Finite Group Databasebeta

← C2×#1020⋊C3 #10596774

Subgroups — C2×#1020⋊C3 #10596774

Order 576.

149 conjugacy classes of subgroups; only the 16 normal subgroups are shown.

normal subgroups only

This group has 149 conjugacy classes of subgroups — too many to draw. Only its 16 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×A42C211yesmaximal, characteristic, complemented
2#1020⋊C3C212yesmaximal, direct product factor
3C2×#1020C311yesmaximal, characteristic, complemented
4C2×#120⋊C3—31nomaximal
5A42C2211yescharacteristic, complemented
6C2×C22⋊A4D311yescharacteristic, complemented
7C2×C22⋊A4C2×C311yescharacteristic, complemented
8C23×A4—21no—
9#1020C2×C312yescomplemented
10#120⋊C3—32no—
11C2×C3×A4—81no—
12C2×#120—31noSylow
13C22⋊A4C2×D311yescharacteristic, complemented
14C22⋊A4C22×C311yescharacteristic, complemented
15C22×A4—21no—
16C22×A4—61no—
17C22×A4—61no—
18C22×A4—121no—
19C2×S4—121no—
20C2×C3×D3—161nomaximal
21C3×A4—81no—
22C25C3×D311yescharacteristic, complemented
23C22×D4—91no—
24#120—32no—
25#120—92no—
26C2×C22⋊C4—91no—
27C23×C3—81no—
28C2×A4—21no—
29C2×A4—61no—
30C2×A4—61no—
31C2×A4—81no—
32C2×A4—81no—
33C2×A4—121no—
34C2×A4—121no—
35C2×A4—122no—
36S4—122no—
37C2×C32—161no—
38C3×D3—162no—
39C24—31no—
40C24—61no—
41C24—61no—
42C24—91no—
43C24—91no—
44C24C2×C3×D311yescharacteristic, complemented
45C2×D4—92no—
46C2×D4—92no—
47C2×D4—181no—
48C2×D4—181no—
49C2×D4—181no—
50C2×D4—181no—
51C22×C4—91no—
52C22⋊C4—92no—
53C22⋊C4—92no—
54C22×C3—81no—
55C22×C3—241no—
56C22×C3—241no—
57C22×C3—481no—
58C2×D3—161no—
59A4—21no—
60A4—81no—
61A4—81no—
62A4—121no—
63A4—121no—
64C32—161noSylow
65C23—21no—
66C23—31no—
67C23—31no—
68C23—32no—
69C23—61no—
70C23—61no—
71C23—91no—
72C23—91no—
73C23—91no—
74C23—91no—
75C23—91no—
76C23—181no—
77C23—181no—
78C23—181no—
79C23—182no—
80C23—181no—
81C23—181no—
82D4—182no—
83D4—182no—
84D4—182no—
85D4—182no—
86C2×C4—92no—
87C2×C4—181no—
88C2×C4—181no—
89C2×C3—81no—
90C2×C3—161no—
91C2×C3—161no—
92C2×C3—241no—
93C2×C3—241no—
94C2×C3—482no—
95D3—162no—
96C22—21no—
97C22—31no—
98C22—31no—
99C22—61no—
100C22—61no—
101C22—91no—
102C22—91no—
103C22—91no—
104C22—91no—
105C22—91no—
106C22—121no—
107C22—181no—
108C22—181no—
109C22—181no—
110C22—182no—
111C22—182no—
112C22—361no—
113C4—182no—
114C3—81no—
115C3—161no—
116C3—161no—
117C2—61no—
118C2—61no—
119C2—91no—
120C2—91no—
121C2—122no—
122C2#1020⋊C311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2#1020⋊C3
commutator, cosocle, hypocenterC22⋊A4C22×C3
FrattiniC1G
Fitting, socleC25C3×D3
LCSG ▷ C22⋊A4
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×A42C2semidirect
2. #1020⋊C3C2direct (N × H)
3. C2×#1020C3semidirect
5. A42C22semidirect
6. C2×C22⋊A4D3semidirect
7. C2×C22⋊A4C2×C3semidirect
9. #1020C2×C3semidirect
13. C22⋊A4C2×D3semidirect
14. C22⋊A4C22×C3semidirect
22. C25C3×D3semidirect
44. C24C2×C3×D3semidirect
122. C2#1020⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×A422
#1020⋊C32
C2×#10203
C2×#120⋊C33
C2×C3×D316