Finite Group Databasebeta

← #10591135

Subgroups — #10591135

Order 576.

245 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 245 conjugacy classes of subgroups — too many to draw. Only its 72 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#64133C211yesmaximal, characteristic
2C2×C3×C4⋊Dic3C211yesmaximal, characteristic
3C3×#830C211yesmaximal, characteristic
4#63575C212yesmaximal, complemented
5#63567C212yesmaximal, complemented
6#4970—31nomaximal
7#4722—31nomaximal
8C22×C32×C4C2211yescharacteristic
9C2×#634C2211yescharacteristic
10C22×C3×Dic3—21no—
11#3757—21no—
12C4⋊(C3⋊Dic3)C2211yescharacteristic
13#3750—21no—
14C3×C4⋊Dic3—21no—
15C3×C4⋊Dic3C2212yes—
16C2×C3×C3⋊C8C2212yes—
17C2×C3×C4⋊C4—31no—
18C2×C4⋊Dic3D311yescharacteristic
19#924—31no—
20#924—31no—
21#924—61no—
22C3×C22⋊C8—31no—
23#830D311yescharacteristic
24#818—32no—
25#816—32no—
26#810—32no—
27#807—32no—
28C23×C32D411yescharacteristic
29C2×C32×C4—22no—
30C2×C32×C4D411yescharacteristic
31C2×C32×C4C2311yescharacteristic
32C2×C3⋊Dic3—21no—
33C2×C3⋊Dic3—21no—
34#634—22no—
35C2×C3×Dic3—22no—
36C2×C3×Dic3—42no—
37C3×C3⋊C8—22no—
38#484—91noSylow
39C22×C3×C4—21no—
40C22×C3×C4—61no—
41C22×C3×C4C2×D311yescharacteristic
42C22×C3×C4C2×D311yescharacteristic
43C22×Dic3—21no—
44C2×Dic6—31no—
45C2×Dic6—31no—
46C2×Dic6—61no—
47C2×C3×C8—32no—
48C3×C4⋊C4—32no—
49C3×C4⋊C4—61no—
50#217—62no—
51#217—61no—
52#217—61no—
53C4⋊Dic3—21no—
54C4⋊Dic3—31no—
55C4⋊Dic3—31no—
56C4⋊Dic3—61no—
57C4⋊Dic3C2×D312yes—
58Dic3⋊C4—62no—
59Dic3⋊C4—61no—
60Dic3⋊C4—61no—
61C2×C3⋊C8C2×D312yes—
62C22×C32—21no—
63C22×C32—21no—
64C22×C32Q1612yes—
65C22×C32C2×D411yescharacteristic
66C32×C4—21no—
67C32×C4#4112yes—
68C3⋊Dic3—41no—
69C3⋊Dic3—41no—
70C3×Dic3—42no—
71C22⋊Q8—91no—
72C2×C4⋊C4—31no—
73#107—92no—
74#103—92no—
75C22⋊C8—31no—
76C23×C3—21no—
77C23×C3D1211yescharacteristic
78C23×C3#6711yescharacteristic
79C2×C3×C4—22no—
80C2×C3×C4—22no—
81C2×C3×C4—21no—
82C2×C3×C4—21no—
83C2×C3×C4—42no—
84C2×C3×C4—62no—
85C2×C3×C4—122no—
86C2×C3×C4D1211yescharacteristic
87C2×C3×C4#6711yescharacteristic
88C2×C3×C4C22×D311yescharacteristic
89C2×C3×C4C22×D311yescharacteristic
90C2×Dic3—22no—
91C2×Dic3—42no—
92C2×Dic3—62no—
93C2×Dic3—62no—
94C2×Dic3—61no—
95C2×Dic3—61no—
96C2×Dic3—61no—
97C2×Dic3—61no—
98Dic6—62no—
99Dic6—62no—
100Dic6—122no—
101C3×C8—62no—
102C3⋊C8—22no—
103C2×C32—22no—
104C2×C32#12311yescharacteristic
105C2×C32C2×Q1611yescharacteristic
106C2×C32AGL(1,ℤ/8)11yescharacteristic
107C2×Q8—91no—
108C22×C4—61no—
109C22×C4D3211yescharacteristic
110C2×C8—32no—
111C4⋊C4—32no—
112C4⋊C4—61no—
113C4⋊C4—91no—
114C4⋊C4—181no—
115C22⋊C4—181no—
116C22×C3—21no—
117C22×C3—21no—
118C22×C3—21no—
119C22×C3—21no—
120C22×C3—22no—
121C22×C3—21no—
122C22×C3—41no—
123C22×C3—41no—
124C22×C3Dic1212yes—
125C22×C3#21612yes—
126C22×C3C2×D1211yescharacteristic
127C22×C3C2×#6711yescharacteristic
128C3×C4—21no—
129C3×C4—21no—
130C3×C4—22no—
131C3×C4—41no—
132C3×C4—122no—
133C3×C4#23512yes—
134C3×C4#23712yes—
135Dic3—42no—
136Dic3—122no—
137Dic3—122no—
138Dic3—121no—
139Dic3—121no—
140Dic3—121no—
141Dic3—121no—
142C32#48411yescharacteristic, complemented, Sylow
143C23#62611yescharacteristic
144Q8—182no—
145C2×C4—22no—
146C2×C4—62no—
147C2×C4—122no—
148C2×C4—181no—
149C2×C4—181no—
150C2×C4#62611yescharacteristic
151C2×C4C2×D3211yescharacteristic
152C8—62no—
153C2×C3—22no—
154C2×C3—22no—
155C2×C3—21no—
156C2×C3—21no—
157C2×C3—21no—
158C2×C3—42no—
159C2×C3#88611yescharacteristic
160C2×C3C2×Dic1211yescharacteristic
161C2×C3#90811yescharacteristic
162C2×C3#92911yescharacteristic
163C2×C3#93211yescharacteristic
164C2×C3C2×#21611yescharacteristic
165C22—21no—
166C22—21no—
167C22#371912yes—
168C22C2×#62611yescharacteristic
169C4—21no—
170C4—122no—
171C4—361no—
172C4—361no—
173C4#380412yes—
174C3—21no—
175C3#472211yescharacteristic, complemented
176C3#497011yescharacteristic, complemented
177C2—22no—
178C2#6383011yescharacteristic
179C2C2×#371911yescharacteristic
180C2#6396611yescharacteristic
subgroupG/H
centerC22C2×#626
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
FittingC22×C32×C4C22
socleC22×C32C2×D4
prime radicalC23×C32D4
hypercenterC22×C4D32
hypocenterC32#484
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #63575C2semidirect
5. #63567C2semidirect
142. C32#484semidirect
175. C3#4722semidirect
176. C3#4970semidirect

Maximal subgroups

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

subgroupindex
#641332
C2×C3×C4⋊Dic32
C3×#8302
#635752
#635672
#49703
#47223