Finite Group Databasebeta

← C3×#3195 #85059

Subgroups — C3×#3195 #85059

Order 384.

410 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 176 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
1C2×C3×C22⋊Q8C212yesmaximal
2C3×#483C214yesmaximal, complemented
3C3×#470C214yesmaximal, complemented
4C3×#451C214yesmaximal, complemented
5C3×#407C211yesmaximal, characteristic
6#3195C311yesmaximal, characteristic, direct product factor, Sylow
7C22×C3×Q8C2212yes—
8C23×C3×C4C2211yescharacteristic
9C2×C3×Q16C2214yescomplemented
10C2×C3×M16C2212yes—
11C3×C22⋊Q8—22no—
12C3×C22⋊Q8—22no—
13C3×C22⋊Q8C2214yes—
14C3×C22⋊Q8C2214yes—
15C2×C3×C4⋊C4—22no—
16C2×C3×C4⋊C4C2212yes—
17C2×C3×C22⋊C4—22no—
18C3×#106C2214yescomplemented
19C3×#103C2218yescomplemented
20C3×C22⋊C8C2214yes—
21C2×C22⋊Q8C2×C312yes—
22#483C2×C314yescomplemented
23#470C2×C314yescomplemented
24#451C2×C314yescomplemented
25#407C2×C311yescharacteristic
26C24×C3D411yescharacteristic
27C2×C3×Q8—22no—
28C2×C3×Q8—44no—
29C2×C3×Q8C2314yes—
30C22×C3×C4—22no—
31C22×C3×C4—22no—
32C22×C3×C4—42no—
33C22×C3×C4D412yes—
34C22×C3×C4D411yescharacteristic
35C22×C3×C4C2312yes—
36C22×C3×C4C2311yescharacteristic
37C3×Q16—44no—
38C3×M16—42no—
39C2×C3×C8C2314yes—
40C3×C4⋊C4—24no—
41C3×C4⋊C4—24no—
42C3×C4⋊C4—22no—
43C3×C4⋊C4C2314yes—
44C3×C22⋊C4—24no—
45C3×C22⋊C4—24no—
46C22×Q8C22×C312yes—
47C23×C4C22×C311yescharacteristic
48C2×Q16C22×C314yescomplemented
49C2×M16C22×C312yes—
50C22⋊Q8—22no—
51C22⋊Q8—22no—
52C22⋊Q8C22×C314yes—
53C22⋊Q8C22×C314yes—
54C2×C4⋊C4—22no—
55C2×C4⋊C4C22×C312yes—
56C2×C22⋊C4—22no—
57#106C22×C314yescomplemented
58#103C22×C318yescomplemented
59C22⋊C8C22×C314yes—
60C23×C3—24no—
61C23×C3—41no—
62C23×C3C2×D411yescharacteristic
63C23×C3C2×D412yes—
64C3×Q8—28no—
65C3×Q8—44no—
66C2×C3×C4—22no—
67C2×C3×C4—24no—
68C2×C3×C4—24no—
69C2×C3×C4—24no—
70C2×C3×C4—42no—
71C2×C3×C4—41no—
72C2×C3×C4—44no—
73C2×C3×C4—44no—
74C2×C3×C4C2×D411yescharacteristic
75C2×C3×C4C2×D412yes—
76C2×C3×C4C2411yescharacteristic
77C3×C8—24no—
78C24C3×D411yescharacteristic
79C2×Q8—22no—
80C2×Q8—44no—
81C2×Q8C23×C314yes—
82C22×C4—22no—
83C22×C4—22no—
84C22×C4—42no—
85C22×C4C3×D412yes—
86C22×C4C3×D411yescharacteristic
87C22×C4C23×C312yes—
88C22×C4C23×C311yescharacteristic
89Q16—44no—
90M16—42no—
91C2×C8C23×C314yes—
92C4⋊C4—24no—
93C4⋊C4—24no—
94C4⋊C4—22no—
95C4⋊C4C23×C314yes—
96C22⋊C4—24no—
97C22⋊C4—24no—
98C22×C3—22no—
99C22×C3—22no—
100C22×C3—21no—
101C22×C3—22no—
102C22×C3—44no—
103C22×C3#13714yes—
104C22×C3C22×D411yescharacteristic
105C3×C4—21no—
106C3×C4—22no—
107C3×C4—44no—
108C3×C4—44no—
109C3×C4H(5,𝔽2)12yes—
110C23—24no—
111C23—41no—
112C23C2×C3×D411yescharacteristic
113C23C2×C3×D412yes—
114Q8—28no—
115Q8—44no—
116C2×C4—22no—
117C2×C4—24no—
118C2×C4—24no—
119C2×C4—24no—
120C2×C4—41no—
121C2×C4—42no—
122C2×C4—44no—
123C2×C4—44no—
124C2×C4C2×C3×D411yescharacteristic
125C2×C4C2×C3×D412yes—
126C2×C4C24×C311yescharacteristic
127C8—24no—
128C2×C3—24no—
129C2×C3—41no—
130C2×C3#53411yescharacteristic
131C2×C3C2×#13712yes—
132C22—22no—
133C22—22no—
134C22—22no—
135C22—21no—
136C22—44no—
137C22C3×#13714yes—
138C22C22×C3×D411yescharacteristic
139C4—22no—
140C4—21no—
141C4—44no—
142C4—44no—
143C4C3×H(5,𝔽2)12yes—
144C3#319511yescharacteristic, direct product factor, Sylow
145C2—24no—
146C2—41no—
147C2C3×#53411yescharacteristic
148C2C2×C3×#13712yes—
subgroupG/H
center, socleC22×C3C22×D4
commutator, Frattini, cosocleC2×C4C24×C3
prime radicalC24×C3D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×#483C2semidirect
3. C3×#470C2semidirect
4. C3×#451C2semidirect
6. #3195C3direct (N × H)
9. C2×C3×Q16C22semidirect
18. C3×#106C22semidirect
19. C3×#103C22semidirect
22. #483C2×C3semidirect
23. #470C2×C3semidirect
24. #451C2×C3semidirect
48. C2×Q16C22×C3semidirect
57. #106C22×C3semidirect
58. #103C22×C3semidirect
144. C3#3195direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C22⋊Q82
C3×#4832
C3×#4702
C3×#4512
C3×#4072
#31953