Finite Group Databasebeta

← #44536844

Subgroups — #44536844

Order 31424.

104 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 45 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#30628357C211yesmaximal, characteristic
2#30628345C211yesmaximal, characteristic, complemented
3#30628344C211yesmaximal, characteristic, complemented
4#30628272C211yesmaximal, characteristic, complemented
5#30628265C211yesmaximal, characteristic, complemented
6#30628248C211yesmaximal, characteristic, complemented
7#104×C491C211yesmaximal, characteristic, complemented
8#21463328C2211yescharacteristic
9#21463318C411yescharacteristic, complemented
10#21463316C411yescharacteristic, complemented
11#21463315C411yescharacteristic, complemented
12#21463313C411yescharacteristic, complemented
13#21463312—21no—
14#21463312C2211yescharacteristic
15#21463311—21no—
16C2×C491⋊C8—21no—
17C2×C491⋊C8C2211yescharacteristic
18C2×C491⋊C8C2211yescharacteristic
19C8×D491—21no—
20#41×C491C2211yescharacteristic
21M16×C491C2211yescharacteristic
22C42×C491C2211yescharacteristic
23Dic982C2×C411yescharacteristic
24D1964C2×C411yescharacteristic
25C22⋊D491—21no—
26C4×D491—21no—
27C491⋊C8—21no—
28C491⋊C8C2×C411yescharacteristic
29C491⋊C8C2×C411yescharacteristic
30C491⋊C8D411yescharacteristic
31C491⋊C8D411yescharacteristic
32Q8×C491C2×C411yescharacteristic
33D4×C491—21no—
34D4×C491C2×C411yescharacteristic
35C2×C4×C491—21no—
36C2×C4×C491—21no—
37C2×C4×C491C2311yescharacteristic
38C8×C491—21no—
39C22×C491—21no—
40C22×C491#4111yescharacteristic
41C2×D491—21no—
42C4×C491—21no—
43C4×C491—41no—
44C4×C491C22×C411yescharacteristic
45C4×C491C2×D411yescharacteristic
46Dic491—21no—
47C2×C491—21no—
48C2×C491—41no—
49C2×C491C4×D411yescharacteristic
50D491—41no—
51C491#44411yescharacteristic, complemented, Sylow
52#444—4911nomaximal, Sylow
53#135—4911no—
54#131—4911no—
55#131—4911no—
56#108—4911no—
57#104—4911no—
58#104D49111yescharacteristic, complemented
59#97—4911no—
60#41—4911no—
61#41C2×D49111yescharacteristic
62Q16—4911no—
63SD16—4911no—
64SD16—4911no—
65D8—4911no—
66M16—9821no—
67M16—9821no—
68M16—4911no—
69M16C2×D49111yescharacteristic
70C2×C8—9821no—
71C2×C8—9821no—
72C2×C8—4911no—
73C2×C8—4911no—
74C42C2×D49111yescharacteristic
75Q8—4911no—
76Q8C4×D49111yescharacteristic
77D4—21no—
78D4—9821no—
79D4—4911no—
80D4C4×D49111yescharacteristic
81C2×C4—21no—
82C2×C4—21no—
83C2×C4—9821no—
84C2×C4C22×D49111yescharacteristic
85C8—21no—
86C8—9821no—
87C8—4911no—
88C8—4911no—
89C8—4911no—
90C8—4911no—
91C22—21no—
92C22—9821no—
93C22#2146332711yescharacteristic
94C4—21no—
95C4—41no—
96C4—9821no—
97C4C2×C4×D49111yescharacteristic
98C4D4×D49111yescharacteristic
99C2—21no—
100C2—41no—
101C2—19641no—
102C2(C22⋊D491)⋊C411yescharacteristic
subgroupG/H
centerC4D4×D491
commutatorC4×C491C22×C4
FrattiniC2×C4C22×D491
Fitting#104×C491C2
socleC2×C491C4×D4
prime radical#30628357C2
cosocleC2×C4×C491C23
hypercenter#104D491
hypocenterC491#444
LCSG ▷ C4×C491 ▷ C2×C491 ▷ C491
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #30628345C2semidirect
3. #30628344C2semidirect
4. #30628272C2semidirect
5. #30628265C2semidirect
6. #30628248C2semidirect
7. #104×C491C2semidirect
9. #21463318C4semidirect
10. #21463316C4semidirect
11. #21463315C4semidirect
12. #21463313C4semidirect
51. C491#444semidirect
58. #104D491semidirect

Maximal subgroups

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

subgroupindex
#306283572
#306283452
#306283442
#306282722
#306282652
#306282482
#104×C4912
#444491