Finite Group Databasebeta

← #17993103

Subgroups — #17993103

Order 4736.

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

normal subgroups only

This group has 272 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#14558083C211yesmaximal, characteristic
2#14557590C211yesmaximal, characteristic, complemented
3#14557266C214yesmaximal, complemented
4C37×#376C211yesmaximal, characteristic, complemented
5C2×#10596962—21no—
6#11924536C411yescharacteristic, complemented
7#11924533C411yescharacteristic, complemented
8#11924524—21no—
9#11924510—21no—
10#11924510C2212yes—
11C4×D148—21no—
12C4×D148C412yescomplemented
13C4⋊#64436—21no—
14C22⋊#64436C2212yes—
15#11924447—21no—
16C2×C42×C37—21no—
17C2×C42×C37C2211yescharacteristic
18#95×C37—21no—
19#95×C37C2212yes—
20C22×C4×C37—22no—
21C22×C4×C37D411yescharacteristic
22C22×C4×C37D411yescharacteristic
23C22×C4×C37C2311yescharacteristic
24C2×C22⋊D37—22no—
25#10596962—44no—
26C2×D148—21no—
27C2×D148—21no—
28C2×D148C2×C412yes—
29C2×C4×D37—22no—
30C2×Dic74—21no—
31C42×C37—24no—
32C42×C37C2×C411yescharacteristic
33C42×C37C2×C411yescharacteristic
34C42×C37D411yescharacteristic
35C42×C37D411yescharacteristic
36#10596938—22no—
37#10596938—22no—
38C4⋊Dic37—21no—
39C4⋊Dic37C2×C412yes—
40C2×#64436—22no—
41C23×C37C2×D411yescharacteristic
42C22×D37—22no—
43C2×C4×C37—22no—
44C2×C4×C37—22no—
45C2×C4×C37—24no—
46C2×C4×C37—41no—
47C2×C4×C37—42no—
48C2×C4×C37—42no—
49C2×C4×C37C22⋊C411yescharacteristic
50C2×C4×C37C22⋊C411yescharacteristic
51C2×C4×C37C22⋊C411yescharacteristic
52C2×C4×C37C22⋊C411yescharacteristic
53C2×C4×C37C22×C411yescharacteristic
54C2×C4×C37C2×D411yescharacteristic
55C22⋊D37—44no—
56C2×Dic37—22no—
57D148—42no—
58D148—42no—
59D148—42no—
60C4×D37—44no—
61Dic74—42no—
62#64436—42no—
63C22×C37—21no—
64C22×C37—21no—
65C22×C37C2×C22⋊C411yescharacteristic
66C22×C37AGL(1,ℤ/8)12yes—
67C2×D37—42no—
68C2×D37—42no—
69C2×D37—42no—
70C4×C37—21no—
71C4×C37—21no—
72C4×C37—21no—
73C4×C37—21no—
74C4×C37—21no—
75C4×C37—44no—
76C4×C37#10412yes—
77Dic37—42no—
78#1505—371nomaximal, Sylow
79C2×C37—22no—
80C2×C37#41011yescharacteristic
81C2×C37#41811yescharacteristic
82C2×C37C2×#10411yescharacteristic
83D37—82no—
84#532—371no—
85#432—371no—
86#376D3711yescharacteristic, complemented
87#327—374no—
88C37#150511yescharacteristic, complemented, Sylow
89C2×#41—741no—
90C4⋊Q8—371no—
91#127—371no—
92#124—741no—
93#121—372no—
94#121—741no—
95C4×D4—372no—
96C4×D4—741no—
97C2×C42—21no—
98C2×C42C2×D3711yescharacteristic
99C4⋊C8—741no—
100C22⋊C8—372no—
101#97—741no—
102#95—21no—
103#95C2×D3712yes—
104#41—1484no—
105C2×Q8—741no—
106C2×D4—372no—
107C2×D4—742no—
108C2×D4—741no—
109C2×D4—741no—
110C22×C4—22no—
111C22×C4—742no—
112C22×C4C22⋊D3711yescharacteristic
113C22×C4C22⋊D3711yescharacteristic
114C22×C4C22×D3711yescharacteristic
115C2×C8—742no—
116C4⋊C4—372no—
117C4⋊C4—741no—
118C22⋊C4—742no—
119C22⋊C4—742no—
120C42—24no—
121C42C4×D3711yescharacteristic
122C42C4×D3711yescharacteristic
123C42D14811yescharacteristic
124C42D14811yescharacteristic
125C23—742no—
126C23C2×C22⋊D3711yescharacteristic
127Q8—1482no—
128D4—1482no—
129D4—1482no—
130D4—1484no—
131D4—1482no—
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—24no—
135C2×C4—41no—
136C2×C4—42no—
137C2×C4—42no—
138C2×C4—742no—
139C2×C4—1484no—
140C2×C4#1059693811yescharacteristic
141C2×C4#1059693811yescharacteristic
142C2×C4#1059693811yescharacteristic
143C2×C4#1059693811yescharacteristic
144C2×C4C2×C4×D3711yescharacteristic
145C2×C4C2×D14811yescharacteristic
146C8—1482no—
147C22—21no—
148C22—21no—
149C22—1482no—
150C22—1482no—
151C22—1482no—
152C22C2×#1059693811yescharacteristic
153C22#1192456112yes—
154C4—21no—
155C4—21no—
156C4—21no—
157C4—21no—
158C4—21no—
159C4—44no—
160C4—1482no—
161C4#1192446412yes—
162C2—22no—
163C2—2962no—
164C2#1455750611yescharacteristic
165C2#1455753711yescharacteristic
166C2C2×#1192446411yescharacteristic
subgroupG/H
centerC22C2×#10596938
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#376C2
socleC22×C37C2×C22⋊C4
prime radical#14558083C2
cosocleC22×C4×C37C23
hypercenter#376D37
hypocenterC37#1505
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C42 ◁ #376

Complements

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

NH ≅ G/Ntype
2. #14557590C2semidirect
3. #14557266C2semidirect
4. C37×#376C2semidirect
6. #11924536C4semidirect
7. #11924533C4semidirect
12. C4×D148C4semidirect
86. #376D37semidirect
88. C37#1505semidirect

Maximal subgroups

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

subgroupindex
#145580832
#145575902
#145572662
C37×#3762
#150537