Finite Group Databasebeta

← #49130172

Subgroups — #49130172

Order 36224.

458 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 185 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#31827265C211yesmaximal, characteristic
2#31827231C212yesmaximal, complemented
3#31826588C214yesmaximal, complemented
4#31826583C214yesmaximal, complemented
5#31826514C211yesmaximal, characteristic, complemented
6C2×#22583538C212yesmaximal, complemented
7C4×M16×C283C211yesmaximal, characteristic, complemented
8C2×#17985392C2212yes—
9#22583643C414yescomplemented
10#22583638C414yescomplemented
11#22583632C2214yes—
12#22583618—24no—
13#22583616C2218yescomplemented
14C2×#17985376C2212yes—
15M16×D283—24no—
16#22583546C2214yescomplemented
17#22583538C2214yescomplemented
18#22583538C2214yescomplemented
19C2×M16×C283C2211yescharacteristic
20C2×M16×C283C2211yescharacteristic
21C2×C42×C283C2211yescharacteristic
22#97×C283C2212yescomplemented
23C4×C8×C283C2212yescomplemented
24#17985392—22no—
25#17985392—22no—
26#17985392C2×C414yes—
27#17985392C2314yes—
28C2×Dic566C2×C412yes—
29C2×D1132C2×C412yes—
30C2×C22⋊D283—22no—
31C2×C4×D283—22no—
32Dic1132C2×C414yescomplemented
33#17985381C2×C418yescomplemented
34D2264C2×C414yescomplemented
35#17985376—22no—
36#17985376C2314yes—
37#17985375—28no—
38C2×C283⋊C8—22no—
39C8×D283—28no—
40C22×C4×C283—21no—
41C22×C4×C283C2311yescharacteristic
42M16×C283C2×C414yes—
43M16×C283D414yes—
44C2×C8×C283C2312yes—
45C2×C8×C283C2312yes—
46C42×C283—21no—
47C42×C283C2311yescharacteristic
48C42×C283C2311yescharacteristic
49C22×D283—22no—
50Dic566—22no—
51Dic566C22×C414yes—
52D1132—22no—
53D1132C22×C414yes—
54C22⋊D283—24no—
55C22⋊D283—24no—
56C2×Dic283—22no—
57C4×D283—24no—
58C4×D283—24no—
59C283⋊C8—24no—
60C23×C283#4111yescharacteristic
61C2×C4×C283—21no—
62C2×C4×C283—21no—
63C2×C4×C283—42no—
64C2×C4×C283C22×C412yes—
65C2×C4×C283C2×D412yes—
66C2×C4×C283#4111yescharacteristic
67C2×C4×C283C2411yescharacteristic
68C8×C283C22×C414yes—
69C8×C283C2×D414yes—
70C22×C283—41no—
71C22×C283C4×D412yes—
72C22×C283C2×#4111yescharacteristic
73C2×D283—24no—
74C2×D283—82no—
75C4×C283—22no—
76C4×C283—41no—
77C4×C283C4×D412yes—
78C4×C283C23×C411yescharacteristic
79C4×C283C22×D411yescharacteristic
80Dic283—24no—
81C2×C283—21no—
82C2×C283—22no—
83C2×C283C2×C4×D411yescharacteristic
84D283—44no—
85C283#295611yescharacteristic, complemented, Sylow
86#2956—2831nomaximal, Sylow
87#575—2831no—
88#568—2832no—
89#444—2834no—
90#443—2834no—
91#430—2831no—
92C2×#104—2832no—
93C4×M16D28311yescharacteristic, complemented
94C2×#41—2832no—
95#137—2834no—
96AGL(1,ℤ/8)—2834no—
97#135—2834no—
98#131—2838no—
99#131—5664no—
100C2×M16—2832no—
101C2×M16—5664no—
102C2×M16C2×D28311yescharacteristic
103C2×M16C2×D28311yescharacteristic
104C2×C42C2×D28311yescharacteristic
105#108—2834no—
106#104—2834no—
107#104—2834no—
108#97C2×D28312yescomplemented
109C4×C8C2×D28312yescomplemented
110#41—2834no—
111#41—2834no—
112#41—5662no—
113#41—5662no—
114C2×Q8—2832no—
115C2×D4—2832no—
116C2×D4—5662no—
117C22×C4—21no—
118C22×C4—5662no—
119C22×C4C22×D28311yescharacteristic
120Q16—2834no—
121SD16—2838no—
122D8—2834no—
123M16—2834no—
124M16—5662no—
125M16—5668no—
126M16C4×D28314yes—
127M16D113214yes—
128C2×C8—5662no—
129C2×C8—5668no—
130C2×C8C22×D28312yes—
131C2×C8C22×D28312yes—
132C42—21no—
133C42C22×D28311yescharacteristic
134C42C22×D28311yescharacteristic
135C23—5662no—
136C23#1798539211yescharacteristic
137Q8—2834no—
138Q8—5662no—
139D4—2834no—
140D4—5664no—
141D4—5664no—
142D4—5662no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—42no—
146C2×C4—5662no—
147C2×C4—5664no—
148C2×C4—5664no—
149C2×C4C2×C4×D28312yes—
150C2×C4C2×D113212yes—
151C2×C4#1798539211yescharacteristic
152C2×C4C23×D28311yescharacteristic
153C8—5664no—
154C8C2×C4×D28314yes—
155C8C2×D113214yes—
156C22—41no—
157C22—5664no—
158C22—22642no—
159C22C4×D113212yes—
160C22C2×#1798539211yescharacteristic
161C4—22no—
162C4—41no—
163C4—5664no—
164C4C4×D113212yes—
165C4C22×C4×D28311yescharacteristic
166C4C22×D113211yescharacteristic
167C2—21no—
168C2—22no—
169C2—11324no—
170C2C2×C4×D113211yescharacteristic
subgroupG/H
centerC4C22×D1132
commutatorC4×C283C23×C4
FrattiniC2×C4C23×D283
FittingC4×M16×C283C2
socleC2×C283C2×C4×D4
prime radical#31827265C2
cosocleC2×C4×C283C24
hypercenterC4×M16D283
hypocenterC283#2956
LCSG ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C4 ◁ C2×M16 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
2. #31827231C2semidirect
3. #31826588C2semidirect
4. #31826583C2semidirect
5. #31826514C2semidirect
6. C2×#22583538C2semidirect
7. C4×M16×C283C2semidirect
9. #22583643C4semidirect
10. #22583638C4semidirect
13. #22583616C22semidirect
16. #22583546C22semidirect
17. #22583538C22semidirect
18. #22583538C22semidirect
22. #97×C283C22semidirect
23. C4×C8×C283C22semidirect
32. Dic1132C2×C4semidirect
33. #17985381C2×C4semidirect
34. D2264C2×C4semidirect
85. C283#2956semidirect
93. C4×M16D283semidirect
108. #97C2×D283semidirect
109. C4×C8C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318272652
#318272312
#318265882
#318265832
#318265142
C2×#225835382
C4×M16×C2832
#2956283