Finite Group Databasebeta

← #32973849

Subgroups — #32973849

Order 18688.

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#22609557C211yesmaximal, characteristic
2#22608094C211yesmaximal, characteristic
3C73×#1408C211yesmaximal, characteristic
4#17988985C411yescharacteristic, complemented
5#17988959—21no—
6#17988933—21no—
7#17988380—21no—
8#17988308C411yescharacteristic, complemented
9#493×C73C2211yescharacteristic
10#353×C73—21no—
11C2×#11924016—42no—
12#14556591—21no—
13#14556523—41no—
14#14556512—42no—
15#14556506—41no—
16C4×#10596831—21no—
17C2×D8×C73—41no—
18#127×C73D411yescharacteristic
19#127×C73D411yescharacteristic
20#99×C73—41no—
21C4×C8×C73C2×C411yescharacteristic
22C2×Dic146—41no—
23#11924016—84no—
24C2×#10596831—22no—
25C4⋊Dic73—41no—
26C4⋊Dic73—41no—
27C22⋊Dic73—81no—
28C2×D4×C73—21no—
29C2×D4×C73—21no—
30C2×D4×C73—41no—
31C2×D4×C73—41no—
32D8×C73—82no—
33C2×C8×C73—21no—
34C22⋊C4×C73—81no—
35C42×C73C22⋊C411yescharacteristic
36C23×C73—41no—
37C23×C73—41no—
38D4×C73—81no—
39D4×C73—81no—
40D4×C73—82no—
41D4×C73—82no—
42C2×C4×C73—21no—
43C2×C4×C73—161no—
44C2×C4×C73#9911yescharacteristic
45C2×Dic73—81no—
46C2×Dic73—161no—
47Dic146—82no—
48C8×C73—22no—
49#10596831—42no—
50C22×C73—81no—
51C22×C73—81no—
52C22×C73—161no—
53C22×C73—161no—
54C22×C73#35311yescharacteristic
55C4×C73—22no—
56C4×C73—21no—
57C4×C73—321no—
58Dic73—161no—
59Dic73—321no—
60#7533—731nomaximal, Sylow
61C2×C73—21no—
62C2×C73—161no—
63C2×C73—161no—
64C2×C73#140911yescharacteristic
65#1715—731no—
66#1408—731no—
67#1408D7311yescharacteristic
68C73#753311yescharacteristic, complemented, Sylow
69#498—731no—
70#493C2×D7311yescharacteristic
71#492—1461no—
72#486—1461no—
73#353—21no—
74#353—1461no—
75#322—731no—
76C2×SD16—2922no—
77C2×D8—41no—
78C4⋊Q8—1461no—
79#127D29211yescharacteristic
80#127C22⋊D7311yescharacteristic
81#106—2921no—
82#102—2922no—
83#99—41no—
84#99—2921no—
85C4×C8—1461no—
86C4×C8C4×D7311yescharacteristic
87C2×Q8—2921no—
88C2×D4—21no—
89C2×D4—21no—
90C2×D4—41no—
91C2×D4—41no—
92SD16—5844no—
93D8—82no—
94C2×C8—21no—
95C2×C8—1462no—
96C4⋊C4—2921no—
97C4⋊C4—2921no—
98C22⋊C4—81no—
99C22⋊C4—5841no—
100C42#1192400511yescharacteristic
101C23—41no—
102C23—41no—
103Q8—5842no—
104D4—81no—
105D4—81no—
106D4—82no—
107D4—82no—
108C2×C4—21no—
109C2×C4—161no—
110C2×C4—5841no—
111C2×C4—11681no—
112C2×C4#1455650511yescharacteristic
113C8—22no—
114C8—2922no—
115C22—81no—
116C22—81no—
117C22—161no—
118C22—161no—
119C22#1798837911yescharacteristic
120C4—22no—
121C4—21no—
122C4—321no—
123C4—23361no—
124C4—11681no—
125C2—21no—
126C2—161no—
127C2—161no—
128C2#2260809511yescharacteristic
subgroupG/H
centerC2#22608095
commutatorC4×C8×C73C2×C4
Frattini#493C2×D73
FittingC73×#1408C2
socleC2×C73#1409
prime radical, cosocle#493×C73C22
hypercenter#1408D73
hypocenterC73#7533
LCSG ▷ C4×C8×C73 ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #493 ◁ #1408

Complements

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

NH ≅ G/Ntype
4. #17988985C4semidirect
8. #17988308C4semidirect
68. C73#7533semidirect

Maximal subgroups

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

subgroupindex
#226095572
#226080942
C73×#14082
#753373