Finite Group Databasebeta

← #42119230

Subgroups — #42119230

Order 27584.

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#28352236C211yesmaximal, characteristic, complemented
2#28352215C211yesmaximal, characteristic, complemented
3#28352176C211yesmaximal, characteristic, complemented
4#28352116C211yesmaximal, characteristic, complemented
5#28352115C211yesmaximal, characteristic, complemented
6#28352107C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C431C211yesmaximal, characteristic, complemented
8#20293800—21no—
9#20293800C2211yescharacteristic
10#20293799—22no—
11#20293799—21no—
12C2×Dic862—21no—
13C2×Dic862C2211yescharacteristic
14Q8×D431—21no—
15#20293788—21no—
16#20293785—21no—
17#20293784C2211yescharacteristic
18C22⋊Dic431—22no—
19C4×Dic431C2211yescharacteristic
20#41×C431C2211yescharacteristic
21C2×D4×C431C2211yescharacteristic
22SD16×C431—21no—
23D8×C431—21no—
24M16×C431C2211yescharacteristic
25Dic862—22no—
26Dic862—21no—
27Dic862—21no—
28Dic862D411yescharacteristic
29D1724D411yescharacteristic
30C22⋊D431—22no—
31C22⋊D431—21no—
32C2×Dic431—22no—
33C2×Dic431—21no—
34C2×Dic431D412yes—
35C4×D431—22no—
36C4×D431—21no—
37C431⋊C8—21no—
38C23×C431—21no—
39Q8×C431D411yescharacteristic
40D4×C431—21no—
41D4×C431—21no—
42D4×C431—21no—
43D4×C431D411yescharacteristic
44C2×C4×C431—21no—
45C2×C4×C431C2311yescharacteristic
46C8×C431—21no—
47C22×C431—21no—
48C22×C431—42no—
49C22×C431—41no—
50C22×C431C2×D411yescharacteristic
51C2×D431—21no—
52C4×C431—21no—
53C4×C431C2×D411yescharacteristic
54C4×C431C2×D411yescharacteristic
55Dic431—21no—
56Dic431—22no—
57Dic431—41no—
58C2×C431—21no—
59C2×C431—41no—
60C2×C431—81no—
61C2×C431#12011yescharacteristic
62D431—41no—
63C431#45411yescharacteristic, complemented, Sylow
64#454—4311nomaximal, Sylow
652−1+4—4311no—
66AGL(1,ℤ/8)—4311no—
67AGL(1,ℤ/8)D43111yescharacteristic, complemented
68#124—4311no—
69#104—4311no—
70#104—4311no—
71#101—4311no—
72#41—8621no—
73#41—8621no—
74#41—8622no—
75#41—4311no—
76#41C2×D43111yescharacteristic
77C2×Q8—8621no—
78C2×Q8—8621no—
79C2×Q8—4311no—
80C2×D4C2×D43111yescharacteristic
81SD16—21no—
82SD16—8621no—
83D8—21no—
84D8—8621no—
85M16—4311no—
86M16C2×D43111yescharacteristic
87C22⋊C4—8622no—
88C42—4311no—
89C23—21no—
90Q8—8622no—
91Q8—8621no—
92Q8—8621no—
93Q8—4311no—
94Q8C22⋊D43111yescharacteristic
95D4—21no—
96D4—21no—
97D4—21no—
98D4—8622no—
99D4—8621no—
100D4—4311no—
101D4C22⋊D43111yescharacteristic
102C2×C4—21no—
103C2×C4—8622no—
104C2×C4—8622no—
105C2×C4—8621no—
106C2×C4—8621no—
107C2×C4—4312no—
108C2×C4C22×D43111yescharacteristic
109C8—21no—
110C8—8621no—
111C22—21no—
112C22—42no—
113C22—41no—
114C22—8621no—
115C22D4×D43111yescharacteristic
116C4—21no—
117C4—8621no—
118C4—8622no—
119C4—17241no—
120C4D4×D43111yescharacteristic
121C4C2×C22⋊D43111yescharacteristic
122C2—21no—
123C2—41no—
124C2—81no—
125C2—17241no—
126C2#2835215711yescharacteristic
subgroupG/H
centerC2#28352157
commutator, cosocleC2×C4×C431C23
FrattiniC2×C4C22×D431
FittingAGL(1,ℤ/8)×C431C2
socleC2×C431#120
hypercenterAGL(1,ℤ/8)D431
hypocenterC431#454
LCSG ▷ C2×C4×C431 ▷ C2×C431 ▷ C431
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #28352236C2semidirect
2. #28352215C2semidirect
3. #28352176C2semidirect
4. #28352116C2semidirect
5. #28352115C2semidirect
6. #28352107C2semidirect
7. AGL(1,ℤ/8)×C431C2semidirect
63. C431#454semidirect
67. AGL(1,ℤ/8)D431semidirect

Maximal subgroups

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

subgroupindex
#283522362
#283522152
#283521762
#283521162
#283521152
#283521072
AGL(1,ℤ/8)×C4312
#454431