Finite Group Databasebeta

← C3×#2061 #72776

Subgroups — C3×#2061 #72776

Order 384.

230 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 92 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
2C3×#428C212yesmaximal
3C3×#382C211yesmaximal, characteristic
4C3×#343C211yesmaximal, characteristic
5C3×#339C212yesmaximal
6#2061C311yesmaximal, characteristic, direct product factor, Sylow
7C2×C3×M16C2212yes—
8C3×C4⋊Q8—22no—
9C3×#125—22no—
10C3×C22⋊Q8—22no—
11C3×#117C2212yes—
12C2×C3×C4⋊C4C2211yescharacteristic
13C2×C3×C4⋊C4C2211yescharacteristic
14C2×C3×C42C2211yescharacteristic
15C3×#107—22no—
16C3×#106—22no—
17C3×#95—22no—
18#544C2×C311yescharacteristic
19#428C2×C312yes—
20#382C2×C311yescharacteristic
21#343C2×C311yescharacteristic
22#339C2×C312yes—
23C2×C3×Q8—22no—
24C22×C3×C4—21no—
25C22×C3×C4—21no—
26C22×C3×C4D412yes—
27C22×C3×C4C2311yescharacteristic
28C3×M16—22no—
29C3×M16Q814yescomplemented
30C2×C3×C8—22no—
31C3×C4⋊C4—22no—
32C3×C4⋊C4—24no—
33C3×C4⋊C4—22no—
34C3×C4⋊C4—22no—
35C3×C4⋊C4D412yes—
36C3×C4⋊C4D412yes—
37C3×C22⋊C4—22no—
38C3×C42—22no—
39C3×C42—21no—
40C3×C42Q812yescomplemented
41C2×M16C22×C312yes—
42C4⋊Q8—22no—
43#125—22no—
44C22⋊Q8—22no—
45#117C22×C312yes—
46C2×C4⋊C4C22×C311yescharacteristic
47C2×C4⋊C4C22×C311yescharacteristic
48C2×C42C22×C311yescharacteristic
49#107—22no—
50#106—22no—
51#95—22no—
52C23×C3C2×D411yescharacteristic
53C3×Q8—82no—
54C2×C3×C4—22no—
55C2×C3×C4—22no—
56C2×C3×C4—22no—
57C2×C3×C4—22no—
58C2×C3×C4—41no—
59C2×C3×C4—41no—
60C2×C3×C4—42no—
61C2×C3×C4—42no—
62C2×C3×C4—41no—
63C2×C3×C4C2×D412yes—
64C2×C3×C4C2×Q812yes—
65C2×C3×C4C2×Q811yescharacteristic
66C2×C3×C4#4111yescharacteristic
67C3×C8—24no—
68C2×Q8—22no—
69C22×C4—21no—
70C22×C4—21no—
71C22×C4C3×D412yes—
72C22×C4C23×C311yescharacteristic
73M16—22no—
74M16C3×Q814yescomplemented
75C2×C8—22no—
76C4⋊C4—22no—
77C4⋊C4—24no—
78C4⋊C4—22no—
79C4⋊C4—22no—
80C4⋊C4C3×D412yes—
81C4⋊C4C3×D412yes—
82C22⋊C4—22no—
83C42—22no—
84C42—21no—
85C42C3×Q812yescomplemented
86C22×C3—21no—
87C22×C3—21no—
88C22×C3#12011yescharacteristic
89C22×C3C22⋊Q811yescharacteristic
90C22×C3C4⋊Q811yescharacteristic
91C3×C4—42no—
92C3×C4—42no—
93C3×C4—42no—
94C3×C4—42no—
95C3×C4—81no—
96C3×C4C22⋊Q812yes—
97C3×C4C4⋊Q812yes—
98C23C2×C3×D411yescharacteristic
99Q8—82no—
100C2×C4—22no—
101C2×C4—22no—
102C2×C4—22no—
103C2×C4—22no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—42no—
107C2×C4—42no—
108C2×C4—41no—
109C2×C4C2×C3×D412yes—
110C2×C4C2×C3×Q812yes—
111C2×C4C2×C3×Q811yescharacteristic
112C2×C4C3×#4111yescharacteristic
113C8—24no—
114C2×C3—21no—
115C2×C3—21no—
116C2×C3#39511yescharacteristic
117C2×C3#45411yescharacteristic
118C2×C3#45511yescharacteristic
119C22—21no—
120C22—21no—
121C22C3×#12011yescharacteristic
122C22C3×C22⋊Q811yescharacteristic
123C22C3×C4⋊Q811yescharacteristic
124C4—42no—
125C4—42no—
126C4—42no—
127C4—42no—
128C4—81no—
129C4C3×C22⋊Q812yes—
130C4C3×C4⋊Q812yes—
131C3#206111yescharacteristic, direct product factor, Sylow
132C2—21no—
133C2—21no—
134C2C3×#39511yescharacteristic
135C2C3×#45411yescharacteristic
136C2C3×#45511yescharacteristic
subgroupG/H
center, socleC22×C3#120
commutator, Frattini, cosocleC22×C4C23×C3
prime radicalC23×C3C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
6. #2061C3direct (N × H)
29. C3×M16Q8semidirect
40. C3×C42Q8semidirect
74. M16C3×Q8semidirect
85. C42C3×Q8semidirect
131. C3#2061direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#5442
C3×#4282
C3×#3822
C3×#3432
C3×#3392
#20613