Finite Group Databasebeta

← #18006062

Subgroups — #18006062

Order 4736.

346 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 109 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#14558156C212yesmaximal, complemented
2#14557822C212yesmaximal, complemented
3#14557816C212yesmaximal, complemented
4#14557786C211yesmaximal, characteristic
5#14557764C212yesmaximal, complemented
6#14557757C212yesmaximal, complemented
7#14557751C212yesmaximal, complemented
8#14557561C211yesmaximal, characteristic, complemented
9C37×#470C211yesmaximal, characteristic, complemented
10C2×#10596941C2212yes—
11C2×D296C2211yescharacteristic
12C22×#64436C2211yescharacteristic
13#11924535C2212yes—
14#11924531—22no—
15#11924525C2212yes—
16#11924522—22no—
17#11924518—22no—
18#11924516—22no—
19#11924510C2212yes—
20Q8×Dic37C2212yes—
21#11924498C2212yes—
22#11924495C2211yescharacteristic
23#11924468C2211yescharacteristic
24#11924467C2212yes—
25#11924465C2212yes—
26#11924465C2212yes—
27#11924460C2212yes—
28#11924458C2212yes—
29#11924456C2212yes—
30C2×Q16×C37C2211yescharacteristic
31C2×M16×C37C2211yescharacteristic
32C22⋊Q8×C37C2212yes—
33#106×C37C2211yescharacteristic
34#103×C37C2212yes—
35C2×Q8×C37C2312yes—
36C22×C4×C37C2311yescharacteristic
37C2×C22⋊D37—22no—
38C2×D148C2312yes—
39C2×C4×D37—22no—
40C2×Dic74—22no—
41Q16×C37—41no—
42M16×C37—41no—
43C2×C8×C37C2311yescharacteristic
44C2×C8×C37C2311yescharacteristic
45C4⋊C4×C37—22no—
46C4⋊C4×C37C2312yes—
47C22⋊C4×C37—22no—
48C22⋊Dic37D411yescharacteristic
49C22⋊Dic37D411yescharacteristic
50#10596941—42no—
51#10596938—22no—
52#10596938—22no—
53#10596938—22no—
54#10596938—22no—
55C4⋊Dic37—22no—
56C4⋊Dic37D412yes—
57C4⋊Dic37C2312yes—
58#10596936—22no—
59C4×Dic37—22no—
60C4×Dic37C2312yes—
61C2×#64436—41no—
62C2×#64436C2312yes—
63D296—41no—
64C23×C37C2×D411yescharacteristic
65C22×D37—22no—
66Q8×C37—22no—
67Q8×C37—22no—
68C2×C4×C37—21no—
69C2×C4×C37—21no—
70C2×C4×C37—22no—
71C2×C4×C37—22no—
72C2×C4×C37C2×D411yescharacteristic
73C2×C4×C37C2411yescharacteristic
74C22⋊D37—82no—
75C2×Dic37—22no—
76C2×Dic37C2×D412yes—
77C2×Dic37C2×D412yes—
78D148—22no—
79D148—22no—
80C4×D37—82no—
81Dic74—82no—
82C8×C37—21no—
83C8×C37—21no—
84#64436—22no—
85C22×C37—21no—
86C22×C37—22no—
87C22×C37C22×D411yescharacteristic
88C2×D37—42no—
89C2×D37—42no—
90C2×D37—42no—
91C4×C37—21no—
92C4×C37—42no—
93C4×C37—42no—
94C4×C37H(5,𝔽2)11yescharacteristic
95C4×C372−1+411yescharacteristic
96Dic37—22no—
97Dic37—22no—
98Dic37—42no—
99#3263—371nomaximal, Sylow
100C2×C37—41no—
101C2×C37#53711yescharacteristic
102C2×C37#57712yes—
103D37—82no—
104#542—372no—
105#476—372no—
106#475—372no—
107#470D3711yescharacteristic, complemented
108#469—371no—
109#465—372no—
110#464—372no—
111#463—372no—
112#424—371no—
113C37#326311yescharacteristic, complemented, Sylow
114C2×Q16C2×D3711yescharacteristic
115C2×SD16—372no—
116C2×D8—371no—
117C2×M16C2×D3711yescharacteristic
118C22×C8—371no—
119C4⋊Q8—372no—
120#126—742no—
121#124—372no—
122#124—742no—
123#123—742no—
124C22⋊Q8—742no—
125C22⋊Q8C2×D3712yes—
126#121—372no—
127C4×Q8—372no—
128C4×D4—372no—
129#117—371no—
130#106—371no—
131#106—372no—
132#106C2×D3711yescharacteristic
133C4⋊C8—372no—
134C4⋊C8—372no—
135#103—372no—
136#103C2×D3712yes—
137#102—372no—
138#102—372no—
139C2×Q8—742no—
140C2×Q8C22×D3712yes—
141C2×D4—372no—
142C2×D4—742no—
143C22×C4—742no—
144C22×C4C22×D3711yescharacteristic
145Q16—41no—
146SD16—1482no—
147D8—1481no—
148M16—41no—
149C2×C8—372no—
150C2×C8—1481no—
151C2×C8C22×D3711yescharacteristic
152C2×C8C22×D3711yescharacteristic
153C4⋊C4—22no—
154C4⋊C4—372no—
155C4⋊C4—372no—
156C4⋊C4—742no—
157C4⋊C4—742no—
158C4⋊C4C22×D3712yes—
159C22⋊C4—22no—
160C22⋊C4—371no—
161C22⋊C4—371no—
162C22⋊C4—742no—
163C22⋊C4—742no—
164C22⋊C4—742no—
165C22⋊C4—742no—
166C42—372no—
167C42—742no—
168C23—742no—
169C23D4×D3711yescharacteristic
170Q8—22no—
171Q8—22no—
172Q8—2962no—
173D4—2962no—
174D4—742no—
175D4—742no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—372no—
181C2×C4—372no—
182C2×C4—2962no—
183C2×C4—742no—
184C2×C4D4×D3711yescharacteristic
185C2×C4C23×D3711yescharacteristic
186C8—21no—
187C8—21no—
188C8—742no—
189C22—22no—
190C22—21no—
191C22—1482no—
192C22—1482no—
193C22—1482no—
194C22C2×D4×D3711yescharacteristic
195C4—21no—
196C4—42no—
197C4—42no—
198C4—742no—
199C4—742no—
200C4—1482no—
201C4#1192458111yescharacteristic
202C4#1192458311yescharacteristic
203C2—41no—
204C2—2962no—
205C2#1455811011yescharacteristic
206C2#1455834212yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#470C2
socleC22×C37C22×D4
prime radical#14557786C2
hypercenter#470D37
hypocenterC37#3263
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #14558156C2semidirect
2. #14557822C2semidirect
3. #14557816C2semidirect
5. #14557764C2semidirect
6. #14557757C2semidirect
7. #14557751C2semidirect
8. #14557561C2semidirect
9. C37×#470C2semidirect
107. #470D37semidirect
113. C37#3263semidirect

Maximal subgroups

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

subgroupindex
#145581562
#145578222
#145578162
#145577862
#145577642
#145577572
#145577512
#145575612
C37×#4702
#326337