Finite Group Databasebeta

← #34060590

Subgroups — #34060590

Order 19072.

316 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 74 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#23750595C212yesmaximal
2#23750505C214yesmaximal, complemented
3C22×#14558715C211yesmaximal, characteristic
4C2×#14558745C2214yes—
5C22⋊#11924753—22no—
6C22⋊#11924753—22no—
7C23×Dic149C411yescharacteristic
8C23×Dic149C2211yescharacteristic
9C2×#14558715—22no—
10C2×#14558715—22no—
11C2×#14558715C412yes—
12C2×#14558715C2212yes—
13C23×C4×C149C411yescharacteristic
14#14558745—28no—
15C2×#11924753—24no—
16C22×Dic149—24no—
17C22×Dic149—21no—
18C22×Dic149—21no—
19C22×Dic149—42no—
20C22×Dic149C2×C411yescharacteristic
21C22×Dic149C2×C412yes—
22C22×Dic149D412yes—
23C22×Dic149D412yes—
24C22×Dic149C2311yescharacteristic
25#14558715—24no—
26#14558715—24no—
27C24×C149C2×C411yescharacteristic
28C22×C4×C149—21no—
29C22×C4×C149—21no—
30C22×C4×C149—42no—
31C22×C4×C149C2×C412yes—
32#11924753—44no—
33C2×Dic149—22no—
34C2×Dic149—24no—
35C2×Dic149—24no—
36C2×Dic149—22no—
37C2×Dic149—42no—
38C2×Dic149—42no—
39C2×Dic149—42no—
40C2×Dic149C22⋊C412yes—
41C2×Dic149C2×D412yes—
42C2×Dic149#4114yes—
43C23×C149—22no—
44C23×C149—22no—
45C23×C149—22no—
46C23×C149C22⋊C411yescharacteristic
47C23×C149C22⋊C411yescharacteristic
48C23×C149C22×C411yescharacteristic
49C2×C4×C149—22no—
50C2×C4×C149—42no—
51C2×C4×C149—42no—
52C2×C4×C149—42no—
53C22×C149—28no—
54C22×C149—21no—
55C22×C149—21no—
56C22×C149—21no—
57C22×C149—21no—
58C22×C149—21no—
59C22×C149—21no—
60C22×C149#10012yes—
61C22×C149#10112yes—
62C22×C149C2×C22⋊C411yescharacteristic
63C22×C149#11712yes—
64C4×C149—42no—
65Dic149—22no—
66Dic149—42no—
67Dic149#12314yes—
68C2×C149—22no—
69C2×C149—22no—
70C2×C149—22no—
71C2×C149#38111yescharacteristic
72C2×C149C2×#10011yescharacteristic
73C2×C149C2×#10111yescharacteristic
74C149#182111yescharacteristic, complemented, Sylow
75#1821—1491nomaximal, Sylow
76C22×C4⋊C4—1491no—
77#407—1492no—
78#343—1494no—
79C23×C4—1491no—
80C23×C4—1491no—
81C23×C4#1059701011yescharacteristic
82C2×M16—1494no—
83C2×C4⋊C4—2982no—
84C2×C4⋊C4—2982no—
85C2×C4⋊C4—1492no—
86C2×C4⋊C4—1492no—
87C22⋊C8—2982no—
88C22⋊C8—2982no—
89C24C2×#1059701011yescharacteristic
90C22×C4—21no—
91C22×C4—21no—
92C22×C4—42no—
93C22×C4—2984no—
94C22×C4—2981no—
95C22×C4—2981no—
96C22×C4—5962no—
97C22×C4—1492no—
98C22×C4—1492no—
99C22×C4—1491no—
100C22×C4—1492no—
101C22×C4—1491no—
102C22×C4C2×#1059701012yes—
103M16—2988no—
104C2×C8—2984no—
105C4⋊C4—2984no—
106C4⋊C4—2984no—
107C23—22no—
108C23—22no—
109C23—22no—
110C23C22⋊#1059701011yescharacteristic
111C23C22⋊#1059701011yescharacteristic
112C23C22×#1059701011yescharacteristic
113C2×C4—22no—
114C2×C4—42no—
115C2×C4—42no—
116C2×C4—42no—
117C2×C4—2982no—
118C2×C4—2984no—
119C2×C4—2984no—
120C2×C4—2982no—
121C2×C4—5962no—
122C2×C4—5962no—
123C2×C4—5962no—
124C2×C4—1492no—
125C2×C4—1492no—
126C2×C4—1494no—
127C8—5964no—
128C22—28no—
129C22—21no—
130C22—21no—
131C22—21no—
132C22—21no—
133C22—21no—
134C22—21no—
135C22#1801197112yes—
136C22#1801197212yes—
137C22C2×C22⋊#1059701011yescharacteristic
138C22#1801199012yes—
139C4—42no—
140C4—2982no—
141C4—5962no—
142C4—1494no—
143C2—22no—
144C2—22no—
145C2—22no—
146C2#2375056811yescharacteristic
147C2C2×#1801197111yescharacteristic
148C2C2×#1801197211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC23×C4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC24×C149C2×C4
cosocleC22×Dic149C23
hypercenterC23×C4#10597010
hypocenterC149#1821
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #23750505C2semidirect
74. C149#1821semidirect

Maximal subgroups

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

subgroupindex
#237505952
#237505052
C22×#145587152
#1821149