Finite Group Databasebeta

← #43247893

Subgroups — #43247893

Order 28352.

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

normal subgroups only

This group has 152 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
2#28381917C211yesmaximal, characteristic, complemented
3#28381875C211yesmaximal, characteristic, complemented
4#28381813C211yesmaximal, characteristic, complemented
5#28381812C211yesmaximal, characteristic, complemented
6#28381802C211yesmaximal, characteristic, complemented
7#137×C443C211yesmaximal, characteristic, complemented
8#20296788—21no—
9#20296787—21no—
10#20296787C2211yescharacteristic
11C2×D1772—21no—
12C2×D1772C2211yescharacteristic
13D4×D443—22no—
14D4×D443—21no—
15#20296777—21no—
16#20296774—21no—
17#20296771C2211yescharacteristic, complemented
18(C2×D443)⋊C4—22no—
19C4×Dic443C2211yescharacteristic, complemented
20#41×C443C2211yescharacteristic
21C2×Q8×C443C2211yescharacteristic, complemented
22Q16×C443—21no—
23SD16×C443—21no—
24M16×C443C2211yescharacteristic, complemented
25C22×D443—22no—
26C22×D443D412yes—
27Dic886D411yescharacteristic
28D1772—22no—
29D1772—21no—
30D1772—21no—
31D1772D411yescharacteristic
32C22⋊D443—22no—
33C22⋊D443—21no—
34C2×Dic443—21no—
35C4×D443—22no—
36C4×D443—21no—
37C443⋊C8—21no—
38Q8×C443—21no—
39Q8×C443—21no—
40Q8×C443D411yescharacteristic
41D4×C443—21no—
42D4×C443D411yescharacteristic
43C2×C4×C443—21no—
44C2×C4×C443—21no—
45C2×C4×C443C2311yescharacteristic
46C8×C443—21no—
47C22×C443—21no—
48C22×C443C2×D411yescharacteristic
49C2×D443—22no—
50C2×D443—21no—
51C2×D443—42no—
52C2×D443—82no—
53C4×C443—21no—
54C4×C443—41no—
55C4×C443C2×D411yescharacteristic
56C4×C443C2×D411yescharacteristic
57Dic443—21no—
58Dic443—41no—
59C2×C443—21no—
60C2×C443—41no—
61C2×C443#12011yescharacteristic
62D443—42no—
63D443—41no—
64C443#45511yescharacteristic, complemented, Sylow
65#455—4431nomaximal, Sylow
66H(5,𝔽2)—4431no—
67#137—4431no—
68#137D44311yescharacteristic, complemented
69#124—4431no—
70#104—4431no—
71#104—4431no—
72#100—4431no—
73#41—8861no—
74#41—8861no—
75#41—4431no—
76#41C2×D44311yescharacteristic
77C2×Q8C2×D44311yescharacteristic, complemented
78C2×D4—8861no—
79C2×D4—8862no—
80C2×D4—8861no—
81C2×D4—4431no—
82Q16—21no—
83Q16—8861no—
84SD16—21no—
85SD16—8861no—
86M16—4431no—
87M16C2×D44311yescharacteristic, complemented
88C22⋊C4—8862no—
89C42—4431no—
90C23—8862no—
91C23—4432no—
92Q8—21no—
93Q8—21no—
94Q8—4431no—
95Q8C22⋊D44311yescharacteristic
96D4—21no—
97D4—8862no—
98D4—8862no—
99D4—8861no—
100D4—8861no—
101D4—8861no—
102D4—4431no—
103D4C22⋊D44311yescharacteristic
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—8862no—
107C2×C4—8861no—
108C2×C4—8861no—
109C2×C4C22×D44311yescharacteristic
110C8—21no—
111C8—8861no—
112C22—21no—
113C22—8862no—
114C22—8861no—
115C22—35442no—
116C22—17722no—
117C22D4×D44311yescharacteristic
118C4—21no—
119C4—41no—
120C4—8861no—
121C4—17721no—
122C4D4×D44311yescharacteristic
123C4C2×C22⋊D44311yescharacteristic
124C2—21no—
125C2—41no—
126C2—17721no—
127C2—17722no—
128C2#2838185411yescharacteristic
subgroupG/H
centerC2#28381854
commutator, cosocleC2×C4×C443C23
FrattiniC2×C4C22×D443
Fitting#137×C443C2
socleC2×C443#120
prime radical#28381932C2
hypercenter#137D443
hypocenterC443#455
LCSG ▷ C2×C4×C443 ▷ C2×C443 ▷ C443
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
2. #28381917C2semidirect
3. #28381875C2semidirect
4. #28381813C2semidirect
5. #28381812C2semidirect
6. #28381802C2semidirect
7. #137×C443C2semidirect
17. #20296771C22semidirect
19. C4×Dic443C22semidirect
21. C2×Q8×C443C22semidirect
24. M16×C443C22semidirect
64. C443#455semidirect
68. #137D443semidirect
77. C2×Q8C2×D443semidirect
87. M16C2×D443semidirect

Maximal subgroups

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

subgroupindex
#283819322
#283819172
#283818752
#283818132
#283818122
#283818022
#137×C4432
#455443