Finite Group Databasebeta

← #49130653

Subgroups — #49130653

Order 36224.

766 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 766 conjugacy classes of subgroups — too many to draw. Only its 161 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#31826972C213yesmaximal, complemented
2#31826655C214yesmaximal, complemented
3#31826652C214yesmaximal, complemented
4#31826439C213yesmaximal, complemented
5#585×C283C211yesmaximal, characteristic, complemented
6C22×C4×D283C2211yescharacteristic, complemented
7#22583591C2216yescomplemented
8#22583586—23no—
9#22583581—23no—
10#22583578C2216yescomplemented
11C4×C22⋊D283—26no—
12#22583569C2213yescomplemented
13#22583525C22112yescomplemented
142−1+4×C283—23no—
15H(5,𝔽2)×C283—23no—
16H(5,𝔽2)×C283C2214yes—
17C2×#41×C283—26no—
18C2×#41×C283C2213yes—
19C23×D283C2311yescharacteristic
20C2×C22⋊D283—26no—
21C22×Dic283C2311yescharacteristic
22C2×C4×D283—23no—
23C2×C4×D283—23no—
24C4⋊Dic283—23no—
25Dic283⋊C4—26no—
26C22⋊Dic283—26no—
27C22⋊Dic283C2316yes—
28(C2×D283)⋊C4—26no—
29C4×Dic283—23no—
30#41×C283—24no—
31#41×C283—212no—
32#41×C283—26no—
33#41×C283—212no—
34#41×C283—26no—
35C2×Q8×C283—26no—
36C2×Q8×C283D413yescomplemented
37C2×D4×C283—26no—
38C2×D4×C283—212no—
39C2×D4×C283D413yescomplemented
40C2×D4×C283C2316yes—
41C22×C4×C283—24no—
42C22×C4×C283D416yescomplemented
43C22×C4×C283C2311yescharacteristic
44C22×D283—23no—
45C22×D283—42no—
46C22⋊D283—412no—
47C2×Dic283—26no—
48C2×Dic283—23no—
49C4×D283—43no—
50C4×D283—41no—
51C23×C283—24no—
52C23×C283C2×D416yes—
53C23×C283C2411yescharacteristic
54Q8×C283—24no—
55Q8×C283—26no—
56D4×C283—212no—
57D4×C283—212no—
58D4×C283—26no—
59C2×C4×C283—212no—
60C2×C4×C283—26no—
61C2×C4×C283—26no—
62C2×C4×C283C2×D416yes—
63C2×C4×C283C2×D413yes—
64C2×C4×C283C2×D413yes—
65C22×C283—26no—
66C22×C283—41no—
67C22×C283—46no—
68C22×C283—84no—
69C22×C283C22×D413yes—
70C2×D283—26no—
71C2×D283—43no—
72C2×D283—41no—
73C4×C283—26no—
74C4×C283#12013yes—
75C4×C283#12011yescharacteristic
76Dic283—46no—
77Dic283—41no—
78C2×C283—23no—
79C2×C283—46no—
80C2×C283C2×#12011yescharacteristic
81D283—42no—
82C283#302511yescharacteristic, complemented, Sylow
83#3025—2831nomaximal, Sylow
84#585D28311yescharacteristic, complemented
85#525—2833no—
86#458—2834no—
87B(4,𝔽2)—2834no—
88#410—2833no—
892−1+4—23no—
90H(5,𝔽2)—23no—
91H(5,𝔽2)C2×D28314yes—
92C2×#41—26no—
93C2×#41C2×D28313yes—
94C23×C4—2831no—
95#123—2836no—
96C22⋊Q8—5663no—
97#121—5663no—
98#120—2836no—
99C4×D4—5666no—
100#117—2833no—
101#99—28312no—
102C24—2831no—
103#41—24no—
104#41—212no—
105#41—26no—
106#41—212no—
107#41—26no—
108C2×Q8—26no—
109C2×Q8C22⋊D28313yescomplemented
110C2×D4—26no—
111C2×D4—212no—
112C2×D4—5666no—
113C2×D4C22⋊D28313yescomplemented
114C2×D4C22×D28316yes—
115C22×C4—24no—
116C22×C4—2831no—
117C22×C4—5663no—
118C22×C4—5663no—
119C22×C4C22⋊D28316yescomplemented
120C22×C4C22×D28311yescharacteristic
121C4⋊C4—5666no—
122C4⋊C4—5663no—
123C22⋊C4—2836no—
124C22⋊C4—5666no—
125C22⋊C4—5666no—
126C42—5663no—
127C23—24no—
128C23—5663no—
129C23—11322no—
130C23C2×C22⋊D28316yes—
131C23C23×D28311yescharacteristic
132Q8—24no—
133Q8—26no—
134D4—212no—
135D4—212no—
136D4—26no—
137D4—113212no—
138C2×C4—212no—
139C2×C4—26no—
140C2×C4—26no—
141C2×C4—5666no—
142C2×C4—5663no—
143C2×C4—11323no—
144C2×C4—11321no—
145C2×C4C2×C22⋊D28316yes—
146C2×C4C2×C22⋊D28313yes—
147C2×C4C2×C22⋊D28313yes—
148C22—26no—
149C22—41no—
150C22—46no—
151C22—84no—
152C22—5666no—
153C22—11323no—
154C22—11321no—
155C22C22×C22⋊D28313yes—
156C4—26no—
157C4—11326no—
158C4—11321no—
159C4#2258357913yes—
160C4#2258357911yescharacteristic
161C2—23no—
162C2—46no—
163C2—11322no—
164C2C2×#2258357911yescharacteristic
subgroupG/H
centerC4#22583579
commutator, cosocleC23×C283C24
FrattiniC23C23×D283
Fitting#585×C283C2
socleC2×C283C2×#120
hypercenter#585D283
hypocenterC283#3025
LCSG ▷ C23×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C4 ◁ C22×C4 ◁ #585

Complements

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

NH ≅ G/Ntype
1. #31826972C2semidirect
2. #31826655C2semidirect
3. #31826652C2semidirect
4. #31826439C2semidirect
5. #585×C283C2semidirect
6. C22×C4×D283C22semidirect
7. #22583591C22semidirect
10. #22583578C22semidirect
12. #22583569C22semidirect
13. #22583525C22semidirect
36. C2×Q8×C283D4semidirect
39. C2×D4×C283D4semidirect
42. C22×C4×C283D4semidirect
82. C283#3025semidirect
84. #585D283semidirect
109. C2×Q8C22⋊D283semidirect
113. C2×D4C22⋊D283semidirect
119. C22×C4C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
#318269722
#318266552
#318266522
#318264392
#585×C2832
#3025283