Finite Group Databasebeta

← #34059635

Subgroups — #34059635

Order 19072.

158 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 36 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#23750468C211yesmaximal, characteristic
2#23750468C211yesmaximal, characteristic
3#23749500C211yesmaximal, characteristic
4C22⋊#11924753—21no—
5C22⋊#11924753—21no—
6C23×Dic149C411yescharacteristic
7C2×C4⋊Dic149—21no—
8C2×C22⋊Dic149C2211yescharacteristic
9#18011818—21no—
10C2×C22⋊C4×C149C411yescharacteristic
11C2×#11924753—41no—
12C2×#11924753—41no—
13C22×Dic149—21no—
14C22×Dic149—41no—
15C22×Dic149—42no—
16C22×Dic149D411yescharacteristic
17C22×Dic149D411yescharacteristic
18C4⋊Dic149—42no—
19C22⋊Dic149—41no—
20C24×C149C2×C411yescharacteristic
21C22×C4×C149—21no—
22C22⋊C4×C149—21no—
23C22⋊C4×C149C812yescomplemented
24#11924753—81no—
25#11924753—81no—
26C2×Dic149—22no—
27C2×Dic149—21no—
28C2×Dic149—21no—
29C2×Dic149—41no—
30C2×Dic149—42no—
31C2×Dic149—41no—
32C2×Dic149—41no—
33C2×Dic149—41no—
34C2×Dic149—42no—
35C23×C149—21no—
36C23×C149—21no—
37C23×C149—41no—
38C23×C149—41no—
39C23×C149C22⋊C411yescharacteristic
40C23×C149C2×C811yescharacteristic
41C23×C149M1611yescharacteristic
42C2×C4×C149—22no—
43C2×C4×C149—41no—
44C2×C4×C149—41no—
45C22×C149—21no—
46C22×C149—21no—
47C22×C149—21no—
48C22×C149—21no—
49C22×C149—41no—
50C22×C149—41no—
51C22×C149—42no—
52C22×C149—41no—
53C22×C149—41no—
54C22×C149C22⋊C811yescharacteristic
55C22×C149#9911yescharacteristic
56C22×C149#10111yescharacteristic
57C4×C149—42no—
58Dic149—42no—
59Dic149—41no—
60Dic149—41no—
61C2×C149—21no—
62C2×C149—21no—
63C2×C149—41no—
64C2×C149—41no—
65C2×C149#32411yescharacteristic
66C2×C149AΣL(1,𝔽16)11yescharacteristic
67C2×C149#35211yescharacteristic
68C149#132611yescharacteristic, complemented, Sylow
69#1326—1491nomaximal, Sylow
70#385—1491no—
71#323—1491no—
72#323—1491no—
73C23×C4—1491no—
74C2×C4⋊C4—2981no—
75C2×C22⋊C4—1491no—
76C2×C22⋊C4#1059701011yescharacteristic
77C22⋊C8—2981no—
78C22⋊C8—2981no—
79#95—2981no—
80C24C2×#1059701011yescharacteristic
81C22×C4—21no—
82C22×C4—2981no—
83C22×C4—5962no—
84C22×C4—5961no—
85C22×C4—1491no—
86C22×C4—1491no—
87C2×C8—5961no—
88C2×C8—5961no—
89C4⋊C4—5962no—
90C22⋊C4—21no—
91C22⋊C4—5961no—
92C22⋊C4#1192475312yescomplemented
93C23—21no—
94C23—21no—
95C23—41no—
96C23—41no—
97C23C22⋊#1059701011yescharacteristic
98C23C2×#1192475311yescharacteristic
99C23#1455874511yescharacteristic
100C2×C4—22no—
101C2×C4—41no—
102C2×C4—41no—
103C2×C4—2982no—
104C2×C4—2981no—
105C2×C4—2981no—
106C2×C4—5961no—
107C2×C4—5962no—
108C2×C4—5961no—
109C2×C4—5961no—
110C2×C4—5961no—
111C2×C4—5962no—
112C8—11921no—
113C8—11921no—
114C22—21no—
115C22—21no—
116C22—21no—
117C22—21no—
118C22—41no—
119C22—41no—
120C22—42no—
121C22—41no—
122C22—41no—
123C22C22⋊#1192475311yescharacteristic
124C22#1801197011yescharacteristic
125C22#1801197211yescharacteristic
126C4—42no—
127C4—5961no—
128C4—5962no—
129C4—5961no—
130C2—21no—
131C2—21no—
132C2—41no—
133C2—41no—
134C2#2375047011yescharacteristic
135C2#2375052611yescharacteristic
136C2#2375052811yescharacteristic
subgroupG/H
centerC22#18011970
commutatorC23×C149C2×C8
FrattiniC24C2×#10597010
FittingC2×C22⋊C4×C149C4
socleC22×C149#99
prime radicalC24×C149C2×C4
cosocleC2×C22⋊Dic149C22
hypercenterC2×C22⋊C4#10597010
hypocenterC149#1326
LCSG ▷ C23×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C23 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
23. C22⋊C4×C149C8semidirect
68. C149#1326semidirect
92. C22⋊C4#11924753semidirect

Maximal subgroups

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

subgroupindex
#237504682
#237495002
#1326149