Finite Group Databasebeta

← #49131634

Subgroups — #49131634

Order 36224.

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

normal subgroups only

This group has 484 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#31827021C211yesmaximal, characteristic, complemented
2#127×D283C211yesmaximal, characteristic
3#31826831C211yesmaximal, characteristic, complemented
4#31826830C211yesmaximal, characteristic, complemented
5#31826829C211yesmaximal, characteristic, complemented
6#31826810C214yesmaximal, complemented
7#31826468C214yesmaximal, complemented
8#31826417C211yesmaximal, characteristic, complemented
9#490×C283C211yesmaximal, characteristic, complemented
10C2×D4×D283—22no—
11C2×D4×D283C2212yes—
12C2×#17985375C2212yes—
13#22583609C2212yescomplemented
14#22583607C2211yescharacteristic
15#22583606—22no—
16#22583606C2212yes—
17#22583602C2211yescharacteristic, complemented
18#22583588—22no—
19#22583575—22no—
20#22583568C2212yes—
21C42×D283C2211yescharacteristic
22#22583532C2214yescomplemented
23#22583531C2214yescomplemented
24#22583530C2214yescomplemented
25#22583521C2211yescharacteristic, complemented
26C8×Dic283C2212yescomplemented
27#127×C283C2211yescharacteristic
28#125×C283C2211yescharacteristic, complemented
29#102×C283C2214yescomplemented
30#97×C283C2211yescharacteristic, complemented
31C23×D283—22no—
32C2×Dic566—22no—
33C2×D1132—22no—
34C2×D1132C2312yes—
35C2×C22⋊D283—22no—
36C2×C22⋊D283—24no—
37D4×D283—28no—
38D4×D283—48no—
39C2×C4×D283D412yes—
40C2×C4×D283C2311yescharacteristic
41#17985375—24no—
42C2×C283⋊C8C2312yes—
43C4⋊Dic283C2312yes—
44Dic283⋊C4—22no—
45Dic283⋊C4—22no—
46(C2×D283)⋊C4—22no—
47C4×Dic283—22no—
48C4×Dic283D412yes—
49C4×Dic283C2311yescharacteristic
50C2×D4×C283—22no—
51C2×D4×C283C2312yes—
52C2×C8×C283C2312yes—
53C4⋊C4×C283—22no—
54C4⋊C4×C283C2312yes—
55C42×C283C2311yescharacteristic
56C22×D283—22no—
57C22×D283—48no—
58C22×D283—44no—
59C22×D283C2×D411yescharacteristic
60Dic566—44no—
61D1132—24no—
62D1132—44no—
63C22⋊D283—44no—
64C22⋊D283—48no—
65C2×Dic283—22no—
66C2×Dic283C2×D411yescharacteristic
67C2×Dic283C2×D412yes—
68C4×D283—24no—
69C4×D283#4114yes—
70C283⋊C8—22no—
71C23×C283—22no—
72D4×C283—24no—
73D4×C283—44no—
74C2×C4×C283—22no—
75C2×C4×C283C2×D412yes—
76C2×C4×C283C2411yescharacteristic
77C8×C283—22no—
78C22×C283—42no—
79C22×C283—44no—
80C22×C283C22×D411yescharacteristic
81C2×D283—22no—
82C2×D283—42no—
83C2×D283—44no—
84C2×D283—88no—
85C2×D283#12412yes—
86C4×C283—22no—
87C4×C283—42no—
88C4×C283C2×#4112yes—
89Dic283—42no—
90Dic283#12412yes—
91Dic283AGL(1,ℤ/8)14yes—
92C2×C283—82no—
93C2×C283C2×#12411yescharacteristic
94C2×C283C2×AGL(1,ℤ/8)12yes—
95D283—22no—
96D283—82no—
97C283#313811yescharacteristic, complemented, Sylow
98#3138—2831nomaximal, Sylow
99#533—2831no—
100C2×#127—2831no—
101#490—2831no—
102#490—2831no—
103#490—2831no—
104#490D28311yescharacteristic, complemented
105#486—2834no—
106#418—2834no—
107C4×M16—2831no—
108C22×D4—2832no—
109C22×D4—5662no—
110C2×M16—2832no—
111C4⋊Q8—2832no—
112#127—2832no—
113#127—2831no—
114#127—5662no—
115#127C2×D28311yescharacteristic
116#125—2831no—
117#125C2×D28311yescharacteristic, complemented
118C22⋊Q8—5662no—
119C4×Q8—5662no—
120#117—2832no—
121C2×C42—2831no—
122#102—2834no—
123#102—2834no—
124#102—2834no—
125#102C2×D28314yescomplemented
126#97—2831no—
127#97C2×D28311yescharacteristic, complemented
128C4×C8—2832no—
129C24—5662no—
130C2×Q8—5662no—
131C2×D4—22no—
132C2×D4—2832no—
133C2×D4—5668no—
134C2×D4—5664no—
135C2×D4—5662no—
136C2×D4—5662no—
137C2×D4—11328no—
138C2×D4C22×D28312yes—
139C22×C4—2831no—
140C22×C4—2832no—
141M16—5664no—
142C2×C8—2832no—
143C2×C8C22×D28312yes—
144C4⋊C4—22no—
145C4⋊C4—2832no—
146C4⋊C4—5662no—
147C4⋊C4—5662no—
148C4⋊C4C22×D28312yes—
149C22⋊C4—5662no—
150C42—2832no—
151C42—2831no—
152C42—5662no—
153C42C22×D28311yescharacteristic
154C23—22no—
155C23—2831no—
156C23—5662no—
157C23—11324no—
158C23—11328no—
159Q8—11324no—
160D4—24no—
161D4—44no—
162D4—5664no—
163D4—11324no—
164D4—11324no—
165D4—11328no—
166C2×C4—22no—
167C2×C4—2831no—
168C2×C4—2832no—
169C2×C4—2834no—
170C2×C4—5664no—
171C2×C4—5662no—
172C2×C4D4×D28312yes—
173C2×C4C23×D28311yescharacteristic
174C8—22no—
175C8—5662no—
176C22—42no—
177C22—44no—
178C22—2832no—
179C22—5662no—
180C22—11322no—
181C22—11324no—
182C22—22648no—
183C22C2×D4×D28311yescharacteristic
184C4—22no—
185C4—42no—
186C4—2832no—
187C4—2834no—
188C4—11322no—
189C4#41×D28312yes—
190C2—82no—
191C2—5662no—
192C2—22642no—
193C2#124×D28311yescharacteristic
194C2AGL(1,ℤ/8)×D28312yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#490×C283C2
socleC22×C283C22×D4
prime radical#127×D283C2
hypercenter#490D283
hypocenterC283#3138
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #31827021C2semidirect
3. #31826831C2semidirect
4. #31826830C2semidirect
5. #31826829C2semidirect
6. #31826810C2semidirect
7. #31826468C2semidirect
8. #31826417C2semidirect
9. #490×C283C2semidirect
13. #22583609C22semidirect
17. #22583602C22semidirect
22. #22583532C22semidirect
23. #22583531C22semidirect
24. #22583530C22semidirect
25. #22583521C22semidirect
26. C8×Dic283C22semidirect
28. #125×C283C22semidirect
29. #102×C283C22semidirect
30. #97×C283C22semidirect
97. C283#3138semidirect
104. #490D283semidirect
117. #125C2×D283semidirect
125. #102C2×D283semidirect
127. #97C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318270212
#127×D2832
#318268312
#318268302
#318268292
#318268102
#318264682
#318264172
#490×C2832
#3138283