Finite Group Databasebeta

← #44536985

Subgroups — #44536985

Order 31424.

104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 37 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#30628368C211yesmaximal, characteristic, complemented
2#30628363C211yesmaximal, characteristic
3#30628343C211yesmaximal, characteristic, complemented
4#30628273C211yesmaximal, characteristic, complemented
5#30628256C211yesmaximal, characteristic, complemented
6#30628254C211yesmaximal, characteristic, complemented
7C2×SD16×C491C211yesmaximal, characteristic, complemented
8#21463328C2211yescharacteristic
9#21463318—21no—
10#21463316—21no—
11#21463315—21no—
12#21463313—21no—
13#21463312C2211yescharacteristic
14#21463312C2211yescharacteristic
15#21463312C2211yescharacteristic
16#21463311—21no—
17C8×D491—21no—
18C2×Q8×C491C2211yescharacteristic
19C2×D4×C491C2211yescharacteristic
20SD16×C491—21no—
21SD16×C491—21no—
22C2×C8×C491C2211yescharacteristic
23Dic982D411yescharacteristic
24D1964D411yescharacteristic
25C22⋊D491—21no—
26C4×D491—21no—
27C491⋊C8—21no—
28C491⋊C8—21no—
29C491⋊C8—21no—
30C23×C491—21no—
31Q8×C491—21no—
32Q8×C491—21no—
33D4×C491—21no—
34D4×C491—21no—
35C2×C4×C491—21no—
36C2×C4×C491C2311yescharacteristic
37C8×C491D411yescharacteristic
38C8×C491D411yescharacteristic
39C22×C491—41no—
40C22×C491—81no—
41C22×C491#4111yescharacteristic
42C2×D491—21no—
43C4×C491—41no—
44C4×C491C2×D411yescharacteristic
45C4×C491C2×D411yescharacteristic
46Dic491—21no—
47C2×C491—21no—
48C2×C491—81no—
49C2×C491#12111yescharacteristic
50D491—41no—
51C491#47111yescharacteristic, complemented, Sylow
52#471—4911nomaximal, Sylow
53#137—4911no—
54AGL(1,ℤ/8)—4911no—
55C2×SD16D49111yescharacteristic, complemented
56#131—4911no—
57#108—4911no—
58#101—4911no—
59#100—4911no—
60#41—4911no—
61C2×Q8C2×D49111yescharacteristic
62C2×D4C2×D49111yescharacteristic
63Q16—9821no—
64SD16—21no—
65SD16—21no—
66SD16—9821no—
67SD16—9821no—
68D8—9821no—
69M16—9821no—
70M16—4911no—
71M16—4911no—
72M16—4911no—
73C2×C8—9821no—
74C2×C8C2×D49111yescharacteristic
75C23—21no—
76Q8—21no—
77Q8—21no—
78Q8—4911no—
79D4—21no—
80D4—21no—
81D4—9821no—
82D4—4911no—
83C2×C4—21no—
84C2×C4—9821no—
85C2×C4C22×D49111yescharacteristic
86C8—9821no—
87C8—9821no—
88C8—9821no—
89C8C22⋊D49111yescharacteristic
90C8C22⋊D49111yescharacteristic
91C22—41no—
92C22—81no—
93C22—9821no—
94C22#2146332711yescharacteristic
95C4—41no—
96C4—9821no—
97C4D4×D49111yescharacteristic
98C4C2×C22⋊D49111yescharacteristic
99C2—21no—
100C2—81no—
101C2—19641no—
102C2#3062830811yescharacteristic
subgroupG/H
centerC2#30628308
commutator, cosocleC2×C4×C491C23
FrattiniC2×C4C22×D491
FittingC2×SD16×C491C2
socleC2×C491#121
prime radical#30628363C2
hypercenterC2×SD16D491
hypocenterC491#471
LCSG ▷ C2×C4×C491 ▷ C2×C491 ▷ C491
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #30628368C2semidirect
3. #30628343C2semidirect
4. #30628273C2semidirect
5. #30628256C2semidirect
6. #30628254C2semidirect
7. C2×SD16×C491C2semidirect
51. C491#471semidirect
55. C2×SD16D491semidirect

Maximal subgroups

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

subgroupindex
#306283682
#306283632
#306283432
#306282732
#306282562
#306282542
C2×SD16×C4912
#471491