Finite Group Databasebeta

← C3×#2028 #72743

Subgroups — C3×#2028 #72743

Order 384.

246 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 84 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×#419C212yesmaximal
3C3×#391C211yesmaximal, characteristic
4C3×#343C211yesmaximal, characteristic
5C3×#339C212yesmaximal
6#2028C311yesmaximal, characteristic, direct product factor, Sylow
7C22×C3×Q8C2211yescharacteristic
8C2×C3×M16C2212yes—
9C3×C4⋊Q8—22no—
10C3×#125—22no—
11C3×C22⋊Q8—22no—
12C3×#117C2212yes—
13C2×C3×C4⋊C4C2211yescharacteristic
14C2×C3×C42C2211yescharacteristic
15C3×#103—22no—
16C3×#103—22no—
17C3×#95—22no—
18#544C2×C311yescharacteristic
19#419C2×C312yes—
20#391C2×C311yescharacteristic
21#343C2×C311yescharacteristic
22#339C2×C312yes—
23C2×C3×Q8—22no—
24C2×C3×Q8—21no—
25C2×C3×Q8—22no—
26C2×C3×Q8—22no—
27C2×C3×Q8Q812yescomplemented
28C22×C3×C4—21no—
29C22×C3×C4—21no—
30C22×C3×C4D412yes—
31C22×C3×C4C2311yescharacteristic
32C3×M16—22no—
33C3×M16—22no—
34C2×C3×C8—22no—
35C3×C4⋊C4—22no—
36C3×C4⋊C4—24no—
37C3×C4⋊C4—22no—
38C3×C4⋊C4D412yes—
39C3×C4⋊C4D412yes—
40C3×C22⋊C4—22no—
41C3×C42—22no—
42C3×C42—22no—
43C22×Q8C22×C311yescharacteristic
44C2×M16C22×C312yes—
45C4⋊Q8—22no—
46#125—22no—
47C22⋊Q8—22no—
48#117C22×C312yes—
49C2×C4⋊C4C22×C311yescharacteristic
50C2×C42C22×C311yescharacteristic
51#103—22no—
52#103—22no—
53#95—22no—
54C23×C3C2×D411yescharacteristic
55C3×Q8—24no—
56C3×Q8—42no—
57C3×Q8—82no—
58C2×C3×C4—22no—
59C2×C3×C4—22no—
60C2×C3×C4—22no—
61C2×C3×C4—22no—
62C2×C3×C4—22no—
63C2×C3×C4—41no—
64C2×C3×C4—41no—
65C2×C3×C4—41no—
66C2×C3×C4—41no—
67C2×C3×C4—42no—
68C2×C3×C4C2×D412yes—
69C2×C3×C4C2×Q811yescharacteristic
70C2×C3×C4#4112yes—
71C2×C3×C4#4111yescharacteristic
72C3×C8—42no—
73C2×Q8—22no—
74C2×Q8—21no—
75C2×Q8—22no—
76C2×Q8—22no—
77C2×Q8C3×Q812yescomplemented
78C22×C4—21no—
79C22×C4—21no—
80C22×C4C3×D412yes—
81C22×C4C23×C311yescharacteristic
82M16—22no—
83M16—22no—
84C2×C8—22no—
85C4⋊C4—22no—
86C4⋊C4—24no—
87C4⋊C4—22no—
88C4⋊C4C3×D412yes—
89C4⋊C4C3×D412yes—
90C22⋊C4—22no—
91C42—22no—
92C42—22no—
93C22×C3—21no—
94C22×C3—21no—
95C22×C3#12011yescharacteristic
96C22×C3C22⋊Q811yescharacteristic
97C22×C3#12411yescharacteristic
98C3×C4—42no—
99C3×C4—42no—
100C3×C4—42no—
101C3×C4—42no—
102C3×C4—42no—
103C3×C4C22⋊Q812yes—
104C3×C4#12412yes—
105C23C2×C3×D411yescharacteristic
106Q8—24no—
107Q8—42no—
108Q8—82no—
109C2×C4—22no—
110C2×C4—22no—
111C2×C4—22no—
112C2×C4—22no—
113C2×C4—22no—
114C2×C4—41no—
115C2×C4—41no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—42no—
119C2×C4C2×C3×D412yes—
120C2×C4C2×C3×Q811yescharacteristic
121C2×C4C3×#4112yes—
122C2×C4C3×#4111yescharacteristic
123C8—42no—
124C2×C3—21no—
125C2×C3—21no—
126C2×C3#39311yescharacteristic
127C2×C3#45511yescharacteristic
128C2×C3#45611yescharacteristic
129C22—21no—
130C22—21no—
131C22C3×#12011yescharacteristic
132C22C3×C22⋊Q811yescharacteristic
133C22C3×#12411yescharacteristic
134C4—42no—
135C4—42no—
136C4—42no—
137C4—42no—
138C4—42no—
139C4C3×C22⋊Q812yes—
140C4C3×#12412yes—
141C3#202811yescharacteristic, direct product factor, Sylow
142C2—21no—
143C2—21no—
144C2C3×#39311yescharacteristic
145C2C3×#45511yescharacteristic
146C2C3×#45611yescharacteristic
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. #2028C3direct (N × H)
27. C2×C3×Q8Q8semidirect
77. C2×Q8C3×Q8semidirect
141. C3#2028direct (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×#4192
C3×#3912
C3×#3432
C3×#3392
#20283