Finite Group Databasebeta

← #38762713

Subgroups — #38762713

Order 25408.

160 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 39 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#27163141C211yesmaximal, characteristic
2#27163080C212yesmaximal, complemented
3#27163077C211yesmaximal, characteristic, complemented
4#27163010C212yesmaximal, complemented
5#99×C397C211yesmaximal, characteristic, complemented
6#20263731—21no—
7#20263730—22no—
8C2×C22⋊D397—21no—
9C2×C22⋊D397C2212yes—
10D4×D397—22no—
11C22×Dic397C2211yescharacteristic, complemented
12C4⋊Dic397—22no—
13#20263710—21no—
14C22⋊Dic397—21no—
15C22⋊Dic397C2211yescharacteristic, complemented
16#20263708—22no—
17C2×D4×C397C2211yescharacteristic
18C22⋊C4×C397C2212yescomplemented
19C22×D397—21no—
20C22×D397D412yes—
21Dic794—21no—
22D1588—21no—
23C22⋊D397—22no—
24C22⋊D397—22no—
25C22⋊D397—22no—
26C2×Dic397—21no—
27C2×Dic397—22no—
28C2×Dic397—21no—
29C2×Dic397—21no—
30C2×Dic397D412yes—
31C4×D397—22no—
32C23×C397D411yescharacteristic
33C23×C397C2311yescharacteristic
34D4×C397—22no—
35C2×C4×C397—22no—
36C2×C4×C397D411yescharacteristic
37C22×C397—21no—
38C22×C397—41no—
39C22×C397—41no—
40C22×C397C2×D412yes—
41C22×C397C2×D411yescharacteristic
42C2×D397—22no—
43C2×D397—42no—
44C2×D397—81no—
45C4×C397—21no—
46C4×C397—42no—
47Dic397—22no—
48Dic397—41no—
49Dic397—41no—
50C2×C397—21no—
51C2×C397—22no—
52C2×C397—41no—
53C2×C397#12011yescharacteristic
54D397—42no—
55C397#45811yescharacteristic, complemented, Sylow
56#458—3971nomaximal, Sylow
57H(5,𝔽2)—3971no—
58#123—3971no—
59#123—3972no—
60#99—3972no—
61#99D39711yescharacteristic, complemented
62#41—7942no—
63#41—7941no—
64C2×D4—7942no—
65C2×D4—7941no—
66C2×D4—3972no—
67C2×D4C2×D39711yescharacteristic
68C22×C4—3971no—
69C4⋊C4—7942no—
70C4⋊C4—7941no—
71C22⋊C4—7942no—
72C22⋊C4—7941no—
73C22⋊C4—3971no—
74C22⋊C4C2×D39712yescomplemented
75C23—7941no—
76C23—3972no—
77C23D158811yescharacteristic
78C23C22×D39711yescharacteristic
79Q8—7941no—
80D4—22no—
81D4—7941no—
82D4—7942no—
83D4—7942no—
84D4—7942no—
85C2×C4—22no—
86C2×C4—7942no—
87C2×C4—7941no—
88C2×C4—7942no—
89C2×C4—7941no—
90C2×C4—7941no—
91C2×C4—3972no—
92C2×C4D158811yescharacteristic
93C22—21no—
94C22—41no—
95C22—41no—
96C22—7942no—
97C22—15882no—
98C22—31761no—
99C22D4×D39712yes—
100C22C2×D158811yescharacteristic
101C4—21no—
102C4—42no—
103C4—7942no—
104C4—15881no—
105C4—15881no—
106C2—22no—
107C2—21no—
108C2—41no—
109C2—15882no—
110C2#2716306611yescharacteristic
subgroupG/H
centerC2#27163066
commutator, cosocleC23×C397C23
FrattiniC23C22×D397
Fitting#99×C397C2
socleC2×C397#120
prime radical#27163141C2
hypercenter#99D397
hypocenterC397#458
LCSG ▷ C23×C397 ▷ C2×C397 ▷ C397
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
2. #27163080C2semidirect
3. #27163077C2semidirect
4. #27163010C2semidirect
5. #99×C397C2semidirect
11. C22×Dic397C22semidirect
15. C22⋊Dic397C22semidirect
18. C22⋊C4×C397C22semidirect
55. C397#458semidirect
61. #99D397semidirect
74. C22⋊C4C2×D397semidirect

Maximal subgroups

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

subgroupindex
#271631412
#271630802
#271630772
#271630102
#99×C3972
#458397