Finite Group Databasebeta

← C2×#14270965 #16821191

Subgroups — C2×#14270965 #16821191

Order 3712.

272 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 101 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×D232C211yesmaximal, characteristic
2C2×#11745166C211yesmaximal, characteristic, complemented
3#14270965C214yesmaximal, direct product factor
4C22×C16×C29C211yesmaximal, characteristic, complemented
5C22×D116—21no—
6C22×C8×C29C2211yescharacteristic
7C2×C4⋊Dic29—21no—
8C2×D232—21no—
9C2×D232—22no—
10C2×D232C414yescomplemented
11C2×D232C2212yes—
12C2×C16×C29—22no—
13C2×C16×C29C2212yescomplemented
14#11745166—21no—
15#11745166C2212yescomplemented
16C23×D29—41no—
17C22×C4×C29D411yescharacteristic
18C22×Dic29—41no—
19C2×D116—24no—
20C2×D116—22no—
21C2×D116—41no—
22C2×D116—42no—
23C2×C8×C29C2×C412yes—
24C2×C8×C29D411yescharacteristic
25C2×C8×C29D412yes—
26C2×C8×C29C2311yescharacteristic
27C4⋊Dic29—22no—
28C4⋊Dic29—41no—
29D232—24no—
30D232—22no—
31D232C2×C414yescomplemented
32C16×C29—22no—
33C23×C29D811yescharacteristic
34C22×D29—44no—
35C22×D29—42no—
36C22×D29—82no—
37C22×D29—82no—
38C2×C4×C29C22⋊C412yes—
39C2×C4×C29D811yescharacteristic
40C2×C4×C29SD1612yes—
41C2×C4×C29C2×D411yescharacteristic
42C2×Dic29—42no—
43C2×Dic29—82no—
44D116—24no—
45D116—44no—
46D116—42no—
47C8×C29C22⋊C412yes—
48C8×C29C22×C411yescharacteristic
49C8×C29C2×D411yescharacteristic
50C2×#357—291nomaximal, Sylow
51C22×C29#10212yes—
52C22×C29D1612yes—
53C22×C29SD3212yes—
54C22×C29C2×D811yescharacteristic
55C2×D29—44no—
56C2×D29—88no—
57C2×D29—82no—
58C2×D29—82no—
59C4×C29#10212yes—
60C4×C29C2×C22⋊C411yescharacteristic
61C4×C29C2×SD1611yescharacteristic
62Dic29—82no—
63C22×D8—291no—
64C22×C16D2911yescharacteristic, complemented
65C2×#107—291no—
66#357—294no—
67C2×C29#35714yescomplemented
68C2×C29C2×#10211yescharacteristic
69C2×C29C2×D1611yescharacteristic
70C2×C29C2×SD3211yescharacteristic
71D29—84no—
72C22×D4—581no—
73C2×D8—294no—
74C2×D8—292no—
75C2×D8—581no—
76C2×D8—582no—
77C22×C8C2×D2911yescharacteristic
78C2×C4⋊C4—581no—
79C2×C16—22no—
80C2×C16C2×D2912yescomplemented
81#107—292no—
82#107—581no—
83C29C2×#35711yescharacteristic, complemented, Sylow
84C24—1161no—
85C2×D4—584no—
86C2×D4—582no—
87C2×D4—1162no—
88C2×D4—1161no—
89C22×C4—1161no—
90C22×C4D11611yescharacteristic
91D8—294no—
92D8—584no—
93D8—582no—
94C2×C8C4×D2912yes—
95C2×C8D11611yescharacteristic
96C2×C8C22⋊D2912yes—
97C2×C8C22×D2911yescharacteristic
98C4⋊C4—582no—
99C4⋊C4—1161no—
100C16—22no—
101C23—1164no—
102C23—1162no—
103C23—2322no—
104C23—2322no—
105C23D23211yescharacteristic
106D4—584no—
107D4—1164no—
108D4—1162no—
109C2×C4—1162no—
110C2×C4—2322no—
111C2×C4#9077312yes—
112C2×C4D23211yescharacteristic
113C2×C4#9078112yes—
114C2×C4C2×D11611yescharacteristic
115C8#9078112yes—
116C8C2×C4×D2911yescharacteristic
117C8C2×C22⋊D2911yescharacteristic
118C22—1164no—
119C22—2322no—
120C22—2322no—
121C22—2328no—
122C22D46412yes—
123C22#1174514812yes—
124C22#1174516912yes—
125C22C2×D23211yescharacteristic
126C4—2322no—
127C4#1174516912yes—
128C4C2×#9077311yescharacteristic
129C4C2×#9078111yescharacteristic
130C2—2324no—
131C2#1427096514yesdirect product factor
132C2C2×#1174516911yescharacteristic
133C2C2×D46411yescharacteristic
134C2C2×#1174514811yescharacteristic
subgroupG/H
centerC23D232
commutatorC8×C29C22×C4
FrattiniC2×C8C22×D29
FittingC22×C16×C29C2
socleC23×C29D8
prime radicalC22×D232C2
cosocleC2×C8×C29C23
hypercenterC22×C16D29
hypocenterC29C2×#357
LCSG ▷ C8×C29 ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

Complements

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

NH ≅ G/Ntype
2. C2×#11745166C2semidirect
3. #14270965C2direct (N × H)
4. C22×C16×C29C2semidirect
10. C2×D232C4semidirect
13. C2×C16×C29C22semidirect
15. #11745166C22semidirect
31. D232C2×C4semidirect
64. C22×C16D29semidirect
67. C2×C29#357semidirect
80. C2×C16C2×D29semidirect
83. C29C2×#357semidirect
131. C2#14270965direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D2322
C2×#117451662
#142709652
C22×C16×C292
C2×#35729