Finite Group Databasebeta

← #36374404

Subgroups — #36374404

Order 22336.

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#26013670C211yesmaximal, characteristic, complemented
2#26013665C211yesmaximal, characteristic
3#26013645C211yesmaximal, characteristic, complemented
4#26013575C211yesmaximal, characteristic, complemented
5#26013558C211yesmaximal, characteristic, complemented
6#26013556C211yesmaximal, characteristic, complemented
7C2×SD16×C349C211yesmaximal, characteristic, complemented
8#19150233C2211yescharacteristic
9#19150223—21no—
10#19150221—21no—
11#19150220—21no—
12#19150218—21no—
13#19150217C2211yescharacteristic
14#19150217C2211yescharacteristic
15#19150217C2211yescharacteristic
16#19150216—21no—
17C8×D349—21no—
18C2×Q8×C349C2211yescharacteristic
19C2×D4×C349C2211yescharacteristic
20SD16×C349—21no—
21SD16×C349—21no—
22C2×C8×C349C2211yescharacteristic
23Dic698D411yescharacteristic
24D1396D411yescharacteristic
25C22⋊D349—21no—
26C4×D349—21no—
27#14584095—21no—
28#14584095—21no—
29#14584095—21no—
30C23×C349—21no—
31Q8×C349—21no—
32Q8×C349—21no—
33D4×C349—21no—
34D4×C349—21no—
35C2×C4×C349—21no—
36C2×C4×C349C2311yescharacteristic
37C8×C349D411yescharacteristic
38C8×C349D411yescharacteristic
39C22×C349—41no—
40C22×C349—81no—
41C22×C349#4111yescharacteristic
42C2×D349—21no—
43C4×C349—41no—
44C4×C349C2×D411yescharacteristic
45C4×C349C2×D411yescharacteristic
46Dic349—21no—
47C2×C349—21no—
48C2×C349—81no—
49C2×C349#12111yescharacteristic
50D349—41no—
51C349#47111yescharacteristic, complemented, Sylow
52#471—3491nomaximal, Sylow
53#137—3491no—
54AGL(1,ℤ/8)—3491no—
55C2×SD16D34911yescharacteristic, complemented
56#131—3491no—
57#108—3491no—
58#101—3491no—
59#100—3491no—
60#41—3491no—
61C2×Q8C2×D34911yescharacteristic
62C2×D4C2×D34911yescharacteristic
63Q16—6981no—
64SD16—21no—
65SD16—21no—
66SD16—6981no—
67SD16—6981no—
68D8—6981no—
69M16—3491no—
70M16—3491no—
71M16—3491no—
72M16—6981no—
73C2×C8—6981no—
74C2×C8C2×D34911yescharacteristic
75C23—21no—
76Q8—21no—
77Q8—21no—
78Q8—3491no—
79D4—21no—
80D4—21no—
81D4—3491no—
82D4—6981no—
83C2×C4—21no—
84C2×C4—6981no—
85C2×C4C22×D34911yescharacteristic
86C8—6981no—
87C8—6981no—
88C8—6981no—
89C8C22⋊D34911yescharacteristic
90C8C22⋊D34911yescharacteristic
91C22—41no—
92C22—81no—
93C22—6981no—
94C22#1915023211yescharacteristic
95C4—41no—
96C4—6981no—
97C4D4×D34911yescharacteristic
98C4C2×C22⋊D34911yescharacteristic
99C2—21no—
100C2—81no—
101C2—13961no—
102C2#2601361011yescharacteristic
subgroupG/H
centerC2#26013610
commutator, cosocleC2×C4×C349C23
FrattiniC2×C4C22×D349
FittingC2×SD16×C349C2
socleC2×C349#121
prime radical#26013665C2
hypercenterC2×SD16D349
hypocenterC349#471
LCSG ▷ C2×C4×C349 ▷ C2×C349 ▷ C349
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #26013670C2semidirect
3. #26013645C2semidirect
4. #26013575C2semidirect
5. #26013558C2semidirect
6. #26013556C2semidirect
7. C2×SD16×C349C2semidirect
51. C349#471semidirect
55. C2×SD16D349semidirect

Maximal subgroups

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

subgroupindex
#260136702
#260136652
#260136452
#260135752
#260135582
#260135562
C2×SD16×C3492
#471349