Finite Group Databasebeta

← C137×#7527 #46856913

Subgroups — C137×#7527 #46856913

Order 35072.

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

normal subgroups only

This group has 164 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#1721×C137C211yesmaximal, characteristic
2#1410×C137C211yesmaximal, characteristic, complemented
3#1409×C137C211yesmaximal, characteristic, complemented
4#493×C137—21no—
5#493×C137C411yescharacteristic, complemented
6#492×C137C2211yescharacteristic
7#486×C137—21no—
8#356×C137—21no—
9#353×C137—21no—
10#322×C137C411yescharacteristic, complemented
11C2×SD16×C137—41no—
12C2×D8×C137—42no—
13C2×D8×C137—41no—
14C4⋊Q8×C137D411yescharacteristic
15#127×C137—21no—
16#127×C137D411yescharacteristic
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×D4×C137—21no—
24C2×D4×C137—41no—
25C2×D4×C137—41no—
26C2×D4×C137—41no—
27C2×D4×C137—41no—
28SD16×C137—82no—
29D8×C137—82no—
30D8×C137—84no—
31M16×C137—81no—
32C2×C8×C137—21no—
33C2×C8×C137—22no—
34C4⋊C4×C137—41no—
35C22⋊C4×C137—81no—
36C42×C137C22⋊C411yescharacteristic
37C23×C137—41no—
38C23×C137—81no—
39Q8×C137—81no—
40D4×C137—81no—
41D4×C137—82no—
42D4×C137—82no—
43D4×C137—82no—
44D4×C137—82no—
45C2×C4×C137—21no—
46C2×C4×C137—41no—
47C2×C4×C137—161no—
48C2×C4×C137#9911yescharacteristic
49C8×C137—22no—
50C8×C137—42no—
51C8×C137—161no—
52C22×C137—81no—
53C22×C137—161no—
54C22×C137—161no—
55C22×C137—161no—
56C22×C137—161no—
57C22×C137#35311yescharacteristic
58C4×C137—22no—
59C4×C137—21no—
60C4×C137—81no—
61C4×C137—321no—
62C2×C137—21no—
63C2×C137—161no—
64C2×C137—321no—
65C2×C137#140811yescharacteristic
66#7527C13711yesmaximal, characteristic, direct product factor, Sylow
67C137#752711yescharacteristic, direct product factor, Sylow
68#1721C2×C13711yescharacteristic
69#1410C2×C13711yescharacteristic, complemented
70#1409C2×C13711yescharacteristic, complemented
71#493—21no—
72#493C4×C13711yescharacteristic, complemented
73#492C22×C13711yescharacteristic
74#486—21no—
75#356—21no—
76#353—21no—
77#322C4×C13711yescharacteristic, complemented
78C2×SD16—41no—
79C2×D8—41no—
80C2×D8—42no—
81C4⋊Q8D4×C13711yescharacteristic
82#127—21no—
83#127D4×C13711yescharacteristic
84#102—42no—
85#101—41no—
86#99—41no—
87C4×C8—21no—
88C4×C8C2×C4×C13711yescharacteristic
89C2×Q8—21no—
90C2×D4—21no—
91C2×D4—41no—
92C2×D4—41no—
93C2×D4—41no—
94C2×D4—41no—
95SD16—82no—
96D8—82no—
97D8—84no—
98M16—81no—
99C2×C8—21no—
100C2×C8—22no—
101C4⋊C4—41no—
102C22⋊C4—81no—
103C42C22⋊C4×C13711yescharacteristic
104C23—41no—
105C23—81no—
106Q8—81no—
107D4—81no—
108D4—82no—
109D4—82no—
110D4—82no—
111D4—82no—
112C2×C4—21no—
113C2×C4—41no—
114C2×C4—161no—
115C2×C4#99×C13711yescharacteristic
116C8—22no—
117C8—42no—
118C8—161no—
119C22—81no—
120C22—161no—
121C22—161no—
122C22—161no—
123C22—161no—
124C22#353×C13711yescharacteristic
125C4—22no—
126C4—21no—
127C4—81no—
128C4—321no—
129C2—21no—
130C2—161no—
131C2—321no—
132C2#1408×C13711yescharacteristic
subgroupG/H
center, socleC2×C137#1408
commutatorC4×C8C2×C4×C137
Frattini, cosocle#492C22×C137
prime radical#1721×C137C2
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
2. #1410×C137C2semidirect
3. #1409×C137C2semidirect
5. #493×C137C4semidirect
10. #322×C137C4semidirect
66. #7527C137direct (N × H)
67. C137#7527direct (N × H)
69. #1410C2×C137semidirect
70. #1409C2×C137semidirect
72. #493C4×C137semidirect
77. #322C4×C137semidirect

Maximal subgroups

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

subgroupindex
#1721×C1372
#1410×C1372
#1409×C1372
#7527137