Finite Group Databasebeta

← #44397883

Subgroups — #44397883

Order 29056.

112 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 23 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#28409209C211yesmaximal, characteristic
2#28408829C211yesmaximal, characteristic, complemented
3#329×C227C211yesmaximal, characteristic, complemented
4#20300333C411yescharacteristic
5#20300319—21no—
6#20300216—21no—
7#20300207—21no—
8#20300205C411yescharacteristic
9#124×C227C2211yescharacteristic
10#97×C227—21no—
11#16813884—21no—
12#16813883—41no—
13C2×C22⋊D227—41no—
14D4×D227—41no—
15#16813874—41no—
16#16813871—41no—
17#16813868—21no—
18#16813868—41no—
19C2×Q8×C227D411yescharacteristic
20C2×D4×C227C2×C411yescharacteristic
21C2×C8×C227—41no—
22C22⋊C4×C227—41no—
23C42×C227D411yescharacteristic
24C22×D227—41no—
25Dic454—21no—
26D908—21no—
27C22⋊D227—42no—
28C22⋊D227—41no—
29C2×Dic227—41no—
30C4×D227—41no—
31C227⋊C8—41no—
32C227⋊C8—81no—
33C23×C227—21no—
34Q8×C227—41no—
35D4×C227—41no—
36C2×C4×C227—21no—
37C2×C4×C227—21no—
38C2×C4×C227C22⋊C411yescharacteristic
39C8×C227—42no—
40C22×C227—41no—
41C22×C227—81no—
42C22×C227#9911yescharacteristic
43C2×D227—41no—
44C2×D227—161no—
45C4×C227—21no—
46C4×C227—41no—
47C4×C227—41no—
48Dic227—41no—
49C2×C227—21no—
50C2×C227—81no—
51C2×C227AΣL(1,𝔽16)11yescharacteristic
52D227—81no—
53C227#140311yescharacteristic, complemented, Sylow
54#1403—2271nomaximal, Sylow
55#455—2271no—
56#355—2271no—
57#329D22711yescharacteristic, complemented
58H(5,𝔽2)—2271no—
59#137—4541no—
60#124C2×D22711yescharacteristic
61#104—4541no—
62#101—4541no—
63#100—2271no—
64#97—21no—
65#41—9081no—
66#41—4541no—
67C2×Q8D90811yescharacteristic
68C2×D4—9081no—
69C2×D4—9081no—
70C2×D4C4×D22711yescharacteristic
71Q16—9081no—
72SD16—9081no—
73M16—9081no—
74M16—4541no—
75C2×C8—41no—
76C22⋊C4—41no—
77C42C22⋊D22711yescharacteristic
78C23—21no—
79C23—9081no—
80Q8—41no—
81Q8—4541no—
82D4—41no—
83D4—9082no—
84D4—9081no—
85D4—4541no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—9081no—
89C2×C4—9081no—
90C2×C4(C2×D227)⋊C411yescharacteristic
91C8—42no—
92C8—18161no—
93C8—9081no—
94C22—41no—
95C22—81no—
96C22—36321no—
97C22—9081no—
98C22#2030020211yescharacteristic
99C4—21no—
100C4—41no—
101C4—41no—
102C4—9081no—
103C2—21no—
104C2—81no—
105C2—18161no—
106C2#2840882011yescharacteristic
subgroupG/H
centerC2#28408820
commutatorC2×D4×C227C2×C4
Frattini#124C2×D227
Fitting#329×C227C2
socleC2×C227AΣL(1,𝔽16)
prime radical#20300333C4
cosocle#124×C227C22
hypercenter#329D227
hypocenterC227#1403
LCSG ▷ C2×D4×C227 ▷ C2×C4×C227 ▷ C22×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #28408829C2semidirect
3. #329×C227C2semidirect
53. C227#1403semidirect
57. #329D227semidirect

Maximal subgroups

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

subgroupindex
#284092092
#284088292
#329×C2272
#1403227