Finite Group Databasebeta

← #43247883

Subgroups — #43247883

Order 28352.

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

normal subgroups only

This group has 168 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#28381932C211yesmaximal, characteristic, complemented
2#28381912C211yesmaximal, characteristic, complemented
3#28381882C211yesmaximal, characteristic, complemented
4#28381813C211yesmaximal, characteristic, complemented
5#28381812C211yesmaximal, characteristic, complemented
6#28381802C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C443C211yesmaximal, characteristic, complemented
8#20296788—21no—
9#20296787—21no—
10#20296787C2211yescharacteristic
11C2×D1772—21no—
12C2×D1772C2211yescharacteristic
13C2×C22⋊D443—22no—
14D4×D443—22no—
15D4×D443—21no—
16#20296775—21no—
17#20296772—21no—
18#20296771C2211yescharacteristic, complemented
19C4×Dic443C2211yescharacteristic, complemented
20#41×C443C2211yescharacteristic
21C2×D4×C443C2211yescharacteristic, complemented
22SD16×C443—21no—
23D8×C443—21no—
24M16×C443C2211yescharacteristic, complemented
25C22×D443—22no—
26C22×D443D412yes—
27Dic886D411yescharacteristic, complemented
28D1772—22no—
29D1772—21no—
30D1772—21no—
31D1772D411yescharacteristic, complemented
32C22⋊D443—22no—
33C22⋊D443—21no—
34C22⋊D443—44no—
35C2×Dic443—21no—
36C4×D443—22no—
37C4×D443—21no—
38C443⋊C8—21no—
39C23×C443—21no—
40Q8×C443D411yescharacteristic, complemented
41D4×C443—21no—
42D4×C443—21no—
43D4×C443—21no—
44D4×C443D411yescharacteristic, complemented
45C2×C4×C443—21no—
46C2×C4×C443C2311yescharacteristic
47C8×C443—21no—
48C22×C443—21no—
49C22×C443—42no—
50C22×C443—41no—
51C22×C443C2×D411yescharacteristic
52C2×D443—22no—
53C2×D443—21no—
54C2×D443—42no—
55C2×D443—82no—
56C4×C443—21no—
57C4×C443C2×D411yescharacteristic
58C4×C443C2×D411yescharacteristic
59Dic443—22no—
60Dic443—21no—
61C2×C443—21no—
62C2×C443—41no—
63C2×C443—81no—
64C2×C443#12011yescharacteristic
65D443—42no—
66D443—41no—
67C443#45311yescharacteristic, complemented, Sylow
68#453—4431nomaximal, Sylow
69H(5,𝔽2)—4431no—
70AGL(1,ℤ/8)—4431no—
71AGL(1,ℤ/8)D44311yescharacteristic, complemented
72#127—4431no—
73#104—4431no—
74#104—4431no—
75#100—4431no—
76#41—8861no—
77#41—8861no—
78#41—4431no—
79#41C2×D44311yescharacteristic
80C2×D4—8861no—
81C2×D4—8862no—
82C2×D4—8861no—
83C2×D4—8862no—
84C2×D4—4431no—
85C2×D4C2×D44311yescharacteristic, complemented
86SD16—21no—
87SD16—8861no—
88D8—21no—
89D8—8861no—
90M16—4431no—
91M16C2×D44311yescharacteristic, complemented
92C42—4431no—
93C23—21no—
94C23—8862no—
95C23—4432no—
96Q8—4431no—
97Q8C22⋊D44311yescharacteristic, complemented
98D4—21no—
99D4—21no—
100D4—21no—
101D4—8862no—
102D4—8862no—
103D4—8861no—
104D4—8861no—
105D4—8861no—
106D4—4431no—
107D4—17724no—
108D4C22⋊D44311yescharacteristic, complemented
109C2×C4—21no—
110C2×C4—8862no—
111C2×C4—8861no—
112C2×C4—8861no—
113C2×C4C22×D44311yescharacteristic
114C8—21no—
115C8—8861no—
116C22—21no—
117C22—42no—
118C22—41no—
119C22—8862no—
120C22—8861no—
121C22—35442no—
122C22—17722no—
123C22D4×D44311yescharacteristic
124C4—21no—
125C4—8862no—
126C4—8861no—
127C4D4×D44311yescharacteristic
128C4C2×C22⋊D44311yescharacteristic
129C2—21no—
130C2—41no—
131C2—81no—
132C2—17721no—
133C2—17722no—
134C2#2838185411yescharacteristic
subgroupG/H
centerC2#28381854
commutator, cosocleC2×C4×C443C23
FrattiniC2×C4C22×D443
FittingAGL(1,ℤ/8)×C443C2
socleC2×C443#120
hypercenterAGL(1,ℤ/8)D443
hypocenterC443#453
LCSG ▷ C2×C4×C443 ▷ C2×C443 ▷ C443
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #28381932C2semidirect
2. #28381912C2semidirect
3. #28381882C2semidirect
4. #28381813C2semidirect
5. #28381812C2semidirect
6. #28381802C2semidirect
7. AGL(1,ℤ/8)×C443C2semidirect
18. #20296771C22semidirect
19. C4×Dic443C22semidirect
21. C2×D4×C443C22semidirect
24. M16×C443C22semidirect
27. Dic886D4semidirect
31. D1772D4semidirect
40. Q8×C443D4semidirect
44. D4×C443D4semidirect
67. C443#453semidirect
71. AGL(1,ℤ/8)D443semidirect
85. C2×D4C2×D443semidirect
91. M16C2×D443semidirect
97. Q8C22⋊D443semidirect
108. D4C22⋊D443semidirect

Maximal subgroups

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

subgroupindex
#283819322
#283819122
#283818822
#283818132
#283818122
#283818022
AGL(1,ℤ/8)×C4432
#453443