Finite Group Databasebeta

← #18004848

Subgroups — #18004848

Order 4736.

394 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 125 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#14558145C211yesmaximal, characteristic, complemented
2#14557874C212yesmaximal, complemented
3#14557833C212yesmaximal, complemented
4#14557738C212yesmaximal, complemented
5#14557684C212yesmaximal
6#14557633C212yesmaximal, complemented
7C4×#10596940C212yesmaximal, complemented
8#14557594C211yesmaximal, characteristic, complemented
9C37×#518C211yesmaximal, characteristic
10C2×#10596940C2212yes—
11C2×#10596940C2212yes—
12#11924536C2211yescharacteristic, complemented
13#11924529—22no—
14#11924528C2211yescharacteristic, complemented
15#11924526—22no—
16#11924515C2212yes—
17C4×Dic74C2212yescomplemented
18#11924469C2212yescomplemented
19#11924467C2212yescomplemented
20C4⋊#64436C2212yescomplemented
21#11924459C2212yescomplemented
22#11924459C2212yescomplemented
23#11924457C2212yes—
24#11924457C2212yes—
25C22⋊#64436C2212yes—
26#11924447C2211yescharacteristic, complemented
27C4×#64436C2211yescharacteristic, complemented
28C22×D4×C37C2211yescharacteristic
29C4×D4×C37—22no—
30C4×D4×C37C2212yes—
31C4×D4×C37C2212yes—
32#117×C37C2211yescharacteristic
33#117×C37C2211yescharacteristic
34C2×C22⋊C4×C37—22no—
35C24×C37—21no—
36C2×D4×C37—24no—
37C2×D4×C37—21no—
38C2×D4×C37C2312yes—
39C22×C4×C37—22no—
40C22×C4×C37—22no—
41C22×C4×C37C2311yescharacteristic
42C2×Dic74C2312yes—
43C4⋊C4×C37D412yes—
44C4⋊C4×C37C2312yes—
45C22⋊C4×C37—21no—
46C22⋊C4×C37—22no—
47C22⋊C4×C37—22no—
48C22⋊C4×C37D412yes—
49C42×C37—21no—
50C42×C37C2311yescharacteristic
51C42×C37C2311yescharacteristic
52C22⋊Dic37—22no—
53#10596940—24no—
54#10596940—24no—
55C4⋊Dic37—22no—
56C4⋊Dic37C2312yes—
57#10596936—22no—
58#10596936—22no—
59#10596936—22no—
60C4×Dic37—22no—
61C2×#64436C2312yes—
62C2×#64436C2312yes—
63C23×C37—24no—
64C23×C37—22no—
65C23×C37—82no—
66C23×C37C2×D411yescharacteristic
67D4×C37—24no—
68D4×C37—22no—
69D4×C37#4114yes—
70C2×C4×C37—22no—
71C2×C4×C37—22no—
72C2×C4×C37—82no—
73C2×C4×C37—82no—
74C2×C4×C37C2×D412yes—
75C2×C4×C37C2×D411yescharacteristic
76C2×C4×C37C2×D412yes—
77C2×C4×C37C2411yescharacteristic
78C2×Dic37—22no—
79C2×Dic37—22no—
80Dic74—22no—
81Dic74—22no—
82#64436—22no—
83#64436—22no—
84C22×C37—21no—
85C22×C37—24no—
86C22×C37—22no—
87C22×C37—42no—
88C22×C37—42no—
89C22×C37—84no—
90C22×C37C22×D411yescharacteristic
91C4×C37—21no—
92C4×C37—22no—
93C4×C37—22no—
94C4×C37—42no—
95C4×C37C2×#4112yes—
96Dic37—42no—
97Dic37—42no—
98#3123—371nomaximal, Sylow
99C2×C37—41no—
100C2×C37—44no—
101C2×C37#52511yescharacteristic
102C2×C37#57712yes—
103#541—371no—
104#518D3711yescharacteristic
105#485—372no—
106#478—372no—
107#461—372no—
108#450—372no—
109#440—372no—
110C4×SD16—372no—
111#433—371no—
112C37#312311yescharacteristic, complemented, Sylow
113C22×D4C2×D3711yescharacteristic
114C2×SD16—372no—
115C2×SD16—372no—
116C4⋊Q8—371no—
117#126—742no—
118#125—371no—
119#125—742no—
120C22⋊Q8—372no—
121C4×Q8—372no—
122C4×D4—22no—
123C4×D4C2×D3712yes—
124C4×D4C2×D3712yes—
125#117C2×D3711yescharacteristic
126#117C2×D3711yescharacteristic
127C2×C22⋊C4—22no—
128#107—372no—
129#106—372no—
130C4⋊C8—372no—
131#103—372no—
132#103—372no—
133#102—372no—
134#102—372no—
135C22⋊C8—372no—
136#97—371no—
137C4×C8—371no—
138C24—21no—
139C2×Q8—372no—
140C2×D4—24no—
141C2×D4—21no—
142C2×D4C22×D3712yes—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4C22×D3711yescharacteristic
146SD16—744no—
147SD16—744no—
148C2×C8—372no—
149C2×C8—372no—
150C4⋊C4—372no—
151C4⋊C4—742no—
152C4⋊C4—742no—
153C4⋊C4—742no—
154C4⋊C4—742no—
155C4⋊C4C22⋊D3712yes—
156C4⋊C4C22×D3712yes—
157C22⋊C4—21no—
158C22⋊C4—22no—
159C22⋊C4—22no—
160C22⋊C4—742no—
161C22⋊C4C22⋊D3712yes—
162C42—21no—
163C42—742no—
164C42C22×D3711yescharacteristic
165C42C22×D3711yescharacteristic
166C23—24no—
167C23—22no—
168C23—82no—
169C23C2×C22⋊D3711yescharacteristic
170Q8—742no—
171Q8—742no—
172D4—24no—
173D4—22no—
174D4#1059696214yes—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—82no—
178C2×C4—82no—
179C2×C4—742no—
180C2×C4—742no—
181C2×C4C2×C22⋊D3711yescharacteristic
182C2×C4C2×C22⋊D3712yes—
183C2×C4C2×C22⋊D3712yes—
184C2×C4C23×D3711yescharacteristic
185C8—742no—
186C8—742no—
187C22—21no—
188C22—24no—
189C22—22no—
190C22—42no—
191C22—42no—
192C22—84no—
193C22C22×C22⋊D3711yescharacteristic
194C4—21no—
195C4—22no—
196C4—22no—
197C4—42no—
198C4—1482no—
199C4—1482no—
200C4C2×#1059696212yes—
201C2—41no—
202C2—44no—
203C2#1455804411yescharacteristic
204C2#1455834412yes—
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#518C2
socleC22×C37C22×D4
prime radicalC22×D4×C37C22
hypercenter#518D37
hypocenterC37#3123
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #14558145C2semidirect
2. #14557874C2semidirect
3. #14557833C2semidirect
4. #14557738C2semidirect
6. #14557633C2semidirect
7. C4×#10596940C2semidirect
8. #14557594C2semidirect
12. #11924536C22semidirect
14. #11924528C22semidirect
17. C4×Dic74C22semidirect
18. #11924469C22semidirect
19. #11924467C22semidirect
20. C4⋊#64436C22semidirect
21. #11924459C22semidirect
22. #11924459C22semidirect
26. #11924447C22semidirect
27. C4×#64436C22semidirect
112. C37#3123semidirect

Maximal subgroups

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

subgroupindex
#145581452
#145578742
#145578332
#145577382
#145576842
#145576332
C4×#105969402
#145575942
C37×#5182
#312337