Finite Group Databasebeta

← #44537533

Subgroups — #44537533

Order 31424.

258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 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
1#30628383C211yesmaximal, characteristic, complemented
2#30628368C213yesmaximal, complemented
3#30628362C213yesmaximal, complemented
4#30628357C213yesmaximal, complemented
5C2×#21463315C213yesmaximal, complemented
6#30628344C211yesmaximal, characteristic, complemented
72−1+4×C491C211yesmaximal, characteristic, complemented
8#21463329—21no—
9#21463328C2213yes—
10C2×D1964C2213yes—
11D4×D491—23no—
12#21463318C2213yescomplemented
13#21463316C2211yescharacteristic, complemented
14#21463315C2213yescomplemented
15#21463315C2216yescomplemented
16#21463313C2213yescomplemented
17#21463312C2213yescomplemented
18C2×C491⋊C8C2213yescomplemented
19#41×C491—23no—
20#41×C491C2211yescharacteristic
21#41×C491C2213yescomplemented
22C2×Q8×C491—21no—
23C2×Q8×C491C2213yescomplemented
24C22×D491—23no—
25Dic982C2311yescharacteristic
26D1964—23no—
27D1964C2313yes—
28C22⋊D491—23no—
29C4×D491—23no—
30C491⋊C8C2311yescharacteristic
31C491⋊C8C2313yes—
32Q8×C491—23no—
33Q8×C491D411yescharacteristic
34Q8×C491C2313yes—
35D4×C491—23no—
36D4×C491D413yes—
37D4×C491C2311yescharacteristic
38C2×C4×C491—23no—
39C2×C4×C491—23no—
40C2×C4×C491C2313yes—
41C22×C491—21no—
42C22×C491C2×D413yes—
43C2×D491—23no—
44C2×D491—83no—
45C4×C491—23no—
46C4×C491C2×D413yes—
47C4×C491C2411yescharacteristic
48Dic491—21no—
49C2×C491—23no—
50C2×C491—41no—
51C2×C491C22×D411yescharacteristic
52D491—43no—
53C491#57711yescharacteristic, complemented, Sylow
54#577—4911nomaximal, Sylow
552−1+4D49111yescharacteristic, complemented
56H(5,𝔽2)—4911no—
57#137—4913no—
58AGL(1,ℤ/8)—4913no—
59#135—4913no—
60C2×SD16—4913no—
61#131—4911no—
62#41—23no—
63#41—9821no—
64#41—4913no—
65#41C2×D49111yescharacteristic
66#41C2×D49113yescomplemented
67C2×Q8—21no—
68C2×Q8C2×D49113yescomplemented
69C2×D4—9823no—
70C2×D4—4913no—
71Q16—4913no—
72SD16—4913no—
73SD16—4916no—
74SD16—4911no—
75D8—4913no—
76M16—4913no—
77C2×C8—4913no—
78C23—9823no—
79Q8—23no—
80Q8—4911no—
81Q8C22⋊D49111yescharacteristic
82Q8C22×D49113yes—
83D4—23no—
84D4—9823no—
85D4—9823no—
86D4—4913no—
87D4C22⋊D49113yes—
88D4C22×D49111yescharacteristic
89C2×C4—23no—
90C2×C4—23no—
91C2×C4—9823no—
92C2×C4C22×D49113yes—
93C8—4911no—
94C8—4913no—
95C22—21no—
96C22—39283no—
97C22—9823no—
98C22C2×C22⋊D49113yes—
99C4—23no—
100C4—9821no—
101C4C2×C22⋊D49113yes—
102C4C23×D49111yescharacteristic
103C2—23no—
104C2—41no—
105C2—19643no—
106C2C22×C22⋊D49111yescharacteristic
subgroupG/H
centerC2C22×C22⋊D491
commutator, cosocleC4×C491C24
FrattiniC4C23×D491
Fitting2−1+4×C491C2
socleC2×C491C22×D4
hypercenter2−1+4D491
hypocenterC491#577
LCSG ▷ C4×C491 ▷ C2×C491 ▷ C491
UCSC1 ◁ C2 ◁ #41 ◁ 2−1+4

Complements

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

NH ≅ G/Ntype
1. #30628383C2semidirect
2. #30628368C2semidirect
3. #30628362C2semidirect
4. #30628357C2semidirect
5. C2×#21463315C2semidirect
6. #30628344C2semidirect
7. 2−1+4×C491C2semidirect
12. #21463318C22semidirect
13. #21463316C22semidirect
14. #21463315C22semidirect
15. #21463315C22semidirect
16. #21463313C22semidirect
17. #21463312C22semidirect
18. C2×C491⋊C8C22semidirect
21. #41×C491C22semidirect
23. C2×Q8×C491C22semidirect
53. C491#577semidirect
55. 2−1+4D491semidirect
66. #41C2×D491semidirect
68. C2×Q8C2×D491semidirect

Maximal subgroups

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

subgroupindex
#306283832
#306283682
#306283622
#306283572
C2×#214633152
#306283442
2−1+4×C4912
#577491