Finite Group Databasebeta

← #34060155

Subgroups — #34060155

Order 19072.

212 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 62 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#23750646C211yesmaximal, characteristic
2C4×#14558745C211yesmaximal, characteristic
3#23750482C214yesmaximal, complemented
4C2×#18011902C211yesmaximal, characteristic
5C2×#14558745—21no—
6C4⋊#11924753—21no—
7C22⋊#11924753—21no—
8#18011966C2212yes—
9#18011966C2212yes—
10C4×#11924753—21no—
11#18011902—21no—
12#18011902—21no—
13#18011902C412yes—
14#18011902C2212yes—
15C2×C4⋊Dic149—21no—
16C2×C4⋊Dic149C411yescharacteristic
17C2×#14558715—21no—
18C2×C4×Dic149C2211yescharacteristic
19C2×C4⋊C4×C149C411yescharacteristic
20#14558745—24no—
21C2×#11924753—22no—
22C2×#11924753—22no—
23C22×Dic149—21no—
24C22×Dic149D411yescharacteristic
25C22×Dic149D411yescharacteristic
26C4⋊Dic149—22no—
27C4⋊Dic149—22no—
28C4⋊Dic149—21no—
29C4⋊Dic149C2×C412yes—
30#14558715—22no—
31#14558715—22no—
32C4×Dic149C2×C411yescharacteristic
33C4×Dic149D411yescharacteristic
34C4×Dic149D411yescharacteristic
35C4×Dic149C2311yescharacteristic
36C22×C4×C149—21no—
37C22×C4×C149C2×C411yescharacteristic
38C4⋊C4×C149—21no—
39C4⋊C4×C149C2×C412yes—
40#11924753—24no—
41#11924753—42no—
42C2×Dic149—22no—
43C2×Dic149—22no—
44C2×Dic149—41no—
45C2×Dic149—42no—
46C2×Dic149C22⋊C411yescharacteristic
47C2×Dic149C22⋊C411yescharacteristic
48C2×Dic149C2×D411yescharacteristic
49C2×Dic149C2×D411yescharacteristic
50C23×C149C22⋊C411yescharacteristic
51C2×C4×C149—22no—
52C2×C4×C149—22no—
53C2×C4×C149—42no—
54C2×C4×C149C22⋊C411yescharacteristic
55C2×C4×C149C22×C411yescharacteristic
56C22×C149—21no—
57C22×C149—21no—
58C22×C149#10412yes—
59C22×C149C2×C22⋊C411yescharacteristic
60C4×C149—21no—
61C4×C149—42no—
62C4×C149#10112yes—
63Dic149—21no—
64Dic149—21no—
65Dic149—21no—
66Dic149—21no—
67Dic149—42no—
68C2×C149—22no—
69C2×C149C2×#10111yescharacteristic
70C2×C149C2×#10411yescharacteristic
71C2×C149#42111yescharacteristic
72C149#152811yescharacteristic, complemented, Sylow
73#1528—1491nomaximal, Sylow
74C2×#125—1491no—
75#432—1491no—
76C4×M16—1491no—
77#330—1494no—
78C2×M16—2981no—
79#125—2981no—
80#125—2981no—
81#125—1492no—
82#125—1492no—
83C2×C4⋊C4—2981no—
84C2×C4⋊C4—2981no—
85C2×C4⋊C4—1491no—
86C2×C4⋊C4#1059701011yescharacteristic
87C2×C42—1491no—
88C4⋊C8—2981no—
89C22⋊C8—2981no—
90#97—1492no—
91#97—1492no—
92C4×C8—2981no—
93C22×C4—21no—
94C22×C4—2981no—
95C22×C4—1491no—
96C22×C4—1491no—
97C22×C4C2×#1059701011yescharacteristic
98M16—2984no—
99C2×C8—2982no—
100C2×C8—2982no—
101C4⋊C4—21no—
102C4⋊C4—2982no—
103C4⋊C4—2982no—
104C4⋊C4—2982no—
105C4⋊C4—2982no—
106C4⋊C4—2981no—
107C4⋊C4—1492no—
108C4⋊C4C2×#1059701012yes—
109C42—1491no—
110C42—1491no—
111C42—1491no—
112C42—1491no—
113C23C22⋊#1059701011yescharacteristic
114C2×C4—22no—
115C2×C4—22no—
116C2×C4—42no—
117C2×C4—2982no—
118C2×C4—2982no—
119C2×C4—5961no—
120C2×C4—5962no—
121C2×C4—1491no—
122C2×C4—1491no—
123C2×C4—1491no—
124C2×C4—1491no—
125C2×C4C22⋊#1059701011yescharacteristic
126C2×C4C22×#1059701011yescharacteristic
127C8—2984no—
128C8—5962no—
129C22—21no—
130C22—21no—
131C22#1801197612yes—
132C22C2×C22⋊#1059701011yescharacteristic
133C4—21no—
134C4—42no—
135C4—2981no—
136C4—2981no—
137C4—2981no—
138C4—2981no—
139C4—5962no—
140C4#1801197212yes—
141C2—22no—
142C2C2×#1801197211yescharacteristic
143C2C2×#1801197611yescharacteristic
144C2#2375062311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC2×C4⋊C4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC23×C149C22⋊C4
cosocleC4×Dic149C23
hypercenterC2×C4⋊C4#10597010
hypocenterC149#1528
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #23750482C2semidirect
72. C149#1528semidirect

Maximal subgroups

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

subgroupindex
#237506462
C4×#145587452
#237504822
C2×#180119022
#1528149