Finite Group Databasebeta

← C137×#7536 #46856922

Subgroups — C137×#7536 #46856922

Order 35072.

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

normal subgroups only

This group has 138 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#1708×C137C211yesmaximal, characteristic
2#1410×C137C211yesmaximal, characteristic
3#1409×C137C211yesmaximal, characteristic
4#498×C137C411yescharacteristic, complemented
5#492×C137C2211yescharacteristic
6#487×C137—21no—
7#486×C137—21no—
8#356×C137—21no—
9#353×C137—21no—
10C82×C137C411yescharacteristic, complemented
11C2×SD16×C137—41no—
12C4⋊Q8×C137—21no—
13C4⋊Q8×C137D411yescharacteristic
14#127×C137D411yescharacteristic
15#106×C137—41no—
16#103×C137—42no—
17#102×C137—42no—
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—
27M16×C137—81no—
28C2×C8×C137—21no—
29C2×C8×C137—22no—
30C4⋊C4×C137—41no—
31C4⋊C4×C137—41no—
32C4⋊C4×C137—41no—
33C22⋊C4×C137—81no—
34C42×C137C22⋊C411yescharacteristic
35C23×C137—41no—
36Q8×C137—81no—
37Q8×C137—82no—
38D4×C137—81no—
39D4×C137—82no—
40C2×C4×C137—21no—
41C2×C4×C137—41no—
42C2×C4×C137—81no—
43C2×C4×C137—161no—
44C2×C4×C137#9911yescharacteristic
45C8×C137—22no—
46C8×C137—42no—
47C8×C137—161no—
48C22×C137—81no—
49C22×C137—161no—
50C22×C137#35311yescharacteristic
51C4×C137—22no—
52C4×C137—21no—
53C4×C137—81no—
54C4×C137—161no—
55C4×C137—321no—
56C2×C137—21no—
57C2×C137—161no—
58C2×C137#140911yescharacteristic
59#7536C13711yesmaximal, characteristic, direct product factor, Sylow
60C137#753611yescharacteristic, direct product factor, Sylow
61#1708C2×C13711yescharacteristic
62#1410C2×C13711yescharacteristic
63#1409C2×C13711yescharacteristic
64#498C4×C13711yescharacteristic, complemented
65#492C22×C13711yescharacteristic
66#487—21no—
67#486—21no—
68#356—21no—
69#353—21no—
70C82C4×C13711yescharacteristic, complemented
71C2×SD16—41no—
72C4⋊Q8—21no—
73C4⋊Q8D4×C13711yescharacteristic
74#127D4×C13711yescharacteristic
75#106—41no—
76#103—42no—
77#102—42no—
78#101—41no—
79#99—41no—
80C4×C8—21no—
81C4×C8C2×C4×C13711yescharacteristic
82C2×Q8—21no—
83C2×Q8—41no—
84C2×D4—21no—
85C2×D4—41no—
86SD16—82no—
87M16—81no—
88C2×C8—21no—
89C2×C8—22no—
90C4⋊C4—41no—
91C4⋊C4—41no—
92C4⋊C4—41no—
93C22⋊C4—81no—
94C42C22⋊C4×C13711yescharacteristic
95C23—41no—
96Q8—81no—
97Q8—82no—
98D4—81no—
99D4—82no—
100C2×C4—21no—
101C2×C4—41no—
102C2×C4—81no—
103C2×C4—161no—
104C2×C4#99×C13711yescharacteristic
105C8—22no—
106C8—42no—
107C8—161no—
108C22—81no—
109C22—161no—
110C22#353×C13711yescharacteristic
111C4—22no—
112C4—21no—
113C4—81no—
114C4—161no—
115C4—321no—
116C2—21no—
117C2—161no—
118C2#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
4. #498×C137C4semidirect
10. C82×C137C4semidirect
59. #7536C137direct (N × H)
60. C137#7536direct (N × H)
64. #498C4×C137semidirect
70. C82C4×C137semidirect

Maximal subgroups

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

subgroupindex
#1708×C1372
#1410×C1372
#1409×C1372
#7536137