Finite Group Databasebeta

← #32973857

Subgroups — #32973857

Order 18688.

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

normal subgroups only

This group has 150 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#22609517C211yesmaximal, characteristic
2#22608096C211yesmaximal, characteristic
3C73×#1410C211yesmaximal, characteristic
4#17988985C411yescharacteristic, complemented
5#17988983—21no—
6#17988959—21no—
7#17988380—21no—
8C8×#10596831C411yescharacteristic, complemented
9#492×C73C2211yescharacteristic
10#356×C73—21no—
11C2×#11924016—42no—
12#14556591—21no—
13#14556523—41no—
14#14556522—42no—
15#14556506—41no—
16C4×#10596831—21no—
17C2×SD16×C73—41no—
18C4⋊Q8×C73D411yescharacteristic
19#127×C73D411yescharacteristic
20#101×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×Q8×C73—21no—
29C2×D4×C73—21no—
30C2×D4×C73—41no—
31SD16×C73—82no—
32M16×C73—81no—
33C2×C8×C73—21no—
34C4⋊C4×C73—41no—
35C42×C73C22⋊C411yescharacteristic
36C23×C73—41no—
37Q8×C73—81no—
38D4×C73—81no—
39D4×C73—82no—
40C2×C4×C73—21no—
41C2×C4×C73—41no—
42C2×C4×C73#9911yescharacteristic
43C2×Dic73—81no—
44C2×Dic73—161no—
45Dic146—82no—
46C8×C73—22no—
47C8×C73—161no—
48#10596831—24no—
49C22×C73—81no—
50C22×C73—161no—
51C22×C73#35311yescharacteristic
52C4×C73—22no—
53C4×C73—21no—
54C4×C73—81no—
55Dic73—161no—
56Dic73—321no—
57#7535—731nomaximal, Sylow
58C2×C73—21no—
59C2×C73—161no—
60C2×C73#140911yescharacteristic
61#1705—731no—
62#1410D7311yescharacteristic
63#1409—731no—
64C73#753511yescharacteristic, complemented, Sylow
65#498—731no—
66#498—1461no—
67#492—1461no—
68#492C2×D7311yescharacteristic
69#356—21no—
70#353—1461no—
71C82—731no—
72C2×SD16—41no—
73C2×SD16—2922no—
74C4⋊Q8—1461no—
75C4⋊Q8C22⋊D7311yescharacteristic
76#127D29211yescharacteristic
77#106—2922no—
78#106—2921no—
79#101—41no—
80#99—2921no—
81C4×C8—1461no—
82C4×C8C4×D7311yescharacteristic
83C2×Q8—21no—
84C2×Q8—2921no—
85C2×D4—21no—
86C2×D4—41no—
87SD16—82no—
88SD16—5844no—
89M16—81no—
90C2×C8—21no—
91C2×C8—1462no—
92C4⋊C4—41no—
93C4⋊C4—2921no—
94C4⋊C4—2921no—
95C22⋊C4—5841no—
96C42#1192400511yescharacteristic
97C23—41no—
98Q8—81no—
99Q8—5842no—
100D4—81no—
101D4—82no—
102C2×C4—21no—
103C2×C4—41no—
104C2×C4—5841no—
105C2×C4—11681no—
106C2×C4#1455650511yescharacteristic
107C8—22no—
108C8—161no—
109C8—1464no—
110C22—81no—
111C22—161no—
112C22#1798837911yescharacteristic
113C4—22no—
114C4—21no—
115C4—81no—
116C4—23361no—
117C4—11681no—
118C2—21no—
119C2—161no—
120C2#2260809511yescharacteristic
subgroupG/H
centerC2#22608095
commutatorC4×C8×C73C2×C4
Frattini#492C2×D73
FittingC73×#1410C2
socleC2×C73#1409
prime radical#127×C73D4
cosocle#492×C73C22
hypercenter#1410D73
hypocenterC73#7535
LCSG ▷ C4×C8×C73 ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #492 ◁ #1410

Complements

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

NH ≅ G/Ntype
4. #17988985C4semidirect
8. C8×#10596831C4semidirect
64. C73#7535semidirect

Maximal subgroups

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

subgroupindex
#226095172
#226080962
C73×#14102
#753573