Finite Group Databasebeta

← #34060591

Subgroups — #34060591

Order 19072.

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

normal subgroups only

This group has 316 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#23750597C212yesmaximal
2#23750505C214yesmaximal, complemented
3C2×C4⋊C4×D149C211yesmaximal, characteristic
4C2×#14558745C2214yes—
5#18011968—22no—
6#18011968—22no—
7C22×C4×D149C412yes—
8C22×C4×D149C2211yescharacteristic
9C2×C4⋊Dic149C411yescharacteristic
10C2×#14558715C2212yes—
11C4⋊C4×D149—22no—
12C4⋊C4×D149—22no—
13C2×C4⋊C4×C149C411yescharacteristic
14#14558745—28no—
15C2×#11924753—24no—
16C23×D149C2×C411yescharacteristic
17C22×Dic149C2×C412yes—
18C22×Dic149C2311yescharacteristic
19C2×C4×D149—24no—
20C2×C4×D149—22no—
21C2×C4×D149—22no—
22C2×C4×D149—44no—
23C2×C4×D149D412yes—
24C2×C4×D149D412yes—
25C4⋊Dic149—22no—
26#14558715—24no—
27C22×C4×C149C2×C411yescharacteristic
28C22×C4×C149C2×C412yes—
29C4⋊C4×C149—22no—
30#11924753—44no—
31C22×D149—22no—
32C22×D149—22no—
33C22×D149—22no—
34C22×D149C22⋊C411yescharacteristic
35C22×D149C22⋊C411yescharacteristic
36C2×Dic149—22no—
37C2×Dic149—42no—
38C2×Dic149C2×D412yes—
39C2×Dic149#4114yes—
40C4×D149—24no—
41C4×D149—24no—
42C4×D149—44no—
43C4×D149—44no—
44C23×C149C22×C411yescharacteristic
45C2×C4×C149—22no—
46C2×C4×C149—22no—
47C2×C4×C149—42no—
48C2×C4×C149C22⋊C412yes—
49C22×C149—21no—
50C22×C149—21no—
51C22×C149C2×C22⋊C411yescharacteristic
52C22×C149#11712yes—
53C2×D149—28no—
54C2×D149—21no—
55C2×D149—21no—
56C2×D149—21no—
57C2×D149—21no—
58C2×D149#10012yes—
59C2×D149#10112yes—
60C4×C149—22no—
61C4×C149—42no—
62Dic149—42no—
63Dic149#12314yes—
64C2×C149—22no—
65C2×C149#38111yescharacteristic
66C2×C149C2×#10011yescharacteristic
67C2×C149C2×#10111yescharacteristic
68D149—22no—
69D149—22no—
70C149#182111yescharacteristic, complemented, Sylow
71#1821—1491nomaximal, Sylow
72C22×C4⋊C4—1491no—
73#407—1492no—
74#343—1494no—
75C23×C4—1491no—
76C23×C4—1492no—
77C2×M16—1494no—
78C2×C4⋊C4—2982no—
79C2×C4⋊C4—2982no—
80C2×C4⋊C4—1492no—
81C2×C4⋊C4—1491no—
82C2×C4⋊C4#1059701011yescharacteristic
83C22⋊C8—2982no—
84C22⋊C8—2982no—
85C24—1491no—
86C22×C4—2984no—
87C22×C4—2982no—
88C22×C4—2982no—
89C22×C4—5964no—
90C22×C4—1492no—
91C22×C4—1492no—
92C22×C4—1492no—
93C22×C4—1491no—
94C22×C4C2×#1059701012yes—
95C22×C4C2×#1059701011yescharacteristic
96M16—2988no—
97C2×C8—2984no—
98C4⋊C4—22no—
99C4⋊C4—2984no—
100C4⋊C4—2982no—
101C23—2982no—
102C23—2982no—
103C23—2982no—
104C23—1491no—
105C23—1491no—
106C23C22×#1059701011yescharacteristic
107C2×C4—22no—
108C2×C4—22no—
109C2×C4—42no—
110C2×C4—2984no—
111C2×C4—2984no—
112C2×C4—2982no—
113C2×C4—5964no—
114C2×C4—5964no—
115C2×C4—5962no—
116C2×C4—1492no—
117C2×C4—1494no—
118C2×C4C22⋊#1059701012yes—
119C8—5964no—
120C22—21no—
121C22—21no—
122C22—2988no—
123C22—2981no—
124C22—2981no—
125C22—2981no—
126C22—2981no—
127C22—1492no—
128C22—1492no—
129C22C2×C22⋊#1059701011yescharacteristic
130C22#1801199012yes—
131C4—22no—
132C4—42no—
133C4—5962no—
134C4—1494no—
135C2—22no—
136C2—2982no—
137C2—2982no—
138C2#2375056811yescharacteristic
139C2D149⋊#10011yescharacteristic
140C2D149⋊#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC2×C4⋊C4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC23×D149C2×C4
cosocleC22×Dic149C23
hypercenterC2×C4⋊C4#10597010
hypocenterC149#1821
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

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

Maximal subgroups

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

subgroupindex
#237505972
#237505052
C2×C4⋊C4×D1492
#1821149