Finite Group Databasebeta

← #44399037

Subgroups — #44399037

Order 29056.

182 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C227⋊#564C211yesmaximal, characteristic, complemented
2#28409398C211yesmaximal, characteristic
3#28409397C212yesmaximal
4#28408773C212yesmaximal, complemented
5#330×C227C211yesmaximal, characteristic, complemented
6#20300285C2211yescharacteristic
7#20300280C2212yes—
8#20300279—22no—
9#20300278—22no—
10#20300278—22no—
11#20300210—22no—
12#20300210—22no—
13#20300208—22no—
14#20300199C2211yescharacteristic
15#125×C227C2211yescharacteristic
16#97×C227C2212yes—
17C2×D908—21no—
18C2×D908—22no—
19C2×C227⋊C8—21no—
20C4⋊Dic227—22no—
21C4⋊Dic227D412yes—
22C4⋊Dic227D412yes—
23Dic227⋊C4—22no—
24Dic227⋊C4—22no—
25Dic227⋊C4—22no—
26Dic227⋊C4—22no—
27C4×Dic227—22no—
28C2×C8×C227—22no—
29C4⋊C4×C227—22no—
30C4⋊C4×C227D412yes—
31C42×C227C2311yescharacteristic
32C22×D227—41no—
33D908—44no—
34D908—42no—
35C2×Dic227—22no—
36C2×Dic227—22no—
37C227⋊C8—41no—
38C2×C4×C227—22no—
39C2×C4×C227C2×D412yes—
40C2×C4×C227C2×D411yescharacteristic
41C8×C227—42no—
42C22×C227#12011yescharacteristic
43C2×D227—82no—
44C2×D227—81no—
45C4×C227—22no—
46C4×C227—21no—
47C4×C227—42no—
48Dic227—42no—
49Dic227—42no—
50C2×C227#45412yes—
51C2×C227#45411yescharacteristic
52D227—161no—
53C227#165811yescharacteristic, complemented, Sylow
54#1658—2271nomaximal, Sylow
55#564—2271no—
56#490—2271no—
57#490—2272no—
58#330—2272no—
59#330D22711yescharacteristic, complemented
60#127—2271no—
61#125—4542no—
62#125—4542no—
63#125—4542no—
64#125—2272no—
65#125C2×D22711yescharacteristic
66#102—4542no—
67#102—4542no—
68#102—4542no—
69#97—2271no—
70#97C2×D22712yes—
71C2×D4—4542no—
72C2×D4—4541no—
73C2×C8—22no—
74C2×C8—4541no—
75C4⋊C4—22no—
76C4⋊C4—4542no—
77C4⋊C4—4542no—
78C4⋊C4—4542no—
79C4⋊C4—4542no—
80C4⋊C4—4542no—
81C4⋊C4—2272no—
82C4⋊C4—2272no—
83C4⋊C4D90812yes—
84C42—4542no—
85C42C22×D22711yescharacteristic
86C23—9081no—
87D4—9084no—
88D4—9082no—
89C2×C4—22no—
90C2×C4—4542no—
91C2×C4—4542no—
92C2×C4D4×D22712yes—
93C2×C4C2×D90811yescharacteristic
94C8—42no—
95C8—9081no—
96C22—18162no—
97C22—18161no—
98C22#2030025811yescharacteristic
99C4—22no—
100C4—21no—
101C4—42no—
102C4—9082no—
103C4—9082no—
104C2—36321no—
105C2#2840920612yes—
106C2#2840920711yescharacteristic
subgroupG/H
centerC22#20300258
commutator, cosocleC42×C227C23
FrattiniC42C22×D227
Fitting#330×C227C2
socleC22×C227#120
prime radical#20300285C22
hypercenter#330D227
hypocenterC227#1658
LCSG ▷ C42×C227 ▷ C22×C227 ▷ C227
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. C227⋊#564C2semidirect
4. #28408773C2semidirect
5. #330×C227C2semidirect
53. C227#1658semidirect
59. #330D227semidirect

Maximal subgroups

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

subgroupindex
C227⋊#5642
#284093982
#284093972
#284087732
#330×C2272
#1658227