Finite Group Databasebeta

← #10591654

Subgroups — #10591654

Order 576.

333 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 333 conjugacy classes of subgroups — too many to draw. Only its 68 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
1C2×#3797C211yesmaximal, characteristic
2#64155C211yesmaximal, characteristic
3C2×C3×#216C212yesmaximal, complemented
4#63566C212yesmaximal, complemented
5#63557C211yesmaximal, characteristic
6#5186—32nomaximal
7C2×C32×Q8C2211yescharacteristic
8C2×C4×C3⋊D3C2211yescharacteristic
9C2×C3×Dic6C2212yes—
10C2×#627—21no—
11C2×#624—21no—
12#3797—24no—
13#3752—21no—
14C4⋊(C3⋊Dic3)C2211yescharacteristic
15#3750—21no—
16C3×#216—24no—
17C2×C3×C3⋊C8C2212yes—
18C2×D3×Q8—32no—
19C2×C3×Q16—32no—
20#946—32no—
21#946—61no—
22C2×#216D312yescomplemented
23#835—32no—
24(C2×D3)⋊C8—32no—
25#816—32no—
26C22×C3⋊D3D411yescharacteristic
27C32×Q8—22no—
28C2×C32×C4—21no—
29C2×C32×C4C2311yescharacteristic
30C2×C3⋊Dic3—21no—
31C2×C3⋊Dic3D411yescharacteristic
32C4×C3⋊D3—22no—
33C2×C3×Dic3—22no—
34C3×Dic6—22no—
35C3×Dic6D414yes—
36#627—24no—
37#624—24no—
38C3×C3⋊C8—22no—
39#451—91noSylow
40C2×C3×Q8—21no—
41C2×C3×Q8—32no—
42C2×C3×Q8C2×D312yes—
43D3×Q8—64no—
44D3×Q8—64no—
45C2×C4×D3—32no—
46C2×C4×D3—61no—
47C2×C4×D3—62no—
48C2×Dic6—62no—
49C2×Dic6C2×D312yes—
50C3×Q16—64no—
51C2×C3×C8—32no—
52#216—24no—
53(C2×D3)⋊C4—62no—
54(C2×D3)⋊C4—62no—
55C4⋊Dic3—32no—
56C4⋊Dic3—61no—
57Dic3⋊C4—62no—
58Dic3⋊C4—62no—
59C2×C3⋊C8C2×D312yes—
60C22×C32C2×D411yescharacteristic
61C2×C3⋊D3—21no—
62C2×C3⋊D3—21no—
63C2×C3⋊D3Q1612yescomplemented
64C32×C4—41no—
65C32×C4C2×D412yes—
66C3⋊Dic3—21no—
67C3⋊Dic3—41no—
68C3×Dic3—24no—
69C22×Q8—91no—
70C2×Q16—32no—
71C22⋊Q8—91no—
72#103—92no—
73C22⋊C8—91no—
74C22×D3—32no—
75C22×D3—61no—
76C3×Q8—22no—
77C3×Q8—22no—
78C3×Q8—34no—
79C3×Q8—42no—
80C3×Q8—62no—
81C2×C3×C4—22no—
82C2×C3×C4—22no—
83C2×C3×C4—21no—
84C2×C3×C4—62no—
85C2×C3×C4C22×D312yes—
86C2×Dic3—22no—
87C2×Dic3—32no—
88C2×Dic3—61no—
89C2×Dic3—62no—
90C2×Dic3—62no—
91C4×D3—68no—
92C4×D3—62no—
93C4×D3—62no—
94C4×D3—122no—
95Dic6—22no—
96Dic6—68no—
97Dic6#6714yes—
98C3×C8—62no—
99C3⋊C8—22no—
100C2×C32#12011yescharacteristic
101C2×C32C2×Q1611yescharacteristic
102C2×C32#13711yescharacteristic
103C3⋊D3—22no—
104C2×Q8—32no—
105C2×Q8—181no—
106C2×Q8—184no—
107C2×Q8D3211yescharacteristic
108C22×C4—91no—
109C22×C4—181no—
110Q16—64no—
111C2×C8—32no—
112C4⋊C4—91no—
113C4⋊C4—181no—
114C22⋊C4—181no—
115C22×C3—21no—
116C22×C3D3×D412yes—
117C2×D3—34no—
118C2×D3—62no—
119C2×D3—62no—
120C2×D3—62no—
121C2×D3—121no—
122C2×D3—121no—
123C3×C4—22no—
124C3×C4—42no—
125C3×C4—42no—
126C3×C4—64no—
127C3×C4D3×D412yes—
128C3×C4C2×#6712yes—
129Dic3—24no—
130Dic3—62no—
131Dic3—121no—
132Dic3—122no—
133Dic3—122no—
134C32#45111yescharacteristic, complemented, Sylow
135C23—91no—
136Q8—22no—
137Q8—34no—
138Q8—62no—
139Q8—184no—
140C2×C4—21no—
141C2×C4—62no—
142C2×C4—91no—
143C2×C4—184no—
144C2×C4—182no—
145C2×C4—181no—
146C2×C4C2×D3211yescharacteristic
147C8—62no—
148C2×C3—21no—
149C2×C3—21no—
150C2×C3—21no—
151C2×C3D3×Q1612yes—
152C2×C3#91812yes—
153C2×C3#93712yes—
154D3—64no—
155D3—122no—
156C22—92no—
157C22—181no—
158C22—181no—
159C22#381111yescharacteristic
160C4—41no—
161C4—64no—
162C4—181no—
163C4—361no—
164C4D3×#6712yes—
165C3—21no—
166C3#518612yescomplemented
167C2—182no—
168C2#6394411yescharacteristic
169C2#6394511yescharacteristic
170C2#6398311yescharacteristic
subgroupG/H
centerC22#3811
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
FittingC2×C32×Q8C22
socleC22×C32C2×D4
prime radicalC22×C3⋊D3D4
hypercenterC2×Q8D32
hypocenterC32#451
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
3. C2×C3×#216C2semidirect
4. #63566C2semidirect
22. C2×#216D3semidirect
63. C2×C3⋊D3Q16semidirect
134. C32#451semidirect
166. C3#5186semidirect

Maximal subgroups

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

subgroupindex
C2×#37972
#641552
C2×C3×#2162
#635662
#635572
#51863