Finite Group Databasebeta

← #10594595

Subgroups — #10594595

Order 576.

435 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 435 conjugacy classes of subgroups — too many to draw. Only its 142 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#64096C211yesmaximal, characteristic
2C3×#887C212yesmaximal
3C4×#627C212yesmaximal
4C4×#627C211yesmaximal, characteristic
5#63873C211yesmaximal, characteristic
6#63870C212yesmaximal
7#63867C214yesmaximal
8#63866C212yesmaximal
9#5567—32nomaximal
10C2×#634C2211yescharacteristic
11C2×C3×Dic6C2212yes—
12C2×#627C2211yescharacteristic
13C32×C4⋊C4C2211yescharacteristic
14#3750C2212yes—
15C4×C3⋊Dic3C2212yes—
16C4×C3⋊Dic3C2211yescharacteristic
17C3×Dic3⋊C4C2214yes—
18C3×C4×Dic3C2212yes—
19C3×C4×Dic3C2214yes—
20#3724C2212yes—
21#3724C2211yescharacteristic
22#3724C2212yes—
23Dic3⋊Dic3C2214yes—
24Dic3⋊Dic3C2214yes—
25Dic3⋊Dic3C2212yes—
26C3×C4×Q8—32no—
27#944—32no—
28#944—32no—
29#889—34no—
30#889—34no—
31#887—32no—
32#887—61no—
33#887D312yes—
34#870—34no—
35#869—32no—
36C4×Dic6—34no—
37C4×Dic6—32no—
38C2×C32×C4C2312yes—
39C2×C32×C4C2311yescharacteristic
40C2×C3⋊Dic3C2312yes—
41C2×C3⋊Dic3C2311yescharacteristic
42C2×C3⋊Dic3C2311yescharacteristic
43#634—22no—
44C2×C3×Dic3C2312yes—
45C2×C3×Dic3C2314yes—
46C2×C3×Dic3C2312yes—
47C3×Dic6—24no—
48#627Q814yescomplemented
49#557—91noSylow
50C2×C3×Q8—32no—
51C2×Dic6—32no—
52C2×Dic6—32no—
53C2×Dic6—61no—
54C2×Dic6C2×D312yes—
55C3×C4⋊C4—21no—
56C3×C4⋊C4—34no—
57C3×C4⋊C4C2×D312yes—
58C3×C42—32no—
59C3×C42—34no—
60C4⋊Dic3—34no—
61C4⋊Dic3—32no—
62C4⋊Dic3—34no—
63Dic3⋊C4—34no—
64Dic3⋊C4—32no—
65Dic3⋊C4—32no—
66Dic3⋊C4—34no—
67Dic3⋊C4—34no—
68Dic3⋊C4—34no—
69Dic3⋊C4—34no—
70Dic3⋊C4—62no—
71Dic3⋊C4C2×D314yes—
72C4×Dic3—34no—
73C4×Dic3—32no—
74C4×Dic3—62no—
75C4×Dic3—61no—
76C4×Dic3C2×D314yes—
77C4×Dic3C2×D312yes—
78C22×C32C2411yescharacteristic
79C32×C4—22no—
80C32×C4#4112yes—
81C3⋊Dic3—22no—
82C3⋊Dic3—21no—
83C3⋊Dic3C2×Q812yes—
84C3×Dic3—24no—
85C3×Dic3—22no—
86C3×Dic3C2×Q814yes—
87C4⋊Q8—92no—
88C4⋊Q8—91no—
89#125—94no—
90#125—92no—
91C4×Q8—32no—
92C4×Q8—92no—
93C4×Q8—91no—
94C4×Q8—91no—
95C3×Q8—64no—
96C2×C3×C4—21no—
97C2×C3×C4—22no—
98C2×C3×C4—32no—
99C2×C3×C4—34no—
100C2×C3×C4—32no—
101C2×C3×C4C22×D314yes—
102C2×C3×C4C22×D312yes—
103C2×Dic3—32no—
104C2×Dic3—32no—
105C2×Dic3—34no—
106C2×Dic3—61no—
107C2×Dic3—62no—
108C2×Dic3—61no—
109C2×Dic3C22×D312yes—
110C2×Dic3C22×D314yes—
111C2×Dic3C22×D312yes—
112Dic6—24no—
113Dic6—38no—
114Dic6—64no—
115Dic6—64no—
116C2×C32C22×Q811yescharacteristic
117C2×C32C2×#4111yescharacteristic
118C2×C322−1+411yescharacteristic
119C2×Q8—32no—
120C2×Q8—91no—
121C2×Q8—91no—
122C4⋊C4—34no—
123C4⋊C4—91no—
124C4⋊C4—92no—
125C4⋊C4—92no—
126C4⋊C4—94no—
127C4⋊C4—92no—
128C4⋊C4—94no—
129C4⋊C4—92no—
130C4⋊C4D3211yescharacteristic
131C42—34no—
132C42—32no—
133C42—92no—
134C42—91no—
135C22×C3—21no—
136C22×C3C23×D312yes—
137C3×C4—24no—
138C3×C4—22no—
139C3×C4—34no—
140C3×C4—42no—
141C3×C4—64no—
142C3×C4—62no—
143C3×C4#23514yes—
144Dic3—24no—
145Dic3—22no—
146Dic3—34no—
147Dic3—62no—
148Dic3—64no—
149Dic3—64no—
150Dic3—62no—
151Dic3—121no—
152Dic3D3×Q814yes—
153C32#55711yescharacteristic, complemented, Sylow
154Q8—64no—
155Q8—94no—
156Q8—182no—
157C2×C4—32no—
158C2×C4—32no—
159C2×C4—34no—
160C2×C4—91no—
161C2×C4—91no—
162C2×C4—92no—
163C2×C4C2×D3212yes—
164C2×C4C2×D3211yescharacteristic
165C2×C3—21no—
166C2×C3—21no—
167C2×C3—21no—
168C2×C3C2×#23512yes—
169C2×C3C2×D3×Q812yes—
170C2×C3#101012yes—
171C22C22×D3211yescharacteristic
172C4—22no—
173C4—34no—
174C4—64no—
175C4—62no—
176C4—92no—
177C4—182no—
178C4—181no—
179C4#379812yes—
180C3—21no—
181C3#556712yescomplemented
182C2C2×#379811yescharacteristic
183C2#6430911yescharacteristic
184C2D32×Q811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, prime radical, cosocleC22×C32C24
FittingC32×C4⋊C4C22
hypercenterC4⋊C4D32
hypocenterC32#557
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
48. #627Q8semidirect
153. C32#557semidirect
181. C3#5567semidirect

Maximal subgroups

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

subgroupindex
#640962
C3×#8872
C4×#6272
#638732
#638702
#638672
#638662
#55673