Finite Group Databasebeta

← #38762703

Subgroups — #38762703

Order 25408.

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

normal subgroups only

This group has 142 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#27163143C211yesmaximal, characteristic
2#27163127C211yesmaximal, characteristic, complemented
3#27163094C211yesmaximal, characteristic, complemented
4#27163023C211yesmaximal, characteristic, complemented
5#27163022C211yesmaximal, characteristic, complemented
6#27163014C211yesmaximal, characteristic, complemented
7#137×C397C211yesmaximal, characteristic, complemented
8#20263731—21no—
9#20263731C2211yescharacteristic
10#20263730—22no—
11#20263730—21no—
12C2×Dic794—21no—
13C2×Dic794C2211yescharacteristic
14Q8×D397—21no—
15#20263721—21no—
16#20263718—21no—
17#20263715C2211yescharacteristic
18#20263710—22no—
19C4×Dic397C2211yescharacteristic
20#41×C397C2211yescharacteristic
21C2×Q8×C397C2211yescharacteristic
22Q16×C397—21no—
23SD16×C397—21no—
24M16×C397C2211yescharacteristic
25Dic794—22no—
26Dic794—21no—
27Dic794—21no—
28Dic794D411yescharacteristic
29D1588D411yescharacteristic
30C22⋊D397—22no—
31C22⋊D397—21no—
32C2×Dic397—22no—
33C2×Dic397—21no—
34C2×Dic397D412yes—
35C4×D397—22no—
36C4×D397—21no—
37#15691787—21no—
38Q8×C397—21no—
39Q8×C397—21no—
40Q8×C397D411yescharacteristic
41D4×C397—21no—
42D4×C397D411yescharacteristic
43C2×C4×C397—21no—
44C2×C4×C397—21no—
45C2×C4×C397C2311yescharacteristic
46C8×C397—21no—
47C22×C397—21no—
48C22×C397C2×D411yescharacteristic
49C2×D397—21no—
50C4×C397—21no—
51C4×C397—41no—
52C4×C397C2×D411yescharacteristic
53C4×C397C2×D411yescharacteristic
54Dic397—22no—
55Dic397—21no—
56Dic397—22no—
57C2×C397—21no—
58C2×C397—41no—
59C2×C397#12011yescharacteristic
60D397—41no—
61C397#45611yescharacteristic, complemented, Sylow
62#456—3971nomaximal, Sylow
632−1+4—3971no—
64#137—3971no—
65#137D39711yescharacteristic, complemented
66C4⋊Q8—3971no—
67#104—3971no—
68#104—3971no—
69#101—3971no—
70#41—7941no—
71#41—7941no—
72#41—7942no—
73#41—3971no—
74#41C2×D39711yescharacteristic
75C2×Q8—7941no—
76C2×Q8—7941no—
77C2×Q8—3971no—
78C2×Q8C2×D39711yescharacteristic
79Q16—21no—
80Q16—7941no—
81SD16—21no—
82SD16—7941no—
83M16—3971no—
84M16C2×D39711yescharacteristic
85C4⋊C4—7942no—
86C42—3971no—
87Q8—21no—
88Q8—21no—
89Q8—7942no—
90Q8—7941no—
91Q8—7941no—
92Q8—3971no—
93Q8C22⋊D39711yescharacteristic
94D4—21no—
95D4—7942no—
96D4—7941no—
97D4—3971no—
98D4C22⋊D39711yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—7942no—
102C2×C4—7942no—
103C2×C4—7941no—
104C2×C4—7941no—
105C2×C4—3972no—
106C2×C4C22×D39711yescharacteristic
107C8—21no—
108C8—7941no—
109C22—21no—
110C22—7941no—
111C22D4×D39711yescharacteristic
112C4—21no—
113C4—41no—
114C4—7942no—
115C4—7941no—
116C4—7942no—
117C4D4×D39711yescharacteristic
118C4C2×C22⋊D39711yescharacteristic
119C2—21no—
120C2—41no—
121C2—15881no—
122C2#2716306411yescharacteristic
subgroupG/H
centerC2#27163064
commutator, cosocleC2×C4×C397C23
FrattiniC2×C4C22×D397
Fitting#137×C397C2
socleC2×C397#120
prime radical#27163143C2
hypercenter#137D397
hypocenterC397#456
LCSG ▷ C2×C4×C397 ▷ C2×C397 ▷ C397
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
2. #27163127C2semidirect
3. #27163094C2semidirect
4. #27163023C2semidirect
5. #27163022C2semidirect
6. #27163014C2semidirect
7. #137×C397C2semidirect
61. C397#456semidirect
65. #137D397semidirect

Maximal subgroups

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

subgroupindex
#271631432
#271631272
#271630942
#271630232
#271630222
#271630142
#137×C3972
#456397