Finite Group Databasebeta

← #17993288

Subgroups — #17993288

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#14558081C211yesmaximal, characteristic
2#14557589C211yesmaximal, characteristic, complemented
3C4⋊C8×D37C211yesmaximal, characteristic, complemented
4#14557281C211yesmaximal, characteristic, complemented
5#14557281C211yesmaximal, characteristic, complemented
6#14557277C211yesmaximal, characteristic, complemented
7C37×#331C211yesmaximal, characteristic, complemented
8C2×#10596964C412yes—
9C2×C8×D37—21no—
10#11924536C2211yescharacteristic
11#11924523C412yes—
12#11924507—21no—
13#11924507—21no—
14D4×Dic37—21no—
15D4×Dic37—21no—
16C42×D37C2211yescharacteristic
17C4⋊#64436C2211yescharacteristic
18C4⋊#64436C2211yescharacteristic
19#11924465—21no—
20#11924448—21no—
21#11924446—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—44no—
31C2×C4×D37C2×C411yescharacteristic
32C2×C4×D37D411yescharacteristic
33C2×C4×D37D411yescharacteristic
34C2×Dic74C2×C412yes—
35C2×C8×C37—21no—
36C2×C8×C37—21no—
37C42×C37C2311yescharacteristic
38C22⋊Dic37—22no—
39C22⋊Dic37—22no—
40C4⋊Dic37—21no—
41C4⋊Dic37—21no—
42C4×Dic37C2×C411yescharacteristic
43C4×Dic37D411yescharacteristic
44C4×Dic37D411yescharacteristic
45C2×#64436—21no—
46C2×#64436—21no—
47C8×D37—42no—
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—22no—
65C4×D37—21no—
66C4×D37—21no—
67C4×D37—21no—
68C4×D37—21no—
69Dic74—42no—
70C8×C37—41no—
71C8×C37—41no—
72#64436—41no—
73#64436—41no—
74C22×C37—42no—
75C22×C37—42no—
76C22×C37—42no—
77C22×C37C2×C22⋊C411yescharacteristic
78C2×D37—21no—
79C2×D37—21no—
80C2×D37#10012yes—
81C4×C37—21no—
82C4×C37#13511yescharacteristic
83C4×C37#13511yescharacteristic
84C4×C37AGL(1,ℤ/8)11yescharacteristic
85C4×C37#13711yescharacteristic
86Dic37—21no—
87Dic37—21no—
88Dic37—21no—
89Dic37—42no—
90#1551—371nomaximal, Sylow
91C2×C37—82no—
92C2×C37C2×#10011yescharacteristic
93C2×C37#41611yescharacteristic
94C2×C37#41711yescharacteristic
95D37—22no—
96#532—371no—
97#432—371no—
98C2×C4⋊C8—371no—
99#333—371no—
100#333—371no—
101#331—371no—
102#331D3711yescharacteristic, complemented
103C37#155111yescharacteristic, complemented, Sylow
104C2×#41—372no—
105C22×C8—741no—
106C4⋊Q8—371no—
107#127C2×D3711yescharacteristic
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×Q8—372no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—742no—
126C2×D4C4×D3712yes—
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—741no—
137C4⋊C4—741no—
138C22⋊C4—742no—
139C22⋊C4—742no—
140C42—371no—
141C42—371no—
142C42—371no—
143C42C22×D3711yescharacteristic
144C23—22no—
145C23—371no—
146Q8—1482no—
147D4—42no—
148D4—41no—
149D4—41no—
150D4—41no—
151D4—41no—
152D4—1484no—
153C2×C4—371no—
154C2×C4—371no—
155C2×C4—371no—
156C2×C4—742no—
157C2×C4—741no—
158C2×C4—741no—
159C2×C4—741no—
160C2×C4—741no—
161C2×C4—742no—
162C2×C4—1484no—
163C2×C4C2×C4×D3711yescharacteristic
164C2×C4D4×D3711yescharacteristic
165C2×C4D4×D3711yescharacteristic
166C8—41no—
167C8—41no—
168C8—1481no—
169C8—1481no—
170C22—42no—
171C22—42no—
172C22—42no—
173C22—372no—
174C22—741no—
175C22—741no—
176C22C22⋊C4×D3711yescharacteristic
177C4—21no—
178C4—741no—
179C4—741no—
180C4—741no—
181C4—1482no—
182C4#1192455511yescharacteristic
183C4#1192455711yescharacteristic
184C4#1192456011yescharacteristic
185C4#1192456511yescharacteristic
186C2—82no—
187C2—742no—
188C2#100×D3711yescharacteristic
189C2#1455752611yescharacteristic
190C2#1455753111yescharacteristic
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#1551
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. C4⋊C8×D37C2semidirect
4. #14557281C2semidirect
5. #14557281C2semidirect
6. #14557277C2semidirect
7. C37×#331C2semidirect
102. #331D37semidirect
103. C37#1551semidirect

Maximal subgroups

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

subgroupindex
#145580812
#145575892
C4⋊C8×D372
#145572812
#145572772
C37×#3312
#155137