Finite Group Databasebeta

← #71900

Subgroups — #71900

Order 384.

246 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C3×#544C211yesmaximal, characteristic
2#4995C212yesmaximal
3#4975C211yesmaximal, characteristic
4#4532C212yesmaximal
5#4530C211yesmaximal, characteristic
6#2060—31nomaximal, Sylow
7C3×C4⋊Q8—22no—
8C3×#125—22no—
9C3×C22⋊Q8—22no—
10C3×#117C2212yes—
11C2×C3×C4⋊C4C2211yescharacteristic
12C2×C4⋊Dic3C2211yescharacteristic
13C2×Dic3⋊C4—22no—
14C2×C4×Dic3C2211yescharacteristic
15C2×#208C2212yes—
16#808—22no—
17#807—22no—
18#544D311yescharacteristic
19#428—32no—
20#384—31no—
21#343—31no—
22#339—32no—
23C2×C3×Q8—22no—
24C22×C3×C4D412yes—
25C22×C3×C4C2311yescharacteristic
26C22×Dic3—21no—
27C22×Dic3—21no—
28C3×C4⋊C4—22no—
29C3×C4⋊C4—24no—
30C3×C4⋊C4—22no—
31C3×C4⋊C4D412yes—
32C3×C4⋊C4D412yes—
33C3×C22⋊C4—22no—
34C3×C42—22no—
35C4⋊Dic3—22no—
36Dic3⋊C4—44no—
37C4×Dic3—21no—
38C4×Dic3Q812yescomplemented
39#208—22no—
40#208Q814yescomplemented
41C2×C3⋊C8—22no—
42C2×M16—32no—
43C4⋊Q8—22no—
44#125—22no—
45C22⋊Q8—22no—
46#117C2×D312yes—
47C2×C4⋊C4—31no—
48C2×C4⋊C4—62no—
49C2×C4⋊C4C2×D311yescharacteristic
50C2×C42—31no—
51#107—62no—
52#106—62no—
53C23×C3C2×D411yescharacteristic
54C3×Q8—82no—
55C2×C3×C4—22no—
56C2×C3×C4—22no—
57C2×C3×C4—22no—
58C2×C3×C4—42no—
59C2×C3×C4C2×D412yes—
60C2×C3×C4C2×Q812yes—
61C2×C3×C4C2×Q811yescharacteristic
62C2×C3×C4#4111yescharacteristic
63C2×Dic3—22no—
64C2×Dic3—22no—
65C2×Dic3—22no—
66C2×Dic3—42no—
67C2×Dic3—41no—
68C3⋊C8—24no—
69C2×Q8—22no—
70C22×C4—61no—
71C22×C4—61no—
72C22×C4#6712yes—
73C22×C4C22×D311yescharacteristic
74M16—34no—
75M16—62no—
76C2×C8—62no—
77C4⋊C4—22no—
78C4⋊C4—24no—
79C4⋊C4—22no—
80C4⋊C4—62no—
81C4⋊C4—124no—
82C4⋊C4#6712yes—
83C4⋊C4#6712yes—
84C22⋊C4—22no—
85C42—22no—
86C42—32no—
87C42—61no—
88C22×C3—21no—
89C22×C3—21no—
90C22×C3#12011yescharacteristic
91C22×C3C22⋊Q811yescharacteristic
92C22×C3C4⋊Q811yescharacteristic
93C3×C4—42no—
94C3×C4—42no—
95C3×C4—42no—
96C3×C4C22⋊Q812yes—
97C3×C4C4⋊Q812yes—
98Dic3—24no—
99Dic3—81no—
100C23C2×#6711yescharacteristic
101Q8—82no—
102C2×C4—22no—
103C2×C4—22no—
104C2×C4—22no—
105C2×C4—42no—
106C2×C4—62no—
107C2×C4—62no—
108C2×C4—62no—
109C2×C4—122no—
110C2×C4—121no—
111C2×C4D3×Q811yescharacteristic
112C2×C4D3×Q812yes—
113C2×C4#23911yescharacteristic
114C2×C4C2×#6712yes—
115C8—64no—
116C2×C3—21no—
117C2×C3—21no—
118C2×C3#39511yescharacteristic
119C2×C3#45311yescharacteristic
120C2×C3#45611yescharacteristic
121C22—21no—
122C22—21no—
123C22#94411yescharacteristic
124C22#94611yescharacteristic
125C22#95311yescharacteristic
126C4—42no—
127C4—42no—
128C4—42no—
129C4—64no—
130C4—241no—
131C4#94412yes—
132C4#94612yes—
133C3#206011yescharacteristic, complemented, Sylow
134C2—21no—
135C2—21no—
136C2#523011yescharacteristic
137C2#524111yescharacteristic
138C2#524611yescharacteristic
subgroupG/H
centerC22#953
commutator, cosocleC22×C3×C4C23
FrattiniC22×C4C22×D3
FittingC3×#544C2
socleC22×C3#120
prime radicalC23×C3C2×D4
hypercenter#544D3
hypocenterC3#2060
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
38. C4×Dic3Q8semidirect
40. #208Q8semidirect
133. C3#2060semidirect

Maximal subgroups

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

subgroupindex
C3×#5442
#49952
#49752
#45322
#45302
#20603