Finite Group Databasebeta

← #34059951

Subgroups — #34059951

Order 19072.

300 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 68 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#23750645C212yesmaximal, complemented
2#23750468C214yesmaximal, complemented
3C2×D4×Dic149C211yesmaximal, characteristic
4#18011978—22no—
5C22⋊#11924753C2214yes—
6#18011966—22no—
7C23×Dic149C412yes—
8D4×Dic149—22no—
9D4×Dic149—22no—
10C2×C4⋊Dic149C411yescharacteristic
11C2×C22⋊Dic149C2212yes—
12C2×C4×Dic149C2211yescharacteristic
13C22×D4×C149C411yescharacteristic
14C2×#11924753—24no—
15C22×Dic149—22no—
16C22×Dic149—22no—
17C22×Dic149—44no—
18C22×Dic149C2×C411yescharacteristic
19C22×Dic149C2×C412yes—
20C22×Dic149C2311yescharacteristic
21C4⋊Dic149—22no—
22C22⋊Dic149—24no—
23C4×Dic149D412yes—
24C4×Dic149D412yes—
25C24×C149C2×C412yes—
26C2×D4×C149—24no—
27C2×D4×C149—22no—
28C22×C4×C149C2×C411yescharacteristic
29#11924753—44no—
30C2×Dic149—22no—
31C2×Dic149—22no—
32C2×Dic149—41no—
33C2×Dic149—44no—
34C2×Dic149—44no—
35C2×Dic149—42no—
36C2×Dic149C22⋊C411yescharacteristic
37C2×Dic149C22⋊C411yescharacteristic
38C2×Dic149C2×D412yes—
39C23×C149—22no—
40C23×C149—22no—
41C23×C149—42no—
42C23×C149—42no—
43C23×C149M1614yes—
44C23×C149C22×C411yescharacteristic
45D4×C149—28no—
46C2×C4×C149—22no—
47C2×C4×C149C22⋊C412yes—
48C22×C149—21no—
49C22×C149—21no—
50C22×C149—24no—
51C22×C149—44no—
52C22×C149—44no—
53C22×C149—42no—
54C22×C149—42no—
55C22×C149C2×C22⋊C411yescharacteristic
56C22×C149C2×M1612yes—
57C4×C149—22no—
58Dic149—22no—
59Dic149—21no—
60Dic149—42no—
61Dic149#10012yes—
62C2×C149—22no—
63C2×C149—44no—
64C2×C149#40711yescharacteristic
65C2×C149#41011yescharacteristic
66C2×C149C2×#10011yescharacteristic
67C149#146611yescharacteristic, complemented, Sylow
68#1466—1491nomaximal, Sylow
69C2×C4×D4—1491no—
70#432—1492no—
71#323—1494no—
72C22×D4#1059701011yescharacteristic
73C23×C4—1492no—
74C4×D4—2982no—
75C4×D4—2982no—
76C2×C4⋊C4—1491no—
77C2×C22⋊C4—1492no—
78C2×C42—1491no—
79C4⋊C8—2982no—
80C22⋊C8—1494no—
81#97—2982no—
82C24C2×#1059701012yes—
83C2×D4—24no—
84C2×D4—22no—
85C22×C4—2982no—
86C22×C4—2982no—
87C22×C4—5964no—
88C22×C4—1491no—
89C22×C4—1492no—
90C22×C4—1491no—
91C22×C4C2×#1059701011yescharacteristic
92C2×C8—2984no—
93C4⋊C4—2982no—
94C22⋊C4—2984no—
95C42—1492no—
96C42—1492no—
97C23—22no—
98C23—22no—
99C23—42no—
100C23—42no—
101C23#1455874514yes—
102C23C22×#1059701011yescharacteristic
103D4—28no—
104C2×C4—22no—
105C2×C4—2982no—
106C2×C4—2982no—
107C2×C4—5961no—
108C2×C4—5964no—
109C2×C4—5964no—
110C2×C4—5962no—
111C2×C4—1491no—
112C2×C4—1492no—
113C2×C4—1491no—
114C2×C4C22⋊#1059701012yes—
115C8—5964no—
116C22—21no—
117C22—21no—
118C22—24no—
119C22—44no—
120C22—44no—
121C22—42no—
122C22—42no—
123C22C2×C22⋊#1059701011yescharacteristic
124C22C2×#1455874512yes—
125C4—22no—
126C4—2982no—
127C4—2981no—
128C4—5962no—
129C4—1492no—
130C2—22no—
131C2—44no—
132C2#2375059511yescharacteristic
133C2#2375060511yescharacteristic
134C2D149⋊#10011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
Fitting, prime radicalC22×D4×C149C4
socleC22×C149C2×C22⋊C4
cosocleC22×Dic149C23
hypercenterC22×D4#10597010
hypocenterC149#1466
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #23750645C2semidirect
2. #23750468C2semidirect
67. C149#1466semidirect

Maximal subgroups

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

subgroupindex
#237506452
#237504682
C2×D4×Dic1492
#1466149