Finite Group Databasebeta

← #44543272

Subgroups — #44543272

Order 31936.

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#30630398C211yesmaximal, characteristic, complemented
2#30630379C211yesmaximal, characteristic, complemented
3#30630376C211yesmaximal, characteristic, complemented
4#30630339C211yesmaximal, characteristic, complemented
5#30630279C211yesmaximal, characteristic, complemented
6#30630269C211yesmaximal, characteristic, complemented
7#104×C499C211yesmaximal, characteristic, complemented
8#22547811—21no—
9#22547811C2211yescharacteristic
10#22547810—21no—
11#22547810—22no—
12C2×Dic998—21no—
13C2×Dic998C2211yescharacteristic
14Q8×D499—21no—
15C2×D1996C2211yescharacteristic
16#22547800—21no—
17#22547798—21no—
18D3992—21no—
19#22547796—21no—
20#22547795C2211yescharacteristic
21(C2×D499)⋊C4—22no—
22#41×C499C2211yescharacteristic
23M16×C499C2211yescharacteristic
24C42×C499C2211yescharacteristic
25C22×D499—21no—
26Dic998—22no—
27Dic998—21no—
28Dic998—21no—
29Dic998D411yescharacteristic
30D1996—21no—
31D1996—21no—
32D1996D411yescharacteristic
33C22⋊D499—22no—
34C22⋊D499—21no—
35C2×Dic499—22no—
36C2×Dic499D412yes—
37C4×D499—22no—
38C4×D499—21no—
39C499⋊C8—21no—
40Q8×C499D411yescharacteristic
41D4×C499—21no—
42D4×C499D411yescharacteristic
43C2×C4×C499—21no—
44C2×C4×C499—21no—
45C2×C4×C499C2311yescharacteristic
46C8×C499—21no—
47C22×C499—21no—
48C22×C499C2×D411yescharacteristic
49C2×D499—21no—
50C2×D499—42no—
51C2×D499—41no—
52C4×C499—21no—
53C4×C499—41no—
54C4×C499C2×D411yescharacteristic
55C4×C499C2×D411yescharacteristic
56Dic499—21no—
57Dic499—22no—
58C2×C499—21no—
59C2×C499—41no—
60C2×C499#12011yescharacteristic
61D499—41no—
62D499—81no—
63C499#45411yescharacteristic, complemented, Sylow
64#454—4991nomaximal, Sylow
652−1+4—4991no—
66AGL(1,ℤ/8)—4991no—
67AGL(1,ℤ/8)—4991no—
68#124—4991no—
69#104—4991no—
70#104D49911yescharacteristic, complemented
71#101—4991no—
72#41—9981no—
73#41—9981no—
74#41—9982no—
75#41—4991no—
76#41C2×D49911yescharacteristic
77C2×Q8—9981no—
78C2×Q8—9981no—
79C2×Q8—4991no—
80C2×D4—4991no—
81SD16—9981no—
82SD16—9981no—
83D8—9981no—
84D8—9981no—
85M16—4991no—
86M16C2×D49911yescharacteristic
87C22⋊C4—9982no—
88C42C2×D49911yescharacteristic
89C23—9981no—
90Q8—9982no—
91Q8—9981no—
92Q8—9981no—
93Q8—4991no—
94Q8D199611yescharacteristic
95D4—21no—
96D4—9982no—
97D4—9981no—
98D4—9981no—
99D4—9981no—
100D4—4991no—
101D4D199611yescharacteristic
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—9982no—
105C2×C4—9982no—
106C2×C4—9981no—
107C2×C4—4992no—
108C2×C4C22×D49911yescharacteristic
109C8—21no—
110C8—9981no—
111C22—21no—
112C22—19962no—
113C22—19961no—
114C22—9981no—
115C22D4×D49911yescharacteristic
116C4—21no—
117C4—41no—
118C4—9981no—
119C4—9982no—
120C4D4×D49911yescharacteristic
121C4C2×D199611yescharacteristic
122C2—21no—
123C2—41no—
124C2—39921no—
125C2—19961no—
126C2#3063032111yescharacteristic
subgroupG/H
centerC2#30630321
commutator, cosocleC2×C4×C499C23
FrattiniC2×C4C22×D499
Fitting#104×C499C2
socleC2×C499#120
hypercenter#104D499
hypocenterC499#454
LCSG ▷ C2×C4×C499 ▷ C2×C499 ▷ C499
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
1. #30630398C2semidirect
2. #30630379C2semidirect
3. #30630376C2semidirect
4. #30630339C2semidirect
5. #30630279C2semidirect
6. #30630269C2semidirect
7. #104×C499C2semidirect
63. C499#454semidirect
70. #104D499semidirect

Maximal subgroups

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

subgroupindex
#306303982
#306303792
#306303762
#306303392
#306302792
#306302692
#104×C4992
#454499