Finite Group Databasebeta

← C137×#7535 #46856921

Subgroups — C137×#7535 #46856921

Order 35072.

150 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 30 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#1705×C137C211yesmaximal, characteristic
2#1410×C137C211yesmaximal, characteristic
3#1409×C137C211yesmaximal, characteristic
4#498×C137—21no—
5#498×C137C411yescharacteristic, complemented
6#492×C137—21no—
7#492×C137C2211yescharacteristic
8#356×C137—21no—
9#353×C137—21no—
10C82×C137C411yescharacteristic, complemented
11C2×SD16×C137—41no—
12C2×SD16×C137—42no—
13C4⋊Q8×C137—21no—
14C4⋊Q8×C137D411yescharacteristic
15#127×C137D411yescharacteristic
16#106×C137—42no—
17#106×C137—41no—
18#101×C137—41no—
19#99×C137—41no—
20C4×C8×C137—21no—
21C4×C8×C137C2×C411yescharacteristic
22C2×Q8×C137—21no—
23C2×Q8×C137—41no—
24C2×D4×C137—21no—
25C2×D4×C137—41no—
26SD16×C137—82no—
27SD16×C137—84no—
28M16×C137—81no—
29C2×C8×C137—22no—
30C2×C8×C137—21no—
31C4⋊C4×C137—41no—
32C4⋊C4×C137—41no—
33C4⋊C4×C137—41no—
34C22⋊C4×C137—81no—
35C42×C137C22⋊C411yescharacteristic
36C23×C137—41no—
37Q8×C137—81no—
38Q8×C137—82no—
39D4×C137—81no—
40D4×C137—82no—
41C2×C4×C137—21no—
42C2×C4×C137—41no—
43C2×C4×C137—81no—
44C2×C4×C137—161no—
45C2×C4×C137#9911yescharacteristic
46C8×C137—24no—
47C8×C137—22no—
48C8×C137—161no—
49C22×C137—81no—
50C22×C137—161no—
51C22×C137#35311yescharacteristic
52C4×C137—22no—
53C4×C137—21no—
54C4×C137—81no—
55C4×C137—161no—
56C4×C137—321no—
57C2×C137—21no—
58C2×C137—161no—
59C2×C137#140911yescharacteristic
60#7535C13711yesmaximal, characteristic, direct product factor, Sylow
61C137#753511yescharacteristic, direct product factor, Sylow
62#1705C2×C13711yescharacteristic
63#1410C2×C13711yescharacteristic
64#1409C2×C13711yescharacteristic
65#498—21no—
66#498C4×C13711yescharacteristic, complemented
67#492—21no—
68#492C22×C13711yescharacteristic
69#356—21no—
70#353—21no—
71C82C4×C13711yescharacteristic, complemented
72C2×SD16—41no—
73C2×SD16—42no—
74C4⋊Q8—21no—
75C4⋊Q8D4×C13711yescharacteristic
76#127D4×C13711yescharacteristic
77#106—42no—
78#106—41no—
79#101—41no—
80#99—41no—
81C4×C8—21no—
82C4×C8C2×C4×C13711yescharacteristic
83C2×Q8—21no—
84C2×Q8—41no—
85C2×D4—21no—
86C2×D4—41no—
87SD16—82no—
88SD16—84no—
89M16—81no—
90C2×C8—22no—
91C2×C8—21no—
92C4⋊C4—41no—
93C4⋊C4—41no—
94C4⋊C4—41no—
95C22⋊C4—81no—
96C42C22⋊C4×C13711yescharacteristic
97C23—41no—
98Q8—81no—
99Q8—82no—
100D4—81no—
101D4—82no—
102C2×C4—21no—
103C2×C4—41no—
104C2×C4—81no—
105C2×C4—161no—
106C2×C4#99×C13711yescharacteristic
107C8—24no—
108C8—22no—
109C8—161no—
110C22—81no—
111C22—161no—
112C22#353×C13711yescharacteristic
113C4—22no—
114C4—21no—
115C4—81no—
116C4—161no—
117C4—321no—
118C2—21no—
119C2—161no—
120C2#1409×C13711yescharacteristic
subgroupG/H
center, socleC2×C137#1409
commutatorC4×C8C2×C4×C137
Frattini, cosocle#492C22×C137
prime radical#127×C137D4
LCSG ▷ C4×C8 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C137 ◁ C22×C137 ◁ C2×C4×C137 ◁ C42×C137 ◁ #492×C137 ◁ G

Complements

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

NH ≅ G/Ntype
5. #498×C137C4semidirect
10. C82×C137C4semidirect
60. #7535C137direct (N × H)
61. C137#7535direct (N × H)
66. #498C4×C137semidirect
71. C82C4×C137semidirect

Maximal subgroups

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

subgroupindex
#1705×C1372
#1410×C1372
#1409×C1372
#7535137