Finite Group Databasebeta

← #34059965

Subgroups — #34059965

Order 19072.

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

normal subgroups only

This group has 204 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
2#23750642C211yesmaximal, characteristic
3#23750471C214yesmaximal
4C2×#18011902C211yesmaximal, characteristic
5#18011978—21no—
6C4⋊#11924753—21no—
7C22⋊#11924753C2212yes—
8C22⋊#11924753C2212yes—
9#18011966—21no—
10C4×#11924753—21no—
11#18011902—21no—
12#18011902—21no—
13#18011902—21no—
14#18011902—21no—
15C2×C4⋊Dic149C411yescharacteristic
16C2×C4⋊Dic149C412yes—
17C2×#14558715C2212yes—
18C2×C4×Dic149C2211yescharacteristic
19C2×C4⋊C4×C149C411yescharacteristic
20C2×#11924753—22no—
21C2×#11924753—22no—
22C22×Dic149C2×C412yes—
23C22×Dic149C2×C411yescharacteristic
24C22×Dic149C2311yescharacteristic
25C4⋊Dic149—22no—
26C4⋊Dic149—22no—
27C4⋊Dic149—21no—
28C4⋊Dic149—21no—
29#14558715—22no—
30#14558715—22no—
31C4×Dic149D411yescharacteristic
32C4×Dic149D411yescharacteristic
33C4×Dic149D411yescharacteristic
34C4×Dic149D411yescharacteristic
35C22×C4×C149C2×C411yescharacteristic
36C22×C4×C149C2×C412yes—
37C4⋊C4×C149—21no—
38C4⋊C4×C149—21no—
39#11924753—42no—
40#11924753—42no—
41C2×Dic149—22no—
42C2×Dic149—22no—
43C2×Dic149—24no—
44C2×Dic149—41no—
45C2×Dic149C22⋊C411yescharacteristic
46C2×Dic149C22⋊C411yescharacteristic
47C2×Dic149C2×D411yescharacteristic
48C2×Dic149C2×D411yescharacteristic
49C23×C149C22×C411yescharacteristic
50C2×C4×C149—22no—
51C2×C4×C149—22no—
52C2×C4×C149—42no—
53C2×C4×C149C22⋊C411yescharacteristic
54C2×C4×C149C22⋊C411yescharacteristic
55C22×C149—21no—
56C22×C149—21no—
57C22×C149C2×C22⋊C411yescharacteristic
58C22×C149#13112yes—
59C4×C149—21no—
60C4×C149—42no—
61C4×C149#10112yes—
62Dic149—21no—
63Dic149—21no—
64Dic149—21no—
65Dic149—21no—
66Dic149—42no—
67C2×C149—22no—
68C2×C149#40811yescharacteristic
69C2×C149#41011yescharacteristic
70C2×C149C2×#10111yescharacteristic
71C149#147011yescharacteristic, complemented, Sylow
72#1470—1491nomaximal, Sylow
73C2×#125—1491no—
74#432—1491no—
75#431—1491no—
76#324—1494no—
77#125—2981no—
78#125—2981no—
79#125—2981no—
80#125—2981no—
81C2×C4⋊C4—1492no—
82C2×C4⋊C4—1492no—
83C2×C4⋊C4—1491no—
84C2×C4⋊C4#1059701011yescharacteristic
85C2×C42—1491no—
86C4⋊C8—2981no—
87C4⋊C8—2981no—
88C22⋊C8—1492no—
89C22⋊C8—1492no—
90#97—2981no—
91C4×C8—2981no—
92C22×C4—1492no—
93C22×C4—1491no—
94C22×C4—1491no—
95C22×C4C2×#1059701012yes—
96C22×C4C2×#1059701011yescharacteristic
97C2×C8—2982no—
98C2×C8—2982no—
99C4⋊C4—21no—
100C4⋊C4—21no—
101C4⋊C4—2982no—
102C4⋊C4—2982no—
103C4⋊C4—2982no—
104C4⋊C4—2982no—
105C4⋊C4—2981no—
106C4⋊C4—2981no—
107C42—1491no—
108C42—1491no—
109C42—1491no—
110C42—1491no—
111C23C22×#1059701011yescharacteristic
112C2×C4—22no—
113C2×C4—22no—
114C2×C4—42no—
115C2×C4—2982no—
116C2×C4—2982no—
117C2×C4—2984no—
118C2×C4—5961no—
119C2×C4—1491no—
120C2×C4—1491no—
121C2×C4—1491no—
122C2×C4—1491no—
123C2×C4C22⋊#1059701011yescharacteristic
124C2×C4C22⋊#1059701011yescharacteristic
125C8—5962no—
126C8—5962no—
127C22—21no—
128C22—21no—
129C22C2×C22⋊#1059701011yescharacteristic
130C22#1801199912yes—
131C4—21no—
132C4—42no—
133C4—2981no—
134C4—2981no—
135C4—2981no—
136C4—2981no—
137C4—5962no—
138C4#1801197212yes—
139C2—22no—
140C2#2375060011yescharacteristic
141C2#2375060511yescharacteristic
142C2C2×#1801197211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutator, prime radicalC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC2×C4⋊C4×C149C4
socleC22×C149C2×C22⋊C4
cosocleC22×Dic149C23
hypercenterC2×C4⋊C4#10597010
hypocenterC149#1470
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
71. C149#1470semidirect

Maximal subgroups

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

subgroupindex
#237506462
#237506422
#237504712
C2×#180119022
#1470149