Finite Group Databasebeta

← #17993303

Subgroups — #17993303

Order 4736.

198 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 65 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#14558088C211yesmaximal, characteristic
2#14557589C211yesmaximal, characteristic
3#14557585C211yesmaximal, characteristic
4#14557281C211yesmaximal, characteristic, complemented
5#14557281C211yesmaximal, characteristic, complemented
6#14557279C211yesmaximal, characteristic, complemented
7C37×#332C211yesmaximal, characteristic, complemented
8#11924536C2211yescharacteristic
9#11924527—21no—
10#11924516C412yes—
11#11924512—21no—
12Q8×Dic37—21no—
13#11924501C412yes—
14#11924494—21no—
15C42×D37C2211yescharacteristic
16C4⋊#64436C2211yescharacteristic
17C4⋊#64436C2211yescharacteristic
18#11924448—21no—
19#11924448—21no—
20#11924446—21no—
21C8×Dic37—21no—
22C4⋊Q8×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24C4⋊C8×C37C2211yescharacteristic
25C2×Q8×C37—21no—
26C2×C4×D37C2×C411yescharacteristic
27C2×C4×D37D411yescharacteristic
28C2×C4×D37D411yescharacteristic
29C2×Dic74C2×C412yes—
30C2×C8×C37—21no—
31C2×C8×C37—21no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37C2×C412yes—
34C42×C37C2311yescharacteristic
35#10596938—22no—
36C4⋊Dic37—21no—
37C4⋊Dic37—21no—
38C4⋊Dic37—22no—
39#10596936—22no—
40C4×Dic37—22no—
41C4×Dic37C2×C411yescharacteristic
42C4×Dic37D411yescharacteristic
43C4×Dic37D411yescharacteristic
44C2×#64436—21no—
45C2×#64436—21no—
46C22×D37C22⋊C411yescharacteristic
47Q8×C37—41no—
48Q8×C37—41no—
49C2×C4×C37—22no—
50C2×C4×C37C22×C411yescharacteristic
51C2×C4×C37C2×D411yescharacteristic
52C2×C4×C37C2×D411yescharacteristic
53C2×Dic37—22no—
54C2×Dic37C22⋊C411yescharacteristic
55C2×Dic37C22⋊C411yescharacteristic
56C2×Dic37C22⋊C411yescharacteristic
57C4×D37—21no—
58C4×D37—21no—
59C4×D37—21no—
60C4×D37—21no—
61C4×D37—41no—
62Dic74—42no—
63C8×C37—41no—
64C8×C37—41no—
65#64436—41no—
66#64436—41no—
67C22×C37C2×C22⋊C411yescharacteristic
68C2×D37—21no—
69C2×D37—21no—
70C2×D37—21no—
71C4×C37—21no—
72C4×C37—42no—
73C4×C37#13511yescharacteristic
74C4×C37#13511yescharacteristic
75C4×C37#13711yescharacteristic
76C4×C37#13711yescharacteristic
77Dic37—21no—
78Dic37—21no—
79Dic37—21no—
80Dic37—42no—
81#1554—371nomaximal, Sylow
82C2×C37#41311yescharacteristic
83C2×C37#41611yescharacteristic
84C2×C37#41911yescharacteristic
85D37—41no—
86#533—371no—
87#432—371no—
88#431—371no—
89#333—371no—
90#333—371no—
91#332—371no—
92#332D3711yescharacteristic, complemented
93C37#155411yescharacteristic, complemented, Sylow
94C4⋊Q8—371no—
95C4⋊Q8C2×D3711yescharacteristic
96#125—741no—
97C22⋊Q8—372no—
98C22⋊Q8—741no—
99C4×Q8—372no—
100C4×Q8—741no—
101#117—741no—
102C2×C42—371no—
103C4⋊C8—371no—
104C4⋊C8—371no—
105C4⋊C8C2×D3711yescharacteristic
106C4⋊C8C2×D3711yescharacteristic
107C22⋊C8—741no—
108C22⋊C8—741no—
109#97—741no—
110C4×C8—741no—
111C2×Q8—21no—
112C2×Q8—372no—
113C22×C4—371no—
114C22×C4—371no—
115C22×C4—371no—
116C2×C8—21no—
117C2×C8—21no—
118C2×C8—741no—
119C2×C8—741no—
120C4⋊C4—21no—
121C4⋊C4—742no—
122C4⋊C4—742no—
123C4⋊C4—741no—
124C4⋊C4—741no—
125C4⋊C4C4×D3712yes—
126C22⋊C4—742no—
127C42—371no—
128C42—371no—
129C42—371no—
130C42—742no—
131C42C22×D3711yescharacteristic
132C23—371no—
133Q8—41no—
134Q8—41no—
135Q8—1482no—
136C2×C4—22no—
137C2×C4—371no—
138C2×C4—371no—
139C2×C4—371no—
140C2×C4—741no—
141C2×C4—741no—
142C2×C4—741no—
143C2×C4—741no—
144C2×C4—742no—
145C2×C4—1481no—
146C2×C4C2×C4×D3711yescharacteristic
147C2×C4D4×D3711yescharacteristic
148C2×C4D4×D3711yescharacteristic
149C8—41no—
150C8—41no—
151C8—1481no—
152C8—1481no—
153C22—741no—
154C22—741no—
155C22—741no—
156C22C22⋊C4×D3711yescharacteristic
157C4—21no—
158C4—42no—
159C4—741no—
160C4—741no—
161C4—741no—
162C4—1482no—
163C4#1192455511yescharacteristic
164C4#1192455711yescharacteristic
165C4#1192456511yescharacteristic
166C4#1192456811yescharacteristic
167C2—1481no—
168C2#1455751611yescharacteristic
169C2#1455752611yescharacteristic
170C2#1455754011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC2×C4×C37C22×C4
FrattiniC42C22×D37
FittingC37×#332C2
socleC22×C37C2×C22⋊C4
prime radicalC22×D37C22⋊C4
cosocleC42×C37C23
hypercenter#332D37
hypocenterC37#1554
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
4. #14557281C2semidirect
5. #14557281C2semidirect
6. #14557279C2semidirect
7. C37×#332C2semidirect
92. #332D37semidirect
93. C37#1554semidirect

Maximal subgroups

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

subgroupindex
#145580882
#145575892
#145575852
#145572812
#145572792
C37×#3322
#155437