Finite Group Databasebeta

← #18004843

Subgroups — #18004843

Order 4736.

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

normal subgroups only

This group has 394 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
2#14557871C212yesmaximal, complemented
3#14557830C212yesmaximal, complemented
4#14557735C212yesmaximal, complemented
5#14557683C212yesmaximal
6#14557631C212yesmaximal, complemented
7C4×#10596941C212yesmaximal, complemented
8#14557594C211yesmaximal, characteristic, complemented
9C37×#541C211yesmaximal, characteristic, complemented
10C22×D148C2211yescharacteristic
11C2×#10596941C2212yes—
12C2×#10596941C2212yes—
13C4×D148C2212yes—
14C4×D148C2212yes—
15#11924498—22no—
16#11924495C2211yescharacteristic
17C22⋊C4×D37—22no—
18#11924469C2212yescomplemented
19#11924467C2212yescomplemented
20C4⋊#64436C2212yescomplemented
21#11924460C2212yescomplemented
22#11924460C2212yescomplemented
23#11924456C2212yes—
24#11924456C2212yes—
25C22⋊#64436C2212yes—
26#11924447C2211yescharacteristic, complemented
27C4×#64436C2211yescharacteristic, complemented
28C4⋊Q8×C37C2211yescharacteristic, complemented
29#126×C37—22no—
30#125×C37—22no—
31#125×C37C2211yescharacteristic, complemented
32C22⋊Q8×C37C2212yes—
33C4×Q8×C37C2212yescomplemented
34#117×C37C2211yescharacteristic
35C23×D37—21no—
36C2×Q8×C37C2312yes—
37C22×C4×C37C2311yescharacteristic
38C2×D148—21no—
39C2×D148—24no—
40C2×D148C2312yes—
41C2×C4×D37—22no—
42C2×C4×D37—22no—
43C4⋊C4×C37—22no—
44C4⋊C4×C37—22no—
45C4⋊C4×C37—22no—
46C4⋊C4×C37—22no—
47C4⋊C4×C37D412yes—
48C4⋊C4×C37C2312yes—
49C22⋊C4×C37—22no—
50C22⋊C4×C37D412yes—
51C42×C37—22no—
52C42×C37C2311yescharacteristic
53C42×C37C2311yescharacteristic
54C22⋊Dic37—21no—
55#10596941—24no—
56#10596941—24no—
57#10596938—22no—
58#10596938—22no—
59C4⋊Dic37C2312yes—
60C4×Dic37—21no—
61C2×#64436C2312yes—
62C2×#64436C2312yes—
63C23×C37C2×D411yescharacteristic
64C22×D37—22no—
65C22×D37—24no—
66C22×D37—82no—
67Q8×C37—22no—
68Q8×C37—22no—
69C2×C4×C37—22no—
70C2×C4×C37—22no—
71C2×C4×C37—22no—
72C2×C4×C37C2×D411yescharacteristic
73C2×C4×C37C2×D412yes—
74C2×C4×C37C2×D412yes—
75C2×C4×C37C2411yescharacteristic
76C2×Dic37—22no—
77D148—24no—
78D148—22no—
79D148#4114yes—
80C4×D37—82no—
81C4×D37—82no—
82#64436—22no—
83#64436—22no—
84C22×C37—21no—
85C22×C37—22no—
86C22×C37C22×D411yescharacteristic
87C2×D37—24no—
88C2×D37—42no—
89C2×D37—42no—
90C2×D37—84no—
91C4×C37—21no—
92C4×C37—22no—
93C4×C37—22no—
94C4×C37—42no—
95C4×C37—42no—
96C4×C37C2×#4112yes—
97Dic37—42no—
98#3123—371nomaximal, Sylow
99C2×C37—41no—
100C2×C37#52511yescharacteristic
101C2×C37#57712yes—
102D37—44no—
103#541D3711yescharacteristic, complemented
104#518—371no—
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×D4—371no—
114C2×SD16—372no—
115C2×SD16—372no—
116C4⋊Q8C2×D3711yescharacteristic, complemented
117#126—22no—
118#125—22no—
119#125C2×D3711yescharacteristic, complemented
120C22⋊Q8C2×D3712yes—
121C4×Q8C2×D3712yescomplemented
122C4×D4—372no—
123C4×D4—372no—
124C4×D4—742no—
125#117—371no—
126#117C2×D3711yescharacteristic
127C2×C22⋊C4—742no—
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—741no—
139C2×Q8C22×D3712yes—
140C2×D4—372no—
141C2×D4—744no—
142C2×D4—741no—
143C22×C4—742no—
144C22×C4—742no—
145C22×C4C22×D3711yescharacteristic
146SD16—744no—
147SD16—744no—
148C2×C8—372no—
149C2×C8—372no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—22no—
153C4⋊C4—22no—
154C4⋊C4—372no—
155C4⋊C4C22⋊D3712yes—
156C4⋊C4C22×D3712yes—
157C22⋊C4—22no—
158C22⋊C4—741no—
159C22⋊C4—742no—
160C22⋊C4—742no—
161C22⋊C4C22⋊D3712yes—
162C42—22no—
163C42—741no—
164C42C22×D3711yescharacteristic
165C42C22×D3711yescharacteristic
166C23—2962no—
167C23—744no—
168C23—742no—
169C23C2×C22⋊D3711yescharacteristic
170Q8—22no—
171Q8—22no—
172D4—374no—
173D4—744no—
174D4—742no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—2962no—
179C2×C4—2962no—
180C2×C4—742no—
181C2×C4C2×C22⋊D3712yes—
182C2×C4C2×C22⋊D3711yescharacteristic
183C2×C4C2×C22⋊D3712yes—
184C2×C4C23×D3711yescharacteristic
185C8—742no—
186C8—742no—
187C22—21no—
188C22—22no—
189C22—2964no—
190C22—744no—
191C22—1482no—
192C22—1482no—
193C22C22×C22⋊D3711yescharacteristic
194C4—21no—
195C4—22no—
196C4—22no—
197C4—42no—
198C4—42no—
199C4—1482no—
200C4#41×D3712yes—
201C2—41no—
202C2—1484no—
203C2#1455804011yescharacteristic
204C2#1455834112yes—
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#541C2
socleC22×C37C22×D4
prime radicalC22×D148C22
hypercenter#541D37
hypocenterC37#3123
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #14557871C2semidirect
3. #14557830C2semidirect
4. #14557735C2semidirect
6. #14557631C2semidirect
7. C4×#10596941C2semidirect
8. #14557594C2semidirect
9. C37×#541C2semidirect
18. #11924469C22semidirect
19. #11924467C22semidirect
20. C4⋊#64436C22semidirect
21. #11924460C22semidirect
22. #11924460C22semidirect
26. #11924447C22semidirect
27. C4×#64436C22semidirect
28. C4⋊Q8×C37C22semidirect
31. #125×C37C22semidirect
33. C4×Q8×C37C22semidirect
103. #541D37semidirect
112. C37#3123semidirect
116. C4⋊Q8C2×D37semidirect
119. #125C2×D37semidirect
121. C4×Q8C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145580072
#145578712
#145578302
#145577352
#145576832
#145576312
C4×#105969412
#145575942
C37×#5412
#312337