Finite Group Databasebeta

← #10591397

Subgroups — #10591397

Order 576.

410 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 114 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
1C22×#627C211yesmaximal, characteristic
2C2×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic
3C2×Dic3⋊Dic3C212yesmaximal
4C3×C3⋊#95C212yesmaximal
5#63579C211yesmaximal, characteristic
6#4656—32nomaximal
7C22×C32×C4C2211yescharacteristic
8C22×C3⋊Dic3C2211yescharacteristic
9C22×C3⋊Dic3C2211yescharacteristic
10C22×C3×Dic3C2212yes—
11C22×C3×Dic3C2212yes—
12C2×#627—22no—
13C2×#627—24no—
14C4⋊(C3⋊Dic3)—22no—
15Dic3⋊Dic3—24no—
16C22×Dic6—32no—
17C2×C4⋊Dic3—32no—
18C2×C4⋊Dic3—32no—
19C2×C4⋊Dic3—61no—
20C2×Dic3⋊C4—32no—
21C3×#95—32no—
22C3⋊#95—32no—
23C3⋊#95D312yes—
24C23×C32C2311yescharacteristic
25C2×C32×C4—21no—
26C2×C32×C4—21no—
27C2×C32×C4Q812yescomplemented
28C2×C3⋊Dic3—21no—
29C2×C3⋊Dic3—22no—
30C2×C3⋊Dic3—22no—
31C2×C3⋊Dic3D412yes—
32C2×C3×Dic3—22no—
33C2×C3×Dic3—22no—
34C2×C3×Dic3—22no—
35C2×C3×Dic3—22no—
36C2×C3×Dic3D414yes—
37C2×C3×Dic3Q814yescomplemented
38#627—28no—
39#395—91noSylow
40C22×C3×C4—21no—
41C22×C3×C4—32no—
42C22×C3×C4—32no—
43C22×C3×C4C2×D312yes—
44C22×Dic3—32no—
45C22×Dic3—32no—
46C22×Dic3—61no—
47C22×Dic3—61no—
48C22×Dic3C2×D312yes—
49C22×Dic3C2×D312yes—
50C2×Dic6—64no—
51C2×Dic6—64no—
52C2×Dic6—64no—
53C4⋊Dic3—64no—
54C4⋊Dic3—64no—
55C4⋊Dic3—64no—
56Dic3⋊C4—64no—
57C22×C32C2×D412yes—
58C22×C32C2×D411yescharacteristic
59C22×C32C2×Q811yescharacteristic
60C22×C32C2×Q812yes—
61C22×C32#4111yescharacteristic
62C32×C4—22no—
63C3⋊Dic3—22no—
64C3⋊Dic3—41no—
65C3×Dic3—24no—
66C3×Dic3—24no—
67C22×Q8—91no—
68C2×C4⋊C4—92no—
69C2×C4⋊C4—91no—
70#95—32no—
71#95—91no—
72C23×C3—21no—
73C23×C3C22×D312yes—
74C2×C3×C4—22no—
75C2×C3×C4—22no—
76C2×C3×C4—22no—
77C2×C3×C4—22no—
78C2×C3×C4—22no—
79C2×C3×C4—34no—
80C2×C3×C4—34no—
81C2×C3×C4—62no—
82C2×C3×C4—62no—
83C2×C3×C4—62no—
84C2×C3×C4—62no—
85C2×C3×C4Dic614yescomplemented
86C2×Dic3—22no—
87C2×Dic3—22no—
88C2×Dic3—22no—
89C2×Dic3—22no—
90C2×Dic3—34no—
91C2×Dic3—62no—
92C2×Dic3—62no—
93C2×Dic3—62no—
94C2×Dic3—62no—
95C2×Dic3—62no—
96C2×Dic3—62no—
97C2×Dic3—62no—
98C2×Dic3—122no—
99C2×Dic3—122no—
100C2×Dic3Dic614yescomplemented
101C2×Dic3D1214yes—
102Dic6—616no—
103C2×C32#12011yescharacteristic
104C2×C32C22⋊Q811yescharacteristic
105C2×C32C22⋊Q812yes—
106C2×C32C4⋊Q812yes—
107C2×C32C4⋊Q811yescharacteristic
108C2×Q8—184no—
109C2×Q8—182no—
110C22×C4—32no—
111C22×C4—32no—
112C22×C4—91no—
113C22×C4—91no—
114C22×C4D3211yescharacteristic
115C4⋊C4—182no—
116C4⋊C4—184no—
117C22×C3—22no—
118C22×C3—22no—
119C22×C3—21no—
120C22×C3—21no—
121C22×C3—21no—
122C22×C3C2×Dic612yes—
123C22×C3C2×Dic612yes—
124C22×C3C2×D1212yes—
125C22×C3D3×D412yes—
126C22×C3D3×D412yes—
127C22×C3#23712yes—
128C22×C3D3×Q812yes—
129C3×C4—24no—
130C3×C4—24no—
131C3×C4—64no—
132C3×C4—64no—
133Dic3—24no—
134Dic3—24no—
135Dic3—64no—
136Dic3—122no—
137Dic3—122no—
138Dic3—122no—
139C32#39511yescharacteristic, complemented, Sylow
140C23C2×D3211yescharacteristic
141Q8—188no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—34no—
145C2×C4—34no—
146C2×C4—62no—
147C2×C4—62no—
148C2×C4—62no—
149C2×C4—62no—
150C2×C4—92no—
151C2×C4—182no—
152C2×C4—182no—
153C2×C4—181no—
154C2×C4#62712yescomplemented
155C2×C3—21no—
156C2×C3—22no—
157C2×C3—22no—
158C2×C3—21no—
159C2×C3—21no—
160C2×C3#86912yes—
161C2×C3#87812yes—
162C2×C3#87812yes—
163C2×C3#88212yes—
164C2×C3#88812yes—
165C2×C3#88812yes—
166C2×C3#89712yes—
167C22D3×Dic612yes—
168C22D3×D1212yes—
169C22#380511yescharacteristic
170C22C2×#62711yescharacteristic
171C22#381111yescharacteristic
172C4—22no—
173C4—64no—
174C4—64no—
175C4—182no—
176C4—361no—
177C3—21no—
178C3#465612yescomplemented
179C2#6384011yescharacteristic
180C2#6389312yes—
181C2#6391812yes—
182C2#6392311yescharacteristic
183C2#6398211yescharacteristic
subgroupG/H
center, FrattiniC23C2×D32
commutator, socle, prime radical, cosocleC23×C32C23
FittingC22×C32×C4C22
hypercenterC22×C4D32
hypocenterC32#395
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
27. C2×C32×C4Q8semidirect
37. C2×C3×Dic3Q8semidirect
85. C2×C3×C4Dic6semidirect
100. C2×Dic3Dic6semidirect
139. C32#395semidirect
154. C2×C4#627semidirect
178. C3#4656semidirect

Maximal subgroups

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

subgroupindex
C22×#6272
C2×C4⋊(C3⋊Dic3)2
C2×Dic3⋊Dic32
C3×C3⋊#952
#635792
#46563