Finite Group Databasebeta

← #49123366

Subgroups — #49123366

Order 36224.

150 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 49 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×#22583549C211yesmaximal, characteristic
2#31826703C212yesmaximal
3#31826293C211yesmaximal, characteristic, complemented
4#31826269C212yesmaximal, complemented
5C2×Q32×C283C211yesmaximal, characteristic, complemented
6C2×C8×D283C2211yescharacteristic
7#22583586—22no—
8#22583549—22no—
9C2×C283⋊C16C2211yescharacteristic
10#22583544C2212yes—
11#22583534—22no—
12C2×Q16×C283C2212yes—
13Q32×C283—22no—
14C2×C16×C283C2211yescharacteristic
15C2×C4×D283D411yescharacteristic
16C2×C283⋊C8D411yescharacteristic
17C8×D283—21no—
18C8×D283—21no—
19C4⋊Dic283—22no—
20Dic283⋊C4—42no—
21(C2×D283)⋊C4—42no—
22C283⋊C16—21no—
23C2×Q8×C283—22no—
24Q16×C283—22no—
25Q16×C283—22no—
26C2×C8×C283C2311yescharacteristic
27C16×C283D412yes—
28C22×D283D811yescharacteristic
29C2×Dic283—42no—
30C2×Dic283D811yescharacteristic
31C4×D283—21no—
32C4×D283—21no—
33C283⋊C8—21no—
34Q8×C283—42no—
35Q8×C283—42no—
36C2×C4×C283—42no—
37C2×C4×C283C2×D411yescharacteristic
38C8×C283C2×D411yescharacteristic
39C8×C283#4111yescharacteristic
40C22×C283C2×D811yescharacteristic
41C2×D283—21no—
42C2×D283—22no—
43C4×C283—82no—
44C4×C283#12111yescharacteristic
45C4×C283#13511yescharacteristic
46Dic283—21no—
47Dic283—82no—
48C2×C283#46611yescharacteristic
49C2×C283#51012yes—
50D283—41no—
51C283#221911yescharacteristic, complemented, Sylow
52#2219—2831nomaximal, Sylow
53C2×Q32D28311yescharacteristic, complemented
54C2×M32—2831no—
55#467—2832no—
56#367—2831no—
57#358—2832no—
58C2×Q16C2×D28312yes—
59C22×C8—2831no—
60C22⋊Q8—5662no—
61Q32—22no—
62M32—5662no—
63C2×C16—2831no—
64C2×C16C2×D28311yescharacteristic
65#107—2832no—
66#103—5662no—
67C2×Q8—22no—
68C22×C4—2831no—
69Q16—22no—
70Q16—22no—
71C2×C8—2831no—
72C2×C8—5661no—
73C2×C8—5661no—
74C2×C8C22×D28311yescharacteristic
75C4⋊C4—5662no—
76C4⋊C4—11322no—
77C22⋊C4—11322no—
78C16—5661no—
79C16C22⋊D28312yes—
80C23—2831no—
81Q8—42no—
82Q8—42no—
83C2×C4—42no—
84C2×C4—2831no—
85C2×C4—5661no—
86C2×C4—5661no—
87C2×C4—11322no—
88C2×C4D4×D28311yescharacteristic
89C8—5661no—
90C8C2×C22⋊D28311yescharacteristic
91C8#1798539111yescharacteristic
92C22—5661no—
93C22—5662no—
94C22D8×D28311yescharacteristic
95C4—82no—
96C4—5661no—
97C4—22642no—
98C4#2258358111yescharacteristic
99C4#2258362911yescharacteristic
100C2—11321no—
101C2#3182669811yescharacteristic
102C2#3182690712yes—
subgroupG/H
centerC22D8×D283
commutator, cosocleC2×C8×C283C23
FrattiniC2×C8C22×D283
FittingC2×Q32×C283C2
socleC22×C283C2×D8
prime radicalC22×D283D8
hypercenterC2×Q32D283
hypocenterC283#2219
LCSG ▷ C2×C8×C283 ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q32

Complements

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

NH ≅ G/Ntype
3. #31826293C2semidirect
4. #31826269C2semidirect
5. C2×Q32×C283C2semidirect
51. C283#2219semidirect
53. C2×Q32D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225835492
#318267032
#318262932
#318262692
C2×Q32×C2832
#2219283