Finite Group Databasebeta

← #44417576

Subgroups — #44417576

Order 29248.

262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C2×#20300742C211yesmaximal, characteristic, complemented
2#41×D457C211yesmaximal, characteristic, complemented
3#28410584C212yesmaximal, complemented
4#28410583C211yesmaximal, characteristic, complemented
5#28410580C211yesmaximal, characteristic, complemented
6#28410579C212yesmaximal, complemented
7#28410577C211yesmaximal, characteristic, complemented
8#28410575C212yesmaximal, complemented
9#28410573C212yesmaximal, complemented
10M16×D457C211yesmaximal, characteristic, complemented
11#137×C457C211yesmaximal, characteristic, complemented
12#20300742—21no—
13#20300742—21no—
14#20300742C2212yes—
15#20300742C2212yescomplemented
16#20300742C2211yescharacteristic, complemented
17#20300741—21no—
18#20300741C2211yescharacteristic
19#20300740—21no—
20#20300740C2211yescharacteristic, complemented
21Q8×D457C2211yescharacteristic, complemented
22C2×D1828—21no—
23C2×D1828C2211yescharacteristic, complemented
24D4×D457—21no—
25D4×D457C2211yescharacteristic, complemented
26C2×C4×D457—21no—
27C2×C4×D457—21no—
28C2×C4×D457C2211yescharacteristic
29#20300731C2212yescomplemented
30#20300730C2212yescomplemented
31#20300728C2212yescomplemented
32#20300728C2212yescomplemented
33D3656C2212yescomplemented
34#20300726C2212yescomplemented
35#20300725C2211yescharacteristic, complemented
36#20300724C2212yescomplemented
37C8×D457C2212yescomplemented
38#41×C457C2211yescharacteristic
39C2×Q8×C457C2211yescharacteristic, complemented
40Q16×C457C2212yescomplemented
41SD16×C457C2212yescomplemented
42M16×C457C2211yescharacteristic, complemented
43C22×D457—21no—
44C22×D457—21no—
45C22×D457D411yescharacteristic
46Dic914—21no—
47Dic914C2311yescharacteristic
48D1828—21no—
49D1828—22no—
50D1828—22no—
51D1828—21no—
52D1828C2312yes—
53D1828C2311yescharacteristic
54C22⋊D457—21no—
55C22⋊D457—21no—
56C22⋊D457—21no—
57C2×Dic457—21no—
58C2×Dic457D411yescharacteristic
59C4×D457—21no—
60C4×D457—21no—
61C4×D457—21no—
62C4×D457—22no—
63C4×D457—22no—
64C4×D457D411yescharacteristic
65C4×D457D411yescharacteristic
66C4×D457C2311yescharacteristic
67C4×D457C2311yescharacteristic
68#16814532C2312yes—
69Q8×C457—21no—
70Q8×C457C2312yes—
71Q8×C457C2311yescharacteristic
72D4×C457—21no—
73D4×C457C2311yescharacteristic
74C2×C4×C457—21no—
75C2×C4×C457—21no—
76C2×C4×C457C2311yescharacteristic
77C8×C457C2312yes—
78C22×C457—21no—
79C22×C457C2×D411yescharacteristic
80C2×D457—21no—
81C2×D457—22no—
82C2×D457—41no—
83C2×D457—42no—
84C2×D457—42no—
85C2×D457C2×D411yescharacteristic
86C2×D457C2×D411yescharacteristic
87C4×C457—21no—
88C4×C457—22no—
89C4×C457C2×D411yescharacteristic
90C4×C457C2411yescharacteristic
91Dic457—21no—
92Dic457C2×D411yescharacteristic
93Dic457C2×D411yescharacteristic
94C2×C457—21no—
95C2×C457—41no—
96C2×C457C22×D411yescharacteristic
97D457—21no—
98D457—21no—
99D457—41no—
100D457—42no—
101C457#57511yescharacteristic, complemented, Sylow
102#575—4571nomaximal, Sylow
103C2×#41—4571no—
104C2×#41—4571no—
105#137—4571no—
106#137—4572no—
107#137D45711yescharacteristic, complemented
