70C4⋊Dic3—61no—
71C4⋊Dic3C2×D311yescharacteristic
72Dic3⋊C4—61no—
73Dic3⋊C4—61no—
74Dic3⋊C4—61no—
75Dic3⋊C4—62no—
76C2×C3⋊C8C2×D311yescharacteristic
77C2×C3⋊C8C2×D311yescharacteristic
78C22×C32C2×D411yescharacteristic
79C2×C3⋊D3—21no—
80C2×C3⋊D3—21no—
81C2×C3⋊D3SD1612yes—
82C32×C4—41no—
83C32×C4#4111yescharacteristic
84C32×C4#4111yescharacteristic
85C3⋊Dic3—21no—
86C3⋊Dic3—41no—
87C3×Dic3—41no—
88C3×Dic3—41no—
89C22⋊Q8—91no—
90C2×C4⋊C4—91no—
91#106—31no—
92#106—91no—
93#103—31no—
94#103—91no—
95C22⋊C8—91no—
96C22×D3—31no—
97C22×D3—31no—
98C22×D3—61no—
99C3×Q8—61no—
100C3×Q8—61no—
101C2×C3×C4—22no—
102C2×C3×C4—21no—
103C2×C3×C4—21no—
104C2×C3×C4—21no—
105C2×C3×C4—61no—
106C2×C3×C4—61no—
107C2×C3×C4C22×D311yescharacteristic
108C2×C3×C4C22×D311yescharacteristic
109C2×Dic3—21no—
110C2×Dic3—21no—
111C2×Dic3—31no—
112C2×Dic3—31no—
113C2×Dic3—61no—
114C2×Dic3—62no—
115C2×Dic3—61no—
116C2×Dic3—61no—
117C4×D3—62no—
118C4×D3—62no—
119C4×D3—61no—
120C4×D3—61no—
121C4×D3—61no—
122C4×D3—61no—
123C4×D3—122no—
124C4×D3—122no—
125C4×D3—124no—
126Dic6—21no—
127Dic6—21no—
128C3×C8—61no—
129C3×C8—61no—
130C3⋊C8—21no—
131C3⋊C8—21no—
132C2×C32#12311yescharacteristic
133C2×C32C2×SD1611yescharacteristic
134C2×C32#13711yescharacteristic
135C3⋊D3—22no—
136C2×Q8—31no—
137C22×C4—91no—
138C22×C4—181no—
139C2×C8—31no—
140C2×C8—31no—
141C4⋊C4—31no—
142C4⋊C4—91no—
143C4⋊C4—181no—
144C4⋊C4—181no—
145C4⋊C4D3211yescharacteristic
146C22⋊C4—181no—
147C22×C3—21no—
148C22×C3D3×D411yescharacteristic
149C22×C3D3×D411yescharacteristic
150C2×D3—32no—
151C2×D3—32no—
152C2×D3—62no—
153C2×D3—62no—
154C2×D3—62no—
155C2×D3—61no—
156C2×D3—61no—
157C2×D3—61no—
158C2×D3—61no—
159C3×C4—21no—
160C3×C4—21no—
161C3×C4—42no—
162C3×C4—41no—
163C3×C4—41no—
164C3×C4—121no—
165C3×C4—121no—
166C3×C4#23511yescharacteristic
167C3×C4#23511yescharacteristic
168C3×C4#23711yescharacteristic
169C3×C4#23911yescharacteristic
170Dic3—41no—
171Dic3—41no—
172Dic3—62no—
173Dic3—61no—
174Dic3—61no—
175Dic3—122no—
176Dic3—121no—
177Dic3—121no—
178C32#48311yescharacteristic, complemented, Sylow
179C23—91no—
180Q8—61no—
181Q8—61no—
182C2×C4—21no—
183C2×C4—61no—
184C2×C4—61no—
185C2×C4—91no—
186C2×C4—181no—
187C2×C4—181no—
188C2×C4—181no—
189C2×C4—362no—
190C2×C4C2×D3211yescharacteristic
191C8—61no—
192C8—61no—
193C2×C3—21no—
194C2×C3—21no—
195C2×C3—21no—
196C2×C3#88311yescharacteristic
197C2×C3#89411yescharacteristic
198C2×C3D3×SD1611yescharacteristic
199C2×C3D3×SD1611yescharacteristic
200C2×C3#91511yescharacteristic
201C2×C3#91811yescharacteristic
202D3—64no—
203D3—62no—
204D3—62no—
205C22—92no—
206C22—181no—
207C22—181no—
208C22#381111yescharacteristic
209C4—41no—
210C4—121no—
211C4—121no—
212C4—181no—
213C4—361no—
214C4#379611yescharacteristic
215C4#379811yescharacteristic
216C3—21no—
217C3#480511yescharacteristic, complemented
218C3#486211yescharacteristic, complemented
219C2—182no—
220C2#6385311yescharacteristic
221C2#6393011yescharacteristic
222C2#6395111yescharacteristic
subgroupG/H
centerC22#3811
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
FittingC32×C4⋊C4C22
socleC22×C32C2×D4
prime radicalC22×C3⋊D3D4
hypercenterC4⋊C4D32
hypocenterC32#483
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C3×#810C2semidirect
4. C3×#808C2semidirect
5. #63573C2semidirect
6. #63566C2semidirect
33. #810D3semidirect
35. #808D3semidirect
178. C32#483semidirect
217. C3#4805semidirect
218. C3#4862semidirect

Maximal subgroups

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

subgroupindex
C4⋊C4×C3⋊D32
#638712
C3×#8102
C3×#8082
#635732
#635662
#635572
#48623
#48053