Finite Group Databasebeta

← #38786285

Subgroups — #38786285

Order 25664.

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

normal subgroups only

This group has 146 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, complemented
2#27165763C211yesmaximal, characteristic, complemented
3#27165724C211yesmaximal, characteristic, complemented
4#27165664C211yesmaximal, characteristic, complemented
5#27165663C211yesmaximal, characteristic, complemented
6#27165655C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C401C211yesmaximal, characteristic, complemented
8#20264366—21no—
9#20264366C2211yescharacteristic
10#20264365—22no—
11#20264365—21no—
12C2×Dic802—21no—
13C2×Dic802C2211yescharacteristic
14Q8×D401—21no—
15#20264354—21no—
16#20264351—21no—
17#20264350C2211yescharacteristic
18C22⋊Dic401—22no—
19C4×Dic401C2211yescharacteristic
20#41×C401C2211yescharacteristic
21C2×D4×C401C2211yescharacteristic
22SD16×C401—21no—
23D8×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—
38C23×C401—21no—
39Q8×C401D411yescharacteristic
40D4×C401—21no—
41D4×C401—21no—
42D4×C401—21no—
43D4×C401D411yescharacteristic
44C2×C4×C401—21no—
45C2×C4×C401C2311yescharacteristic
46C8×C401—21no—
47C22×C401—21no—
48C22×C401—42no—
49C22×C401—41no—
50C22×C401C2×D411yescharacteristic
51C2×D401—21no—
52C4×C401—21no—
53C4×C401C2×D411yescharacteristic
54C4×C401C2×D411yescharacteristic
55Dic401—21no—
56Dic401—22no—
57Dic401—41no—
58C2×C401—21no—
59C2×C401—41no—
60C2×C401—81no—
61C2×C401#12011yescharacteristic
62D401—41no—
63C401#45411yescharacteristic, complemented, Sylow
64#454—4011nomaximal, Sylow
652−1+4—4011no—
66AGL(1,ℤ/8)—4011no—
67AGL(1,ℤ/8)D40111yescharacteristic, complemented
68#124—4011no—
69#104—4011no—
70#104—4011no—
71#101—4011no—
72#41—8021no—
73#41—8021no—
74#41—8022no—
75#41—4011no—
76#41C2×D40111yescharacteristic
77C2×Q8—8021no—
78C2×Q8—8021no—
79C2×Q8—4011no—
80C2×D4C2×D40111yescharacteristic
81SD16—21no—
82SD16—8021no—
83D8—21no—
84D8—8021no—
85M16—4011no—
86M16C2×D40111yescharacteristic
87C22⋊C4—8022no—
88C42—4011no—
89C23—21no—
90Q8—8022no—
91Q8—8021no—
92Q8—8021no—
93Q8—4011no—
94Q8C22⋊D40111yescharacteristic
95D4—21no—
96D4—21no—
97D4—21no—
98D4—8022no—
99D4—8021no—
100D4—4011no—
101D4C22⋊D40111yescharacteristic
102C2×C4—21no—
103C2×C4—8022no—
104C2×C4—8022no—
105C2×C4—8021no—
106C2×C4—8021no—
107C2×C4—4012no—
108C2×C4C22×D40111yescharacteristic
109C8—21no—
110C8—8021no—
111C22—21no—
112C22—42no—
113C22—41no—
114C22—8021no—
115C22D4×D40111yescharacteristic
116C4—21no—
117C4—8021no—
118C4—8022no—
119C4—16041no—
120C4D4×D40111yescharacteristic
121C4C2×C22⋊D40111yescharacteristic
122C2—21no—
123C2—41no—
124C2—81no—
125C2—16041no—
126C2#2716570511yescharacteristic
subgroupG/H
centerC2#27165705
commutator, cosocleC2×C4×C401C23
FrattiniC2×C4C22×D401
FittingAGL(1,ℤ/8)×C401C2
socleC2×C401#120
hypercenterAGL(1,ℤ/8)D401
hypocenterC401#454
LCSG ▷ C2×C4×C401 ▷ C2×C401 ▷ C401
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #27165784C2semidirect
2. #27165763C2semidirect
3. #27165724C2semidirect
4. #27165664C2semidirect
5. #27165663C2semidirect
6. #27165655C2semidirect
7. AGL(1,ℤ/8)×C401C2semidirect
63. C401#454semidirect
67. AGL(1,ℤ/8)D401semidirect

Maximal subgroups

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

subgroupindex
#271657842
#271657632
#271657242
#271656642
#271656632
#271656552
AGL(1,ℤ/8)×C4012
#454401