Finite Group Databasebeta

← C37×#2129 #17990947

Subgroups — C37×#2129 #17990947

Order 4736.

238 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 84 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
1C37×#536C211yesmaximal, characteristic
2C37×#410C212yesmaximal
3C37×#354C214yesmaximal, complemented
4C2×#41×C37C2211yescharacteristic
5C22×Q8×C37C411yescharacteristic, complemented
6C4⋊Q8×C37C412yescomplemented
7#124×C37C2212yes—
8#123×C37—22no—
9C22⋊Q8×C37—22no—
10#117×C37—22no—
11#117×C37C411yescharacteristic, complemented
12#99×C37—22no—
13#99×C37C2214yes—
14#41×C37—42no—
15C2×Q8×C37—21no—
16C2×Q8×C37—42no—
17C2×Q8×C37C2×C412yes—
18C2×Q8×C37C2×C411yescharacteristic
19C2×D4×C37D412yes—
20C2×D4×C37C2311yescharacteristic
21C22×C4×C37—21no—
22C22×C4×C37C2×C411yescharacteristic
23C22×C4×C37D412yes—
24C4⋊C4×C37—24no—
25C4⋊C4×C37—21no—
26C4⋊C4×C37—42no—
27C22⋊C4×C37—21no—
28C22⋊C4×C37—24no—
29C22⋊C4×C37—24no—
30C42×C37—42no—
31C42×C37C2×C412yes—
32C23×C37C22⋊C411yescharacteristic
33C23×C37C2×D412yes—
34Q8×C37—41no—
35Q8×C37—42no—
36Q8×C37—42no—
37D4×C37—42no—
38D4×C37—41no—
39C2×C4×C37—22no—
40C2×C4×C37—22no—
41C2×C4×C37—22no—
42C2×C4×C37—22no—
43C2×C4×C37—22no—
44C2×C4×C37—42no—
45C2×C4×C37—44no—
46C2×C4×C37C22⋊C412yes—
47C2×C4×C37C22⋊C411yescharacteristic
48C2×C4×C37C22×C411yescharacteristic
49C22×C37—21no—
50C22×C37—22no—
51C22×C37—41no—
52C22×C37—42no—
53C22×C37C2×C22⋊C411yescharacteristic
54C4×C37—22no—
55C4×C37—21no—
56C4×C37—42no—
57C4×C37—42no—
58C4×C37—84no—
59C4×C37#9912yes—
60#2129C3711yesmaximal, characteristic, direct product factor, Sylow
61C2×C37—21no—
62C2×C37—42no—
63C2×C37—41no—
64C2×C37C2×#9911yescharacteristic
65#536C2×C3711yescharacteristic
66#410C2×C3712yes—
67#354C2×C3714yescomplemented
68C37#212911yescharacteristic, direct product factor, Sylow
69C2×#41C22×C3711yescharacteristic
70C22×Q8C4×C3711yescharacteristic, complemented
71C4⋊Q8C4×C3712yescomplemented
72#124C22×C3712yes—
73#123—22no—
74C22⋊Q8—22no—
75#117—22no—
76#117C4×C3711yescharacteristic, complemented
77#99—22no—
78#99C22×C3714yes—
79#41—42no—
80C2×Q8—21no—
81C2×Q8—42no—
82C2×Q8C2×C4×C3712yes—
83C2×Q8C2×C4×C3711yescharacteristic
84C2×D4D4×C3712yes—
85C2×D4C23×C3711yescharacteristic
86C22×C4—21no—
87C22×C4C2×C4×C3711yescharacteristic
88C22×C4D4×C3712yes—
89C4⋊C4—21no—
90C4⋊C4—24no—
91C4⋊C4—42no—
92C22⋊C4—21no—
93C22⋊C4—24no—
94C22⋊C4—24no—
95C42—42no—
96C42C2×C4×C3712yes—
97C23C22⋊C4×C3711yescharacteristic
98C23C2×D4×C3712yes—
99Q8—41no—
100Q8—42no—
101Q8—42no—
102D4—42no—
103D4—41no—
104C2×C4—22no—
105C2×C4—22no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—22no—
109C2×C4—42no—
110C2×C4—44no—
111C2×C4C22⋊C4×C3712yes—
112C2×C4C22⋊C4×C3711yescharacteristic
113C2×C4C22×C4×C3711yescharacteristic
114C22—21no—
115C22—22no—
116C22—41no—
117C22—42no—
118C22C2×C22⋊C4×C3711yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—42no—
123C4—84no—
124C4#99×C3712yes—
125C2—21no—
126C2—42no—
127C2—41no—
128C2C2×#99×C3711yescharacteristic
subgroupG/H
center, socleC2×C37C2×#99
commutatorC2×C4C22×C4×C37
Frattini, cosocleC2×D4C23×C37
prime radicalC2×#41×C37C22
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C37 ◁ C2×C4×C37 ◁ C2×#41×C37 ◁ G

Complements

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

NH ≅ G/Ntype
3. C37×#354C2semidirect
5. C22×Q8×C37C4semidirect
6. C4⋊Q8×C37C4semidirect
11. #117×C37C4semidirect
60. #2129C37direct (N × H)
67. #354C2×C37semidirect
68. C37#2129direct (N × H)
70. C22×Q8C4×C37semidirect
71. C4⋊Q8C4×C37semidirect
76. #117C4×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#5362
C37×#4102
C37×#3542
#212937