Finite Group Databasebeta

← #38786295

Subgroups — #38786295

Order 25664.

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#27165784C211yesmaximal, characteristic
2#27165768C211yesmaximal, characteristic, complemented
3#27165735C211yesmaximal, characteristic, complemented
4#27165664C211yesmaximal, characteristic, complemented
5#27165663C211yesmaximal, characteristic, complemented
6#27165655C211yesmaximal, characteristic, complemented
7#137×C401C211yesmaximal, characteristic, complemented
8#20264366—21no—
9#20264366C2211yescharacteristic
10#20264365—22no—
11#20264365—21no—
12C2×Dic802—21no—
13C2×Dic802C2211yescharacteristic
14Q8×D401—21no—
15#20264356—21no—
16#20264353—21no—
17#20264350C2211yescharacteristic
18#20264345—22no—
19C4×Dic401C2211yescharacteristic
20#41×C401C2211yescharacteristic
21C2×Q8×C401C2211yescharacteristic
22Q16×C401—21no—
23SD16×C401—21no—
24M16×C401C2211yescharacteristic
25Dic802—22no—
26Dic802—21no—
27Dic802—21no—
28Dic802D411yescharacteristic
29D1604D411yescharacteristic
30C22⋊D401—22no—
31C22⋊D401—21no—
32C2×Dic401—22no—
33C2×Dic401—21no—
34C2×Dic401D412yes—
35C4×D401—22no—
36C4×D401—21no—
37#15691999—21no—
38Q8×C401—21no—
39Q8×C401—21no—
40Q8×C401D411yescharacteristic
41D4×C401—21no—
42D4×C401D411yescharacteristic
43C2×C4×C401—21no—
44C2×C4×C401—21no—
45C2×C4×C401C2311yescharacteristic
46C8×C401—21no—
47C22×C401—21no—
48C22×C401C2×D411yescharacteristic
49C2×D401—21no—
50C4×C401—21no—
51C4×C401—41no—
52C4×C401C2×D411yescharacteristic
53C4×C401C2×D411yescharacteristic
54Dic401—22no—
55Dic401—21no—
56Dic401—22no—
57C2×C401—21no—
58C2×C401—41no—
59C2×C401#12011yescharacteristic
60D401—41no—
61C401#45611yescharacteristic, complemented, Sylow
62#456—4011nomaximal, Sylow
632−1+4—4011no—
64#137—4011no—
65#137D40111yescharacteristic, complemented
66C4⋊Q8—4011no—
67#104—4011no—
68#104—4011no—
69#101—4011no—
70#41—8021no—
71#41—8021no—
72#41—8022no—
73#41—4011no—
74#41C2×D40111yescharacteristic
75C2×Q8—8021no—
76C2×Q8—8021no—
77C2×Q8—4011no—
78C2×Q8C2×D40111yescharacteristic
79Q16—21no—
80Q16—8021no—
81SD16—21no—
82SD16—8021no—
83M16—4011no—
84M16C2×D40111yescharacteristic
85C4⋊C4—8022no—
86C42—4011no—
87Q8—21no—
88Q8—21no—
89Q8—8022no—
90Q8—8021no—
91Q8—8021no—
92Q8—4011no—
93Q8C22⋊D40111yescharacteristic
94D4—21no—
95D4—8022no—
96D4—8021no—
97D4—4011no—
98D4C22⋊D40111yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—8022no—
102C2×C4—8022no—
103C2×C4—8021no—
104C2×C4—8021no—
105C2×C4—4012no—
106C2×C4C22×D40111yescharacteristic
107C8—21no—
108C8—8021no—
109C22—21no—
110C22—8021no—
111C22D4×D40111yescharacteristic
112C4—21no—
113C4—41no—
114C4—8022no—
115C4—8021no—
116C4—8022no—
117C4D4×D40111yescharacteristic
118C4C2×C22⋊D40111yescharacteristic
119C2—21no—
120C2—41no—
121C2—16041no—
122C2#2716570511yescharacteristic
subgroupG/H
centerC2#27165705
commutator, cosocleC2×C4×C401C23
FrattiniC2×C4C22×D401
Fitting#137×C401C2
socleC2×C401#120
prime radical#27165784C2
hypercenter#137D401
hypocenterC401#456
LCSG ▷ C2×C4×C401 ▷ C2×C401 ▷ C401
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
2. #27165768C2semidirect
3. #27165735C2semidirect
4. #27165664C2semidirect
5. #27165663C2semidirect
6. #27165655C2semidirect
7. #137×C401C2semidirect
61. C401#456semidirect
65. #137D401semidirect

Maximal subgroups

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

subgroupindex
#271657842
#271657682
#271657352
#271656642
#271656632
#271656552
#137×C4012
#456401