Finite Group Databasebeta

← #17993290

Subgroups — #17993290

Order 4736.

252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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
3C4⋊C8×D37C211yesmaximal, characteristic, complemented
4#14557282C211yesmaximal, characteristic, complemented
5#14557276C211yesmaximal, characteristic, complemented
6#14557276C211yesmaximal, characteristic, complemented
7C37×#333C211yesmaximal, characteristic, complemented
8C2×#10596966C412yes—
9C2×C8×D37—21no—
10#11924533C2211yescharacteristic
11#11924525C412yes—
12#11924511—21no—
13#11924511—21no—
14#11924498—21no—
15#11924498—21no—
16C42×D37C2211yescharacteristic
17C4⋊#64436C2211yescharacteristic
18C4⋊#64436C2211yescharacteristic
19#11924465—21no—
20#11924448—21no—
21#11924446—21no—
22C4⋊Q8×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24C4⋊C8×C37C2211yescharacteristic
25C2×Q8×C37C2×C412yes—
26#10596966—44no—
27C2×D148—22no—
28C2×D148—21no—
29C2×D148—21no—
30C2×D148C2×C412yes—
31C2×C4×D37—22no—
32C2×C4×D37C2×C411yescharacteristic
33C2×C4×D37D411yescharacteristic
34C2×C4×D37D411yescharacteristic
35C2×C8×C37—21no—
36C2×C8×C37—21no—
37C4⋊C4×C37—21no—
38C4⋊C4×C37—21no—
39C42×C37C2311yescharacteristic
40#10596938—22no—
41#10596938—22no—
42C4×Dic37C2×C411yescharacteristic
43C4×Dic37D411yescharacteristic
44C4×Dic37D411yescharacteristic
45C2×#64436—21no—
46C2×#64436—21no—
47C8×D37—42no—
48C22×D37—22no—
49C22×D37C22⋊C411yescharacteristic
50Q8×C37—42no—
51C2×C4×C37—22no—
52C2×C4×C37C22×C411yescharacteristic
53C2×C4×C37C2×D411yescharacteristic
54C2×C4×C37C2×D411yescharacteristic
55C2×Dic37C22⋊C411yescharacteristic
56C2×Dic37C22⋊C411yescharacteristic
57C2×Dic37C22⋊C411yescharacteristic
58D148—42no—
59D148—44no—
60D148—41no—
61D148—41no—
62D148—41no—
63D148—41no—
64C4×D37—22no—
65C4×D37—21no—
66C4×D37—21no—
67C4×D37—21no—
68C4×D37—21no—
69C4×D37—44no—
70C8×C37—41no—
71C8×C37—41no—
72#64436—41no—
73#64436—41no—
74C22×C37C2×C22⋊C411yescharacteristic
75C2×D37—21no—
76C2×D37—21no—
77C2×D37—42no—
78C2×D37—42no—
79C2×D37—42no—
80C2×D37#10012yes—
81C4×C37—21no—
82C4×C37—42no—
83C4×C37#13511yescharacteristic
84C4×C37#13511yescharacteristic
85C4×C37AGL(1,ℤ/8)11yescharacteristic
86C4×C37#13711yescharacteristic
87Dic37—21no—
88Dic37—21no—
89Dic37—21no—
90#1551—371nomaximal, Sylow
91C2×C37C2×#10011yescharacteristic
92C2×C37#41611yescharacteristic
93C2×C37#41711yescharacteristic
94D37—22no—
95D37—82no—
96#532—371no—
97#432—371no—
98C2×C4⋊C8—371no—
99#333—371no—
100#333D3711yescharacteristic, complemented
101#331—371no—
102#331—371no—
103C37#155111yescharacteristic, complemented, Sylow
104C2×#41—372no—
105C22×C8—741no—
106C4⋊Q8C2×D3711yescharacteristic
107#127—371no—
108#124—372no—
109#121—741no—
110#121—741no—
111C4×D4—741no—
112C4×D4—741no—
113C2×C42—371no—
114C4⋊C8—371no—
115C4⋊C8—371no—
116C4⋊C8—741no—
117C4⋊C8C2×D3711yescharacteristic
118C4⋊C8C2×D3711yescharacteristic
119C22⋊C8—741no—
120#97—741no—
121#41—1484no—
122C2×Q8C4×D3712yes—
123C2×D4—372no—
124C2×D4—742no—
125C2×D4—741no—
126C2×D4—741no—
127C22×C4—371no—
128C22×C4—371no—
129C22×C4—371no—
130C22×C4—742no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—741no—
134C2×C8—741no—
135C2×C8—1482no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C22⋊C4—742no—
139C22⋊C4—742no—
140C42—371no—
141C42—371no—
142C42—371no—
143C42C22×D3711yescharacteristic
144C23—371no—
145C23—742no—
146Q8—42no—
147D4—1482no—
148D4—1484no—
149D4—1481no—
150D4—1481no—
151D4—1481no—
152D4—1481no—
153C2×C4—22no—
154C2×C4—371no—
155C2×C4—371no—
156C2×C4—371no—
157C2×C4—742no—
158C2×C4—741no—
159C2×C4—741no—
160C2×C4—741no—
161C2×C4—741no—
162C2×C4—1484no—
163C2×C4C2×C4×D3711yescharacteristic
164C2×C4D4×D3711yescharacteristic
165C2×C4D4×D3711yescharacteristic
166C8—41no—
167C8—41no—
168C8—1481no—
169C8—1481no—
170C22—372no—
171C22—741no—
172C22—741no—
173C22—1482no—
174C22—1482no—
175C22—1482no—
176C22C22⋊C4×D3711yescharacteristic
177C4—21no—
178C4—42no—
179C4—741no—
180C4—741no—
181C4—741no—
182C4#1192455711yescharacteristic
183C4#1192455911yescharacteristic
184C4#1192456311yescharacteristic
185C4#1192456811yescharacteristic
186C2—2962no—
187C2—742no—
188C2#100×D3711yescharacteristic
189C2#1455752811yescharacteristic
190C2#1455753311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC2×C4×C37C22×C4
FrattiniC42C22×D37
FittingC37×#333C2
socleC22×C37C2×C22⋊C4
prime radical#14558084C2
cosocleC42×C37C23
hypercenter#333D37
hypocenterC37#1551
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #14557589C2semidirect
3. C4⋊C8×D37C2semidirect
4. #14557282C2semidirect
5. #14557276C2semidirect
6. #14557276C2semidirect
7. C37×#333C2semidirect
100. #333D37semidirect
103. C37#1551semidirect

Maximal subgroups

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

subgroupindex
#145580842
#145575892
C4⋊C8×D372
#145572822
#145572762
C37×#3332
#155137