Finite Group Databasebeta

← #49134399

Subgroups — #49134399

Order 36224.

370 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 113 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#31827267C212yesmaximal, complemented
2#31826902C214yesmaximal, complemented
3#31826900C212yesmaximal, complemented
4#31826898C212yesmaximal, complemented
5C2×D4528C211yesmaximal, characteristic, complemented
6D16×D283C212yesmaximal, complemented
7#31826881C211yesmaximal, characteristic, complemented
8#508×C283C211yesmaximal, characteristic, complemented
9#22583656—22no—
10#22583637—24no—
11#22583635—22no—
12#22583633C2214yescomplemented
13C2×D2264C2212yescomplemented
14D8×D283C2214yescomplemented
15#22583616C2211yescharacteristic
16#22583553C2214yescomplemented
17D4528C2212yescomplemented
18D4528C2212yescomplemented
19#22583551C2214yescomplemented
20#22583550C2211yescharacteristic, complemented
21#22583549C2212yescomplemented
22C16×D283C2212yescomplemented
23#135×C283C2212yescomplemented
24Q32×C283C2211yescharacteristic, complemented
25SD32×C283C2212yescomplemented
26D16×C283C2211yescharacteristic, complemented
27C2×C16×C283C2211yescharacteristic, complemented
28#17985393—24no—
29#17985392—42no—
30#17985392D411yescharacteristic
31C2×D1132—22no—
32C2×D1132—42no—
33D4×D283—24no—
34D4×D283—44no—
35#17985379—24no—
36D2264—22no—
37D2264C2314yes—
38#17985377—24no—
39#17985376D411yescharacteristic
40#17985375D412yes—
41C8×D283C2312yes—
42C283⋊C16C2312yes—
43#41×C283—22no—
44Q16×C283C2312yes—
45SD16×C283—22no—
46D8×C283C2312yes—
47C2×C8×C283C2311yescharacteristic
48C16×C283C2311yescharacteristic
49C16×C283C2311yescharacteristic
50C22×D283—42no—
51C22×D283—44no—
52Dic566D811yescharacteristic
53D1132—24no—
54D1132—44no—
55D1132—42no—
56D1132D811yescharacteristic
57C22⋊D283—44no—
58C22⋊D283D812yes—
59C4×D283—44no—
60C4×D283C2×D412yes—
61C283⋊C8C2×D412yes—
62Q8×C283—22no—
63D4×C283—22no—
64D4×C283—42no—
65C2×C4×C283—42no—
66C2×C4×C283C2×D411yescharacteristic
67C8×C283C2×D411yescharacteristic
68C8×C283C2411yescharacteristic
69C22×C283—42no—
70C22×C283C2×D811yescharacteristic
71C2×D283—44no—
72C2×D283—164no—
73C2×D283—162no—
74C2×D283C2×D812yes—
75C4×C283—42no—
76C4×C283C2×D811yescharacteristic
77C4×C283C22×D411yescharacteristic
78Dic283C2×D812yes—
79C2×C283—21no—
80C2×C283—82no—
81C2×C283C22×D811yescharacteristic
82D283—22no—
83D283—84no—
84C283#341511yescharacteristic, complemented, Sylow
85#3415—2831nomaximal, Sylow
86#576—2832no—
87#509—2832no—
88#509—2834no—
89#508—2832no—
90#508D28311yescharacteristic, complemented
91C2×D16—2832no—
92C2×D16—2831no—
93#504—2831no—
94H(5,𝔽2)—5662no—
95AGL(1,ℤ/8)—5664no—
96AGL(1,ℤ/8)—5662no—
97#135—2834no—
98#135C2×D28312yescomplemented
99C2×D8—2834no—
100C2×D8—2832no—
101#131—2831no—
102Q32C2×D28311yescharacteristic, complemented
103SD32—2834no—
104SD32C2×D28312yescomplemented
105D16—2834no—
106D16—2832no—
107D16—2832no—
108D16C2×D28311yescharacteristic, complemented
109M32—2831no—
110M32—2832no—
111C2×C16—2832no—
112C2×C16C2×D28311yescharacteristic, complemented
113#41—22no—
114#41—2831no—
115#41—5664no—
116#41—11322no—
117C2×D4—5664no—
118C2×D4—5662no—
119C2×D4—11322no—
120C2×D4—11324no—
121Q16C22×D28312yes—
122SD16—22no—
123SD16—5664no—
124D8—2834no—
125D8—5664no—
126D8—5662no—
127D8C22×D28312yes—
128M16—2831no—
129M16—2832no—
130C2×C8—2832no—
131C2×C8C22×D28311yescharacteristic
132C16—2832no—
133C16C22×D28311yescharacteristic
134C16C22×D28311yescharacteristic
135C23—11324no—
136C23—11322no—
137Q8—22no—
138Q8—2831no—
139D4—22no—
140D4—42no—
141D4—2832no—
142D4—2831no—
143D4—5664no—
144D4—11324no—
145D4—11324no—
146D4—11322no—
147C2×C4—42no—
148C2×C4—2832no—
149C2×C4—11324no—
150C2×C4D4×D28311yescharacteristic
151C8—2832no—
152C8D4×D28311yescharacteristic
153C8C23×D28311yescharacteristic
154C22—42no—
155C22—2832no—
156C22—11324no—
157C22—45282no—
158C22—45284no—
159C22D8×D28311yescharacteristic
160C4—42no—
161C4—2832no—
162C4D8×D28311yescharacteristic
163C4C2×D4×D28311yescharacteristic
164C2—21no—
165C2—82no—
166C2—5662no—
167C2—22644no—
168C2C2×D8×D28311yescharacteristic
subgroupG/H
centerC2C2×D8×D283
commutator, cosocleC8×C283C24
FrattiniC8C23×D283
Fitting#508×C283C2
socleC2×C283C22×D8
hypercenter#508D283
hypocenterC283#3415
LCSG ▷ C8×C283 ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #31827267C2semidirect
2. #31826902C2semidirect
3. #31826900C2semidirect
4. #31826898C2semidirect
5. C2×D4528C2semidirect
6. D16×D283C2semidirect
7. #31826881C2semidirect
8. #508×C283C2semidirect
12. #22583633C22semidirect
13. C2×D2264C22semidirect
14. D8×D283C22semidirect
16. #22583553C22semidirect
17. D4528C22semidirect
18. D4528C22semidirect
19. #22583551C22semidirect
20. #22583550C22semidirect
21. #22583549C22semidirect
22. C16×D283C22semidirect
23. #135×C283C22semidirect
24. Q32×C283C22semidirect
25. SD32×C283C22semidirect
26. D16×C283C22semidirect
27. C2×C16×C283C22semidirect
84. C283#3415semidirect
90. #508D283semidirect
98. #135C2×D283semidirect
102. Q32C2×D283semidirect
104. SD32C2×D283semidirect
108. D16C2×D283semidirect
112. C2×C16C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318272672
#318269022
#318269002
#318268982
C2×D45282
D16×D2832
#318268812
#508×C2832
#3415283