Finite Group Databasebeta

← #17993157

Subgroups — #17993157

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#14557399C211yesmaximal, characteristic, complemented
3#14557268C214yesmaximal, complemented
4C37×#431C211yesmaximal, characteristic, complemented
5C2×#10596962—21no—
6#11924536C411yescharacteristic, complemented
7#11924533C411yescharacteristic, complemented
8#11924524—21no—
9#11924510—21no—
10#11924510C2212yes—
11C4×D148—21no—
12C4×D148C412yescomplemented
13C2×C4⋊Dic37—21no—
14#11924443—21no—
15#11924443C2212yes—
16C2×C42×C37C2211yescharacteristic
17C4⋊C8×C37—21no—
18C22⋊C8×C37C2212yes—
19C4×C8×C37—21no—
20C22×C4×C37D411yescharacteristic
21C22×C4×C37D411yescharacteristic
22C22×C4×C37C2311yescharacteristic
23C2×C22⋊D37—22no—
24C22×Dic37—22no—
25#10596962—42no—
26#10596962—42no—
27C2×D148—21no—
28C2×D148—21no—
29C2×D148C2×C412yes—
30C2×C4×D37—22no—
31C2×Dic74—21no—
32C2×C8×C37—22no—
33C42×C37C2×C411yescharacteristic
34C42×C37C2×C411yescharacteristic
35C42×C37D411yescharacteristic
36C42×C37D411yescharacteristic
37#10596938—22no—
38#10596938—22no—
39C4⋊Dic37—21no—
40C4⋊Dic37—42no—
41C4⋊Dic37C2×C412yes—
42C23×C37C2×D411yescharacteristic
43C22×D37—22no—
44C2×C4×C37—41no—
45C2×C4×C37—41no—
46C2×C4×C37C22⋊C411yescharacteristic
47C2×C4×C37C22⋊C411yescharacteristic
48C2×C4×C37C22⋊C411yescharacteristic
49C2×C4×C37C22⋊C411yescharacteristic
50C2×C4×C37D812yes—
51C2×C4×C37SD1612yes—
52C2×C4×C37C22×C411yescharacteristic
53C2×C4×C37C2×D411yescharacteristic
54C22⋊D37—42no—
55C22⋊D37—42no—
56C2×Dic37—22no—
57C2×Dic37—42no—
58C2×Dic37—42no—
59C2×Dic37—42no—
60D148—42no—
61D148—42no—
62D148—42no—
63C4×D37—44no—
64Dic74—42no—
65C8×C37—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#10212yes—
79C4×C37#10212yes—
80Dic37—42no—
81Dic37—82no—
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#431D3711yescharacteristic, complemented
91#382—371no—
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—741no—
103C2×C42C2×D3711yescharacteristic
104C4⋊C8—21no—
105C22⋊C8C2×D3712yes—
106C4×C8—21no—
107#95—372no—
108#95—741no—
109#41—1482no—
110#41—1482no—
111C2×Q8—741no—
112C2×D4—372no—
113C2×D4—742no—
114C2×D4—741no—
115C2×D4—741no—
116C22×C4—742no—
117C22×C4—742no—
118C22×C4D14811yescharacteristic
119C22×C4D14811yescharacteristic
120C22×C4C22×D3711yescharacteristic
121C2×C8—22no—
122C4⋊C4—372no—
123C4⋊C4—741no—
124C4⋊C4—1482no—
125C22⋊C4—742no—
126C22⋊C4—742no—
127C42C4×D3711yescharacteristic
128C42C4×D3711yescharacteristic
129C42C22⋊D3711yescharacteristic
130C42C22⋊D3711yescharacteristic
131C23—742no—
132C23C2×D14811yescharacteristic
133Q8—1482no—
134D4—1482no—
135D4—1482no—
136D4—1482no—
137D4—1482no—
138D4—1482no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—742no—
142C2×C4—1482no—
143C2×C4—1482no—
144C2×C4—1482no—
145C2×C4—1484no—
146C2×C4#1059693012yes—
147C2×C4D29612yes—
148C2×C4#1059693811yescharacteristic
149C2×C4#1059693811yescharacteristic
150C2×C4#1059693811yescharacteristic
151C2×C4#1059693811yescharacteristic
152C2×C4C2×C4×D3711yescharacteristic
153C2×C4C2×C22⋊D3711yescharacteristic
154C8—42no—
155C22—21no—
156C22—21no—
157C22—1482no—
158C22—1482no—
159C22—1482no—
160C22C2×#1059693811yescharacteristic
161C22C2×D29611yescharacteristic
162C22C2×#1059693011yescharacteristic
163C4—21no—
164C4—21no—
165C4—21no—
166C4—21no—
167C4—2962no—
168C4—1482no—
169C4#1192445812yes—
170C4#1192445812yes—
171C2—21no—
172C2—21no—
173C2—2962no—
174C2#1455750611yescharacteristic
175C2C2×#1192445811yescharacteristic
176C2#1455754911yescharacteristic
subgroupG/H
centerC22C2×#10596938
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#431C2
socleC22×C37C2×C22⋊C4
prime radical#14558083C2
cosocleC22×C4×C37C23
hypercenter#431D37
hypocenterC37#1517
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #14557399C2semidirect
3. #14557268C2semidirect
4. C37×#431C2semidirect
6. #11924536C4semidirect
7. #11924533C4semidirect
12. C4×D148C4semidirect
90. #431D37semidirect
93. C37#1517semidirect

Maximal subgroups

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

subgroupindex
#145580832
#145573992
#145572682
C37×#4312
#151737