Finite Group Databasebeta

← #44401807

Subgroups — #44401807

Order 29056.

170 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 47 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#28409468C212yesmaximal, complemented
2#28409150C211yesmaximal, characteristic, complemented
3#28408853C211yesmaximal, characteristic, complemented
4#28408845C212yesmaximal, complemented
5#493×C227C211yesmaximal, characteristic, complemented
6#20300310C2211yescharacteristic
7#20300294—21no—
8#20300232—22no—
9#20300229—22no—
10#20300228C2212yes—
11#20300224C2211yescharacteristic
12#20300216—21no—
13C2×D8×C227—21no—
14C2×D8×C227C2212yes—
15#127×C227—21no—
16C4×C8×C227C2211yescharacteristic
17#16813884—21no—
18Dic908D411yescharacteristic, complemented
19#16813873—21no—
20D1816D411yescharacteristic, complemented
21#16813868—21no—
22#16813867—41no—
23C8×D227—41no—
24C227⋊C16—22no—
25C2×D4×C227—22no—
26C2×D4×C227—42no—
27D8×C227—22no—
28D8×C227—22no—
29D8×C227—41no—
30D8×C227—41no—
31C2×C8×C227D411yescharacteristic
32C2×C8×C227C2311yescharacteristic
33C42×C227D411yescharacteristic
34Dic454—21no—
35D908—21no—
36C22⋊D227—41no—
37C4×D227—41no—
38C227⋊C8—41no—
39C23×C227—42no—
40D4×C227—42no—
41D4×C227—42no—
42D4×C227—84no—
43C2×C4×C227—21no—
44C2×C4×C227C2×D411yescharacteristic
45C8×C227D811yescharacteristic
46C8×C227D811yescharacteristic
47C8×C227C2×D411yescharacteristic
48C8×C227#4111yescharacteristic
49C22×C227—84no—
50C22×C227—82no—
51C22×C227AGL(1,ℤ/8)11yescharacteristic
52C2×D227—41no—
53C4×C227—22no—
54C4×C227#12111yescharacteristic
55C4×C227C2×D811yescharacteristic
56Dic227—41no—
57C2×C227—21no—
58C2×C227—162no—
59C2×C227#45911yescharacteristic
60D227—81no—
61C227#221311yescharacteristic, complemented, Sylow
62#2213—2271nomaximal, Sylow
63#509—2272no—
64#493D22711yescharacteristic, complemented
65#443—2271no—
66#364—2271no—
67#361—2272no—
68#135—2271no—
69C2×D8—21no—
70C2×D8C2×D22712yes—
71#131—4541no—
72#127—21no—
73SD32—4542no—
74D16—4542no—
75M32—2272no—
76#108—2271no—
77#104—4541no—
78C4×C8C2×D22711yescharacteristic
79#41—4541no—
80C2×D4—22no—
81C2×D4—42no—
82Q16—2271no—
83SD16—4541no—
84D8—22no—
85D8—22no—
86D8—41no—
87D8—41no—
88D8—2271no—
89M16—9081no—
90M16—4541no—
91C2×C8—9081no—
92C2×C8C22⋊D22711yescharacteristic
93C2×C8C22×D22711yescharacteristic
94C42C22⋊D22711yescharacteristic
95C16—4542no—
96C23—42no—
97Q8—4541no—
98D4—42no—
99D4—42no—
100D4—84no—
101D4—9081no—
102D4—4541no—
103C2×C4—21no—
104C2×C4—9081no—
105C2×C4C2×C22⋊D22711yescharacteristic
106C8—9081no—
107C8#1681386911yescharacteristic
108C8#1681386911yescharacteristic
109C8D4×D22711yescharacteristic
110C8#1681388311yescharacteristic
111C22—84no—
112C22—82no—
113C22—9081no—
114C22#2030031411yescharacteristic
115C4—22no—
116C4—9081no—
117C4#2030025911yescharacteristic
118C4C2×#1681386911yescharacteristic
119C2—21no—
120C2—162no—
121C2—18161no—
122C2#2840922411yescharacteristic
subgroupG/H
centerC2#28409224
commutator, cosocleC2×C8×C227C23
FrattiniC2×C8C22×D227
Fitting#493×C227C2
socleC2×C227#459
hypercenter#493D227
hypocenterC227#2213
LCSG ▷ C2×C8×C227 ▷ C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #28409468C2semidirect
2. #28409150C2semidirect
3. #28408853C2semidirect
4. #28408845C2semidirect
5. #493×C227C2semidirect
18. Dic908D4semidirect
20. D1816D4semidirect
61. C227#2213semidirect
64. #493D227semidirect

Maximal subgroups

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

subgroupindex
#284094682
#284091502
#284088532
#284088452
#493×C2272
#2213227