108AGL(1,ℤ/8)—4571no—
109AGL(1,ℤ/8)—4572no—
110AGL(1,ℤ/8)—4571no—
111#135—4572no—
112#135—4572no—
113C2×M16—4571no—
114#41—9141no—
115#41—9141no—
116#41—9141no—
117#41—9141no—
118#41—4571no—
119#41—4572no—
120#41—4572no—
121#41—4571no—
122#41—4571no—
123#41C2×D45711yescharacteristic
124C2×Q8—4571no—
125C2×Q8C2×D45711yescharacteristic, complemented
126C2×D4—9141no—
127C2×D4—9141no—
128C2×D4—4571no—
129C2×D4—4571no—
130C22×C4—9141no—
131C22×C4—9141no—
132C22×C4—4571no—
133Q16—4572no—
134Q16C2×D45712yescomplemented
135SD16—4572no—
136SD16—4572no—
137SD16—4572no—
138SD16C2×D45712yescomplemented
139D8—4572no—
140D8—4572no—
141M16—4571no—
142M16—4572no—
143M16C2×D45711yescharacteristic, complemented
144C2×C8—4572no—
145C23—9141no—
146C23—9141no—
147C23—4571no—
148Q8—21no—
149Q8—9141no—
150Q8—4571no—
151Q8C22×D45711yescharacteristic
152Q8C22×D45712yes—
153D4—21no—
154D4—9141no—
155D4—9142no—
156D4—9142no—
157D4—9141no—
158D4—9141no—
159D4—9141no—
160D4—9141no—
161D4—4572no—
162D4—4571no—
163D4C22×D45711yescharacteristic
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—9141no—
167C2×C4—9141no—
168C2×C4—9142no—
169C2×C4—9142no—
170C2×C4—9141no—
171C2×C4—9141no—
172C2×C4—4571no—
173C2×C4—4571no—
174C2×C4—4571no—
175C2×C4—4571no—
176C2×C4—4571no—
177C2×C4C22×D45711yescharacteristic
178C8—4572no—
179C8C22×D45712yes—
180C22—21no—
181C22—18282no—
182C22—18281no—
183C22—18282no—
184C22—9142no—
185C22—9141no—
186C22—4571no—
187C22—4571no—
188C22D4×D45711yescharacteristic
189C4—21no—
190C4—22no—
191C4—9141no—
192C4—4571no—
193C4—4571no—
194C4D4×D45711yescharacteristic
195C4C23×D45711yescharacteristic
196C2—21no—
197C2—41no—
198C2—18282no—
199C2—18281no—
200C2—9141no—
201C2—9141no—
202C2C2×D4×D45711yescharacteristic
subgroupG/H
centerC2C2×D4×D457
commutator, cosocleC4×C457C24
FrattiniC4C23×D457
Fitting#137×C457C2
socleC2×C457C22×D4
hypercenter#137D457
hypocenterC457#575
LCSG ▷ C4×C457 ▷ C2×C457 ▷ C457
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. C2×#20300742C2semidirect
2. #41×D457C2semidirect
3. #28410584C2semidirect
4. #28410583C2semidirect
5. #28410580C2semidirect
6. #28410579C2semidirect
7. #28410577C2semidirect
8. #28410575C2semidirect
9. #28410573C2semidirect
10. M16×D457C2semidirect
11. #137×C457C2semidirect
15. #20300742C22semidirect
16. #20300742C22semidirect
20. #20300740C22semidirect
21. Q8×D457C22semidirect
23. C2×D1828C22semidirect
25. D4×D457C22semidirect
29. #20300731C22semidirect
30. #20300730C22semidirect
31. #20300728C22semidirect
32. #20300728C22semidirect
33. D3656C22semidirect
34. #20300726C22semidirect
35. #20300725C22semidirect
36. #20300724C22semidirect
37. C8×D457C22semidirect
39. C2×Q8×C457C22semidirect
40. Q16×C457C22semidirect
41. SD16×C457C22semidirect
42. M16×C457C22semidirect
101. C457#575semidirect
107. #137D457semidirect
125. C2×Q8C2×D457semidirect
134. Q16C2×D457semidirect
138. SD16C2×D457semidirect
143. M16C2×D457semidirect

Maximal subgroups

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

subgroupindex
C2×#203007422
#41×D4572
#284105842
#284105832
#284105802
#284105792
#284105772
#284105752
#284105732
M16×D4572
#137×C4572
#575457