Finite Group Databasebeta

← #34176136

Subgroups — #34176136

Order 20224.

156 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 25 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#23763026C211yesmaximal, characteristic
2#23761563C211yesmaximal, characteristic
3C79×#1408C211yesmaximal, characteristic
4#19098961C411yescharacteristic, complemented
5#19098935—21no—
6#19098909—21no—
7#19098356—21no—
8#19098284C411yescharacteristic, complemented
9#493×C79C2211yescharacteristic
10#353×C79—21no—
11C2×#11929612—42no—
12#14579161—21no—
13#14579093—41no—
14#14579082—42no—
15#14579076—41no—
16C4×C79⋊C8—21no—
17C2×D8×C79—41no—
18#127×C79D411yescharacteristic
19#127×C79D411yescharacteristic
20#99×C79—41no—
21C4×C8×C79C2×C411yescharacteristic
22C2×Dic158—41no—
23#11929612—84no—
24C2×C79⋊C8—22no—
25C4⋊Dic79—41no—
26C4⋊Dic79—41no—
27C22⋊Dic79—81no—
28C2×D4×C79—21no—
29C2×D4×C79—21no—
30C2×D4×C79—41no—
31C2×D4×C79—41no—
32D8×C79—82no—
33C2×C8×C79—21no—
34C22⋊C4×C79—81no—
35C42×C79C22⋊C411yescharacteristic
36C23×C79—41no—
37C23×C79—41no—
38D4×C79—81no—
39D4×C79—81no—
40D4×C79—82no—
41D4×C79—82no—
42C2×C4×C79—21no—
43C2×C4×C79—161no—
44C2×C4×C79#9911yescharacteristic
45C2×Dic79—81no—
46C2×Dic79—161no—
47Dic158—82no—
48C8×C79—22no—
49C79⋊C8—42no—
50C22×C79—81no—
51C22×C79—81no—
52C22×C79—161no—
53C22×C79—161no—
54C22×C79#35311yescharacteristic
55C4×C79—22no—
56C4×C79—21no—
57C4×C79—321no—
58Dic79—161no—
59Dic79—321no—
60#7533—791nomaximal, Sylow
61C2×C79—21no—
62C2×C79—161no—
63C2×C79—161no—
64C2×C79#140911yescharacteristic
65#1715—791no—
66#1408—791no—
67#1408D7911yescharacteristic
68C79#753311yescharacteristic, complemented, Sylow
69#498—791no—
70#493C2×D7911yescharacteristic
71#492—1581no—
72#486—1581no—
73#353—21no—
74#353—1581no—
75#322—791no—
76C2×SD16—3162no—
77C2×D8—41no—
78C4⋊Q8—1581no—
79#127D31611yescharacteristic
80#127C22⋊D7911yescharacteristic
81#106—3161no—
82#102—3162no—
83#99—41no—
84#99—3161no—
85C4×C8—1581no—
86C4×C8C4×D7911yescharacteristic
87C2×Q8—3161no—
88C2×D4—21no—
89C2×D4—21no—
90C2×D4—41no—
91C2×D4—41no—
92SD16—6324no—
93D8—82no—
94C2×C8—21no—
95C2×C8—1582no—
96C4⋊C4—3161no—
97C4⋊C4—3161no—
98C22⋊C4—81no—
99C22⋊C4—6321no—
100C42(C2×D79)⋊C411yescharacteristic
101C23—41no—
102C23—41no—
103Q8—6322no—
104D4—81no—
105D4—81no—
106D4—82no—
107D4—82no—
108C2×C4—21no—
109C2×C4—161no—
110C2×C4—6321no—
111C2×C4—12641no—
112C2×C4#1457907511yescharacteristic
113C8—22no—
114C8—3162no—
115C22—81no—
116C22—81no—
117C22—161no—
118C22—161no—
119C22#1909835511yescharacteristic
120C4—22no—
121C4—21no—
122C4—321no—
123C4—25281no—
124C4—12641no—
125C2—21no—
126C2—161no—
127C2—161no—
128C2#2376156411yescharacteristic
subgroupG/H
centerC2#23761564
commutatorC4×C8×C79C2×C4
Frattini#493C2×D79
FittingC79×#1408C2
socleC2×C79#1409
prime radical, cosocle#493×C79C22
hypercenter#1408D79
hypocenterC79#7533
LCSG ▷ C4×C8×C79 ▷ C42×C79 ▷ C2×C4×C79 ▷ C22×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #493 ◁ #1408

Complements

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

NH ≅ G/Ntype
4. #19098961C4semidirect
8. #19098284C4semidirect
68. C79#7533semidirect

Maximal subgroups

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

subgroupindex
#237630262
#237615632
C79×#14082
#753379