Finite Group Databasebeta

← #43247888

Subgroups — #43247888

Order 28352.

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#28381933C211yesmaximal, characteristic, complemented
2#28381912C211yesmaximal, characteristic, complemented
3#28381873C211yesmaximal, characteristic, complemented
4#28381813C211yesmaximal, characteristic, complemented
5#28381812C211yesmaximal, characteristic, complemented
6#28381804C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C443C211yesmaximal, characteristic, complemented
8#20296787—21no—
9#20296787C2211yescharacteristic
10#20296786—22no—
11#20296786—21no—
12C2×Dic886—21no—
13C2×Dic886C2211yescharacteristic
14Q8×D443—21no—
15#20296775—21no—
16#20296772—21no—
17#20296771C2211yescharacteristic
18C22⋊Dic443—22no—
19C4×Dic443C2211yescharacteristic
20#41×C443C2211yescharacteristic
21C2×D4×C443C2211yescharacteristic
22SD16×C443—21no—
23D8×C443—21no—
24M16×C443C2211yescharacteristic
25Dic886—22no—
26Dic886—21no—
27Dic886—21no—
28Dic886D411yescharacteristic
29D1772D411yescharacteristic
30C22⋊D443—22no—
31C22⋊D443—21no—
32C2×Dic443—22no—
33C2×Dic443—21no—
34C2×Dic443D412yes—
35C4×D443—22no—
36C4×D443—21no—
37C443⋊C8—21no—
38C23×C443—21no—
39Q8×C443D411yescharacteristic
40D4×C443—21no—
41D4×C443—21no—
42D4×C443—21no—
43D4×C443D411yescharacteristic
44C2×C4×C443—21no—
45C2×C4×C443C2311yescharacteristic
46C8×C443—21no—
47C22×C443—21no—
48C22×C443—42no—
49C22×C443—41no—
50C22×C443C2×D411yescharacteristic
51C2×D443—21no—
52C4×C443—21no—
53C4×C443C2×D411yescharacteristic
54C4×C443C2×D411yescharacteristic
55Dic443—21no—
56Dic443—22no—
57Dic443—41no—
58C2×C443—21no—
59C2×C443—41no—
60C2×C443—81no—
61C2×C443#12011yescharacteristic
62D443—41no—
63C443#45411yescharacteristic, complemented, Sylow
64#454—4431nomaximal, Sylow
652−1+4—4431no—
66AGL(1,ℤ/8)—4431no—
67AGL(1,ℤ/8)D44311yescharacteristic, complemented
68#124—4431no—
69#104—4431no—
70#104—4431no—
71#101—4431no—
72#41—8861no—
73#41—8861no—
74#41—8862no—
75#41—4431no—
76#41C2×D44311yescharacteristic
77C2×Q8—8861no—
78C2×Q8—8861no—
79C2×Q8—4431no—
80C2×D4C2×D44311yescharacteristic
81SD16—21no—
82SD16—8861no—
83D8—21no—
84D8—8861no—
85M16—4431no—
86M16C2×D44311yescharacteristic
87C22⋊C4—8862no—
88C42—4431no—
89C23—21no—
90Q8—8862no—
91Q8—8861no—
92Q8—8861no—
93Q8—4431no—
94Q8C22⋊D44311yescharacteristic
95D4—21no—
96D4—21no—
97D4—21no—
98D4—8862no—
99D4—8861no—
100D4—4431no—
101D4C22⋊D44311yescharacteristic
102C2×C4—21no—
103C2×C4—8862no—
104C2×C4—8862no—
105C2×C4—8861no—
106C2×C4—8861no—
107C2×C4—4432no—
108C2×C4C22×D44311yescharacteristic
109C8—21no—
110C8—8861no—
111C22—21no—
112C22—42no—
113C22—41no—
114C22—8861no—
115C22D4×D44311yescharacteristic
116C4—21no—
117C4—8861no—
118C4—8862no—
119C4—17721no—
120C4D4×D44311yescharacteristic
121C4C2×C22⋊D44311yescharacteristic
122C2—21no—
123C2—41no—
124C2—81no—
125C2—17721no—
126C2#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#454
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. #28381933C2semidirect
2. #28381912C2semidirect
3. #28381873C2semidirect
4. #28381813C2semidirect
5. #28381812C2semidirect
6. #28381804C2semidirect
7. AGL(1,ℤ/8)×C443C2semidirect
63. C443#454semidirect
67. AGL(1,ℤ/8)D443semidirect

Maximal subgroups

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

subgroupindex
#283819332
#283819122
#283818732
#283818132
#283818122
#283818042
AGL(1,ℤ/8)×C4432
#454443