Finite Group Databasebeta

← #10593874

Subgroups — #10593874

Order 576.

472 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 152 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#64079C211yesmaximal, characteristic, complemented
2C3×C42×D3C211yesmaximal, characteristic
3C3×#870C211yesmaximal, characteristic, complemented
4#63918C212yesmaximal, complemented
5#63851C214yesmaximal
6#63841C212yesmaximal
7#63837C214yesmaximal, complemented
8#5688—31nomaximal
9#5470—31nomaximal
10C2×C3×C4×D3C2212yes—
11C2×C3×C4×D3C2211yescharacteristic
12C2×#627C2214yes—
13C32×C42C2211yescharacteristic
14C4⋊(C3⋊Dic3)C2212yes—
15#3750C2214yes—
16C3×C4⋊Dic3C2212yes—
17C3×Dic3⋊C4C2214yes—
18C3×C4×Dic3C2212yes—
19C3×C4×Dic3C2211yescharacteristic
20Dic3⋊Dic3C2214yes—
21(C2×D3)⋊Dic3C2214yes—
22Dic32C2214yes—
23C3×#125—31no—
24C2×C3×C42—31no—
25#926—32no—
26#924—34no—
27#896—34no—
28#892—32no—
29#888—32no—
30#887—34no—
31C42×D3D311yescharacteristic
32#870—31no—
33#870—31no—
34#870—61no—
35#870D311yescharacteristic, complemented
36#869—32no—
37C4×Dic6—34no—
38C22×C3×D3C2311yescharacteristic
39C2×C32×C4C2312yes—
40C2×C32×C4C2311yescharacteristic
41C2×C3⋊Dic3C2314yes—
42C2×C3×Dic3C2314yes—
43C2×C3×Dic3C2311yescharacteristic
44C2×C3×Dic3C2312yes—
45C3×C4×D3—24no—
46C3×C4×D3Q814yescomplemented
47#627—28no—
48#533—91noSylow
49C22×C3×C4—31no—
50C22×C3×C4—32no—
51C2×C4×D3C2×D312yes—
52C2×C4×D3C2×D311yescharacteristic
53C2×Dic6—34no—
54C2×Dic6—34no—
55C3×C4⋊C4—34no—
56C3×C4⋊C4—32no—
57C3×C42—21no—
58C3×C42—32no—
59C3×C42—31no—
60C3×C42C2×D311yescharacteristic
61C3×C42C2×D311yescharacteristic
62#217—34no—
63(C2×D3)⋊C4—34no—
64C4⋊Dic3—32no—
65C4⋊Dic3—32no—
66C4⋊Dic3—34no—
67C4⋊Dic3—62no—
68C4⋊Dic3C2×D312yes—
69Dic3⋊C4—34no—
70Dic3⋊C4—34no—
71Dic3⋊C4—34no—
72Dic3⋊C4—64no—
73Dic3⋊C4C2×D314yes—
74C4×Dic3—34no—
75C4×Dic3—34no—
76C4×Dic3C2×D312yes—
77C4×Dic3C2×D311yescharacteristic
78C22×C32C2411yescharacteristic
79C2×C3×D3—22no—
80C2×C3×D3C2×Q812yes—
81C32×C4—22no—
82C32×C4C2×Q812yes—
83C3⋊Dic3—24no—
84C3×Dic3—24no—
85C3×Dic3C2×Q812yes—
86C3×Dic3#4114yes—
87C4⋊Q8—92no—
88#125—31no—
89#125—91no—
90C22⋊Q8—94no—
91C4×Q8—94no—
92#117—92no—
93C2×C42—31no—
94C23×C3—31no—
95C22×D3C22×D311yescharacteristic
96C2×C3×C4—21no—
97C2×C3×C4—22no—
98C2×C3×C4—31no—
99C2×C3×C4—32no—
100C2×C3×C4—34no—
101C2×C3×C4—34no—
102C2×C3×C4—64no—
103C2×C3×C4C22×D312yes—
104C2×C3×C4C22×D312yes—
105C2×C3×C4C22×D311yescharacteristic
106C2×C3×C4C22×D311yescharacteristic
107C2×Dic3—34no—
108C2×Dic3—34no—
109C2×Dic3—64no—
110C2×Dic3C22×D314yes—
111C2×Dic3C22×D311yescharacteristic
112C2×Dic3C22×D312yes—
113C4×D3—24no—
114C4×D3Dic614yescomplemented
115Dic6—68no—
116Dic6—68no—
117C2×C32C22×Q811yescharacteristic
118C2×C32C2×#4112yes—
119C3×D3—22no—
120C2×Q8—94no—
121C22×C4—31no—
122C22×C4—32no—
123C4⋊C4—32no—
124C4⋊C4—34no—
125C4⋊C4—94no—
126C4⋊C4—92no—
127C4⋊C4—94no—
128C22⋊C4—94no—
129C42—32no—
130C42—31no—
131C42—94no—
132C42D3211yescharacteristic
133C22×C3—21no—
134C22×C3—32no—
135C22×C3—62no—
136C22×C3C23×D311yescharacteristic
137C22×C3C23×D311yescharacteristic
138C2×D3—22no—
139C2×D3C2×Dic612yes—
140C3×C4—22no—
141C3×C4—22no—
142C3×C4—22no—
143C3×C4—32no—
144C3×C4—34no—
145C3×C4—42no—
146C3×C4—64no—
147C3×C4C2×Dic612yes—
148C3×C4D3×Q812yes—
149Dic3—24no—
150Dic3—64no—
151Dic3—64no—
152Dic3—124no—
153Dic3C2×Dic612yes—
154Dic3#23514yes—
155C32#53311yescharacteristic, complemented, Sylow
156C23—31no—
157Q8—188no—
158C2×C4—31no—
159C2×C4—32no—
160C2×C4—34no—
161C2×C4—34no—
162C2×C4—64no—
163C2×C4—94no—
164C2×C4C2×D3212yes—
165C2×C4C2×D3211yescharacteristic
166C2×C3—21no—
167C2×C3—22no—
168C2×C3—62no—
169C2×C3C22×Dic611yescharacteristic
170C2×C3C2×#23512yes—
171C2×C3C2×D3×Q811yescharacteristic
172C2×C3D3×#4112yes—
173D3—22no—
174C22—32no—
175C22—62no—
176C22C22×D3211yescharacteristic
177C4—22no—
178C4—32no—
179C4—34no—
180C4—64no—
181C4—184no—
182C4D3×Dic612yes—
183C3—21no—
184C3#547011yescharacteristic, complemented
185C3#568811yescharacteristic, complemented
186C2—62no—
187C2C2×D3×Dic611yescharacteristic
188C2D3×#23512yes—
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC32×C42C22
prime radicalC22×C3×D3C23
hypercenterC42D32
hypocenterC32#533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. #64079C2semidirect
3. C3×#870C2semidirect
4. #63918C2semidirect
7. #63837C2semidirect
35. #870D3semidirect
46. C3×C4×D3Q8semidirect
114. C4×D3Dic6semidirect
155. C32#533semidirect
184. C3#5470semidirect
185. C3#5688semidirect

Maximal subgroups

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

subgroupindex
#640792
C3×C42×D32
C3×#8702
#639182
#638512
#638412
#638372
#56883
#54703