Finite Group Databasebeta

← #18005181

Subgroups — #18005181

Order 4736.

368 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 129 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#14558088C211yesmaximal, characteristic
2#14558088C211yesmaximal, characteristic
3#14557936C211yesmaximal, characteristic, complemented
4#14557912C211yesmaximal, characteristic, complemented
5#14557884C211yesmaximal, characteristic, complemented
6#14557773C214yesmaximal
7#14557625C214yesmaximal, complemented
8C4×C8×D37C211yesmaximal, characteristic
9C37×#487C211yesmaximal, characteristic, complemented
10C2×#10596942C2214yes—
11C2×C8×D37C2212yes—
12#11924536C2211yescharacteristic
13#11924536C2211yescharacteristic
14#11924527—21no—
15#11924527—21no—
16#11924516—21no—
17#11924516C2212yes—
18#11924512—21no—
19#11924512C2212yes—
20Q8×Dic37—21no—
21Q8×Dic37C2212yes—
22#11924501—21no—
23#11924501C2212yes—
24#11924494—21no—
25#11924494—21no—
26C42×D37C2211yescharacteristic
27#11924469C2214yes—
28#11924461C2214yes—
29C4×#64436C2211yescharacteristic
30C8×Dic37C2212yes—
31C4⋊Q8×C37C2211yescharacteristic
32C4⋊Q8×C37C2211yescharacteristic
33#103×C37C2214yes—
34C4×C8×C37C2211yescharacteristic
35C2×Q8×C37—21no—
36C2×Q8×C37C2312yes—
37C2×C4×D37D411yescharacteristic
38C2×C4×D37D411yescharacteristic
39C2×C4×D37C2311yescharacteristic
40C2×Dic74—21no—
41C2×Dic74C2312yes—
42C2×C8×C37C2312yes—
43C4⋊C4×C37—21no—
44C4⋊C4×C37—21no—
45C4⋊C4×C37—21no—
46C4⋊C4×C37C2312yes—
47C42×C37C2311yescharacteristic
48#10596942—28no—
49#10596938—22no—
50#10596938—22no—
51C4⋊Dic37—21no—
52C4⋊Dic37—21no—
53C4⋊Dic37—21no—
54C4⋊Dic37—22no—
55C4⋊Dic37—22no—
56C4⋊Dic37C2312yes—
57#10596936—22no—
58#10596936—22no—
59C4×Dic37—22no—
60C4×Dic37—22no—
61C4×Dic37D411yescharacteristic
62C4×Dic37D411yescharacteristic
63C4×Dic37C2311yescharacteristic
64C2×#64436C2312yes—
65C8×D37—24no—
66C22×D37C2×D411yescharacteristic
67Q8×C37—24no—
68Q8×C37—42no—
69C2×C4×C37—22no—
70C2×C4×C37—22no—
71C2×C4×C37C2×D411yescharacteristic
72C2×C4×C37C2×D411yescharacteristic
73C2×C4×C37C2411yescharacteristic
74C2×Dic37—22no—
75C2×Dic37—22no—
76C2×Dic37C2×D411yescharacteristic
77C2×Dic37C2×D411yescharacteristic
78C2×Dic37C2×D411yescharacteristic
79C4×D37—22no—
80C4×D37—22no—
81C4×D37Q1614yescomplemented
82Dic74—24no—
83Dic74—42no—
84C8×C37—22no—
85#64436#4114yes—
86C22×C37C22×D411yescharacteristic
87C2×D37—21no—
88C2×D37—21no—
89C2×D37C2×Q1612yes—
90C4×C37—42no—
91C4×C37—42no—
92C4×C37C2×Q1612yes—
93C4×C37#13512yes—
94C4×C37C2×#4112yes—
95Dic37—21no—
96Dic37—21no—
97Dic37—42no—
98Dic37—42no—
99Dic37C2×Q1612yes—
100#3170—371nomaximal, Sylow
101C2×C37#53211yescharacteristic
102C2×C37C22×Q1611yescharacteristic
103C2×C37C2×#13511yescharacteristic
104D37—22no—
105#533—371no—
106#533—371no—
107#500—371no—
108#494—371no—
109#487—371no—
110#487D3711yescharacteristic, complemented
111#467—374no—
112C4×Q16—374no—
113C2×C4×C8—371no—
114C37#317011yescharacteristic, complemented, Sylow
115C2×Q16—374no—
116C22×C8—372no—
117C4⋊Q8—371no—
118C4⋊Q8—371no—
119C4⋊Q8C2×D3711yescharacteristic
120C4⋊Q8C2×D3711yescharacteristic
121#125—741no—
122#125—741no—
123C22⋊Q8—372no—
124C22⋊Q8—372no—
125C22⋊Q8—741no—
126C22⋊Q8—741no—
127C4×Q8—372no—
128C4×Q8—372no—
129C4×Q8—741no—
130C4×Q8—741no—
131#117—741no—
132#117—741no—
133C2×C42—371no—
134#107—374no—
135#103—374no—
136#103C2×D3714yes—
137C4×C8—372no—
138C4×C8—371no—
139C4×C8C2×D3711yescharacteristic
140C2×Q8—21no—
141C2×Q8—372no—
142C2×Q8—741no—
143C2×Q8C22×D3712yes—
144C22×C4—371no—
145C22×C4—371no—
146C22×C4—371no—
147Q16—748no—
148C2×C8—372no—
149C2×C8—744no—
150C2×C8C22×D3712yes—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—21no—
154C4⋊C4—372no—
155C4⋊C4—742no—
156C4⋊C4—742no—
157C4⋊C4—742no—
158C4⋊C4—742no—
159C4⋊C4—741no—
160C4⋊C4—741no—
161C4⋊C4—741no—
162C4⋊C4C22×D3712yes—
163C22⋊C4—742no—
164C22⋊C4—742no—
165C42—371no—
166C42—371no—
167C42—371no—
168C42—742no—
169C42—742no—
170C42C22×D3711yescharacteristic
171C23—371no—
172Q8—24no—
173Q8—42no—
174Q8—744no—
175Q8—1482no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—371no—
179C2×C4—374no—
180C2×C4—371no—
181C2×C4—371no—
182C2×C4—742no—
183C2×C4—742no—
184C2×C4—742no—
185C2×C4—742no—
186C2×C4D4×D3711yescharacteristic
187C2×C4D4×D3711yescharacteristic
188C2×C4C23×D3711yescharacteristic
189C8—22no—
190C8—374no—
191C22—372no—
192C22—741no—
193C22—741no—
194C22C2×D4×D3711yescharacteristic
195C4—42no—
196C4—42no—
197C4—372no—
198C4—741no—
199C4—741no—
200C4—1482no—
201C4—1482no—
202C4Q16×D3712yes—
203C4#1192455712yes—
204C4#41×D3712yes—
205C2—742no—
206C2#1455808211yescharacteristic
207C2C2×Q16×D3711yescharacteristic
208C2C2×#1192455711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#487C2
socleC22×C37C22×D4
prime radicalC22×D37C2×D4
hypercenter#487D37
hypocenterC37#3170
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #14557936C2semidirect
4. #14557912C2semidirect
5. #14557884C2semidirect
7. #14557625C2semidirect
9. C37×#487C2semidirect
81. C4×D37Q16semidirect
110. #487D37semidirect
114. C37#3170semidirect

Maximal subgroups

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

subgroupindex
#145580882
#145579362
#145579122
#145578842
#145577732
#145576252
C4×C8×D372
C37×#4872
#317037