Finite Group Databasebeta

← C3×#3189 #85053

Subgroups — C3×#3189 #85053

Order 384.

416 conjugacy classes of subgroups; only the 188 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 188 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×#484C214yesmaximal, complemented
3C3×#467C214yesmaximal, complemented
4C3×#451C214yesmaximal, complemented
5C2×C3×C22⋊C8C211yesmaximal, characteristic
6#3189C311yesmaximal, characteristic, direct product factor, Sylow
7C22×C3×Q8C2212yes—
8C23×C3×C4C2211yescharacteristic
9C2×C3×Q16C2214yescomplemented
10C22×C3×C8C2212yes—
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×#107C2214yescomplemented
19C3×#103C2218yescomplemented
20C3×C22⋊C8C2214yes—
21C2×C22⋊Q8C2×C312yes—
22#484C2×C314yescomplemented
23#467C2×C314yescomplemented
24#451C2×C314yescomplemented
25C2×C22⋊C8C2×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—
38C2×C3×C8—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
49C22×C8C22×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#107C22×C314yescomplemented
58#103C22×C318yescomplemented
59C22⋊C8C22×C314yes—
60C23×C3—41no—
61C23×C3—41no—
62C23×C3Q1614yescomplemented
63C23×C3C2×D411yescharacteristic
64C23×C3C2×D412yes—
65C3×Q8—28no—
66C3×Q8—44no—
67C2×C3×C4—22no—
68C2×C3×C4—24no—
69C2×C3×C4—24no—
70C2×C3×C4—24no—
71C2×C3×C4—42no—
72C2×C3×C4—41no—
73C2×C3×C4—44no—
74C2×C3×C4—44no—
75C2×C3×C4C2×D411yescharacteristic
76C2×C3×C4C2×D412yes—
77C2×C3×C4C2411yescharacteristic
78C3×C8—24no—
79C24C3×D411yescharacteristic
80C2×Q8—22no—
81C2×Q8—44no—
82C2×Q8C23×C314yes—
83C22×C4—22no—
84C22×C4—22no—
85C22×C4—42no—
86C22×C4C3×D412yes—
87C22×C4C3×D411yescharacteristic
88C22×C4C23×C312yes—
89C22×C4C23×C311yescharacteristic
90Q16—44no—
91C2×C8—42no—
92C2×C8C23×C314yes—
93C4⋊C4—24no—
94C4⋊C4—24no—
95C4⋊C4—22no—
96C4⋊C4C23×C314yes—
97C22⋊C4—24no—
98C22⋊C4—24no—
99C22×C3—22no—
100C22×C3—21no—
101C22×C3—22no—
102C22×C3—21no—
103C22×C3—44no—
104C22×C3C2×Q1612yes—
105C22×C3C2×Q1614yes—
106C22×C3C22×D411yescharacteristic
107C3×C4—21no—
108C3×C4—22no—
109C3×C4—44no—
110C3×C4—44no—
111C3×C4H(5,𝔽2)12yes—
112C23—41no—
113C23—41no—
114C23C3×Q1614yescomplemented
115C23C2×C3×D411yescharacteristic
116C23C2×C3×D412yes—
117Q8—28no—
118Q8—44no—
119C2×C4—22no—
120C2×C4—24no—
121C2×C4—24no—
122C2×C4—24no—
123C2×C4—41no—
124C2×C4—42no—
125C2×C4—44no—
126C2×C4—44no—
127C2×C4C2×C3×D411yescharacteristic
128C2×C4C2×C3×D412yes—
129C2×C4C24×C311yescharacteristic
130C8—24no—
131C2×C3—24no—
132C2×C3—22no—
133C2×C3#53411yescharacteristic
134C2×C3C22×Q1611yescharacteristic
135C2×C3#57511yescharacteristic
136C22—22no—
137C22—21no—
138C22—22no—
139C22—21no—
140C22—44no—
141C22C2×C3×Q1612yes—
142C22C2×C3×Q1614yes—
143C22C22×C3×D411yescharacteristic
144C4—22no—
145C4—21no—
146C4—44no—
147C4—44no—
148C4C3×H(5,𝔽2)12yes—
149C3#318911yescharacteristic, direct product factor, Sylow
150C2—24no—
151C2—22no—
152C2C3×#53411yescharacteristic
153C2C22×C3×Q1611yescharacteristic
154C2C3×#57511yescharacteristic
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×#484C2semidirect
3. C3×#467C2semidirect
4. C3×#451C2semidirect
6. #3189C3direct (N × H)
9. C2×C3×Q16C22semidirect
18. C3×#107C22semidirect
19. C3×#103C22semidirect
22. #484C2×C3semidirect
23. #467C2×C3semidirect
24. #451C2×C3semidirect
48. C2×Q16C22×C3semidirect
57. #107C22×C3semidirect
58. #103C22×C3semidirect
62. C23×C3Q16semidirect
114. C23C3×Q16semidirect
149. C3#3189direct (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×#4842
C3×#4672
C3×#4512
C2×C3×C22⋊C82
#31893