Finite Group Databasebeta

← #18004834

Subgroups — #18004834

Order 4736.

418 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 121 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#14558007C211yesmaximal, characteristic, complemented
2#14557854C212yesmaximal, complemented
3#14557830C212yesmaximal, complemented
4#14557725C212yesmaximal, complemented
5#14557666C212yesmaximal, complemented
6#14557643C212yesmaximal, complemented
7C4×#10596939C212yesmaximal, complemented
8#14557594C211yesmaximal, characteristic, complemented
9C37×#540C211yesmaximal, characteristic, complemented
10C22×D148C2211yescharacteristic
11C2×#10596939C2212yes—
12C2×#10596939C2212yes—
13C4×D148C2212yes—
14C4×D148C2212yes—
15#11924498—22no—
16#11924495C2211yescharacteristic
17C22⋊C4×D37—22no—
18#11924469C2212yescomplemented
19#11924467C2212yescomplemented
20C4⋊#64436C2212yescomplemented
21#11924457C2212yescomplemented
22#11924457C2212yescomplemented
23#11924456C2212yes—
24#11924456C2212yes—
25C22⋊#64436C2212yes—
26#11924447C2211yescharacteristic, complemented
27C4×#64436C2211yescharacteristic, complemented
28#127×C37C2211yescharacteristic, complemented
29#125×C37C2211yescharacteristic, complemented
30#123×C37—22no—
31#121×C37—22no—
32#121×C37C2212yes—
33C4×D4×C37C2212yescomplemented
34#117×C37C2211yescharacteristic
35C23×D37—21no—
36C2×D4×C37—22no—
37C2×D4×C37—22no—
38C2×D4×C37C2312yes—
39C22×C4×C37—22no—
40C22×C4×C37C2311yescharacteristic
41C2×D148—21no—
42C2×D148—24no—
43C2×D148C2312yes—
44C2×C4×D37—22no—
45C2×C4×D37—22no—
46C4⋊C4×C37—22no—
47C4⋊C4×C37D412yes—
48C4⋊C4×C37C2312yes—
49C22⋊C4×C37—22no—
50C22⋊C4×C37—22no—
51C22⋊C4×C37D412yes—
52C42×C37C2311yescharacteristic
53C42×C37C2311yescharacteristic
54C22⋊Dic37—21no—
55#10596939—24no—
56#10596939—24no—
57#10596938—22no—
58#10596938—22no—
59C4⋊Dic37C2312yes—
60C4×Dic37—21no—
61C2×#64436C2312yes—
62C2×#64436C2312yes—
63C23×C37—22no—
64C23×C37C2×D411yescharacteristic
65C22×D37—22no—
66C22×D37—24no—
67C22×D37—82no—
68D4×C37—22no—
69D4×C37—22no—
70D4×C37—82no—
71D4×C37—82no—
72C2×C4×C37—22no—
73C2×C4×C37—22no—
74C2×C4×C37—82no—
75C2×C4×C37C2×D411yescharacteristic
76C2×C4×C37C2×D412yes—
77C2×C4×C37C2×D412yes—
78C2×C4×C37C2411yescharacteristic
79C2×Dic37—22no—
80D148—24no—
81D148—22no—
82D148#4114yes—
83C4×D37—82no—
84C4×D37—82no—
85#64436—22no—
86#64436—22no—
87C22×C37—21no—
88C22×C37—22no—
89C22×C37—42no—
90C22×C37—42no—
91C22×C37—42no—
92C22×C37C22×D411yescharacteristic
93C2×D37—24no—
94C2×D37—42no—
95C2×D37—42no—
96C2×D37—84no—
97C4×C37—21no—
98C4×C37—22no—
99C4×C37—22no—
100C4×C37—42no—
101C4×C37C2×#4112yes—
102Dic37—42no—
103#3122—371nomaximal, Sylow
104C2×C37—41no—
105C2×C37—82no—
106C2×C37#52511yescharacteristic
107C2×C37#57612yes—
108D37—44no—
109#540D3711yescharacteristic, complemented
110#518—371no—
111#482—372no—
112#478—372no—
