Finite Group Databasebeta

← #34060587

Subgroups — #34060587

Order 19072.

504 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 70 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#23750566C212yesmaximal
2#23750503C214yesmaximal, complemented
3C2×C22⋊C4×D149C211yesmaximal, characteristic
4C2×C22⋊#10597010—24no—
5C2×C22⋊#10597010C2214yes—
6C24×D149C2211yescharacteristic
7C22×C4×D149C412yescomplemented
8C2×C22⋊Dic149C411yescharacteristic, complemented
9C2×#14558713C2212yes—
10C22⋊C4×D149—24no—
11C2×C22⋊C4×C149C411yescharacteristic, complemented
12C22×#10597010—24no—
13C22⋊#10597010—28no—
14C22⋊#10597010—48no—
15C23×D149—24no—
16C23×D149—44no—
17C23×D149C2×C411yescharacteristic
18C23×D149D414yes—
19C23×D149C2311yescharacteristic
20C22×Dic149C2×C412yes—
21C2×C4×D149—22no—
22C2×C4×D149—22no—
23C2×C4×D149—44no—
24C22⋊Dic149—22no—
25#14558713—24no—
26C24×C149C2×C411yescharacteristic
27C22×C4×C149C2×C412yes—
28C22⋊C4×C149—22no—
29C2×#10597010—48no—
30C2×#10597010—44no—
31C22×D149—22no—
32C22×D149—24no—
33C22×D149—28no—
34C22×D149—28no—
35C22×D149—44no—
36C22×D149—42no—
37C22×D149—416no—
38C22×D149C22⋊C412yes—
39C22×D149C2×D412yes—
40C22×D149#4114yes—
41C2×Dic149—22no—
42C2×Dic149—42no—
43C4×D149—44no—
44C4×D149—44no—
45C23×C149—22no—
46C23×C149—42no—
47C23×C149C22⋊C412yes—
48C23×C149C22×C411yescharacteristic
49C2×C4×C149—22no—
50C2×C4×C149—42no—
51C22×C149—22no—
52C22×C149—22no—
53C22×C149—24no—
54C22×C149—44no—
55C22×C149C2×C22⋊C411yescharacteristic
56C22×C149#11712yes—
57C2×D149—28no—
58C2×D149—22no—
59C2×D149—22no—
60C2×D149—24no—
61C2×D149—44no—
62C2×D149—416no—
63C2×D149#9914yes—
64C2×D149#12314yes—
65#10597010—84no—
66C4×C149—42no—
67Dic149—42no—
68C2×C149—22no—
69C2×C149—42no—
70C2×C149#38111yescharacteristic
71C2×C149C2×#9912yes—
72D149—24no—
73D149—24no—
74C149#181911yescharacteristic, complemented, Sylow
75#1819—1491nomaximal, Sylow
76C22×C22⋊C4—1491no—
77#379—1492no—
78#342—1494no—
79C25—1491no—
80C23×C4—1492no—
81C2×C22⋊C4—2984no—
82C2×C22⋊C4—2984no—
83C2×C22⋊C4—1494no—
84C2×C22⋊C4—1491no—
85C2×C22⋊C4—1492no—
86C2×C22⋊C4#1059701011yescharacteristic, complemented
87C24—2984no—
88C24—5964no—
89C24—1491no—
90C24—1494no—
91C24—1491no—
92C24C2×#1059701011yescharacteristic
93C22×C4—2982no—
94C22×C4—2982no—
95C22×C4—2984no—
96C22×C4—5964no—
97C22×C4—1492no—
98C22×C4C2×#1059701012yes—
99C22⋊C4—22no—
100C22⋊C4—2984no—
101C22⋊C4—2982no—
102C22⋊C4—2988no—
103C22⋊C4—5968no—
104C23—22no—
105C23—42no—
106C23—2984no—
107C23—2988no—
108C23—2988no—
109C23—2982no—
110C23—5962no—
111C23—5964no—
112C23—59616no—
113C23—1492no—
114C23—1492no—
115C23—1494no—
116C23C22⋊#1059701012yes—
117C23C22×#1059701011yescharacteristic
118C2×C4—22no—
119C2×C4—42no—
120C2×C4—2982no—
121C2×C4—5964no—
122C2×C4—5964no—
123C2×C4—5962no—
124C2×C4—5968no—
125C2×C4—5964no—
126C22—22no—
127C22—22no—
128C22—24no—
129C22—44no—
130C22—2988no—
131C22—2982no—
132C22—2984no—
133C22—2982no—
134C22—5964no—
135C22—59616no—
136C22—1494no—
137C22—1494no—
138C22C2×C22⋊#1059701011yescharacteristic
139C22#1801199012yes—
140C4—42no—
141C4—5962no—
142C4—11924no—
143C2—22no—
144C2—42no—
145C2—2984no—
146C2—2984no—
147C2#2375056811yescharacteristic
148C2D149⋊#9912yes—
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC2×C22⋊C4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC24×D149C22
cosocleC23×D149C23
hypercenterC2×C22⋊C4#10597010
hypocenterC149#1819
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #23750503C2semidirect
7. C22×C4×D149C4semidirect
8. C2×C22⋊Dic149C4semidirect
11. C2×C22⋊C4×C149C4semidirect
74. C149#1819semidirect
86. C2×C22⋊C4#10597010semidirect

Maximal subgroups

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

subgroupindex
#237505662
#237505032
C2×C22⋊C4×D1492
#1819149