Finite Group Databasebeta

← C2×SD16×D541 #46830946

Subgroups — C2×SD16×D541 #46830946

Order 34624.

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×D541C211yesmaximal, characteristic, complemented
2C2×D4×D541C211yesmaximal, characteristic
3C2×#22575825C211yesmaximal, characteristic, complemented
4C2×#22575824C211yesmaximal, characteristic, complemented
5C2×#22575823C211yesmaximal, characteristic, complemented
6SD16×D541C218yesmaximal, direct product factor
7C2×C8×D541C211yesmaximal, characteristic, complemented
8C2×SD16×C541C211yesmaximal, characteristic, complemented
9C23×D541—21no—
10C2×Dic1082—21no—
11C2×Dic1082C2211yescharacteristic, complemented
12Q8×D541—22no—
13Q8×D541C2214yescomplemented
14C2×D2164C2211yescharacteristic
15C2×C22⋊D541—21no—
16D4×D541—22no—
17D4×D541C2214yes—
18C2×C4×D541—21no—
19C2×C4×D541C2211yescharacteristic
20#22575825C2214yescomplemented
21#22575824C2214yescomplemented
22#22575823C2214yescomplemented
23C2×#16864513C2211yescharacteristic, complemented
24C8×D541C2214yescomplemented
25C2×Q8×C541C2211yescharacteristic, complemented
26C2×D4×C541C2211yescharacteristic
27SD16×C541C2214yescomplemented
28C2×C8×C541C2211yescharacteristic, complemented
29C22×D541—21no—
30C22×D541—24no—
31C22×D541—44no—
32C22×D541D411yescharacteristic
33Dic1082—21no—
34Dic1082—24no—
35Dic1082C2312yescomplemented
36D2164—21no—
37D2164C2312yes—
38C22⋊D541—24no—
39C2×Dic541—21no—
40C2×Dic541D411yescharacteristic
41C4×D541—24no—
42C4×D541D412yes—
43C4×D541C2312yes—
44#16864513C2312yescomplemented
45C23×C541—21no—
46Q8×C541—21no—
47Q8×C541C2312yescomplemented
48D4×C541—21no—
49D4×C541C2312yes—
50C2×C4×C541—21no—
51C2×C4×C541C2311yescharacteristic
52C8×C541C2312yescomplemented
53C22×C541—22no—
54C22×C541—42no—
55C22×C541C2×D411yescharacteristic
56C2×D541—22no—
57C2×D541—42no—
58C2×D541—48no—
59C2×D541SD1614yesdirect product factor
60C2×D541C2×D412yes—
61C4×C541—22no—
62C4×C541C2×D411yescharacteristic
63C4×C541C2411yescharacteristic
64Dic541—22no—
65Dic541C2×D412yes—
66C2×C541—42no—
67C2×C541C2×SD1612yescomplemented
68C2×C541C22×D411yescharacteristic
69D541—42no—
70D541C2×SD1614yesdirect product factor
71C541C22×SD1611yescharacteristic, complemented, Sylow
72C22×SD16—5411nomaximal, Sylow
73C22×Q8—5411no—
74C22×D4—5411no—
75C2×SD16—5411no—
76C2×SD16—5411no—
77C2×SD16—5418no—
78C2×SD16—5411no—
79C2×SD16D54111yescharacteristic, direct product factor
80C22×C8—5411no—
81C24—10821no—
82C2×Q8—5414no—
83C2×Q8—5411no—
84C2×Q8—10821no—
85C2×Q8—10822no—
86C2×Q8C2×D54111yescharacteristic, complemented
87C2×D4—5414no—
88C2×D4—5411no—
89C2×D4—10822no—
90C2×D4—10821no—
91C2×D4C2×D54111yescharacteristic
92C22×C4—5411no—
93C22×C4—10821no—
94SD16—5414no—
95SD16—5414no—
96SD16—5414no—
97SD16C2×D54114yesdirect product factor
98C2×C8—5411no—
99C2×C8—5414no—
100C2×C8C2×D54111yescharacteristic, complemented
101C23—21no—
102C23—5411no—
103C23—10824no—
104C23—10821no—
105C23—21644no—
106Q8—21no—
107Q8—5412no—
108Q8—10824no—
109Q8—10821no—
110Q8C22×D54112yescomplemented
111D4—21no—
112D4—5412no—
113D4—10824no—
114D4—10821no—
115D4C22×D54112yes—
116C2×C4—21no—
117C2×C4—5411no—
118C2×C4—5412no—
119C2×C4—5412no—
120C2×C4—10824no—
121C2×C4—10821no—
122C2×C4C22×D54111yescharacteristic
123C8—5412no—
124C8C22×D54112yescomplemented
125C22—22no—
126C22—42no—
127C22—5414no—
128C22—5412no—
129C22—10822no—
130C22—21648no—
131C22—21642no—
132C22D4×D54111yescharacteristic
133C4—22no—
134C4—5412no—
135C4—10822no—
136C4D4×D54111yescharacteristic
137C4C23×D54111yescharacteristic
138C2—42no—
139C2—5414no—
140C2—21642no—
141C2SD16×D54112yesdirect product factor
142C2C2×D4×D54111yescharacteristic
subgroupG/H
centerC22D4×D541
commutator, cosocleC4×C541C24
FrattiniC4C23×D541
FittingC2×SD16×C541C2
socleC22×C541C2×D4
prime radicalC2×D4×D541C2
hypercenterC2×SD16D541
hypocenterC541C22×SD16
LCSG ▷ C4×C541 ▷ C2×C541 ▷ C541
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×Q8×D541C2semidirect
3. C2×#22575825C2semidirect
4. C2×#22575824C2semidirect
5. C2×#22575823C2semidirect
6. SD16×D541C2direct (N × H)
7. C2×C8×D541C2semidirect
8. C2×SD16×C541C2semidirect
11. C2×Dic1082C22semidirect
13. Q8×D541C22semidirect
20. #22575825C22semidirect
21. #22575824C22semidirect
22. #22575823C22semidirect
23. C2×#16864513C22semidirect
24. C8×D541C22semidirect
25. C2×Q8×C541C22semidirect
27. SD16×C541C22semidirect
28. C2×C8×C541C22semidirect
35. Dic1082C23semidirect
44. #16864513C23semidirect
47. Q8×C541C23semidirect
52. C8×C541C23semidirect
59. C2×D541SD16direct (N × H)
67. C2×C541C2×SD16semidirect
70. D541C2×SD16direct (N × H)
71. C541C22×SD16semidirect
79. C2×SD16D541direct (N × H)
86. C2×Q8C2×D541semidirect
97. SD16C2×D541direct (N × H)
100. C2×C8C2×D541semidirect
110. Q8C22×D541semidirect
124. C8C22×D541semidirect
141. C2SD16×D541direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×D5412
C2×D4×D5412
C2×#225758252
C2×#225758242
C2×#225758232
SD16×D5412
C2×C8×D5412
C2×SD16×C5412
C22×SD16541