113#459—372no—
114#447—372no—
115#442—372no—
116C4×D8—372no—
117#433—371no—
118C37#312211yescharacteristic, complemented, Sylow
119C22×D4—371no—
120C2×D8—372no—
121C2×D8—372no—
122#127C2×D3711yescharacteristic, complemented
123#125C2×D3711yescharacteristic, complemented
124#123—22no—
125#121—22no—
126#121C2×D3712yes—
127C4×D4—372no—
128C4×D4—372no—
129C4×D4—742no—
130C4×D4C2×D3712yescomplemented
131#117—371no—
132#117C2×D3711yescharacteristic
133C2×C22⋊C4—742no—
134#107—372no—
135#106—372no—
136C4⋊C8—372no—
137#102—372no—
138#102—372no—
139#102—372no—
140#102—372no—
141C22⋊C8—372no—
142#97—371no—
143C4×C8—371no—
144C24—741no—
145C2×D4—22no—
146C2×D4—22no—
147C2×D4—372no—
148C2×D4—744no—
149C2×D4—741no—
150C2×D4C22×D3712yes—
151C22×C4—22no—
152C22×C4—742no—
153C22×C4—742no—
154C22×C4C22×D3711yescharacteristic
155D8—744no—
156D8—744no—
157C2×C8—372no—
158C2×C8—372no—
159C4⋊C4—22no—
160C4⋊C4—372no—
161C4⋊C4C22⋊D3712yes—
162C4⋊C4C22×D3712yes—
163C22⋊C4—22no—
164C22⋊C4—22no—
165C22⋊C4—741no—
166C22⋊C4—742no—
167C22⋊C4—742no—
168C22⋊C4C22⋊D3712yes—
169C42—741no—
170C42C22×D3711yescharacteristic
171C42C22×D3711yescharacteristic
172C23—22no—
173C23—2962no—
174C23—744no—
175C23—742no—
176C23C2×C22⋊D3711yescharacteristic
177D4—22no—
178D4—22no—
179D4—82no—
180D4—82no—
181D4—374no—
182D4—744no—
183D4—742no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—2962no—
188C2×C4—2962no—
189C2×C4—742no—
190C2×C4C2×C22⋊D3711yescharacteristic
191C2×C4C2×C22⋊D3712yes—
192C2×C4C2×C22⋊D3712yes—
193C2×C4C23×D3711yescharacteristic
194C8—742no—
195C8—742no—
196C22—21no—
197C22—22no—
198C22—42no—
199C22—42no—
200C22—42no—
201C22—2964no—
202C22—744no—
203C22—1482no—
204C22—1482no—
205C22C22×C22⋊D3711yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—1482no—
211C4#41×D3712yes—
212C2—41no—
213C2—82no—
214C2—1484no—
215C2#1455804011yescharacteristic
216C2#1455833612yes—
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#540C2
socleC22×C37C22×D4
hypercenter#540D37
hypocenterC37#3122
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #14558007C2semidirect
2. #14557854C2semidirect
3. #14557830C2semidirect
4. #14557725C2semidirect
5. #14557666C2semidirect
6. #14557643C2semidirect
7. C4×#10596939C2semidirect
8. #14557594C2semidirect
9. C37×#540C2semidirect
18. #11924469C22semidirect
19. #11924467C22semidirect
20. C4⋊#64436C22semidirect
21. #11924457C22semidirect
22. #11924457C22semidirect
26. #11924447C22semidirect
27. C4×#64436C22semidirect
28. #127×C37C22semidirect
29. #125×C37C22semidirect
33. C4×D4×C37C22semidirect
109. #540D37semidirect
118. C37#3122semidirect
122. #127C2×D37semidirect
123. #125C2×D37semidirect
130. C4×D4C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145580072
#145578542
#145578302
#145577252
#145576662
#145576432
C4×#105969392
#145575942
C37×#5402
#312237