Finite Group Databasebeta

← #10591494

Subgroups — #10591494

Order 576.

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

normal subgroups only

This group has 263 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
1D4×C3⋊Dic3C211yesmaximal, characteristic
2#63919C211yesmaximal, characteristic, complemented
3C3×#832C212yesmaximal
4#63575C212yesmaximal, complemented
5#63572C211yesmaximal, characteristic, complemented
6#4759—32nomaximal
7C2×C32×D4C2211yescharacteristic
8C22×C3⋊Dic3—21no—
9C2×#627—21no—
10#3757—21no—
11C4⋊(C3⋊Dic3)C2211yescharacteristic
12C4×C3⋊Dic3C2211yescharacteristic
13C3×C4⋊Dic3C2212yes—
14C2×C3×C3⋊C8C2212yes—
15#3724—21no—
16D4×Dic3—32no—
17D4×Dic3—61no—
18#888—32no—
19C3×#102—32no—
20#832D312yes—
21#818—32no—
22Dic3⋊C8—32no—
23#807—32no—
24C23×C32—21no—
25C32×D4—21no—
26C32×D4Q812yescomplemented
27C2×C32×C4C2311yescharacteristic
28C2×C3⋊Dic3—21no—
29C2×C3⋊Dic3—42no—
30C2×C3⋊Dic3D411yescharacteristic
31C2×C3⋊Dic3D411yescharacteristic
32C2×C3×Dic3—22no—
33#627—42no—
34C3×C3⋊C8—22no—
35#474—91noSylow
36C2×C3×D4—21no—
37C2×C3×D4C2×D312yes—
38C22×Dic3—62no—
39C22×Dic3—62no—
40C2×Dic6—62no—
41C2×C3×C8—32no—
42C3×C4⋊C4—32no—
43#217—62no—
44#217—62no—
45C4⋊Dic3—32no—
46C4⋊Dic3—61no—
47C4⋊Dic3C2×D312yes—
48Dic3⋊C4—62no—
49C4×Dic3—32no—
50C4×Dic3—61no—
51C2×C3⋊C8C2×D312yes—
52C22×C32—22no—
53C22×C32—41no—
54C22×C32—41no—
55C22×C32C2×D411yescharacteristic
56C32×C4C2×Q811yescharacteristic
57C32×C4#4111yescharacteristic
58C3⋊Dic3—21no—
59C3⋊Dic3—41no—
60C3⋊Dic3D812yes—
61C3×Dic3—42no—
62C4⋊Q8—91no—
63C4×D4—91no—
64#107—92no—
65C4⋊C8—91no—
66#102—32no—
67C23×C3—22no—
68C23×C3—22no—
69C3×D4—22no—
70C3×D4—22no—
71C3×D4—22no—
72C3×D4Dic614yescomplemented
73C2×C3×C4—21no—
74C2×C3×C4—62no—
75C2×C3×C4C22×D312yes—
76C2×Dic3—22no—
77C2×Dic3—32no—
78C2×Dic3—32no—
79C2×Dic3—61no—
80C2×Dic3—61no—
81C2×Dic3—62no—
82C2×Dic3—62no—
83C2×Dic3—124no—
84C2×Dic3—124no—
85Dic6—124no—
86C3×C8—62no—
87C3⋊C8—22no—
88C2×C32—42no—
89C2×C32C22⋊Q811yescharacteristic
90C2×C32C2×D811yescharacteristic
91C2×C32#13711yescharacteristic
92C2×Q8—181no—
93C2×D4D3211yescharacteristic
94C22×C4—181no—
95C2×C8—32no—
96C4⋊C4—32no—
97C4⋊C4—91no—
98C4⋊C4—181no—
99C22⋊C4—181no—
100C42—91no—
101C22×C3—24no—
102C22×C3—24no—
103C22×C3—21no—
104C22×C3—42no—
105C22×C3—42no—
106C22×C3—42no—
107C22×C3—42no—
108C22×C3D3×D412yes—
109C3×C4—21no—
110C3×C4—21no—
111C3×C4—122no—
112C3×C4C2×Dic612yes—
113C3×C4#23712yes—
114Dic3—34no—
115Dic3—42no—
116Dic3—62no—
117Dic3—62no—
118Dic3—121no—
119Dic3—122no—
120Dic3—122no—
121C32#47411yescharacteristic, complemented, Sylow
122C23—21no—
123Q8—362no—
124D4—21no—
125D4#62712yescomplemented
126C2×C4—62no—
127C2×C4—91no—
128C2×C4—91no—
129C2×C4—181no—
130C2×C4—362no—
131C2×C4C2×D3211yescharacteristic
132C8—62no—
133C2×C3—21no—
134C2×C3—21no—
135C2×C3—21no—
136C2×C3—44no—
137C2×C3—44no—
138C2×C3#87812yes—
139C2×C3D3×D812yes—
140C2×C3#91512yes—
141C22—22no—
142C22—41no—
143C22—41no—
144C22#381111yescharacteristic
145C4—92no—
146C4—122no—
147C4—181no—
148C4—361no—
149C4#380511yescharacteristic
150C4C2×#62711yescharacteristic
151C3—21no—
152C3#475912yescomplemented
153C2—42no—
154C2#6392611yescharacteristic
155C2#6393111yescharacteristic
156C2#6398211yescharacteristic
subgroupG/H
centerC22#3811
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
Fitting, prime radicalC2×C32×D4C22
socleC22×C32C2×D4
hypercenterC2×D4D32
hypocenterC32#474
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #63919C2semidirect
4. #63575C2semidirect
5. #63572C2semidirect
26. C32×D4Q8semidirect
72. C3×D4Dic6semidirect
121. C32#474semidirect
125. D4#627semidirect
152. C3#4759semidirect

Maximal subgroups

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

subgroupindex
D4×C3⋊Dic32
#639192
C3×#8322
#635752
#635722
#47593