Finite Group Databasebeta

← #17993300

Subgroups — #17993300

Order 4736.

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

normal subgroups only

This group has 242 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#14558084C211yesmaximal, characteristic
2#14557589C211yesmaximal, characteristic, complemented
3#14557585C211yesmaximal, characteristic, complemented
4#14557279C211yesmaximal, characteristic, complemented
5#14557276C211yesmaximal, characteristic, complemented
6#14557276C211yesmaximal, characteristic, complemented
7C37×#332C211yesmaximal, characteristic, complemented
8C2×#10596966—21no—
9#11924533C2211yescharacteristic
10#11924525—21no—
11#11924511—21no—
12#11924511C412yes—
13#11924498—21no—
14#11924498C412yes—
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—
26#10596966—42no—
27#10596966—42no—
28C2×D148—22no—
29C2×D148—21no—
30C2×D148—21no—
31C2×D148C2×C412yes—
32C2×C4×D37—22no—
33C2×C4×D37C2×C411yescharacteristic
34C2×C4×D37D411yescharacteristic
35C2×C4×D37D411yescharacteristic
36C2×C8×C37—21no—
37C2×C8×C37—21no—
38C4⋊C4×C37—21no—
39C4⋊C4×C37C2×C412yes—
40C42×C37C2311yescharacteristic
41#10596938—22no—
42#10596938—22no—
43C4×Dic37C2×C411yescharacteristic
44C4×Dic37D411yescharacteristic
45C4×Dic37D411yescharacteristic
46C2×#64436—21no—
47C2×#64436—21no—
48C22×D37—22no—
49C22×D37C22⋊C411yescharacteristic
50Q8×C37—41no—
51Q8×C37—41no—
52C2×C4×C37—22no—
53C2×C4×C37C22×C411yescharacteristic
54C2×C4×C37C2×D411yescharacteristic
55C2×C4×C37C2×D411yescharacteristic
56C2×Dic37C22⋊C411yescharacteristic
57C2×Dic37C22⋊C411yescharacteristic
58C2×Dic37C22⋊C411yescharacteristic
59D148—42no—
60D148—44no—
61D148—41no—
62D148—41no—
63D148—41no—
64D148—41no—
65C4×D37—21no—
66C4×D37—21no—
67C4×D37—21no—
68C4×D37—21no—
69C4×D37—41no—
70C4×D37—44no—
71C8×C37—41no—
72C8×C37—41no—
73#64436—41no—
74#64436—41no—
75C22×C37C2×C22⋊C411yescharacteristic
76C2×D37—21no—
77C2×D37—21no—
78C2×D37—21no—
79C2×D37—42no—
80C2×D37—42no—
81C2×D37—42no—
82C4×C37—21no—
83C4×C37—42no—
84C4×C37#13511yescharacteristic
85C4×C37#13511yescharacteristic
86C4×C37AGL(1,ℤ/8)11yescharacteristic
87C4×C37AGL(1,ℤ/8)11yescharacteristic
88Dic37—21no—
89Dic37—21no—
90Dic37—21no—
91#1553—371nomaximal, Sylow
92C2×C37#41311yescharacteristic
93C2×C37#41611yescharacteristic
94C2×C37#41811yescharacteristic
95D37—41no—
96D37—82no—
97#532—371no—
98#432—371no—
99#431—371no—
100#332—371no—
101#332D3711yescharacteristic, complemented
102#331—371no—
103#331—371no—
104C37#155311yescharacteristic, complemented, Sylow
105C2×#41—741no—
106C4⋊Q8C2×D3711yescharacteristic
107#127—371no—
108#124—741no—
109#121—372no—
110#121—741no—
111C4×D4—372no—
112C4×D4—741no—
113C2×C42—371no—
114C4⋊C8—371no—
115C4⋊C8—371no—
116C4⋊C8C2×D3711yescharacteristic
117C4⋊C8C2×D3711yescharacteristic
118C22⋊C8—741no—
119C22⋊C8—741no—
120#97—741no—
121C4×C8—741no—
122#41—1482no—
123#41—1482no—
124C2×Q8—21no—
125C2×D4—372no—
126C2×D4—742no—
127C2×D4—741no—
128C2×D4—741no—
129C22×C4—371no—
130C22×C4—371no—
131C22×C4—371no—
132C22×C4—742no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—741no—
136C2×C8—741no—
137C4⋊C4—21no—
138C4⋊C4C4×D3712yes—
139C22⋊C4—742no—
140C22⋊C4—742no—
141C42—371no—
142C42—371no—
143C42—371no—
144C42C22×D3711yescharacteristic
145C23—371no—
146C23—742no—
147Q8—41no—
148Q8—41no—
149D4—1482no—
150D4—1484no—
151D4—1481no—
152D4—1481no—
153D4—1481no—
154D4—1481no—
155C2×C4—22no—
156C2×C4—371no—
157C2×C4—371no—
158C2×C4—371no—
159C2×C4—741no—
160C2×C4—741no—
161C2×C4—741no—
162C2×C4—741no—
163C2×C4—1481no—
164C2×C4—1484no—
165C2×C4C2×C4×D3711yescharacteristic
166C2×C4D4×D3711yescharacteristic
167C2×C4D4×D3711yescharacteristic
168C8—41no—
169C8—41no—
170C8—1481no—
171C8—1481no—
172C22—741no—
173C22—741no—
174C22—741no—
175C22—1482no—
176C22—1482no—
177C22—1482no—
178C22C22⋊C4×D3711yescharacteristic
179C4—21no—
180C4—42no—
181C4—741no—
182C4—741no—
183C4—741no—
184C4#1192455711yescharacteristic
185C4#1192455911yescharacteristic
186C4#1192456011yescharacteristic
187C4#1192456311yescharacteristic
188C2—2962no—
189C2—1481no—
190C2#1455751611yescharacteristic
191C2#1455752811yescharacteristic
192C2#1455753611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC2×C4×C37C22×C4
FrattiniC42C22×D37
FittingC37×#332C2
socleC22×C37C2×C22⋊C4
prime radical#14558084C2
cosocleC42×C37C23
hypercenter#332D37
hypocenterC37#1553
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
2. #14557589C2semidirect
3. #14557585C2semidirect
4. #14557279C2semidirect
5. #14557276C2semidirect
6. #14557276C2semidirect
7. C37×#332C2semidirect
101. #332D37semidirect
104. C37#1553semidirect

Maximal subgroups

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

subgroupindex
#145580842
#145575892
#145575852
#145572792
#145572762
C37×#3322
#155337