Finite Group Databasebeta

← #34060589

Subgroups — #34060589

Order 19072.

300 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 66 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
1#23750568C212yesmaximal
2#23750503C214yesmaximal
3C2×#18011869C211yesmaximal, characteristic
4C2×C22⋊#10597010C2214yes—
5(C2×#10597010)⋊C4—24no—
6C22×C4×D149C2211yescharacteristic
7#18011869—24no—
8C2×C4⋊Dic149C411yescharacteristic, complemented
9C2×#14558713C2212yes—
10C2×C4×Dic149C412yescomplemented
11C2×C4⋊C4×C149C411yescharacteristic, complemented
12C22×#10597010—24no—
13C22⋊#10597010—28no—
14C23×D149C2311yescharacteristic
15C22×Dic149C2×C411yescharacteristic
16C22×Dic149C2×C412yes—
17C2×C4×D149—24no—
18C2×C4×D149D414yes—
19C4⋊Dic149—22no—
20#14558713—24no—
21C4×Dic149—24no—
22C22×C4×C149C2×C411yescharacteristic
23C22×C4×C149C2×C412yes—
24C4⋊C4×C149—22no—
25C2×#10597010—44no—
26C2×#10597010—44no—
27C2×#10597010—44no—
28C22×D149—41no—
29C22×D149—41no—
30C22×D149C2×D412yes—
31C22×D149#4114yes—
32C2×Dic149—22no—
33C2×Dic149—22no—
34C2×Dic149—42no—
35C2×Dic149C22⋊C412yes—
36C4×D149—28no—
37C23×C149C22×C411yescharacteristic
38C2×C4×C149—22no—
39C2×C4×C149—22no—
40C2×C4×C149—42no—
41C2×C4×C149C22⋊C412yes—
42C22×C149—21no—
43C22×C149—21no—
44C22×C149C2×C22⋊C411yescharacteristic
45C22×C149#11712yes—
46C2×D149—22no—
47C2×D149—22no—
48C2×D149—44no—
49C2×D149#12314yes—
50#10597010—84no—
51C4×C149—22no—
52C4×C149—42no—
53Dic149—22no—
54Dic149—42no—
55C2×C149—22no—
56C2×C149#38111yescharacteristic
57C2×C149#41011yescharacteristic
58C2×C149#41011yescharacteristic
59D149—24no—
60C149#182011yescharacteristic, complemented, Sylow
61#1820—1491nomaximal, Sylow
62C2×#117—1491no—
63#381—1492no—
64#342—1494no—
65C23×C4—1491no—
66#117—2984no—
67C2×C4⋊C4—1491no—
68C2×C4⋊C4#1059701011yescharacteristic, complemented
69C2×C22⋊C4—1494no—
70C2×C22⋊C4—1492no—
71C2×C42—1492no—
72#95—2984no—
73C24—1491no—
74C22×C4—2984no—
75C22×C4—2984no—
76C22×C4—1491no—
77C22×C4—1494no—
78C22×C4—1492no—
79C22×C4C2×#1059701012yes—
80C22×C4C2×#1059701011yescharacteristic
81C4⋊C4—22no—
82C4⋊C4—2982no—
83C22⋊C4—2984no—
84C22⋊C4—2988no—
85C42—2984no—
86C23—5961no—
87C23—5961no—
88C23—1492no—
89C23—1494no—
90C23C22×#1059701011yescharacteristic
91C2×C4—22no—
92C2×C4—22no—
93C2×C4—42no—
94C2×C4—2988no—
95C2×C4—2982no—
96C2×C4—2982no—
97C2×C4—5962no—
98C2×C4—5964no—
99C2×C4—5964no—
100C2×C4—5964no—
101C2×C4—1492no—
102C2×C4C22⋊#1059701012yes—
103C22—21no—
104C22—21no—
105C22—2982no—
106C22—2982no—
107C22—5964no—
108C22—1494no—
109C22C2×C22⋊#1059701011yescharacteristic
110C22#1801199012yes—
111C4—22no—
112C4—42no—
113C4—2982no—
114C4—5962no—
115C4—11924no—
116C2—22no—
117C2—2984no—
118C2#2375056811yescharacteristic
119C2#2375060511yescharacteristic
120C2#2375060611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC2×C4⋊C4×C149C4
socleC22×C149C2×C22⋊C4
prime radical, cosocleC23×D149C23
hypercenterC2×C4⋊C4#10597010
hypocenterC149#1820
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
8. C2×C4⋊Dic149C4semidirect
10. C2×C4×Dic149C4semidirect
11. C2×C4⋊C4×C149C4semidirect
60. C149#1820semidirect
68. C2×C4⋊C4#10597010semidirect

Maximal subgroups

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

subgroupindex
#237505682
#237505032
C2×#180118692
#1820149