Finite Group Databasebeta

← #17993298

Subgroups — #17993298

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#14558081C211yesmaximal, characteristic
2#14557589C211yesmaximal, characteristic, complemented
3#14557585C211yesmaximal, characteristic, complemented
4#14557280C211yesmaximal, characteristic, complemented
5#14557278C211yesmaximal, characteristic, complemented
6#14557277C211yesmaximal, characteristic, complemented
7C37×#331C211yesmaximal, characteristic, complemented
8C2×#10596964—21no—
9#11924536C2211yescharacteristic
10#11924523—21no—
11#11924507—21no—
12#11924507C412yes—
13D4×Dic37—21no—
14D4×Dic37C412yes—
15C42×D37C2211yescharacteristic
16C4⋊#64436C2211yescharacteristic
17C4⋊#64436C2211yescharacteristic
18#11924448—21no—
19#11924448—21no—
20#11924446—21no—
21C8×Dic37—21no—
22#127×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24C4⋊C8×C37C2211yescharacteristic
25C2×D4×C37—21no—
26C2×D4×C37—21no—
27C2×D4×C37C2×C412yes—
28C2×C22⋊D37—22no—
29C22×Dic37—22no—
30#10596964—42no—
31#10596964—42no—
32C2×C4×D37C2×C411yescharacteristic
33C2×C4×D37D411yescharacteristic
34C2×C4×D37D411yescharacteristic
35C2×Dic74—21no—
36C2×C8×C37—21no—
37C2×C8×C37—21no—
38C42×C37C2311yescharacteristic
39C22⋊Dic37—22no—
40C22⋊Dic37—22no—
41C4⋊Dic37—21no—
42C4⋊Dic37C2×C412yes—
43C4×Dic37C2×C411yescharacteristic
44C4×Dic37D411yescharacteristic
45C4×Dic37D411yescharacteristic
46C2×#64436—21no—
47C2×#64436—21no—
48C23×C37—22no—
49C22×D37C22⋊C411yescharacteristic
50D4×C37—42no—
51D4×C37—41no—
52D4×C37—41no—
53D4×C37—41no—
54D4×C37—41no—
55C2×C4×C37C22×C411yescharacteristic
56C2×C4×C37C2×D411yescharacteristic
57C2×C4×C37C2×D411yescharacteristic
58C22⋊D37—44no—
59C2×Dic37—22no—
60C2×Dic37—44no—
61C2×Dic37C22⋊C411yescharacteristic
62C2×Dic37C22⋊C411yescharacteristic
63C2×Dic37C22⋊C411yescharacteristic
64C4×D37—21no—
65C4×D37—21no—
66C4×D37—21no—
67C4×D37—21no—
68C4×D37—41no—
69Dic74—41no—
70Dic74—41no—
71C8×C37—41no—
72C8×C37—41no—
73#64436—41no—
74#64436—41no—
75C22×C37—42no—
76C22×C37—42no—
77C22×C37—42no—
78C22×C37C2×C22⋊C411yescharacteristic
79C2×D37—21no—
80C2×D37—21no—
81C2×D37—21no—
82C4×C37—21no—
83C4×C37#13511yescharacteristic
84C4×C37#13511yescharacteristic
85C4×C37AGL(1,ℤ/8)11yescharacteristic
86C4×C37AGL(1,ℤ/8)11yescharacteristic
87Dic37—21no—
88Dic37—21no—
89Dic37—21no—
90Dic37—42no—
91#1553—371nomaximal, Sylow
92C2×C37—82no—
93C2×C37#41311yescharacteristic
94C2×C37#41611yescharacteristic
95C2×C37#41811yescharacteristic
96D37—41no—
97#532—371no—
98#432—371no—
99#431—371no—
100#332—371no—
101#332—371no—
102#331—371no—
103#331D3711yescharacteristic, complemented
104C37#155311yescharacteristic, complemented, Sylow
105C2×#41—741no—
106C4⋊Q8—371no—
107#127C2×D3711yescharacteristic
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—741no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—742no—
128C2×D4C4×D3712yes—
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—372no—
138C4⋊C4—741no—
139C22⋊C4—742no—
140C22⋊C4—742no—
141C42—371no—
142C42—371no—
143C42—371no—
144C42C22×D3711yescharacteristic
145C23—22no—
146C23—371no—
147Q8—1481no—
148Q8—1481no—
149D4—42no—
150D4—41no—
151D4—41no—
152D4—41no—
153D4—41no—
154D4—1484no—
155C2×C4—371no—
156C2×C4—371no—
157C2×C4—371no—
158C2×C4—741no—
159C2×C4—741no—
160C2×C4—741no—
161C2×C4—741no—
162C2×C4—742no—
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—42no—
173C22—42no—
174C22—42no—
175C22—741no—
176C22—741no—
177C22—741no—
178C22C22⋊C4×D3711yescharacteristic
179C4—21no—
180C4—741no—
181C4—741no—
182C4—741no—
183C4—1482no—
184C4#1192455511yescharacteristic
185C4#1192455711yescharacteristic
186C4#1192456011yescharacteristic
187C4#1192456311yescharacteristic
188C2—82no—
189C2—1481no—
190C2#1455751411yescharacteristic
191C2#1455752611yescharacteristic
192C2#1455753611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC2×C4×C37C22×C4
FrattiniC42C22×D37
FittingC37×#331C2
socleC22×C37C2×C22⋊C4
prime radical#14558081C2
cosocleC42×C37C23
hypercenter#331D37
hypocenterC37#1553
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #14557589C2semidirect
3. #14557585C2semidirect
4. #14557280C2semidirect
5. #14557278C2semidirect
6. #14557277C2semidirect
7. C37×#331C2semidirect
103. #331D37semidirect
104. C37#1553semidirect

Maximal subgroups

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

subgroupindex
#145580812
#145575892
#145575852
#145572802
#145572782
#145572772
C37×#3312
#155337