Finite Group Databasebeta

← #43247898

Subgroups — #43247898

Order 28352.

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

normal subgroups only

This group has 142 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
2#28381917C211yesmaximal, characteristic, complemented
3#28381884C211yesmaximal, characteristic, complemented
4#28381813C211yesmaximal, characteristic, complemented
5#28381812C211yesmaximal, characteristic, complemented
6#28381804C211yesmaximal, characteristic, complemented
7#137×C443C211yesmaximal, characteristic, complemented
8#20296787—21no—
9#20296787C2211yescharacteristic
10#20296786—22no—
11#20296786—21no—
12C2×Dic886—21no—
13C2×Dic886C2211yescharacteristic
14Q8×D443—21no—
15#20296777—21no—
16#20296774—21no—
17#20296771C2211yescharacteristic
18Dic443⋊C4—22no—
19C4×Dic443C2211yescharacteristic
20#41×C443C2211yescharacteristic
21C2×Q8×C443C2211yescharacteristic
22Q16×C443—21no—
23SD16×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—
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—21no—
50C4×C443—21no—
51C4×C443—41no—
52C4×C443C2×D411yescharacteristic
53C4×C443C2×D411yescharacteristic
54Dic443—22no—
55Dic443—21no—
56Dic443—22no—
57C2×C443—21no—
58C2×C443—41no—
59C2×C443#12011yescharacteristic
60D443—41no—
61C443#45611yescharacteristic, complemented, Sylow
62#456—4431nomaximal, Sylow
632−1+4—4431no—
64#137—4431no—
65#137D44311yescharacteristic, complemented
66C4⋊Q8—4431no—
67#104—4431no—
68#104—4431no—
69#101—4431no—
70#41—8861no—
71#41—8861no—
72#41—8862no—
73#41—4431no—
74#41C2×D44311yescharacteristic
75C2×Q8—8861no—
76C2×Q8—8861no—
77C2×Q8—4431no—
78C2×Q8C2×D44311yescharacteristic
79Q16—21no—
80Q16—8861no—
81SD16—21no—
82SD16—8861no—
83M16—4431no—
84M16C2×D44311yescharacteristic
85C4⋊C4—8862no—
86C42—4431no—
87Q8—21no—
88Q8—21no—
89Q8—8862no—
90Q8—8861no—
91Q8—8861no—
92Q8—4431no—
93Q8C22⋊D44311yescharacteristic
94D4—21no—
95D4—8862no—
96D4—8861no—
97D4—4431no—
98D4C22⋊D44311yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—8862no—
102C2×C4—8862no—
103C2×C4—8861no—
104C2×C4—8861no—
105C2×C4—4432no—
106C2×C4C22×D44311yescharacteristic
107C8—21no—
108C8—8861no—
109C22—21no—
110C22—8861no—
111C22D4×D44311yescharacteristic
112C4—21no—
113C4—41no—
114C4—8862no—
115C4—8861no—
116C4—8862no—
117C4D4×D44311yescharacteristic
118C4C2×C22⋊D44311yescharacteristic
119C2—21no—
120C2—41no—
121C2—17721no—
122C2#2838185411yescharacteristic
subgroupG/H
centerC2#28381854
commutator, cosocleC2×C4×C443C23
FrattiniC2×C4C22×D443
Fitting#137×C443C2
socleC2×C443#120
prime radical#28381933C2
hypercenter#137D443
hypocenterC443#456
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. #28381884C2semidirect
4. #28381813C2semidirect
5. #28381812C2semidirect
6. #28381804C2semidirect
7. #137×C443C2semidirect
61. C443#456semidirect
65. #137D443semidirect

Maximal subgroups

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

subgroupindex
#283819332
#283819172
#283818842
#283818132
#283818122
#283818042
#137×C4432
#456443