Finite Group Databasebeta

← #43272191

Subgroups — #43272191

Order 28736.

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#28385387C211yesmaximal, characteristic
2#28385373C211yesmaximal, characteristic, complemented
3#28385370C211yesmaximal, characteristic, complemented
4#28385340C211yesmaximal, characteristic, complemented
5#28385268C211yesmaximal, characteristic, complemented
6#28385258C211yesmaximal, characteristic, complemented
7#104×C449C211yesmaximal, characteristic, complemented
8#20297736—21no—
9#20297736C2211yescharacteristic
10#20297735—21no—
11#20297735—22no—
12C2×Dic898—21no—
13C2×Dic898C2211yescharacteristic
14C2×Dic898C2211yescharacteristic
15Q8×D449—21no—
16Dic1796—21no—
17#20297726—21no—
18#20297725—21no—
19#20297724—21no—
20#20297720C2211yescharacteristic
21C4⋊Dic449—22no—
22#41×C449C2211yescharacteristic
23M16×C449C2211yescharacteristic
24C42×C449C2211yescharacteristic
25Dic898—22no—
26Dic898—21no—
27Dic898—21no—
28Dic898—21no—
29Dic898—21no—
30Dic898D411yescharacteristic
31D1796D411yescharacteristic
32C22⋊D449—22no—
33C22⋊D449—21no—
34C2×Dic449—22no—
35C2×Dic449—21no—
36C2×Dic449D412yes—
37C4×D449—22no—
38C4×D449—21no—
39#16813311—21no—
40Q8×C449D411yescharacteristic
41D4×C449—21no—
42D4×C449D411yescharacteristic
43C2×C4×C449—21no—
44C2×C4×C449—21no—
45C2×C4×C449C2311yescharacteristic
46C8×C449—21no—
47C22×C449—21no—
48C22×C449C2×D411yescharacteristic
49C2×D449—21no—
50C4×C449—22no—
51C4×C449—21no—
52C4×C449C2×D411yescharacteristic
53C4×C449C2×D411yescharacteristic
54Dic449—21no—
55Dic449—22no—
56Dic449—41no—
57C2×C449—21no—
58C2×C449—41no—
59C2×C449#12011yescharacteristic
60D449—41no—
61C449#45611yescharacteristic, complemented, Sylow
62#456—4491nomaximal, Sylow
632−1+4—4491no—
64#137—4491no—
65#137—4491no—
66C4⋊Q8—4491no—
67#104—4491no—
68#104D44911yescharacteristic, complemented
69#101—4491no—
70#41—8981no—
71#41—8981no—
72#41—8982no—
73#41—4491no—
74#41C2×D44911yescharacteristic
75C2×Q8—8981no—
76C2×Q8—8981no—
77C2×Q8—4491no—
78C2×Q8—4491no—
79Q16—8981no—
80Q16—8981no—
81SD16—8981no—
82SD16—8981no—
83M16—4491no—
84M16C2×D44911yescharacteristic
85C4⋊C4—8982no—
86C42C2×D44911yescharacteristic
87Q8—8982no—
88Q8—8981no—
89Q8—8981no—
90Q8—8981no—
91Q8—8981no—
92Q8—4491no—
93Q8D179611yescharacteristic
94D4—21no—
95D4—8982no—
96D4—8981no—
97D4—4491no—
98D4D179611yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—8982no—
102C2×C4—8981no—
103C2×C4—8982no—
104C2×C4—8981no—
105C2×C4—4492no—
106C2×C4C22×D44911yescharacteristic
107C8—21no—
108C8—8981no—
109C22—21no—
110C22—8981no—
111C22D4×D44911yescharacteristic
112C4—22no—
113C4—21no—
114C4—17961no—
115C4—8981no—
116C4—8982no—
117C4D4×D44911yescharacteristic
118C4C2×D179611yescharacteristic
119C2—21no—
120C2—41no—
121C2—17961no—
122C2#2838531011yescharacteristic
subgroupG/H
centerC2#28385310
commutator, cosocleC2×C4×C449C23
FrattiniC2×C4C22×D449
Fitting#104×C449C2
socleC2×C449#120
prime radical#28385387C2
hypercenter#104D449
hypocenterC449#456
LCSG ▷ C2×C4×C449 ▷ C2×C449 ▷ C449
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #28385373C2semidirect
3. #28385370C2semidirect
4. #28385340C2semidirect
5. #28385268C2semidirect
6. #28385258C2semidirect
7. #104×C449C2semidirect
61. C449#456semidirect
68. #104D449semidirect

Maximal subgroups

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

subgroupindex
#283853872
#283853732
#283853702
#283853402
#283852682
#283852582
#104×C4492
#456449