Finite Group Databasebeta

← C137×#7528 #46856914

Subgroups — C137×#7528 #46856914

Order 35072.

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

normal subgroups only

This group has 142 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#1722×C137C211yesmaximal, characteristic
2#1410×C137C211yesmaximal, characteristic
3#1409×C137C211yesmaximal, characteristic
4#500×C137—21no—
5#494×C137C411yescharacteristic, complemented
6#492×C137C2211yescharacteristic
7#486×C137—21no—
8#356×C137—21no—
9#353×C137—21no—
10#322×C137C411yescharacteristic, complemented
11C2×Q16×C137—41no—
12C2×SD16×C137—41no—
13C4⋊Q8×C137—21no—
14C4⋊Q8×C137D411yescharacteristic
15#127×C137D411yescharacteristic
16#107×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—
26Q16×C137—82no—
27SD16×C137—82no—
28M16×C137—81no—
29C2×C8×C137—21no—
30C2×C8×C137—22no—
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—22no—
47C8×C137—42no—
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#140811yescharacteristic
60#7528C13711yesmaximal, characteristic, direct product factor, Sylow
61C137#752811yescharacteristic, direct product factor, Sylow
62#1722C2×C13711yescharacteristic
63#1410C2×C13711yescharacteristic
64#1409C2×C13711yescharacteristic
65#500—21no—
66#494C4×C13711yescharacteristic, complemented
67#492C22×C13711yescharacteristic
68#486—21no—
69#356—21no—
70#353—21no—
71#322C4×C13711yescharacteristic, complemented
72C2×Q16—41no—
73C2×SD16—41no—
74C4⋊Q8—21no—
75C4⋊Q8D4×C13711yescharacteristic
76#127D4×C13711yescharacteristic
77#107—42no—
78#102—42no—
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—
87Q16—82no—
88SD16—82no—
89M16—81no—
90C2×C8—21no—
91C2×C8—22no—
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—22no—
108C8—42no—
109C8—161no—
110C22—81no—
111C22—161no—
112C22#353×C13711yescharacteristic
113C4—22no—
114C4—21no—
115C4—81no—
116C4—161no—
117C4—321no—
118C2—21no—
119C2—161no—
120C2#1408×C13711yescharacteristic
subgroupG/H
center, socleC2×C137#1408
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. #494×C137C4semidirect
10. #322×C137C4semidirect
60. #7528C137direct (N × H)
61. C137#7528direct (N × H)
66. #494C4×C137semidirect
71. #322C4×C137semidirect

Maximal subgroups

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

subgroupindex
#1722×C1372
#1410×C1372
#1409×C1372
#7528137