Finite Group Databasebeta

← C2×#34062742 #50306678

Subgroups — C2×#34062742 #50306678

Order 38336.

298 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 103 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×#23751079C211yesmaximal, characteristic, complemented
2C2×D4×D599C211yesmaximal, characteristic, complemented
3#34062742C218yesmaximal, direct product factor
4C2×#23751065C211yesmaximal, characteristic, complemented
5C2×D4792C211yesmaximal, characteristic, complemented
6C2×#23751063C211yesmaximal, characteristic, complemented
7C2×#23751061C211yesmaximal, characteristic, complemented
8C2×SD16×C599C211yesmaximal, characteristic, complemented
9C23×D599—21no—
10#23751079—22no—
11#23751079C2214yescomplemented
12C2×D2396—21no—
13C2×D2396C2211yescharacteristic
14C2×D2396C2211yescharacteristic, complemented
15C2×C22⋊D599—21no—
16D4×D599—22no—
17D4×D599C2214yescomplemented
18C2×C4×D599—21no—
19C2×C4×D599C2211yescharacteristic
20#23751065C2214yescomplemented
21D4792C2214yescomplemented
22#23751063C2214yescomplemented
23#23751061C2214yescomplemented
24C2×C599⋊C8C2211yescharacteristic, complemented
25C2×Q8×C599C2211yescharacteristic, complemented
26C2×D4×C599C2211yescharacteristic
27SD16×C599C2214yescomplemented
28C2×C8×C599C2211yescharacteristic, complemented
29C22×D599—21no—
30C22×D599—21no—
31C22×D599—24no—
32C22×D599—44no—
33C22×D599D411yescharacteristic
34D2396—24no—
35D2396—21no—
36D2396—21no—
37D2396C2312yes—
38D2396C2312yescomplemented
39C22⋊D599—24no—
40C2×Dic599D411yescharacteristic
41C4×D599—24no—
42C4×D599D412yes—
43C4×D599C2312yes—
44C599⋊C8C2312yescomplemented
45C23×C599—21no—
46Q8×C599—21no—
47Q8×C599C2312yescomplemented
48D4×C599—21no—
49D4×C599C2312yes—
50C2×C4×C599—21no—
51C2×C4×C599C2311yescharacteristic
52C8×C599C2312yescomplemented
53C22×C599—22no—
54C22×C599—42no—
55C22×C599C2×D411yescharacteristic
56C2×D599—22no—
57C2×D599—22no—
58C2×D599—22no—
59C2×D599—48no—
60C2×D599—42no—
61C2×D599—42no—
62C2×D599C2×D412yes—
63C4×C599—22no—
64C4×C599C2×D411yescharacteristic
65C4×C599C2411yescharacteristic
66Dic599C2×D412yes—
67C2×C599—42no—
68C2×C599AGL(1,ℤ/8)12yescomplemented
69C2×C599C22×D411yescharacteristic
70D599—22no—
71D599—42no—
72D599—42no—
73C599C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
74C2×AGL(1,ℤ/8)—5991nomaximal, Sylow
75C2×#41—5991no—
76C22×D4—5991no—
77AGL(1,ℤ/8)—5998no—
78C2×SD16—5991no—
79C2×SD16D59911yescharacteristic, complemented
80C2×D8—5991no—
81C2×D8—5991no—
82C2×M16—5991no—
83C24—11981no—
84#41—5994no—
85#41—11982no—
86C2×Q8C2×D59911yescharacteristic, complemented
87C2×D4—5994no—
88C2×D4—5991no—
89C2×D4—5991no—
90C2×D4—11981no—
91C2×D4—11982no—
92C2×D4—11981no—
93C2×D4C2×D59911yescharacteristic
94C22×C4—5991no—
95C22×C4—11981no—
96SD16—5994no—
97SD16C2×D59914yescomplemented
98D8—5994no—
99D8—5994no—
100M16—5994no—
101C2×C8—5991no—
102C2×C8C2×D59911yescharacteristic, complemented
103C23—21no—
104C23—5991no—
105C23—23964no—
106C23—11984no—
107C23—11981no—
108C23—11981no—
109Q8—21no—
110Q8C22×D59912yescomplemented
111D4—21no—
112D4—5992no—
113D4—5992no—
114D4—11984no—
115D4—11984no—
116D4—11981no—
117D4—11981no—
118D4C22×D59912yes—
119C2×C4—21no—
120C2×C4—5991no—
121C2×C4—5992no—
122C2×C4—5992no—
123C2×C4—11984no—
124C2×C4C22×D59911yescharacteristic
125C8—5992no—
126C8C22×D59912yescomplemented
127C22—22no—
128C22—42no—
129C22—5992no—
130C22—23968no—
131C22—23962no—
132C22—23962no—
133C22—11982no—
134C22—11982no—
135C22—11982no—
136C22D4×D59911yescharacteristic
137C4—22no—
138C4—5992no—
139C4D4×D59911yescharacteristic
140C4C23×D59911yescharacteristic
141C2—42no—
142C2—23962no—
143C2—23962no—
144C2—11982no—
145C2#3406274212yesdirect product factor
146C2C2×D4×D59911yescharacteristic
subgroupG/H
centerC22D4×D599
commutator, cosocleC4×C599C24
FrattiniC4C23×D599
FittingC2×SD16×C599C2
socleC22×C599C2×D4
hypercenterC2×SD16D599
hypocenterC599C2×AGL(1,ℤ/8)
LCSG ▷ C4×C599 ▷ C2×C599 ▷ C599
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#23751079C2semidirect
2. C2×D4×D599C2semidirect
3. #34062742C2direct (N × H)
4. C2×#23751065C2semidirect
5. C2×D4792C2semidirect
6. C2×#23751063C2semidirect
7. C2×#23751061C2semidirect
8. C2×SD16×C599C2semidirect
11. #23751079C22semidirect
14. C2×D2396C22semidirect
17. D4×D599C22semidirect
20. #23751065C22semidirect
21. D4792C22semidirect
22. #23751063C22semidirect
23. #23751061C22semidirect
24. C2×C599⋊C8C22semidirect
25. C2×Q8×C599C22semidirect
27. SD16×C599C22semidirect
28. C2×C8×C599C22semidirect
38. D2396C23semidirect
44. C599⋊C8C23semidirect
47. Q8×C599C23semidirect
52. C8×C599C23semidirect
68. C2×C599AGL(1,ℤ/8)semidirect
73. C599C2×AGL(1,ℤ/8)semidirect
79. C2×SD16D599semidirect
86. C2×Q8C2×D599semidirect
97. SD16C2×D599semidirect
102. C2×C8C2×D599semidirect
110. Q8C22×D599semidirect
126. C8C22×D599semidirect
145. C2#34062742direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#237510792
C2×D4×D5992
#340627422
C2×#237510652
C2×D47922
C2×#237510632
C2×#237510612
C2×SD16×C5992
C2×AGL(1,ℤ/8)599