Finite Group Databasebeta

← C2×SD16×D359 #37527214

Subgroups — C2×SD16×D359 #37527214

Order 22976.

298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 111 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
1C2×Q8×D359C211yesmaximal, characteristic, complemented
2C2×D4×D359C211yesmaximal, characteristic
3C2×#19153330C211yesmaximal, characteristic, complemented
4C2×#19153329C211yesmaximal, characteristic, complemented
5C2×#19153328C211yesmaximal, characteristic, complemented
6SD16×D359C218yesmaximal, direct product factor
7C2×C8×D359C211yesmaximal, characteristic, complemented
8C2×SD16×C359C211yesmaximal, characteristic, complemented
9C23×D359—21no—
10C2×Dic718—21no—
11C2×Dic718C2211yescharacteristic, complemented
12Q8×D359—22no—
13Q8×D359C2214yescomplemented
14C2×D1436C2211yescharacteristic
15C2×C22⋊D359—21no—
16D4×D359—22no—
17D4×D359C2214yes—
18C2×C4×D359—21no—
19C2×C4×D359C2211yescharacteristic
20#19153330C2214yescomplemented
21#19153329C2214yescomplemented
22#19153328C2214yescomplemented
23C2×C359⋊C8C2211yescharacteristic, complemented
24C8×D359C2214yescomplemented
25C2×Q8×C359C2211yescharacteristic, complemented
26C2×D4×C359C2211yescharacteristic
27SD16×C359C2214yescomplemented
28C2×C8×C359C2211yescharacteristic, complemented
29C22×D359—21no—
30C22×D359—24no—
31C22×D359—44no—
32C22×D359D411yescharacteristic
33Dic718—21no—
34Dic718—24no—
35Dic718C2312yescomplemented
36D1436—21no—
37D1436C2312yes—
38C22⋊D359—24no—
39C2×Dic359—21no—
40C2×Dic359D411yescharacteristic
41C4×D359—24no—
42C4×D359D412yes—
43C4×D359C2312yes—
44C359⋊C8C2312yescomplemented
45C23×C359—21no—
46Q8×C359—21no—
47Q8×C359C2312yescomplemented
48D4×C359—21no—
49D4×C359C2312yes—
50C2×C4×C359—21no—
51C2×C4×C359C2311yescharacteristic
52C8×C359C2312yescomplemented
53C22×C359—22no—
54C22×C359—42no—
55C22×C359C2×D411yescharacteristic
56C2×D359—22no—
57C2×D359—42no—
58C2×D359—48no—
59C2×D359SD1614yesdirect product factor
60C2×D359C2×D412yes—
61C4×C359—22no—
62C4×C359C2×D411yescharacteristic
63C4×C359C2411yescharacteristic
64Dic359—22no—
65Dic359C2×D412yes—
66C2×C359—42no—
67C2×C359C2×SD1612yescomplemented
68C2×C359C22×D411yescharacteristic
69D359—42no—
70D359C2×SD1614yesdirect product factor
71C359C22×SD1611yescharacteristic, complemented, Sylow
72C22×SD16—3591nomaximal, Sylow
73C22×Q8—3591no—
74C22×D4—3591no—
75C2×SD16—3591no—
76C2×SD16—3591no—
77C2×SD16—3598no—
78C2×SD16—3591no—
79C2×SD16D35911yescharacteristic, direct product factor
80C22×C8—3591no—
81C24—7181no—
82C2×Q8—3594no—
83C2×Q8—3591no—
84C2×Q8—7181no—
85C2×Q8—7182no—
86C2×Q8C2×D35911yescharacteristic, complemented
87C2×D4—3594no—
88C2×D4—3591no—
89C2×D4—7182no—
90C2×D4—7181no—
91C2×D4C2×D35911yescharacteristic
92C22×C4—3591no—
93C22×C4—7181no—
94SD16—3594no—
95SD16—3594no—
96SD16—3594no—
97SD16C2×D35914yesdirect product factor
98C2×C8—3591no—
99C2×C8—3594no—
100C2×C8C2×D35911yescharacteristic, complemented
101C23—21no—
102C23—3591no—
103C23—14364no—
104C23—7184no—
105C23—7181no—
106Q8—21no—
107Q8—3592no—
108Q8—7184no—
109Q8—7181no—
110Q8C22×D35912yescomplemented
111D4—21no—
112D4—3592no—
113D4—7184no—
114D4—7181no—
115D4C22×D35912yes—
116C2×C4—21no—
117C2×C4—3591no—
118C2×C4—3592no—
119C2×C4—3592no—
120C2×C4—7184no—
121C2×C4—7181no—
122C2×C4C22×D35911yescharacteristic
123C8—3592no—
124C8C22×D35912yescomplemented
125C22—22no—
126C22—42no—
127C22—3594no—
128C22—3592no—
129C22—14368no—
130C22—14362no—
131C22—7182no—
132C22D4×D35911yescharacteristic
133C4—22no—
134C4—3592no—
135C4—7182no—
136C4D4×D35911yescharacteristic
137C4C23×D35911yescharacteristic
138C2—42no—
139C2—3594no—
140C2—14362no—
141C2SD16×D35912yesdirect product factor
142C2C2×D4×D35911yescharacteristic
subgroupG/H
centerC22D4×D359
commutator, cosocleC4×C359C24
FrattiniC4C23×D359
FittingC2×SD16×C359C2
socleC22×C359C2×D4
prime radicalC2×D4×D359C2
hypercenterC2×SD16D359
hypocenterC359C22×SD16
LCSG ▷ C4×C359 ▷ C2×C359 ▷ C359
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×Q8×D359C2semidirect
3. C2×#19153330C2semidirect
4. C2×#19153329C2semidirect
5. C2×#19153328C2semidirect
6. SD16×D359C2direct (N × H)
7. C2×C8×D359C2semidirect
8. C2×SD16×C359C2semidirect
11. C2×Dic718C22semidirect
13. Q8×D359C22semidirect
20. #19153330C22semidirect
21. #19153329C22semidirect
22. #19153328C22semidirect
23. C2×C359⋊C8C22semidirect
24. C8×D359C22semidirect
25. C2×Q8×C359C22semidirect
27. SD16×C359C22semidirect
28. C2×C8×C359C22semidirect
35. Dic718C23semidirect
44. C359⋊C8C23semidirect
47. Q8×C359C23semidirect
52. C8×C359C23semidirect
59. C2×D359SD16direct (N × H)
67. C2×C359C2×SD16semidirect
70. D359C2×SD16direct (N × H)
71. C359C22×SD16semidirect
79. C2×SD16D359direct (N × H)
86. C2×Q8C2×D359semidirect
97. SD16C2×D359direct (N × H)
100. C2×C8C2×D359semidirect
110. Q8C22×D359semidirect
124. C8C22×D359semidirect
141. C2SD16×D359direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×D3592
C2×D4×D3592
C2×#191533302
C2×#191533292
C2×#191533282
SD16×D3592
C2×C8×D3592
C2×SD16×C3592
C22×SD16359