Finite Group Databasebeta

← #18004072

Subgroups — #18004072

Order 4736.

584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#11924562C212yesmaximal, complemented
2C4×#10596962C211yesmaximal, characteristic, complemented
3#14557730C214yesmaximal, complemented
4#14557725C214yesmaximal, complemented
5#14557557C211yesmaximal, characteristic, complemented
6#14557538C212yesmaximal, complemented
7C2×#127×C37C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9#11924562—28no—
10C2×#10596940C2214yescomplemented
11C2×#10596939C2214yescomplemented
12C2×#10596934C2212yes—
13C4×Dic74C2212yescomplemented
14C4×D148C2212yescomplemented
15C4×C22⋊D37—22no—
16#11924495C2211yescharacteristic
17#11924493—21no—
18C42×D37—21no—
19C4⋊#64436C2214yescomplemented
20#11924457C2218yescomplemented
21C22×D4×C37—22no—
22C22×D4×C37C2212yes—
23#127×C37—21no—
24#127×C37—21no—
25#127×C37C2214yes—
26C2×C42×C37C2211yescharacteristic
27C24×C37—22no—
28C2×D4×C37—24no—
29C2×D4×C37—22no—
30C2×D4×C37—24no—
31C2×D4×C37—24no—
32C2×D4×C37—24no—
33C2×D4×C37—48no—
34C2×D4×C37C2314yes—
35C22×C4×C37D412yes—
36C22×C4×C37C2311yescharacteristic
37C2×C22⋊D37—21no—
38#10596962—22no—
39#10596962D414yescomplemented
40C2×D148C2311yescharacteristic
41C2×C4×D37—21no—
42C2×C4×D37—22no—
43C2×Dic74C2311yescharacteristic
44C42×C37D411yescharacteristic
45C42×C37D411yescharacteristic
46C42×C37C2312yes—
47C22⋊Dic37—21no—
48#10596940—28no—
49#10596939—28no—
50#10596938—22no—
51C4⋊Dic37C2312yes—
52#10596936—22no—
53C4×Dic37—21no—
54C4×Dic37—22no—
55#10596934—24no—
56C2×#64436C2314yes—
57C23×C37—24no—
58C23×C37—48no—
59C23×C37—44no—
60C23×C37C2×D411yescharacteristic
61C22×D37—21no—
62D4×C37—24no—
63D4×C37—24no—
64D4×C37—48no—
65D4×C37—44no—
66D4×C37—48no—
67C2×C4×C37—24no—
68C2×C4×C37C2×D412yes—
69C2×C4×C37C2×D412yes—
70C2×C4×C37C2×D411yescharacteristic
71C2×C4×C37C2×D412yes—
72C2×C4×C37#4112yes—
73C2×C4×C37C2411yescharacteristic
74C22⋊D37—24no—
75C2×Dic37—21no—
76C2×Dic37—22no—
77D148—21no—
78D148C2×D412yescomplemented
79C4×D37—24no—
80C4×D37—44no—
81Dic74—21no—
82Dic74C2×D412yescomplemented
83#64436—24no—
84C22×C37—22no—
85C22×C37—44no—
86C22×C37—48no—
87C22×C37—88no—
88C22×C37#12112yes—
89C22×C37C22×D411yescharacteristic
90C2×D37—22no—
91C2×D37—42no—
92C4×C37—22no—
93C4×C37#12112yes—
94C4×C37AGL(1,ℤ/8)14yescomplemented
95C4×C37C22×D411yescharacteristic
96C4×C37C2×#4111yescharacteristic
97Dic37—22no—
98Dic37—42no—
99#3038—371nomaximal, Sylow
100C2×C37—22no—
101C2×C37—84no—
102C2×C37C2×#12111yescharacteristic
103C2×C37C2×AGL(1,ℤ/8)12yes—
104D37—42no—
105C2×AGL(1,ℤ/8)—372no—
106C2×#127D3711yescharacteristic, complemented
107C4×#41—371no—
108#460—374no—
109#459—374no—
110#423—371no—
111#418—372no—
