Finite Group Databasebeta

← #17993155

Subgroups — #17993155

Order 4736.

264 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 85 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#14557586C211yesmaximal, characteristic, complemented
3#14557266C214yesmaximal, complemented
4C37×#382C211yesmaximal, 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—
15C4×#64436—21no—
16C2×C4⋊C4×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—42no—
26#10596962—42no—
27C2×D148—21no—
28C2×D148—21no—
29C2×D148C2×C412yes—
30C2×C4×D37—22no—
31C2×Dic74—21no—
32C4⋊C4×C37—42no—
33C42×C37C2×C411yescharacteristic
34C42×C37C2×C411yescharacteristic
35C42×C37D411yescharacteristic
36C42×C37D411yescharacteristic
37#10596938—22no—
38#10596938—22no—
39C4⋊Dic37—21no—
40C4⋊Dic37C2×C412yes—
41C2×#64436—22no—
42C23×C37C2×D411yescharacteristic
43C22×D37—22no—
44C2×C4×C37—41no—
45C2×C4×C37—41no—
46C2×C4×C37—42no—
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×C37D812yes—
54C2×C4×C37SD1612yes—
55C2×C4×C37C22×C411yescharacteristic
56C2×C4×C37C2×D411yescharacteristic
57C22⋊D37—42no—
58C22⋊D37—42no—
59C2×Dic37—22no—
60D148—42no—
61D148—42no—
62D148—42no—
63C4×D37—44no—
64Dic74—42no—
65#64436—42no—
66C22×C37—21no—
67C22×C37—21no—
68C22×C37C2×C22⋊C411yescharacteristic
69C22×C37C2×D811yescharacteristic
70C22×C37C2×SD1611yescharacteristic
71C2×D37—42no—
72C2×D37—42no—
73C2×D37—42no—
74C4×C37—21no—
75C4×C37—21no—
76C4×C37—21no—
77C4×C37—21no—
78C4×C37—82no—
79C4×C37#10212yes—
80C4×C37#10212yes—
81Dic37—42no—
82#1517—371nomaximal, Sylow
83C2×C37—21no—
84C2×C37—21no—
85C2×C37#41011yescharacteristic
86C2×C37C2×#10211yescharacteristic
87C2×C37#42111yescharacteristic
88D37—82no—
89#532—371no—
90#431—371no—
91#382D3711yescharacteristic, complemented
92#327—374no—
93C37#151711yescharacteristic, complemented, Sylow
94C2×#41—741no—
95C4⋊Q8—371no—
96#127—371no—
97#124—741no—
98#121—372no—
99#121—741no—
100C4×D4—372no—
101C4×D4—741no—
102C2×C4⋊C4—21no—
103C2×C42C2×D3711yescharacteristic
104C4⋊C8—741no—
105C22⋊C8—372no—
106C4×C8—741no—
107#95—21no—
108#95C2×D3712yes—
109#41—1482no—
110#41—1482no—
111C2×Q8—741no—
112C2×D4—372no—
113C2×D4—742no—
114C2×D4—741no—
115C2×D4—741no—
116C22×C4—22no—
117C22×C4—742no—
118C22×C4C22⋊D3711yescharacteristic
119C22×C4C22⋊D3711yescharacteristic
120C22×C4C22×D3711yescharacteristic
121C2×C8—742no—
122C4⋊C4—42no—
123C4⋊C4—372no—
124C4⋊C4—741no—
125C22⋊C4—742no—
126C22⋊C4—742no—
127C42C4×D3711yescharacteristic
128C42C4×D3711yescharacteristic
129C42D14811yescharacteristic
130C42D14811yescharacteristic
131C23—742no—
132C23C2×C22⋊D3711yescharacteristic
133Q8—1482no—
134D4—1482no—
135D4—1482no—
136D4—1482no—
137D4—1482no—
138D4—1482no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—42no—
142C2×C4—42no—
143C2×C4—42no—
144C2×C4—742no—
145C2×C4—1484no—
146C2×C4#1059693811yescharacteristic
147C2×C4#1059693811yescharacteristic
148C2×C4#1059693811yescharacteristic
149C2×C4#1059693811yescharacteristic
150C2×C4#1059693912yes—
151C2×C4#1059694112yes—
152C2×C4C2×C4×D3711yescharacteristic
153C2×C4C2×D14811yescharacteristic
154C8—1482no—
155C22—21no—
156C22—21no—
157C22—1482no—
158C22—1482no—
159C22—1482no—
160C22C2×#1059693811yescharacteristic
161C22C2×#1059693911yescharacteristic
162C22C2×#1059694111yescharacteristic
163C4—21no—
164C4—21no—
165C4—21no—
166C4—21no—
167C4—82no—
168C4—1482no—
169C4#1192445612yes—
170C4#1192445612yes—
171C2—21no—
172C2—21no—
173C2—2962no—
174C2#1455750611yescharacteristic
175C2C2×#1192445611yescharacteristic
176C2#1455755111yescharacteristic
subgroupG/H
centerC22C2×#10596938
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#382C2
socleC22×C37C2×C22⋊C4
prime radical#14558083C2
cosocleC22×C4×C37C23
hypercenter#382D37
hypocenterC37#1517
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #14557586C2semidirect
3. #14557266C2semidirect
4. C37×#382C2semidirect
6. #11924536C4semidirect
7. #11924533C4semidirect
12. C4×D148C4semidirect
91. #382D37semidirect
93. C37#1517semidirect

Maximal subgroups

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

subgroupindex
#145580832
#145575862
#145572662
C37×#3822
#151737