Finite Group Databasebeta

← C2×SD16×D199 #27164789

Subgroups — C2×SD16×D199 #27164789

Order 12736.

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×D199C211yesmaximal, characteristic, complemented
2C2×D4×D199C211yesmaximal, characteristic
3C2×#15691875C211yesmaximal, characteristic, complemented
4C2×#15691874C211yesmaximal, characteristic, complemented
5C2×#15691873C211yesmaximal, characteristic, complemented
6SD16×D199C218yesmaximal, direct product factor
7C2×C8×D199C211yesmaximal, characteristic, complemented
8C2×SD16×C199C211yesmaximal, characteristic, complemented
9C23×D199—21no—
10C2×Dic398—21no—
11C2×Dic398C2211yescharacteristic, complemented
12Q8×D199—22no—
13Q8×D199C2214yescomplemented
14C2×D796C2211yescharacteristic
15C2×C22⋊D199—21no—
16D4×D199—22no—
17D4×D199C2214yes—
18C2×C4×D199—21no—
19C2×C4×D199C2211yescharacteristic
20#15691875C2214yescomplemented
21#15691874C2214yescomplemented
22#15691873C2214yescomplemented
23C2×C199⋊C8C2211yescharacteristic, complemented
24C8×D199C2214yescomplemented
25C2×Q8×C199C2211yescharacteristic, complemented
26C2×D4×C199C2211yescharacteristic
27SD16×C199C2214yescomplemented
28C2×C8×C199C2211yescharacteristic, complemented
29C22×D199—21no—
30C22×D199—24no—
31C22×D199—44no—
32C22×D199D411yescharacteristic
33Dic398—21no—
34Dic398—24no—
35Dic398C2312yescomplemented
36D796—21no—
37D796C2312yes—
38C22⋊D199—24no—
39C2×Dic199—21no—
40C2×Dic199D411yescharacteristic
41C4×D199—24no—
42C4×D199D412yes—
43C4×D199C2312yes—
44C199⋊C8C2312yescomplemented
45C23×C199—21no—
46Q8×C199—21no—
47Q8×C199C2312yescomplemented
48D4×C199—21no—
49D4×C199C2312yes—
50C2×C4×C199—21no—
51C2×C4×C199C2311yescharacteristic
52C8×C199C2312yescomplemented
53C22×C199—22no—
54C22×C199—42no—
55C22×C199C2×D411yescharacteristic
56C2×D199—22no—
57C2×D199—42no—
58C2×D199—48no—
59C2×D199SD1614yesdirect product factor
60C2×D199C2×D412yes—
61C4×C199—22no—
62C4×C199C2×D411yescharacteristic
63C4×C199C2411yescharacteristic
64Dic199—22no—
65Dic199C2×D412yes—
66C2×C199—42no—
67C2×C199C2×SD1612yescomplemented
68C2×C199C22×D411yescharacteristic
69D199—42no—
70D199C2×SD1614yesdirect product factor
71C199C22×SD1611yescharacteristic, complemented, Sylow
72C22×SD16—1991nomaximal, Sylow
73C22×Q8—1991no—
74C22×D4—1991no—
75C2×SD16—1991no—
76C2×SD16—1991no—
77C2×SD16—1998no—
78C2×SD16—1991no—
79C2×SD16D19911yescharacteristic, direct product factor
80C22×C8—1991no—
81C24—3981no—
82C2×Q8—3981no—
83C2×Q8—3982no—
84C2×Q8—1994no—
85C2×Q8—1991no—
86C2×Q8C2×D19911yescharacteristic, complemented
87C2×D4—3982no—
88C2×D4—3981no—
89C2×D4—1994no—
90C2×D4—1991no—
91C2×D4C2×D19911yescharacteristic
92C22×C4—3981no—
93C22×C4—1991no—
94SD16—1994no—
95SD16—1994no—
96SD16—1994no—
97SD16C2×D19914yesdirect product factor
98C2×C8—1991no—
99C2×C8—1994no—
100C2×C8C2×D19911yescharacteristic, complemented
101C23—21no—
102C23—7964no—
103C23—3984no—
104C23—3981no—
105C23—1991no—
106Q8—21no—
107Q8—3984no—
108Q8—3981no—
109Q8—1992no—
110Q8C22×D19912yescomplemented
111D4—21no—
112D4—3984no—
113D4—3981no—
114D4—1992no—
115D4C22×D19912yes—
116C2×C4—21no—
117C2×C4—3984no—
118C2×C4—3981no—
119C2×C4—1991no—
120C2×C4—1992no—
121C2×C4—1992no—
122C2×C4C22×D19911yescharacteristic
123C8—1992no—
124C8C22×D19912yescomplemented
125C22—22no—
126C22—42no—
127C22—7968no—
128C22—7962no—
129C22—3982no—
130C22—1994no—
131C22—1992no—
132C22D4×D19911yescharacteristic
133C4—22no—
134C4—3982no—
135C4—1992no—
136C4D4×D19911yescharacteristic
137C4C23×D19911yescharacteristic
138C2—42no—
139C2—7962no—
140C2—1994no—
141C2SD16×D19912yesdirect product factor
142C2C2×D4×D19911yescharacteristic
subgroupG/H
centerC22D4×D199
commutator, cosocleC4×C199C24
FrattiniC4C23×D199
FittingC2×SD16×C199C2
socleC22×C199C2×D4
prime radicalC2×D4×D199C2
hypercenterC2×SD16D199
hypocenterC199C22×SD16
LCSG ▷ C4×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×Q8×D199C2semidirect
3. C2×#15691875C2semidirect
4. C2×#15691874C2semidirect
5. C2×#15691873C2semidirect
6. SD16×D199C2direct (N × H)
7. C2×C8×D199C2semidirect
8. C2×SD16×C199C2semidirect
11. C2×Dic398C22semidirect
13. Q8×D199C22semidirect
20. #15691875C22semidirect
21. #15691874C22semidirect
22. #15691873C22semidirect
23. C2×C199⋊C8C22semidirect
24. C8×D199C22semidirect
25. C2×Q8×C199C22semidirect
27. SD16×C199C22semidirect
28. C2×C8×C199C22semidirect
35. Dic398C23semidirect
44. C199⋊C8C23semidirect
47. Q8×C199C23semidirect
52. C8×C199C23semidirect
59. C2×D199SD16direct (N × H)
67. C2×C199C2×SD16semidirect
70. D199C2×SD16direct (N × H)
71. C199C22×SD16semidirect
79. C2×SD16D199direct (N × H)
86. C2×Q8C2×D199semidirect
97. SD16C2×D199direct (N × H)
100. C2×C8C2×D199semidirect
110. Q8C22×D199semidirect
124. C8C22×D199semidirect
141. C2SD16×D199direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×D1992
C2×D4×D1992
C2×#156918752
C2×#156918742
C2×#156918732
SD16×D1992
C2×C8×D1992
C2×SD16×C1992
C22×SD16199