112C37#303811yescharacteristic, complemented, Sylow
113C2×#41—371no—
114C22×D4—22no—
115C22×D4C2×D3712yes—
116AGL(1,ℤ/8)—748no—
117C2×SD16—374no—
118C2×D8—374no—
119C2×M16—372no—
120#127—21no—
121#127—21no—
122#127C2×D3714yes—
123C4×Q8—372no—
124C4×D4—372no—
125C4×D4—742no—
126#117—371no—
127#117—741no—
128C2×C42—741no—
129C2×C42C2×D3711yescharacteristic
130C4⋊C8—374no—
131#102—378no—
132C24—22no—
133#41—374no—
134#41—742no—
135C2×Q8—371no—
136C2×D4—24no—
137C2×D4—24no—
138C2×D4—22no—
139C2×D4—24no—
140C2×D4—24no—
141C2×D4—48no—
142C2×D4—371no—
143C2×D4—741no—
144C2×D4C22×D3714yes—
145C22×C4—741no—
146C22×C4—742no—
147C22×C4C22⋊D3712yes—
148C22×C4C22×D3711yescharacteristic
149SD16—748no—
150D8—748no—
151M16—744no—
152C2×C8—374no—
153C4⋊C4—372no—
154C4⋊C4—742no—
155C22⋊C4—741no—
156C22⋊C4—742no—
157C42—741no—
158C42—742no—
159C42C22⋊D3711yescharacteristic
160C42C22⋊D3711yescharacteristic
161C42C22×D3712yes—
162C23—24no—
163C23—48no—
164C23—44no—
165C23—741no—
166C23C2×C22⋊D3711yescharacteristic
167Q8—372no—
168Q8—741no—
169D4—24no—
170D4—24no—
171D4—48no—
172D4—44no—
173D4—48no—
174D4—372no—
175D4—744no—
176D4—741no—
177C2×C4—24no—
178C2×C4—741no—
179C2×C4—744no—
180C2×C4—742no—
181C2×C4—1484no—
182C2×C4D4×D3712yes—
183C2×C4#1059696412yes—
184C2×C4C2×C22⋊D3712yes—
185C2×C4C2×C22⋊D3711yescharacteristic
186C2×C4C2×C22⋊D3712yes—
187C2×C4C23×D3711yescharacteristic
188C8—744no—
189C22—22no—
190C22—44no—
191C22—48no—
192C22—88no—
193C22—742no—
194C22—1482no—
195C22#1192450712yes—
196C22C22×C22⋊D3711yescharacteristic
197C4—22no—
198C4—742no—
199C4—1482no—
200C4#1192450712yes—
201C4#1192456214yescomplemented
202C4C2×D4×D3711yescharacteristic
203C4C2×#1059696411yescharacteristic
204C2—22no—
205C2—84no—
206C2—1482no—
207C2C2×#1192450711yescharacteristic
208C2C2×#1192456212yes—
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×#127×C37C2
socleC22×C37C22×D4
hypercenterC2×#127D37
hypocenterC37#3038
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×#11924562C2semidirect
2. C4×#10596962C2semidirect
3. #14557730C2semidirect
4. #14557725C2semidirect
5. #14557557C2semidirect
6. #14557538C2semidirect
7. C2×#127×C37C2semidirect
10. C2×#10596940C22semidirect
11. C2×#10596939C22semidirect
13. C4×Dic74C22semidirect
14. C4×D148C22semidirect
19. C4⋊#64436C22semidirect
20. #11924457C22semidirect
39. #10596962D4semidirect
78. D148C2×D4semidirect
82. Dic74C2×D4semidirect
94. C4×C37AGL(1,ℤ/8)semidirect
106. C2×#127D37semidirect
112. C37#3038semidirect
201. C4#11924562semidirect

Maximal subgroups

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

subgroupindex
C2×#119245622
C4×#105969622
#145577302
#145577252
#145575572
#145575382
C2×#127×C372
#303837