Finite Group Databasebeta

← C2×#30628364 #44537513

Subgroups — C2×#30628364 #44537513

Order 31424.

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×#21463329C211yesmaximal, characteristic, complemented
2C2×D4×D491C211yesmaximal, characteristic, complemented
3#30628364C218yesmaximal, direct product factor
4C2×#21463315C211yesmaximal, characteristic, complemented
5C2×D3928C211yesmaximal, characteristic, complemented
6C2×#21463313C211yesmaximal, characteristic, complemented
7C2×#21463311C211yesmaximal, characteristic, complemented
8C2×SD16×C491C211yesmaximal, characteristic, complemented
9C23×D491—21no—
10#21463329—22no—
11#21463329C2214yescomplemented
12C2×D1964—21no—
13C2×D1964C2211yescharacteristic
14C2×D1964C2211yescharacteristic, complemented
15C2×C22⋊D491—21no—
16D4×D491—22no—
17D4×D491C2214yescomplemented
18C2×C4×D491—21no—
19C2×C4×D491C2211yescharacteristic
20#21463315C2214yescomplemented
21D3928C2214yescomplemented
22#21463313C2214yescomplemented
23#21463311C2214yescomplemented
24C2×C491⋊C8C2211yescharacteristic, complemented
25C2×Q8×C491C2211yescharacteristic, complemented
26C2×D4×C491C2211yescharacteristic
27SD16×C491C2214yescomplemented
28C2×C8×C491C2211yescharacteristic, complemented
29C22×D491—21no—
30C22×D491—21no—
31C22×D491—24no—
32C22×D491—44no—
33C22×D491D411yescharacteristic
34D1964—24no—
35D1964—21no—
36D1964—21no—
37D1964C2312yes—
38D1964C2312yescomplemented
39C22⋊D491—24no—
40C2×Dic491D411yescharacteristic
41C4×D491—24no—
42C4×D491D412yes—
43C4×D491C2312yes—
44C491⋊C8C2312yescomplemented
45C23×C491—21no—
46Q8×C491—21no—
47Q8×C491C2312yescomplemented
48D4×C491—21no—
49D4×C491C2312yes—
50C2×C4×C491—21no—
51C2×C4×C491C2311yescharacteristic
52C8×C491C2312yescomplemented
53C22×C491—22no—
54C22×C491—42no—
55C22×C491C2×D411yescharacteristic
56C2×D491—22no—
57C2×D491—22no—
58C2×D491—22no—
59C2×D491—48no—
60C2×D491—42no—
61C2×D491—42no—
62C2×D491C2×D412yes—
63C4×C491—22no—
64C4×C491C2×D411yescharacteristic
65C4×C491C2411yescharacteristic
66Dic491C2×D412yes—
67C2×C491—42no—
68C2×C491AGL(1,ℤ/8)12yescomplemented
69C2×C491C22×D411yescharacteristic
70D491—22no—
71D491—42no—
72D491—42no—
73C491C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
74C2×AGL(1,ℤ/8)—4911nomaximal, Sylow
75C2×#41—4911no—
76C22×D4—4911no—
77AGL(1,ℤ/8)—4918no—
78C2×SD16—4911no—
79C2×SD16D49111yescharacteristic, complemented
80C2×D8—4911no—
81C2×D8—4911no—
82C2×M16—4911no—
83C24—9821no—
84#41—9822no—
85#41—4914no—
86C2×Q8C2×D49111yescharacteristic, complemented
87C2×D4—9821no—
88C2×D4—9822no—
89C2×D4—9821no—
90C2×D4—4914no—
91C2×D4—4911no—
92C2×D4—4911no—
93C2×D4C2×D49111yescharacteristic
94C22×C4—9821no—
95C22×C4—4911no—
96SD16—4914no—
97SD16C2×D49114yescomplemented
98D8—4914no—
99D8—4914no—
100M16—4914no—
101C2×C8—4911no—
102C2×C8C2×D49111yescharacteristic, complemented
103C23—21no—
104C23—19644no—
105C23—9824no—
106C23—9821no—
107C23—9821no—
108C23—4911no—
109Q8—21no—
110Q8C22×D49112yescomplemented
111D4—21no—
112D4—9824no—
113D4—9824no—
114D4—9821no—
115D4—9821no—
116D4—4912no—
117D4—4912no—
118D4C22×D49112yes—
119C2×C4—21no—
120C2×C4—9824no—
121C2×C4—4911no—
122C2×C4—4912no—
123C2×C4—4912no—
124C2×C4C22×D49111yescharacteristic
125C8—4912no—
126C8C22×D49112yescomplemented
127C22—22no—
128C22—42no—
129C22—19648no—
130C22—19642no—
131C22—19642no—
132C22—9822no—
133C22—9822no—
134C22—9822no—
135C22—4912no—
136C22D4×D49111yescharacteristic
137C4—22no—
138C4—4912no—
139C4D4×D49111yescharacteristic
140C4C23×D49111yescharacteristic
141C2—42no—
142C2—19642no—
143C2—19642no—
144C2—9822no—
145C2#3062836412yesdirect product factor
146C2C2×D4×D49111yescharacteristic
subgroupG/H
centerC22D4×D491
commutator, cosocleC4×C491C24
FrattiniC4C23×D491
FittingC2×SD16×C491C2
socleC22×C491C2×D4
hypercenterC2×SD16D491
hypocenterC491C2×AGL(1,ℤ/8)
LCSG ▷ C4×C491 ▷ C2×C491 ▷ C491
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#21463329C2semidirect
2. C2×D4×D491C2semidirect
3. #30628364C2direct (N × H)
4. C2×#21463315C2semidirect
5. C2×D3928C2semidirect
6. C2×#21463313C2semidirect
7. C2×#21463311C2semidirect
8. C2×SD16×C491C2semidirect
11. #21463329C22semidirect
14. C2×D1964C22semidirect
17. D4×D491C22semidirect
20. #21463315C22semidirect
21. D3928C22semidirect
22. #21463313C22semidirect
23. #21463311C22semidirect
24. C2×C491⋊C8C22semidirect
25. C2×Q8×C491C22semidirect
27. SD16×C491C22semidirect
28. C2×C8×C491C22semidirect
38. D1964C23semidirect
44. C491⋊C8C23semidirect
47. Q8×C491C23semidirect
52. C8×C491C23semidirect
68. C2×C491AGL(1,ℤ/8)semidirect
73. C491C2×AGL(1,ℤ/8)semidirect
79. C2×SD16D491semidirect
86. C2×Q8C2×D491semidirect
97. SD16C2×D491semidirect
102. C2×C8C2×D491semidirect
110. Q8C22×D491semidirect
126. C8C22×D491semidirect
145. C2#30628364direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#214633292
C2×D4×D4912
#306283642
C2×#214633152
C2×D39282
C2×#214633132
C2×#214633112
C2×SD16×C4912
C2×AGL(1,ℤ/8)491