Finite Group Databasebeta

← #10591226

Subgroups — #10591226

Order 576.

314 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 100 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×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic
2C2×C3×Dic3⋊C4C211yesmaximal, characteristic
3C3×C3⋊#95C211yesmaximal, characteristic
4#63579C212yesmaximal
5#63579C212yesmaximal
6#4986—31nomaximal
7#4659—31nomaximal
8C22×C32×C4C2211yescharacteristic
9C22×C3⋊Dic3C2212yes—
10C22×C3×Dic3C2211yescharacteristic
11C22×C3×Dic3C2212yes—
12C22×C3×Dic3C2211yescharacteristic
13C4⋊(C3⋊Dic3)—22no—
14C3×Dic3⋊C4—22no—
15C2×C3×C4⋊C4—31no—
16C2×C4⋊Dic3—31no—
17C2×C4⋊Dic3—31no—
18C2×C4⋊Dic3—61no—
19C2×Dic3⋊C4D311yescharacteristic
20C3×#95—31no—
21C3⋊#95—32no—
22C3⋊#95—32no—
23C3⋊#95—32no—
24C3⋊#95—32no—
25C3⋊#95D311yescharacteristic
26C23×C32C2311yescharacteristic
27C2×C32×C4—22no—
28C2×C32×C4D412yes—
29C2×C3⋊Dic3—22no—
30C2×C3⋊Dic3—24no—
31C2×C3×Dic3—21no—
32C2×C3×Dic3—21no—
33C2×C3×Dic3—21no—
34C2×C3×Dic3—22no—
35C2×C3×Dic3—22no—
36C2×C3×Dic3—22no—
37C2×C3×Dic3—22no—
38C2×C3×Dic3Q812yes—
39#400—91noSylow
40C22×C3×C4—21no—
41C22×C3×C4—31no—
42C22×C3×C4—32no—
43C22×C3×C4—31no—
44C22×C3×C4C2×D311yescharacteristic
45C22×C3×C4C2×D311yescharacteristic
46C22×Dic3—32no—
47C22×Dic3—32no—
48C22×Dic3—62no—
49C22×Dic3C2×D312yes—
50C22×Dic3C2×D311yescharacteristic
51C22×Dic3C2×D311yescharacteristic
52C3×C4⋊C4—62no—
53C4⋊Dic3—64no—
54C4⋊Dic3—62no—
55C4⋊Dic3—62no—
56Dic3⋊C4—22no—
57C22×C32C2×D411yescharacteristic
58C22×C32C2×Q811yescharacteristic
59C22×C32#4111yescharacteristic
60C22×C32#4112yes—
61C22×C32#4112yes—
62C32×C4—22no—
63C3⋊Dic3—42no—
64C3×Dic3—22no—
65C3×Dic3—41no—
66C3×Dic3—42no—
67C2×C4⋊C4—31no—
68C2×C4⋊C4—91no—
69#95—31no—
70#95—92no—
71#95—92no—
72C23×C3—21no—
73C23×C3C22×D311yescharacteristic
74C23×C3C22×D311yescharacteristic
75C2×C3×C4—24no—
76C2×C3×C4—22no—
77C2×C3×C4—22no—
78C2×C3×C4—22no—
79C2×C3×C4—32no—
80C2×C3×C4—61no—
81C2×C3×C4—61no—
82C2×C3×C4—61no—
83C2×C3×C4—62no—
84C2×C3×C4—62no—
85C2×C3×C4—62no—
86C2×C3×C4—62no—
87C2×C3×C4D1212yes—
88C2×C3×C4#6712yes—
89C2×Dic3—21no—
90C2×Dic3—21no—
91C2×Dic3—22no—
92C2×Dic3—22no—
93C2×Dic3—22no—
94C2×Dic3—22no—
95C2×Dic3—21no—
96C2×Dic3—64no—
97C2×Dic3—62no—
98C2×Dic3—64no—
99C2×Dic3—64no—
100C2×Dic3—62no—
101C2×Dic3—124no—
102C2×Dic3Dic612yes—
103C2×C32C22⋊Q811yescharacteristic
104C2×C32#12311yescharacteristic
105C2×C32#12411yescharacteristic
106C2×C32#12512yes—
107C2×C32#12612yes—
108C22×C4—31no—
109C22×C4—32no—
110C22×C4—31no—
111C22×C4—92no—
112C22×C4D3211yescharacteristic
113C4⋊C4—62no—
114C4⋊C4—182no—
115C22×C3—21no—
116C22×C3—21no—
117C22×C3—22no—
118C22×C3—22no—
119C22×C3—21no—
120C22×C3C2×Dic611yescharacteristic
121C22×C3C2×D1211yescharacteristic
122C22×C3#23511yescharacteristic
123C22×C3#23512yes—
124C22×C3#23711yescharacteristic
125C22×C3#23712yes—
126C22×C3#23712yes—
127C22×C3D3×Q811yescharacteristic
128C22×C3#23912yes—
129C22×C3C2×#6711yescharacteristic
130C3×C4—24no—
131C3×C4—22no—
132C3×C4—22no—
133C3×C4—62no—
134C3×C4—121no—
135C3×C4—122no—
136Dic3—22no—
137Dic3—42no—
138Dic3—41no—
139Dic3—124no—
140Dic3—122no—
141Dic3—122no—
142C32#40011yescharacteristic, complemented, Sylow
143C23C2×D3211yescharacteristic
144C2×C4—22no—
145C2×C4—32no—
146C2×C4—61no—
147C2×C4—61no—
148C2×C4—62no—
149C2×C4—62no—
150C2×C4—62no—
151C2×C4—62no—
152C2×C4—61no—
153C2×C4—184no—
154C2×C4—182no—
155C2×C4#62612yes—
156C2×C3—22no—
157C2×C3—21no—
158C2×C3—22no—
159C2×C3—21no—
160C2×C3—21no—
161C2×C3#87511yescharacteristic
162C2×C3#87912yes—
163C2×C3#88611yescharacteristic
164C2×C3#88912yes—
165C2×C3#89012yes—
166C2×C3#89711yescharacteristic
167C2×C3#89812yes—
168C2×C3#92411yescharacteristic
169C2×C3#93511yescharacteristic
170C2×C3#94711yescharacteristic
171C22D3×Dic611yescharacteristic
172C22#379511yescharacteristic
173C22#379912yes—
174C22#380512yes—
175C22C2×#62611yescharacteristic
176C4—22no—
177C4—62no—
178C4—122no—
179C4—121no—
180C4—362no—
181C3—21no—
182C3#465911yescharacteristic, complemented
183C3#498611yescharacteristic, complemented
184C2#6384512yes—
185C2#6385711yescharacteristic
186C2#6386112yes—
187C2#6386411yescharacteristic
188C2#6396211yescharacteristic
subgroupG/H
center, FrattiniC23C2×D32
commutator, socle, prime radical, cosocleC23×C32C23
FittingC22×C32×C4C22
hypercenterC22×C4D32
hypocenterC32#400
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
142. C32#400semidirect
182. C3#4659semidirect
183. C3#4986semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊(C3⋊Dic3)2
C2×C3×Dic3⋊C42
C3×C3⋊#952
#635792
#49863
#46593