Finite Group Databasebeta

← #17996271

Subgroups — #17996271

Order 4736.

238 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 73 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#14557507C212yesmaximal
2#14557328C214yesmaximal, complemented
3C37×#536C211yesmaximal, characteristic
4#11924495—22no—
5#11924451—22no—
6#11924451C2214yes—
7C2×#41×C37C2211yescharacteristic
8C22×Q8×C37C411yescharacteristic, complemented
9C4⋊Q8×C37C412yescomplemented
10#124×C37C2212yes—
11#123×C37—22no—
12C22⋊Q8×C37—22no—
13#117×C37C411yescharacteristic, complemented
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—21no—
25C4⋊C4×C37—24no—
26C22⋊C4×C37—21no—
27C22⋊C4×C37—24no—
28C42×C37C2×C412yes—
29C22⋊Dic37—24no—
30C4⋊Dic37—42no—
31C4×Dic37—42no—
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×C37C22⋊C412yes—
46C2×C4×C37C22⋊C411yescharacteristic
47C2×C4×C37C22×C411yescharacteristic
48C2×Dic37—44no—
49C22×C37—22no—
50C22×C37—21no—
51C22×C37—41no—
52C22×C37—42no—
53C22×C37C2×C22⋊C411yescharacteristic
54C4×C37—22no—
55C4×C37—21no—
56C4×C37—42no—
57C4×C37—42no—
58C4×C37#9912yes—
59Dic37—84no—
60#2129—371nomaximal, Sylow
61C2×C37—21no—
62C2×C37—42no—
63C2×C37—41no—
64C2×C37C2×#9911yescharacteristic
65#536D3711yescharacteristic
66#410—372no—
67#354—374no—
68C37#212911yescharacteristic, complemented, Sylow
69C2×#41C2×D3711yescharacteristic
70C22×Q8Dic3711yescharacteristic, complemented
71C4⋊Q8Dic3712yescomplemented
72#124C2×D3712yes—
73#123—22no—
74C22⋊Q8—22no—
75#117—742no—
76#117Dic3711yescharacteristic, complemented
77#99—374no—
78#99—742no—
79#41—42no—
80C2×Q8—21no—
81C2×Q8—42no—
82C2×Q8C2×Dic3712yes—
83C2×Q8C2×Dic3711yescharacteristic
84C2×D4C22⋊D3712yes—
85C2×D4C22×D3711yescharacteristic
86C22×C4—21no—
87C22×C4C2×Dic3711yescharacteristic
88C22×C4C22⋊D3712yes—
89C4⋊C4—24no—
90C4⋊C4—21no—
91C4⋊C4—1482no—
92C22⋊C4—21no—
93C22⋊C4—24no—
94C22⋊C4—744no—
95C42—1482no—
96C42C2×Dic3712yes—
97C23C22⋊Dic3711yescharacteristic
98C23C2×C22⋊D3712yes—
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—1484no—
111C2×C4C22⋊Dic3712yes—
112C2×C4C22⋊Dic3711yescharacteristic
113C2×C4C22×Dic3711yescharacteristic
114C22—21no—
115C22—22no—
116C22—41no—
117C22—42no—
118C22C2×C22⋊Dic3711yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—42no—
123C4—2964no—
124C4#1192445112yes—
125C2—21no—
126C2—42no—
127C2—41no—
128C2C2×#1192445111yescharacteristic
subgroupG/H
centerC2C2×#11924451
commutatorC2×C4×C37C22×C4
FrattiniC2×D4C22×D37
FittingC37×#536C2
socleC2×C37C2×#99
prime radicalC2×#41×C37C22
cosocleC2×D4×C37C23
hypercenter#536D37
hypocenterC37#2129
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. #14557328C2semidirect
8. C22×Q8×C37C4semidirect
9. C4⋊Q8×C37C4semidirect
13. #117×C37C4semidirect
68. C37#2129semidirect
70. C22×Q8Dic37semidirect
71. C4⋊Q8Dic37semidirect
76. #117Dic37semidirect

Maximal subgroups

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

subgroupindex
#145575072
#145573282
C37×#5362
#212937