Finite Group Databasebeta

← C2×#23750584 #34061244

Subgroups — C2×#23750584 #34061244

Order 19072.

680 conjugacy classes of subgroups; only the 338 normal subgroups are shown.

normal subgroups only

This group has 680 conjugacy classes of subgroups — too many to draw. Only its 338 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
1C22×D149⋊C8C212yesmaximal
2#23750584C218yesmaximal, direct product factor
3C2×#18011966C214yesmaximal, complemented
4C2×C42×D149C211yesmaximal, characteristic
5C2×D149⋊C8C4116yescomplemented
6C2×D149⋊C8C2218yes—
7C22×#11924753C2214yes—
8#18011966C22116yescomplemented
9C22×C4×D149C412yes—
10C22×C4×D149C2211yescharacteristic
11C2×C4×Dic149C411yescharacteristic
12C2×C4×Dic149C2212yes—
13C42×D149C414yes—
14C42×D149C2214yes—
15C2×C42×C149C411yescharacteristic
16D149⋊C8C2×C4132yescomplemented
17C2×#11924753C2×C4116yescomplemented
18C2×#11924753C2318yes—
19C23×D149C2×C411yescharacteristic
20C22×Dic149C2×C412yes—
21C22×Dic149C2311yescharacteristic
22C2×C4×D149—28no—
23C2×C4×D149C2×C418yes—
24C2×C4×D149C2×C418yes—
25C2×C4×D149C2×C412yes—
26C2×C4×D149C2312yes—
27C4×Dic149C2×C414yes—
28C4×Dic149C2×C414yes—
29C4×Dic149C2314yes—
30C22×C4×C149C2×C412yes—
31C22×C4×C149C2×C411yescharacteristic
32C42×C149C2×C414yes—
33#11924753C22×C4116yescomplemented
34C22×D149C4214yes—
35C22×D149M1618yes—
36C22×D149C22×C412yes—
37C2×Dic149—24no—
38C2×Dic149C22×C414yes—
39C2×Dic149C22×C411yescharacteristic
40C2×Dic149C22×C414yes—
41C2×Dic149C2411yescharacteristic
42C4×D149—216no—
43C4×D149C4218yes—
44C4×D149C22×C418yes—
45C23×C149C22×C411yescharacteristic
46C2×C4×C149—24no—
47C2×C4×C149C4214yes—
48C2×C4×C149C22×C414yes—
49C2×C4×C149C22×C412yes—
50C22×C149C2×C4212yes—
51C22×C149C2×M1614yes—
52C22×C149C23×C411yescharacteristic
53C2×D149#97116yescomplemented
54C2×D149C2×C4214yes—
55C2×D149C2×M1618yes—
56C4×C149—24no—
57C4×C149C2×C4214yes—
58Dic149—24no—
59Dic149C2×C4212yes—
60Dic149C23×C412yes—
61C2×C149C2×#9714yescomplemented
62C2×C149C22×C4211yescharacteristic
63C2×C149C22×M1612yes—
64D149C2×#9718yescomplemented
65C149C22×#9711yescharacteristic, complemented, Sylow
66C22×#97—1491nomaximal, Sylow
67C23×C8—1492no—
68C22×C42—1491no—
69C2×#97—1494no—
70C2×#97—1498no—
71C23×C4—1492no—
72C23×C4—1491no—
73C22×C8—1494no—
74C22×C8—14916no—
75C22×C8—1498no—
76C2×C42—1492no—
77C2×C42—1491no—
78C2×C42—1494no—
79C2×C42—1494no—
80C2×C42#1059701011yescharacteristic
81#97—14916no—
82C24—1491no—
83C22×C4—2988no—
84C22×C4—1492no—
85C22×C4—1498no—
86C22×C4—1491no—
87C22×C4—1498no—
88C22×C4—1492no—
89C22×C4—1492no—
90C22×C4C2×#1059701012yes—
91C22×C4C2×#1059701011yescharacteristic
92C2×C8—14916no—
93C2×C8—1498no—
94C2×C8—14932no—
95C42—1494no—
96C42—1494no—
97C42—1494no—
98C42C2×#1059701014yes—
99C23—1494no—
100C23—1498no—
101C23—1492no—
102C23C22×#1059701011yescharacteristic
103C2×C4—24no—
104C2×C4—29816no—
105C2×C4—2984no—
106C2×C4—1494no—
107C2×C4—1494no—
108C2×C4—1491no—
109C2×C4—1491no—
110C2×C4—1498no—
111C2×C4—1498no—
112C2×C4C4×#1059701014yes—
113C2×C4C22×#1059701014yes—
114C2×C4C22×#1059701012yes—
115C8—14916no—
116C22—1494no—
117C22—1498no—
118C22—14916no—
119C22C2×C4×#1059701012yes—
120C22D149⋊M1614yes—
121C22C23×#1059701011yescharacteristic
122C4—24no—
123C4—2984no—
124C4—1492no—
125C4—1492no—
126C4C2×C4×#1059701014yes—
127C2—1498no—
128C2#2375058414yesdirect product factor
129C2C22×C4×#1059701011yescharacteristic
130C2C2×D149⋊M1612yes—
subgroupG/H
centerC22×C4C2×#10597010
commutatorC2×C149C22×C42
FrattiniC22C23×#10597010
FittingC2×C42×C149C4
socleC23×C149C22×C4
prime radicalC23×D149C2×C4
cosocleC2×Dic149C24
hypercenterC2×C42#10597010
hypocenterC149C22×#97
LCSG ▷ C2×C149 ▷ C149
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #23750584C2direct (N × H)
3. C2×#18011966C2semidirect
5. C2×D149⋊C8C4semidirect
8. #18011966C22semidirect
16. D149⋊C8C2×C4semidirect
17. C2×#11924753C2×C4semidirect
33. #11924753C22×C4semidirect
53. C2×D149#97semidirect
61. C2×C149C2×#97semidirect
64. D149C2×#97semidirect
65. C149C22×#97semidirect
128. C2#23750584direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D149⋊C82
#237505842
C2×#180119662
C2×C42×D1492
C22×#97149