Finite Group Databasebeta

← #10594826

Subgroups — #10594826

Order 576.

422 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 128 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#64135C211yesmaximal, characteristic
2C3×#924C212yesmaximal
3#63956C214yesmaximal
4#63873C211yesmaximal, characteristic, complemented
5#63872C211yesmaximal, characteristic, complemented
6#63845C214yesmaximal, complemented
7#63843C212yesmaximal, complemented
8#5625—32nomaximal
9C22×C32×C4C2211yescharacteristic
10C2×C3×Dic6C2212yes—
11#3757C2212yes—
12C4⋊(C3⋊Dic3)C2212yes—
13C4×C3⋊Dic3C2211yescharacteristic
14C4×C3⋊Dic3C2211yescharacteristic
15C3×#217C2214yes—
16C3×C4⋊Dic3C2212yes—
17C3×Dic3⋊C4C2214yes—
18#3724C2214yes—
19Dic3⋊Dic3C2214yes—
20Dic3⋊Dic3C2214yes—
21Dic32C2214yes—
22C3×C22⋊Q8—32no—
23Q8×Dic3—32no—
24#944—32no—
25#926—32no—
26#926—61no—
27#924D312yes—
28#890—32no—
29#890—34no—
30#889—34no—
31#887—32no—
32#879—34no—
33#879—34no—
34C23×C32C2311yescharacteristic
35C2×C32×C4—22no—
36C2×C32×C4C2311yescharacteristic
37C2×C32×C4C2311yescharacteristic
38C2×C3⋊Dic3C2312yes—
39C2×C3⋊Dic3C2312yes—
40C2×C3×Dic3C2314yes—
41C2×C3×Dic3C2314yes—
42C3×Dic6—24no—
43#541—91noSylow
44C2×C3×Q8—32no—
45C22×C3×C4—21no—
46C22×C3×C4C2×D312yes—
47C2×Dic6C2×D312yes—
48C3×C4⋊C4—32no—
49C3×C4⋊C4—34no—
50C3×C22⋊C4—34no—
51#217—32no—
52#217—32no—
53#217—62no—
54#217C2×D314yes—
55C4⋊Dic3—32no—
56C4⋊Dic3—32no—
57C4⋊Dic3—34no—
58C4⋊Dic3—34no—
59C4⋊Dic3—62no—
60C4⋊Dic3C2×D312yes—
61Dic3⋊C4—34no—
62Dic3⋊C4—34no—
63Dic3⋊C4—34no—
64Dic3⋊C4—34no—
65Dic3⋊C4C2×D314yes—
66C4×Dic3—32no—
67C4×Dic3—32no—
68C4×Dic3—34no—
69C4×Dic3—34no—
70C4×Dic3—61no—
71C4×Dic3—61no—
72C22×C32—21no—
73C22×C32—22no—
74C22×C32C2411yescharacteristic
75C32×C4—21no—
76C32×C4#4112yes—
77C3⋊Dic3—22no—
78C3⋊Dic3—22no—
79C3×Dic3—24no—
80C3×Dic3—24no—
81C4⋊Q8—91no—
82#126—94no—
83#125—94no—
84#125—91no—
85C22⋊Q8—32no—
86C4×Q8—92no—
87#117—91no—
88C23×C3—21no—
89C23×C3C22×D312yes—
90C3×Q8—64no—
91C2×C3×C4—24no—
92C2×C3×C4—24no—
93C2×C3×C4—21no—
94C2×C3×C4—21no—
95C2×C3×C4—34no—
96C2×C3×C4—34no—
97C2×C3×C4C22×D312yes—
98C2×C3×C4C22×D312yes—
99C2×Dic3—32no—
100C2×Dic3—32no—
101C2×Dic3—32no—
102C2×Dic3—32no—
103C2×Dic3—62no—
104C2×Dic3—62no—
105C2×Dic3C22×D314yes—
106C2×Dic3C22×D314yes—
107Dic6—24no—
108C2×C32—41no—
109C2×C32C2×#4111yescharacteristic
110C2×C322−1+412yes—
111C2×Q8—32no—
112C22×C4D3211yescharacteristic
113C4⋊C4—32no—
114C4⋊C4—34no—
115C4⋊C4—94no—
116C4⋊C4—94no—
117C4⋊C4—94no—
118C4⋊C4—92no—
119C22⋊C4—34no—
120C22⋊C4—92no—
121C42—94no—
122C42—91no—
123C42—91no—
124C22×C3—22no—
125C22×C3—22no—
126C22×C3—22no—
127C22×C3—22no—
128C22×C3—21no—
129C22×C3—42no—
130C22×C3C23×D312yes—
131C3×C4—22no—
132C3×C4—22no—
133C3×C4—22no—
134C3×C4—64no—
135C3×C4—64no—
136C3×C4#23714yes—
137Dic3—24no—
138Dic3—24no—
139Dic3—62no—
140Dic3—62no—
141Dic3—62no—
142Dic3—62no—
143Dic3—122no—
144Dic3—122no—
145C32#54111yescharacteristic, complemented, Sylow
146C23C2×D3211yescharacteristic
147Q8—64no—
148C2×C4—22no—
149C2×C4—34no—
150C2×C4—34no—
151C2×C4—92no—
152C2×C4—92no—
153C2×C4C2×D3211yescharacteristic
154C2×C4C2×D3211yescharacteristic
155C2×C3—22no—
156C2×C3—21no—
157C2×C3—42no—
158C2×C3—42no—
159C2×C3C2×#23712yes—
160C2×C3#100712yes—
161C2×C3#101012yes—
162C22—22no—
163C22—21no—
164C22C22×D3211yescharacteristic
165C4—21no—
166C4—64no—
167C4—64no—
168C4—182no—
169C4—182no—
170C4#380512yes—
171C3—21no—
172C3#562512yescomplemented
173C2—41no—
174C2#6429712yes—
175C2C2×#380511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC22×C32×C4C22
prime radicalC23×C32C23
hypercenterC22×C4D32
hypocenterC32#541
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #63873C2semidirect
5. #63872C2semidirect
6. #63845C2semidirect
7. #63843C2semidirect
145. C32#541semidirect
172. C3#5625semidirect

Maximal subgroups

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

subgroupindex
#641352
C3×#9242
#639562
#638732
#638722
#638452
#638432
#56253