Finite Group Databasebeta

← #43272178

Subgroups — #43272178

Order 28736.

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#28385387C211yesmaximal, characteristic, complemented
2#28385366C211yesmaximal, characteristic, complemented
3#28385327C211yesmaximal, characteristic, complemented
4#28385267C211yesmaximal, characteristic, complemented
5#28385266C211yesmaximal, characteristic, complemented
6#28385258C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C449C211yesmaximal, characteristic, complemented
8#20297736—21no—
9#20297736C2211yescharacteristic
10#20297735—21no—
11#20297735—22no—
12C2×Dic898—21no—
13C2×Dic898C2211yescharacteristic
14Q8×D449—21no—
15#20297724—21no—
16#20297721—21no—
17#20297720C2211yescharacteristic
18C22⋊Dic449—22no—
19C4×Dic449C2211yescharacteristic
20#41×C449C2211yescharacteristic
21C2×D4×C449C2211yescharacteristic
22SD16×C449—21no—
23D8×C449—21no—
24M16×C449C2211yescharacteristic
25Dic898—22no—
26Dic898—21no—
27Dic898—21no—
28Dic898D411yescharacteristic
29D1796D411yescharacteristic
30C22⋊D449—22no—
31C22⋊D449—21no—
32C2×Dic449—22no—
33C2×Dic449—21no—
34C2×Dic449D412yes—
35C4×D449—22no—
36C4×D449—21no—
37#16813311—21no—
38C23×C449—21no—
39Q8×C449D411yescharacteristic
40D4×C449—21no—
41D4×C449—21no—
42D4×C449—21no—
43D4×C449D411yescharacteristic
44C2×C4×C449—21no—
45C2×C4×C449C2311yescharacteristic
46C8×C449—21no—
47C22×C449—21no—
48C22×C449—42no—
49C22×C449—41no—
50C22×C449C2×D411yescharacteristic
51C2×D449—21no—
52C4×C449—21no—
53C4×C449C2×D411yescharacteristic
54C4×C449C2×D411yescharacteristic
55Dic449—21no—
56Dic449—22no—
57Dic449—41no—
58C2×C449—21no—
59C2×C449—41no—
60C2×C449—81no—
61C2×C449#12011yescharacteristic
62D449—41no—
63C449#45411yescharacteristic, complemented, Sylow
64#454—4491nomaximal, Sylow
652−1+4—4491no—
66AGL(1,ℤ/8)—4491no—
67AGL(1,ℤ/8)D44911yescharacteristic, complemented
68#124—4491no—
69#104—4491no—
70#104—4491no—
71#101—4491no—
72#41—8981no—
73#41—8981no—
74#41—8982no—
75#41—4491no—
76#41C2×D44911yescharacteristic
77C2×Q8—8981no—
78C2×Q8—8981no—
79C2×Q8—4491no—
80C2×D4C2×D44911yescharacteristic
81SD16—21no—
82SD16—8981no—
83D8—21no—
84D8—8981no—
85M16—4491no—
86M16C2×D44911yescharacteristic
87C22⋊C4—8982no—
88C42—4491no—
89C23—21no—
90Q8—8982no—
91Q8—8981no—
92Q8—8981no—
93Q8—4491no—
94Q8C22⋊D44911yescharacteristic
95D4—21no—
96D4—21no—
97D4—21no—
98D4—8982no—
99D4—8981no—
100D4—4491no—
101D4C22⋊D44911yescharacteristic
102C2×C4—21no—
103C2×C4—8982no—
104C2×C4—8981no—
105C2×C4—8982no—
106C2×C4—8981no—
107C2×C4—4492no—
108C2×C4C22×D44911yescharacteristic
109C8—21no—
110C8—8981no—
111C22—21no—
112C22—42no—
113C22—41no—
114C22—8981no—
115C22D4×D44911yescharacteristic
116C4—21no—
117C4—17961no—
118C4—8981no—
119C4—8982no—
120C4D4×D44911yescharacteristic
121C4C2×C22⋊D44911yescharacteristic
122C2—21no—
123C2—41no—
124C2—17961no—
125C2—81no—
126C2#2838530811yescharacteristic
subgroupG/H
centerC2#28385308
commutator, cosocleC2×C4×C449C23
FrattiniC2×C4C22×D449
FittingAGL(1,ℤ/8)×C449C2
socleC2×C449#120
hypercenterAGL(1,ℤ/8)D449
hypocenterC449#454
LCSG ▷ C2×C4×C449 ▷ C2×C449 ▷ C449
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #28385387C2semidirect
2. #28385366C2semidirect
3. #28385327C2semidirect
4. #28385267C2semidirect
5. #28385266C2semidirect
6. #28385258C2semidirect
7. AGL(1,ℤ/8)×C449C2semidirect
63. C449#454semidirect
67. AGL(1,ℤ/8)D449semidirect

Maximal subgroups

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

subgroupindex
#283853872
#283853662
#283853272
#283852672
#283852662
#283852582
AGL(1,ℤ/8)×C4492
#454449