Finite Group Databasebeta

← #34060526

Subgroups — #34060526

Order 19072.

564 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 90 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×#18011972C214yesmaximal, complemented
2#23750597C212yesmaximal
3C22×Q8×D149C211yesmaximal, characteristic
4C2×#14558745C2214yes—
5#18011972—28no—
6#18011968—24no—
7C22×Dic298C411yescharacteristic
8C22×Dic298C2212yes—
9C2×Q8×D149—28no—
10C2×Q8×D149—24no—
11C22×C4×D149C412yes—
12C22×C4×D149C2211yescharacteristic
13C22×Q8×C149C411yescharacteristic
14#14558745—28no—
15C2×#11924753—24no—
16C23×D149C2×C411yescharacteristic
17C2×Dic298—24no—
18C2×Dic298—24no—
19C2×Dic298—24no—
20C2×Dic298—22no—
21C2×Dic298D418yes—
22Q8×D149—232no—
23C22×Dic149C2×C412yes—
24C22×Dic149C2311yescharacteristic
25C2×C4×D149—24no—
26C2×C4×D149—24no—
27C2×C4×D149—24no—
28C2×C4×D149—24no—
29C2×C4×D149D414yes—
30C2×Q8×C149—24no—
31C2×Q8×C149—22no—
32C22×C4×C149C2×C412yes—
33C22×C4×C149C2×C411yescharacteristic
34#11924753—44no—
35C22×D149—22no—
36C22×D149—24no—
37C22×D149C22⋊C412yes—
38Dic298—28no—
39Dic298—216no—
40C2×Dic149—22no—
41C2×Dic149—22no—
42C2×Dic149C22⋊C414yes—
43C2×Dic149C2×D414yes—
44C2×Dic149C2×D412yes—
45C4×D149—216no—
46C4×D149—28no—
47C23×C149C22×C411yescharacteristic
48Q8×C149—28no—
49C2×C4×C149—22no—
50C2×C4×C149—22no—
51C2×C4×C149—22no—
52C2×C4×C149C22⋊C414yes—
53C2×C4×C149C22⋊C412yes—
54C22×C149—22no—
55C22×C149C2×C22⋊C412yes—
56C22×C149C2×C22⋊C411yescharacteristic
57C2×D149—28no—
58C2×D149—22no—
59C2×D149—22no—
60C2×D149#10114yescomplemented
61C4×C149—24no—
62C4×C149—22no—
63Dic149—24no—
64Dic149#12014yes—
65C2×C149—22no—
66C2×C149#37911yescharacteristic
67C2×C149C2×#10112yes—
68D149—24no—
69C149#178411yescharacteristic, complemented, Sylow
70#1784—1491nomaximal, Sylow
71C23×Q8—1491no—
72C2×#101—1494no—
73#407—1492no—
74C22×Q8—2988no—
75C22×Q8—2984no—
76C22×Q8—1492no—
77C22×Q8—1491no—
78C22×Q8#1059701011yescharacteristic
79C23×C4—1492no—
80C23×C4—1491no—
81C2×M16—1494no—
82#101—2988no—
83C22⋊C8—2984no—
84C24—1491no—
85C2×Q8—24no—
86C2×Q8—22no—
87C2×Q8—2984no—
88C2×Q8—2984no—
89C2×Q8—2984no—
90C2×Q8—29832no—
91C2×Q8—2982no—
92C2×Q8—1498no—
93C22×C4—2984no—
94C22×C4—2984no—
95C22×C4—2984no—
96C22×C4—2984no—
97C22×C4—1492no—
98C22×C4—1494no—
99C22×C4—1491no—
100C22×C4C2×#1059701012yes—
101C22×C4C2×#1059701011yescharacteristic
102M16—2988no—
103C2×C8—2984no—
104C23—2984no—
105C23—2982no—
106C23—1492no—
107C23C22×#1059701011yescharacteristic
108Q8—28no—
109Q8—2988no—
110Q8—29816no—
111C2×C4—22no—
112C2×C4—22no—
113C2×C4—22no—
114C2×C4—29816no—
115C2×C4—2988no—
116C2×C4—2982no—
117C2×C4—2982no—
118C2×C4—1494no—
119C2×C4—1494no—
120C2×C4—1492no—
121C2×C4C22⋊#1059701014yes—
122C2×C4C22⋊#1059701012yes—
123C8—5964no—
124C22—22no—
125C22—2988no—
126C22—2982no—
127C22—2982no—
128C22—1494no—
129C22C2×C22⋊#1059701012yes—
130C22C2×C22⋊#1059701011yescharacteristic
131C4—24no—
132C4—22no—
133C4—2984no—
134C4—1494no—
135C2—22no—
136C2—2984no—
137C2#2375056611yescharacteristic
138C2D149⋊#10112yes—
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC22×Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC23×D149C2×C4
cosocleC22×Dic149C23
hypercenterC22×Q8#10597010
hypocenterC149#1784
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#18011972C2semidirect
60. C2×D149#101semidirect
69. C149#1784semidirect

Maximal subgroups

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

subgroupindex
C2×#180119722
#237505972
C22×Q8×D1492
#1784149