Finite Group Databasebeta

← #34061538

Subgroups — #34061538

Order 19072.

500 conjugacy classes of subgroups; only the 244 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 244 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
1D4×#11924753C218yesmaximal, complemented
2#23750641C212yesmaximal, complemented
3C2×C22⋊#11924753C214yesmaximal, complemented
4C2×D4×Dic149C211yesmaximal, characteristic
5C22×#11924753C2218yescomplemented
6C4⋊#11924753C2214yescomplemented
7C22⋊#11924753C2214yes—
8C22⋊#11924753C2218yescomplemented
9C4×#11924753C2214yescomplemented
10C23×Dic149C2212yes—
11D4×Dic149C414yes—
12D4×Dic149C2214yes—
13C2×C4⋊Dic149C411yescharacteristic
14C2×C22⋊Dic149C412yes—
15C2×C4×Dic149C2211yescharacteristic
16C22×D4×C149C411yescharacteristic
17C2×#11924753—48no—
18C2×#11924753C2318yes—
19C22×Dic149—44no—
20C22×Dic149C2×C412yes—
21C22×Dic149C2×C414yes—
22C22×Dic149C2×C411yescharacteristic
23C22×Dic149C2311yescharacteristic
24C22×Dic149C2314yes—
25C4⋊Dic149C2×C414yes—
26C22⋊Dic149C2×C418yes—
27C4×Dic149C2×C412yes—
28C4×Dic149C2312yes—
29C24×C149C2×C412yes—
30C2×D4×C149C818yescomplemented
31C2×D4×C149C2×C414yes—
32C22×C4×C149C2×C411yescharacteristic
33#11924753—28no—
34C2×Dic149—22no—
35C2×Dic149—28no—
36C2×Dic149—44no—
37C2×Dic149—42no—
38C2×Dic149—41no—
39C2×Dic149C22×C411yescharacteristic
40C2×Dic149C22×C414yes—
41C2×Dic149C22×C412yes—
42C2×Dic149C2411yescharacteristic
43C23×C149—42no—
44C23×C149—42no—
45C23×C149C2×C818yescomplemented
46C23×C149C22×C411yescharacteristic
47C23×C149C22×C414yes—
48D4×C149C2×C8116yescomplemented
49C2×C4×C149C2×C814yescomplemented
50C2×C4×C149C22×C412yes—
51C22×C149—21no—
52C22×C149—24no—
53C22×C149—21no—
54C22×C149—24no—
55C22×C149—48no—
56C22×C149C22×C812yes—
57C22×C149C22×C818yes—
58C22×C149C23×C411yescharacteristic
59C4×C149C22×C814yes—
60Dic149—21no—
61Dic149—24no—
62Dic149—22no—
63Dic149H(5,𝔽2)12yes—
64C2×C149—22no—
65C2×C149—28no—
66C2×C149#51811yescharacteristic
67C2×C149C23×C811yescharacteristic
68C2×C149#56811yescharacteristic
69C149#297211yescharacteristic, complemented, Sylow
70#2972—1491nomaximal, Sylow
71C2×C4×D4—1491no—
72C8×D4—1498no—
73#431—1492no—
74C2×C22⋊C8—1494no—
75C22×D4#1059701011yescharacteristic
76C23×C4—1492no—
77C22×C8—1498no—
78C4×D4—1494no—
79C4×D4—1494no—
80C2×C4⋊C4—1491no—
81C2×C22⋊C4—1492no—
82C2×C42—1491no—
83C4⋊C8—1494no—
84C22⋊C8—1494no—
85C22⋊C8—1498no—
86C4×C8—1494no—
87C24C2×#1059701012yes—
88C2×D4#1192475318yescomplemented
89C2×D4C2×#1059701014yes—
90C22×C4—5964no—
91C22×C4—1491no—
92C22×C4—1494no—
93C22×C4—1491no—
94C22×C4—1492no—
95C22×C4—1494no—
96C22×C4C2×#1059701011yescharacteristic
97C2×C8—5968no—
98C2×C8—1498no—
99C4⋊C4—1494no—
100C22⋊C4—1498no—
101C42—1492no—
102C42—1492no—
103C23—42no—
104C23—42no—
105C23C2×#1192475318yescomplemented
106C23C22×#1059701014yes—
107C23C22×#1059701011yescharacteristic
108D4C2×#11924753116yescomplemented
109C2×C4—2988no—
110C2×C4—2982no—
111C2×C4—5964no—
112C2×C4—5962no—
113C2×C4—5961no—
114C2×C4—1492no—
115C2×C4—1491no—
116C2×C4—1494no—
117C2×C4—1491no—
118C2×C4C2×#1192475314yescomplemented
119C2×C4C22×#1059701012yes—
120C8—2988no—
121C22—21no—
122C22—24no—
123C22—21no—
124C22—24no—
125C22—48no—
126C22C22×#1192475312yes—
127C22C22×#1192475318yes—
128C22C23×#1059701011yescharacteristic
129C4—2981no—
130C4—2984no—
131C4—2982no—
132C4—1492no—
133C4C22×#1192475314yes—
134C2—22no—
135C2—28no—
136C2#2375069211yescharacteristic
137C2C23×#1192475311yescharacteristic
138C2#2375070311yescharacteristic
subgroupG/H
center, FrattiniC22C23×#10597010
commutatorC2×C149C23×C8
Fitting, prime radicalC22×D4×C149C4
socleC22×C149C23×C4
cosocleC2×Dic149C24
hypercenterC22×D4#10597010
hypocenterC149#2972
LCSG ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. D4×#11924753C2semidirect
2. #23750641C2semidirect
3. C2×C22⋊#11924753C2semidirect
5. C22×#11924753C22semidirect
6. C4⋊#11924753C22semidirect
8. C22⋊#11924753C22semidirect
9. C4×#11924753C22semidirect
30. C2×D4×C149C8semidirect
45. C23×C149C2×C8semidirect
48. D4×C149C2×C8semidirect
49. C2×C4×C149C2×C8semidirect
69. C149#2972semidirect
88. C2×D4#11924753semidirect
105. C23C2×#11924753semidirect
108. D4C2×#11924753semidirect
118. C2×C4C2×#11924753semidirect

Maximal subgroups

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

subgroupindex
D4×#119247532
#237506412
C2×C22⋊#119247532
C2×D4×Dic1492
#2972149