Finite Group Databasebeta

← #32973850

Subgroups — #32973850

Order 18688.

156 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 27 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#22608094C211yesmaximal, characteristic
2#22608094C211yesmaximal, characteristic
3C73×#1715C211yesmaximal, characteristic
4#17988380—21no—
5#17988380—21no—
6#498×C73C411yescharacteristic, complemented
7#493×C73C2211yescharacteristic
8#492×C73—21no—
9#486×C73—21no—
10#322×C73C411yescharacteristic, complemented
11#14556506—41no—
12#14556506—41no—
13C2×SD16×C73—42no—
14C2×D8×C73—41no—
15C4⋊Q8×C73—21no—
16#127×C73D411yescharacteristic
17#127×C73D411yescharacteristic
18#106×C73—41no—
19#102×C73—42no—
20C4×C8×C73—21no—
21C4×C8×C73C2×C411yescharacteristic
22C22⋊Dic73—81no—
23C22⋊Dic73—81no—
24C2×Q8×C73—41no—
25C2×D4×C73—21no—
26C2×D4×C73—21no—
27C2×D4×C73—41no—
28C2×D4×C73—41no—
29SD16×C73—84no—
30D8×C73—82no—
31C2×C8×C73—21no—
32C2×C8×C73—22no—
33C4⋊C4×C73—41no—
34C4⋊C4×C73—41no—
35C42×C73C22⋊C411yescharacteristic
36C23×C73—41no—
37C23×C73—41no—
38Q8×C73—82no—
39D4×C73—81no—
40D4×C73—81no—
41D4×C73—82no—
42D4×C73—82no—
43C2×C4×C73—21no—
44C2×C4×C73—81no—
45C2×C4×C73#9911yescharacteristic
46C2×Dic73—161no—
47C2×Dic73—161no—
48C8×C73—22no—
49C8×C73—42no—
50C22×C73—81no—
51C22×C73—81no—
52C22×C73—161no—
53C22×C73—161no—
54C22×C73#35311yescharacteristic
55C4×C73—22no—
56C4×C73—21no—
57C4×C73—161no—
58Dic73—321no—
59Dic73—321no—
60#7533—731nomaximal, Sylow
61C2×C73—21no—
62C2×C73—161no—
63C2×C73—161no—
64C2×C73#140911yescharacteristic
65#1715D7311yescharacteristic
66#1408—731no—
67#1408—731no—
68C73#753311yescharacteristic, complemented, Sylow
69#498Dic7311yescharacteristic, complemented
70#493C2×D7311yescharacteristic
71#492—21no—
72#486—21no—
73#353—1461no—
74#353—1461no—
75#322Dic7311yescharacteristic, complemented
76C2×SD16—42no—
77C2×D8—41no—
78C4⋊Q8—21no—
79#127C22⋊D7311yescharacteristic
80#127C22⋊D7311yescharacteristic
81#106—41no—
82#102—42no—
83#99—2921no—
84#99—2921no—
85C4×C8—21no—
86C4×C8C2×Dic7311yescharacteristic
87C2×Q8—41no—
88C2×D4—21no—
89C2×D4—21no—
90C2×D4—41no—
91C2×D4—41no—
92SD16—84no—
93D8—82no—
94C2×C8—21no—
95C2×C8—22no—
96C4⋊C4—41no—
97C4⋊C4—41no—
98C22⋊C4—5841no—
99C22⋊C4—5841no—
100C42C22⋊Dic7311yescharacteristic
101C23—41no—
102C23—41no—
103Q8—82no—
104D4—81no—
105D4—81no—
106D4—82no—
107D4—82no—
108C2×C4—21no—
109C2×C4—81no—
110C2×C4—11681no—
111C2×C4—11681no—
112C2×C4#1455650611yescharacteristic
113C8—22no—
114C8—42no—
115C22—81no—
116C22—81no—
117C22—161no—
118C22—161no—
119C22#1798838011yescharacteristic
120C4—22no—
121C4—21no—
122C4—161no—
123C4—23361no—
124C4—23361no—
125C2—21no—
126C2—161no—
127C2—161no—
128C2#2260809611yescharacteristic
subgroupG/H
centerC2#22608096
commutatorC4×C8×C73C2×C4
Frattini#493C2×D73
FittingC73×#1715C2
socleC2×C73#1409
prime radical, cosocle#493×C73C22
hypercenter#1715D73
hypocenterC73#7533
LCSG ▷ C4×C8×C73 ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #493 ◁ #1715

Complements

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

NH ≅ G/Ntype
6. #498×C73C4semidirect
10. #322×C73C4semidirect
68. C73#7533semidirect
69. #498Dic73semidirect
75. #322Dic73semidirect

Maximal subgroups

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

subgroupindex
#226080942
C73×#17152
#753373